ORNL/TM—6248 u 3 VilWm •
Meteorological Effects of Thermal Energy Releases (METER) Program Annual Progress Report October 1976 to September 1977
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OAK RIDGE NATIONAL LABORATORY OPERATED BV UNION CARBIDE CORPORATION • FOR THE DEPARTMENT OF ENERGY ORNL/TM-6248 Dist. Category UC-12
Contract No. W-7405-eng-26
METEOROLOGICAL EFFECTS OF THERMAL ENERGY RELEASES (METER) PROGRAM ANNUAL PROGRESS REPORT October 1976 to September 1977
Contributions by:
Argonne National Laboratory Atmospheric Turbulence and Diffusion Laboratory (NOAA) Battelle Pacific Northwest Laboratories Oak Ridge National Laboratory Pennsylvania State University Rand Corporation,
Compiled by: A. A. Patrinos H. W. Hoffman
Date Published: August 1978
NOTICE: This document contains information of a preliminary nature. It is subject to revision or correction and therefore does not represent a final report.
Prepared by the NOTICE Th» report WII prepared ai ,„ account of work OAK RIDGE NATIONAL LABORATORY iponxired by rh« United Sutn G-^.rm-trt Nerrher the Unilld Sum nor the United Slate! Department or Energy. not any or their employees, not any or their Oak Ridge, Tennessee 37830 contractors, juhcomrjctori, or thin employeei, maker any warranty, exptets or implied, or auutnei arty legal operated by liability or rnponUbiltty for the accuracy, completeneu or uiefulaeu of any information, apparatus, product or UNION CARBIDE CORPORATION procca diKkned. or rcprncnts Uiii tu UK would not infringe pnvatcty owned nghu. for the DEPARTMENT OF ENERGY iii
CONTENTS Page
BACKGROUND 1
FIELD STUDIES 1. PRECIPITATION STUDIES AROUND PLANT BOWEN 9 1.1 INTRODUCTION 9 1.2 THE CLIMATOLOGICAL STUDY 11 1.2.1 Data Quality Evaluations 13 1.2.2 Data Stratification and Presentation 17 1.3 THE FIELD STUDY 33 1.4 SUMMARY 34 1.5 ACKNOWLEDGMENTS 35 REFERENCES 35 APPENDIX A 36 APPENDIX B 40 2. STUDIES OF THE ENVIRONMENTAL IMPACT OF EVAPORATIVE COOLING TOWER PLUMES 41 2.1 INTRODUCTION 41 2.2 AIRBORNE MEASUREMENTS 42 2.3 AEROSOL AND AIR CHEMISTRY MEASUREMENTS 43 2.4 INDIRECT SOUNDING OF PLUMES USING S0DAR 45 2.5 APPLICATIONS OF ONE-DIMENSIONAL PLUME MODELS .1 46 2.6 PLANT ENERGY BALANCE MODELING 46 REFERENCES 47 3. COOLING TOWER DRIFT: EXPERIMENT DESIGN FOR COMPREHENSIVE CASE STUDY 48 3.1 INTRODUCTION 48 3.2 MEASUREMENT PROGRAM 49 3.3 FIELD DATA APPLIED TO MODEL VALIDATION 53 3.4 CONCLUSIONS 57 REFERENCES 58 4. COOLING FOND FOG STUDIES 59 4.1 INTRODUCTION 59 4.2 1974 "SIMULATOR" DATA 61 4.3 1976 DRESDEN OBSERVATIONS 61 BLANK PAGE iv
4.4 STABILITY REGIMES ASSOCIATED WITH COOLING PONDS 63 4.5 CONCLUSIONS 65 4.6 NOMENCLATURE 65 4.7 ACKNOWLEDGMENTS 66 REFERENCES 66
MATHEMATICAL MODELING 5. REPORT ON ATDL RESEARCH ON METEOROLOGICAL EFFECTS OF THERMAL ENERGY RELEASES, AUGUST I, 1976-SEPTEMBE& 31, 1977 69 5.1 INTRODUCTION 69 5.2 APPLICATIONS OF ATDL PLUME AND CLOUD GROWTH MODEL 69 5.2.1 John E. Amos riant 69 5.2.2 Los Angelas Oil Refineries 72 5.2.3 Chalk Point Plant 72 5.2.4 Paradise Plant 76 5.2.5 Sensitivity o£ Model to Elevated Inversions .... 77 5.3 SECONDARY MOTIONS IN COOLING TOWER PLUMES 78 5.4 CHAPTER FOR ATMOSPHERIC SCIENCE AND POWER PRODUCTION .. 78 5.5 ANALYSIS OF OBSERVED PLUME CROSS SECTIONS AT CHALK POINT 79 5.5.1 June 22, 1976: Bent-Over Plune 80 5.5.2 June 23, 1976: Vertical Plume 83 5.6 ANALYSES OF SATELLITE PHOTOGRAPHS OF MOISTURE AND SMOKE PLUMES 87 5.6.1 Cooling Towers 87 5.6.2 Dispersion of Smoke Plumes ...... 87 5.7 A NUMERICAL MODEL OF METEOROLOGICAL EFFECTS OF WASTE HEAT AND MOISTURE RELEASES FROM HYPOTHETICAL POWER PARKS 88 5.8 ACKNOWLEDGMENTS 89 REFERENCES 89 APPENDIX A. MODEL PREDICTIONS AND OBSERVATIONS OF CLOUDS FORMED BY OIL REFINERIES IN LOS ANGELES . 9i APPENDIX B. SECONDARY MOTIONS IN COOLING TOWER PLUMES 95 APPENDIX C. A NUMERICAL STUDY OF METEOROLOGICAL EFFECTS OF WASTE HEAT AND MOISTURE RELEASES FROM HYPOTHETICAL POWER PARKS . 105 V
Page
6. NUMERICAL SIMULATION OF AN INDUSTRIAL CUMULUS AND COMPARI- SON WITH OBSERVATIONS 133 ABSTRACT 133 6.1 INTRODUCTION 133 6.2 DESCRIPTION OF MODEL 134 6.3 IMPLEMENTATION 138 6.3.1 Ambient Atmospheric Conditions 138 6.3.2 Energy Input 139 6.4 COMPARISON OF SIMULATION RESULTS AND OBSERVATIONS 142 6.5 SENSITIVITY STUDIES 150 6.5.1 Turbulent Mixing 150 5.2 Ambient Wind 151 6. ..3 Heat Flux 156 6.6 CONCLUSION 161 6.7 LIST OF SYMBOLS 163 6.3 ACKNOWLEDGMENTS 165 REFERENCES 165 7. DIFFERENCES IN ATMOSPHERIC CONVECTION CAUSED BY WASTE ENERGY REJECTED IN THE FORMS OF SENSIBLE AND LATENT HEATS .. 168 7.1 INTRODUCTION 168 7.2 MODEL DESCRIPTION 170 7.3 RESULTS 171 7.4 DISCUSSION 177 7.5 CONCLUSIONS 182 REFERENCES 183 8. A MATHEMATICAL MODEL OF DRIFT DEPOSITION FROM A BIFURCATED COOLING TOWER PLUME 184 ABSTRACT ] 84 8.1 INTRODUCTION 184 8.2 COMPARISON OF THE CENTRIFUGAL FORCE TO THE GRAVITATIONAL FORCE 186 8.3 DROPLET TRAJECTORIES IN AN UNBOUNDED FREE VORTEX FIELD - A TWO-DIMENSIONAL CALCULATION 187 8.3.1 Equations of Motion: Cartesian Coordinates .... 188 8.3.2 Equations of Motion: Polar Coordinates 192 -Vi
8.3.3 Variation of the Droplet Emission Positions 194 8.3.A Variation of the Vortex Strength 196 8.3.5 Variation of the Drag Coefficient 197 8.4 DROPLET TRAJECTORIES IN A BOUNDED FREE VORTEX WITH AN AMBIENT WIND - A THREE-DIMENSIONAL CALCULATION 201 P.4.1 Equations of Motion 202 b.4.2 Calculational Procedure 205 8.4.3 Results 206 8.5 SUMMARY 208 REFERENCES 210
PHYSICAL MODELING 9. PLUMES FROM ONE AND TWO COOLING TOWERS 213 9.1 INTRODUCTION 213 9.2 EXPERIMENTAL DESIGN AND EQUIPMENT 214 9.3 EXPERIMENTAL RESULTS 216 9.3.1 A Single Tower in Crossflow Wind 216 9.3.2 Froude Number Effects 220 9.3.3 A Single Tower, In-Line Flow 221 9.3.4 Two Towers In Crossflow 221 9.4 BRIGGS' FORMULATION COMPARISON 231 9.5 CONCLUSIONS 236 9.6 NOMENCLATURE 237 9.7 ACKNOWLEDGMENTS 238 REFERENCES 238
ANALOG STUDIES 10. THE FIRE ANALOG: A COMPARISON BETWEEN FIRE PLUMES AND ENERGY CENTER COOLING TOWER PLUMES 241 10.1 INTRODUCTION 241 10.2 TYPES OF FIRES .242 10.3 CHARACTERISTICS OF MASS FIRES 244 10.4 COOLING TOWERS AND ENERGY CENTERS 245 10.5 FIRE ANALOG HYPOTHESIS 246 10.6 GEOMETRIC SIMILARITY 249 vii
page 10.7 DYNAMIC SIMILARITY 249 10.8 THERMAL ANL ENERGY SIMILARITY 250 10.9 KINEMATIC SIMILARITY 253 10.10 BOUNDARY CONDITIONS 254 10.11 CONCLUSIONS 256 REFERENCES 258
PREDICTIVE METHODS 11. LOCAL PRECIPITATION INCREASES CAUSED BY SCAVENGING OF COOLING TOWER PLUMES 263 ABSTRACT 263 11.1 INTRODUCTION 263 11.2 APPROACH 263 11.3 APPLICATION 267 11.4 CONCLUDING REMARKS 271 REFERENCES 271 12. RAINFALL ENHANCEMENT DUE TO SCAVENGING OF COOLING TOWER CONDENSATE 273 12.1 INTRODUCTION 273 12.2 AEROSOL SCAVENGING THEORY 274 12.3 CALCULATION OF RAINFALL ENHANCEMENT 275 12.4 SAMPLE CALCULATIONS 280 12.5 CONCLUSIONS AND RECOMMENDATIONS 289 REFERENCES 292 APPENDIX A. DETERMINATION OF APPARENT CONDENSATE FLOW RATE FROM A TYPICAL, LARGE NATURAL-DRAFT COOLING TOWER 294 APPENDIX B. PLUME DROPLET SIZE DISTRIBUTION USED IN SCAVENGING ESTIMATES 296
SUPPORT ACTIVITIES 13. THE METER INVENTORY 301 METEOROLOGICAL EFFECTS OF THERMAL ENERGY RELEASES (METER) PROGRAM ANNUAL TECHNICAL PROGRESS REPORT
October 1976-September 1977
A. A. Patrinos H. W. Hoffman
BACKGROUND
D. M. Eissenberg
The Meteorological Effects of Thermal Energy Releases (METER) Pro- gram* originated in 1976 as a response by the Energy Research and Develop- + ment Administration (ERDA) to questions raised in regard to tue potential environmental effects of future nuclear energy centers. These questions were raised in a U.S. Nuclear Regulatory Commission study, Nuclear Energy Center Site Survey 1975 (NUREG-0001), which contained a thorough analysis of available data regarding the effects of existing power plant atmo- spheric cooling systems (cooling towers and cooling ponds) on the atmo- sphere and also of analogous large natural and manmade heat releases com- parable to those of the proposed nuclear energy centers. Because of a perceived lack of sufficient information to make adequate judgments from available data on the potential impact of energy centers on the atmosphere,
Originally the Atmospheric Effects of Nuclear Energy Centers (AENEC) Program. f Now Department of Energy (DOE). BLANK PAGE 2 along wi h the conclusion that significant impacts may occur based on the analysis of the analogs, the study recommended a substantial program of theoretical and observational research to provide a guide to the evaluation of heat dissipation systems an! their climatic effects. The METER program was initiated under the sponsorship of the ERDA Division of Nuclear Research and Applications with the cooperation and assistance of the Division of Biomedical and Environmental Research. Program coordination was assigned to Oak Ridge National Laboratory. In 1977, the program name was changed to METER to reflect the broader con- cern of DOE for the effects of smaller heat releases than from energy ters, including those from fossil energy sources. The objective of the METER program is to develop suitable methodology and supporting lata for predicting the nature and magnitude of each of the meteorological effects resulting from the release of heat and lrois- ture from cooling towers and ponds which may have advr.rse environmental consequences. The effects identified as being of current concern in- clude :
1. drift transport and deposition, 2. precipitation augmentation, 3. ground-level temperature and humidity (T/h) increases, 4. shadowing, 5. fog and icing, 6. augmented transport of atmospheric pollutants, 7. triggering of severe storms (including tornadoes, hailstorms, etc.).
The intent in developing the predictive methodology is to provide regulatory agencies, utilities, and consulting firms with improved methods for assessing the environmental impact of future power plant atmospheric cooling systems. The program will also provide sufficient information to assist utilities in the layout, spacing, and location of future large energy centers so as to niinimize -he potential adverse impacts. The METER program is divided into the six elements described below: Field studies. The major effect is directed toward carrying out field studies at existing power plants having cooling systems with significant heat and moisture release to the atmosphere, in order to develop a data 3 base of observed effects. The field studies will generally be of a case study type, that is, short duration studies at representative power plants aimed toward obtaining sets of observations coupled with appropri- ate measures of the ambient atmosphere and of the emission characteristics cf the cooling system. Studies of this type are projected to be carried out for each effect. In addition, statistical-type studies of long dura- tion will be carried out where the statistical variability of natural weather effects appears to be sufficiently great so that case studies would not be useful. Mathematical modeling. Theoretical analyses provide insight into the mechanisms responsible for specific effects and provide the basis for developing mathematical models that describe and predict the inter- actions of plumes ami the atmosphere. Mathematical models which describe the observed behavior of plumes (either as observed in field studies or in physical modeling experiments) while retaining theoretical validity are useful in extrapolating those results to larger sizes or different atmospheric conditions.
Physical modeling. Labors tory'-scale experiments are useful in simu- lating certain aspects of the interactions between heat and moisture plumes and the ambient atmosphere. Experiments of three general types will be carried out as needed:
1. those which _xamine one feature of the interaction process with the objective of increasing the understanding of the fundamental mecha- nisms involved; 2. those which extrapolate from simple systems for which mathematical analyses are available to more complex systems, such that the mathe- matical analyses can be extended to predict these more complex inter- J i ^ actions; • 3. those which simulate actual proposed atmospheric cooling systems in order to predict specific effects at those sites. o
Analog studies. The study of the atmospheric effects of natural and manmade analogs to the heat and moisture plumes expected fr .a large energy centers can provide insight into the mechanisms responsible and a method • (7 A for validating the extrapolations of mathematical model." from the existing size cooling systems to those associated with energy centers. Predictive methods. The needs of the regulatory agencies and power plant operators with regard to assessing the environmental impacts of pro- posed atmospheric cooling systems can be met by developing standardized predictive methods for estimating the magnitude of each atmospheric effect as related to a possible environmental impact. Thus, the mean annual fre- quency and magnitude of the expected effect may be needed for some; whereas the maximum expected magnitude is more important for others. The accuracy, of prediction will depend partly on the difficulty of measuring the effect and partly on its importance in causing an impact. Predictive methods will be developed for each effect based on the above considerations. These may include the use of theo;etically based mathematical models, empirical or statistical correlations, or qualita- tive guidelines. Support activities. A number of support activities will be carried out to provide assistance and to coordinate the preceding elements. These will include the compilation of power plant inventories, the organizing of workshops and technical sessions at professional meetings, and the coordination of METER activities with similar programs not part of the METER program. There are six participants currently carrying out work in support of the METER program. These include Argonne Natio'nal Laboratory (DOE), Atmospheric Turbulence and Diffusion Laboratory (NOAA), Oak Ridge National Laboratory (DOE), Pacific Northwest Laboratories (DOE), Pennsylvania State University, and Rand Corporation. The specific tasks carried out by the participants result from dis- cussions between the participants, the DOE program managers, and the METER program coordinator and are intended to be in support of one or more of the METER program elements. This annual report contains contributions by each METER participant describing work carried out during the period October 1, 1976, to Septem- ber 30, 1977. The contributions have been reviewed and edited as neces- sary to conform to the general outline and format of this report. Con- tributions from each participant appear in more than one chapter. 5
This report was compiled, edited, and processed by the Technical Re- ports Section of the Engineering Technology Division, Oak Ridge National Laboratory. FIELD STUDIES 1. PRECIPITATION STfDir.S AKOEND PLAN'i BOV.T.N
A. A. N. Patrinos N. C. .1. Clit-n K. L. Miller
ABSTF\CT
The Nuclear Research and Applications and the Biomedi- cal and Environmental Research Divisions of the Department of Energy are sponsoring a program called METER (Meteorologi- ia] Effects of Thermal Energy Releases) to investigate the atmospheric effects of the heat and moisture releases from large cooling towers and ponds.
i tie OKNL portion ol the program deals with a precipi- tation modification study around Plant Bowen in northwest Georgia which utilizes four natural-draft cooling towers. The study is composed ol two parts: (i) the statistical analysis of historic National Weather Service climatologica] data from the general area of the plant and (2) a field study involving, primarily, a high-density recording rain-gage net- work. !k>th parts are aimed toward obtaining quantitative estimates of potential plant-induced precipitation augmen- tation and storm pattern disruption.
1.1 INTRODUCTION
1-14 One of the causes suggested for inadvertent weather modification is the significant amounts of heaL and moisture discharged by the cooling towers of large power generating facilities. Current-generation power plants with cooling towers dissipate about 5000 MW in the form of sensible and latent heat, and plants of the next generation are expected to double that amount. Moreover, some consideration is presently being given to
the concept of power parks, especially for nuclear plants4 to ensure plu- tonium safeguards among other things. Such power parks are expected to dissipate about 30,000 MW of heat. To investigate the atmospheric effects of the heat and moisture re- leases from cooling towers and ponds of large power plants, the Nuclear Research and Applications and the Biomedical and Environmental Research Divisions of the Department of Energy (formerly the Energy Research and Development Administration) are sponsoring a program called METER (Meteoro- logical Effects of Thermal Energy Releases). Participants in this program 10 include the National Oceanic and Atmospheric Administration (NOAA) Atmos- pheric Turbulence and Diffusion Laboratory, Battelle Pacific Northwest
Laboratories, Argonne National Laboratory, Oak Ridge National Laboratory,
Pennsylvania State University, and Rand Corporation. Among the various possible atmospheric effects linked to cooling tower emissions is that of precipitation modification. Despite the fact that the amounts of heat and moisture involved with the towers of a large plant are negligible compared with those released by even a moderately sized thunderstorm,5'6 there is some speculation that the cooling tower plumes function as a triggering mechanism to upset latent instabilities in the atmosphere, thus modifying precipitation and disrupting storm patterns. The delineation of the precipitation modification effect is a dif- ficult task because it requires a thorough understanding of natural pre- cipitation variability,7 a subject which has frustrated many students of weather modification phenomena (e.g., the cloud seeding field).' The quantitative characterization of natural variability requires the care- ful implementation of the available statistical tools and a concise understanding of the quality of the available data. Qualitative evalu- ations of precipitation events also play an important role in the study, as, for example, in the storm-type stratification of those events. For the purpose of studying the potential precipitation modification effects induced by cooling tower plumes, Plant Bowen of the Georgia Power Company was chosen as a test site. It is situated about 40 mi northwest of Atlanta and has four natural-draft cooling towers. Composed of four units (the first unit commenced operation in October 1971 and the fourth in November 1975), it is one of the largest plants in the world, especially among those using cooling towers as the sole cooling method. The precipitation study is composed of two parts: (1) a statistical study of climatological data recorded by the National Weather Service (NWS) at its regular stations and the stations of the Cooperative Network; and (2) a field study involving recording rain gages and windsets which will be installed around the plant within a radius of about 30 mi. The main purpose of the first study is to utilize already available cliinatological data taken prior and subsequent to the plant's initial 11 operation in order to form a comprehensive picture of rainfall patterns and variability for the preoperational and postoperational periods. Comparisons of results for the two periods yield possible indications of plant-induced effects. This study also serves in laying the ground- work for the field study in the identification of the appropriate target areas and the determination of the METER-ORNL network density and shape. It is a fortunate coincidence that the density and quality of the NWS and cooperative networks in northwest Georgia are above average for the southeast U.S. Nevertheless, this density of about 1 rain gage per 200 sq mi is about one order of magnitude less than the one recommended from the current state of the art of precipitation studies of the type con- sidered here.8 Consequently, all conclusions regarding plant-induced effects and stemming from the NWS climatological data should be con- sidered as tentative, awaiting confirmation from data to be obtained following the installation and oparation of the METER-ORNL precipitation network. This netwoii. will have a density of about 1 recording rain gage per 15 sq mi and will be situated within a radius of about 30 mi from the plant. Recording windsets at key locations will be used for the tracking of the surface winds. The METER-ORNL network will provide a continuous data base with the appropriate quality and resolution to fully characterize all precipitation events occurring around the plant and thus provide definitive quantitative evaluations of the plant's po- tential effect on precipitation.
1.2 THE CLIMATOLOGICAL STUDY
The climatological study deals primarily with rainfall data from 59 stations recorded mostly on a daily basis for the period 1949 to the present. Figure 1.1 is a map depicting the area around the plant with most of the considered stations. Four distinct areas in the climatological study can be identified: (1) data quality evaluations, (2) data stratification and presentation, (3) statistical correlations, and (4) storm analyses. The above activi- ties are described and some examples of the work performed to date given. 12
SCALE (miles) ORNL-DWG 77-17696 1 25 50 85 84 Hurphy Chattanooga USO AP T Conasauga 1 NNU Copp.rhllm l Hayravllla 4 WE _A_
>weet Gum +| r 'T*^ ' o. ^ rvn C«. #
9 Precipitation only Precipitation, storage
-3- Precipitation and Temperature
Precipitation, Temperature, and Lafayette-O West Point Evaporation Type of gage: O Non-recording ^ Hamilton 4 W I 0 Recording I ® O Both types N Opelika Double circle combinations indicate 1 -O \ I the availability of more detailed \ 1 - I mete oroloRical data.
Fig. 1.1. Map of northwest Georgia depicting the National Weather Service (NWS) and Cooperative Network stations. The stations within the circle are used for the climatological study. 13
1.2.1 Data Quality Evaluations
This activity is the necessary first step in any analysis involving physical data. It is of paramount imports: in the case of a precipita- tion study since the data v .ed are obtains. ~r a long period of time by a large number of observers with different rain gages. Instrument replacements and relocations, changes in exposure (e.g., growth of trees around the rain gages), and observers account for a wide range in the data quality spectrum. Efforts to establish the quality of the available data have been undertaken and are continuing. These efforts are twofold: field visits and double-mass techniques.
Field visits
Members of our staff visited 16 of the stations, met with observers, and evaluated the exposures of the rain gages. On one such visit they were accompanied by representatives of the Illinois State Water Survey (ISWS), who provided expert assistance in the evaluations. Table 1.1 presents our evaluations of the 16 stations with regard to the present instrument exposure situation on a scale of excellent, good, fair, and poor.
Table 1.1. Ir.npection of cooperative substations
Station Date inspected Excellent Good Fair Poor
Cedartown 3/15/77 X Cave Springs 4 SSW 3/15/77 X Rome WSO AP 3/16/77 X Calhoun Exp. Station 3/16/77 X Adairsville 3/16/77 X Cartersville 3 SW 3/16/77 X Cartersville 3/16/77 X Allatoona Dam 2 3/16/77 X Canton 3/16/77 X Ball Ground 3/16/77 X Alpharetta 2 NNW 3/16/77 X Atlanta WSO AP 3/17/77 X Dallas 7 NE 8/31/77 X Embry 8/31/77 X Carrollton 8/31/77 X Douglasville 8/31/77 X Total 4 5 5 2 14
Double-mass techniques
The analytical method known as "double mass"9'15 is used to deter- mine whether some extraneous occurrence (e.g., a change of rain gage lo- cation exposure in the case of a precipitation study) has caused a con- sistent departure of the recorded data from the long-term mean. Data from another station with dependable data are used as a basis for com- parison. A specific application of this technique as used in this study follows. Assume the recorded data from rain-gage station x and x^, where i = 1, 2, ..., N and i is the constant time period over which the data are recorded (e.g., daily, monthly, or annually). From the above data, we create the following cumulative record:
Vi = s xi • J 1=1
where j = 1, 2, N (Xi = 0). Similarly, for station y we have
= Vi s y± CYx = 0) .
Now assume that rain-gage station x has dependable data and has remained in one location; station y is a nearby station which has been frequently relocated. The question arises as to whether t-.he data from station y can be considered as one continuous record representing the area around which the instrument has been relocated. By eliminating j from X^ and Yj, we plot the relationship Y = f(X) on a cartesian coordinate frame. The result will be a series of data points in the first quadrant. If the straight-line segments that best approximate consecutive groups of points (i.e., the least-squares fits) have approximately equal slopes, we can safely conclude that the station y data can be considered as one continuous record. If an obvious change in the slope is evident after some point, we can conclude that after the time corresponding to that point the continuity of the record has been severed. In this case, we either consider the record as being composed of two different records 15 from two different stations prior and subsequent to that point (e.g., in the case of an instrument relocation); or in the case of multiple signifi- cant slope changes with no apparent reason, we disqualify the station. Appendix A contains the details of the computational least-squares fit utilized in this analysis. Figure 1.2 displays the double-mass graph of winter precipitation totals (December through January) for the Atlanta Bolton station vs the Atlanta Airport station. This graph, as well as initial contour maps containing the Atlanta Bolton station, raised sus- picions regarding the reliability of its record. Communication with the
ORNL-DWG 77-17697
ATLANTA WSO AP (inches precip.)
Fig. 1.2. Double-mass graph of winter precipitation totals for the Atlanta Bolton station vs the Atlanta Airport station. 16
NOAA representative of the Georgia Cooperative Network confirmed that the data coaid not be trusted prior to May 1972. As a result, Atlanta Bolton was dropped from our considered network before May 1972. Figure 1.3 presents the double-mass graphs for the Dallas station's winter record vs the respective ones for the Embry and Douglasville stations. Despite the fact that the Dallas station has bee«i relocated six times
ORNL- DWG 7 7-17698
EMBRY AND DOUGLASVILLE (inches precip )
Fig. 1.3. Double-mass graphs of winter precipitation totals for the Dallas station vs the Embry and Douglasville stations. Arrows indicate the years during which the Dallas station was relocated. 17 during the period 1948 to the present, the double-mass graphs show no appreciable changes in the slope. As a result, the records from all Dallas stations were joined together into one continuous record repre- senting the general area over which the Dallas station has been located.
1.2.2 Data Stratification and Presentation
The climatologicai study is based on data since 1949 from 59 stations which have operated continuously or intermittently. These data are avail- able in the form of data sheets (Climatological Data, Hourly Precipitation Data, and Local Climatological Data) and computer tapes. Precipitation amounts are recorded daily at 41 of the stations, hourly at 7 of the sta- tions, and both daily and hourly at the remaining ones. Surface wind recordings are obtained from two of the stations (Rome Airport and Atlanta Airport). Upper air soundings from Athens, Georgia, situated about 90 mi east of the plant, will be utilized in conjunction with North American surface and upper air weather maps for the storm analyses. Both the Athens soundings and the weather maps are available at the National Cli- matic Center in Asheville, North Carolina. The availability of all pertinent data in the form of computer tapes will prove to be a valuable asset tc the climatological study. Rapid accessibility and versatility will enhance the data stratification and the statistical analyses. The tapes are scheduled to be incorporated into our study in October 1977. To date, most of the results of our climatological study are derived from data obtained from the data sheets for 32 stations within a 40-mi radius of the plant; Fig. 1.4 displays this network. This preliminary study deals primarily with the precipitation totals for the winter sea- son (December through February). Of the 32 stations, one was dropped (Atlanta Bolton) as discussed in the previous section and two were com- bined into one (Jasper and Jasper 1 NNW) because of proximity. Future work will consider all 59 stations and will include the re- maining se.-iuons (spring, summer, and fall), the monthly totals and the dry and wet period totals (the lengths of these periods will have to be estimated), tor the storm analyses, precipitation totals will be 18
ORNl DWG 77 — 1 7699
CASTERS RESACA
S'JMMERVILLE 1 SSW •32 JASPER 1 NNW •29 CALHOUN EXK STA. >31 JASPER CURRYVILLE 2 W FAIRMOUNT
•30 ADAIRSVILLE BALL GROUND ROME WSO A? •8 • 10 WALESKA 028 ROME • 3 •11 KINGSTON CARTERSVILLE CANTON •9 • 27 CARTERSVILLE 3 SW 013 ROME 8 SW •12 ALLATOONA DAM 2 ®PLANT BOWEN < •15 • 14 •24 WOODSTOCK ALPHARETTA 2 NNW •26 TAYLORSVILLE CAVE SPRING• •j S 4 SSW '25 • '6 CEDARTOWN ALPHARETTA 5 SSW • 18 DALLAS 7 NE
<421 EMBRY • 17 •23 ATLANTA BOLTON TALLAPOOSA 2 « • 20 DOUGLASVILLE
• 19 ATLANTA WSO AP •22 CARROLLTON SCALE (miles) H 1 1 h 10 15 20 25
Fig. 1.4. Map of the 32 stations within s, 40-mi radius of Plant Bowen; these stations are used for the preliminary climatological study. .19 determined trc individual precipitation events which often implies a resolution of .. few hours. Three examples of the work performed to date in this area are pre- sented.
Wind speed and direction frequency distribution
From the recorded surface winds at Atlanta Airport for the winters of 1950 through 1977, a surface wind rose was constructed (Fig. 1.5). The obtained distribution displays predominant northwesterly winds for the winter months. This is a very encouraging fact for the climatological study, since it shows that the city of Atlanta with its potential urban effect lies downwind of the Dlant. If the opposite were true, the urban effect would have masked any potential plant-induced precipitation modi- fication.
Contour maps of normalized precipitation ratios
The contour maps shown in this study are generated with a computer "routine which triangulates the network grid and linearly interpolates between values at adjacent stations. A series of performance checks on this computer routine produced satisfactory results. Figure 1.6 displays the contour map for the ratios of postoperational (P0) to preoperational (PREOP) normalized precipitation means for the 30 stations considered initially. The normalized precipitation means are generated as follows. The total precipitation amounts for each winter season at each sta- tion are divided by the arithmetic areal r.ean for each winter season. This guarantees that the areal variations of precipitation for each winter season will contribute equally to the subsequent averaging (wet and dry seasons have equal weights). The preoperational means are the arithmetic means of the normalized precipitation values for the period 1950 to 1971, and the postoperational ones are for 1972 to 1976. The ratios of the latter (P0) to the former (PREOP) are displayed in Fig. 1.6. A precipi- tation high appears in the general downwind area of the plant (to the southeast). As discussed earlier, it is premature to attribute this result to a plant-induced effect. Nevertheless, it serves as a starting 20
ORNL DWG 77-17700 N WINTER WIND ROSE 1950-1977 FOR (FROM DAILY AVERAGES ATLANTA. GA BASED ON 2468 DAYS)
Fig. 1.5. Surface wind rose for the Atlanta Airport station for the winters of 1950 through 1977. 21
ORNL DWG 77-17701
Fig. 1.10. Contour map of ratios of postoperational (PO: 1972—1976) to preoperational (PREOP: 1966-1970) normalized precipitation means. 22 point for the detailed statistical and field studies planned for the future. Figures 1.7 to 1.10 display the contour plots for the ratios of the five-year postoperational normalized means to four different five-year preoperational means (51—55, 56r-60, 61—65, and 66—70). Taking into ac- count the obvious natural variations, we observe that the precipitation high persistently appears to the south and east of the plant (the down- wind region). Similar five-year running mean ratio plots were generated with various preoperational five-year periods in the numerator for com- parison. The plots displayed considerable random behavior with the precipitation highs and lows alternating between different regions of the network.
Frequency distributions of precipitation differences between stations
An example of this approach is displayed in Fig. 1.11. In this example, the daily totals of precipitation were used. Two five-year periods were considered: the preoperational five-year period 1967 to 1971 and the postoperational one 1972 to 1976. The precipitation events were stratified according to the recorded predominant surface winds, with only the events corresponding to the northwest winds being used for this distribution. Figure 1.11 displays the frequency distribution of those events according to the normalized precipitation difference between an upwind station (Rome) and a downwind one (Dallas). Although not pro- nounced, there is a marked shift of high positive precipitation differ- ences at the downwind station during the postoperational period. The definition of a precipitation event for this example was defined as the period of time during which precipitation occurred over the network and which was preceded and succeeded by at least one day with no precipita- tion over the entire network. This definition serves as a crude first approximation to the storm stratification work planned for the future.
Statistical correlations
As was mentioned in the Introduction, the understanding of natural precipitation variability is a necessary prerequisite for the delineation 23
ORNL-DWG 77 -17702
Fig. 1.10. Contour map of ratios of postoperational (PO: 1972—1976) to preoperational (PREOP: 1966-1970) normalized precipitation means. 24
ORNL DWG 77- 17703
PO/WINTER MEAN 56-60 r ne;
0.85
0.90
0.95
1.00
SCALE (miles) H 1 1 h 0 5 10 15 20 25
Fig. 1.10. Contour map of ratios of postoperational (PO: 1972—1976) to preoperational (PREOP: 1966-1970) normalized precipitation means. 25
ORNL-DWG 77- 17704
1.05 SCALE (miles) I 1 1 1 1 1 0 5 10 15 20 25
Fig. 1.10. Contour map of ratios of postoperational (PO: 1972—1976) to preoperational (PREOP: 1966-1970) normalized precipitation means. 26
ORNL DWG 77-17705
PO/WINTER MEAN 66-70 0.95 A
0.90
1.05 SCALE (miles) H 1 1 1 1 5 10 15 20 25
Fig. 1.10. Contour map of ratios of postoperational (PO: 1972—1976) to preoperational (PREOP: 1966-1970) normalized precipitation means. 27
ORNl DWG 7/—17706
POSTOPERATIONAL (1972-1976)
-100 -80 -60 -40 -20 20 40 60 80 100
PREOPERATIONAL (1967-1971)
-100 •80 -60 -40 -20 20 40 60 80 100 (P — P IMP + P DALLAS ROME DALLAS ROME 1 (%>
Fig. 1.11. Frequency distributions of normalized precipitation dif- ferences between the Rome and Dallas stations for the preoperational period 1967-1971 and the postoperational period 1972-1976. Events which have differences coinciding with divisions are divided equally among ad- jacent slots. 28 of a potential plant-induced effect. In an effort to produce a quanti- tative measure of the precipitation relationships between stations, a series of statistical spatial correlations11 were produced. Details of the spatial correlation are given in Appendix B. Figures 1.12 to 1.15 display the correlation coefficient contour plots for four stations (Dallas, Atlanta Airport, Douglasville, and Embry). These correlation coefficients were computed from the preoperational winter season totals (1950—1971). Note that the greatest gradient of the correlation coeffi- cient function for each plot is in the NW-SE direction; this coincides with the direction of the prevailing winds. Since the postoperational period does not have sufficient length to produce meaningful correlations • for comparison, special statistical tests will be developed for this pur- pose. Correlation coefficients based on the monthly (or precipitation event) totals will also be explored after the computer tapes are made available to our study. With regard to temporal correlations (time series analysis), no de- cision has yet been made. Preliminary investigations have been hampered by the lack of sufficient data to resolve fully the low frequency vari- ations. Nevertheless, some time and offort will be devoted to this approach.
Storm analyses
This activity will concentrate on the stratification of all precipi- tation events for the period 1949 to 1977 according to storm type, sur- face and upper air wind direction, and precipitation amount. The strati- fication of events according to storm type and wind direction will be accomplished using the North American surface and upper air weather maps (3-hr intervals) and the upper-air soundings (12-hr intervals) from Athens, Georgia. Seven main storm typ^s will be identified: cold front, warm front, stationary front, occluded front, air mass, squall line, and low-pressure center. The stratification according to the storm precipi- tation amount (p) will be done according to some suitable combination between the storm precipitation areal mean and the maximum amount measured within the network. Five precipitation, levels (in.) are considered: p < 0.1, 0.1 S p < 0.5, 0.5 S p < 1.0, 1.0 5 p < 2, 2 < p. In the above 29
ORNL DWG 77-17707
SCALE (miles) I 1 1 1 1 1 0 5 10 15 20 25
Fig. 1.12. Contour inap of the spatial correlation coefficients for the Dallas station. 30
ORNL—DWG 77-17708
Fig. 1.13. Contour map of the spatial correlation coefficients for the Atlanta Airport station. 31
ORNL DWG 77-17/09
Fig. 1.14. Contour map of the spatial correlation coefficients for the Douglasville station. 32
ORNL DWG 77 17710
SP CORR COEF STA 21 0.85 A
0.85
0.90 SCALE (miles) —I—I—I—I—I 0 5 10 15 20 25
Fig. 1.15. Contour map of the spatial correlation coefficients for the Embry station. 33 analyses., a precipitation event will usually be an individual storm re- gardless of the time length. This activity, which will draw heavily from the experience and expertise of the Illinois State Water Survey (ISWS), will make full use of all available climatological data. It will produce a sufficient statistical base for characterizing preopera- tional storm frequency distributions. Comparisons with the postopera- tional distributions should depict potential plant-induced effects to the best of the existing data capabilities.
1.3 THE FIELD STUDY
Starting in FY 1978 (October 1977), we will commence planning for the installation of the METER-ORNL precipitation network.12 This net- work will initially be composed of about 50 to 60 recording Bel fort rain gages and 6 recording R. M. Young windsets. Present tentative plans predict a square-shape network with the plant situated at its center. The length of the square's side will be between 25 and 30 mi for a rain- gage density between 11 and 15 sq mi per rain gage. The recording wind- sets will be located equidistantly on the perimeter of a circle of about a 5-mi radius with its center at the plant. The rain gages ai-e of the weighing-bucket type and will record continuously on a weekly chart. Some will be battery operated, while the remainder will utilize a winding clock mechanism. The windsets include a cup-anemometer, a wind-vane, and a strip-chart recorder operating on a monthly basis. The network will be serviced weekly and the data returned to ORNL for digitization and computer processing. Negotiations are currently under way with the Georgia Power Company representatives for the provision of an appropriate facility within the Bowen Plant to serve as a base for the field operations and for the temporary storage of equipment and data. The various stages of the field study along with the corresponding timetable for FY 1978 are depicted in Table 1.2. 34
Table 1.2. Stages and timetable of the METER-ORNL field study
Activities Dates
Final determination of network shape and density, selec- 10/77--11/77 tion of preferred instrument sites, and instrument checking and calibration Contact with local inhabitants and final selection of 12/77-1/7 8 instrument sites, completion of instrument calibration, and transportation of instruments to the Bowen Plant Instrument installation, instrument field checking, 1/78-2/78 development of data-collection procedure, and organi- zation of the ORNL-based data processing operation Initial full-time operation of the METER-ORNL precipi- 3/78 tation network Evaluation of the network's weaknesses and needs, major 9/78 potential instrument additions, and relocations
1.4 SUMMARY
As part of the Department of Energy sponsored program called METER (Meteorological Effects of Thermal Energy Releases), ORNL is studying the effects of Plant Bowen (in Northwest Georgia) on the local precipi- tation. This fossil-powered power plant has four natural-draft cooling towers and generates 3200 MW(e). The study is composed of the following two parts. 1. A climatological study utilising precipitation data from 59 Na- tional Weather Service (NWS) stations in the general area of the plant, wind data from three key stations, and the North American 3-hr weather maps (all data are for the period 1949 to 1977). Preliminary results indicate a plant-induced precipitation high in the downwind area from the plant. 2. A field study utilizing 60 recording rain gages and 6 recording windsets which will be installed around the plant with a density of about 1 rain gage per 15 sq mi. This network will provide the data to sub- stantiate the findings of the climatological study and explore other possible plant-induced effects on precipitation patterns. 35
1.5 ACKNOWLEDGMENTS
.Tie preparation of this report was supported by the Department of i..^rgy as part of the program on the Meteorological Effects of Thermal .'.nergy Releases (METER). The authors are indebted to H. W. Hoffman, Section Head of the heat Transfer and Fluid Dynamics Section, and D. M. Eissenberg, METER Program Coordinator, for reviewing the manuscript.
References
1. F. A. Huff, "Evaluation of Precipitation Records in Weather Modifi- cation Experiments," Advan. Geophys. 15, 59—135 (1971).
2. H. E. Landsberg, "Discussions — Rainfall Variations Around a Thermal Power Station," Atmos. Environ. 11, 565-67 (1977).
3. A. M. Selvam, G. K. Manohar, and B. V. R. Murty, "Rainfall Variations Around a Thermal Power Station," Atmos. Environ. 10, 963-68 (1976).
4. A. A. Patrinos and H. W. Hoffman, Atmospheric Effects of Nuclear Energy Centers (AENEC) Program Annual Technical Progress Report for Period July 1975-September 1976, ORNL/TM-5778 (1977).
5. F. A. Huff, "Potential Augmentation of Precipitation from Cooling Tower Effluents," Bull. Amer. Meteor. Soc. 53, 639-^44 (1972).
6. S. R. Hanna and F. A. Gifford, "Meteorological Effects of Energy Dissipation at Large Power Parks," Bull. Amer. Meteor. Soc. 56, 1069-76 (1975).
7. A. B. Pittock, "On the Causes of Local Ciimatic Anomalies, with Special Reference to Precipitation in Washington State," J. Appl. Meteor. 16, 223-30 (1977).
8. F. A. Huff, "Precipitation Detection by Fixed Sampling Densities," J. Appl. Meteor. 8, 824-37 (1969).
9. M. A. Kohler, "On the Use of Double-Mass Analysis for Testing the Consistency of Meteorological Records and for Making Required Ad- justments," Bull. Amer. Meteor. Soc. 30, 188r-89 (1949).
10. C. 0. Wisler and E. F. Brater, Hydrology, Wiley, 2d ed., New York, 1949.
11. M. Ezekiel, Methods of Correlation Analysis, Wiley, 2d ed., New York, 1941.
12. S. A. Changnon, Jr., "Operations of Mesoscale Networks, Illustrated by METROMEX," Bull. Amer. Meteor. Soc. 56, 971-77 (1975). 36
APPENDIX A
For the purpose of obtaining quantitative estimates of the slope of the straight line that best approximates a group of points in the "double- mass" technique, a special version of the least-squares fit is developed. Assume N data points with coordinates X^ and Y^ (i = 1, 2, ..., N). We seek the slope of the straight line through the origin which best approxi- mates the N points. Since both X^ and Y^ are physical data subject to systematic and random errors, we define the approximating straight line as that which goes through the origin and minimizes the sum of the squares of the vertical distances between the individual points and the straight line. In Fig. A. 1, Z^ is the vertical distance of the ±th data point from the least-squares straight line. We seek to minimize the expression
N S = £ Z. . (1) i=l
ORNL DWG 11
Fig. A.l. Graph depicting the vertical distances used in the "double-mass least-squares" fit. 37
If a is the angle of the straight line with the x-axis, we have
Z. = Y. cosa — X. sina . (2) 11 i
Consequently, we minimize the expression
N S = Y\ (Y. cosa — X. sina): (3) i=l 1
To minimize, we set dS/da = 0 and obtain
N N N 2 2 2 X.Y. = 0 tan a £ X.Y. - tana £ (Y. - X. ) - £ l l (4) i=l 11 i=l 1 1 i=l
Since only the positive slope is sought, we have that
1/2 N N 2 2 £
The least-squares sum is thus
1 / N N N \ s 2 + tan2a £ X.2 — 2 tana (6) = r(£ Yi 1 + tan a \i=l i=l £
For the specific application of the above technique to the cumulative precipitation amounts, we compute the slopes for consecutive groups of points (e.g., 5 or 10). This is equivalent to moving the center of the considered coordinate system to consecutive data points and evaluating the least-squares slope on the basis of the following group of 5 or 10 data points. This method permits the quantitative evaluation and com- parison of slope changes. The computed least-squares sum gives a measure of the goodness of fit. Figures A.2 and A.3 display the slope variations and least-squares sums for the Dallas-Embry, Dallas-Douglasville, and the Atlanta Airport—Atlanta Bolton stations (the slopes were computed on the basis of consecutive groups of 5 points). Fig. A.2. Graphs of the "least-squares" slopes and residuals for the Atlanta Airport—Atlanta Bolton "double-mass" graph (based on con- secutive groups of 5 points). 7.12
•V i \ / \ 1 08 \ i—DAI LAS - DO JGLASVIL LE" tj Ik \
\ £ 1.04 V \ O • > > > • in / / \ t \ / 1.00 \ / \
096 .AS - EMB HY '
DALLAS - EMBRY-
< A ALLAS - C LLE Q f V OUGLASV yK / x / N r A f* \ / V / / ** / ' V r < // y\ .j V \ '— \ \ J 1 '54 56 '58 '60 '62 '64 •66 '68 '70 '72
YEAR Fig. A. 3. Graphs of the "least-squares" slopes and residuals for the Dallas-Embry and Dallas-Douglasville "double-mass" graphs (based on consecutive groups of 5 points). 40
APPENDIX B
The cumulative spatial correlation coefficients for the various net- work stations are defined as follows.
Assume that the measured data for stations i and j are x.1 , K. and x. , where k = 1, 2, N. The subscript k refers to the time period J > k over which the data were recorded (e.g., k = 1, the winter of 1950; k = 2, the winter of 1951; etc.). The statistical correlation coefficient of station i with station j for the 5 time periods is defined as
E
where
l * — 1 X. . and X. „ = j £ X (2) = E i,k k=l k=i j'k
For the specific examples presented in this report, the individual data represented winter seasonal totals. The available data provide 27 winter seasonal totals for most stations (1950—1976); and as a result, N = 27. The displayed correlation plots refer to the preoperational time period (i.e., up to and including the winter of 1971). This implies that in Eqs. (1) and (2) we have I = 22. 41
2. STUDIES OF THE ENVIRONMENTAL IMPACT OF EVAPORATIVE COOLING TOWER PLUMES
D. W. Thomson*
2.1 INTRODUCTION
This ongoing research program of the environmental impact of natural- draft evaporative cooling tower plumes consists principally of a compre- hensive series of airborne measurements of a variety of the physical char- acteristics of the plumes and, to a lesser extent, of preliminary studies of remote sodar plume probing techniques and the development of simplified dynamical numerical models suitable for use in conducting field measure- ment programs. The 1976—77 contract year included the following notable program activities or changes. 1. The airborne field measurements program was significantly re- duced in order to enable members^ of the research group to complete processing of the backlog of recorded aircraft data. The airborne meas- urements made consisted almost entirely of studies of cooling tower and merged cooling tower—stack plume aerosol and chemistry. 2. In the fall of 1976, the PSU Doppler sodar was used at the Key- stone Power Plant in southwestern Pennsylvania for an extended series of remote measurements of the characteristics of plume turbulent temperature and velocity fluctuations. 3. Some additional evaluative studies of the PSU plume model were also performed. 4. Finally, to facilitate interpretation of the airborne measure- ments, a power plant energy balance model was developed and applied to •e Keystone Plant.
Department of Meteorology, The Pennsylvania State University, Uni- versity Park, Pa. + D. W. Thomson, Assoc. Prof. (10%); J. M. Norman, Assoc. Prr>f. (15%); R. G. de Pena, Assoc. Prof. (15%); J. Lee, Assist. Prof. (15%); J. Pena, Research Meteorologist (20%); R. L. Coulter, Project Associate (50%); T. Chin, Project Assistant (33%); A. Dittenhoefer, Research Assistant (50%); S. Perry, Research Assistant (50%); K. Underwood, Research Assistant (50%); A. Korrell, Research Assistant (50%). 42
Progress in the above research topics is summarized below.
2.2 AIRBORNE MEASUREMENTS
For convenience, the airborne plume measurements have been divided into the following subgroups:
1. detailed mean values of the ambient profile, plume, and source char- acteristics appropriate for numerical modeling of plume behavior; 2. detailed in-plume measurements of turbulent temperature, humidity, and velocity fluctuations; 3. plume hydrometer (drift and cloud water) sampling; 4. aerosol and air chemistry measurements.
Results to date of the mean plume measurements are summarized in an 86-page technical progress report which has been submitted to ERDA for publication: Airborne Studies of Natural Draft Cooling Tower Plumes: Meteorological Profiles and a Summary of In-plume Turbulent Temperature and Velocity Fluctuations. In the report, case studies including the following data are presented for 22 plumes observed during widely vary- ing conditions:
1. detailed analysis of mesoscale synoptic conditions, 2. skew T—Jin p plots of Pittsburgh radiosonde sounding closest in time to the airborne measurements, 3. a picture of the measured plume taken from the aircraft at a position approximately orthogonal to the mean plume axis, 4. a sketch to scale of the plume from which its rise trajectory and length may be determined, 5. aircraft vertical temperature and relative humidity soundings made immediately (1 to 5 km) upwind of the power plant, 6. representative samples of time series of turbulent temperature and velocity fluctuations obtained by penetrating through the plume at distances ranging from less than 50 m to more than 20 km from the cooling tower,
7. a summary of plant operating data from which plume source terms can be accurately determined. 43
Preliminary results of the in-plume turbulent temperature and ve- locity measurements have been summarized in Miller (1977), Thomson et al. (1976), and Chin (1978). Scientific results of all the various turbu- lence measurements will be summarized in a paper now in preparation for submission to the Journal of Applied Meteorology. For the first time this past year, we attempted to measure in-plume turbulent water vapor fluctuations. Figure 2.1 illustrates the time series of the state parameters and derived sensible and latent heat fluxes for one penetration. Multipenetration average heat fluxes are in good agreement with plant operating data. Because flux measurements are of great potential value to scientists performing plume modeling but have never before been available, we have proposed an extensive series of plume penetrations which include fast-response Lyman-ot water vapor meas- urements . Results of plume drift water measurements to date have been sum- marized in "Airborne Measurement of Drop-Size Distributions for Drops Larger than 60 ccm," which has been accepted for publication in Atmo- spheric Environment. The abstract follows. "An airborne instrument that can selectively collect and replicate large drops (diameter greater than 60 ym) is described. "The large drops reach the collector by their inertia, while the small ones moving along with the air are not collected even though their number concentration uiay be more than 1000 times larger than the large drops. "This instrument, which can be mounted on a light aircraft, can be used either to determine the concentration on the drift drops in cooling tower plumes or precipitation elements in clouds. "Data are included from flights through cooling tower plumes." The airborne samplers are presently being modified to facilitate collection of smaller hydrometers for plume water chemistry studies.
2.3 AEROSOL AND AIR CHEMISTRY MEASUREMENTS
Atmospheric Environment has also accepted two papers (Dittenhoefer and de Pena, 1977; Mamane and de Pena, 1977) reporting the results of the airborne air chemistry and aerosol measurements. Abstracts of the two papers follow in the order mentioned. Aircraft data obtained (roa flight 3-101 (April 1, 1977). frofll««, acatured perpendicular to the pluM axis, lncluda a) vertical velocity (•/•ec), b) temperature
"A number of airborne plume sampling experiments designed to examine the importance of sulfate particle-generating chemical reactions within coalburning power station plumes are described. The flights were con- ducted downwind of the Keystone Generating Station, in western Pennsyl- vania, with The Penn State University research aircraft, an Aerocommander 680E. O^-board aerosol sampling instrumentation included a condensation nucleus co\inter, an optical particle counter, and an electrical aerosol analyzer. A Casella cascade impactor containing electron microscope copper grids coated with carbon film was used to collect particles at varying distances from the stacks. These samples were analyzed for sul- fate content and particle size distribution. Measurements of SO2 were made with a rapid-response pulsed fluorescent analyzer. Atmospheric pressure, temperature, dewpoint, winds, and aircraft position were also monitored. "For each flight, a vertical spiral aircraft sounding was made up- wind of the power station to determine atmospheric stability and back- ground aerosol particle and S02 concentrations. Downwind, the flight pattern consisted of a series of cross wind and longitudinal plume pene- trations out to distances at which SO2 reached background levels. During the case in which cooling tower plume and stack plume merger occurred, sampling continued out to regions where the liquid plume had dissipated. "It was found that when relative humidity was low, stability near- neutral, and solar radiation intense, the production of new Aitken par- ticles was the primary mechanism of SO2 oxidation. In the case of mer- ger between the stack plume and the cooling tower plume, the formation of sulfate on pre-existing particles predominated over the formation of new particles. During cases with intermediate meteorological conditions, both processes were of equal importance." "A quantitative method for the analysis of individual submicrometer size sulfate particles has been developed. It is based on the reaction of the sulfate ion with barium chloride and can be applied only to soluble sulfates. The method is specific for sulfates. Carbonates sulfites and nitrates can be distinguished from sulfates. "The size of the halo depends on the size of the particle, the thick- ness of the barium chloride film and the relative humidity at which the reaction takes place. By fixing the values of the last two parameters, a single correlation can be established between the halo and the particle size. The method requires sampling timt "n the order of minutes for clean air to seconds for very polluted a:ias. An example of the appli- cation of the method to atmospheric aerosol is shown."
2.4 INDIRECT SOUNDING OF PLUMES USING SODAR
Analysis to date of the sodar plume measurements has for the most part been performed by R. L. Coulter* and K. Underwood. Their results
Present affiliation: Argonne National Laboratory. 46 are to be presented in a paper submitted-to the Fourth Symposium on Meteorological Observations ar«d Instrumentation in Denver, Colorado. Underwood's M.S. thesis* study investigated the potential and limitations of sodar for analyses of plume turbulence. The necessary acoustic propa- gation, probing system, and turbulence concepts were developed and the sodar measurements then evaluated in terms of the plant operating and ambient atmospheric conditions. Sodar studies now in progress consist of further evaluation of existing data and ambient acoustic noise studies at a mechanical draft tower complex to determine whether or not it will be possible to use sodar for measurements of mechanical draft tower plumes.
2.5 APPLICATIONS OF ONE-DIMENSIONAL PLUME MODELS
We had originally intended to undertake intercomparison studies to evaluate as many as possible of the various available one-dimensional plume models. Since this has already been undertaken at the Argonne National Laboratory, the modeling effort at Penn State has been re- directed toward a fundamental evaluation of the limitations (and poten- tial) of one-dimensional models for plume behavior predictions. Since the present Penn State airborne observations are the best presently available for this purpose, Korrell and Lee have assisted in the analyses of the "mean" plume, atmosphere, and power plant data which are summarized in the previously mentioned technical progress report and in the analysis of plant data required for the energy balance modeling.
2.6 PLANT ENERGY BALANCE MODELING
Norman's plant energy balance model has been designed to provide information on the following factors given operating information which is available at a plant such as the Keystone complex:
1. total plant energy input from coal, 2. plant efficiency,
*"A Quantitative Study of Cooling Tower Plumes Using a Monostatic Sodar." 47
3. gross electric generation, 4. sensible heat output f^e cooling tower(s), 5. latent heat output of the cooling tower(s), 6. exit cooling tower air temperature, 7. mean cooling tower exit air vertical velocity, 8. cooling tower exit plume excess liquid water.
Redundancy observations are under way to facilitate testing of the per- formance of this mode]. Simultaneously, it is being applied to aid our interpretation of the airborne and acoustic measurements «ind to facili- tate evaluation of the one-dimensional dynamical numerical model.
References
Chin, T. N. (1978), "Airborne Measurements of Turbulent Velocity Fluctua- tions and Sensible Heat Fluxes in Cooling Tower Plumes," M.S. thesis in preparation, The Penn. State University, University Park. Dittenhoefer, A. C., and R. G. de Pena (1977), "A Study of the Production and Growth of Sulfate Particles in Coal Operated Power Plant Plumes," accepted for publication in Atmos. Environ. Mamane, Y., and R. G. de Pena (1977), "A Quantitative Method for the De- tection of Individual Submicronter Size Sulfate Particles," accepted for publication in Atmos. Environ. Miller, R. L. (1977), "Characteristics of Temperature Fluctuations in Cooling Tower Plumes," M.S. thesis, The Penn. State University, University Park. Pena, J., J. M. Norman, and D. Thomson (1977), "Airborne Measurement of Drop Size Distributions for Drops Larger than 60 ym," accepted for publication in Atmos. Environ. Thomson, D. W., J. M. Norman, and R. L. Miller (1976), "Airborne Measure- ments of Turbulent Temperature and Velocity Fluctuations in Cooling Tower Plumes," Illrd Symposium on Atmospheric Turbulence Diffusion and Air Quality, Oct. 19—22, American Meteorology Society, Boston, Mass.
Thomson, D. W., J. M. Norman, T. N. Chin, and R. L. Miller (1977), Airborne Studies of Natural Draft Cooling Tower Plumes: Meteorological Pro- files and a Summary of In-Plume Turbulent Temperature and Velocity Fluctuations, Technical Progress Report to DOE, submitted for publi- cation. 48
3. COOLING TOWER DRIFT: EXPERIMENT DESIGN FOR COMPREHENSIVE CASE STUDY
N. S. Laulainen*
3.1 INTRODUCTION
Drift from a cooling tower is defined as that component of the cir- culating water which is entrained in the airflow as small droplets and carried out beyond the tower. The drift droplets are produced mechanically within the tower, whereas the visible plume condensate droplets are cre- ated through cooling of the saturated tower exhaust air. The differen- tiation between thest droplet sources is important as the drift will contain concentrations of dissolved minerals and chemicals similar, if not identical, to concentrations of the circulating water. Depending upon the chemicals present in the circulating water, drift may have an adverse effect on the environment. Consequently, in order to assess environmental impact, it is important that the amount of c'rift and the resulting distributions in the air and on the ground b€ determined. Each cooling tower can be expected to have a unique drift distri- bution, depending on the type and size of the units and the design of the drift eliminators. Meteorological conditions also play an important role in determining drift distribution. Thus a complex model will be required to provide cooling tower drift assessment for any particular tower under the varied modes of its operation and the range of meteoro- logical conditions to which it will be subjected. A number of models have been developed to estimate drift distribu- tions; ten of these models have been reviewed by Chen.1 Using a common set of input parameters, Chen finds that the maximum deposition differs among the models by two orders of magnitude with a wide range in down- wind location of peak deposition. He concludes that no particular model can claim superiority over another without verification from field data, especially ground mineral deposition measurements.
Atmospheric Sciences Department, Battelle Pacific Northwest Labora- tories, Richland, Wash. 49
The most comprehensive study to date of drift from a single cooling tower has been the Chalk Point Cooling Tower Project.2-1* In this study, measurements were made of salt water drift exiting from the natural- draft towers, drift concentrations within the airborne plume, and near- surface air concentration and surface drift deposition. Because of drift emissions from the stack plume, it was necessary to conduct an experiment where Rhodamine-WT dye was added as a tracer to the cooling tower circu- lating water in order to separate drift components from the two plumes.5 It is anticipated that this study will provide important field data to test various drift deposition models for natural-draft cooling towers. The objective of the experimental work described here is to develop a data base which can be used for validation of drift deposition models for mechanical—draft cooling towers. The key aspects of the proposed work are to measure the source characteristics and the meteorological conditions responsible for transport and dispersion of the cooling tower plume containing the drift component and to measure the downwind deposi- tion and air concentrations of drift. The source and transport parameters serve as inputs to the models, while the deposition pattern serves as a comparison to the model outputs. Initially, a comprehensive experimental effort is planned for early spring 1978 on mechanical-draft cooling towers of some suitable power plant site, such as the Pittsburg (CA), Duane Arnold (Cedar Rapids, IA), Prairie Island (Red Wing, MN), Palisades (South Haven, MI) or Jack Watson (Gulfport, MS) plants.
3.2 MEASUREMENT PROGRAM
A major deficiency in evaluating drift transport and deposition is the lack of good field data. As models have become more refined, the need for more accurate measurements of both the source and sink terms has also grown. Thus it is necessary that simultaneous measurements be made of the mineral (or other additive) concentration in the tower basin; the rates of mineral mass and drift water emission and the associated drift droplet size distribution at the tower exit; the ambient meteoro- logical conditions to evaluate plume rise, transport, and dispersion; and the spatial distribution of ground drift deposition, including both 50 mineral mass and drift droplet size distribution. In addition, measure- ments of updraft wet- and dry-bulb air temperature and updraft air velocity profiles are necessary for predicting plume rise and the locus of points where the drift droplets of various sizes break away from the temperature-water plume. Proper source measurements are very crucial to model validation. Chen1 finds that the maximum deposition pattern and its location down- wind of the cooling tower are very sensitive to the mass fraction in larger droplets for all present models. Reliable data for this part of the droplet size spectrum are difficult to achieve because of poor counting statistics; that is, there are very few large droplets but these few can account for an appreciable fraction of the total emitted drift mass. Thus several techniques should be applied to the measurement of the droplet emission spectrum and mineral mass flux to provide a necessary redundancy and to ensure that the results are as accurate as possible. The effective drift droplet emission height is also crucial in determining impact distances and deposition patterns.1 Cooling tower energetics (temperature, relative humidity and updraft velocity profiles), as mentioned above, are necessary for the prediction of plume rise, drop- let evaporation, and drift droplet breakaway point. Some of the dis- crepancies between various drift deposition models can be attributed to different assumptions regarding plume centerline height variations, evaporation, and effective emission height. Indeed, complex circula- tions within the plume have been observed which very likely have a direct influence on effective height of drift emission. Unfortunately, this aspect of plume and drift transport is not included in the present measurement program but should be addressed in the near future. Since the amount of drift mineral to be measured can be expected to be small, the results of field experiments will be sensitive to the ac- curacy and precision of the instruments and methods used. Nearly 100% of the drift mqss is presumably deposited on the ground within a few kilometers of the tower. Most sampling techniques take advantage of the cooling water minerals (e.g., salt), cooling water additives (e.g., sul- furic acid, chromium), or tracers (e.g., Rhodamine-WT dye). Chemical 51 techniques, such as ion chromatography or atomic absorption spectroscopy, can be used to obtain quantitative measurements of various chemical species (e.g., sulfate, Ca2+, Na+) from bulk samples. The use of sen- sitized papers, filters, and/or films as collecting surfaces for indi- vidual droplets, although requiring tedious analysis efforts, provides a method of obtaining drift droplet size distributions from which total drift water mass is calculated by simple integration. When such analysis is applied to the source measurements, the total drift water mass emitted per unit time or drift rate can be estimated. Moreover, by combining the total mineral mass emission with the total drift water emission, a mean drift mineral concentration can be computed and compared to the mineral concentration in the basin waters. In prin- ciple, these two concentrations should be the same if no evaporation has occurred from the region where the drift droplets are generated to the point where the measurements are made near the exit plane. Discrepancies have been observed, but their cause is not yet fully appreciated. Similarly, by combining downwind mineral mass deposition and drift water drift deposition, the mean drift mineral concentration can also be compared to basin water mineral concentration and/or emitted drift min- eral concentration. In this manner, the amount of droplet evaporation can be assessed. It has been suggested that the measured droplet size distributions as a function of downwind distance could be used to calcu- late the size and position of each droplet when it leaves the plume and thereby provide some additional information about the breakaway point as a function of droplet size. Accurate temperature, relative humidity, and wind profiles to plume height would be required. Ideally, a series of sampling stations located downwind and along the centerline of the plume would be sufficient to define the drift depo- sition pattern. The reality of nonideal wind patterns, nonideal plume dispersion, and the possible obstructions to location of surface samplers requires a grid which is composed of a system of downwind arcs with three or more sampling stations per arc.5 Several upwind sampler sites are required to account for ambient background levels of drift chemicals. Sampling periods longer than 1 hr are required to average plume meander but most importantly to assure sufficient collection of drift mineral 52 and droplets for -analysis. To avoid contamination of the receptors by resuspended surfaces material or distortion of the measured distribution due to competition from other receptors such as plants and shrubs, the receptor stations should be elevated above the surface by about 1 m. Each receptor station should include at least one large water-sensitive filter paper and one or two large plain filter papers for obtaining total water droplet deposition and total mineral droplet deposition, respectively. Techniques are available or are being developed for obtaining quan- titative concentrations of salt (chloride) and fluorescent dye in drop- lets from the untreated filter papers.5 A number of water—sensitive filter papers are available,6*7 and evaluations of sensitive gelatin coatings8 and photographic film and other filter paper preparation tech- niques6 are under way. The receptor station should also include one bulk deposition sampler (e.g., a large-area plastic pan or bucket with a tight sealing lid) for the determination of total mineral mass deposition using standard, high-sensitivity analytical chemical methods. Near-surface air concentrations of total drift mineral mass and per- haps drift droplet size distributions can be measured using a high-volume sampler at each receptor station using untreated and water-sensitive filter papers, respectively. The untreated filter papers can be dis- solved in water and analyzed for specific drift minerals using the same chemical techniques used on the bulk deposition samples or may be analyzed directly using x-ray fluorescence techniques. Drift droplet size distri- butions can be obtained from the water-sensitive papers using calibra- tions based on the flow rate of the high-volume sampler. Filter exposure areas should be in the range 100 to 600 cm2. Alternatively, drift drop- let size distributions could be obtained using a rotating-arm sampler with sensitive papers and/or films attached.3 Determination of droplet size distributions from the sensitive papers and/or films is expected to be the most expensive and time-consuming part of the data analyses. By use of a Quantimet 720 automatic sizing and counting system, an estimated 4 to 5 exposed papers can be analyzed per hour at a cost of roughly $40 per hour for equipment and operator time. The system can be programmed to provide hard-copy tables and graphs of 53 the measured distributions. Care must be taken, however, to account for droplet overlap and nonnormal droplet impingement. Meteorological observations are extremely important for data in- terpretation such as distribution pattern, the amount of evaporation the droplets experience, and plume rise. Therefore, profile determina- tions of wind speed and direction and dry- and wet-bulb temperature are required. A monostatic acoustic sounding system and h..gh-quality tethered-balloon telemetry system satisfy these requirements. The tethered-balloon system can provide quantitative data to 500 m above ground level. The acoustic sounder provides qualitative data of tempera- ture variability to several hundred meters above f.round level and pro- vides a real-time display of information related to atmospheric stability and the presence of convection from the surface. Time-lapse photography can also supply valuable information on complex circulations within the plume. It is expected that a synchronized two-camera system, viewing the plume from two different angles, can be employed to provide informa- tion on plume geometry and orientation. Site surveys and preexperiments at several power plant sites are planned to evaluate a number of factors, including the logistics of setting up suitable surface measurement arcs with respect to surface topography and prevailing meteorological conditions, access to fan stack exits, and preliminary measures of the amount of drift deposition which can be expected as a function of downwind distance. Of these latter measurements, the bulk samples are to be used to check the sensitivity of the chemical analysis techniques.
3.3 FIELD DATA APPLIED TO MODEL VALIDATION
Since the data collected in this study are to be used for drift depo- sition model validation, it is useful to estimate the sensitivity of the models to variations of input data. The Hosier, Pena, and Pena model,9 a ballistic trajectory model incorporating evaporation of the drift droplets, provides a suitable starting point because of its relative simplicity. 54
In this model, particles in the size range d^ to d^ + Ad^ released from the plume at height h^ into an ambient wind field having uniform and constant wind speed W are deposited at the ground into a sector having an angular width 0 and radial extremities at x^ and x^.— Ax^ determined uniquely by d^ and d^ + Ad^, respectively. The deposition rate for each size class is given by
2cQ 2 2,-2 1 D. - [x. - (x. - Ax.) ] (1) where Q^ is the emitted drift mass in the size range d^ to d^ + Ad^ and c is a constant related to the frequency of humidity and wind direction toward the sector. Changes in mineral concentration are directly proportional to changes in Q^; similarly, the fraction of drift mass emitted in the size range interval is also directly proportional to Q^.10 Thus a given un- certainty or variation in mineral concentration and drift mass fraction results in a proportionate change in drift deposition for a given size range interval; for example, a +15% error in either of these quantities leads to a +15% error in the predicted deposition. Other sources of uncertainty in model output include error in the effective release height h^, error in the effective terminal settling speed V , and error in the measured particle size d^. Pena and Hosier11 have discussed the errors in estimating the settling velocity of drift droplets because of droplet evaporation and have suggested approximations to minimize these errors. Schrecker et al.12 have discussed the errors in effective release height and particle size and have concluded that errors in particle-size determinations, especially for trajectory-type models, have the greatest impact on the transport calculations. To illustrate this result further, a summary of the discussion by Schreekcr et al. is given. Subscripts are dropped for simplicity. The error in ground-level deposition due to error In effective re- lease height can be calculated by noting in Eq. (1) that
(2) 55 and that
A = -I [x2 - (x - Ax)2] (3) is the area of the sector into which the emitted mass is deposited. Con- sequently, a fractional error of 6 in h^ [i.e., h^ -»- h^(l + 6)] results in a fractional error in the deposition rate D of
D' A x2 - (x - Ax)2 1 ... D~ = T = x-2 - (x' - x-)" = (1 + 6)2 > (4) where the primes indicate the perturbed parameters. For 6 = +0.15, D'/D - 0.76, a 24% decrease in ground-level deposition. The estimate for errors in the particle-size measurements is more complicated and requires the additional assumptions that the tquilibrium particle size (after evaporation) is a constant fraction of the original size (i.e., d = 3d) and tnat the number of droplets per unit volume of e air sampled is the same in the size intervals [d, d + Ad = d(l + A)] and [d' = d(l + S), d' + Ad' = d(l + A)(1 + 6)]. For particles in the range 2 2 0 < d < 100 ym, Vr = Kxde = K,,d , while for large droplets Vr = Kd. Be- cause of the size change, there is also a mass change to account for in Q of Eq. (1). Thus, the fractional error in the deposition rate is, from Eqs. (1) and (2),
Bl _ fil A m" x2 - (x - Ax)2 /dA3 \ (dr* - [d(l + A)]~\ j D ~ A' " Q ~ m x'z - (x' - Ax')* = \d / / (d')-" - [d'(l + A)]_H (
= (1 + 6)3 (1 + 6)14 = (1 + S)7 (5) for particles in the range of 0 < d < 100 ym and
^ = (1 + S)5 (6) for large particles. Thus with 6 = +0.15, Eq. (5) gives D'/D = 2.66 and Eq. (6) gives D'/D = 2.01. These errors are substantial and clearly point out the need for precise size distribution measurements of the source. Meyer and Stanbro have also carried out sensitivity analyses 56 of several drift deposition models and have made similar conclusions re- garding size distribution measurements of the source, ambient relative humidity, and effective drift release height. It is instructive to estimate the downwind mineral deposition rates with the ballistic trajectory model of Hosier, Pena, and Pena.9 Chen1 has carried out calculations for a natural-draft cooling tower using a drift rate of 2 * If)"5, an ambient relative humidity of 70%, and a wind speed and tower exit speed of 4.3 m/s. The tower is 100 m high with a plume rise of 500 m. Source emission parameters are shown in Table 3.1, along with the downwind drift nass and droplet deposition rates. The mineral mass and droplet numbers in each size category were assumed to be con- served and deposited into a sector bounded by impact distances of those droplets whose sizes were at the extreme of each size category. A maxi- mum deposition case was also calculated by Chen,1 where the droplets are emitted from the top of the tower and do not evaporate. Results of these calculations are shown in Table 3.2.
Table 3.1. Estimated salt deposition rates from a ballistic drift model (see Chen1) at ambient relative humidity of 70%
Emitted Final Emitted Salt Droplet droplet Downwind droplet drift deposition deposition diameter distance diameter mass rate rate interval (km) 2 interval 2 (g/s) (yg/hr/dm ) (#/hr/dm ) (Mm) (ym)
600-500 0.6 1.2-2.3 25 360-220 500-400 1.7 2.3-3.4 56 220-170 29 400-300 3.4 3.4-6.5 21 170-110 25 300-200 9.0 6.5-14 12 110-70 37 200-100 6.7 14-32 1.4 70-50 25 100-0 1.1 32-180 <.01 50-0 -v-3
Since the results in Table 3.1 are rather conservative while those of Table 3.2 represent an upper limit, actual deposition patterns from a mechanical-draft tower can be expected to be somewhere between these two cases. It is clear that evaporation is extremely important in pre- dicting drift droplet deposition. 57
Table 3.2. Estimated maximum salt deposition rates from a ballistic trajectory model (see Chen1) with no evaporation and the droplets emitted from the top of the tower
Emitted Emitted Salt Droplet droplet Downwind drift deposition deposition diameter distance mass rate rate (km) interval (g/s) (yg/hr/dm2) (#/hr/dm2) (wm)
600-500 0.6 0.18-0.22 6,900 2,100 500-400 1.7 0.22-0.27 11,000 7,400 400-300 3.4 0.27-0.38 8,300 11,000 300-200 9.0 0.38-0.61 6,900 24,000 200-100 6.7 0.61-1.6 .490 9,000 100-0 1.1 1.6-150 0.01 ^2
From an experimental standpoint, a 1-hr sample with a 1-dm2 receptor area, using the deposition rates of Table -3*1, would be close to the sen- sitivity limit of the various detection methods. For example, a 25-ug sample when diluted with 10 m& of rinse water results in a 2.5 ppm salt concentration. The ion chromatograph is sensitive to 0.5 ppm but operates best in the range 5 to 50 ppm. For droplet size distribution measurements, several hundred droplet stains are necessary for good statistics. Thus an experiment run of 5 to 10 hr would be required to reasonably character- ize drift deposition with the rates given in Table 3.1. On the other hand, only 10 to 20 min would be required for similar accuracy with the rates given in Table 3.2.
3.4 CONCLUSIONS
A drift experiment program to develop a data base which can be used for validation of drift deposition models has been formulated. The first field effort is designed for a suitable mechanical-draft cooling tower to be selected after site visits have been conducted. The discussion here demonstrates the importance of characterizing the droplet size spectrum emitted from the tower and to accurately account for droplet evaporation, because the downwind droplet deposition patterns and near-surface air- borne concentrations are extremely sensitive to these parameters. 58
References
1. N. C. J. Chen, A Review of Cooling Tower Drift Deposition Models, ORNL/TM-5357 (June 1977), 96 pp.
2. G. J. Woffinden, P. R. Harrison, and J. A. Anderson, Airborne l4oni- toring of Cooling Tower Effluents. Vol. 1. Technical Summary-, EPRI EA-420/EPA No. 803969, Meteorology Research Inc. (June 1977), 43 pp.
3. R. 0. Webb, G. 0. Schrecker, and D. A. Guild, Drift from the Chalk Point Natural Draft Brackish Water Cooling Tower: Source Defini- tiony Downwind Measurementsa Transport Modeling, Environmental Systems Corporation (May 1977), 36 pp.
4. J. H. Meyer and W. D. Stanbro, Chalk Point Cooling Terser Project Final Report FY 1977, Vol. 2y Cooling Tower Drift Dye Tracer Experi- ment, June 16 and 173 1977, JHU PPSP-CTCTP-16, Johns Hopkins Uni- versity, Applied Physics Laboratory, Laurel, Md. (August 1977).
5. J. H. Meyer and W. D. Stanbro, "Fluorescent Dye, A Novel Technique to Trace Cooling Tower Drift," presented at 4th Joint Conference on the Sensing of Environmental Pollutants, November 6-11, 1977, New Orleans, La., Johns Hopkins University, Applied Physics Laboratory, Laurel, Md.
6. A. Martin and F. R. Barker, "Some Water Droplet Measurements inside Cooling Towers," Atmos. Environ. 8, 325-36 (1977).
7. H. J. Love, "The Measurement of Precipitation from Water Cooling Towers," Trans. Inst. Chem. Eng. 30, 246 (1952).
8. H. F. Liddel and N. W. Wooten, "The Detection and Measurement of Water Droplets," Quart. J. Roy. Meteorol. Soc. 83, 263-66 (1957).
9. C. Hosier, J. Pena, and R. Pena, "Determination of Salt Deposition Rates from Drift from Evaporative Cooling Towers," Trans. ASME3 Ser. A, J. Eng. Power 96, 283-91 (1974).
10. J. H. Meyer and W. D. Stanbro, Chalk Point Cooling Tower Project Final Report FY 19773 Vol. 2, Salt Loadingt Modeling and Aircraft Hazard Studies, JHU P PSP-CPCTP-16, Johns Hopkins University, Ap- plied Physics Laboratory, Laurel, Md. (August 1977).
11. J. Pena and C. Hosier, "Influence of the Choice of the Plume Dif- fusion Formula on the Salt-Deposition-Rate Calculation," Cooling Tower Environment - 1974, CONF-740303, pp. 573-84 (1975). 12. G. 0. Schrecker, K. R. Wilber, and F. M. Shofner, "Prediction and Measurement of Airborne Particulate Concentrations from Cooling Device Sources and in the Ambient Atmosphere," Cooling Tower En- vironment - 1974, C0NF-74Q303, pp. 455-82 (1975). 59
4. COOLING POND FOG STUDIES
B. B. Hicks*
4.1 INTRODUCTION
During the colder parts of the year, the generation of steam fog above exposed water surfaces is relatively common. For obvious reasons, the situation is considerably more frequent when the water surfaces in question are artificially heated. In the case of cooling ponds, the matter might be much more than a mere curiosity, since at times the fog generated above industrial cooling ponds might give rise to thick stratus from which precipitation might occur. For the purposes of predicting the susceptibility of a given proposed installation to fog-related problems, a number of factors concerning the planned cooling pond need to be de- termined. Clearly, the prevailing meteorological conditions will play a crucial part, but so must the characteristics of the pond itself, es- pecially its surface temperature. Estimated surface temperatures are routinely obtained in the early stages of the planning process, normally as an output of some numerical model. Then these must be coupled with meteorological data obtained in the region of interest in order to de- velop statistics regarding the formation of fog. The present intent is to look into the matter of fog prediction and to test the applicability of the Fog Excess Water Index (FEWI) presented earlier by Hicks.1 A number of field studies have addressed the problem of cooling pond fog generation. Notable among these is the study reported by Currier et al.2 of fog over the Coffeen and Four Corners cooling ponds. Currier et al. suggest the adoption of a Fog Index Number (FIN) defined as (To —
Ta)/(eQ — . This property is found to be a good empirical indicator of fog intensity. However, It has been shown recently that there is some benefit in following the lead of cloud physicists and consider the excess water vapor in air that is thoroughly mixed above the surface under consideration. The average vapor pressure of this mixed air is clearly
Atmospheric Physics Section, Radiological and Environmental Research Division, Argonne National Laboratory, Argonne, 111. 60
(e " + ec l )/2. The mixing process will result in an average temperature
(T„ + Ta)/2- It is hypothesized that fog will occur whenever the average vapor pressure exceeds the saturated vapor pressure at the average tem- perature. These simple considerations led to the definition of the FEWI e as (or the excess vapor pressure, xg)
exs = [es(T0> + ea]/2 - esI(T0 + Ta)/21 '
The present purpose is to examine the practicality of this new fog index and to test it by use of recent field observations. As has already been pointed out (e.g., by Hicks and Shannon3), the data presented in some considerable detail by Currier et al. tend to support the new index rather than the old. Figure 4.1 illustrates this by comparing the ability of the two fog indices to differentiate between conditions of no fog and occasions in which some fog was reported. By selecting a value of about 0.7 mb for the excess water index, the error margin resulting from the Currier et al. data set is less than 8%. This is substantially less than the minimum error margin (about 18%) derived from the appli- cation of the FIN method to the same data.
ORNI—DWG 78-8309
FIN (F/mb)
Fig. 4.1. A comparison of the Fog Index Number and the Fog Excess Water Index as indicators of the formation of steam fog. Data used are those of Currier et al.2 61
4.2 1974 "SIMULATOR" DATA
During 1974 and 1975, a pair of cooling pond simulators was operated at Argonne as part of a study of the efficiency of heat exchange from disturbed water surfaces. These simulators were each of about 10 m2 area and were exposed in natural surroundings in a grassy field. The ponds were constructed of expanded polystyrene foam blocks of about 10 cm thickness so that conductive losses of heat through the sides were mici^lied. Each pond was lined with black polyethylene sheet in an at- tempt to simulate the radiative properties of deeper water and was filled with clean filtered water to a depth of about 10 cm. Electrical heater cables laid along the bottom of each pond generated heat at adjustable rates up to about 5 kW. The data reported here were obtained by the use of one simulator in which a series of sunken perforated pipes allowed air to be ejected in fine streams of bubbles along rows spaced about 20 cm apart. In the case of this particular pond, therefore, the subsurface thermal film that had been a problem in some previous studies was elimi- tated. Figure 4.2 shows that the fog observations made in conjunction with the simulator studies confirm the main points of the earlier arguments. However, it is clear that in this particular case the theoretically based criterion of zero for the excess vapor pressure is far more satisfactory than the empirical value of 0.7 mb derived from the Currier et al. data. This finding tends to support the theory thaL the subsurface thermal film controls this matter. It should be noted, in passing, that there is no evidence of a wind speed effect in Fig. 4.2, as indeed was the case in the earlier investigations of Coffeen and Four Corners data.
4.3 1976 DRESDEN OBSERVATIONS
Also shown in Fig. 4.2 are the results of a number of fog observa- tions made at the Dresden cooling lake (near Morris, 111.) of the Common- wealth Edison Company. The number of data points is quite small; this first winter of the ANL fog-observation program was exceedingly cold and a considerable number of logistic and technical difficulties arose 62
OONl-OWG 1*010 10 •• : | —j 1" 1 1 A A
- / A
E A 1 A A A A Q A & o tiuii 5 o. A A o A A* (« — • • 1 1 1 1 1 -4 -2 0 FEWI (mb) Fig. 4.2. Results of some recent tests of the ability of the Fog Excess Water Index to predict the formation of steam fog above heated water surfaces. Solid symbols indicate occasions in which fog was observed. (q.v. Everett and Zerbe"). The plotted values are derived from water temperatures measured by an immersed thermometer and air temperatures and humidities measured upwind of the fog area by means of a hand-held psychrometer. This limited data set confirms the general picture de- veloped so far, but it is not clear whether the observations support the theoretical 0-mb criterion or the empirical 0.7-mb one. Once again, there is no obvious influence of wind speed. As a caustic test of the excess vapor pressure method, an attempt has been made to relate fog observations made at Dresden to ambient temperature and humidity data reported at the nearest meteorological ob- serving station, some 60 km distant at Argonne National Laboratory. For this purpose, accurate surface temperatures of the cooling pond are critical, and hence it has been necessary to employ data recorded by an automatic system centrally located in the warmest subpond of the Dresden lake. Scrutiny of the data shows that the FEWI provides a good method for ordering the density of observed fog except in the early morning. The reason for difficulties to be encountered immediately following sun- rise is not clear, but it is possible that at these times the tacit i: 63 assumption of horizontal homogeneity over a distance of 60 km is quite wrong. Figure 4.3 illustrates the ability of the present methods to ex- plain fog observations at Dresden in this manner, on the basis of meteoro- logical data obtained at Argonne. Only observations made after 9 AM local time have been included. The data seem to support the use of the 0.7-mb criterion or even a slightly greater value. ORNL DWG 7H 83)1 FEWI (mb) Fig. 4.3. The probability of finding fog, slight fog, or no fog above the Dresden, Illinois, cooling pond, based on meteorological data reported at Argonne. 4.4 STABILITY REGIMES ASSOCIATED WITH COOLING PONDS The development of an improved method for predicting the formation of steam fog above cooling ponds presents only a partial answer to the more general problem of estimating the downwind visibility and riming effects. In the past, a number of attempts to apply the simple Gaussian- plume models favored by air pollution meteorologists have been made. However, a moment's thought will verify that the large instabilities that are characteristic of flow over heated surfaces of any kind will have a major effect on the dispersion of fog. The data set presented by Currier et al. is sufficiently complete that a comparison between micrometeorologi- cal stability parameters and the stability classification scheme common in 64 numerical modeling circles is possible. Table 4.1 lists the average values (and standard errors) of the Obukhov scale lengths L deduced from the tabulated data and sorted according to stability classification. An infinite value of L would indicate neutrality; positive values indicate stability and negative instability. As expected, no stable occasions can be identified. The methods used in deriving L, described elsewhere,5 require that the wind speed be above 1 m/s (since otherwise conditions are either too stable or too unstable to be accommodated by contemporary formulations). Consequently, the most unstable data are omitted from Table 4.1. Nevertheless, it is clear that the association of stability categories C, D, E, and F with most of the occasions is rather misleading, although they are possibly accurate indications of stability regimes sur- rounding the hot water surfaces. To address the net effect of strongly heated surfaces embedded in prevailingly stable (or at least near-neutral) flow requires the use of far more complex modeling methods, such as the second-order closure schemes presented by Yamada.6 Table 4.1. Average values of the Obukhov scale length L corresponding to the Currier et al.2 stability classes0*^ Stability L Number of class (m) values A 0 B -0.29 ± 87% 3 C -0.32 + 21% 18 D -1.27 ± 23% 41 E -0.33 ± 31% 7 F -0.14 ± 14% 11 aCurrier et al. identified these sta- bility classes as appropriate for their Coffeen and Four Corners cooling-pond data. T. Only data associated with reported wind speeds greater than 1 m/s have been analyzed; the remaining occasions are all highly unstable (i.e., L is exceedingly small and negative). 65 No matter what scheme is adopted for investigation of the dispersion of fog emanating from a cooling pond, it is critical that the stability parameter employed take the buoyancy of water vapor into account. It seems grossly illogical to omit this factor when the main aim is to study the dispersion of the water itself. 4.5 CONCLUSIONS The FEWI method of fog prediction has been verified by the use of data obtained at the Dresden cooling pond during 1976 and 1977 and by a reanalysis of observations made in conjunction with a study of cooling pond simulators during 1974. For applications in which the method is applied to measurements or estimates of bulk water temperature, a criti- cal value of about 0.7 mb appears to be most appropriate. The present analyses confirm the earlier finding that wind speed plays little part in determining the susceptibility for fog generation. The extension of the philosophies that enter into the derivation of the FEWI to the case of downwind fog dispersion and riming is a matter that remains to be investigated. Field investigations planned for the coming winter will start to address this problem. 4.6 NOMENCLATURE e ambient vapor pressure (mb) e0 surface vapor pressure (mb) e (T) saturated vapor pressure at temperature T (mb) s e excess vapor pressure (mb) xs - FEWI Fog Excess Water Index (mb) FIN Fog Index Number (°C mb-1) L Obukhov scale length (m) T ambient temperature (°C) a T0 surface temperature (°C) 66 4.7 ACKNOWLEDGMENTS J. D. Shannon, R. G. Everett, and G. A. Zerbe of Argonne National Laboratory made most of the observations reported here. W. P. Pogliano made the visual fog observations at Dresden. References 1. B. B. Hicks, "The Prediction of Fog over Cooling Ponds," J. Air Pollut. Control Assoc. 27, 140-42 (1977). 2. E. L. Currier, J. B. Knox, and T. V. Crawford, "Cooling Pond Steam Fog," J. Air Pollut. Control Assoc. 24, 860-64 (1974). 3. B. B. Hicks and J. D. Shannon, "A New Cooling Pond Fog Index," Argonne National Laboratory Radiological and Environmental Research Division Annual Report, January-December 1976, ANL-76-88, Part IV, pp. 104—107 (1977) . 4. R. G. Everett and G. A. Zerbe, "Winter Field Program at the Dresden Cooling Ponds," Argonne National Laboratory Radiological and Environ- mental Research Division Annual Reports January—December 1976, ANL- 76-88, Part IV, pp. 108-113 (1977). 5. B. B. Hicks, M. L. Wesely, and C. M. Sheih, "A Study of Heat Trans- fer Processes above a Cooling Pond," Water Resources Res., in press (1977). 6. T. Yamada, "A Preliminary Result of a Three-Dimension Numerical Simu- lation of Cloud Formation over a Cooling Pond," Proceedings} 2nd AIAA/ASME Thermophysics and Heat Transfer Conference, Palo Alto, California, May 24-26, 1978. MATHEMATICAL MODELING 69 5. REPORT ON ATDL RESEARCH ON METEOROLOGICAL EFFECTS OF THERMAL ENERGY RELEASES, AUGUST 1, 1976-5EPTEMBER 31, 1S77 S. R. Hanna* K. Shankar Rao* R. P. Hosker* 5.1 INTRODUCTION Several different projects were carried out during this report period. The ATDL plume and cloud growth model, developed in previous years, was applied to new sets of data from four separate sites and to contrived data as part of a sensitivity study. A chapter entitled "Atmospheric Effects of Energy Generation" was written for the book Atmospheric Science and Pouter Production. An experimental program was conducted in which time lapse photographs of cooling tower plumes in Oak Ridge, Tennessee, and Paradise, Kentucky, were taken and analyzed in order to determine the magnitudes of secondary motions. In addition, plume cross sections were drawn and analyzed using raw data from the Chalk Point Cooling Tower Project. The results of all these studies are summarized. 5.2 APPLICATIONS OF ATDL PLUME AND CLOUD GROWTH MODEL The ATDL plume and cloud growth model agrees with Briggs* (1975) plume rise theory near the source and Weinstein's (1970) cloud growth theory at greater heights. It is fully described by Hanna (1976) and has been validated using several sets of cooling tower plume observa- tions. During the past year the model was further applied to data from the John E. Amos plant (year 2), the Chalk Point plant, the Paradise plant, oil refineries in Los Angeles, and several contrived sets of ini- tial and boundary conditions. The contrived data were used in a sensi- t-ity analysis of the model. 5.2.1 John E. Amos Plant The cooling towers at the John E. Amos plant were described by Hanna (1976), who used data from the winter of 1974-1975 as input to the ATDL *Air Resources Atmospheric Turbulence and Diffusion Laboratory, National Oceanic and Atmospheric Administration, Oak Ridge, Tenn. BLANK PAGE 70 model. During the past year data from the winter of 1975—1976 were re- ceived from Mark Kramer of Meteorological Evaluation Services, Inc. The resulting model estimates of plume rise for these cases are compared with observations in Fig. 5.1. The scatter of the data points is similar to that obtained using data from the previous winter. Since the results of this study are nearly identical to those of the previous study at the John E. Amos plant, no further work with the data from the winter of 1975-1976 is planned. Snow was observed in a plume-shaped sector 40 km downwind of the cooling towers on January 18, 1976, by Kramer et al. (1976). The plume and cloud growth model was run for this day using the profiles in Fig. 5.2. Entrainment rates of 0.4 and 0.3 were used for two separate model ornl- dwg 77-19012 2000 JOHN E. AMOS PLUME RISE o 1974-5 r - 0.49 • 1975-6 r = 0.47 1500 E & • / «m ° o • o • VT 500 - •• o XP o 0 0 500 1000 4500 PREDICTED PLUME RISE (m) Fig. 5.1. Observed and predicted cooling tower plume rise for the John E. Amos plant. 71 ORNL-OWG 77-19013 T CK) Fig. 5.2. Dry bulb and wet bulb profiles and modeled and observed cloud depths for the snow case at the John E. Amos plant on January 18, 1976. The modeled cloud is based on an entrainment rate of 0.3. runs; the value 0.4 is valid for most smoke plumes (Briggs, 1975) and had been used in all model runs up to this date, while the value 0.3 has been found by Slawson et al. (1974) to provide a better fit to Paradise cooling tower data. The plume remained just barely below saturation for an entrainment rate of 0.4 and produced a cloud with the dimensions shown in Fig. 5.2 for an entrainment rate of 0.3. Because ice microphysics is so important for this one day and the ATDL model does not include a detailed ice phase, an agreement was made with Dr. R. Koenig of the Rand Corpora- tion that he would run his model, with detailed ice microphysics, for this case. u \\ 72 5.2.2 Los Angeles Oil Refineries NOAA requested us to look into the possibility of weather modifica- tion by oil refineries in Los Angeles. The results of this study are given in Appendix A, which is a paper published in the Proceedings of the 6th AMS Conference on Inadvertent and Planned Weather Modification. 5.2.3 Chalk Point Plant December 1975 test Visible plume observations at the Chalk Point cooling tower for the December 1975 intensive study period were reported by the Environmental Systems Corporation (1976). Atmospheric soundings for these days were given by Meyer et al. (1976). Using these data, the plume and cloud growth model was run in order to estimate the visible plume length. Ob- served and estimated visible plume outlines for four specific experiments are given in Figs. 5.3 to 5.6. The model sometimes overpredicts and some- times underpredicts, although agreement is generally within a factor of 2. ORNL-DWG 77-19044 300 VISIBLE PLUME CHALK POINT OBSERVED N 400 Fig. 5.3* Observed and modeled visible plume outlines for the Chalk Point cooling tower plume on the morning of December 15, 1975. 73 Fig. 5.4. Observed and predicted cooling tower plume rise for the afternoon of December 15, 1975. ORNL-DWG 77-19016 Fig. 5.5. Observed and predicted cooling tower plume rise for the afternoon of December 16, 1975. 74 ORNL-DWG 7T-19017 1200 1 I I VISIBLE PLUME CHALK POINT DECEMBER 17, 1975 OBSERVED 800 FINAL MODEL RISE FINAL OBSERVED RISE MODEL / —^ 400 200 /2 200 400 800 1200 1600 2000 jr(m) Fig. 5.6. Observed and predicted cooling tower plume rise for the afternoon of December 17, 1975. In the case of the December 17 experiment, the observed plume evaporated at about 400 m downwind of the tower but recondensed to form a long visible cloud beginning at a distance of about 1000 m from the tower. The model cloud, on the other hand, evaporated at 400 m but did not recondense. The downwash of the plume is quite significant in Figs. 5.3 to 5.6. No means of accounting for the effect are presently available for the model. However, wind tunnel work at ATDL in the coming year should pro- vide some data for incorporating a parameterization of this phenomenon into the numerical modeling schemes. June 1976 test Data from the June 1976 intensive study period were used to test the sensitivity of the model to slight changes in atmospheric profiles. De- tailed soundings were reported by Meyer et al. (1977) at intervals from 30 min to 2 hr, beginning near sunrise. The model is steady state but in reaiity can be applied to atmospheric soundings which are steady for more thaa about 5 min. This time estimate is made by calculating the time required for a plume rising at a speed of 4 or 5 m/sec to rise 75 through a vertical depth of about 1000 m. The results of the model ap- plication, using an entrainment rate of 0.3 in one set of calculations and a rate of 0.4 in another, for 11 soundings taken on June IS, 1976, are given in Table 5.1. Plume dimensions and liquid water contents are listed in the table, showing the progression from long plumes in the early morning to short plumes in the afternoon. During the afternoon, when atmospheric conditions are expected to be nearly steady, there is a Table 5.1. Predicted plume parameters for a series of environmental profiles at Chalk Point on June 18, 1976 Visible plum' e „Maximu m Plume rise, Time u , , T u . liq. wat., .(., Length "ST Entrainment rate =0.3 604 807 Plume condensed at 2.28 742 1035 all points in 2.36 842 720 model 2.21 930 1350 2.21 1010 422 410 250 2.00 1110 906 200 268 1.98 Reforms at 350 Top 1312 887 125 70 1408 697 156 75 1449 672 148 75 1545 544 182 100 1640 547 177 60 Entrainmen? rate = 0.4 604 445 i-P 2.27 742 684 Top 2.42 842 540 Top 2.23 930 440 Top 2.21 1010 314 200 140 1110 313 160 110 1312 500 84 45 1408 359 109 50 1449 304 114 50 1545 459 150 70 1640 437 126 40 76 variation in predicted visible plume length and plume rise of ±25%. It is found that slight variations in temperature profiles, especially high above the ground, can have great influence on plume rise. Sensitivity test with varying initial plume temperature The question has often come up as to whether accurate measurements of initial plume parameters are necessary. Consequently, the model was run using the December 1975 data but varying the initial plume tempera- ture T by ±5°C. The results are given in Table 5.2, assuming an en- Po trainment rate of 0.3. In the case of a uniform vertical temperature gradient on December 15 (a.m.) and 19, the variations in plume rise are just what one would predict using basic plume rise theory. However, when a strong capping inversion is present, the plume rises to this level and quickly stops, nearly independent of T . Variations in visible plume Po height are nearly the same for all five cases, with an increase of about 70% in visible plume height as T increases by 10°C. Po Table 5.2. Sensitivity test using Chalk Point data for three different initial plume temperatures T , +5°C T -5°C po P»* Run Plume Visible Plume Visible Plume Visible rise height rise height rise height (m) (m) (m) (m) (m) (m) 12/15/75 310 200 270 150 228 120 562 160 557 125 381 85 12/16/75 990 120 980 90 973 65 12/17/75 851 700 810 600 783 450 12/2.9/75 576 220 509 170 418 130 5.2.4 Paradise Plant The type of analysis described above was also applied to data from TVA's Paradise, Kentucky, cooling towers. March 4, 1971, was selected by Slawson et al. (1975) for detailed analysis because of the long per- sistent visible plume which was observed on that day. Temperature and 77 dew point profiles were measured by radiosondes, ana wind profiles were measured by pilot balloons. Table 5.3 summarizes the results .of the model application, using an entrainment rate of 0.3. At midday, plumes were calculated to be highest and longest due to high humidities and a well-mixed boundary layer. For the period 1050 to 1517, calculated plume rise varies by only ±8% from 1110 m because of a persistent isothermal layer capping the well-mixed layer at a height of 800 m. Table 5.3. Predicted plume parameters for a series of environmental profiles at Paradise on March 4, 1971 Visible plume Radiosonde Towers Plume Liq. water time operating rise max. (g/kg) Length Height (m) (m) 0615 1 449 1060 350 2.71 0753 1 524 870 400 2.67 0955 2 766 766+ 766 2.61 1015 2 714 730+ 714 2.53 1050 2 1196 942 1196 2.86 1059 2 1155 895+ 1155 2.84 1504 2 1128 711+ 1128 2.30 1517 2 1026 548+ 1026 2.31 1631 2 558 350 95 1.92 1644 2 498 345 95 1.93 5.2. 5 Sensitivity of Model to Elevated Inversions An environment with constant wind speed (4.45 m/s), surface tempera- ture (20°C), and mixing rat > (7.5 g/kg) was assumed. The lapse rate was assumed adiabatic except for a 2°C inversion over 100 m with its base at Z. In the eight different runs, Z varied from the surface to 700 m. Initial plume conditions are constant (w = 3.4 m/s, R = 24 m, T = u P 33.5°C). The results are given in Table 5.4. When the inversion is at the surface, the plume breaks through and rises through the adiabatic layer aloft. However, when the inversion base is at 100 m or higher, the plume cannot break through. The higher the inversion base, the less the plume AT and the less the penetration of the plume. The results Ik Table 5.4. Model t<-st with adiabatif atmosphere, except for a 2'' inversion over 100 ra, vith base at some nultij.le of ] 00 ~ Inversion Penetration AT at !'lur,< base at in inversion inversion base ri:-,i (m) (m) ("•(.) (nj 700 38 0.08 7 3H 600 Al 0.0'J 641 500 44 0.12 544 400 49 0.16 449 300 55 0.25 355 200 67 0.47 267 100 90 * O ' 1'Ju Surface Breaks H. 50 through roughly conform to Briggs' (1975) prediction that a plume will not pene- trate an elevated inversion if the AT in the plume is less than the tem- perature increase across the inversion. 5.3 SECONDARY MOTIONS IN COOLING TOWER PLUMES A photographic study of cooling tower plumes was made during 1976 and 1977. Photographs of the mechanical-draft cooling tower plume a the Oak Ridge Gaseous Diffusion Plant were analyzed during the summer of 1976, and photographs of the natural-draft cooling tower plumes at TVA's Paradise, Kentucky, steam plant were analyzed during this past summer. The results were combined into the paper attached as Appendix h- 5.4 CHAPTER FOR ATMOSPHERIC SCIENCE AND POWER PRODUCT 10!, The revision to Meteorology — 1968 (D. Slade, ed.) is to be c^jfed Atmospheric Science and Power Production (D. Randerson, ed.). S. devoted about two months during this year to preparing the first of a chapter entitled "Atmospheric. Effects of Energy Generatidh." it has 63 pages of text, 10 tables, 20 figures, and 105 references. Thfe 79 chapter is too bulky to appear as a:i appendix, but *„::>_• i:;li..c is tin- folloving: 1. lnt r >duct i on 1.1 S'- ,r» L characteristics of cool in.' t •v.ri .-> 1.2 S "irct characteristics of cooling pomis 1.3 Source characteristics of .spray pond.s 1.4 River, lake, and ocean cooling 1.5 Heat releases over large areas 2. Fumraarv of current observed effects 2.1 Sun shading 2.2 Ground fog 2.3 Drift deposition 2.4 Interference with aircraft 2.3 interactions with chemical plumes 2.6 High winds 2.7 Changes in cloudiness, temperature, and precipitation 3. Estimating the effects of energy generation at a single large power plant 3.1 Direct cooling by lakes, oceans, and rivers 3.2 Cooling ponds 3.3 Cooling towers 3.3.1 Plume rise 3.3.2 Fog formation 3.3.3 Drift deposition 3.3.4 Visible plume and cloud growth 3.3.5 Interactions of moist plume with S02 plume 3.4 Dry cooling towers 4. Effects of energy generation in mesoscale power parks 4.1 Energy dissipation in urban areas 4.2 Models of the atmospheric effects of power parks 5. Effects of energy generation on a synoptic or global scale Copies of this chapter are available from the author. 5.5 ANALYSIS OF OBSERVED PLUME CROSS SECTIONS AT CHALK POINT Woffinden et al. (1977) report observations of plume parameters made foy dft alre^ft dtitittg the June 1976 field study at the Chalk Point cooling towers. Dozens of plume cross sections were drawn using the raw data in this report. Unfortunately, it was discovered that the only days that could be analyzed were June 22 and 23 because of obvious problems with the temperature instruments on the other days (analysis was limited to data from the- fast-response instruments,). Another instrument problem is that t he Lyirum-'J. inst ru.iient registers erroneous d<-v points far above the plume temperature whenever the plume is saturate/1. This problem may be due to condensation on the instrument or to abnormal scattering by water drops. Our major interest was determining whether the observed plume struc- ture conformed to our idealized models. Is the cross-plume distribution Gaussian or top hat? Do the temperature, humidity, and water drop plume coincide? Do the radius and plume rise increase with downwind distance according to Briggs' prodict ions? Fortunately, the two days available for analysts include both bent-over and vertical plumes. 5.5.1 June 22, 1976: Bent-Over Plume Numerous aircraft passes through the visible plume were made at sev- eral heights at a distance of 150 m downwind of the tower. Traverses 19—27 were averaged to produce the excess temperature AT and excess dew- point ATj cross sections in Figs. 5.7 and 5.B. The positions of the tem- perature and dew-point plume edges nearly coincide on these figures. The little piece of plume on the upper left of the AT^ plume may be the stack plume. Inside the dotted line on Fig. 5.8, erroneous high supersaturation is indicated by the Lyman-a instrument. The shape of the temperature excess distribution in Fig. 5.7 is definitely not top hat (sharp edged). The AT distribution is fairly close to Gaussian in the y direction, as shown by the cut through the plume in Fig. 5.8 at an elevation of 200 m (see Fig. 5.9). The centerline of the plume in these figures is at a height of about 220 m, which is about 100 m above the top of the tower. The observed plume radius is about 70 m, while theory predicts a radius of RQ + 0.4z, or 24 HI + 40 m = 64 m. Thus the observed and predicted radii are in fair . agreement. The average observed temperature excess at this distance dawnwind is about 1.5°C. To calculate the predicted temperature excess, the following initial parameters were obtained from the report by Environmental Systems HI ORNL-DWG 77-19CM8 250 Fig. 5.7. Cross section of temperature excess AT, Chalk Point plume June 22, 1976, 150 m downwind, traverses 19—27. Bent-over plume. Corporation (1977): wQ = 4.6 m/s, Tp o„ = 36.8°C, T , . = 24°C, ambient AT„o = T po. — Ta = 13°C, U = 4 m/s, R = 24 m. o A formula for variation of «if sur^ested by Hanna (1974) is l/2 2 AT/AT0 = [1 + O.4(z/R0)(w0/u) r = [1 + 0.4(100m/24m)(4.6n/s/4m/s) 1/21—] 2 = 1/7.8 . 0*( } o & 200 100 200 200 Tig. r}.H. Cross section of dew-point temperature excess ATj in the Chnlk Point plume June 72, 1976, 150 m downwind, average of traverses 19 27. tent-over plume. ORNL-DWG 7T-W020 100 Fig. 5.9. Temperature excess AT in the Chalk Point plume at height 200 m, downwind distance 150 m, traverses 19—27 on June 22, 1976. 6 3 Therefore, the predicted .'.1 = .M. 'T.S = 1.7°C. The theoretical tempera- ture excess is 20". higher than the observed. A similar comparison for ."_T. cannot be made because of the failure of the Lvman-.i instrument in d the visible portion of the plume. 5- 5•2 June 23, 1976: Vertical Plume To permit construction of cross sections comparable to those in Figs. 5.7 and 5.8, several traverses in the x-y plane should have been made for this vertical plume. However, since the data consist of tra- verses through the middle of the plume at various heights, the data have to be presented in the y-z plots in Figs. 5.10 and 5.11. It must be realized that the bubble appearance of the plume, with vertical wave length of about 70 m, is only an artifact of the manner of presenting the data. This is not an instantaneous cross section, but was constructed from traverses with turnaround times of about 2 min. In those 2 min, air leaving the cooling tower can pass completely through the plume and ar- rive at the plume top. We feel that the instantaneous plume is probably relatively smooth but that the cooling tower does "pump" with a period of about 5 to 10 min. That is, the emissions fluctuate by a factor of 2 over that period due. to some reason which perhaps the site engineers can give. As with the bent-over plume, the boundaries of the AT and AT^ plumes nearly coincide. Also, the distribution of AT is closer to Gaussian than top hat, even very near the mouth of the plume. In Figs. 5.10 and 5.11, the radius bi nearly constant with height. Photographs from June 23 were also analyzed, and it was found that the visible plume radius (see Fig. 5.12) could be simulated by R = R0 + 0.105z. The constant 0.105 is about 30% less than that recommended by Briggs (1975). The average observed temperature excess AT is plotted as a function of height in Fig. 5.13. It is assumed that the average AT equals one- half the maximum AT. The simple formula recommended (Hanna, 1974) for estimating AT in vertical plumes is 2 AT/ATq = (1 + O.15z/R0)~ ORNL-DWG 7 7-19021 y(m) Fig. 5.10. y-z cross section of temperature excess AT in the Chalk Point plume June 23, 1976, traverses 1—12. Vertical plume. 85 ORNL-DWG 77-19022 / (m) Fig. 5.11. y-z cross section of dew-point temperature excess ATd in the Chalk Point cooling tower plume June 23, 1976, traverses 1—12. Ver- tical plume. 86 - Vn'i TT >V,?! 6G ^ 40 o «x or 30 DA5HFD LINE : • 2««n • 0 105 J 20 I i J o 100 200 300 ^•(m) (above tower lop) Fig. 5.12. Plume radius as a function of height based on photograph of visible plume on June 23, 1976, at Chalk Point. Vertical plume. ORHt-DWG IT- 19074 Fig. 5.13. Observed (points) and predicted (line) temperature excess AT in the Chalk Point cooling tower plume on June 23, 1976. Vertical plume. S7 This formula is plotted as the solid line r i . S.M (usinr .'.T; = 1 3°C) and is seen to overestimate the observ.it ions b\ about a !.n tor o: 2 at all heights. The rate of decrease of ,'.T with height is tairiv well simulated. As seen from these figures and ealculations, the Chalk Point data are useful in answering the questions posed earlier. It can be concluded that the cross-plune distributions are better simulated by .1 ('..mssiar than a top-hat curve, the temperature and humidity plumes do coincide, the in- crease of radius and plume rise with distance from the tower conforms reasonably well with theoretical predictions, and the decrease of ,\T with distance can be predicted by simple theories within a factor of 2. 5.6 ANALYSES OF SATELLITE PHOTOGkAPHS OF MOISTURE AND SMOKE PLUMES 5.6.1 Cool mg Towers LANDSAT satellite takes photographs of a given geographical area 185 ka * 185 km, with 60 m resolution, at 9:30 a.m. every 18 days. All photographs of the Keystone, Pennsylvania, and Paradise, Kentucky, areas fr^tn a three-year period were ordered and examined. On only 3 out of about 50 photographs was the plume from the cooling towers visible, and on those dates the plume was very small. The reason for this "failure" is that satellite photographs are available only for clear days. On cloudy or humid days, when long visible plumes are likely, the satellite cannot sse through to the surface. 5.6.2 Dispersion of Smoke Plumes the visible edges of smoke plumes on satellite photographs can be plotted to provide data for use in estimating mesoscale and large-scale dispersion. The reference book by Shor et al. (1976) contains hundreds of LANDSAT photographs, 25 of which include plumes. Sources from smoke •tack* to volcanoes end forest fires are represented. In addition, two photographs of the Northport, New York, power plant plume were available for analyals. A summary of the observed variation of plume width with downwind distance is given in Fig. 5.14, which suggests that plume width 88 Fig. 5.14. Variations of visible plume width with downwind distance observed by satellite for four types of sources. The number of observa- tions that are averaged together for each source type is given in paren- theses. is roughly proportional to distance raised to the 0.70 power for all of the source types. The variation in the scale of the four curves repre- sented in the figure is probably caused by variations in the initial size of the plume. 5.7 A NUMERICAL MODEL OF METEOROLOGICAL EFFECTS OF WASTE HEAT AND MOISTURE RELEASES FROM HYPOTHETICAL POWER PARKS This research is described in Appendix C, which is to be published in the Proceedings of the 2nd AIAA/ASME Theraophysics and Heat Transfer Conference, Palo Alto, May 1978. During the next year, this model will be tested using observations obtained by Argonne National Laboratory at the Dresden, Illinois, cooling ponds. =>9 ;.r: acknowledcm:-::. : s Ka::v ••:" : i-r.putvr i>; i'r.it ii>ns «vrv , .irrii ; :: : •. «• Ni.'i'er. J.ivid Elliott. and Hove 11 Sn.'drr i- . Martin -'ike an.: r'e. ' • itter. Oak Kitii't- Ass Ti.itt-d i v<-r s i t i» ^wnrsi-r tr.iiiH'<". r'r ••; < * > i ! ant: Ii: ti~e-lapsv ; . une photographs. The assistance of Jesse (.oien.m of the leimessee Vallev Authority and Richard Neitubirz of the Chalk Point Cool- ing Tover i'ro jett is great lv appreciated. This research w.-s carried out as part of an agreement among the National Oceanic and Atmospheric Ad- Tt*i r^ i c: r -j f i oo ^ '1 lie I'rivii'^n^nf .l] I'mffict in*) Me n * r f .n t r * Energy (DOE). The work falls under the Meteorological Effects of Thermal Energy Releases Progr.ira of the DOE. References Briggs, G. A., Plume Rise Predictions, Lecturcs on Air> Pollution and Envzwwi,.ntal .'rr-i.'t Aruilycin, Am. Meteorol. Soc., 59-111 (1975). Environmental Systems Corporation, Chalk Point Coolin.j Tower Project Sccisoyvzl Tect Data for ihi Period December 15—19, 1975, Report No. PPSP-CPCTP-8, prepared by ESC, Knoxville, TN, for the Maryland Power Plant Siting Program, 157 pp. (1976). Environmental Systems Corporation, Chalk Point Cooling Tower Project Final Report for the Period 1 October 1975—SO June 1976 (2 volumes), Report No. PI,SP-CPCTP-12, by ESC, Knoxville, TN (1977). Hanna, S. R., "Meteorological Effects of the Mechanical Draft Cooling Towers of the Oak Ridge Gaseous Diffusion Plant," Cooling Tower En- vironment — 1974, ERDA Symposium Series, C0NF-740302, NTIS, U.S. Dept. of Comm., Springfield, VA 22161, '.91-306 (1974). Hanna, S. R., "A Comparison of Observed -d Predicted Cooling Tower Plume Rise and Visible Plume Length," Atmos. 3ivir Shor, N. M., et al., Mission to Earth: LANDSAT Views the World. NASA, Washington, D.C. , NASA SP 360 (1976). Slawson, P. R., J. H. Coleman, and J. P. Blackwell, Natural Draft Cooling Tower Plume Behavior at Paradise Steam Plant (Part I). Report No. E- AQ-76-1, TVA, Chattanooga, TN (1975). Slawson, P. R., J- H. Coleman, and J. W. Frey, "Some Observations on Cool- ing Tower Plume Behavior at the Paradise Steam Plant," Cooling Tower En- vironment - 1974, ERDA Symposium Series, CONF-740302, NTIS, U.S. Dept. of Comm., Springfield, VA 22161, 147-60 (1974). Weinstein, A. I., "A Numerical Model of Cumulus Dynamics and Microphysics," J. Atmos. Sci. 27, 246-55 (1970). /! Woffinden, G. J., P. R. Harrison, and J. A. Anderson, Cooling Tower Plume Survey, 4 volumes, Report PPSP-CPCTP-15 by Meteorol. Res., Inc., Altadena, CA (1977). 91 Appendix A MODEL PREDICTIONS AND OBSERVATIONS OF CLOUDS FORMED BY OIL REFINERIES IN LOS ANGELES* Steven R. Hanna' 1. BACKGROUND 2. OBSERVATIONS IS LOS ANGELES Inadvertanc weather modification by large The main subject of this report is cloud power planes and Induscries is familiar Co many formation over oil refineries in the Los Angeles people who live -within a few kilometers of basin. Figure 1 Is taken from Xoenxg (1976), who chess facilities. Under conditions when she tabulated the refinery capacities and heat outputs capability of Che atmosphere to absorb excess in Los Angelas. He suggests the relations 10° water vapcr is low, cumulus or stratocusulus barrels/day 5 7S0 MU, and sensible heat/latent clouds aany kilometers long can form. These heat = 1.8. The total heat output due to refineries clouds are often noc noticed because they in the basin Is 7300 IW. 3oth Koenig (1976) and. usually occur in association with natural clouds. Stinson and 3pown (1976) photographed clouds formed by the heat and moisture releases from the oil During Che past few years, as our environ- refineries. Koenig (1976) points out that It is mental avarenesa has grown and as cooling towers often difficult to isolate the cloud changes due are increasingly used, meteorologists have begun to the refineries from the cloud changes due to Co study and report these clouds in meteorological the Palos Verdes Hills or the sea breeze conver- journals and reports. One of the earliest reports gence. Stinson and Brown (1976) photographed was by Culkowskl (1961), uho observed a light refinery clouds for more than a year and concluded snowfall which fell from a cloud forsed by that there la "a direct connection between emissions froa the 2000 HU cooling cowers at che refinery sources and clouds on a variety of Caseous Diffusion Plant in Oak Ridge, Tennessee. scales froa small cumulus Co 3iant thunderstorms." In another study at chls same site. Hanna (1974) They also say that "Two cases of hail and strong concluded that clouds formed over che cooling winds, though associated with natural orographic cowers 30Z of the time. A striking collection clouds, ware apparently affected by refinery of color photographs o£ clouds forned by cooling clouds." Photographs of clouds formed by four towers at the 2900 JlUe John E. ADOS power plant refinery complexes on six different days are near Charleston, Vest Virginia, was published by given in their report. On all of these days, Smith et al. (1974). A 2 inch snowfall occuring there was much natural cloudiness. The clouds In a strip about 5 la wide and at a distance 5 from the refineries, however, usually farmed to SO ka downwind of ,this power plant was observed slightly below the main cloud deck. jj by Kramer et al. (1976). Subsequently Ott (1976), of the nearby Charleston Weather Service office, reported 6" snowfalls downwind of the Arras plane 3. PLUME AND CLOUD GROWTH MODEL on two occasions during the winter of 1975-1976. The snow producing stratocumulus clouds typically The model to be used, which is thoroughly formed in a cold (~10*C) well-mixed layer capped described elsewhere (Hanna (19/6b)), is sceady- by an Inversion. ^ scate with variables a function only of height. It conforms to Briggs' (1975) plume rise theory at Auer (1976) used a cloud physics research low heights, where the cooling tower plume aircraft to observe a cumulus cloud forming over behaves essentially like a dry buoyant plume, and the 800 Mtf plume from the Vood River refinery Co Uelnsceln's (1970) cloud model at greater near St. Louis. The energy release Is split heights, after cloud development processes dominate between sensible and latent heat. Vertical speeds pluae dynamics. It has been tested against plume in the cloud were 4 m/s and liquid water content and cloud observations at several industries and was about .6 g/kg. This cloud was the first one power plants (e.g., Kanna, (1976a and b)). developing on a day chat was narked by thunder- Visible plume length, final plume rise, maximum storms In the lace afternoon. The cloud base and vertical speed, excess temperaturecand water vapor, top heights, vertical speeds, and excess temperature and liquid water content are tha parameters that and moisture in the Uood River cloud were satis- are used Eor model validation. ?rcm previous factorily simulated by Hanna (1976a) using a one- tests it has been concluded that the physical dlaenslonal pluae and cloud model. Wolf et al. characteristics of clouds fanned Inadvertantly (1976) and Thomson et al. (1976) have also flown by man's activities are similar to che physical aircraft through cooling tower plumes and report characteristics of natural clouds, which provides liquid water contents in the same range as those the required basis for the cloud physics found in natural clouds (.1-1 3/kg). parameterization. ; . *Reprinted from Preprint Volume: Sixth Conference on Inadvertent andJPlanned Weather Modification, Oct. 10—13, 1977; Champaign-Urbana, 11. Published bv die American Meteorological Society, Boston, Mass. t •>/ Air Resources Atmospheric Turbulence and Diffusion Laboratory, National Oceanic and Atmospheric Ad- ministration, Oak Ridge, Tennessee. 92 L • Uaiday - Tha^flj . UR .fcfacfcltlUA fttnf-F'M ScK O ~ Oouglu P • rawfrw T - TAMO 75 < SOC • SIMM CM 0< C«1.I NO K M - MOM 130 K S - SM M < a - GuH si < 'ALOS VtnOtS U - UMM MM Ct - bun tw >1 < tmraum A - Ml CO IBS * E* Eis^fiftoA W K * - Flmw 19 « C - Owntfin 31 f. A • Oamtnquu Hilli » Fig. 1. Locations of petroleum refineries in the Los Angeles basin. The unit K represents thousands of barrels per day. This figure is taken from Koenlg (1976). 4. INPUT FOR .MODEL Tabla 1 The Initial. radius and vertical speed of Initial pluaw data for four refineries In the plunas from the Los Angeles oil refineries Los Angeles; tr« assumed to be 250 a and 1 a/a, respectively. Thasa values vara used successfully Is the Wood Refinery Energy Loss aivar refinery analysis (Hnima, 1976a). Sensitivity AT(*C) Aq 5. MODEL RESULTS for environmental air, and the cloud base in the plane is close Co the natural cloud base. The node! was run for tvo different: entrainaenc races, a 2 3R/3z, that have been The only evidence of rapid canvectiv» clau/d proposed for bant-over pluses. The value of .4 developaeot in che aodel results is for refinery vaa suggested by Brlgga (1975) after aa analysis 3 on 17 April, 1975. For this case che piuae of hundreds of stack pluses, and che value of broke into a conditionally unscable layer of air .3 vas suggested by Slavaon et al. (1974) based at heights between about 1000 and ;000 3 and on their studies of cooling tower plumes at TVA's achieved a plus* rise of 2240 a, "hich is =ora Paradise, Kentucky, steaa plant. For the 28 runs than twice chat of the pluice froa refinury 1. (4 refineries x 7 days) In Los Angeles, the value a - yielded a cloud on 17 runs, and 6. CONCLUSIONS U the value a - .3 yielded a cloud on 22 runs. Average final pluaa rises for the entrainaent Photographs on seven occasions indicate rates .4 and .3 vere 910 a and 1090 a, respec- cloud developocnt over Los Angeles oil refineries. tively. For the purposes of this study, the The pluae and cloud growth model successfully results using an enrrainnent rate of .3 vill be simulated these clouds In about S0Z of these analyzed, since this value was derived using cases. In all of che model predictions, the data from cooling covers. cloud is equivalent in physical characteristics to saall to medium size natural clouds. Of Predicted values of ruaTlnmm vertical speed course it is possible in che real vorld for the c H.„, aaxiaua liquid vater content, Qaax* *oud heat Input froti oil refineries to trigger natural base, and final pluae rise (also cloud top if clouds or to interact wich topography or the liquid vacer is present) for Che 29 runs are Seabreeze co create large store clouds; but the Listed in Table 2. staple ooa-disensioaal aodel used In this work cannot creac chese effects. Furthermore, H enrralnsent processes are aore complicated In Table '2 large developing clouds than the simple a - .3 assumption used here. Model predictions for Los Angeles refinery clouds The Los Angeles refinery clouds are no mn Pluae Cloud Qmax "max spectacular, either in photographs or in coaputer Date Refinery Rise(a) Base(a) (g/kg) (o/s) model output, Chan similar clouds photographed and aodeled over power plants and industries in other parts of the country. The conclusions of 2/05/75 1 1300 250 .82 4.2 other investigators that the Lea Angeles refineries 2 1150 200 .65 3.0 cause unusually severe phenooena such as hail 3 1360 350 .33 4.9 should be very carefully studied by aeans of 4 320 200 .58 2.9 comprehensive field programs. 4/16/75 1 1920 950 .94 5.2 .80 , 2 1710 950 , 4.0 Acknowledgements: L. R. Koenig of the Sand 1.05 5.9 3 2070 950 Corporation provided much Information regarding 4 .77 1690 950 3.9 the oil refineries in Los Angeles. Moac of the .49 4.4 4/17/75 1 1060 550 coaputer operations were handled by Lee Hipper 2 660 500 .19 3.2 of this laboratory. This research vas performed 3 2240 550 .95 5.0 under an agreement between che Macional Oceanic 4 ; .14 3.0 610 - 500 and Acnospheric Administration and Che Energy 10/27/75 1 410 350 .07 3.5 Research and Development Adainistracion. 2 300 230 .04 2.5 450 350 .07 4.0 3 REFERENCES 4 280 270 .01 2.4 2/05/76 1 2100 850 1.23 3.9 Auer, A. H-, Jr., 1976: Observations of an no cloud 2.6 2 750 industrial cumulus. J. Aopl. Heteorol.. 3 2180 NN. 850 1.27 4.7 15, 406-413. ^ 4 ^ 660 "no cloud 2.5 3/03/76 1 X10B0 1050 .04 3.0 Briggs, G. A.. 1975: Plum rise predictions. 2 950 no cloud 2.2 •Preprints, Lectures on Air Pollution and 1160\\ 1050 .12 3.5 3 Environmental Impact Analysis. Aast. 4 690 cloud * Meteor. Soc., 59-111. */U/76 1 770 Xo50 .23 3.7 •j 2 2.7 570 no-cloud Culkowskl, U. M., 1961: An anomalous snow ac / 3 910 650 .43 4.2 Oak Ridg;, Tennessee. Men. ,»ea. Rev.. 90 4 540 no cloud 2.6 /r (5), 194-196. Fletcher, X. H., 1962: The Physics of Rainclouds. Cambridge Univ. Press, London. The aaxiaus liquid uates content is 1.27 g/kg; Uanna, S. R., 1974: Meteorological effects the maximum vertical speed is S.9 a/a; and the , of che mechanical draft cooling cowers of pluae rise or cloud tap is 2240 a. These " the Oak Ridge Gaseous Diffusion Plant, values are all within che range of small co sedium Cooling Tower Environaenc-1974. ERDA . size natural clouds (Fletcher, 1962). In che si* Symposium Series, COSF-74032,.. Sac. Tech. runs chat produced no cloud, the pluses scopped Inf. Service, O.S. Dept. of Cotmarce, rising before the lifting condensation level vas Springfield, VA 22161. 291-30S. reached. Since the entrainaent rate Is so great, ' by che time the pluae reaches a height of about Henna, S. R., 1976a;, Consents on "Observations 500 o it consists aostly of entrained environmental of an industrial cumulus." J. Appl. , air. Consequently the pluaa acts as a lifting agent Meteor.. 15, 1232-1233. ~yi)' c 94 Hanna, S. R., 1976b: Predicted and observed Smith, M. E., H. L. Kramer, D. Seymour and T. ?. cooling cower plume rise and pluae length rrankenberg, 1974: Cooling Towers lad the ac the John E. Amos pover plant. Atmos. Environment, available from American Environ.. 10. 1043-1052. Electric Power Service Corporation, 2 3roadway, Sew "fork.. SI 10004, 9 pp. Koealg, L. 1976: Analogs for Vasts Heac Dissipation Effect*, In Atmospheric Effects SClnson, J. R. and C. D. 3rown, 1976: Inadvertant of Nuclear Energy Centers (AENEC) Program. Cloud Formation and Modification by Annual Tech. Prog. Report for July 1975 - Refineries and Power plants, Report SP.A September 1976. A. A. Patriae* and H. 'J. 76-01, Stlason Research Associates, Mo. 1 Hoffman, eds., nRKL/TM-5778, Oait. Ridge Third Place, Suite 603,- Long 3each, CA Na Clonal Laboratory, Oak Ridge, TM 37830, 90302. 14 pp. 84-115. Thomson, D. W.. J. M. Soman, and R. L. Miller, Kramer, M. L., 0. E. Seymour, M. E. Smith, R. V. 1976: Airborne measurements of turbulent Raeves, and T. T. Frankenburg, 1976: temperature and velocity fluctuations ia Snowfall observations from natural draft cooling tower plumes. Proceedings, Third cooling tower plumes. Science, 193. Syap. on Atoos. Turb., Diffusion, and Air 1239-1241. j Duality, Raleigh, SC. by' Acer. Meteorol. Soc.. 45 3eacon St., Boston. *!A, 576-580 Ott, P. 1976: Locally Heavy Snow Downwind (Oct. 19-22, 1976). . iron Cooling Towers. NOAA Tech. Meao. NWS T&-6Z, 'leather Service forecast Office, Velnsteln, A. I., 1970: A numerical model of Charleston, 8 pp. cumulus dynamics and olcrophyaics. J. Atmos. Sci.. 27, 246-255^ Slaws on, P. R., J. H. Coleman, and J. "J. Frey. 1974: Some observations on cooling tower •JOlf, M. A., 1976: Natural drift Pooling tower plume bahavlor ac the Paradise steam plant. plume characteristics determined with Cooling Tower Envlronmenc-1974, ERDA Symp. airborne instrumentation, ?3C. .Northwest Lab. Series CONF-740302, Hat. Teen. Inf. Service, Annual Rep. :or 1975 to the USERDA 03ER. U.S. Depc. of Commerce, Sorlngfield, VA Part 3 Atmospheric Sciences. B5WI-2000 PT3: 22161, 147-160. 281-238. ' d/"N i o • ^ "V ry 95 Appendix B SECONDARY MOTIONS IN COOLING TOWER PLUMES A I 2 Steven R. Hanna, Martin Pike , and Keith Seitter Air Resources Atmospheric Turbulence and Diffusion Laboratory Oak Ridge, Tennessee O Abstract Tine—lapse photography was used to estimate the speed of the secondary motions in the condensed plumes from a hyperbolic natural draft cooling tower and a bank of mechanical draft cooling towers. At a distance of about 30 m from the towers, the median tangential speed is about 2.5 n/s in the downward direction, for ambient wind speeds of 7 to 13 m/s. 1. Introduction <.< /y Drift deposition, that is deposition on the surface bf large, mechanically generated droplets, is a major environmental effect of cooling towers. Current models of the transport of drift v) droplets in plumes do not account for the'influence of turbulence or secondary^motions in the plume (see Cooling Tower Environment - 1974), As suggested by Chen and Hanna (1977), it is possible that the centrifugal forces exerted on the drops by secondary motioas, as in a strongly bifurcated ordownwashed plume, may be sufficient to eject the drops from the plume. The secondary motions are also of interest for'understanding the internal dynamics of .'^Oak Ridge Associated Universities summer trainee from Union "College, Schenectady, New York. ,2 , - o Oak Ridge Associated Universities summer trainee from The Pennsylvania State University, University Park, Pennsylvania. o 96 buoyant plumes. Since there have been no reported measurements of the magnitude of these secondary motions, an experimental program was carried out at sites where typical mechanical draft and hyperbolic natural draft cooling towers were in operation. 2. The Experiments .11 2.1 Mechanical Draft Cooling- Towers Three bank•b*.s of mechanical draft cooling towers dissipate about 1000 to 2000 MW of waste heat at the Oak Ridge Gaseous Diffusion Plant. Hanna (1974) reported a series of drift deposition and fog experiments that were performed at these towers. Because of u their bluff shape and their orientation perpendicular to the dominant wind direction, these towers are plagued by dovnwash about a third of the time. During moderate to high crosswinds, a ° strong secondary vortex forms in the plume near the edge of the towers, as diagrammed in Figure 1. On three days during the winter 1975-1976 it was possible to obtain gooa photographs of the visible plume from these towers, ft when puffs of condensed plume easily could be followed through the trajectories associated with the secondary motions. A. 16 mm movie (i camera with a one-second time lapse was set up perpendicular to the o plume at a distance of about 400 m. The sequence taken on 30 January / u 1976 was chosen for detailed analysis. West winds of. abut 7 m/s occurred and the ambient air temperature was 5°C. ^^ Natural Draft Cooling Towers if '"On 6 April 1977, time-lapse photographs were taken of the - ' " aft natural-draft cooling towers at the Paradise Power Plant, 97 ORNL-DWG 78-8386 WIND it VVj , . ^ V Fig. 1. Secondary motions in ORGDPxbooling tower plume. /J Paradise, Kentucky. Cooling tower no.c3 was photographed because it was the upwind tower on this day and was therefore less likely to have its plume influenced by turbulence caused by the other ^ * Ci two towers. Figure 2 contains a schematic drawing of the cooling o - ° ° = „ \\ tower >\an d the typical secondary motions in the plume. Three sequences of l/2-second "tiae-lapse>photographs (930, 1000, and 1020 CST) .were made with a 35-nm time-lapse camera designed to use bulk roll jp; » ' 0 » film, allowing about 250 consecutive pictures for each run. Two more runs (1035 and 1105 CST) were made, using>the same 35-inm camera, in which only 35 time—lapse pictures were obtained for each .run. J Cj The camera was located perpendicular to the plume at a distance of about 400 m. 98 ORNL-DWG 78-8387 / / / / / / / / Fig. 2. Secondary motions in Paradise cooling tower plume. The average temperature during the runs was about 4.5°C and the dewpoint was about \r3 C. The average .wind speed was about 13 m/s The generating'load on cooling tower no. 3 at this time was 855 MWe. \s Analysis 6 Successive pictures were projected onto a gridded screen and *c the trajectories of individual puffs of condensed plume were plotted. The trajectories near the middle of the plume were % to "CT o considered the iaost important since they could best give the magnitude of the mention and were leas tyaf fee ted by geometric O - corrections and projection error. Puffs were tracked in the region of the plume between 20 m and 110 m downwind of the tower. 99 \ * V; The plume centerline was found by plotting the position of the plume edges over a period when the plume angle remained relatively constant (generally about 30 seconds). The best-fit line between the plume edges was then determined and taken as the plume centerline, and the centerline angle, a, was found. Vectors were inferred from the trajectories,, and horizontal- vertical components were obtained in the cartesian coordinate (*„ systea determined by the gridded screen. However, since the plump angle was variable, the components of the resulting vectors were V- converta.1 to a coordinate system based on the olume centerline. _ * Jr The known' cooling towelvradius was -used as a length scale, /o permitting the magnitude of"the trajectory components to be converted into speeds by dividing by the time « increment. 4. Results /) " * -4.1 Mechanical Draft Towers • , ' & ' 1 The trajectories of 35 plume segments were analyzed and ' a 92 individual estimates of tangential speed were made. The calculated vertical speed of the plume's axis ranges from .0 to 2. m/s, with a O II a median of .20 m/s. An example of "a,puff trajectory is given in Figure 3. The tangential speed of,the secondary motions, relative to the plume's axis, ranges from -15 m/s to +4 m/s, with a median of-5-2 m/s. The minus sign indicates downward motion. ^Figure 4 " O O containsothe frequency distribution of the tangential speeds, O * o showing that two thirds of the observations are within about' VN 0 0 1.8 m/s of the median. It is expected that this»distribution ' ' ''- ' • \ would approach a Gaussian form if the number and accuracy of the ' f? ~' ' <•7 ->< • ' observations were to increase. " ' „ .•> , r 100 ORNL-DWG 78-8388 9 Fig. 3. The trajectory of puff 2, with positions plotted each second. W o o 4.2 Natural Draft Tower (Hi Vr « A total of 293 trajectories of plume segments were plotted and <1534 vectors were resolved. The frequency distribution of the t * ^ " - velocity components perpendicular to the plume axis is shown as .fi'gure 5.; The distribution appears to be nearly Gaussian, vith o, a mean of -2.6 m/s and °a range from -9.1 m/v s to +1.6 m/s. The o ' • ' " a„ o standard deviation of the distribution is the same (1.8 m/s) as Ir* O the standard deviation ofo the velocity components measured at the n .--mechanica* l draft tower. 5 b o 101 5. Implications for Drift Drops The(ratio, A, of centrifugal to gravitational force for a drop near the edge of a plume is: A - CV2/R)/g , (1) Our experiments suggest that the tangential speed, V, is about 2 m/s. Therefore the ratic>A equals .02 for a radius ofv20 m, implying that centrifugal forces are not very important for the average tangential soeed. However, Figures 4 and 5 show that -I ' ^ '' - Cj 4 m/s. In this case the ratic A equals .08 and (the centrifugal force is marginally important. Occasionally tangential speeds V> * ' _ ° ° " o " 9 of 10 to 15 m/s were 'observed, for which the centrifugal force is nearly equal to the gravitational force. ' , ,, i\ <• " ^ ' " % ' . c^ ' \\ The strength of the secondary vortex is probably related to « the wind speed. Although these experiments were limited to moderate • - ' " " * \' ""' 1 - wind speeds, it is''expected that the vortex would not exist in calm, winds, would reach maximum intensity., during .moderate winds, « " and' would be broken up by very high winds. o a „ ; ° J •0 ,, <> ° , uit CI' ,, • V ' c „-9 • Or D „ ^C0 'J - " - V' ' <" ° ,<•„ , ^ 6. Acknowledgements Q c u -„ ' a ' •'' , ° ,o - j , ^ , 4 c "" ci 4- ' ' to <> , -> a - - vt O The cameras at Paradise, Kentucky,, were operated by Rayford P. Hosker,1 of this laboratory. We are grataful'co Jesse Coleman " .• • d '.• c' a « , ,-i .. - 'v " ° and Robert Rubendall of the Tennessee Valley"Authority for 0 their ^ ~ -• » -P . r, " ' - ' •> » - > rj o ' 'a , vcooperatio i-> nn during, the experimentrS s" a-t Paradise' ... = •. °ra ^ c h or ORNL-DWG 77-20064 or ZD 15 (J u o Q LLJ LL) Q_ CO 10 LU > O < CO H Lu) O ONE CASE AT-13 m/s iL 1 o AND ANOTHER I z cr AT-15 m/s UJ 2 M. CD w Ws Vst/XWA mmm M'M 3 0 lilt mm -9.1 -6.0 = -3.0 0 3.0 TANGENTIAL SPEED (m/s) Fig..4. Frequency distribution of tangential speeds at^the Oak Ridge Gaseous Diffusion Plant. " c ORNL-DWG 77-20065 -5 -4 -3 -2 -1 TANGENTIAL SPEED (m/s) Hi Fig. 5. Frequency distribution of tangential speeds at the Paradise Steam Plant. . . j. 104 References Chen, H. C. and S. R. Hanna, 1977: Drift-Modeling and Monitoring comparisons, Proceedings, Cooling Tower Institute 1977 Winter Meeting, Houston, Texas, available from Oak Ridge National Lab., Oak Ridge, TN, 37330, 30 pp. Cooling Tower Environment - 1974, ERDA Syraposiuia Series CONF-740302, Nat. Tech. Inf. Service, U.S. Dept. of Conmerce, Springfield, VA, 22161, 633 pp. Hanna, S. R., 1974: Meteorological Effects of the JIEchanical- Draft Cooling Towers of the Oak Ridge Gaseous Diffusion Plant, loc. cit., 291-306. 105 Appendix C A NUMERICAL STUDY OF METEOROLOGICAL EFFECTS OF WASTE HEAT AND MOISTURE RELEASES FROM HYPOTHETICAL POWER PARKS K. S. RAO and R. P. HOSKER Atmospheric Turbulence and Diffusion Laboratory National Oceanic and Atmospheric Administration Oak Ridge, Tennessee 37830 ABSTRACT A two-dimensional nonprecipitating shallow cloud model has been developed for the Meteorological Effects of Thermal Energy Releases (METER) program'. This second-order-closure turbulence model utilizes a full set of"equations for mean wind velocities, potential temperature, specific humidity, and liquid water content, as well as equations for the corresponding turbulent fluxes which are closed approximately. f. Vapor-liquid water phase changes are included in tens of saturation adjustments. The hypothetical power park was treated as an area source with idealized distributions of waste heat and water vapor fluxes from several cooling towers. These fluxes were directly input as additional boundary conditions to che model. Numerical experiments were performed for a 10,000 Mwe power park in a convective atmosphere with variable surface relative humidity.- Mean wind direction, was allowed to vary with respect to the cooling tower alignment. The total waste heat flux over the power park area was also arbitrarily varied. The model provides information on CUEMIUS cloud formation due to power parks. Results presented include typical vertical profiles of mean potential temperature, specific homidity, and liquid water in the atmosphere, as well as perturbatic is in,, the surface temperature and humidity due to the power park. Some areas,for future research and modeling are outlined. 1. INTRODUCTION 0 Inadvertent weather modification due to the dissipation of waste // energy from large (10,000 to 50,000 Mwe) power parks is a topic of •• 1} current research interest, though such large power parks are still 106 only in the conceptual stage. Hanna and Gifford (1975) discussed possible meteorological effects of the power parks and recommended, among other things, the development of mathematical models of cloud growth due to large, continuous, latent and sensible heat plumes from multiple fixed sources, and of their interactions with the environment. Hanna (1976) and Lee (1976) developed steady-state one-dimensional models of wet cooling tower plumes and the growth of induced connective clouds. Hanna's model has been tested against plume and cloud observations at several industrial and power plant sites (see Hanna, 1976, 1977). Trepp (1975), 3humralkar (1976), and Wolf et al. (1977) applied time-dependent too-dimensional deep convection models to cooling tower plumes from power parks. In their models, the nonresolvable subgrid-scale turbulent fluxes were parameterized in terms of eddy diffusion coefficients (see, e.g., Lilly, 1962), and the waste heat from the power park was introduced into the model in the form of perturbations in the mean potential temperature and specific humidity. The formation of clouds by effluents from cooling towers in a typically convective atmosphere characterized by high relative humidities is well-documented experimentally (Smith tit al., 1974; Hanna, 1974). These clouds are often not noticed since they usually occur in association wi£li .natural clouds. In addition to cumulus cloud formation and reduction of visibility, meteorologists are interested in the increase of average„temperature and humidity of the atmosphere, loss of sunshine due to increased cloud cover, modification of the^r ,A surface energy balance, arid the'resulting climatic changes due to the power parks (see, e.g., Moore,0 3;y76). To obtain such information n 107 for as-yet hypothetical power production centers, one must model the modification of the convective atmosphere due to the expected large waste heat and vapor emissions. Further, it is desirable to input the known sensible and latent heat fluxes from the power park directly into the model rather than to rely on estimated perturbations of temperature and humidity. This paper presents preliminary results of a numerical study, basedvon a higher-order turbulence closure theory, of the meteorological effects of waste heat and aoisture releases from a hypothetical 10,000 !-fwe power park. Through higher-order closure models, one hopes to obtain a better representation of the turbulence in moist convection than is possible with eddy diffusivity approximations. This 'j should lead to more accurate mean field predictions, ana to so-far unavailable information on the behavior of the turbulence field. Thus, in addition to cumulus cloud formation due to the power park, the model predicts the modification of the vertical,profiles of mean potential temperature, specific humidity and liquid water in the atmosphere,, as well as the turbulent flux distributions. 2. THE MODEL 2.1 EQUATIONS The analysis holds when the time-averaged motion of the turbulent flow is steady. We assume the power park is operating at a constant load factor and can be represented as a continuous source emitting waste heat and vapor fluxes independent of time. "The incompressible flow consists of a mixture of two perfect gases, dry air and water vapor, with liquid water droplets in J c? 108 suspension. Incompressibility is a good approximation for shallow convection problems where the pressure perturbations are usually ' t small compared to the reference-state pressure (Button and Finhtl, 1969). For simplicity, we assume the flow is in geostrophic balance with the synoptic flow. Neglecting the molecular contributions to the fluxes, and the horizontal variation of turbulent fluxes compared to the vertical variation, the mean * field equations for a steady two-dimensional flow, within Boussinesq approximations, are U(3U/3x) + i;(3U/3z) = -(3uw/3z) + A' (V-V g) U(3V/3x) + W(3V/3z) = -(3w/3z) + a' (U -U) & (3U/3x)'^ + (3W/3z) =0 (1) i I 'i U(30/3x) + V(3S/3z) = -(3«w/3z) + (3G/3t) c U(3Qv/3z) + V7(3Qv/3z) = -(3^qv/3z)-(3Qv/3t)c 0 U(3Q2/3Z) + W(3Qa/3z) = -(3wqa/3z) + (3Q£/3t)c x X re resent the Here,the-'coordinates x, y, z or x^ 2» 3 P along- wind, cross-wind, and vertical directions, respectively; (U, V, w) or OJj^, U2» is the mean wind velocity vector, 0 is the mean potential temperature, Q^ is the mean specific humidity and Q^ is the mean specific liquid water content. The corresponding o fluctuating quantities are denoted by (u, v, w) or (u^j- u2» u.j) » 3, qv and q^ respectively; & = 2ft sin $ is the Coriolis parameter, where fl is the .earth's rotation rate,and $ is the latitude (taken as 45"N). The terms (30/dt^, (3Qv/3t)c and (SQ^/St^ 109 are saturation adjustments, to be described later on, representing the rate of change of 3, Q^ and Q^ due to condensation (or evaporation); U and V are geostrophic wind components defined by 8 § i, ( > > U = -(l/a')(3P/3y) , V = (1/a') (S?/3x) , 3 o where P is the mean kinematic pressure. We do not perait precipitation of liquid water droplets, thus conserving total moisture content while allowing for changes of state due to condensation and evaporation. This assumption is justified sinc2 precipitation is not significant when liquid water concent (LWC) is less than about 1 g kg ^ (Takeca, 1966). Thus o all the liquid water is assumed to exist as suspended cloud droplets. (' The transport equations for the turbulent fluxes of momentum, heat, water vapor and LWC are written as V; U. (u.u, ) , . + u.u, U. . + u.u.u, .-(g//v0 ) (u, e 5_. + U.9 o,, ) j x K 'j j fe X,J j i k,j o IT V 3x 1 ty 3k n + 2n(e..n n. u n + e, .. n. u.u.) = ijZ j ZTx. kj2 j I i -(5iV? 'j + V^P"25 5ik/3 (2) V U^fu^,. + fu.U.^ ^VjF,j-(8/Vf9v53i + 2fl Eijk fUk o- -(fu^J^-fp^ u .. (3) where differentiation is indicated by a comma, and repeated indices indicate summation; i" is mean viscous dissipation rate of turbulent ft J 1 kinetic energy (E = 1/2 uTuT) , p is fluctuating., kinematic pressure, 9 = 9 + 0.61Q q ~0 q^ is fluctuating virtual potential temperature, q v o o 110 3q is the mean reference potential temperature, is the unit vector along the earth's rotation, axis, and g is the acceleration due to gravity. In Eq. (3) , F = 3 and f = S for heat flux equation, F = Q^ and f = q^ for water vapor flux equation, and F = Q^ and f = q^ for liquid water flux equation. The calculation of the buoyancy terms in Eq. (3) requires the variances and the covariances of the scalar quantities 1 0 5, qv and q^. The variances are given by the. equation, ujCf2)*j + 2 V F'j= "^V'j ~ 2£f (4) — ~~2 where e^ is the rate of destruction of f by molecular effects. The equation for covariance is, 8q + + U q = 2E V v>'j V ^.J i v "^V'J " eqv (3) ,0 where Eg^ is the molecular destruction,rate of 3q^. The eq„ equation is analogous, and can be obtained by replacing Q^ and qv in Eq'. (5~)jjby Q^ and respectively. ° 2.2 CLOSURE ••• ' o All terms on the right hand side of the second moment tj equations (2) to (5) are unknowns; the latter are of three i ^ types: (i) velocity (or scalar) and pressure-gradient covariances (ii) third-moment divergence (turbulent transport) terms, and (iii) molecular destruction terms. -To close the equations, we approximate these unknowns in terms of dimensionally-consistent, physically plausible,- semi-empirical expressions involving the mean field variables, the second moments, and a turbulence relaxation time r = 2E/e; the latter is determined by the model Ill itself, not specified a priori, since the model carries a dynamical equation for e. These approximations constitute the higher-order closure technique discussed by Lumlay and Khajeh—Nouri (1974), Wyngaard et al. (1974 a, b), and Wyngaard (1975). Reference should be made to these papers for details of the turbulence closure models. The closed 2-D model consists of six mean field (U, V, W, ~~2 ~2 ~~2 — — QJ Q^) equations, five Reynolds stress (u , v , w , uw, vw) equations, two heat flux (w5, u=) equations, two water vapor flux CwqvJ uq^) equations, one liquid water flux (wq^) equation, ~2 2" two scalar variance (8 , q^ ) equations, two scalar covariance equations, and one equation for the energy dissipation rate (e). In order to simplify the model, we;dropped the equationci " s for the turbulent moments uv, v3, vqV , uqko , vq A , . . qV q.Jb, and qX0i ; preliminary calculations established that these ' ^ - variables can be eliminated without altering the results significantly. >) This gives"a set of 21 coupled partial differential equations which are solved as discussed in Section 3. 2.3 POWER PARK FLUX INPUTS Let us consider a power park with a 10,000 Mwe generating capacity utilizing a series of mechanical draft evaporative O ;> ,( cooling towels (height =10 m) for the rejection of waste heat to the atmosphere. For an overall plant efficiency of 33%, the total waste heat released from this park is about 2p,000 Mw. Of 0 J , ' ft thisabout 80% or 16,000 Mw will be in the form of latent heat >i which is released to the atmosphere only when the water vapor condenses. The remaining 20% or 4000 Mw is^sensible heat • - #/ u 112 which is immediately available for atmospheric heating. We assume the total waste heat is distributed over the power park area at an average flux of 1000 Mw km . This figure is, by way of comparison, about three times greater than the average flux of solar energy (340 Mw km ) at/;the outer edge of the earth's atmosphere (Hanna and Gifford, 1975). This would give an emission area A = 20 km" -1 _9 for the power park, with a latent heat flux Gq = 800 Mw km (or 192 cal m ~s ) and a sensible heat flux H =* 200 Mw km- 2 (or 48 cal m -2 s -1) . o The power park is assumed co be rectangular in shape with sides a = VIo" km and b = 2vTo km, chosen suchx that a-b = A. The 0 * ^ • cooling towers are assumed t(o be located along the centerline W of the park parallel to the side b. Then the effective length I of the power park in the direction of the mean wind is " 2 9 2 2 1/2 I = (a sin a + b cos a) (6) M where a is the angle between the mean wind vector and the cooling ''' tower alignment. If the wind is perpendicular to the cooling tower alignment (a = TT/2) , then £ = a = /l0 km; if the wind is along ("the cooling tower alignment (a = 0), then Z = b = 2*^10 km. The maximum environmental impact of the cooling towerws is expected for this latter wind direction. For 0 a<2. uniform flux distributions over length the latent and « sensible heat fluxes (G and H) are specified by equivalent i". 113 sinusoidal distributions: G(:<) = t/2 • G sin(TC/2) n 0 £ x < I (7) H(x) = ~/2 • Hq sinCnx/i) The corresponding specific huaidity flux and specific heat flux are given by __ wq (x) = G(x)/pLv , (x) = S(x) /oCpd (8) where p is density of air, c^ is specific heat at constant pressure of dry air (0.24 cal g , and L is latent heat of vaporization (597.2 cal g . The peak fluxes thus occur over the mid-point of the power park. The peak sensible specific heat flux due to the power park is tt/2-I^/pc^ = 0.26 K m s \ which is about the same as the typical peak surface heat flux in the atmosphere at midday due to radiative heating from the o sun (see Wyngaard, 1973). The peak humidity flux due to the power park is TT/2-G^/PL^ = 0s 42 m g kg \ which is about 16 times larger than the typical peak humidity flux in the natural convective atmosphere. To study the meteorological effects of the power park, the turbulent flux distributions given by Eqs. (7) and (8) are ' u % directly utilized as additional boundary conditions to the model. 3. NUMERICAL SOLUTION f The closed equation set, together with the specified boundary and 0 initial conditions, was numerically integrated on an IBM 360/91 114 ' • digital computer using a Dufort-Frankel (1953) explicit finite difference scheme, with forward marching in the x direction. To obtain a fine computational mesh, a logarithmic transformation of the 4 vertical coordinate z was used from the lower boundary z^ = 10 m to a height of 421.7 m, where it changed smoothly to a linear grid,; up to the.upner boundary at 2 kn, with a total of 41 points, 3.1 BOUNDARY AND INITIAL CONDITIONS « The lower boundary conditions for the convective atmosphere were based on the equilibrium flux-profile relations (Businger et al.,'1971), recent measurements (Wyngaard and Cot£, 1974b), and numerical experiments (Deardorff, 1974). At z = z^, the lower O boundary, we set 2 uw/u^ -1 fw/fAu ?|= -1 0 -1/4 (kz/uA) 3U/3z = (1-15?) = \ o -1/2 (kz/f^) 3F/.3z = 0.74(1-95) = vw/u^2 = 0 (kz/uj 3V/3z =0 2 2 2/3 2 2 w /Ujfe =* 1.75 + 2(-C) 3U /3Z = 0 - 3V /3Z 2 2 -2/3 fu/f^ - 40m$h , f /f* - eqv/6^vJk - 9q~/8,qjl- 4(1-8.30 w 7 = -w 313/3z + (g/eo) (9) o-, _2 /2) + ln(<1 + $ )/2) U/uA * {£n(z/zo)-[2 £n((l + «m ) m V -2 tan"3"^ ~1) + tt/2] }/k , m O 115 , ' V/uj. = 0 = 1 (F-FQ)/fA = 0.74{£n(z/zQ)—2 £n[(l + (<>h/0.74)" )/2] }/k • 7 w: where 5 = z/L, L = u.9 Q/kg S .is the Monin-Obukhov length for moist convection, 9 . = 9. + 9 (0.61 q ^ - q„.), k =>0.35 is the v* ' * o v* Z* Von Karman constant, Zq is the surface aerodynamic roughness length, taken as 0.01 a, and ? is the surface (at z ) value o o i ; of the scalar variable ?. ' At the upper boundary (2 km), which lies within the upper level inversion, all turbulent quantities and mean gradients ' c were set to zero. 'cJ . To start the computations, the initial distributions of the variables in the atmosphere upwind of the power park, located //at x = 0, must be specified. The initial profiles, for the present study were generated by integrating the same model, together with the appropriate 'oimndary conditions, but excluding the power park, until steady-state equilibrium distributions c typical of a convective daytine atmosphere were established. The initial surface heat flux is 0.2;3 K m s , surface humidity flux is 0.023 B s ^ g kg \ the geostrophic wind is 5 m s u^ 31 0.3 m s ^ and L = -10 m. Three sets of^initial profiles were generated for RH = 60, 75 and 90%, where RH is the initial surface relative humidity." For simplicity, we assumed the q initial liquid water content to be zero. . " 3.2 SATURATION ADJUSTMENTS ^ ° /j' o ——————— a - IV The source terms for condensation or evaporation, indicated ~ G * ° 1 byGsubscript c in Eq. (1), are incorporated through a saturation 116 adjustment procedure. In general, for each integration step, some imbalance exists between the calculated humidity and the saturation humidity corresponding to the calculated temperature. If the air is supersaturated, some excess vapor has to be condensed (cloud formation); if the air is in a subsaturatea state, some of the previously formed liquid water must be evaporated (cloud dissipation). In either case, this instantaneous saturation adjustment process occurs adiabatically,and isobarically, and is accompanied by potential temperature, specific humidity and liquid water changes that are calculated as follows: 2 2 6Q0 = (Q "Q )/[l + (L /R C )-(Q /T )] a V VS V V p vs but 60^ = -Qr if < Qvs and Q£ < 50^ , (10) and 60 = (G/To)(Lv/cp)6Q2 where c = (1-0 -Q )c . + c Q + c.Q. " (11) p ^v 20, pd pv v £1 is the specific heat of moist air, Tq is the temperature of the o referenc„ e state, is the specific heat at constant pressure -1 _1 of water vapor (0.45 cal g K ), c is thea specific heat of X0r -1 -1 " water (1 cal g K ) and R is the gas constant for water V 0 vapo-S-1 (0.110 cal g- 1 K -1). The temperature T and the saturation o r <> specific humidity are computed from C d T/e = (?/1000)V P w , (12) and 0 = 0.622 e /(P - 0.378 ej , (13) -, vS s S 117 where eg = 6.1078 exp{cT/(d + T)} , (14) with c = 17.2694, d = 237.29 for T > 0°C, and c = 21.8746, d = 265.49 for T < 0°C. Here, P (in mb.) is atmospheric pressure taken to he hydrostatic, eg (in mb.) is saturation vapor pressure, and Rj is the gas constant for dry air (0.069 cal g ^K " 3.3 RUN PARAMETERS In this preliminary study of the meteorological effects of ^ power parks, seven computer runs were made, sequentially varying the initial surface relative humidity (RH = 75, 60, 90%), the wind direction with respect to cooling tower alignment k' (a = u/2, 0, ir/4), and the total waste heat flux from the -2 power park (GQ + HQ = 1000, 500, 2000 Mw km ) . The various parameters for these numerical experiments are shown in Table 1. ,f 4. RESULTS AND DISCUSSION Figures 1 and 2 show the modification of the vertical profiles of potential temperature and specific humidity by the power park as a function of downwind distance. The initial (x = 0) equilibrium profiles show a typical convective mixed layer capped by an inversion (Deardorff, 1974; Wyngaard and Cot£, 1974b). The well-mixed layer is characterized by an unstably stratified surface layer at its base, and vertical gradients of Q and Q^ aloft which are small in comparison with those occurring in the inversion just above. The initial thickness of the convective boundary layer, defined as the height z. of the TABLE 1 PARAMETERS FOR NUMERICAL EXPERIMENTS RUN < NO. INITIAL ATMOSPHERIC CONDITIONS POWER PARK PARAMETERS Surface Wind Total relative direction waste heat Effective humidity angle * flux „ Area Sides length Peak haat flux 2 (*) (radians) -zjL (Mw km) (km2) (km) (km) (cal nf s -1) RH a G + H A I sensible latent 0 0 a b . ^ r 1 | 60 t/2 107 1000 20 /To 2/10 3.162 75.4 301.6 2, I 75 IT/2 59 1000 20 /lO 2/10 3.162 75.4 301.6 90 IT/2 30 1000 20 /To 2/10 3.162 75.4 301.6 3 " A 4 75 ,,/2 59 2000 10 /? /20 2.236 150.8 603.2 5 75 ii/2 59 500 40 2/20 4.472 37.7 150.8 6 75 0 59 1000 20 /To 2/10 6.324 75.4 301.6 7 75 TT/4 59 1000 20 /To 2/10 5.000 75.4 301.6 * L = -10 m 119 ORNL-DWG 78-5777 Fig. 1. Calculated vertical profiles of mean potential temperature showing modification due to power park (Run 2). ORNL-DWG 78-5778 Fig. 2. Calculated vertical profiles of mean specific humidity showing modification due to power park (Run 2). 120 lowest inversion base, is 580 m. For x>0, the convective heating from the power park increases both z^ and the temperature in the mixed layer. The maximum surface temoerature gradient occurs in the /"J middle of the power park (x = 1.6 km) where the heat flux is maximum.'' Away from the power park, the surface temperature gradient decreases until a new equilibrium convective mixed layer with a larger z^ is established. At x = 18 km, z.i is 737 m, a 27% increase over the initial value. The mean specific humidity (Fig. 2) in the mixed layer also increases due to the vapor emission from the power park; the maximum Q^ occurs at x = 1.6 km where the vapor flux from the park is maximum. For x>3.2 km, the vapor diffuses upward and the humidity near the surface decreases until a new equilibrium humidity profile is established in the rising mixed layer. At x = 18 km, the temperature increase (A0) due to the power park at elevation z = 200 m is 1.5°C, while at z = £00 m, AG=1.26°C. The corresponding AQ^ values are 0.3 and 0.2 g kg \ respectively. The vertical profiles of sensible heat flux and specific \v\ humidity flux are shown in Figures 3 and 4. The initial flux profiles are similar to those given by Wyngaard and Cotd (1974b) for a convective boundary layer. The top of the mixed layer, z^, can be defined as the height where the virtual heat flux w9v reaches its negative maximum. The initial heat flux profile is essentially linear in the region z<0.85 z± with its maximum positive value near o the surface. The initial humidity flux, however, is not larger in magnitude at the surface than at zThis is due to the eihtrainment of dry air aloft down into the mixed layer accompanied by rapid upward movement of the more humid mixed layer air, giving rise to 121 ORNL-DWG 78-5779 -.(too - HOO •100 o Fig. 3. Calculated vertical profiles of sensible heat flux showing modification due to power park (Run 2). ORNL-DWG 78-5780 LEGEND SYMBOL X(km) • 00 o 1 6 A 32 I.MO + 7.9 X 12.0 ? o 180 BOO i V, -0.1 0.0 0.2 I'; 0.3 ' 0.5 qw (g kg"1 m'~see"1) 6' ^ ti Fig. 4. Calculated vertical profiles af specific humidity flux showing modification due to power park (Rur( 2). 122 a substantial upward moisture flux in the vicinity of z^ (Deardorff, 1974). The maximum surface heat and humidity fluxes, 0.5 K m s 1 and 0.45 g kg ^ m s ^ respectively, occur over the center of the power park. Downwind of the park (x>3.2 km), the surface fluxes return to their initial values, but the fluxes aloft in the mixed layer remain larger than their earlier values, producing the above-described increases of 0 and Q^. in this region. The top of the mixed layer rises as,the warmer humid well—mixed air penetrates the inversion U above. The extent of penetration diminishes, however, as the mixing layer gradually thickens, lifting the base of the inversion layer. The calculated surface (at £q) perturbations in Q and Q^ due to the power park are shown in Figure 5 as functions of the initial surface relative humidity RH. The maximum surface perturbations naturally occur in the middle of the park where its emission fluxes are maximum. The magnitude of the surface perturbations increase with RH, since the depth of the mixing layer must decrease as RH increases, with L kept constant. For example, for RH =» 90%, z^ is only 290 m (~z^/L=30); the maximum perturbations in 0q and Qvq v\. respectively are 9.7°C and 15.7 g kg 1 at x = 1.6 km. The corresponding values at x =» 18 km are 3.2°C and 0.3 g kg"1. These values indicate the typical increases in 9q and Q^ that can be expected downwind of a 10,000 Mwe power park. Figure 6 shows the spatial evolution of the vertical profiles of mean liquid water content. At x = 0, the model is initialized with Q^ = 0 and q^w = 0 at all z, so thatjonly the liquid water created by the power park appears in tha5results. For x>0, the 123 ORNL-OIVG 78-5781 y e Fig. 5. Calculated ground level values of mean potential temperature and mean specific humidity showing perturbations due to power park (RunH>) vapor emissions from the park,diffuse upward and condense upon reaching the lifting condensation level. The LWC increases downwind and peaks at x = 12 km with a maximum Q^ of 0.24 g kg \ Thereafter, the liquid water diffuses upwards and the maximum Q decreases. Figures 7a, b, c show the mean LWC isopleths iii the convective « . cumulus clouds spawned by the power park for three values of RH. ' ' " -1 ^ " "ts> f For convenience, the 0.05 g kg LWC contour was taktii as the cloud ORNL-DWG 78-8399 6. Calculated vertical profiles of mean specific liquid water content in the cumulus clouds formed by power park emissions (Run 2). 125 1600 0-001; ,-0-00 5 '200 800 400 POWER PARK POWER PARK -2 :4 S 10 12 14 It. 18 -2 to) X ( km 1 Fig. 7. Calculated isopleths of mean specific liquid water content in the ci spawned by the power park. (a) 60% (Run 1), (b) RH = 75% (Run 2), and (c) RH = 91 ORNL-OWG 78-12019 1600 >200 0-001 A Mii BOO '0a 400 ,'M POWER PARK -2 6 6 10 12 14 16 18 X (km) Vjl (A) '4 'to 'r§tm •rim 5H "M ,0 ,v. '2 '4 16 X (km) ^liquid water content in the convective cumulus clouds RH = 60%, the cloud base is at 1020 m ar„i,/the cloud top at about 1400 m. For RH = 90%, the cloud base is at only 340 m and the cloud top at about 700 m. For RH = 75%, the cloud is in between. In all three cases, the mean LWC peaks within the investigated range of x, with a maximum value of 0.225 to 0.3 g kg \ These values are in agreement with typical maximum LWC reported by Hanna (1976, 1977) and Auer (1976) for large power plants and industrial cumulus, and by Fletcher (1962) for natural cumulus clouas (0.1-1 g kg . Figures 8a, b, c compare the modification of the vertical profiles of 0, 0 and Q at x = 12 km as a function of the mean wind direction (a) with respect to the cooling tower alignment. The initial profiles are also shown for convenient reference. The S maximum increases in 0, Q and occur when the wind is parallel • v V to the cooling tower alignment- / th e minima when the wind is A ' perpendicular. For a = TI/4, they are in between. Figures 9 a, b,Jc compare the modification of 0, and Q^ profiles at x = 12 km as a function of the total waste heat flux , from the power park; the initial profiles are again indicated. The largest increases in -92, Q^ and of course, occur for the largest heat flux (2000 Mw km ) used in the study. ^ 5. CONCLUSIONS The meteorological effects of waste heat and moisture releases from a large power park were numerically simulated using a higher-order 127 ORNL-DWG 78-12018 Qv (8 kg") 'VV- O a « 7!/2 (Run 2) & cx = ~/4 (Run 71 IJ + a = 0 (Run 6) O Initial profiles (x — 0) o^ 0.08 0.06 0.(77 4 o, & Sit 5/ai calculated at x1 = 12 km, of mean (a) potential tempera- pater content, while, the mean wind direction with respect BLANK PAGE f MOO 1ZOO J 1000- + 500 Mw km-2 (Run 5) O 1000 Mw km"2 (Run 2) A 2000 Mw km-2 (Run 4) 000 e. • Initial profiles (x = 0) s. N tsi 000 coo - CM (o) e (Deg K) 1400 1200 J 0 1000 800 - n, CO eoo 400 200- o -i • 1 , r 0.00 0.01 0.02 o 03 0 04 (e) Ql (s « Fig. 9. Comparison of vertical profiles, all calc ture (2?) specific humidity (e) specific liquid water cc power park varied. 128 ORNL-DWG 78-12020 (6) Qv (8 kg") + 500 Mw km-2 (Run 5) -2 O 1000 MM km (Run 2) A 2000 Mw km-2 (Run 4) • Initial profiles (x = 0) / filiated at x = 12 km, of mean (a) potential tempera- |>tent, while the total waste heat flux from the 129 turbulence closure model. The simulation presented in this paper for a 10,000 Mwe power park has not been quantitatively verified with actual observations since there are no existing power facilities of this size. The model predictions, however, show good qualitative agreement with available observations for similar smaller industrial sources, and the calculated mean and turbulence quantities have physically realistic distributions. Among the areas for future research work are model simplification and validation, and improvement of the source (power park) representation. In a nonprecipitating shallow-cloud model, it Is convenient to use conservative variables such as Betts' (1973) liquid-water potential temperature (Q^) and total moisture content (Q^) : e. = G-(L 0 /c T )Q I v o p o (15) Qvs + Q£ (saturated) V Qy. (unsaturated) Some advantages of the —Q^ system are (see Deardorff, 1976) that one need not carry Q^ as a separate independent variable since it becomes a derived quantity. This saves computer time and storage. Further, supersaturation does not occur during a given integration 0 step so that there is no question of releasing the right amount of 'ent heat through saturation adjustments. It is possible to quantitatively test the model predictions utilizing weather modification data from smaller existing power plants. However, there are few field observations with sufficient detail to provide^ a demanding test of even thea mean profiles, let alone the turbulent flux predictions. 130 The representation, of the power park as a finite area source might be more appropriate for large cooling ponds^than cooling towers. For the latter, it is desirable to improve upon the source characterization in the model to handle directly flux inputs of momentum, heat and moisture from multiple, finite—sized sources with a given horizontal spacing at a given elevation. In such models, presumably, the local updrafts and vertical accelerations would become important, and one should also take into account the dynamic mean pressure perturbations. Tower-effluent interactions such as plume merging and downwasn could conceivably be significant for such a representation. Development of such a model, based on a second-order—closure theory, will be very complex and challenging. ACKNOWLEDGEMENTS This work was performed under an agreement between the National Oceanic and Atmospheric Administration and the Department of Energy. J O - We are grateful to Hal Snodgrass and David Elliott for developing the computer plotting programs, and to Mary Jane Austin,for typing the manuscript/i . Discussions with several of our colleagues in the Atmospheric Turbulence and Diffusion Laboratory were helpful. (l « G REFERENCES o Auer, A. H., Jr., 1976: Observations of an industrial cumulus. ^ J. Appl. Meteorol., 15, 406-413. Betts, A. K., 1973: Non-precipitating cumulus convection and its parameterization. Quart. J. Roy. Meteor. Soc., 99, 178-196. 131 Bhunralkar, C. M., 1976: Computer simulation of atmospheric affects of waste heat rejected from conceptual large power parks. Presented at the ASME Winter Annual Meeting, New York. Paper No. 76-WA/HT-2G, 8 pp. 'n 3usinger, J. A., J. C. Wyngaard, Y. Izusni, and E. F. Bradley, 1971: Flux-profile relationships in the atmospheric surface layer. J. Atmos. Sci., 28, 181-189. Deardorff, J. W., 1974: Three-diaensional numerical study of the height and mean structure of a heated planetary boundary layer. Boundary-Layer Meteorol.,. 7_, 81-106. Deardorff, J. W., 1976: Usefulness of liquid-water potential temperature in a shallow cloud model. J. Appl. Meteorol., 15, 98-102. Dufort, E. C. and S. f\. Frankel, 1953: Stability conditions in the numerical treatment of parabolic differential equations. = Hat'n. Tables Aids Comput., 7_, 135-152. Dutton, J. A. and G. H. Fichtl, 1969: Approximate equations of motion for gases and liquids. J. Atmos. Sci., 26, 241-254. Fletcher, N. H., 1962: The Physics of Rainclouds, Cambridge Univ. Press, London. w Hanna, S. R., 1974: Meteorological effects of the mechanical- draft 0 cooling towers of the Oak Ridge Gaseous Diffusion Plant. Cooling Tower Environaent-1974, ERDA Symposium Series, CQNF-74032, NTIS, Springfield, Va., 291-306. Hanna, S. R. and F. A. Gifford, 1975: Meteorological effects of energy dissipation at large power parks. Bull. Amer. Meteorol. Soc., 56, 1069-1076. Hanna, S. R., 1976: Predicted and observed cooling tower plume rise and plume length at the John E. Amos power plant. Atmos. Environ., 10, 1043-1052. Ci Hanna, S. R., 1977: Model predictions and observations of clouds 0 formed by oil refineries in Los Angeles. Proceedings of the 0 6th Conf. on Planned and Inadvertent Weather Modifications, Urbana, II., 75-78. ATDL Contribution File No. 77/13. c- Lee, J. L., 1976: A numerical simulation of atmospheric convection caused by heat dissipation at large pow^r centers. Third « Symposium on Atmosheric Turbulence, Diffusion and Air Quality,iRaleigh, N.C., 563-570; available from Amer. Meteorol. ,, Soc., Boston, Ma.. a Lilly, D. K., 1962: On the numerical solution of buoyant convection. Tellus, 14, 148-172. „ p v 132 Lumley, J. L. and 3. Khajeh-Nouri, 1974: Computational modeling of turbulent transport. Adv. Geophys., 18A, 169-192. Moore, F. X., 1976: Regional climatic effects of power plant heat rejection. Araos. Environ., 10, 806-811. Smith, M. E., M. L. Kramer, D. Seymour, and T. T. Frankenburg, 1974: Cooling Towers and the Environment. Available from Amer. Elect. Power Service Corp., 2 3roadway, N.Y., 9 pp. Takeda, T., 1966: The doundraft in the convective cloud and raindrops: A numerical computation. J. Meteorol. Soc. Japan, 44, 1-11. Trepp, J. P., 1975: A two-dimensional hydrodynamic model for cooling- tower plumes. Environmental Effects of Cooling ^Systems at Nuclear Power Plants, Proceedings Series, International Atomic Energy Agency, Vienna, 37-44. Wolf, M. A., C. E. Hane, and R. L. Drake, 1976: Deep convection. Atmospheric Effects of Nuclear Energy Centers (AENEC) Program, Ann. Tech. Prog. Rept. 0RNL/TM-5778, A. A. Patrinos and H. W. Hoffman, eds., Oak Ridge National Laboratory, 116-134. Wyngaard, J. C., 1973: On surface-layer turbulence. Workshop on Micrometeorology, D. A. Haugen, ed., Amer. Meteorol. Soc., Boston, Ma., 101-149. Wyngaard, J. C^l, 0. R. Cot£, and K. S. Rao, 1974a: Modeling the atmospheric boundary layer. Adv. Geophys., 18A, 193-211. Wyngaard, J. C. and 0. R. Cot£, 1974b: The evolution of a convective planetary boundary layer—A higher-order-closure model study. „ Boundary Layer Meteorol., 7_, 289-308. Wyngaard, J. C., 1975: Modeling the planetary boundary layer— Extension to the stable case. Boundary Layer Meteorol., 9_, 441-460. i 'Q O 133 6. NUMERICAL SIMULATION OF AN INDUSTRIAL CUMULUS AND COMPARISON WITH OBSERVATIONS* F. W. Murray L. Randall Koenig"^ P. M. Tag'1" /r ABSTRACT A two-dimensional field-of-flow numerical model of cloud development is used to study a cloud that formed over a re- finery as a result of heat dissipated to the atmosphere. The observed vertical structure of the atmosphere provided initial conditions. The wind necessarily was simplified to a unidi- rectional flow. The cloud-initiating perturbation consisted of sensible and latent heat equal to the waste heat rejected to the atmosphere by the refinery. When conditions were matched to those reported, the simu- lated cloud agreed in most particulars with the observations. Sensitivity tests showed that the simulated cloud depends too strongly on ambient wind speed and shear. This perhaps is a generic defect of two-dimensional formulations. The response of the simulated cloud to expected changes in heat flux den- sity appears more realistic than its response to small changes in ambient wind. The cloud evolution consists of bubbles forming and breaking away from the main cloud mass and then moving down- wind and dissipating. This behavior characterizes real clouds associated with a stationary heat source. The simulations also predict that under appropriate conditions1 secondary clouds form far downwind. £> 6.1 INTRODUCTION )) As a consequence of requirements to reduce thermal pollution of water bodies, industrial concerns have turned to the practice of dissipating uneconomical (waste) heat directly into the atmosphere. The heat "re- jected" to the atmosphere is usually a combination of sensible and latent heat. Increasing concern has been expressed (Hanna and Gifford, 1975) <> ^-TJ'/ * T o be published in Journal of Applied Meteorology. ^The Rand Corporation, Santa Monica, Calif. tt Naval Environmental Prediction Research Facility, Monterey, Calif. 134 that as this practice becomes more common and heat fltox densities become greater, the atmospheric effects caused by the local moisture and buoyancy perturbation will become intolerable. Thus, depending on the local climate and other matters, an upper limit to the amount of hefit that should be re- jected over a particular region is anticipated. It is clear that some means to. predict this upper bound of acceptability is desired, for the capital costs of the facilities are large, and knowledge derived by ac- tually experiencing certain kinds of imputed effects, such as the spawning of hailstorms and tornadoes, ' is clearly not the preferred path. Mathematical simulation offers a potentially useful means to esti- mate the afaiospheric effects of waste heat from proposed facilities. We will be asking much of these models. Since interest centers on facilities that are larger than those now operating, they will be asked to simulate phenomena that cannot be directly observed. For that reason it is desirable to compare any proposed kind of model with appropriate available observations in order to extrapolate its performance to con- editions which cannot yet be observed. The work reported here was pri- marily the result of an effort to evaluate the ability of a two-dimen- sional field-of-flow model of atmospheric convection to simulate atmos- pheric phenomena in general. Observations by Auer (1976) of cloudiness caused by heat rejection from a petroleum refinery at Wood River, Illinois, in the morning hours of August 10, 1973, serve as a basis for comparison. These observations of rather benign cloudiness caused by modest flux of waste heat are of particular interest to the problem of modeling waste heat effects in general. Input conditions were specified to match those of, Auer's observations. Variations in the ambient wind field and heat flux densities were also made. b 6.2 DESCRIPTION OF MODEL U <•> The model used for this study was a modification by Tag (1977) of the cumulus model of Murray (1970). The important changes made by Tag a 0 " , = o 135 are: 1. The condition of symmetry is dropped, and an ambient wind, with or without vertical shear, may be specified along the x-axis. All condi- tions at the upwind boundary are as specified in the initial reference state. Free flow is allowed through the downwind boundary. 2. The vertical mesh length <5z is a function of height. This per- mits high vertical resolution in the lower levels, where most of the activity occurs, but a sufficiently remote upper boundary to minimize adverse effects of the rigid lid, all with a relatively small number of grid points. It is accomplished by effecting a transformation of the vertical coordinate z to another variable s, given, in accordance with Schulman (1970), by / z/z \ + tanh( Z » max £_ a + tanh (l/o) (6.1) \ max / in which zmax is the value of z at the upper boundary. The parameters that control the degree of vertical stretching have the values a = 0.5 and a = 0.1. The domain is 64 mesh units long with 6x = 200 m and 49 mesh units deep with 5z ranging from 29 m at z = 0 to 612 m at z = z = r & b // max 10 km. At levels near the heat source 6z 40 m. 3. Subgrid scale mixing is parameterized by K theory and the use of variable.-eddy exchange coefficients. Computations are in the x-z plane oriented along the direction of the wind, and properties are assumed not to vary in the y-direction. With these assumptions the x and z components of the Boussinesq vorticity equation vanish, leaving only '' •P r, - ai (un) -li (wTl) + 8 qi) + " • (e } o See the List of Symbols for definitions. The bar represents a reference state and the prime a departure from it. A combination of ideas from 136 Deardorff (1970), Lilly (1962), and Hill (1974) led to the formulations 2 \ / 3v\ = KM V2 + ' V + v2 ai" ' VV - v. (6.3) 3s3x . V 2 3z / and >s = 6x 5z *M • V & i£ (6.4) v e 82 Lilly's (1967) value of 0.2 was used for k^. One of the authors (P.M.T.) has determined that a similar value for k^ is inadequate where buoyancy plays a significant role in turbulence generation. A value of 0.7 for k_ 30 36 when < 0 and 0.0 when — 5 0 was adopted from a series of experiments simulating the upward transfer of heat released from a line source at the surface. A more detailed description of the derivation of (6.3) and (6.4) and of alternative formulations, together with comparative computational results, will be given in another paper (Tag et al., 1977). The eddy diffusion term for the ottier properties takes the form ft u F = V (6.5) where T', q^ or q^, can be substituted for No general consensus exists regarding the relative magnitudes of K^ and the eddy diffusivity for the thermodynamic variables. We assumed that K^ = K^ for all values of which ordinarily seems to work well for the larger scales. However, the fact that simulated liquid water content was , A considerably larger than the observed might indicate that K should have q been taken larger than K^. 137 4. The liquid microphysics parameterization of Kessler (1969) as implemented by Murray and Koenig (1972) is incorporated in >Jie model. The introduction of a variable vertical mesK length led to difficulties in computing fallout, however, so autoconversion was suppressed in these calculations. In justification it may be remarked that the actual cloud observed by Auer was not precipitating and that the lifetime of a con— vective element was about 15 min, a period of time too short to develop raindrops. 5. The perturbation consisted of the insertion of a given amount of heat and water vapor at specified grid points each time step. 6. After (6.2) has been solved, a Poisson's equation & \\ = -ti ,(6.6) ' i, f ••• must be solved for the stream function tji, which in turn determines u and w. A "block cyclic reduction" technique originally programmed by Roland " Sweet of the National Center for Atmospheric Research and modified for the» stretched grid by Rosmond (1975) was used. Rosmond and Faulkner (1976) describe thijs "direct solver." For a square grid of 65 points, thef^Tect solver is approximately 35 times faster than successive over-relaxation , (the method used in previous versions of the model), and solutions are correct to machine accuracy. ^ ' , Resources did not permit developing a version of the model especially tailored to the problem considered here. The version used, which was B developed for a different application, was selected because certain of its features (ambient wind, continuous perturbation) were necessary to the * problem and others (variable grid, more sophisticated treatment of eddy diffusion) were useful. This necessitated giving up the more extensive u treatment of liquid and ice microphysics (Koenig and Murray, 1976) and the J fallout that are in other versions.. 3 138 6.3 IMPLEMENTATION > i The model requires as input ambient atmospheric conditions and energy characteristics of the perturbing source. An effort was made to match each item of input data as closely as possible with actual conditions ob- taining on the day on which the refinery cloud was observed by Auer (1976) 6.3.1 Ambient Atmospheric Conditions No fewer than four soundings are available for the approximate time and location of the occurrence under investigation. The regular St. Louis 111 sounding for 1344 CDT August 10, 1973, is the most ccwnplete but least timely. The instrument apparently passed through sefVeral cloud layers, making the sounding uncharacteristic of the undisturbed ambient conditions When this sounding was used to initiate a number^/jf different cloud models for the HIPLEX workshop (Silverman et al., 1976;y/Murray, 1975), most of the models predicted the development of tall cumuli with considerable precipitation. These conditions were actually observed in the afternoon, but not at the time of the refinery cloud. The second sounding, provided to us by Auer, was made by aircraft at 1215 CDT about 13 km northeast of the cloud. Its principal deficiency is that it does not cover the complete layer from the surface to 10 km, as^required by the model. The other two soundings,j from a METROMEO X study (Vogel, 1975), were made at Pere Marquette Park, about 45 km west-northwest of Wood River, at 0736 CDT and 1340 CDT respectively. The first is cooler and more stable, with a pronounced inversion from the surface level up to 800 m, in? contrast to the nearly dry adiabatic lapse rates at low levels re- sulting from several hours of insolation in the other three. r- Q Since none of the four soundings was suitable in its entirety for the purpose at hand, a composite sounding was made,, taking some features from each of them; see Table 6.1; A plot of this sounding is given by Koenig et al. (1977). > The available winds include those from the St. Louis rawinsonde, a pilot balloon sounding given by Auer at a station 3 km west-southwest 139 Table 6.1. Composite sounding, Wood # River, Illinois, forenoon, • ' August 10, 1973 Pressure Temperature Dew point (mb) (°C) (°C) 269 -39.2 -55.0 287 -36.1 -54.8 306 -32.0 -48.6 324 -28.4 -44.4 336 -28.0 -48.7 349 -25.6 -46.7 370 -24.0 -45.4 397 -20.7 •<2.C 400 -20.3 -41.8 450 -13.8 -29.0 500 -10.0 -13.8 525 -7.0 -11.5 550 -5.3 -7.9 600 -2.0 -3.0 720 9.3 2.2 I70 ' 12\ 7 5.6 790 13.8 11.3 850 17.0 15.5 870 18.3 13.9 910 21.0 19.0 950 23.0 21.0 990 26.5 21.9 of the refinery cloud, and several" streamline and isotach analyses given () ^ - - by Vogel from the METROMEX pilot balloon network. A constant ambient wind o£ 0.5 m/s without shear was selected for the control run, but comparison runs were made with other wind conditions. See Section 6.5.2 for a discussion of the appropriateness of this choice. 6.3.2 Energy Input The driving force for the model is the addition of a given amount of energy each time step at specific grid points. This can be in terms of» sensible heat or water vapor (latent heat)(jor both. Either remits" in a variation of T*' in (6.2). Evaporative cooling towers used a.t re- fineries and power stations emit both forms of energy, as do stacks if 140 fossil fuels are burned. In addition, refineries emit sensible heat from a number of other sources, among them being the cooling of warm products placed in storage tanks. Consider a heat-emitting facility having effective length (along the direction of wind flow) of D and effective width of D . Let the rate x y at which the facility emits sensible heat be E , and latent heat E . b L The corresponding flux densities are It follows that the rate of increase of temperature due to addition of energy is ^ 8qv *L at LpD (6.9) z wheire D is the depth of the layer receiving the energy. z In the present instance Auer reported that the refinery emitted 814 MW of heat. He stated that half of this was sensible and half latent heat, so Eg = 407 MW . (6.10) However, he stated that in addition 83.3 kg/s of water was evaporated from some source, which is equivalent to 208 MW, taking L = 2.501 MJ/kg. IV - Thus the total rate of emission of latent heat is ^ E. =407 + 208 = 615 MW . * ^ (6.11) u 141 Using Auer's estimate of the size of the refinery as reported by Hanna (1976) and also by personal communication, the area of the source is about 196,000 m2. If this is equated to D^D^ in (6.7), $ = 2.08 kW/m2 b (6.12) 4> = 3.14 kW/m2 LI ,; For purposes of finite-difference computation it is necessary that D^ be some integral multiple of the mesh length 5x, which in the present instance is 200 m. It was assumed, therefore, that Dx = 2 6x = 400 m \ f • (6.13) D = 196,000/D = 490 m \ y x ; Since D^,, is only 2 1/2 times Sx, negligible variation in the y di- rection, as assumed by the model, is not assured. Limitations of both computer core size and time make a great reduction of fix infeasible, so in examining the results, one must keep in mind the possibility of three-dimensional effects that cannot be simulated with this model. The depth of the affected layer D must be an integral number of z mesh lengths 5z, which in this model depends on the elevation of the layer. In this experiment it was assumed that the introduction of energy was uniform over the volume defined by D , D , and D . Hence the values . 1 x' y z of (6.8) and (6.9) were the same at each affected grid point. The perturbed grid columns must not be located too close to the upwind boundary if the inflow is to represent ambient conditions prop- erly. For this experiment the columns chosen were 2400 and 2600 m from the upwind boundary. Cooling towers represent an elevated source, and air that bears heat is ejected with upward momentum, so the per- turbed layer was not taken to be at the ground surface but at the levels 58 and 88 m above ground, with J>z ~ 59 m. Typically, visual observa- tions of a refinery show many plumes, each of which is too small to be 142 resolved by this model. However, they mix and merge so that at a rela- tively low altitude the mean temperature and mixing ratio over a layer can be assumed to be controlled by (6.8) and (6.9). 6.4 COMPARISON OF SIMULATION RESULTS AND OBSERVATIONS The control run was designed to match as closely as practicable the energy rejectio^^characteristics (flux, flux density, and ratio of sen- sible to latent heat) reported by Auer. These values are as given by (6.30), (6.11), and (6.12). The form of the simulated cloud as a function of time is shown in Fig. 6.]. The input of heat is initially sudden, but thereafter con- stant. Hence there is a startup period of about 35 min during which the flow adjusts to the new conditions. Thereafter, a quasi-steady state ORNL-DWG 78-8396 25 min h<2> /Heat Source F. -Z | 147 kg | U O z •D y O 45 nin 1 ' GC O lli I > o CO <1 | 767 kq (i t- T <7 UJ 2 I 65 min 1498 kg 3' j • ^4 2 3 4 2 3 4 DISTANCE FROM UPWIND BOUNDARY (Km) Fig. 6.1. Evolution of simulated cloud (control run) from 25 to 80 min of simulated time in terms of amount of condensate. Contour values are 0.1, 0.5, 1.0, and 1.5 g/m3. Time is indicated in upper left of the diagrams. Total water content per meter of slab thicknesscis in lower right. 143 characterized by repeated creation and decay of bubbles exists. From the evidence of the control and other longer runs we believe that the period between 45 and 60 min best represents this state. Similar clouds observed to be associated with refineries in the Los Angeles basin often have a bubbling characteristic and a gradual evolution over periods of several hours. The report by Auer (1976) does not mention bubbling, but the upward movement of the center of maximum updraft indicated in Auer's Figs. 5 and 6 suggests a tendency for bubbling, and Auer (personal com- munication) confirmed this tendency. Table 6.2 compares the dimensions of the cloud observed by Auer with those simulated by the control and also with those simulated by Hanna (1976) using a one-dimensional cloud model. The numbers for the control are given for three simulated times to show the variability caused by the bubbling nature of the cloud. At all three times the base is slightly higher than observed and the top somewhat lower; thus the thickness is underestimated. The reverse is true of Hanna's simulation. Both models capture the vertical extent reasonably well, the two- dimensional model showing the greater fidelity. The width of the simu- lated cloud is somewhat greater than that indicated by Auer's drawings, but the differences are not considered significant. Hanna does not pro- vide a value for this property. Table 6.2. Cloud dimensions (m) Predicted (control) Observed Property Predicted (Auer) (Hanna) 50 min 55 min 60 min Cloud topa 2200 2500 1883 2100^ 2100 Cloud basea 850 800 875 870 855 Cloud width N-S: 2100, W-E: 1600 2100 2200 2300 ^Heights"are in meters above mean sea level; ground level is taken as 150 m MSL. t) Height of top is taken as halfway between levels having condensate and no condensate. 11 144 Observed and computed values of liquid water content at several heights are shown in Table 6.3. The two-dimensional simulation is capable of yielding both averages of horizontal traverses through the cloud and maxima in the cloud core. The one-dimensional model assumes a top-hat profile, so its results must be considered as averages. The observa- tions were made in the cloud core and so must be considered more nearly as maxima. Table 6.3. Liquid water content (g/m3) Predicted (control)^ Observed Predicted Heighta (Auer) (Hanna) 50 min 55 min 60 min Maxe Av^ Av Max Av Max Av Max 2010 0.44 1.3 0 0 0.91 1.2 1.5 1.9 1420 0.10 0.74 0.67 1.1 0.57 0.97 0.36 0.78 1080 0.046 0.56 0.22 0.41 0.33 0.46 0.29* 0.50 aHeights are in meters above mean sea level; ground level is taken as 150 m MSL. <>• ^Av indicates average across traverse at specified height; max in- dicates maximum along traverse at specified height. Q Auer's observations were made in the cloud core and so are pre- sumed to be maxima. di P ' Hanna's one-dimensional model with top-hat profiles provides a single value, which is the average. 3y any measure the simulations show larger liquid content than the observations. Auer does not specify the instrumentation used to measure the drop-size distributions from which the liquid water contents are calculated, nor does he indicate the accuracy. The lowest level had no drops larger than 7 ym in diameter, and the median for the highest level was 6.5 ym. Measurement of the smaller drops is usually difficult, so the values determined by Auer may not be very precise, which could be „ one reason for lack of agreement in Table 6.3. 145 The major difficulty, however, must be in the models themselves. The high levels of liquid water content found by Hanna are probably re- lated to the inability, noted by Warner (1970), of steady-state one- dimensional cloud models to simultaneously predict liquid water content and cloud depth in agreement with observations- Although the treatment of entrainment is quite different in a two-dimensional model, some of \\ the same difficulty may arise through the eddy diffusion. Use of a K^ larger than K^j, as some theoretical studies suggest, might have alle- viated the problem. Another possible variation is considered in Section 5. Some of the discrepancy may also be due to the inability of the model, which assumes infinite transverse extent, to properly treat a perturba- tion that has a very limited transverse dimension. Table 6.4 gives departure of temperature from the ambient (undis- turbed) value. The simulated values compare favorably with those ob- served. Note that the simulated cloud did not extend to 2150 m, so Table 6.4. Departure of temperature from ambient value, averaged across traverse at specified height (K) Hei ht* 0bse™edi Predicted0 Predicted (control) eig (Auer) (Hanna) 5Q min „ min 6Q min 2150a -0.2 +0.5 0.12 -0.10 -0.12 e c - 0.28 -0.27 -0.11 1650 -0.5 +0.3 +0.30 +0.21 -0.07 650-^ +0.2 +0.1 +0.39 +0.39 +0.35 aHeights are in meters above sea level; ground level is taken as 150 m MSL. ^As reported by Hanna. Q One-dimensional model with top-hat profile provides a single value, which is the average. ^Traverse at 2150 m MSL is above the top of the cloud simulated in this study, but below the cloud top simulated by Hanna and observed by Auer. Average for the uppermost level containing condensate and next level above. f JTraverse below cloud base. 146 simulated temperature departures at that level (footnote d in the table) are not properly comparable with the observed departures. The comparable values are those within the simulated cloud near the summit (footnote e in the table). The field-of-flow model captures the sign of the tempera- ture departure at most times and levels, but the one-dimensional model does so only at the lowest level, which is below the cloud. . The vertical drafts are shown in Table 6.5. In making comparisons, one must allow for time dependency and asymmetry of the real cloud as evidenced in the differences between the north-south and west-east tra- verses. The greatest disparity between observation and simulation is at the intermediate level. A three-dimensional simulation would result in stronger maximum updrafts [see Murray (1970) and Soong and Ogura (1973)], but the downdrafjts near the cloud wall would be weaker. The average draft would prtfr> ibly increase in value and be closer to observations. Auer states that the uncertainty in updraft determination is 1 m/s. Given this possible error, we conclude that the simulation provides a reasonable portrait of the average draft structure./.i The vertical draft structure of the cloud and its vicinity at 60 min is shown in Fig. 6.2. Auer's Figs. 6.5 and 6.6 are cross sections of draft speed in north-south and west-east orientations. The hodograph of Auer's pilot balloon observation (Fig. 6.3) suggests that our compu- tational plane should be considered as essentially from north-northeast to south-southwest below 1.6 km and from northwest to southeast above. Auer's two cross sections are in general agreement with one updraft maxi- mum at the center of the cloud and downdrafts to the leeward side. In the N-S section the updraft center is lower than in the W-E section; also the downdraft center is within the cloud, (''whereas it is downwind of the cloud in the W-E section. There is consistent updraft at the base of the cloud in the N-S section, but in the W-E section there are .downdrafts in the/region upwind of the cloud and lower than its base. By comparison, the simulation (Fig. 6.2) produces a leaning updraft with two maxima, one immediately above the heat source and below the cloud ft • base, and another within the downwind bubble. The strongest drafts are Table 6.5. Vertical component of wind (m/s) Observed^ (Auer) c Predicted (control) Predicted Height0 N-S W-E o (Hanna) 50 min 55 min 60 min °Av Av Max Av Max Av Max Av Max Av Max 2150e 1.0 3.1 —0.40 0.5 2.3 0.08 0.10 -0.14 0.03 -0.17 -0.01 d 0.41 0.95 0.27 0.42 0.54 1.2 1650, 2.6 3.5,; 2.0 4.0 2.0 0.56 2.1 0.37 1.6 0.28 1.6 , 650e' 2.9 4.5 0.77 1.8 2.0 1.3 2.7 0.77 2.9 1.5 3.0 ^Heights are in meters above mean sea level; ground level is taken as 150 m MSL. Avvindicates average across traverse at specified height; max indicates maximum along traverse. Hanna's one-dimensional model gives a single value, which is the average. - Q Trhverse at 2150 m MSL is above the top of the cloud simulated in this study, but below the cloud top simulated by Hanna and observed by Auer. d Average for the uppermost level containing condensate and the next level above. Traverse below stem of cloud. o c ORNL-DWG 78-8391 DISTANCE FROM UPWIND BOUNDARY (KM) Fig. 6.2." Vertical draft structure at 60 min of simulated time (control run). Solid lines are 0, ±1, 2, and 3 m/s. Dotted lines are ±0.1 and ±0.5 m/s. Cloudy region is shaded. 149 ORNL-DWG 78-8397 0.17 0.63 A N0=T> '0.3?, 0.15 kn 0 1 i i i 1 I I i i I I SCALE (m/s) 0.72 1-94 Fig. 6.3. Hodograph of pilot balloon sounding 3 km west-southwest of refinery cloudyat 1207 CDT. Heights in kilometers above mean sea level are indicated near the ends of the wind vectors. Ground level is 0.15 km. beneath the cloud base. There are downdrafts surrounding the older (down- wind) portion of the cloud. The associated evaporation and drying con- tribute to the division of the cloud into two distinct bubbles at 65 min; see Fig. 6.1. Despite some discrepancies in magnitude, the general con- figuration of predicted drafts matches observation quite well except for the bifurcated updraft. On the basis of other observations we believe^ that this feature often exists in cloud having fixed roots. The feature 150 at the upwind boundary in Fig. 6.2 is a computational artifact that arises from the specified boundary conditions. 6.5 SENSITIVITY STUDIES Model^results become more meaningful with knowledge of how the model responds to various stimuli. Accordingly, some sensitivity studi.es were made. The effects of changing the proportions of sensible and latent heat in the perturbation are discussed in another paper by Koenig et al. (1977) and variations in the parameterization of eddy diffusion are discussed by Tag et al. (1977). Here we consider one change in the eddy diffusion and several variations of ambient wind and heat flux density. Six runs, designated from A to F, were made for the sensitivity o studies reported here. Run A is identical with the control run except that the eddy viscosity is formulated in accordance with (2.5) rather than (2.3), and in (2.4) the last term contains (g/T) OT'/8z) rather than (g/9) (36/3z). The first cf these variations is discussed by Soong and Ogura (1973). The rationale for the second is given below. Runs B, C, and D are identical with Run A except for the specified ambient wind. Runs E and F are identical with Run A except for the flex density of > energy from the perturbation. Hence they are all comparable among them- selves for sensitivity|studies. 0 6.5.1 Turbulent Mixing The large values of liquid water content in both our simulation and Hanna's suggest that insufficient entrainment is modeled. As Warner (1970) has pointed out, this is an unavoidable feature of the usual type of one-dimensional cloud model. A two-dimensional model, however,, should be able to surmount the difficulty. Squires (1958) suggested that hori- zontal entrainment alone cannot explain the observed large departure from adiabatic liquid water content and that entrainment through the top of the cloud in the form of'penetrative downdrafts is necessary. , ° a . ^ .This can easily (although imperfectly) be simulated in our model by in- creasing the eddy diffusion coefficient near the cloud top. Experience 151 has shown that the simulated T' becomes strongly negative in that region, and Squires reports that this is also observed in nature. Hence the sub- stitution of T' for 9 in (2.4) selectively increases turbulent mixing. In general, 3T'/3Z < 0 at many more grid points than 89/3Z < 0, so this formulation produces more turbulent mixing throughout the domain than does the usual one. However, comparison of the values of K^ produced by (2.4) and by this modification of it shows that the latter are significantly larger than the former, mainly near tho tops and edges of the clouds. That this formulation does irxde'ydi decrease the liquid water content in the middle and upper parts of the cloud is demonstrated by comparing Table 6.6 with Table 6.3. Comparison of Figs. 6.1 and 6.4 shows an es- sentially similar evolution in the two runs, but with significantly larger total condensate in the control. Both runs evidence bubbling, but not exactly in phase with ea^ch other. Table 6.6. Liquid water content^ (g/m3) — run A jOi 50 min ,> o 55 min 60 min Height^ Av Max Av Max Av Max 0 2010 0.45 0.70 0.57 0.71 0 0 1420 0.29 0.59 0.26- 0.50 0.58 0.96 1080 0.33 0.44 0.31 0.46 ,0.2VJ 0.42 aAv indicates average across traverse at specified height; max indicates maximum along traverse at specified height'. a Heights are in meters above mcm sea level; ground level is taken at 150 m MSL. 1 6.5^2 Ambient. Wind The hodographs for a pilot balloon sounding near the observed cloud (Fig. 6.3) and for the>noon rawinsonde at St. Louis (not illustrated) suggest that below 1.6 km MSL the computational plane should be oriented " 1 , o from north-northeast to south-southwest, with a mean wind speed of 0.9 152 ORNL-DWG 78-8392 DISTANCE FROM UPWIND BOUNDARY (km) Fig. 6.4. Evolution of simulated cloud'(run A) from 25 to 80 min of simulated time-in terms of amount of C'ondensate. Contour values are 0.01, 0.1, 0.5, and 1.0 g/m3. See" caption to Fig. 6.1. m/s and a shear of 1.4 m s-1 km-1, whereas at higher levels it should be from northwest to southeast with a mean wind speed of 2.8 m/s and a shear of 2.7 m s~J km-1. The rawinsonde suggests a further shift with height to an orientation from'west-southwest: to east-northeast with continuing shear of the same magnitude. " The model is incapable of handling such variation.3 All winds must ii r be in one plane, and the available version requires all ambient winds to be in one direction. Resources did not permit reprogramming this, nor 153 was it considered essential to do so. As a first approximation the winds of Fig. 6.3 were all projected into the northwest to southeast plane, yielding an algebraic mean speed of 0.6 m/s and a shear of 1.3 m s 1 km-1 ii This profile is shown in Fig. 6.5 as the line labeled :,From hodograph." Although this condition is only a rough approximation to reality, it still cannot be used as an input to this model because of the 180° wind shift at 950 m MSL signified by a change in sign of the wind speed. Further simplification is required. ORNL-DWG 78-8398 >u IC O jD Wind Speed (m s"1) Fig. 6.5. Ambient wind speed as a function of height, runs A, B,. C, and D. Average cloud depth between 50 and 60 min is denotedV1by heavy "lines. • 154 The control and run A, therefore, were taken to have an ambient wind of 0;.5 m/s (close to the 0.6 m/s suggested above), but no shear. Three additional runs were made with different values of wind speed and shear but otherwise identical conditions; see Fig. 6.5 and Table 6.7. Shear of the magnitude suggested by the hodograph but starting from zero speed at ground level was not used because it would have produced strong winds at and above the convective condensation level, which, as will be shown, drastically inhibit cloud development. Results of the four runs show that the cloud base is not very sensi- tive to ambient wind, but the cloud top is. Apparently the cloud base is primarily controlled by the convective condensation level (which in this case is 1000 m MSL), with some lowering due to the introduction of mois- ture by the perturbation. This is clearly shown in a related report (Koenig et al., 1977), and observations confirm it. Increased wind speed in the subcloud layer leads to increased mixing with drier ambient air; hence to a raising of cloud base. By contrast, cloud top height varies considerably. Some clues to the variation may lie in the sounding itself. In the layer below the convective condensation level the humidity is 88 percent, but immediately above it drops off to 75 percent at 1275 m MSL. Between 1475 and 2100 m MSL it is again humid and then much drier above for nearly 2 km. The lapse rate shows a slight increase in stability between 1475 and 2875 ,m MSL. The cloud tops for runs A and B appear to be related to the two dry layers; see Table 6.7. Run B, having a weaker effective perturbation at cloud base due to stronger subcloud mixing, cannot surmount the first dry layer, whereas run A is stopped by the second and stronger dry layer. The cloud top in runs C and D seem to be influenced by the stable layer. Figure 6.5 suggests that wind speed within the cloud layer strongly influences cloud top height. In this particular experiment ambient wind in excess of 1 m/s evidently halts further cloud development. Run A, " with light winds at all levels, is limited by a dry layer rather than by wind. Run B, with 1-m/s winds at all levels, develops negligibly. The other two runs are intermediate. Wind speed below cloud base has lesser importance. Despite similar winds at cloud levels, run Dthas much Table 6.7. Effects of ambient wind Specified Input Ambient horizontal wind (m/s) Ground level 0.50 •J 1.00 0.25 0.50 Impulse level 0.50 1.00 0.29 0.54 Cloud base 0.50 1.00 0.61 0.84 Cloud top 0.50 1.00 0.88 1.05 10 km above ground 0.50 1.00 5.00 5.00 Run A Run B Run C Run D 50 min 55 min 60 min 50 min 55 min 60 min 50 min 35 min 60 min 50 min 55 min 60 min Model Results ' Cloud base12 900 900 900 950 950 1000 900 900 900 900 900 900 Cloud topa 2100 2100 1900 1050 1050 1050 1600 1500 1600 1400 1400 1400 Cloud width (m) 2300 2400 1700 400 300 300 2400*-' 26006 1600 1400 1600 1600 Liquid content Maximum (g/m3) 0.97 0.70 0.79 0.005 0.048 0.034 0.44 0.52 0.62 0.39 0.36 0.31 Height0 1800 1800 1400 1000 1000 1030 1150 L200 1250 1150 1150 1150 Cumulative condensation11 (kg) 1843 2127 2481 14.6 16.8 --18.1 1039 1 193 1361 441 531 603 Total content0 (kg) 558 4 67 441 1.0 1.1 0.7 186 L85 230 113 120 118 Temperature departure Maximum (K) 1.36 1.38 1.29 1.51 1.51 1.52 1.25 1 .28 1.31 1.56 1.52 1.49 Height13 300 300 325 300 300 300 303 100 300 300 300 300 Updraft Maximum (m/s) 2.9 2.9 3.0 c 2.0 2.0 2.0 2.9 2.9 3.0 3.0 3.0 Height® 550 550 550 450 450 450 590 >90 550 550 550 550 "Heights are in meters above mean sea level; ground level is taken as 150 m MSL. Cloud is in two separate parts. £ Slab thickness is assumed to be 1 m.. 156 greater growth than run B, probably because of lighter subcloud winds. On the other hand, the lighter subcloud winds of run C are outweighed by the lighter in-cloud winds of run A. Shear itself is also important. The presence of the term 3u/3z in (2.4) indicates greater turbulent mixing when there is shear; hence weaker cloud development. Moreover, the term 3T"*/3z (or 36/3z, as in the control), which is important directly above the level of maximum temperature departure (~300 m MSL in all runs), is likely to be stronger if shear causes cooler ambient air to move in above the heated air. It seems clear from the re- sults of this experiment that stronger ambient wind speed and stronger ambient wind shear both tend to inhibit vertical cloud development. Additional details of the results of the four runs are found in Table 6.7. Run C, having only slightly stronger wind at cloud base than run A and less than half the shear indicated by the hodograph, showed substantially less cloud development than run A. Its bubbling nature was pronounced; at both 50 and 55 min it was broken into two clouds separated by a gap of several hundred meters width. At 60 min the older bubble had completely dissipated, leaving a single cloud of much less total width but slightly increased total liquid content. In all cases the maximum temperature excess is located less than 100 m above the heat source and is relatively constant. Even in the most- vigorous case there is not enough latent heat released by condensation in the cloud to provide a higher excess there. The maximum updraft lies between the level of maximum temperature and the cloud base, and it tends to be constant. When bubbles occur, there is a secondary maximum updraft in a young bubble, later giving way to a downdraft. 6.5.3 Heat Flux Insufficient data were available to specify unequivocally the heat flux and flux density of the refinery source. There is some uncertainty about the total rate of heat,rejection and more about the ratio of latent heat to sensible heat. Most uncertain of all is the effective area of the heat, source, which is not the same as the area of the refinery. Therefore it is of interest to determine the sensitivity of the model 157 to these factors. This will not only permit adjustments for the uncer- tainty in a given case, but also will permit extrapolation to other cases with different parameters. The sensitivity of the model to changes in ratio of latent heat to sensible heat is demonstrated in another re- port (Koenig et al., 1977). Briefly, it was found that increasing the proportion of latent heat decreases the size and vigor of the resulting cloud. Changes in heat flux density will be considered here. The perturbation of run E had half the flux density of run A, but other conditions were identical. In this case no cloud appeared at all until 25 min (Fig. 6.6), and thereafter it remained very small. By 60 min the cloud was less than 300 m deep and only 650 m wide, with maximum liquid content barely over 0.1 g/m3. There were signs that the cloud was still growing, but at a very slow rate. There was no indication that further computation would have produced a cloud in any way com- parable to that of run A. At 35 min, the end of the organization period;' the cloud of run A contained 345 kg of liquid per meter of slab thick- ness, whereas in run E the total had reached only 8 kg by 60 min. The ORNL-DWG 78-8393 2 25 min 30 min 35 min 40 min E 1 a o z Z) Hsa t sour ce o 0.4 kg 0.3 kg 1.6 kg 3 kg rr n 4b min 50 min 55 min 60 min o cp Cs) <• 3 kg 6 kg 7 kg 8 kg" HEIGH T ABOV E G l HEIGH T ABOV E G l O — > r o c 2 3 I 2 3 42 3Q42 3 4 DISTANCE FROM UPWIND BOUNDARY (km) Fig. 6.6. Evolution of simulated cloud (run E) from 25 to 60 min of simulated time in terms of amount of condensate. Contour values are 0.01 and 0.1 g/m3- See caption to Fig. 6.1. 158 very modest cloud that resulted from halving the flux density, however, was still slightly stronger than that resulting from doubling the am- bient wind (run B). By contrast, run F, with double the flux density of run A, produced a very vigorous cloud; see Fig. 6.7. The organization period was only 25 min, by which time the simulated cloud was already slightly thicker than the cloud reported by Auer. The maximum updraft at this time (4.1 m/s at 650 m MSL) well matched that of Auer. Bubbling is very evident in run F. There is a well-developed dual structure at 35 min, but by 40 min the strong older (rightmost) bubble has vanished. During the same time the other bubble has grown so that the decrease in total water content is negligible. The speed with which the first bubble disappeared might be suspect, but the reason for this rapid collapse is clearly shown in the updrafts. At 30 miri"there was a double structure similar to that of Fig. 6.3 with one maximum between the heat source and the cloud base and another within the bubble at the upper right. However, at 35 min the second updraft maximum has vanished, and the region of the bubble at upper right is characterized by moderate downdrafts. In the series shown in Fig. 6.7, the maximum cloud development is reached at 45 min. Computation was terminated at 50 min because the disturbance had propagated upwind with such strength that outflow was indicated at the inflow boundary, a situation with which this version of the model could not cope. The field of flow at -40 min in run F is illustrated in Fig. 6.8. Downwind of the cloud at levels up to 2 km above the summit there is a decided circulation reminiscent of a mountain wave. A minor feature is the updraft that appears at the far right. There is the possibility" that this is a numerical anomaly related to the boundary conditions! Such an interpretation would be appropriate-near the upwind boundary, since the fixed inflow can distort nearby disturbances, especially if the horizontal wind departure is strongly negative. At the down- wind boundary, however, the vertical wind is free, and the horizontal wind near the boundary is very close to the ambient, so such distortions ORNL-DWG 78-8394 15 min 20 min 0 E Q -CO Z 4 o Heat source LU > o 40 min CD < Ul vo X — UJ X 1240 kg DISTANCE FROM UPWIND BOUNDARY (km) c Fig. 6.7. Evolution of simulated cloud (run F) from 15 to 50 mill of simulated time in terms of amount of condensate. Contour values are 0.01, 0.1, 0.5, 1.0, 1.5, and 2.0 g/m3. See caption to Pig. 6.1. 160 ORNL-DWG 78-8395 2 34 56-7 89 10 DISTANCE FROM UPWIND BOUNDARY (km) n Fig. 6.8. Field of flow at 40 min, run F. Streamline spacing has no significance. Cloud region is shaded. should be minimal. In this simulation there is indication of condensa- tion in the downwind updraft, which might suggest the generation of a secondary cloud several kilometers downwind of a strong source. This interpretation should be treated with caution, however. The heat flux density of run F is undoubtedly larger than the av- v- erage flux density over the actual refinery at Wood River, but it is Ji • smaller than that at local sources at the site and at some existing power generating facilities. The sensitivity of the model to heat flux density suggests that moderate increases in the amount of waste heat rejected to the atmosphere over a limited area could lead to significant increases in resulting cloudiness. 161 6.6 CONCLUSION These computations demonstrate that a two-dimensional field-of-flow cloud model can simulate with reasonable fidelity the clouds resulting from continuous.rejection to the atmosphere of heat (both sensible and • -- > latent) by an industrial facility such as a refinery or a power plant. When the ambient temperature structure, the heat flux density, and the ratio of latent to sensible heat were adjusted to the reported values of an actual case, the simulated cloud agreed with observation in most important respects. After an initial organization period, which is necessary to restore equilibrium following the imposition of a continuous heat source on an undisturbed flow, a quasi-steady state is established, which then lasts three quarters of an hour or more. This state is characterized by a cloud of realistic dimensions, temperature departure, and updrafts, but rather high water content, and by a bubbling in which the downdrafts on the periphery of the upper part of the cloud cause it to separate from the main body of the cloud as it moves downwind from the heat source, and eventually to dissipate. Meanwhile the main body of the cloud grows strong again and becomes ripe for the separation of another bubble. This behavior, which occurs despite constancy of heat input and ambient con- ditions, has also been noted in actual refinery-related clouds. It is more exaggerated in the simulation, however, probably because of the lack of a third dimension in the model, combined with limited transverse extent of the actual heat source. The simulations are overly sensitive to the strength and vertical shear of the ambient wind. It does not take much horizontal wind be- tween the level of the heat input and the convective condensation level, at which the cloud, if any, will form, to disperse the perturbation and inhibit cloud formation. Shear increases the eddy exchange coefficient, so it hastens dispersal of the perturbation by promoting mixing with the ambient air. At cloud levels such mixing promotes evaporation and > inhibits cloud growth.L The relative vigor of the four simulated clouds is closely related to wind speed below and within .the cloud layer. 162 Small amounts of ambient wind and shear seem to inhibit simulated cloud growth more than would be expected from observations of real clouds. This may result in part from the lack of resolution necessary to simulate the narrow, strongly convective columns originating at in- dividual cooling towers, and in part from the two-dimensionality of the » model- Eddy diffusion cannot be modeled in an entirely satisfactory way in two dimensions, and the model cannot take into account the transverse convergence that would be the normal result of introducing a heat source of finite dimension into a certain region of the]atmospherej . The model is also sensitive to heat flux density, but a halving of 1 that suppressed the cloud development less than $n increase of ambient wind from 0.5 to 1 m/s. A doubling of heat fluxsdensitI y led to a notable increase in vigor of the simulated cloudy but not to runaway growth. Despite-the uncertainties in determining the actual heat flux density of the refinery, we believe that it lies within these limits and that the model responds to these differences in a realistic way. This suggests that the model would be useful for studying the atmospheric response to an as yet unbuilt facility with larger heat flux density than existing ones. If the heat source is sufficiently strong, the resultant flow re- > sembles that over a heated island. Malkus (1963) showed that a street of clouds extending downwind from a heated island is a common occurrence. Although in the present instance tt\e source is much smaller, there is the suggestion of the formation of a secondary cloud several kilometers down- wind. A casual observer might not link such a cloud with its source, but the-model would show the connection clearly. This is,but a single experiment using a model that has several known< and probably some unknown deficiencies. Among them are the following: 1. Lack of variation in the transverse direction, which leads to stronger downdrafts and weaker updrafts than in nature. This probably, ^accentuates the bubbling. Moreover, the model cannot properly take into 0 Q" ' account the comparatively small transverse extent of the actual heat a source. " 4 ^ • ; 2. Inflexibility at the upwind boundary. The inability to allow a perturbationto develop outflow at the boundary which has inflow in the 163 undisturbed state can cause spurious influences to propagate into the area of interest if there is strong development. The downwind boundary does not suffer from this deficiency in these experiments. 3- Inadequate treatment of eddy diffusion. Although this model uses the formulations that are currently widely accepted, it is realized that problems still remain, including the difficulty in representing three-dimensional turbulence in two dimensions, uncertainties in evalu- ating the constants, and some remaining questions as to the role of atmospheric stability. 4. Inability to resolve individual heat sources. A lower limit on mesh length is imposed by computer capacity, and this limit is larger than what would be required to resolve the contributions of each cooling tower and other heat source individually. Hence a certain amount of plume merging and mixing must be assumed in order to arrive at a per- turbation that can be considered uniform over the volume represented by a single grid point. Hanna (1976) used the results of Briggs (1969) for this purpose. That approach is less applicable to a model such as ours, but we have done, much the same thing in a less formal way. Per- haps a feasible approach for future experimentation would be to develop a separate high-resolution model for the immediate source area to be run in tandem with the larger-scale model, provided sufficiently detailed input data could be assembled. / Despite these deficiencies the model is clearly capable of repro- ducing reasonably well the main characteristics of a cloud produced by an industrial heat source under a variety of atmospheric temperatures, humidities, and wind speeds and shears. Use of such a model can give insight into many of the processes that are too complex to be handled i ii a purely steady state model. In particular, it could be a useful tool in siting and planning for new facilities. 6.7 LIST OF SYMBOLS - 0 specific heat capacity of air at constant pressure longitudinal and transverse dimensions; of energy-emitting source 3 • • 0 " SL * 164 D^ = depth of air layer receiving energy from source F = eddy viscosity term F, = eddy diffusion of property g = gravitational acceleration E O , E u = flux of energy (sensible heat, latent heat) i, k = horizontal (longitudinal) and vertical unit vectors c K^ = eddy viscosity coefficient K, k^ = deformation constant O L = latent heat of vaporization q^ = mixing ratio of condensate q^ = mixing ratio of vapor s = transformed vertical coordinate T* = virtual temperature t = time - °'4 , w o u, w = horizontal and vertical components of wind v - wind vector . » J x, z = horizontal and vertical coordinates ; z = maximum height of' the domain max ° & a, a - coordinate transformation parameters 0 6x, 5z = horizontal and vertical grid spacing o ^ « - u n = transverse component, of vorticity ;0 = potential temperature ° Vv • ' 0 p = air density " * "\ 4>ol if) = stream function V = i — + k I- 2 ~ 3x ~ 3z 6.8 ACKNOWLEDGMENTS The work at Rand was done as a part of the Meteorological Effects of Thermal Energy Release (METER) program of the Energy Research and Development Administration under Contract E(04-3)-1191. The work of the Naval Environmental Prediction Research Facility was done under a general program in atmospheric modeling. The authors are grateful for several useful suggestions made by the reviewers. References Auer, A. H-, Jr., 1976: "Observation of an Industrial Cumulus," Journal of Applied Meteorology, Vol. 15, No. 4, pp. 406^413. Briggs, G. A., 1969: Plume Rise, U.S. Atomic Energy Commission, Division of Technical Information (Clearinghouse for Federal Scientific and Technical Information^ TID-25075), 81 pp. Deardorff, J. W., 1970: "A Numerical Study of Three-Dimensional Turbu- lent Channel Flow at Large Reynolds Numbers," Journal of Fluid Mechan- ics, Vol. 41, Part 2, pp. 453-480. o Hanna, S. R., 1976: "Comments on 'Observations of an Industrial Cumulus', Journal of Applied Meteorology, Vol. 15, No. 11, pp. 1232-1233. Hanna, S. R., and Franklin A. Gifford, 1975: "Meteorological"Effects" of Energy Dissipation at Large Power Parks," Bulletin of the American Meteorological Society, Vol., 56, No. 10, pp. 1069^-1076. 0 Hill, G. E., 1974: "Factors ,Controlling the Size and Spacing^of Cumulus Clouds as Revealed by Numerical Experiments," Journal!),of the Atmos- pheric Sciences, Vol. 31, No. 3, pp. 646-673. 0 Kessler, Edwin, 1969: "On the Distribution and Continuity of Water Sub- stance in Atmospheric Circulations," Meteorological Monographs, Vol." , 10, No. 32, 84 pp. " ~ // ° o Jf 3 Koenig, L. R.,,, and F. W. Murray, 1976: "Ice-Bearing Cumulus Cloud Evo- lution: Numerical Simulation and General Comparison Against Observa- tions," Journal of Applied Meteorology, Vol. 15, No. 7, pp. 747—762. 6 Koenig, L. R., F. W. Murray, and P. M. Tag, 1977: "Differences in Atmos- pheric Convection Caused by Waste Energy Rejected in the Forms of"Sen- sible and Latent0Heats," to be published- in Atmospheric Environment 166 Lilly, D. K., 1962: "On the Numerical Simulation of Buoyant Convection," Tellua, Vol. 14, No. 2, pp. 148-172. Lilly, D. K., 1967: "The Representation of (Small-scale Turbulence in Numerical Simulation Experiments," Proceedings of IBM Scientific Com- puting Symposium on Environmental Sciences, Thomas J. Watson Research Center, Yorktown Heights, New York, pp. 195—210. Malkus, J. S., 1963: "Tropical Rain Induced by a Small Natural Heat Source," Journal of Applied Meteorology,, Vol. 2, No. 5, pp. 547—556- Murray, F. W., 1970: "Numerical Models of a Tropical Cumulus Cloud with Bilateral and Axial Symmetry," Monthly Weather Review, Vol. 98, No. 1, pp. 14-28. Murray, F. W., Computations with the Rand Cloud Model for the HIPLEX Workshops,/June 1975, P-5473, The Rand Corporation, Santa Monica, California, 37 pp. Murray, F. W., and L. R. Koenig, 1972: "Numerical Experiments on the Relation Between Microphysics and Dynamics in Cumulus Convection," Monthly Weather Review, Vol. 100, No. 10, pp. 717-732. Rosmond, T. E., 1975: Subroutines for Direct Solution of Two-Dimensional Elliptic Equations, Computer Programming Note 22, Environmental Pre- diction Research Facility, Monterey, California, 39 pp. Rosmond, T. E., and F. D. Faulkner, 1976: "Direct Solution of Elliptic Equations by Block Cyclic Reduction and Factorization," Monthly Weather Review, Vol. 104, No. 5„ pp. 641—649. Schulman, E. E., 1970: "The Antarctic Circumpolar Current," Proceedings of the 1970 Summer Computer Simulation Conference, Denver, Colorado, " pp. 955-968. Silverman, B. A., D. A. Matthews, L. D. Nelson, H. D. Orville, F. J. Kopp, and R. D. Farley, 1976: "Comparison of Cloud Modlel Predictions: A Case Study Analysis of One- and Two-Dimensional Models," Preprints, International Conference on Cloud Physics, Boulder, Colorado, 26—30 " July 1976, pp. 343—348. (For further information contact Dr. Bernard Silverman, Division of Atmospheric Water Resources Management, Bureau of Reclamation, Denver, Colorado 80225.) y Soong, Su-Tzai, and Yoshimitsu Ogura, J-973: "A Comparison Between Axi- symmetric and Slab-Symmetric Cumulus Cloud Models," Journal of the Atmospheric Sciences, Vol. 30, No. 5, pp. 879-893. Squires, P., 1958: "Penetrative Downdrafts in Cumuli," Tellus, Vol. 10, e No. 3, pp.' 381-389. ~ ^ ' ^" Tag, P. M., 1977: A Numerical Simulation of 'Fog Dissipation Using Pas- i. sive Burner Lines, Ph.D. Dissertation, Pennsylvania State University, University Park, Pennsylvania, 149 pp. Tag, P. F. W. Murray, and L. R.. Koenig,' 1977: "Comparison of Sev- eral Methods of Parameterizing Sub-grid Turbulent Mixing in a Two- Dimensional Cloud Model,""in preparation. 167 Vogel, J. L., 1975: "Air Mass Storms of 10 August 1973," Studies of Selected Precipitation Cases from lletromex (Stanley A. Changnon and Richard G. Semonin, Editors), Illinois State Water Survey Report of Investigation 81, pp. 191—231. Warner, J., 1970: "On the Steady State One-Dimensional Models of Cumulus Convection," Journal of the Atmospheric Sciences, Vol. 27, No. 7, pp. 1035-1040. 168 7. DIFFERENCES IN ATMOSPHERIC CONVECTION CAUSED BY WASTE ENERGY REJECTED IN THE FORMS OF SENSIBLE AND LATENT HEATS L. R. Koenig* F. W. Murray* P. M. TagT 7..1 INTRODUCTION It is recognized that waste heat dissipated into the atmosphere from cooling towers can cause undesirable effects. Obscuration of the sun by plume condensate shadowing is common. Snowfall has been reported (Kramer et al., 1976), and speculations of larger scale effects have been sug- gested (for example, Hanna and Gifford, 1975). Wishing to reduce such effects to the extent practicable, designers have considered alternative cooling practices, one of the choices being between dry and evaporative cooling towers. This work is an attempt to assess some of the differ- ences between these two alternatives. When a plumt; rises from a cooling tower, it entrains some ambient air. As the mixture rises, it cools. The plume may dissipate by this diffusion, but if the cooling extends to the dew point (the lifting con- densation level of the mixture), water will condense, and the release of the latent heat will increase the buoyancy. If the additional buoyancy becomes organized, it might initiate the development of a convective cloud. Therefore, in the study of the interaction of a cooling tower plume with the environment, it is convenient to recognize two categories: (I) water vapor in the ambient air (not passing through the cooling tower) is caused to condense; and (II) no condensation occurs except of water vapor that has passed through the cooling tower. In category I the upward flux of condensate through some horizontal plane" downwind from the cooling tower generally will exceed the flux of r water vapor through the cooling tower. ; In category II the upward flux of condensate through any downwind plane will be less than the flux of 'n water vapor through the cooling tower. n * The Rand Corporation. ^Naval Environmental Prediction Research Facility. 169 to cause cloud formation through condensation of ambient -water vapor. The cloud need not appear to be directly attached to the cooling tower, nor must it have the characteristics of a "plume." It may have the form of a natural convective cloud. A rejuvenation or rebirth of a previously evaporated plume may occur downwind. The extent of the involvement of ambient air will depend on such factors as the variation with height of temperature, moisture, and winds, as well as on the plume characteristics. In the case of a moist, con- ditionally unstable atmosphere, it is possible that the perturbation caused by the cooling tower will be sufficiently great to initiate or "trigger" large convective clouds and thereby cause such related events as rain, lightning, hail, and damaging winds. In category II cases, where ambient vapor does not become condensed, the plume most often is attached to the tower and does not become rejuve~ nated as it travels downwind. The condensate generally is evaporating and emissions have a plumelike appearance. The extent of precipitation is limited by the flux of water vapor passing through the tower. A dry tower, rejecting only sensible heat, essentially precludes a visible plume associated with the second category of behavior and therefore the rather local "shadowing" and "drift" 'associated with wet towers. (How- ever, conceivably, as the plume rises and cools, moisture in the air fed into the tower could condensate and cause a category II effect.) Cate- gory I effects are not precluded by dry towers and both categories may o i occur with evaporative towers. As these towers are constructed to handle increasingly large heat loads, the occurrence of category I effects be- cq'fnfeS more Jijtejy, and cloud initiation becomes a more important environ- 'il&jlh'! P"F»cerh than the shadowing of the sun by the evaporating plume. ijiLi i^pQSe df this work was to examine the relative atmospheric effb. 154fcMli§ji(| fey Hfeiffc injection in the sensible and latent forms. This examination skoiuld provide sofpe notion regarding the relative merit of SJiti hy cba|4HH fcbHf^§ iifll i^t^r W ptaM^ie atmospheric effects. We have uSpji a tWB^ilOThsiofta}. field-of-flow model of atmospheric convec- HiH fid Simulate heat rejection. The model was initialized using heat tejkctioii Mux density and atmospheric structure that were knownto 170 exist at a Lime when a noma 1 ouri cloud formation was observed over a petro- leum refinery in Wood River, Illinois (Auer, 1976). The ability of the model to adequately simulate nature lias been tested in a number of ways; of particular relevance is the work reported by Murray et al. (1977), hereafter referred to as MKT, in which the model simulations were con- trasted with observations of Auer. 7.2 MODEL DESCRIPTION The model used is described in MKT. Briefly, it consists of a two- dimensional Boussinesq field-of-flow description of atmospheric thermo- hydrodynamics with provision For cloud formation and dissipation. The vorticity equation is used to find the motion field. Subgrid scale dif- fusion coefficients are functions of the deformation (motion) field and atmospheric stability. The cloud microphysics is based on Kessler's (1969) procedures; however, only the production of cloud condensate was allowed (that is, precipitation was excluded). The computation domain was 12,800 m in length and 10,000 m in height. Horizontal grid spacing was uniformly 200 m. In the vertical there were 50 nonuniformly spaced levels with mesh length continuously increasing from 29 ro1 at ground level to 612 m at the top. * The middle (25th) grid level was at 852 m, and a spacing of 200 m was,reached near 2000 m. The model was initialized with the same sounding used in MKT (Fig. 7.1). An initially uniform wind field of 0.5 m/s was specified. The total heat flux and flux density are identical in the three cases con- sidered here and are the same as the values used in the "control" in , MKT. The perturbation parameters representing heat rejection to the atmosphere were equivalent to a total of 1022 MW spread over a 196,000- m2 area (5.22 kW/m2). The heat was input as a continuous source at the adjacent 58- and 88-m levels at two consecutive grid points 2400 andi 2600 m from the upwind edge of the domain. The perturbation, in effect, was therefore 400 m long. Since it was input with zero initial momen- tum, vertical motion that developed was caused by internal forces such as the buoyancy due to the reduced" density of the perturbed air in con- trast to,, ambient air. " ORNL - DWG 78 -8412 Fig. 7.1. Composite sounding for Wood River, Illinois, forunoon, August 10, 1973. In case 1 all heat entered the atmosphere in the form of latent heat; in case II it was 50% latent and 50% sensible heat; and iivcase III, the perturbation was entirely sensible heat. ^ Two sets of three simulations were made. The sets were distinguished by different treatments of V-oans to calculate the component of the sub- u .'"Ji - grid scale eddy ''diffusion that is dependent on atmospheric stability. The two sets differed somewhat in vigor (thlx—is, Case la compared with ji case lb, etc.),,|but the ordering of results is the same in both cases. For brevity we tirill only discuss one set. 7.3 RESULTS The simulations used here were based on atmospheric cgnditions and o O total heat flux and flux density that existed during observed benign ( o cloudiness caused by heat rejection from a petroleum refinery. Although " ye are primarily interested in larger heat loads and overall effects, these simulations can be verified against actual observations,°thereby ensuring reasonable fidelity between theoretical1 simulations and nature'. ' o ' Tin- raea *.ure?i of the relativ -t? r* >\;ih«-r i< <-;:>-< : lift .-r i :.;••. Vinds he.»t ail I b<- the niz'- of the flo-id ; There In a tendency for the inn] .it i OHM to develop a quas i-steady state with small periodic var i at ion.H - The tine required to achieve a fully developed circulation i dependent upon the vig6r of the circula- tion. "Characteristic" behavior develops in 40 to *>Q min of simulation time; therefore, in Table 7.1 we compare some properties of the cloud development .Tt 60 min. Average values over the 50 to 60 min period are also included to smooth the data, sinrt- the simulations are nf>t completely in phase, the less vigorous circulations apparently lagging the more vigorous circulations. From Table 7.1, it can be seen that case I (all latent heat) develops a cloud that, is almost two orders of magnitude smaller with respect to total condensate than case III, all sensible heat. The cumulative condensation, a summing of the mass of water Vi-spor that has condensed since zero time, is also nearly two orders of nuignitude smaller in case I than in case 111. This parameter provides a measure of the vigor of the cloud-generating processes. Its value less the cloud condensate is the mass of cloud condensate that has evaporated. The kinetic energy of the circulation is significantly greater in case III than in case I, and the other"data — maximum cloud height, mixing ratio, vertical wind, and temperature departures from initial values — all point to the fact that the perturbation consisting solely of sensible heat has 6J more atmospheric impact than the perturbation consisting solely of re- jected latent heat. Case II, with equal amounts of sensible and latent heat, results in an effect that, by some Eeasures, more closely resembles the all-sensible-heat case rather than what coul^> be expected if the effect were linear with respect to the proportion of latent to sensible heat1. i ^ A more detailed look at the clouds developed in the three cases is shown in^Fig. 7.2. In comparison to t;he other cises, the cloud gene- " 'y }> Q • * crated from all latent heat rejection (case I) is much smaller, both in" U - r, (i vertical and horizontal extent. It is a single bubble cloud confined to the vicinity of the heat rejection site and does not develop appreciable Table 7.1. Comparison of the cases at tfO mln with selected 50- to bO-ixln average values shown in parentheses Maximum values ° ' 0 u Kinetic Cumulative Cloud c a energy in condensation condensate12 Mixing Height Vortical Temperature dom.iina (tons) (tons) ratio .if cloud wind departure (J) (g/kg) (m) (m/s) (K) 6 Case I 0.146 0.024 1 x io 0,14 70*3 0.96 0.28 6 (100% latent) p (0.02) (0.9 x 10 ) (0.13) (690) (0.95) (0.26) Case II ^ 7.22 1.59 1.96 x io7 1.36 1827 3. J'; 1 . 72 o (equal) (1.20) (1.9 x 107) (1.04) (1766) (1.17) (1 .61) Case III o 15l05.,: 1.736 3.8 x io7 1 .38 2064 4 . 39 2.22 (100% sensible) (2.40) (3.9 x 107) (1.60) (2064) (4.2 3) (2.46) a ^Considered as a slab 10,000 m in height, 12,800 m in length, and 2 m wide, ] 74 ORNL—DWG 78-8413 1 1 ! ct-jt i 1 ! ill latent) Ancient 0.5 ra \ Heat source. -— ] | ol 1I 1I I I I 0 1 2 3 4 5 Distance (kilometers I 1 1 1 Case II 1 (equal sensible Ambient wind anc latent J 1 «t 2 0.5 mi" 0 £ c <^p) & I £ 1 Heat sources \ I/>1 | 1 1 ] 2 3 Distance (kilometers) r> 1 1 1 Case III 1 (all sensible) Ambient wind 0.5 ms-1 Q 0 I 1 — O.OCEL Heat source^ (O | | 1 1 lot 3 Distance (kilometers) Fig. 7.2. Profile of clouds after 60 min of simulated time. Values are mixing ratio given in grams of condensate per kilogram of dry air. >3 1 17 3 (chat is, 1 p/kg or non-) quantities of condensate. Tin- cloud in case II is smaller than in ease 111 {all sensible heat). In case III two bubbles are distinguishable. The earlier, furthest downwind (to the right) has a stein leading into the second, younger cloud- Both clouds are being fed by the fixed perturbation, but it is apparent that the older cloud will soon break avray frora its initial source. The combined cloud ex- tends for a horizontal distance of about 2 km. The cloud in case II (equal amounts of sensible and latent heats) has the same "bubbling" characteristic as shown in case III; however, the case II cloud lags the more vigorous case III in phase. The circulation of the downwind cloud (see Fip. i«? «?uppro«?p in?. the vortical growth of the. plume and most of the rejected heat is being carried Into the downwind bubble; in a few more minutes the situation develops the same general configura- tion as shown in case III. As should be expected, the cloud produced by the perturbation having sensible heat only has a higher base than those in which latent heat (water vapor) is included. "rigure 7.3 shows the vertical component of the wind velocity at 60 min for the three cases. All latent heat minimizes the disturbance' to the wind field and all sensible heat maximizes this property. The tight gradients of wind velocity in cases II and III, including transitions 4 -ft ^ -) 0 from updrafts to downdrafts over short distances, indicat„ ' e that the air is turbulent. This turbulence extends over a larger volume in case III 0 . ,, t; than in case II, and although all velocities and gradients are modest, it would seem that with greater heat loads over an equal area (or with more unstable air), the turbulence produced when large proportions of sensible heat are discharged might become of concern for aircraft opera- tions. ih! ° The bubbling nature of the clouds is further shown in these data. 0 ' In case II the upward ascent of air from the source (labeled "A") is in- hibited by the downflow of air (labeled "C") associated with the evapo- 0 ' ' ration of tiioud condensate at the boundary of the downwind bubble (la- beled "B"). Th'ies evaporatio" .n cause' s negativs e temperatur, e departurea s and / consequently the production of relatively dense air that sinks and sup- N presses vertical development around the edge of the cloud. The pertur- bation, restricted in a directly upward ascent,, moves downwind and ORNL-DWG 78-Wt4 • Z- Ioi 2.. 3 4 (, 7 Z 3 4 S 6 Distant Uilomrters) Dutjnct ;nto^tff»t 3 4 5 Distinct (kiloiwtirj) Fig.; 7.3. Vertical wind speeds (m/sec) after 60 min of simulated time. Heavy contours are for 0 -and ±1 m/sec; "light contours are for ±0.1, ±0.5, +2, +3, and +4 m/sec. (A) center of emerging perturba- tion, (B) center of "downwind0cloud, (C) downward motion associated with high-density air caused by evapo- rative cooling, (D) downwind circulation associated with remnants of evaporated bubble. c.T.t inui-s tf feed The cloud bubble. In case III (similarly labeled), Che duvndraft C has less effect on the emerging perturbation. The main bubble i.s slightly higher and further downwind than in case II, and also the emerging density perturbation is greater. In case III there is a fairly well defined cell (labeled "D") that is the remnant of a previous bubble. Figure l.U contains streamlines showing the instantaneous wind fields at 60 min. Again, the benign nature of the all-latent-heat case is shown together with the relatively great vigor of the all-sensible-heat case. Also revealed are the bubbling nature of the convection, the residual o ^ circulation ot an evaporated ceil in case III, and the suppression of development of the younger cell in case II and its release in case III. 0) l.U DISCUSSION The results of the simulation indicate that an atmospheric pertuf- t" <1 bation such as that caused by heat rejected from cooling towers is more likely to Induce cloudiness and associated phenomena if the heat is re- jected in the form of sensible heat th^n if it were rejected as la^te-nt heat. An explanation lies in the nature of the buoyancy forces generated by the differing modes. a 0 The upward velocity o>f the emissions from the cooling _,tower will ^be a function of the change in density caused by the heat being rejected. A comparison of density differences resulting from sensible and latent t heat releases can be examined through the use of the gas law. - o . fr • Let nj be the moles of water vapor (molecular weight Mj = 18.02) in a given volume V0 of gas ^at temperature To and density p0, andjia be, the moles of dry air (molecular weight M2 = 28.966) i^i the same volume VoT^' Since . " ^ < ^ p_ V < =O n, RT + n„RT " (1)< ! n>0o 1 0 2 0 'i - a and 0 » ., OR:,L DWG 78 8415 i iO—i. i I- 4 -I— i-t -J—I—L—4- _ 5 Civ* 1 'ill !a'tr;1> 5 4 o _ 3 ^ tI I HJ-ta 4 I 6 7 A 9 10 11 '12 13 ijr.lanr.c l fcilotneters I 4' 5 6 7 8 9 10 11 1? 13 Distance (kilometers) J I I 1 1ITTTT Case It: (all sensible) ft.* ,4 5 6 7 8,9 10 11 12 13 Distance (kilometers) « , * 7.Streamlines showing the instantaneous wind fielddat 60 min~jofsimulated time. .(A) center of emerging perturbation, (B) center of downwind cloud, (C) downward unotioiV associated''with high-rdensity air caused by evaporative cooling, (D) downwind circulation associated remnants of evaporated bubble.0 ,, i- • " v' 0 tnen -i M + « M : J " :": ( 3) K1 At constant pressure pG the density can be changed ei tHe'c hv changing the temperature or the ratio uf the number of jnole* of\water ' ' V vapor to aolus of dry air. In the 1 irst ra'"e the density heconos n j Mj + n,M, (4) n. + n. k (i „ * l ^ and in the second (Uj + .'in^Mj + n?M, oc + h PL = <5) (n, + Zinjj + n2. RT0 O Subtracting (3) from (4) and"(5), njMJ + n2M2 AT (6) AP RT S>" n + T0 + &T % i, 0 a n2 An, (M2 - M,) RT (7) (ni + + A"l + n2J ii < ' " r IV" Consider a representative! case in which T "o= 300 K; "p = 1000 mb, n^ = 0.02 mole, and n2 = 1 molex These values^of n^ and n2 correspond to a mixing ratio (mass of water vapor per unit mass of dry air) of 0.01244 or a relative humidity of 54%. Let AT = ltK. In accordance with (6) this will-decrease the density by 3.8 x 10 3 kg/m . By equating .'(6) and (7) we find that the same decrease, in density could be effected:by evaporating 0.00916 'moie, of water vapor per mole of dry air; that is, by making Ant = 0.00916.., In terms of mixing ratio, this is the equivalent of3 evaporating 0.0057 kg of-water vapor ^per kg, of dry air , which would bring the relative humidity to 79%. Other values of the" parameters will.change,these figures, but not to the extent, of altering the general"conclusions that will b,e drawn. 180 c, o " These density changes will create buoyancy forces which tend to cause convective currents. Since the density changes are made equal, the effect on the initiation of convection should be substantially equal It now remains to evaluate, for each case, the amount of energy required to cause the equal density change. - The change in specific energy (energy per unit mass of dry air) brought about by a temperature change is ,, Ahg = cp AT ' • „ (8) a . ,,, 1 ' • » ' ' V.' ' ' ' ' " " and, that, caused b'y a change in water vapor,content is ' AhL = LM"TTAni ' " , (9) ; . " • - • • • ° • , ' ,>• where c is the specific heat capacity of dry air at constant pressure - ; p'r" • , 'i z® n" •> ' " " ' '" and L is the latent heat of evaporation (per unit mass) . App'lying (8); 'and-0(9)® with' a Is"K temperature rise and an additional 0.00916 mole of 'water vapor per mole'of<. air,, we find that the addition of sensible heat. 1 1 1 1 • &'"'/• 0 , , .} ' j, v \ • ' • " / Ah = (1005 J kg-1 K-1) x (1 K) ''..- 1005 J/kg (10) 1 1" k.//" " - ' . , ' „ , ' 5 f and for,the addition of latent heat 6 -1 A%= (2.436 x 10 j kg ) x (1) ^ x (0.00916) = 13,882 J/kg . (11) Th..e. - rati- o , i!s „» ' 0 U > :7 (a2) ; -V. v.'..:; This'indicates that t.for a given mass of air passing through, the cooling :J-towers^f it; requires 14 otijnes as much energy in the form of latent heatT,., as: it • does in sensible heat, to decrease the air density (increase the „ : '•^yuoy^n'cy^)s-by; a^ given'amount.• "•'"0^'the'i<^t|ier'|,hand,,-if the, total energy' 181 o o emission is the same in bothscases it would require 14 times as much " s? air to pass through a dry cooling tower rejecting only sensible heat as through an evaporative cooling device rejecting only latent heat in order (i • to achieve the same decrease in air density- The comparison can also be made in terms of equal addition of spe- cific energy. Suppose 13,882 J/kg is added to the air. If this is in terms of latent heat, it requires, as has been shown, that Ani = 0.00916. If it is in terms of sensible heatj (8) states that AT = 13.8 K. The ratio of (6) to (7) is o GijMj + n2M2)(na + An: + n£) AT :. ^ ~ » C13), ApL n2 Ani(M2 - Mj)(T0 + AT) a Substitution of.the numbers into (13) yields Ap/Ap .= 13.2. Thus; for equal increments of specific energy, sensible heat increases the buoyancy 13 times as much as latent- heat. „ - " ^ r, ' • " ° ° , ' • , ^Although the dependence of the characteristics of density perturba- tions (or any perturbation) on convective cloud 'development is not well established, generally the larger the perturbation, ^the more-likely that '• • ' • ' - i. • ' ' f ' o' '. .' ' " '. ^ ' . I i • ," , a.cloud will form and, grow to, a sizeesuch that it will be independent of the, initial or continuing perturbation (that is, the" flux of air and water vapor into'the cloud will be,much greater'than» the flux from the , cooling tower). Also; .the greater the* buoyancy gradient, the greater, the initial velocity of rise of the plume. Greater initial plume veloc- ities,twill cause, higher plume^rlse'even in, the'absence of cloud formation B (see, for example, Briggs^ 1969). The height of rise of the plume is ah important factor: if the entrained ambient air., is not raised to its „ . condensation level, the generation of large clouds that develop substan- :< > tially independently of their initiating.perturbation is precluded.! V " .<• Some numerical work of. Murray et al. (1977) shows^a strong dependence - of cloud"development.on the'size,of the perturbation. He also found:'that,< the rate of growth of asimulated cloud that was initiated by a narrow, ,, ^steep-gradient perturbation was greater 'than one induced by a wide, lower- gradient perturbation having a total energy content; five, times greater,. / ^Variations in thev rate ofJ. growtK1: may'be -of; some: importance if interaction;'; ' 182 between the emerging plume and the previous "bubble" being transported downwind is significant in regulating overall growth. § In this work (and also the related study reported in MKT), it is clear that the size of the cloud initiated by the perturbation is not a simple linear function of the size of the perturbation (measured in terms, of energy content). It' is dependent on the kind of perturbation, but this also is not a simple relationship, for in these experiments it is shown that? doubling the sensible heat content of the perturbation (case III vs case II) has relatively little effect on the cloud development. •y A - I ' This work shows the obvious — that such atmospheric properties as the vertical profile oflmoisture, temperature, and wind will dominate"the , , control of iconvective activity except^ for very local effects. A cumulus congestus cloud of moderate size (the smallest clouds of primary interest to this, work) has a volume of about 16, km3 (radius equal to 1 km^ height 5 km) and an average water content of about 1 g/m3. .This amounts to a total'water content of 16,000 tons. The water equivalent , to 2000 MW,heat rejected [by a 1000-MW(e) plant] is 0.8 ton/sec:1 If the . cooling tower plume feeds the formative stage of the=new cloud for«10,? , min,1 then it will supply 480 tons of,,,water or 3% of the total water con- tent. The remainder, , 97%,, is derived from entrained ambient air. , We u , i1 , - j> , r i ,, ' ^ 1 suspectiohalt energthaty atenterin this; gstage throug, exceph thet co,olinunder gunusua towerls circumstanceswould have littl, thee efaddi-'- ^1 1 - fec't. Vl , - „ 1'-•••/. ' ', '' • , , < # - , * . ° " , ^ f ' , , \ ;„ * 0 " " ' 'q , 1 ^ no' , - „ . " [l - " 0 •,,' ' „ •' ' •• ' ' '; D I , ~ , , 7.5 .CONCLUSIONS „ • •>'. '/-''a • ; , ' /.,- '•. ' • • ' ' ' " " , , ^q ; 1 . 1 v . ' • •' , i' , , ° - 11 'This twork indicates ,that atmospheric ef fects,such as the initiation or "triggering"^of cumulus clouds, caused by cooling towers would, pendent on the size and"gradient of the density perturbation created by, c - the emissions contained in the tower plume. The size and gradient can be minimized if latent heat rather than sensible heat is Rejected by?the ' towers. Latent heat releases can, be realized as sensible heat if ..the latent heat plume condenses,, but if this occurs downwind of the tower - ; after mixing with the environment has occurred, the density gradient will be reduced, and this should reduce overall effects. Thus, according - 183 (j to this work, while dry towers would eliminate shadowing and drift (cate- gory II effects) that commonly occur at wet cooling tower sites, their use would increase the likelihood of atmospheric effects in the form of convective cloud initiation and associated effects such as rain anomalies. A cooling system rejecting solely latent heat might be, ideal/'"ltH/ o mini- mize atmospheric effects (particularly if the plume could be made sub- V n : o f> " saturated), but such a device is not available to industry^ A cooling pond may be a close substitute. , u • u . ' * Since this has been a very limited study the conclusions must neces- 1} - " i » " • : ' sarily be tentative. The principal message to be conveyed,is that it is unwise to assume that more costly dry rather than wet cooling towers will prove to be more, acceptable from all environmental points of view^ i . v c- References o ''[ a 1' - Auer, A. Hl^ Jr., 1976: "Observations o'f^an Industrial CumulusJournall} of Applied Meteorology, Vol. t15, No. 4, pp. 406—413. Briggs; G. A.,1969: Plume Rise^, U.S. Atomic Energy Commission, Division of Technicalolnformation (Clearinghouse for^Federal Scientific^and Technical 8. A MATHEMATICAL MODEL OF DRIFT DEPOSITION FROM A BIFURCATED COOLING TOWER PLUME N.CCrJ. Chen Lincoln Jung • " ABSTRACT o Cooling tower drift deposition "modeling has been extended by including centrifugal force induced through plume bifurca- 6 tion in a crosswind as a mechanism for drift droplet removal from the plume. The model,fin its current state of develop- , ^ ment, is capable of predicting the trajectory of a single droplet from the stage of strong interaction with the vortex field soon after droplet emission at the tower top through s the stage of droplet evaporation in an unsaturated atmosphere after droplet breakaway from the plume. The computer program .developed from the mathematical formulation has been used'^to explore the dependency of the droplet trajectory on droplet size, vortex strength, point of droplet emission, drag co- " efficient, droplet efflux speed, and ambient conditions. A- w specific application to drift from a mechanical-draft cooling tower (for a wind "speed twice the efflux speech, a relative o humidity of 70%, and an initial droplet radius of 100 ym) showed the droplet to follow a helical trajectory within the . plume, with breakaway occurring at 2.5 tower diameters down- wind and ground impact of the droplet (reduced through evapo-. ration to 55 um radius) at 11 tower diameters. ,'• , O . .. ° •',> ° ' , •(' „_ *"" 1 11 , G 8.1 INTRODUCTION ' ' u u . u , o i: fa ' "'' • • ' " • " Meteorological effects associated with cooling tower plumes: include 5such phenomena as fog, icing, shadowing, and driftfl Drift deposition a has been a problem of particular'environmental concern because of its potential negative impact on structures and agriculture in the vicinity !, of the cooling tower. Since significant field;, data are lackingW , most ' - , V "ft ,H J L. ! , "i predictions,of drift deposition rely entirely^ on models of varying ade-, quacy. In an" earlier report, Chen* reviewed?: the state of the art of these models and demonstrated the neerJdS ' fo«r« bot. h ^furthe" r " analysicr s and im- proved field measurements. Accordingly,fthis, study considers the addi- tional mfechanism'foi; ^dropU^t removals^i-'om fk^lume due to the centrifugal force associated with plume bifurcation induced by windy conditions, t-' This situation, of possible significance in,determining drift deposition patte"rns,^has not been considered by prior investigators. • > ' 'ft' • -AP'-v: -'a. -'V "• - - .'v'A'": . , :tt J* „ . •185 v . . A Bifurcation occurs in plumes that are bent over either by a wind or by a temperature inversion. The bifurcated plume consists of two-line vortices of equal strength but opposite sense of ''rotation. The centrifu- gal force induced bv the vortex motion in a bifurcated plume provides an >1 0 additional mechanism for expelling drift droplets from a plume; previously considered drople1 t removal mechanism' O s are gravitational force and turbu- lent diffusion. < Although there is ample observational; evidence for the existence of o bifurcated plumes, the effects-of the centrifugal force on the ground f - deposition patterns of cooling tower drift have received no attention. Thislstudy is thus the first^systematic description of such effects. Specifically, this mathematical (.study proposes to (1) simulate a bifur- cated" plume and (2) use this model to determine both the importance of the centrifugal force on drift droplet removal and a more realistic breakaway point. The latter is perhaps the most critical element in drift deposition prediction in that results are most sensitive,-.to«the , '» « So particular model for breakaway assumed. „ , . ' O "' 3 ., Sr J' 0 Im the proposed model, the presence of the droplets is'assumed not to ' " • to affect the plume dynamics. Furthermore, the droplet< is assumed! to be in thermal equilibrium with the local environment for its entire life- time (i.e., from the emission to"impact). Thus, the energy transport between a droplet and its• surroundings can"be ignored. o Since the^potential effects of the bifurcation on" the droplet drift depositio n were first pointed out by Chen ' (1975), it ""has ! received o . , O o _ 1 • , • z , • , - ' " O -3 " W ' much attention by other researchers., Meyer has made photographs of naturaj-draf t» cooling tower 'plumes at Chalk Point,}> Maryland, =with such Cj 1, ' cleatime.r® detailHannas anthad Pikt fe eature haves, Aoals.V Oaoa vorteobtained'• x'' motio® pictures;n canap, oef see,a bifurcaten for thed, first Q mechanical-draft cooling ,tower plume at Oak Ridge Gaseous Diffusion Plant, Oak Ridge, Tennessee; from thesei' they have determined graphically <5 • a median tangential spe'ed of abou M t 2 m/sec at a downwina d distance of • ; ar • , " - - a ' ° * # , - «* - ° about 30 m. Finally, Smith-,deduced' a„twin vortex motion from?analysis «3 of his data on airborne sulfur dioxide concentration in smoke plumes. tf, ° « ' , "J » " • 0 '' // ' Section 8.2 gives a simple estimate showing that centrifugal force is comparable' to the gravity. force under' some circumstances.' Section 186 8.3 derives a simplified view of the mathematical model excluding plume >1 tl -" ,-t " ' V rise and growth and studies the sensitivity of droplet trajectory to " i-i n it ''j , changes in the individual variables (droplet emission position, vortex // , . ' O l> strength, and drag coefficient). Section 8.4 extends the simplified model to a'I more complicateI d one that includes plume rise and growth", % droplet evaporation, and ambient wind and presents a case study on the- trajectory of a dropletremitted from a mechau Jcal-draft cooling tower. Section 8.5 summarizeI s both the general and specific findings. 8.2 COMPARISON OF THE CENTRIFUGAL FORCE TO THE GRAVITATIONAL FORCE Under windy, humid, overcast conditions, bifurcation has been,ob- served in plumes from smokestacks and mechanical- and natural-draft cooling>towers. A vortex motion in a bent-over plume produces a centrifu- gal force that'might have some significance in removing droplets frpm " jthe plume and, hence, might affect the ground deposition rate and its pattern. To estimate the importance of this effect, the ratio of the centrifugal to the gravitational forces in bifurcated plumes from typical 1 a 1 ' • , . cooling towers and smokestacks was estimated and is presented in Table 1 8.1 for severa"l assume' d vorteR x angulav 2 r/ speeds.^ This ratio, .define'"* d as the rotating Froude number (F^ = /Rvg), depends not only directly on 0 jttie square of the angular speed but^also inverselyo on the tower size. Thus, for a given angular speed, the F^ ratio becomes increasingly im- portant as the tower diamet°er decreases. ' > if " ' ' « - 0 ' , , >1 It,, is noted from Table 8.1 that F covers a'wide rainge, from a mini- mum value<•> Oof 0.011 for a- cooling toweL. rv plume to'a maximum valueco•> f 15.36 for a smokestackoplume1 . yThe first comparison considered, v = w /4, is « >< , , • 0 r«' t 0 7 8 based on the conclusion of studies on smoke plumes vby Briggs ' that the IJ . O \ . Ci ' angular speed is one-fourth the rise rate of the thermal front. This'/ ; 1 ' 0 r, ''„ ° ' "'.[>''' 13 ' - s valueDis "yet to be proved for the' cooling tower plumes. For this case, it might" be reasonable to ignore, the centrifugal effects. However, when the ang;ular speed is taken to be equal to that of the efflux speedy the effects of the centrifugal iforce can no longer be-ignored. «Since°re- J 1 ' f • ° ' > « ° • ° •. ported measurements of thfe magnitud e of^thesP e secondary motions are cf<_ 0° 3t 187 " ' ft \ Table 8.1. Ratios of centrifugal and gravitational L. forces in bifurcated plumes from cooling „ towers and smokestacks ; .t c t1 Natural-draft Mechanical-draft Smokestack cooling tower cooling tower \ 0 /> Ji O i. v 6 Exit diameter D, (m) 60 i0t? \ 0 Vortex radius 15 , 2,5, R = D/4. (m) v o •• 1"' f Efflux velocity 5 "19 ' " 15 wo (m/sec) * V. Rotating Froude number - ,1 tt a - for various angular \ ^ speeds ° ^ & vfc = w0/4 0.011 0.26 0.96 v = w /2 0.044 1.04 ;; t 0 V84 e L; 1 v = w 0.176? t o . . 4.16 , '15.36 - <> ... - i - , 1 ; • I , - ', * - '' : V -H\ •• : limited,; and there are no field 'data available on ground deposition|rate 'near the tower, the magnitude of the centrifugal effect cannot be assessed, , with certainty. ,, v ' . 1 • ' M - & ' This simplifie• d estimatio- n ,has been base Ad on the plume >physica« ' « lSi , quan- ""tities near or at the tower exit. For vortex-motion at a distance away from.the tower mouth,othe angular speed at the plume edgevshould',:be Tde- ; k ' * • , ' , - , • :: i - * 0 , rived either by measurements or by calculations from th'b conservation of - „ - „ ..•.,. • , , ' " • f the angular momentum; .this^ is described in Section 8.4.^, 1 •• 1 > " " • - v>s„ ,, • if '•,, , ^ 0 . . . . - .,"„'- a • '* • , <• = » ; ., |» 8.3 DROPLET TRAJECTORIES IN AN UNBOUNDED FREE " ' I , VORTEX FIELD - A TWO-DIMENSIONAL CALCULATION V 0 - '0 ' <>* ' - I „' < The flow within a bifurcalted plume consists of a counter-rotating n vortex which is similar to a»doublet. This complicated structure is ofurthef sucrh plumecompoundeds can, bliey obtainethe plume-induced by referencd turbulencee to Briggs. -; 7Furthe' 8 r descriptio-;-.''• n M - rf. • h ' ' • • • ' ' . 11 ' • yj • ,' - In order .to simplify the calculations of a droplet trajectory,', it is-assumed that the „»two vortices separate as soon as the plume is bent ;; 188 I. .rf t>'V over and that each branch of the vortex pair acts" independently as a single plume. Furthermore, it is assumed that (1) the plume is stationary with n5wU.se, that is, the plume center line is a horizontal straight line; (2) the plume does not grow, so that the ci|}ss-sectional area nor- mal to the plume axis remains constant for each separated arm; (3) Che angular speed dq^jeases outward in proportion to the inverse of the radius as -a free vortex; (A) the droplet;' neither grows nor evaporates >' Q inside a plume; and (5) the vortex motion inside a> plume is simulated by a free vortexOof circular motion in an infinite domain. The variables which influence a droplet traiectory, such' as the droplet size, initial V5> . i' • •"'ft < pbintrofoemissioni vortex strength, and drag coefficient^ wherEthe drop- let is embedded in^an unbounded vortex field are examined separately. A droplet ^embedded in a circular,, vortex motion experiences two ex- ternal forces simultaneously — the .dragoforce arid the gravitational force. The drag fjorce on a droplet of radius r is proportional, to the droplet surface area, the drag coefficient (C^), and the square of the relative velocity between the droplet'and the surrounding air stream. Expressed ° " " ' ' ' ' " '''"ft, • 6 fin a generalized vector form,0the motion of the Qroplet is given byO , - ' (V s •" "- tn ® a • ^ dv o *5> i-v -y i«+ ->- -v , , m — == Trr^aCD|v - v|(V - v) + mg , to (1) <} t>' . " ' ' "" & i , ' 'O i • • - - . • , i. , . 0 11 ' 17 where m is tfre mass of the droplet, t is the time!', p is the air density, . 1 a 1 - " • i/ " i • -> . • , ', • ~ " ' - ,. ' ," V is the air velocityand v^is the droplet velocity. The first, term on the right-hand side of Eq. (1) RepresentvcpiraciiLSs the,.draLue ^uiag iulucforce, whilwuiice thmee , o ' , ' % ' , " ' ' /J < second term gives 1 the gravitationaona^Ll foijceforjee.. ^ ThiThiss iiss aa nonlineanonlinearr eqequatioi n and,thus necessitates a numerical solution. Some simple cases are 5 examined in the following subsections. e9 » 1 r 1 6 •' ., ' i • ; • ' ' '' a' o- ' J „ , ,, ,''• ', , t, P " * . _ , -, 8.3.1 "Equations'of Motion: "Cartesian Coordinates .',•"•• ^ ' ' E3 ^ is i xK,, „ , • „ - 1 • o ! ' 0 ' • • y TV' a Given a ^coerdinate system with the origin fixed at the vortex center let Xjiy, and z represent^, respectively , the downwind, crosswind, and: ^ .. vertical directions v^ith respect to this' origin (see Fig. 8.1). If it is then assumed that%he droplet acquires the wind speed5;in the x- . , v:, 7 I'dimensionalldirection immediately • .--J-y -upo n *:release ''! ,^ the* problem'pan' ^be'"''' '" treate 0 " d two •>_ : J. nj 0 ,„u v a V3 Fig. 8.1. Cartesian, coordinate system for a bifurcated plume. •s Origin, shown fixed at initial vortex center in right-hand member of»pair ' of. vortices 6f equal strength; x points positively .in downwind direction, "" • .y^toathe lef t, and« z\upward. , , . , , . .-" 1.. : • " ' ' * ° ' ' ^ " " " " , M . • : : v* o o ib Expressing Eq. (1) in the remaining' component^directions (y and z) ' ' " , "•>, , ' , , O , . _ , , ' . '(j " . thj3 droplet velocity is pbtaihed by integrating the set of equations, O, vv -. civ 3C p - v ,; r~——L~ — — v ' )V2 ,:,', • ' <§51 ' (2) «» 1 . dv - ., '• ; /—,, ( — TTPTS—' — > tf o 190 with '" (\ ix - o Vi ., a v " V = -K z/(y2 + z2) and V = K y/(y2 + z2) . Q Q v a y . « ,(•'' " rj ' Having v and v^, the equations dy/dt = v and dz/dt = vyield the0 droplet trajectory. In the above equations, v and v are droplet y * y 2 " and z component velocities, V and V^ are the corresponding y and z component vortex angulaJ r speeds,' and KnU is the- vortex strengtho „, which • a. is defined to be the product of the radius at the plume-jedge and the an- ? gular speed at the edge. o /? 0 This above formulatioa- •• n o-f • the equations" of motioft n '*can,the>'" ' n be' applie1 ' d to the prediction .of droplet traje->,"jr^ with the following1 values-for « ^constant1 s and initial condition s taken to1 be typical for a natfiral-draft j, • .j . o rt e, !i v I b ; J ® cooling towera : , . ^ ». /) ft « •• " • • 'I- , C » " = " 1 f ,J • • # °' ' • 0 . „1. droplet, radius, r = 100 vim,'. ° c » Q al.- drag coefficient, C = 0.44 (i.e., the flow field is assumed to be <° " 0 0 D e . ' - ' ... . c turbulent) , b, , , ' ' . ' Q "v 2 s ° 3. vortex ^strength, K0 = 75 m /sec, ' -ffi * 4. < initial droplet; position a£ the separated plume edge which X corresponds to the tower center, y - 15 m and z = 0$ it °5. initial cros^swind velocity, v = 0 and initial vertical velocity, q 1 v >,5>in/ sec.; ' - w ' • • . ' » ^ •• -' ' v eas ., . . , The calculated droplet^trajectory in a plane normalOto the plume ' tt,. ' 6. ' . -<,. - " - -" - ,J c, '.axis (i.e., the yz-plane) is?th'en shown by the theavveline in, Fig., 8.2 1 u ' ^ . i . P ••: rt ' with* ' the origin,c, as already noted, fixf2d at the vortex center. oThe ° f; f , j ' . . , ''' ' u -r 1 ' ^ . " .' ^ '<•": plume edge, (depicted rotating in a; clockwise"sense) is 15 m .vin radius, • ' . 192 „ ' ^ i Jf u 'edge (9.13 sec aft»r emission for thiS specific case), the droglet has completed almost three-quarters of a revolution; this position and time defines escape from the plume.' „ Since the plume is bent over, the5drop- - ° * " ' .. o ' let will have traveled the distance x = utit = 5y m/sec * 9.13 sec = 45.65 m, ^downwind of the tower by the time of Escape, for a wind speed assumed "'',,' , ' o - " equal to the. efflux speed. - 0 " , - 13 'J . . -J 8.3.2 Equations of Motion;^ Polar Coordinates ' , v ' ' ' ' W I ' a Since the vortex motion is assumed to be circular, it can>"Be con- venient to consider the problem in polar coordinates. In this format, ; the, convention is used Uiat the droplet radial velocity (v ) is positive . - , J.I! ' ( „- • ' ' , R '' •*( when pointing outward and the tangential velocity (vQ) when moving clock- wise. By appropriate transformations, the equations of motion [Eq, (2)] become, in R — !8 (radial-izangential) coordinates, 6 o 2 2 : dv_: , v0 ,0 3Cn p fK. 2vaK , , if R 6 D a o • 2 2 6' 0 ; . " Q v„ V + vft - + v„ L-—nr g sm 0 , ^ -;.dt;, V R „ 8r R f R ,, • oe - R ' "R , dV V V 3C 8-; 6 R , D ... , , R „ V 8r dR = , dt VR ' d6 = ^e .;, where the radial.,distance R is measured from the vortex center and "the, : ^angular displacement 9 ^s/measured" clockwiseifrom the point of emission -.which is* located^ one piume., radius above the tower.'"center,. ^ „ f ^Using the .same set.of constants as for the example of Section 813.1: f\ 2 • Kfl = 75 m /sec"{and^ ; = 0:44, -.'and. the same,, transformed initial values, J ni,;-'60 .,f ',6%'« ' 5 m/sec) / three ^trajectories ^wereV 4 : computed,;for , droplets of 10, 100, ; and 300 ym sraclius . . Results of thesie ;' 1 calculations are given "in Fig.'' 8.3 ;The* trajectory of , the lightest1 ;"yr;|\ :!• f^'l'i i (smallest) droplet (dashed line)p follows roost:closely the\plumei,Tjounda^y^,'-i'' 193 ORNL-DWG 77—7764A 60° 70° 80° Pi 90° 100° 110° 120° 130° 140° 310° 300° 290° 280°; 270°,; .--260° "250° "240° 230° 1 Fig. 8. 3. „ Three tdropl'ec trajectories are computed " based on a,polar- - 0, and at the end of 10 sec- (termination of calculation) is1 still within1' the ,plume.:v In contras,t , the heaviest (largest) droplet '(dotted,-line) , " * deviated'quickly from/the plume boundary -in the first ,7 sec and then p",' /.comes'back to the plume edge. For the droplet with 100 ym radius, the , trajectory J ([solid; line) is -r as expected somewhere in between the as- sumed two" extremes' on droplet size and^corresponds exactly with the one 194 \ generated independently from the formulation in Cartesiaii^c'oordinates (Fig. 8.2). The tick marks along the trajectories again indicate the time in seconds required for the droplet to reach that position. The times of escape, also shown in Fig. 8.3, are 9.13 and 9.16 sec after emission, respectively, for droplets of 100 and 300 ym radius. 8.3.3 Variation of the Droplet Emission Positions ^^ • p The cooling tower exit is of finite area. Hence, droplets are •> a r, 0 emitted over this area rather than from a single-point source. The dis- a tribution of „ droplet sizes and emissio. n location. s acros° s'".,'.' this area„ must' V , thus be described through a stochastic process. The effects can be il- lustrated, however, by developing the trajectories for a droplet of given size emitted at ' various location' s alon" ' g th' e plume boundary"-CJ ' . Result' s' > o fro* m• such a calculation for a droplet of 100 ym radius are given in Fig. 8.4. c. The assumed emission locations are listed in polar coordinates in Table 8.2 along with the appropriate radial and tangential velocities. All calculations presented in Fig. 8.4 were-terminated 10 sec after droplet emission. The droplet emitted at the tower center (labeled 1 ^an d included her•e , foi r reference, ). is of the sam" e characteristi, c as the ; I' f) ' , , one considered in Fig. 8.2. For emission at a point 60° below position 1 -•Or, ' • A 1 „ ': .. " n, V , , , . ' " " ' " - , . ' n " • O „ . • * tU Table 8.2. Points of emissions and the initial velocities yo 1 *, of a droplet at the edge of the plume in : an unbounded free vortex field oo Angle ,, Radius Radial velocity Angular velocity Case 0 (0) ,R (0) vR (0) vQ (0) (deg) (m) o (m/s) (m/s) , • . , ' V ' " ^ ' : ~~"7-. • 1 0 4' 15, .'. 0'',-' " Wft " "» ' c', ' ..»: ••t>." . - 1 • - .<•• » " 0 u , ' , -60 2 / Y : 15 -W0 sin 60° w0 cos 60° 3 - 'is,: i.„ . • . o.,,i.,V' • r 4. -120 15 jj—wQ sin 60° . cos : 60^' , " ; 5f -180 , 15',/„<; „ 0 , * , w , ' u 195 o ORNL-DWG 77—7785A 120° 130° 310° 300° 290° (1 280° . 270° 260° 250° 240° , 01 F^ig. Trajectories for a droplet with radius''of 100 Um are b calculated for various points^ of emission. . The'input/ data are the »samf=ft, as that of Fig. 8.2., »The initial .droplet : po.sitions and initialf,veloci- ; * ties are listed iii T&ble 8.2. Case 1 forthe droplet 'emitted at a height one initial plume radius above the®tower center is included for reference.?' 196 \\ a (labeled 2), the droplet exits the plume quickly and rises weakly. Out— \\ < ° \\ side the plume boundary, rotary motion continues to fall off rapidly and can be considered insignificant; entrainment has not bee'h considered in a this analysis. Similarly, drdplets emitted at 3 and 4 follow downward trajectories limited to even lower maximum rise within the plume. The droplet emitted at 5 never reenters the plume, since at this tangential location, the drag force and the gravitational force are coincidental. The interaction of the droplet with the adjacent plume after exiting is not considered. "8.3.4 Variation of the Vorte x Strength , .1. ' '• u ' p • a <•' 1 The vortex strength, as noted in Section 8.3-1, is defined a's the product of the radius at the plume edge and the angular speed at the -•= edge; thus, the vortex strength is defined as the circulation,,around the - plumi* e edge divided by a factor ,2ir. , In all previou. s calculations, the value of K. was taken to be 75 m2/sec (15 m x 5 m/sec). This subsection o 0 " • , i - 1 ./>•:, examines the effect of'vortex strength on droplet" trajectory with all other variables remaining unchanged. In.,Fig. 8,.5, a vortex of greater strength (15 m x 7 m/sec = 105 mz/sec) was assumed; trajectories are plotted for droplets of 10^, 100, and 300 ym radius emitted at a height one plume radius above the towerJ center. These ;t'raj ectories follow more closely the plume's; boundary "(see Fig. 8.3 for comparison) because the ' » ' " , - * » " ' ' ° * , „ « ' vortex is of sufficient strength to counteract the gravity force. The ,. times of escape are 8.3/c7.0, and 6.65 sec after.emission, respectively, - ' .A' « - 0f ' * , , , . ., for droplets oJ.VlOf 100,"and 300 ym radius. cWhen a weaken vortex was • . , » , '' • ,, " ' ' „ " 1 '' 2 "assumed (15 >m^/3,¥m/sec,• >= 45 ' m »/sec) • , some• - interestin• g° resultO s' •wer . . e "ob- served (Fig. 8t6)While the lighter,-droplets; (those with radius of 10 !ii and 100 ym)* followed* a curved path within the plume similai? to that , ; v , '' 1 ' " li' a "' ; o . • 1 " - . " ' , found in the previous cases,- deviations from the plume edge were,more-; v ' ' • • * ' ; <-v1 • ,,»..-, • • • because of the weaker vortex: For the heaviest droplet (radius of 300 .ym) , the vortex motion is to<2> weak to counteract the gravity; and the r? ' 'I, i , '' . " '' « . , Qf. • ^ 0 ' ' 1 ss'oon atter ,a snort initial cliir ' a . " ' . " 'cf* droplet falls back into the towerft£pon after ,a short initia1l climb.® The ODlets (10. and, 100 ym ifJHradius) remain inside the. plume light^'droplets (10. and, 100 ym if^radius) remain inside the. plume 10 sec«, "dS' "" " !' 1 ; ' - ,, -c • - 197 350° 340' 330° 320° 310° 300° 290° 280° " ' 270° 260° 250° 240° " 230° Fig. 8.5. Trajectories of three droplets with radii of 10 ym (dashed line), 100 ym (solid line),' and 300 ym (dotted line) are calculated with o the drag coefficient C_ = 0.44, with a. vortex strength K -.,= 105 m2/sec. after emission, whereas the heavy droplets (300 ym in radius) escape V r • ° %• >'. ' ' ° 3.23 sec after emission. 8; 3.5 Variation of the Drag Coefficient In the previous calculations, the0drag coefficient CQ was assumed 1 to be a constant. In reality, however, CD depends on the Reynolds,number (Re) based on the droplet diameter. More^specifically, Re = p | V €"- v|D/y, 198 ORNL-DWG 77—7767A 80? 90° 0 100° 110° 120° 130° 310° 300° ! 290° 280° 270° 260° 250° 240° 230° Q 0 -> - . " - „ Fig*. 8.6. Trajectories of three droplets with radii of 10 ym (dashed line), 100 ym (solid line), and 300 ym (dotted line) are cal- culated with the drag coefficient C^ = O.A'kand a vortex of weaker0 2 s strength K. = 45 m /sec. . , • 0 0 f r; where p, y, V, v, and, D are air deinsity," air viscosity, air velocity, droplet velocity, and droplet diameter, respectively. In this subsection, the, effect'of varying drag "coefficient on droplet trajectory is examined by calculating the Reynolds number at each^time.step in,the integration procedure... Thus.^for, each new droplet velocity,0 the corresponding drag $s .cri-. 199 coefficient is obtained and the process is.iterated. A computed tra- jectory for a droplet of radius 100 ym in a vortex' of strength 75 m2/se.c but with variable,C is shown in Fig. 8.7. A segment of the solution o - 51 showing the ^droplet positions and the values of C^ and Re attach time step is presented in Table 8.3. The afunctional relationship between C & D and Re adopted for the present calculation was chosen from an experiment 0 ORNL-DWG 77—7768A C 80° 90° 100° 110° 120° 130° 310o/ 300° 290° 280° 270° 260° 250° 240° 230° " o ' ' * » " •• ' - v' 8 • Fig. 8.7. A trajectory for a droplefe with radius of 100 ym is cal- culated- with the same input data is that of Fig. 8.2, except with a Table 8.3. A segment of the solution 25 for a variable drag force 0 Time Radius Angle Drag '-' ' Reynolds r t R 9 coefficient number (sec) (cm) (deg) eRe 4 CD 0.01 1500 0.18916 22.643 1.0599 0.1 1500.5 1.7741 5.8716 , 6.4694, 1 (( 1499.6 16.552 5.2851 „ 7.'7095;. 2 (/ 1480.3 33.358 5.3780 7.4890'- 3 1443.5 51.291 ° o 5.5029 , 7,. 2082 4 1392.8 71.130 5.6768 6.8436 5 1334.8 93.713 0 5.8789 * 6.4560-1 6 1281.8 119.70 5.9228 6.3764 7 v 1250.9 148.88 5.5705 7.0627 8 ^1254.7 179.48 " 5.1175 8.1351 9 1293.0 209.05 4.8594 8.8679 10 1356.3 235.78 4.7888 9.0868 a 11 ,. 1432.8 259.01 ; 4.8248 8.9740 12 ' 1512.2 278.93' 4.9024" " 8.7387 13 , 1587.1 ({ 296.11 4.9842 8.5010 , 14 1652.8 311.16 5.0545 8.3046 . 15 1706.6 324.65 A 5.1103 8.1542 337.04 16 * 1747.2 ( 0 5.1537 8.0401 17 <». 1774.0 348.71 o 5.1885° 7.9503 18 1786.9 360.0 5.(2188 7.8737 19 1785.9 371.18 5.2482 7.8005 20 • p % 382.55 « 5.2805 f 1771.3 K) 7.''' .• 7209 ft a on a sphere by curve fitting CD = 24/Re for Re = 2 (Laminar flow region) 0 6 CD = 18/(Re) - for 2 < Re = 1000 (Transition flow region) Cj" = 0.44 for 1000 < Re ^ 200,000 (Turbulent flow region). Since the calculated drag coefficients are larger than the constant value of Cn = 0.44 for a turbulent flow, the droplet considered (radius of: 100 ® g . ' ' 1 ' ' i 1 ' :;.( ' ' ' - ^ ym) is constrained to follow closer to the vortex motion. To illustrate^this-, effect," the calculation was extended in this case to more than 20 sec. lftWe observe that escape from the plume was de- • • ' •:».. : v ,.-: • • o , „..'.. • ,.„, • layed J.to somewhat more than 12 sgc vs the 9.13 sec calculated with con- stant C_ (Fig. 8.3). Further, even in" the weaker vortex field outside • ,'1 • " . ' • . - •••,'••••„: ' . Q " "I ' „ • JI , " '/ 201 y -- ' O Vs W * the plume s edge, the droplet continues «to follow a curved trajectory- Note that .as the droplet rises on its second revolution (i.e., beyond 18 sec), gravity begins to bring it back toward.the plume boundaryi While the calculation was terminated at 23.32 se^o , an extrapolated tra— jectory suggests the droplet, might reenter the plume. Jt is speculated that if turbulent diffusion had been included in the analyses, the drop- let would not follow this trajectory^ and would reenter the plume. 8.4 DROPLET TRAJECTORIES IN A BOUNDEDoFREE VORTEX WITH AN " AMBIENT WIND - A THREE-DIMENSIONAL CALCULATION In Section 8.3, the effects'of the physical variables on the drop- let trajectories were studied^ one&by one in a free vortex field' without a bound. This simplified calculation is extended to a more complicated ^ " 0 one which simulates astep closer to the real problem. First, the am-^ : bienCi t wind causingI' ^ the plume to bend over and? form a pair of vortices in a buoyant cooling/tower"plume is included; second,» the vortex motion —.a 1 SJ o u ' '' ' secondary motion induced by a bifurcated plume — is confined within a - plumeuin contrast ..fo an infinite vortex field discussed in the last sec- tion; third, "droplet evaporation in an unsaturated atmosphere is con- sidered; fourth, a rising and growing plume 'a stationary plume studied in°the last section is also accounted for. " It is assumed that each separate arm of thbee bifurcated plume rises . as a single plume obeying a 2/3 -law relation „.betweenprise and downwind; , w - distance from .the tower, grows as a cone following the empirical entrain- ment relation dR/dzu= 0.5in the bent-over rising stage, and rotates as a tube accordinV g to a' 1 fre. e vorteIi x law. °A, maximu. m bifurcation angla e- of about 25° hascbeen recently predicted by Khanderkar and Murty.10 How-, ever, for the present, the two arms of, the bifurcated plume are assumed „ to be parallel and thus the angle between them is ignored. The param- » eters R and z are plume radius and height, respectively, above initial " ' ° » f> 0' " vortex center at the tower exit. => .» f,When an Jambient wind with plume rise, and droplet ^'evaporation is in- 'cluded, the flow field^becomes so complicated that a,two-dimensional rep-: resentation of the droplet's trajectory is So^longer^possible. -The tra- jectory depends, amon"/$ o^hclr things*, on how fast the plume prises, how T fast the plume grows, how strong the vortex/rstrength is, what the size o" • - of the droplet is, where the droplet breaks caway from the plume, how strong the ambient wind is, and to what degree the droplet evaporates in v. an unsaturatedvatmosphere. The complication in the mathematical de- V) • scription of such a" rising and growing bifurcated plume with the inclu- sion of the droplet evaporation is considerable. Therefore, a computer program was written to facilitate a solution. The computer program is "if , . ii ,, ^ not discussed here. The Runge-Kutta method (IBM's routine DRKGS) was J? used to perform the numerical integration with careful attention given 1 0 to assure a proper match of the droplet position and velocity components c 6 • > O ' . in the transition region (division of a domain with a vortex motion from - « • - „ , • f - - a domain without a vortex mojtion, as well'a^va domain without evaporation 11 ififroml , a domain with evaporationO ) . Specifically^O ' on one side of the tran• - ^sition, a droplet of constant diameter is embedded in a vortex field, ' ' 41 W << while on the othe° r ' side • c8.4.1 Equations of Motion .. / ; * o „ ' ' • ' ' The system of equations of motion (expressed in Cartesian coordi- nates) describing droplet motion within the plume is as follows: c> '' 11 „ ' 0 '• , a • ' , 0 „ {t- w ! 1 . J. , ',1 0 O u 15 r >'" " L Conservation of momentum ' O o a o 0 x—component . o dv 3C p - / TT1 = V2 7T" - v > V( Nu-v >y2 + z-component /I dv 3C_ p ., fz D a ~ V(u ~ + ~ VJ2 + (V^Z-X)2 ~ 8 > (4c) dt 8r p^; tz ty tz Velocity x-component dx = (5 a) dt Vx ' cj v-component A- ^ it dz z-component dz "TT = v (5c) dt z o where ^ -o C = drag coefficient, e\V - , <5 « g = gravity acceleration, r ,= droplet' radius, <3 % t = time, ° 0 u = wind speed, 1! '1 o . "i.I, ' = angular speed at (x,y) in the y-component, p o V = angular speed at (x,y) in the z-component, tz , p 0 ^ - , : ' O ' .{I ' v = droplet speed in x-direction, ' , o • » - ' ~ o 0 n " • ' 1 m : v = droplet speed 1 in^y-direction,^ o y , , - , < ' , f , ^ .I O o ' v^ =odrof.ilet. speed in z-direction, ,, z %S » (V x = droplet downwind distance with respect to the, vortexs origin, ,, y> = droplet (Vlatera1 l distance wit 1 h respect to the vortex forigin, ' • "'''"- ,' ' ' ' ' '" - £ ' " - 'I'"' ' C\ ' " (*' t- ' ' '5 Vs ' " ' ' ' s 41 z = droplet vertical distance (with respect to , the svort^x origin, . / Y>- =-. air density, ,.-, •'•«'„ ' =>-'." * . " '" i., „ "> "'^.v jvvi- •:r.. 4 ! ' " ^V'.:-' 1 - v?... ; , „ Pn, = droplet density. •; V • •> • •' o Xs? •• !>o "C* 204 0.; In addition, the plume dynamics are described by the following set of equations: '-> >v' o . plume downwind distance C\ a a 3 1 z = 1.6 F'/ u" x ^ (7) • B I- o plume growth in rising stage 0 5 z % o (8) edge = o edge "b - - . plume centerline vertical velocity O l/a w =3.2 F x , >• o (9). ; K1 cp p • .£v"> ; G droplet-radial position with respect to the local vortex centere r ; R = vfy2 + (z - zo)2 , » (10) rt " '' f overall angular momentum conservation '0 Ko 1 ^edge^Vedge = y-componenttof the vortex velocity : J ... O-.i- -•>...,. • r o . > -V .'•=—— V •'='•, • ty < R t ' . ' ' - ' (12a) ;, z-cdinponent of the vortex velocity>} -i o V (','j. = V . : ' 4 v ' ' • . - ' " ' ^" ' : Q.-r 1 (.' -v c o - . • - - k o ' -r „ ^ q ' Tq = absolute temperature of the efflux,^" » " T = absolute temperature of -the ambient -air, o ° a " -- ( '.i - . , t = angular speed at radial R, ° _ v ( t)e(jge = angular cspeed at the vortex edge.t, » ^ =!"initial angular speed at the vortex edge, ^ w , = plume centerline vertical velocity. • a" r^ 0 cp 'o , • i ~ j^j! • Or wn =" efflux speed. „, - ' * '' v >1 - - '' Pi , :• 0 • Q ." o , ii" • " ; 8.4.2 Calculationa• l Procedure^• „ .? , „ ' , B ' o"V 1 ; T , , „ », v '" - v- • :f , - « ' ' 1 " • a ' " = 0 The calculation of the droplet trajectory is broken into two regions: : (I . ' '1 ".'W I , '•*"'. rijU- - . v,?'i oone foj the droplet inside th4; plume and the other for the droplet outside < , I ' f i ' c • , «• , " , 1 the plume. • c" , „ , ,„ - • ., 1 ° When the droplet is inside the plume, its ^trajectoru J y is calculated! ,, . i, o by integrating th''>> o humidity; details of this dependency are not discussed here. The inte- gration is continued until the droplet reaches the ground. For each time step, when the droplet JLs inside the plume, the pro- gram prints out the droplet position and velocity, the plume radius (with a ' respect to the local vortex center) and rise,,,the Reynolds number, cor- « •• o responding drag coefficient, and the vortex angular rpeed in tha e y- and z-components- Similarly, for each time step, wht-n the droplet is outside the plume, the program prints out the droplet position, diameter, velocity and salt concentration. 1 ^ i ,, Q = * 8.4.3 Results" Although a large value.of the rotating Froude number F (see Table Qi 1 " V 8.1) is associated with smokestack plumes (drift1(may be a problem when a wet scrubber system is used), the ground deposition might be reduced be- cause of the tall stack height. On the other hand, a medium value of the rotating Froude number is found ifor those mechanical-draft cooling tower, plumes; the ground deposition might be enhanced near, the tower because^of the lower tower height. With this in mind, a case study for ; a mechanical-draft-cooling'tower drif t is performed. ,, , " Figure 8.8 presents results of a calculation for a mechanical-, draftfcooling tower using the,input data of Table 8.4 and the following Table 8.4. Inputs parameters for a mechanical-draft ,„• . "" cooling tower' • _ -v Tower height, m '',''„ : - ' •""'&, ' , ' 17'?.* 1 ' "• Q Ambient air saturation mixing ratio, g/g 2.38 x 10"2 e Wind speed,^ m/sec 'V * i> 7 ",'"'<'' o- ,, I. ,» 20 „'; ' Ambient relative humidity, %s « ,,70 Ambient temperature, K . '-','rty"v.i , ORNL-DWG 77—7769R ,„ ? Fig. 8.8. A.helical trajectory of a 100-Um.radius droplet is pro- jected on" the yz-plane with a time progress intseconds after!emissions- Projections of the plume cross section at the'yz-plane at several time steps are shown by a series of circles. For reference, the outline of Sthe mechanical-draft cooling tower isshown by the dashed lines. 208 initial conditions: x = 0 m, y = 2.5 m, z = 0 m, i) v = 0 m/sec, " x « v = 10 m/sec. z f> ' . • Projections of the plume cross section on the yz-plane at several time steps are shown by a series of circles; plume centers are designated by the time increments t = 0, t =0.5, t = 1 sec, etc. For reference, the outline of the mechanical-draft cooling tower is shown by the dashed " lines in Fig. 8.8. A droplet of 100 ym radius emitted at a height of A '' one vortex radius above the tower top center completes almost half of a revolution with respect to the initial vortex centeT by the time it leaves the plume at 1.37 sec. At this time (about 2, 1/2 tower diameters v 1 1 0 ' ' " downstream from thecsource), the droplet is free from the influence of the vortex motion and begins toevaporate under free-fall conditions. Since there is no vortex motion, the y-displacement remains constant in 5 vthis portion of,., the fall path. The droplet finally hits the ground at0 54.77 sec after emission and at a downwind distance of about ll°tower • .• ' , . . , . 1 , , • diameters. (Note that inclusion of the ambient wind engenders a helical droplet trajectory.) The diameter" of the1'droplet cat this time is re— u" duced to a radius of 55 ym, about half0the original size, and the drop- let is fallin' ' g at asi velocit' y o'f about, 0.36 , m/se" c according;,t\ " o thie, compu- - - tation. The calculated fall velocity of 0.36 m/sec is a little bit higher than that of the fall velocity of 0.3 m/sec of the same size pre- dicted by Hosier et al.1For this calculation, the drag coefficient was chosen to be CQ = 0.44 when the droplet is inside the plume but variablei »" when *th '' e " drople' ''' * „ t is outsid- :i, e the •plume ;V. t a '' „' ' - ' ' " ,'' r, " "" : ' ! ; / V ""S • '.,*":*<, & ' - 8.5 -SUMMARY ' ^ ' u •'. " "< ,y; ' A mathematical model and a "computer program have been.developed. ' iThe model takes into account the effects of the centrifugal force, 209 which has.been ignored in all existing deposition models that predict the droplet trajectory. The model assumes that each separate arm of a bifurcated plume rises as a single plume obeying a 2/3 law relation Q between rise and downwind distance from the tower, grows as a cone fol- lowing the empirical entrainment relation dR/dz = 0.5 in the bent^over rising stage, and rotates as a tube according to a free vortex law. t> When a plume is bifurcated, the model predicts that a droplet will follow a helical trajectory. " The shapes of the trajectory depend on droplet size, vortex strength, point of emission, drag coefficient:, and It')' ambient conditions. a „ When the ambient wind and droplet evaporation are ignored and the droplet is embedded in an unbounded vortex field, the model predicts " " ' 41 :u that (1) the smaller the droplet, the closer it" follows the vortex mo- 1 - ^ D -I tions; (2) the larger the drag coefficient, the longer the droplet is retained inside the plume; andc(3) for a heavier droplet in a weak vor- tex, the force of gravity dominates the centrifugal force. ,; ' When the ambient wind and droplet evaporation are included and the droplet is embedded in a bounded vortex field, the model predicts a helical trajectory. For the mechanical-draft cooling tower'studied, the droplet in a bent-over rising plume breaks away from the plume at a distance down- wind of about 2.5 tower diameters and hits the ground at a distance downy wind'of.about 11 tower diameters. ,The droplet, has been displaced'laterally ,mor 1 ' e• •tha ! 'n hal. f1 a a ,towe - r. adiameter^t • • o the righ' t, o. f the initia11 l "point y1 o' f" emis" , • -i. - s'ion,' due to the vortex motion. This lateral .displacement was first pre- 1 dieted by the model. " 0 The model is specifically designed for a single droplet; however, s it can be generalized to compute the ground deposition rate if the dis- tributio>n" o,f droplei> . t siz. e at the tower , mout' CI-' i- hi> is available. . - > " > , " Because the available measurements on,the vortex angular speed,of t a bifurcated plume — a necessary input condition for the computer pro- '.<•', gram — are limited, the results presented here should be viewed as pre- : liminary. ^Nevertheless, the model's description of a helicair trajectory in a vortex^field with anjamliient wind is encouraging. ,, > „ 210 References o N.C.J. Chen, Progress Report for the Atmospheric Effects of Nuclear Energy Centers Program (AENEC), presented for the AENEC Techn/Jal SteeringjCommittee, U.S. Energy Research and Development Admi'nis- trationf'VJashington, DC, December 1975. N.C.J. Chen, A Review of Cooling Tower Drift Deposition Models, URNL/TM-5357 (1977). J. H. Meyer, private communication. S. R. Hanna and M. Pike, Secondary Motions in a Cooling Tower Plume, Progress Report of Atmospheric Turbulence and Diffusion Laboratory, NOAA, Oak Ridge^' Tennessee (1976). T. Smith, "Notes on Bifurcated Plumes," Meteorological Research, Incorporated, 1976. J. P. Catchpole and G. Fulford, "Dimensionless Groups," Ind. Eng. Chem. 58(3), 46 (1966). G. A. Briggs, A Simple Model for Bent-Over Plume Rise, Atmospheric Turbulence and Diffusion Laboratory, NOAA, Oak Ridge, Tennessee' (1970). D. A. Haugen, ed., "Lectures on Air Pollution and Environmental Im- pact Analyses," American Meteorological Society, Boston, 1975. ^ n. O ... H. Schlichting, Boundary Layer Theory, "translated by Jl Kestin, « Q McGraw-Hill, New York, 1968. M. L. Khandekar and T. S. Murty, "A Note on Bifurcation of Buoyant Bent-Over Chimney,, Plumes," Atmos. Environ. 9, 759 (1975). , C. Hosier, J. Pena, and R. Pena, "Determination of Salt Depositiqn 0 Rates from Drift from Evaporative Cooling Towers," Trans. ASME3 Ser. 'AJ. Eng.'Power 96(3), 283 (1974). ^ , ' ,, PHYSICAL MODELING 1206 <5^ 9. PLUMES FROM ONE AND TWO COOLING TOWERS j! ii " L. D. Kannberg* Yasuo Onisbi* 'j| I 9.1 INTRODUCTION 'j Use of mechanical- and natural-draft cooling towers is expanding in It the United States in response tp pressures for better resource allocation il and preservation. Specifically, increasing public and regulatory concern over the effects of the intake and discharge of large volumes of cooling Cs * water has encouraged electric utilities to accept cooling towers as the |j primary method of removing condenser waste heat even though op,ce-through I cooling is considerably less expensive. Other factors encouraging the li ~ use of cooling towers include small water supply and consumption rates, reduction in land requirements (compared to cooling ponds or lakes), and operational flexibilitiyf^^The growing demand for electric energy should ; also add to the increase of\&ooling tower use. j| ~ - il For economic and technical reasons, future electric generating sta- tions will be larger than those currently in use. Because there is roughly'2 MW of waste h2at produced for every megawatt of electricity generated, waste heat disposal becomes a significant factor iJ] the de- L' . (b * ii • " sign of these large generating facilities, particularly with respect to • " • • . i| siting of the station and the towers atcthe station. Economics usually tl ' ' r" sj dictate that the cooling towers be located as close to the generating unit as possible, whereas environmental and cooling tower operational , • j[. <~ considerations encourage widely spaced towers. This opposition of in- terests requires that station designers be capable of assessing the rela- tive impacts of various siting and operational configurations. I| It is, therefore important to understand both the environmental and operational O , 1 • ' 1 " ' characteristics of cooling towers, especially multiple towers, y This " - " . y, «' 1 1 ' ... chapter presents experimental data concerning the temperatures of down- wind plumes and of air drawn into the tower for stations having one or" two mechanical-draft cooling towers in flat terrain.63;! » o G>", " , ' j " « - } - . ',1 II' 0 0 i • - o i „ ^pBattelle Pacific Northwest Laboratories, Richland, Wash. I 214 Parameters (investigated include the effects on plume mixing and re- circulation of wind| speeds, Froude numbers (discharge density and velocity) orientation (relative to wind direction), and spacing between two cooling towers. Mechanical-draft cooling towers similar to those now in opera- tion at the Centralia Power Plant in southwestern Washington were used as prototypes for physical modelsT Simulations employing the physical ^models were made in a glass-walled hydraulic flum|(^ The data obtained from these physical model simulations are presented first for a single tower and then for two towers in series^. Comparisons are also made be- tween data from this study and data from other studies and with formula- ° tions by Briggs„ . . 1»2 ,, ' %v - 9.2 EXPERIMENTAL DESIGN AND EQUIPMENT The simulation of cooling towers in a hydraulic flume is desirable - o because of the special scaling characteristics of water. Since water has a kinematic viscosity nearly 20 times lower than air at standard temperaturQ e and pressure, the length scaling for Reynolds number and, more importantly, for turbulence simulation is improved by ar^order^of magnitude,in water. This is not particularly important ifl high air speedsocan be used; however, when Fro^ide number similarity is also re-% quired, such high velocities are not permissible. 0 The glass-walled hydraulic flume used for ther experiments is 4 ft " S ' ' a, " n ' V wide,, 4 ft deep, and 4Q, ft long. Thev,flow system can circulate up to . " '," It " " ' "JT0 cfs at water depths as. low as 1.5'ft. The facilities are ^also equipped =with separate pumps«for heated discharge and suction from test structures within the flume. Water for the plumes is heate°d by,j a power-controlled 255-kW heater. !j • „ The cooling towers were constructed at a length scale of 250:1,,/ Prototype and model tower characteristics are given in Table 9.1. ,, Warm water was discharged frrpi the tower stacks to simulate the .a " , 1 1 ~ 1'1 J. tz^-- u ' , warm moist plume from the prototypic .cooling tower. At the same time '„ 1 •-' , 1 , o • " a water was being sucked from the tower through the towe'r cell factes rat * 1 ' ' , 1 ' " ' f^, <5- t> , , . the same jrlow rate as the discharge in order to simulate the. induced Q flow into the tower and out of' the stacks that occurs in the prototype 215 Table 9.1. Prototype and model parameters Paramet er/tower Prototype Model (3 r - M No. of ceftlsIK 6 6 * Tower length 241 ft 11.5 in. Cell width top/bottom 75 ft/55.5 ft 3.6 in./2.66 in. Packing height 4,7 ft 4 in. 2.25 in. Total tower height 65 ft 4 in. 3.15 in. Air flow 9,444,000 cfm 13.6 gpm'(water) Stack diameter 26 £tjf\ 1.25 in. Average stack velocity 32.6 fps 0.410 fps Froude number*2 At design point. to measurements, by the same thermistors at an unaffected upwind (1 station. All measurements were made with an analog-to-digital' converter with a multiplexer0controlled by a PDP 11/10 computer system. This enabled rapid data acquisition and analysis with analytic and graphic computer techniques' . '- • . ' • ' • ' * ' • • -4 . ^f'•-..', ? The matrix of measurement parameters is shown in Table 9.2. The = bulk of the tests were conducted to investigate trends in" plume tempera^ tures and recirculation for variations in Froude number, wind speed orientation, and spacing. This pattern allows, the maximum use of infor- mation obtainable from a moderate experimental effort. B - 216 li Table 9.2. Experimental parameter matrix o e 0 n Wind speed (fps)<* Number Froude Orientation® Spacing^ of toweij number*2 3 10 20 35 50 10 3.4 1.6 0.93 0.57 1 C NA 2.4 X X 0 3.2 X X •< 3.5 X X X X X 5.9 „ v X " X 0 0 X X o 9.0 ] x , X Ox X X I <. NA 3.5 11 2 C 6.25 * 3.8 X 10.0 X 2.6 6' 3.0 X o ./ 3.9 7.8 X X ,-X ° X 6'. 4 X .. !' ' 11.8 X 20.0 3.0 X °C — wind perpendicular to major axis to tower. '' I — wind in line of major axis of tower. ^ ' -j b * ^ Distance downwind to second tower in stack diameters, center to centerline. c , . ^ " o Nominal values. = ^Prototype. „ , ^ K =,discharge velocity divided by wind speed . •o ' , * a a 1 * 9.3 EXPERIMENTAL RESULTS o » Cooling tower stack discharges into moderate winds display complex three-dimensional characteristics as evidence of the complex interplay 0 of dynamic forces on the plume. Because this study was basically con- cerned with the gross features of the plume and primarily1* with determining the basic trends of behaviorthe detailed structure of the plume wais not r ^ ' ^ 1 closely examined.,. Instead, the anal/ysir s was confined to a comparison of the maximum plume temperature and trajectory as a function of downwind 1 a 1 1 ' ' ' ' distance for one and two towers. ; 11 L >;> Ov lJ' 1 h o " ° ' ' - . , • '•>'*' • ' 1 • ,T. : , •1 , -a •1, —3 ; .-T. " . - 1 •:<•'/, 9.3.1 A Single Tower: in Crossflow Wind , , . " '' - , ' ' ''.--'M- ' ' -'• ,, , ; Wind affects the plume primarily in two ways: ! (1).the plume is1 bent over more, rapidly, and^is sometimes subjected to, slightly increased mixing 217 in the downstream direction, often with a distinct twin vortex structure; and (2) the cooling tower wake enhances mixing^in the bottom of the plume and draws the plume lower because of the low-pressure zone created there. As an illustration cf the effect of wind on mixing, several tempera- ture plots for different wind speeds are shown in Fig. 9.1 in nondimen- sional form. In the figure, AT is the difference between the temperature m >t, at a measured point and ambient temperature; ATq is the temperature dif- ference between the cooling tower effluent exit temperature and the am- CJ * bient; K is defined as the ratjio of cooling tower effluent exit velocity O ' Q, ' V. to wind velocitJy V ; F^ denotes the.)densimetric I^roude number of the j a' D ^sw cooling tower effluent; and X is the downstream horizontal distance and D is stack diameter. ' o o si Although these data show no obvious trends, mixing appears to de- crease and then increase as wind speed increases; K = 1.6 provides minimum ORNL-DWG 78-8312 1.0 0.8 6 0.6 o 0.4 ' & 0 " 1 0.2 o E " m < o •e. to UJ sfJ41' a: • o C n 0.1 » ocLU a. .08 K ££ ie O ,06i „o 9.70 Vm) 3.73 o 3.39 3.49 .04 A 1.64 3.57 • 0.95 3.61 0 0.67 3.58 .02 * KENNEDY AND <3 FORDYCE (3) „ b 1.02 4.0 .01 .;..» 1 8 10 20 40 60 80 100 HORIZONTAL Dl STANCE - X/D , Fig. 9.1. ; Variation of excess temperature with, wind speed as a.: function of downwind' distance. 4= ^ 0 % " / - - ,•"•••,< *:<:! 218 mixing.1 Another interesting feature of this'^ plot is the temperature de- pression between 4 and 10 diameters downwind for the K = 3.4 case. This gives evidence to the potential for wake mixing for certain K values. Wake mixing appears to have the greatest? effect on plume temperatures for the K = 3.4 case, although some effec.^is also observed for others. The results of a previous experimental study conducted by Kennedy and Fordyce3 are given^in the figure.* The data compare reasonably well. The variation of plume trajectory with wind speeid is also of con- siderable cimportance> in evaluating atmospheric effects of warm vapor w CI ' -if. plumes. Figure 9.2 shows the trajectories of plumes whose temperatures were plotted in Fig. 9.1. The trajectories were selected to^be down- wind elevations of the warmest points of the plume and therefore do not necessarily represent the geometric median of the plume or the vertical energy centroid. In Fig. 9.2, the wind benSs th«J plume ove r rapidly for0 small K values. In the high wind cases ao f K < 1," the plum. e appears to Data were estimated from Fig. 8 of" Ref> 3. CP ORNL-DWG 70-8313 25 £ K _fD_ b O 0 / ' O 9.70 3.73 20 O 3.39 3.49 S ?3 A 1.64 3.57 Q 0.95 3.61 e is O 0.67 3.58 '' -ft5'1' o KENNEDY AND CO c FORDYCE (3) UJ g 10 1.02 4.0 £' \ t/> t Q 5 .j o Hi , o ° Oo° ce LU > o A* A •A • • • o o „ p _L J_ _J 0..-.V- . Fig. 9.2. Variation of trajectory with wind speed. V 3 1. -i.e.' 219 rise and then drop „.irito the low-pressure wake region. While the dynamic pressure forces may,?be one contributor to this apparent behavior, it" should be remembered—chat: the temperature patterns were-.,used to make /•i " >, u ° this determination. It would be natural for the temperature pattern to be skewed down for these very--flat plumes since-the mixing, is retarde1 d a 0 , e _ • by the bottom of the flume (or the ground surface in the prototype).;, o " Ci " V' ' ^ Another factor in "the analysis of plume behavior is recirculation. Moist' warm air from the discharge stacks of the cooling tower is sometimes — Q , drawn into the tower on the downwindtside. Such recirculation of dis- . 'V £ •) • ^ charged airoinhibits efficient operation of the cooling tower and may ultimately lead to a'warmer, more humid plume.In , the cooling tover' r"7777 simulationsthe temperatures of fluid both entering,.and discharging from ^ thet, tower .were measured to obtain an;approximation.ofrthe amount of . re- i circulation taking place. Figure; 9^3 >slJo,ws the variation of recircula- b tion with relative wind speed as p.lolyted^ J ' with the data of Onishi and Trent ORNL-DWG 78-8314 14 cr M , b 13 A ONI SHI AND TRENT (1976) 2.93: a 12 O <' OTHIS STUDY 3.49 Fn 3.73 a .11 220 which was obtained for a dry cooling tower modeling study. The recircula- tion is measured as AT /AT , where AT is the difference between the in- e o' e fluent fluid temperature and the ambient temperature upwind of the tower u and ATQ is the discharge temperature excess above ambient. The data from the present study mesh well with those of the previous work, indicating the maximum recirculation for K = 0.8 (with a Froude number of about 3.3). The data also support the conclusion that the recirculation is minimized both at higher and lower velocity ratios.( > -ft « <• - • " " O 9.3.2 Froude Number Effects " ~ J « o " Experimental results indicate that Froude number variation has a " /significant impact on the excess temperature field downwind of the tower., 11 The 'maximum excess temperature ratio is" shown in Figure 9."A plotted against downwind distance for K = 3.3. The low Froude'number cases experience •g' < aA' i ( d greater mixing, which results i) .^.excess temperatures. The cases / also exhibit a reduction of pi,- /eratures in the wake region. fy-"-^ .•'' ' o ^ The variation of tra\-ec,t6s4;-. .A^th variation of Froude number is • I?. v^ » a" sho-«rn in Fig. 9.5 for K = 3.®^ lV,ie trajectory is affected fby the buoyancy \ o V or the plume. The graph suggests that the increased buoyancy of lower Froude number plumes acts to i/ncrease the trajectory primarily between 10 and 30 diameters downwind-^ The variation of recirculation with Froude number is shown, in Fig. 9.6. The recirculation appears to be dependent on the Froude number; o that is, as Froude number increases, so does the amount of recirculation. This is reasonable since high Froude number discharges have less buoyancy and are more likely to be drawn down into the wake-region immediately downwind of the tower where fluid is being drawn into the tower. The data by Onishi and Trent4 are in agreement with the data obtained by. this'study" . ' u <• 9.3.3 A Single Tower, In-Line Flow . I 1 . 15 . . 1 ' 1 The temperature regime from a tower oriented with its major axis in line with the wind direction was also nnodeled. Results are shown in Figs 9.7 (excess temperature) and 9<.8 (trajectory). Again, similar to the crossflow orientation, the excess temperatures for K = 1.6 are higher than those of other! cases. The excess temperatures for the in- , „ v line flow orientation are also • O , greater (by 20 ' to "30%' ) tha1 n those of the .. ; crossflow orientation (solid symUols) for similar wind speedti and Frpude number conditions. As a result of the warmer plume, "thec trajectories of the in-line, plumes are higher than the crossflow plumbs (Fig'.s 9.8). The'increased bending of the plume as wind-speed increases is also shown, t- There appeaerd to be no significant recirculation of plume fluid to the tower'at any wind speed except K =0.66, for which the"increase was not statistically significant. ' V1 .. ," "'"' -V, » 9.3.4_ Two Towers in Crossflow ' "" ' :i ' • , _ : . ; 'V -b ' 5? • , ; , . ' - / .:• . ; - ,'„ ,, : The investigation of the effects of a downwind tower consisted in varying the wind speed, Froude number,, and "distance between'ttthe towers" 222 OUNt-OAG 78-2316 FD K J> o 8.96 3ir e m 20 A 5.86 3.36 OS • 3.49 3.39 S e o 3.16 3.19 a; 15 o '2.36 3.14 o o 8 LNI - 8 D A a JQ0 8 A A Ct e I I 1 1 » 1 10 o 20 30 40 50 60 70 80 H0R1ZONTAL D1 STANCE - X/D 9.5. Variation of trajectory with Froude number, K = 3. ORNL-DWG 78 831? 28 26 A ONI SHI AND TRENT (4) K- 1.59 1 24 O THIS STUDY 1.612 K ^ 1.64 O THIS STUDY 3.19SK< 3.39 22 223 S) ORNL—DWG 78-8318 K FD 25 8 O 3.25 3.32 ' A 1.61 3.23 i INLINE D 0.96 3.95 A 6 • o O 0.66 3.85 A •A A • 3.39 3.49 v CROSSLINE o a 1.64 3.57 AO a 8 * # A U£ J 0.1 § v*; Q_ S .08 £ ** 06 A LU O cj A X O LU .04 O cfi .02 inn .01 _L 4 6 8 10 20 40 60 80 100 HORIZONTAL DISTANCE - Fig. 9.7. Variation of pxcess temperature with wind speed for ail in-line tower. 1 " < ORNL-DWG 78-8319 - 25 • ' Ji_ JL o 20 3.26 3.32^ Of o o 0 INLINE a 0.96 3.95 / os . a o . OQ . O 0.66 3.85) .S 15 o • 3.39 3.49 XcROSSllNE 0 • 1.64 3.57/ ' . ^ ' '' ! s 10 •'»_','' , ','•.. . O „ , • A UJ * . a A n B d Q O ^ O ,r 5 o o P ^ . J : L _L 3 -10 10 '20- ;.lsi 30/'"'' 40 50 80 • 60 " • • &70/ HORIZONTAL DISTANCE-X/D, . • OO. SS, , • ( " ' • u" , ,-! Fig. 9.8. Variation of trajectory with;wind speed for an in-line tower. • S.: ''-V*1 i' 224 and measuring the temperature fields downwind. The results are sum- marized in Fig. 9.9 through 9.11. Figure 9.9 shows excess temperature as a function of downwind distance for several wind speeds. For this case there is no discernible pattern for correlating wind speed with in- creased or decreased mixing. Figure 9.10 illustrates the trajectory for the cases of varying wind speed. The plumes display the same,trajectory changes as determined for the single tower. Also shown in the figure are the trajectories for two comparable single tower cases. The trajec- tories of the two-tower discharges are significantly higher than com- parable single-tower results. Comparisons of the data in Fig. 9.9 with the data in Fig. 9.1 show temperatures for the two-tower system to be somewhat warmer than those of the single tower for 0 < x < .10 in some cases. Since the towers oc- cupied only 2% of the flume flow cross-sectional area, little flow block- age or flume wall effects were expected to occur. Therefore, such effects » " a ' ' C o , $ . . . o ORNL-DWG 78 - 8320 1.0 0.8 - <> 0.6 a „ - so § 0.4 o • 8 0° 0 - o _ A 0 •0 „ o w » < 1> <3, £ 0.2 1 E ' § O a 55 l * & »• •' ; - A. " n 0.1 — X Fp o 9 ce 1 n , A fi .08° • o 7.75 3.87 o A 0 - •• 3.33 4.06 £ .06 , o 1 >3 I CO o UoJ . 7 „ & 1.65 3.89 A 8 1i.;' 25 .04 • • • A 0.95 3.97 0 - o 0.67 4.00 • « ' 'I .02 - a -- 1 D , <> b 1 1 1 ... 1 ;0l i , • 1 1 I • • • 1 2 * 4 8 10 20 40 60 80 100 HORIZONTAL DISTANCE-X/D ' 1 , - ' _ ORNL-DWG 78-0321 25 i K FD O 7.75 3.87 > o 3.33 4.06 (T 20 - a. 1.65 3.89 Q o,( r5 • 0.95 3.97 ce O 0.67 4.! 00 3 - o 15 • 3.39 3.49 ) SINGLE OO • 1.64 3.57 J TOWER o «CQ o O o o 0 LiJ 10 • o A A 2 «t O ., o A • Qi 00 on « OOO O O o \-o OO ' Oo I _L 10 20 ., 30 , 40 50 60 70 HORIZ0NTAL 01 STANCE - X/D 'c' Fig. 9.10. Variation of trajectory with wind speed for two towers in series. II « ORNL-DWG 78-8322 f 28 1 1 \ 26 - „ FLUID DRAWN INTO TOWER o DOWNWIND, TOWER 1 • 24 n O UPWIND. TOWER 2 22 A DOWNWIND, TOWER 2 " ft i— FD-3.9 2: UJ 20 o DISTANCE BETWEEN TOWERS - 100 ^ - A - ' << - £ 18 ' & •! z & 16 O 0 - o §. 14 0 i 12 i— §* o 10 - OS ' u U ' 8 e 0 , i' " o ; . - ; , £ . 6 L ' O 4 (l! o 2 O S -c 1, '' n , 1 , ". i . 0 . w . . t . 0.1 0.2 0.4 0.6 0.81.0 2 4 6 8 10 AMBIENTT0DISCHARGEVEL0CITYRATI0 -K1"". . €r o Fig. 9.11. Variation of recirculation with wind speed for two" towers' in series.9 cannot account for these differences. There are several features of two- tower plume dynamics which^might account for thigs. There is a dead fluid zone that extends all the way between the two towers—, This zone is only a few diameters at most in downwind length for the single tower. This extended dead water zone reduces mixing at the edges and bottom of the plume, resulting in slightly higher plume temperatures. The length- ening of the dead water zone between the twoV, towers indicates a larger low-pressure zone which tends to pull the plume from the first tower down slightly and into the wake zone and into the plume from the second tower. Finally, the jet action of the second tower plume creates a low- pressure region downwind of the first tower which further acts to draw the plume from the first tower downwind. When the plume is drawn down- wind, its interaction with the atmospheric wind is reduced; its tra- jectory is lowered momentarily; and it experiences slightly less mixing which is represented as higher plume temperatures, particularly when plotted as a function of downwind distance. lf The recirculation of fluid from the plume into the tower was shown to be a function of wind speed for the single tower. Figure 9.110gives the recirculation temperatures as functions of wind speed for the two- tower cases and illustrates the recirculation values for the downwind, face of the first tower and the upwind faces of the second tower. The • » 7 » 0 ^ ' • • S ' • 0 C , • 0 • recirculation into the upwind face of the first tower is always near . zero. The recirculation for „the two-tower system also demonstrates the ' • • 7/ "* , 11 influence of wind, speed on recirculation and the shielding effect on the, second0plunje by the first. For example, the recirculatiorf^back into the tower is less for the downwind side of the second tower than it'li-S for > ' ' " " , * 1 ' •<• o 1 si the downwind side^of the first, tower for slow wind speeds. At high .wind^ speeds, plume shielding is negligible and ground plume, temperatures rise. In turn, the-recirculation isfincreased into both the upwind and^downwind faces of the second tower. " " ' ^ jj . 0 , ,, ^ . . , a. The. variations of plume mixing and trajectory with varying Froude' o ' ''-'"'all "• ' • . ' ..'.,. number are, shown'in Figs. 9.12 and 9.13. Figure 9.12 shows that%he mixing decreases with,increasing Froude"number, a trend that was observed ' . ' ' : 1 ^ ' ' ' ' ,s 1 ' 1 '' ' i '' " for the single; tower. Figure 9.13 indicates that the, trajectories gen-' erally rise as the Froude number decreases. Both figures indicate; that i- 227 ORNL-DWG 7B-B373 1.0 0.8 0.6 8a § 0.4 8 o 8s •i CJO 0.2 • O \ 8 s ° 0 8 * 0.1 — Q 8 .08 JD. K s S o 11.81 1.65 .06 - a 6.38 1.61 B .04 - • 3.89 1.65 8 B o O 3.01 1.63 o : £ o 2.62 1.63 b i .... i .01 2 4 f 6 8 10 20 40 60 80 100 . HORIZONTAL DI STANCE-X/D "„ ' 0 Fig. 9.12. Variation of excess temperatures with Froude number fo two towers in series. " . - c ORNt-OWQ 7Q-8324 25 Fp K •'P. O O 11.81 L65~., 2 • 9 A 6.38 1.61 OS i_u (p ^ | • 3.89 1.65, C? D o 3.01 1.63 S -15 o m o 2.62 u 1.63 L; <: o A <_U>i 0 o c "O I 10 A d to ID a 5, a • O A o O O Q ° F- r ' /" fS 5 & ot?8 & o 1 oooo 0OO 0 aoooqo I J_ J_ _L ' 0 LJ 10 20 30 40 50 » 60 70 HORIZONTAL DISTANCE-X/D Fig. 9.13. ..Variation of trajectory. with^Froi&e numb'er for two towers in series.. " , • , o 228 <3 the buoyancy acts to increase mixing and raise the trajectory of the plume just as observed for the single tower. The variation of recirculation with Froude number, including the marked increase in recirculation for increasing wind speed, is also noted for the two-tower system (Fig. 9.14). The downwind face of the first tower has greater recirculation than that of the second for all cases, again demonstrating"the shielding effect of the first plume even for this relatively high wind igpeed (K = 1.6 corresponds to a prototype wind speed of about 20 fps). The effect of spacing is also a factor in plume mixing and dynamics. o . '•' , Figure 9.15 shows the excess temperature data for each of the" three towers for a representative case and for a single tower. The excess temperatures for the single towerCiare smaller than those of the two-tower system except within 3 or 4 stack diameters of the tower. The spacing of OBNLi own 78- B375 28 ,, " o 26 — ii „ RUID DRAWN INTO TOWER 24 — o DOWNWIND. TOWER 1 : O UPWIND, TOWER 2 0 fe 22 — A DOWNWIND, TOWER 2 H- 1 K - 1.6 z & LU 20 a o as 0 a. 18 Z o © £ 16 J iCi , ' A/ ? 14 — a z o 12 A • ZD 10 1 ^ , 0£ ,o O 8 i o o A a A ^ „-." o 4 , 2 o O <5 ' u ' <>'_,, 1 0 i --—>. i , l .= i . f . ' I . i .1.1.1 J? .9 10 11 12 FROUDE NUMBER - Fn j , rv ;r- " - • O*1) ' i' ' (LFig. 9.14. Variation in recirculation with Froude" number for two towers m>series. 229 ORNL-DWG 78-8326 1.0 0.8 0.6 O O o o o 0.4 • o o 8 o ' o 0.2 i—E <3 8 0.1 — .08 • xct 8° o D FP K .06 6.25 3.84 L61 B o ,D4 10 - 3.89 1.65 20 3.82 1.61 .02 b —I—I—I l-J 6 8 10 £ 20 40 '60 80 100 HORIZONTALSSTANCE - X/D Fig. 9.15. Variation in excess temperature with downwind spacing. the towers appears to have little effect on the dilution beyond about 50 stack diameters downwind from the first tower (for th^range of spacings represented). This^observation is supported by the results given in, Fig. 9.16 which illustrate that the trajectories experience minor influ- ence as a function of spacing beyond about 40 stack diameters' downwind. Examination of the data for two towers indicated little difference in the mixing of the plumes from the first and second towers. Further- more, a plot of the" data for the two-tower system (Fig. 9.17) giving the n ' - W ' ' 1 1 measurements downwind relative to the nearest upwind>tower shows little difference in plume mixing downwind of either of the two towers., ^circulation decreases as the spacing between the towers increases, (Fig. ORNL-MUG 78-8337 ?7 ^ FD - 3.84, K - 1.61 e n 20h ^ F0 - 3.89. K-1.61 ^ FD - 3.82. K-1.61 £ 15, 0 tJ ; n* Q iJH r £ 5 - O O O fl A O „ O o ooo o <£o 'a 00 ao A o Ou -U _L 10 20 30 40 50 60 , 70 80 HORIZ0NTAL DI STANCE - X/D Fig. 9.16. Comparison of trajectories for two towers in series at three downwind spacings. •HNL-DWG 78-8378 1.0 0.8 0.6 •O _ o 0.4 8s. § 0.2 6 O • • • is •; 5 0.1 i>. ia > o ".06 TOWER NO. , D D_ K o 2 1 % 6.25 3.84 1.61 • • B ,04 • , o 1 10 3.89 1.65 • 2 •a •• O 1 .02 20 3.82 1.61* L • " SINGLE 3.56 1.64 (•TOWER .01 _L -< l' 2 4 6 8 10 120 40 , 60 80 100 : HORIZONTAL DISTANCE-flD '; • ' . : V Fig. 9.17. 'Comparison of mixing downwind of each tower in two-tower & series ^ ^ ' , • [ —' v V "v 231 OfWl-OWG 78-B339 28 i/ RUID DRAWN INTO TOWER 26 — " KENNEDY THIS STUDY AND FORDYCE 24 DOWNWIND 22 — TOWER 1 O • UPWIND 20 - • TOWER 2 o 18 - DOWNWIND SUM OF TOWER 2 — TOWER 2 TEMPERATURES 16 • FD 3.8 4 s" 14 - K Q L6 1.0 12 ... 0 10 - O & o 8 A ' A o 6 - 4 - O 2 - O o i 1 i 0 . . . 1 8 10 20 40 SPACING DOWNWIND OF FIRST TOWER "Kg® Fig. 9.18. Variation of recirculation wittLh downwind spacing for two towers in series. downwind. Figure 9.18 also illustrates data obtained by Kennedy and For- dyce,3"where only the average of both faces of the downstream tower in- , ffc • " , r ' - flow temperatures are reported (referred to in the figure as the sum of a ^ . . o . "' * .. • tower two temperatures). 9.4 BRIGGS' FORMULATION COMPARISON, Briggs* formulas* have been advanced as a simple technique for analy- ,sis and prediction of buoyant plumes. These formulas were developed pri- marily from smoke stack observations and mathematical analysis. The < plumes from mechanical-draft towers differ ^significantly?from the smoke. plumes employed for the Briggs analysis/ both with iC"^pect to source I ^ ^ i? ' • ... "rr . i, . ' . 1 ,' > geometry and wake structure. However, Briggs' formulas were compared with the data from this study to explore°-the use of: these simple formu- las to estimate trajectories; for mechanical-draft towers. ; ^ , 1 v.-_ sf 232 <5^ Briggs1 gives the following formulas for trajectories of buoyant cf/ plumes: A ZV3 a X < X* , F" - A-rh (1) 2/'3 (2) 0.4 + 0.64 (X/y*) + 2.20 (X/x*)2 1 + 0.8 2 X > X* > "Q. where x* = 0.52 Fz/s h 3/5 h < 1000 ft, and F = F^- 2 V 3 (D/4). The s D symbols 2 and hg in the above equation are height above the tower and tower height, respectively. The function X* was developed by Briggs to distinguish the,active plume from the passive plume on the basis of the D ambient turbulent intensity,. An active plume disperses primarily by 1 3 , 1 ' " 1 ^ L plume turbulence and rises due to buoyancyrand momentum. In the passive 1 plume, the ambient turbulence is the primary diffusive mechanism and the ' 1 ' 0 ••" plume has .little vertica• l momentum' . . o The physical model study data are compared to predictions by Briggs' •.formulas in Fig. 9.19, whichf,also gives the prototype cooling tower curve. 1 , a f ~ • , "ft ' » . 1 • The data for the case of slow wind speed (K = 9.7) fall within the scatter 3 band of the Briggs equation and have virtually the same slope (2/3). - 0 However, with higher wind speeds, the data run through the£}2/3 curve at } progressively smaller slopes. The flattening^of the data 'curve is prob- ^ably consistent^with increased wake"effects of higher wind speeds and de- creased buoyancy^of higher Froude numbers (F )., The data for K = 1.62 (t an. d FUn =, * 2.6K, 5 ' sugges, , t that, the, plum\ e may experienc- ''/ , e nconsiderabl , ew wak,, e' . , 1 1 1 ', -, " ;! , - - ' • • (.- , • o reduction of trajectory immediately downwind of the tower but still lift ojff according to the:2/3 relation if sufficient buoyancy remains. ' o The dominant wake ^effect is the low-pressure region immediately. downwind of the tower which tends to draw the plume down: and delay lif t- off and retard plume rise. ,, Accompanying the low-pressure effect is in- creased mixing due to increased large-scale turbulence in the wake. ;7: 234 ft - . The role of wake turbulence is similar to that of ambient turbulence // "' ('S .. in the Briggs analysis, except that it is of considerably greater scale and intensity. The effect of wake turbulence on plume rise is probably similar to that of Briggs' ^ ambient atmospheric turbulence,. , that is, , re- i duction of .plume rise as a result of enhanced mixing; however, the ex- tent of that effect Is difficult to gage because of plume draw-down int1 o the wake low-pressure zone. It should be noted othat no attempt was mad e° V ^ r. ( to simulate ambient atmospheric turbulence levels in tne flume. ' Results suggest that highly buoyant mechanical-draft plumes in light r " /' o winds will follow Briggs' relationship for the "activs." plume. However, " Pf ' • wake effects will cause considerable deviation from r.iiese relationships for less-buoyant plumes in moderate winds. „,_.// Plume rise from multiple sources is a topic ogreat concern at present, particularly with respect to the, energy^park concept. The gen- eral subject has been treated by Briggs2 and mathematical plume merging treatments have been advanced by Koh and Fan5 and by Davis.6 These treatments and discussions generally ignore wake effects, not because 11 1 1 -, ''" , , i they are insignificant but because already complex analyses are made 0 seven more difficult with their inclusion. Comparison between laboratory data showing significant wake.effects with analytic models without wake .'Is. W ','.•, : ' ,, " ' " , " ' is ' dynamics is not completely appropriate. However, such a comparison was made for the Briggs,^analysis in order to explore the"significance of ;wake effects on. enhanced plume rise in lieu5of models treating wake ef- fects. Figure 9.20 illustrates trajectories predicted employing Briggs' suggested relationships for plume rise enhancement, " 235 rr ORNL-DWG 78 -8331 26 • SINGLE TOWER DATA O SIDE-BY-SIDE TOWERS O TOWERS IN SERIES BRIGGS* 2/3 FORMULA WITH AMBIENT TURBULENCE BRIGGS* 2/3 FORMULA BRIGGS' 2 TOWER ENHANCED 2/3 FORMULA SPACING BETWEEN TOWERS = 10D IC=1.6 FD= 3.9 30 40 50 60 HORIZONTAL DISTANCE — X/D Fig. 9.20. Trajectory" comparison for multiple plume rise.e \ V where Z^ = plume rise from multiple sources, E- = enhancement factor, .N = number of sources (towers),, " S = distance between sources. s- ••> . . Plume data are from this study. The plume rise enhancement suggested by Briggs is only a portion of that experienced in the near field by two cooling towers in series in crossflow. But the trajectories for;plumes from two cooling towers spaced 1 1/2>tower lengths apart (centerline to centerline)()i side by side show'that increased wake effects pull the . plume «£s v »• 9.5 CONCLUSIONS The experimental program led to the following conclusions: 1. Minimum mixing of the plume appears to occur for K = 1.6, but the differences are very small for varying wind speeds. Wake effects increase mixing locally, particularly for K = 3.5. 3. Increasing wind speed makes the plume bend over more rapidly; tra- jectories are below the stack height for plumes in very high winds (^50 fps). A. Increasing Froude number decreases mixing. 5. Recirculation increases with wind speed, Froude number, and decreased spacing between successive towers positioned perpendicular to °the wind. , 6. The plume from a tower aligned with its major axis in line with the wind mixes less than that from a tower aligned perpendicular to the " wind and displays a higher trajectory, evidencing greater buoyancy. 0 7. Downwind excess temperatures for two sequential towers aligned per- - 1 „ % • . ii "•. pendicular to the wind are only affected by spacing toa distance of, about 50 stack diameters downwind for spacings varying from 6.25 to 20 stack diameters downwind. 8. The trajectories of the two-tower systems simulated are higher than the trajectory of a single tower, probably due primarily to increased (i «> A » " , . •» , buoyancy. - A . . , 9. The excess temperatures of the two-tower systems simulated are greater „ than those of single towers. 10. For two-tower systems, the downwind side of the first tower experi- : , o , '. r o -, . . ; , - .. • ences the greatest plume fluid recirculation. < " a • „ " ' ' ° ' • " ; 0 . ' " ' • .. ' " •; o' Comparisons to Briggs'1»2 relations led to the following conclusions: tl' 1. Highly buoyant plumes from mechanical draft towers will follow Briggs' 0 .single tower 2/3 relationship. However, wake effects will cause con- siderable deviation for less-buoyant plumes in moderate winds. .. • ' , " i, a , • • - .« • .» , , • I,-1-., 2. >» The plume . merger dynamics represented in Briggs1 plume rise enhance- < ;>. - i • • " •>,•••> -I , • • - v - , • • 0 % ment formulation are dwarfed bymore significant plume/wake dynamics for the cases investigated. ^ ' '• ^ • \ i, •• '' " 237 The experimental program and its comparison to model prediction sug gest that optimal siting of cooling towers, particularly multiple towers is a task requiring knowledge of ambient wind history, plume dynamics, and tower operating conditions. Based on the tower wake effects and on the results for interaction of plumes from two cooling towers, site ter- // rain may be a very significant factor in plume dynamics and interaction. 9.6 NOMENCLATURE \7> Port or stack diameter ^Multiple plume rise enhancement factor N F Buoyancy flux parameter 1/2 Densimetric Froude number, F_ = V./{[(p. — p )/p ]gD} FD D j 2 a a g 2 Gravitational acceleration, 32.2 fps i Stack height ' s V./V discharge,to ambient velocity ratio K 3 a N Number of towers S Distance along plume centerline (trajectory) t Effective plume source idiameter for clustered sources Distance between sources ^ T,T m MaximuQ m plume temperatur, e ' ' ' , t, Ambient temperature, _ , ao Ambient temperature at stack height T Discharge temperature AT" m T — T .' • ' ' ' o ^ ; 1 ' • ' a1 1 , =a ' !f - AT T " ''1 ^ ¥ o 1 1 1 , r o c, , a. '• /0 . • ' , AT /AT ^ o Excess temperature (ratio) • V. a •Ambient velocity " - . 5 V. J Discharge velocity X Downwind horizontal distance , z,z 0 Vertical distance (elevation) , , " n . gN Plume'rise from multiple sources r Adiabatic lapse rate, -0.98°C/ Discharge density" pi 238 a ''") p Ambient density V ,/ a ' I X* Critical X value at which ambient turbulencii e dominates plume mixing // 9.7 ACKNOWLEDGMENTS il The authors are indebted to Dr. Edward Arnold for his assistance in preparing this re'port and to the Department of Energy for the financial support of this project under the Meteorological Effects of Thermal Energy Releases (METER) Program. J,. ; p 1 References a 1. G. A. Briggs, "Plume Rise," November 1969, prepared for the Nuclear Safety Information Center, Oak Ridge National Laboratory, by the Air Resources Atmospheric Turbulence and Diffusion Laboratory, Environ- mental Science Services Administration, Oak Ridge, Tenn. t 2. G. A. Briggs, "Plume Rise^ from Multiple Sources," Cooling Tower En- " vironment — 1974j Proceedings of a Symposium Sponsored by the Power ' Pliant Siting Program, p. 161, 1975. 3. J. F. Kennedy and H. Fordyce, "Plume Recirculation and Interference in Mechanical-Draft Cooling Towers," Cooling Tower Environment — 19743 Proceedings of a Symposium Sponsored by the Power Plant Siting Program, p. 58, 1975. , ' i, • ' " ' " 4. Y. Onishi and D.S. Trent, Mathematical and Experimental Investigations on Dispersion and Recirculation of Plumes from Dry Cooling Towers at, Wyodak Power Plant in Wyoming, BNWL-1982 (February 1976). •, 5. R.C.Y. Koh and L. N. Fan, Mathematical Models for the Prediction of Temperature Distributions, Resulting, from the Discharge of Heated Water in Large Bodies of Water, Water Pollution Control Research Series, Rept. No. 16130 DWO 10/70 (October 1970). ' - - ' * ' * " xt ; ' _ 'k 6. L. R. Davis, Analysis of Mechanical Draft Cooling Towers, EPA-660/3- 75-039 (June 1975) . ' • .. ' ' 1 " '/ ANALOG STUDIES ^ 1234 10. THE FIRE ANALOG: A COMPARISON BETWEEN FIRE PLUMES AND ENERGY CENTER COOLING TOWER PLUMES M. M. Orgill* Q 10.1 INTRODUCTION Past studies on the waste heat from cooling towers and proposed en- ergy parks suggest that the dissipation of this waste energy may result in significant meteorological effects. Preliminary calculations have shown that the rate of atmospheric dissipatio("i n of the waste energy from groupings of cooling towers is approximately equal to ,that bygeophysical phenomena such as thunderstorms, volcanoes, and large fires. Cumulus clouds and convective vortices often result from these natural energy releases. „ o One of the geophysical analogs, the large fire, is evaluated in terms of how good a physical analog it is to cooling towers or groups of cooling towers. The literature on experimental and wild fires was re- viewed in relation to how fire thermal plume characteristics may be typical of a thermal plume from cooling towers." Energy^release rates and energy fluxes of fires are generally a little larger than thosje of cooling towers and energy centers but the range is so wide that a fire can possibly be matched with some cooling tower or group, of cooling towers — energywise. , o '' Although the waste energy from groups of cooling towers may be ap-, proximately the same as from large fires, the physical differences between the cooling toweyr plume and fire plume shows tha, t the fir- e, • analog con- cept cannot be accepted unequivocally. In this, report, the physical dif- ferences between cooling tower plumes and fire'plumes are evaluated. . ^commendations for further research are a i 1 1 • ' 1 , ' ; — ——; "V1 ' •' ' • - ' ' fl , 1 1 u " - - . ' ''V a ' Atmospheric Sciences Department, Battelle, Pacific Northwest Lab- oratories . Richland . Wash. 5 242 and convection columns can be obtained. In addition, continuing numerical simulation work on cooling tower and fire plumes is also encouraged. 10.2 TYPES OF FIRES Precise definition of types of fires has'not been fully established, but generally around nine types of fires have been recognized. These are n Structural a • Urban • Prescribed (field and forest slash) • Experimental o • Ordinary wild fires (forest, etc.) • Conflagrations % ' * Mass f-Ires Firestorms 0 " c Moving firestorms J« ^ n <. - ^ An ordinary fire, whether structural, urban, or forest, is one with no particular violent fire behavior. If the fire reaches a certain size or intensity, it may reach a state in/which its behavior becomes more violent. At this initial stage and beyond, the fire may become a "mass fire," a conflagration, or at the extreme limit a ,:firestorm.. w Mass fires, conflagrations, and firestorms are descriptive terms "',«•', o 1 1 • J ; .. given to fires that exhibit the more violent fire behavior.1 General definitions are given below. ° ° n ? Conflagrations — a fire havingca large burning area arid a definite moving "front" or "fronts." Conflagrations are strongly affected by wind and topography^and can move very rapidly. In forest fires, the crown fire is,the major mechanism of propagation. J Mass fire — a fire area resulting from, a mass of near simultaneous ^ignitions that generate high eriergy^output. It can be a part of a con- flagration^ Tall corivective columns, fire-induced winds, and fire,vor- tices are common features of mass fires. Firestorm — a mass^fire^which results'if high energy output is sus- tained over a relatively large area. High rotating inflow winds (>30 m/s) 243 widespread destruction in the fire area, and limited fire spread char'-i acterize the firestorm. Moving firestorm — not well recognized but potentially the most dangerpus iand destructive because it has the characteristics of a fire- storm yet moves rapidly into unburned areas. In the past years, fire phenomena have been extensively studied in the laboratory on a small scale, but there has been some doubt to the validity of extrapolating results from these laboratory experiments to very large fires. The scientific study of adventitious large fires, has proved difficult for several reasons. Therefore, the concept of experi- mental or controlled burns has been utilized as an aid in the study of cS" fire and fire behavior. There have only been a few major exploratory large-scale fire tests because of the expense and significant organizational effort needed for A ' " '• " such experiments. These experimental fires were (1) French Meteotron (1961, 1971-1973), (2) Project Flambeau (1964-1967), (3) Tumut Explora- tory Mass Fire Experiment (1968), and (4) Operation Euroka (1969). In addition to these. , there have been a numbe.r o a prescribe. • d fores" t slas1 h ' or bush fires in the United States, Australia, and other countries whercds^. fire behavior was observed and meteorological and other measurements were obtained over or near the fires. The initial French Meteotron experiments used oil burners to pro- ^ , 5 - Co' duce a strong ascending column and cumulus cloud. Vortices resembling tornadoes were also produced in these experiments.2 The later experi- „ ments, using the same apparatus, provided data to be used for the theo- 3 r retical study of artificial convection. t "„, Project Flambeau was a series of 30 burns of discretely distributed fuel piles ranging in size"from*5 to 50 acres at isolated test sites., in Nevada and California.< The objectives were to investigate threshold conditions that distinguish mass fires from lesser ones and explore the problems of measuring large and intense fire 11 s and to develop instruments capable of getting the needed measurements . i, : >• 1 ' ... 1 • ' . . " . < .. r • . •0 ' /0 '» • " , s The Tumut Exploratory Mass Fire Experiment^was a preliminary burn in Australia prior to Project Euroka.1 The burn was approximately" 33 > o b acres of eucalypt timber. The primary5objective was to test an electrical 6 244 firing system designed to achieve simultaneous ignition of a large area of forest fuel. Other objectives were to field test instrumentation and study fire behavior.5 u Operation Euroka was a mass fire experiment of 52 acres1 of brigalow ^ o •• timber in Langley, Queensland, Australia. The objectives were similar to those of Project Flambeau, and extensive instrumentation was employed to measure fire parameters ~ wind inflow, radiant heat, air temperatures, , • o , 0 etc. A number of wild fires have been documented on fire behavior such as the Sundance Fire7 and the Air Force Bomb Range Fire8 as well as a number 10 of control forest slash and bush fires. 0 \\ The preceding summary on fire types indicates that fires occur over a wide spectrum of sizes and intensities. In order to better understand 1 theV 5behavior o q f fires and how they may compare to cooling tower and energy park waste heat plumes, the available fire literature was reviewed and summarized. The mostr-,relevant fire literature appeared to be that dealing with the French Meteotron and mass fire) experiments.'1 - ^ ' *' ' Lt * « : 10.3. CHARACTERISTICS OF MASS" FIRES \„ , Just where on the scale of fire behavior a fire becomes a mass fire is uncertain. On the basis of data from Project Flambeau,* Countryman1 0 suggests ,that the minimum criteria for a mass fire should be the °fol- •fi lowing: „ " , . , v < „ > ^ » • a fire with massive turbulent flumes, with multiple convective' plumes injthe combustion and transition zones; « -0 o 2 '„ ' v • minimum energ y productior n rate of 5001 0 to 8000 Btu/ft1 /min; > t * ' ,, ' " * fire area of at least 3 acres; 1 „ ^ ambient wind speed less than 3 m/s (exceptions to be noted, later); • fire dominates circulation patterns within the fire area (strong '; ' inflow); ° « ; °c' .° 1 1 - v ' ~ 1 ' ^ 1 Q - C , ' e,,,,, ,, » 1 i i , - . , s development of a convection column over the fire. V »•>'> • f 0 . « "" V"Y 1 ' - ° ' Vf • di * :„: A theory for explaining the change over of an ordinary fire to 'a, , "" ' • o , 1'' ' i ' ' \ 1 i' . 13 ' 1 !, v 111? : • • ' ' ' ' 1-1 mass or "blovmpS fire has been developed by Byram. The basis for „ the theory depends upon a ra'tio between the rate o;f conversion of ^thermal' 245 energy into kinetic energy in the smolf,e plume to the rate of flow of kinetic energy in the wind field. This ratio is called t$e convection number N , where C , 11 i. o N „ = P./P C f w and = L Iv(g) ~ rl3 P P = p P (1U ) f C (T +. 459) ' „ ' 2g ' & c> ' P , t< where I is fire intensity, T is ambient temperature at the elevation of fire, Cp is specific heat of air at constant pressure, p is density of the atmosphere at height z, v(z) is wind speed at height z, r is forward, a 1 i , ' - rate of spread of fire, and g is acceleration of gravity. When Nc is well below unity, the energy flow in the wind field will dictate fire behavior,and a smoke plume rather than a convection column will exist overtlie fire. Erratic fire behavior may occur as N^ approaches unity. When N is greater than unity for a considerable height1(>300 m)« C • 1 1 ^ 1 - ' ' inflow winds and^ updraftsis < , ' turbulence' , concentrated^vorticesth * , and large ' „ quantities of smoke and particulates. For mdre complete details on the ^characteristics of mass fires, consult the complete report./3 u ? R " ' O 1 1 ' , . 1 1 * ' 10.>34 ^ ' COOLING TOWERS'' ' AND tENERG Y CENTER; S ' , / j I I , ~ : > ^ 1 11 Cooling towers are ofj the wet or dry type. Since the majority of cooling towers in operation-are the, wet type, this type was used for 1 comparison with the fire, analog. ' • u • :, „ « , ; 1 ' " , 1 " • ' 1 ^ ' • ,, 1 ' . ' V ' 'L ' •• Wet cooling towers emit visible (i.e., , condenseL d or "wet") plumes ' " ' « ' > ' r f '' ' ' ' ^ l' ' over a wide range of atmospheric conditions. In wet plumes, the buoy- nancy forces are, produced locally rather than being a functionjof.the • thSf initial temperature of.the effluent alone. Thusi the dynamics of 246 wet plume is closely related to that of an isolated cumulus^&tijud^ where condensation warms the core of the plume while evaporation and cooling CJ occur near the edges. , The penetration height of wet tower plumes depends directly on the radius of the tower, the saturation temperature, and the stack velocity. For a given;set of tower parameters, stability influences the penetration height as does the bending-over effect of wind and wind shear. A most significant effect in determining the vertical plume dynamics is^xhe entrainment, which is determined by the stack radius and the angular o spread of the plume. Environmental^relative,humidity is important in controlling "the evaporativ- - e . coolin* g at the-plume, s- edges and hence the rate of depletion of thermal buoyancy. For most cases of light winds (<3 m/s), penetration heights of 300 to 1400 m can be obtained; .for stable conditions with strong wind, the penetration heights are reduced to a few hundred meters.ll* " : 0 ' " The energy center concept generally involves grouping 10 tp 40 power plants and associated cooling towers on a common site. On a^smaller - » , , 0 . " ' , r, ' • , ! scale, a single cluster of 3 to 4 power facilities may be operational in less than 5 years. The waste energy released by power plants may,take severial forms in the atmosphere: increased temperature of the air (sen- sible heat) , increased moisture content (latent heat),-and increased at- a mospheric kinetic energy (wind). Th^e dissipation^of the waste: energy from the la-cge energy centers. (101*' to 5 x 101* MW) " could result in sig-' nificant meteorological effects as discussed by Hanna and others.17-22 10.5 FIRE ANALOG HYPOTHESIS , ; • , ... 8 # 'o ' ' b ' ' - , The previous discussion^ of fires, cooling towers, and energy-parks "' "1 "' ? ' - • ' "4> -> -i • " " • '" briefly presented^some of the physical characteristics of each system. 0 It;is apparent"that there are important^differences as well; as some similarities between the fire ^ystem'and.the coolings tower—energy eerier -system., • • , .. . . • - 0, V, v"/^ ' , ; If the fire system is to simulate the cooling tower system,^modeling theory requires that the two energy systems have geometric, dynamic,^ .thermal (energy), and kinematic similarity. Also, the plumes of two 1 A *" >t " is • >•',' iL - " "o -' s , ', , iri- -'--p'n, 247 energy systems should be affected in the same manner by similar boundary conditions. Figure 10.1 indicates how the plumes may resemble each other in a qualitative sense during relatively calm wind and windy conditions. n Bvram,23 by use of dimensional analysis, has derived a number of 0 important dimensionless groups which for complete similarity should be the same for model (fire) and the full-scale prototype (cooling tower o- v.' system). These dimensionless groups according to general type of simi- larity are: , , ° " ' Geometric similarity II = z/D II = r/D .niV = d/D , (2) 9 •v5 ORNL-DWG 78/'-8332 where z is vertical height, D is diameter of fire on energy center, d is diameter of plume, and r" is radial vector. .^ J ^' v ' 11 « . 1 i » •' s Dynamic similarity 0 1 2 1 2 jl1 = V/CgD) / n3 = At(g/D) n5 = V /(gD) / ^11 = u/cgD)1/2 n = w/CgD)1/2 n " = v/CgD3)1/2 , ° (3)1 6 ' v 1 3 " G >1 « ' where V is reference wind speed, W is central plume updraft velocity, V. is indraft velocity, u is turbulence parameter, At is reference time 1 'V „P interval, V is kinematic viscosity, and "g is acceleration of gravity. Thermal and energy! similarity 1 • - - 1 ,i ' " " .' •""'" v " c ft, -j c ' N, = T /T n = — - , • «' (4) 12 Z 0 2 '•/ .1/2 (gD) ' P0CpT0 • i <» , ' where T is temperature of plume at height z, TQ is free-air temperature at elevation ofHfire, I is fire intensity, and p ; is reference atmospheric density. , •• ' .. i. , / , • •v.- - / ? \ if -' -'•1". • * '1' ,-V, - <\ o •> '' " 1 - V" ; 1 Kinematic similarity » " ! r : n8 = w/g ni5 = ip ni0 = a/d , > • •„' • (5) where w is-updraft acceleration at center of plume, is wind direction \ .«''•• • • « .. '0l • • .- , " ; , sipatiochange ni n length).airflow . movin"-v g into •'plume! , ana Z i, s * turbulenc. ' " e parameter I(dis'm.' -1 / : .Boundary conditions ' - ' v „', . "V " ' 1 " > - ' Vertical wind profile V(z) •"••-. ' " V? • * '.,• V, "-Topography h(x:,y;z) 1 i. ' Atmospheric stability Y - :v '' 1 '. >> »".'': . , ... 1 . Upper-leve^l boundary H f ;;; t V. . « Other dimensionless,. variables couldbe derived from the above set such 1 as I the Reynolds t number II J" 3 = H7/II13 = WD/V based , on the : central convec- tion column updraft velocity. " • • ''.--''V'""! ^ 249 Data are insufficient for both energy systems to make a complete similarity analysis using the above dimensionless groups, but they will be useful in discussing the various qualitative similarities and dif- (•' , 11 o ferences between the fire and cooling tower plumes. 10.6 GEOMETRIC SIMILARIT" Y v.* The principal requirement for geometric similarity is that certain length dimensions for both plume systems be scaled similar. Hence, = d/D requires that this ratio for both plume systems should be approxi- n mately the same. If the source diameter (D) is the same for both sys- .terns, the diameter, of the plume (d) should vary with height in the same a " ! & manner for both plume systems. oSince the thermal plumes of both energy systems generally increase in diameter with height, this type of simi- larity could be»satisfied if the ratios 11^, IIg, andoltj r could be matched J f for^U th ,{e 'tw o ' .energ y ,systems .' ' ,0 \ ' ^ ' 11 ' ' ' • " ' i ' " ' S^s L 1 .. , 1 ' ' ' . . " >- • ; VH , ' 10.7 DYNAMIC SIMILARITY 1 • ' f^ ' ' (1 ' , - „ This type of similarity requires that the ratios J^ to ^i^or^^ be equal for the two systems. If the source diameter (D) is the same • for" both systems, 'this would require the plume inflow and updrafts^to be similar for both energy systems. Generally,,,this is* not true. , In large mass'fires, inflow velocities are very unsteady0in time, varying® ' from 4 to 30 m/s. Updrafts in the lower levels of the,fire may reach , 50 m/s and higher levels maintain a speed of 3 m/'s or more «in rising ' , columns of heated air. ' -/„ .•,...'•'<' - - ••> " ,",• „ In ta cooling tower system the induced near-surface airflow (no wind)" may have inflow velocities of "about 2 m/s at a distance of 21 m from the ><. towers.21* Air movement may not be detected at ground level, for distance's^ , greater than 150"m from the towers. Updrafts a few hundred meters above , the towers may^reach 12 m/s or more but fall^of f rapidly with* tieight'!,? ;*' • .j,. ! the decrease depending ontstability conditions. ',V | ,, >; • \ , ? * : - '' iJU 10.8 THERMAL AND ENERGY SIMILARITY The dimensionless number tl12 = Tz/TQ implies that the plume or con- vection column temperatures should be equal at various heights for both systems. In the lower levels this is obviously not true because a fire is a very intense heat source and does not compare at all to a cooling tower system. Temperatures in a fire's plume decrease rapidly with height, and temperature differences (AT) between plume and clear air have been measured at about 2°C in the upper levels. However, in large fires the value of AT must vary considerably ^depending on intensity of • fire, rate of entrainment, and the presence of heated particulate matter. A major difference between cooling tower and fire plumes is the presence of heated particulates and noxious gases in the fire plume. 'I , O ; w One.of the significant effects of this difference is that warm particu- lates may be transported through the fire plume, enhancing the buoyancy o„"f ' the plume. Also, particulate0 s and . smoke affect the opacity of I-the smoke column which can influence the maximum height a plume will rise. Plumes from both energy systems also contain significant amounts of water vapor (no dimensionless number was derived for this variable). 1 • - , n • 'a " Generally, mixing ratios for both plumes are greater than the surrounding environment. Water vapor associated with both types of plumes can' con- dense to form clouds, and (.intense fires often have cumulus clouds capping a convection;column. Clouds may"also form over cooling tower^plumes. .c' ... 1 .f . : .. u , . '. 1 1 s . ^ Some limited field measurements of; temperature and moisture distri- butions associated with a forest—slash burn plume in Idaho and a cooling tower plume in*California are shown in Fig. 10.2. The aircraft measure- ments show;that plume temperatures and mixing ratios for both systems are generally higher than ambient readings.^ Limited sampling of both plumes in the upper-level portions may explain in part why plume tempera- tures were cooler than the ambient levels. ^ The dissipated energy from fires consists primarily of',sensible * (V37%), "radiant (s\>20%), and latent (VL0-40%) energy, while that from the cooling tower system is divided between sensible (20-30%) and latent^: ^ (70-80%) / One of the quoted similarities between large ^fires and cooling tower systems is that the rate of atmospheric dissipation of the waste B ' 251 ORNL-DWG 78-8333 1000 • TEMPERATURE o MIXING RATIO 750 S PLUME . AMBIENT" 500 ( I NO. OF TRAVERSES g 250 RANCHO SECO COOLING TOWER PLUME <2-18-751 _L 5 6 7 10 TEMPERATURE. C MIXING RATIO, gm/kg 450 FOREST SLASH BURN (10-15-76) MEAN TIME 10 Fig. 10.2. Qualitative comparison of upper-level ambient tempera- tures and mixing ratios for cooling tower;plume arid forest-slash burn , plume/convection column. ; , i D - <• • energy, is*'approximately the same. 0 This implies that, IT - or some equiva- lent energy dimensioriless number should be equal for both systems. : 5 , To put energy releases from fires, cooling towers, and proposed energy parks in perspective, a number of known ^fire energy release rates • and areas were plotted in1' respect to energy release rates from cooling towers, proposed energy centers, and other geophysical phenomena in'Fig. 10.3.21 This figure shows a" number "of interesting poirits. First, the 'fire-, energy release rates; and areas vary over a twideispectrum of values., , ., • ,, -, , • , ' .... , . -f-,7 . ,,, , ' , , , . Second, "mass tfiresJ' have, energy .releases larger than single or" double* , J iVt'". J- "; i, ;::: t a' •fr.VT; 1 vft, , '>,."• .V';.,;,. n.'--.-;, . '.-^.[l..^ 101 102 . 103 lo4 105 106 !07 108 109 lo10 1011 1012 AREA; M2 i" FM - FRENCH 'METEOTRON" 3 - MF' - MINIMUM CRITERIA FOR MASS FIRE , " TF" - TUMUT EXPLORATORY MASS FIRE , , H PE - PROJECT EUROKA ? PF - PROJECT FLAMBEAU (FIRE 460-7) * ' , 1 : ' , - PR - PACK RIVER FIRE STORM (SUNDANCE FIRE) .,'. * . SF - SUNDANCE FIRE (TOTAL AREA) " '. ' ' 0 .L BF - BUCKHEADFIRE " , „ ,, v , HF - HAMBURG FIRESTORM ' 0 " , ' , ' . EC - 40.000 MWe POWER PARK ON 1 KM AREA - " '' • , " " V ' " *'' ' t* '<< • ' i ' l 1 1 1 1 1 v ii • • | • • , ^ • ,, __ ' ^''a ; * A > Fig. 10.3. A qualitative representation of power dissipated by .various fire systems and natural and anthropogenic activities as a function of their scale size.- * ' ; " '. • <% i 253 cooling towers. This may help explain why single or even small groups of cooling towers only perturb the atmosphere to a small extent. The French Meteotron experiment appears to be near the same energy and area range as single or double cooling towers. The fact that the Meteotron experiment generated concentrated vortices and cooling towers do not seems to be related to the physical difference between a fire and cooling tower and how the fire plume interacts with ambient winds.o Third,"the energy release rate of proposed energy centers approximates that of some mass fires, but the energy flux (energy per unit area) appears to be somewhat less than these fires. On the basis of Fig. 10.3, one can generally conclude that the at- mospheric dissipation of energy from "mass" fires is usually larger than that from single or small groups of cooling towers but about the same 1 for energy parks. However, the energy per unit area for mass fires"is generally larger than that for proposed energy parks. u 1 . 3 ,10.9 KINEMATIC SIMILARITY ' • " , " ' - ' " " , This type of similarity requires that the mean and turbulent flow fields of the two energy systems resemble each other. Airflow accelera- .>,,'! , ' ra- tions in the vertical (w) , streamline patterns (ip) , and scales of turbu- lence^(£) should be similar, tAdequate quantitative data are lacking to make such comparisons. "" However, it is known that some turbulent features of fires have not been duplicated by cooling tower systems to date. •< j " ' *'" • " ' tl ' " ' 1 One of these phenomena is the nature of the fire*environment to generate concentrated vortices. These vortices .are associate1 d with the „ S '1 , ' r, ^ ' 'Q . . * O 1^ V ^ , - immediate fire ar^ea as well as with bent-over plumes or columns. The available literature on environmental effects of cooling tower systems^ do not(record any, case where concentrated vortices have been:associated with cooling tower plumes eVen though some 50 years or more of operational experience with cooling towers have taken place throughout the world. • , ' " ^ 1 ' , 1 o * 1 1 ^ 1 1 ' 1 , . It has been speculated that a,plume from an energy center could , lead "to' the development of vortices. , This is postulated to happen by two mechanisms:? (1) by multiple cooling tower., plumes merging rapidly; into a large*',. concentrate- • ' d. plume" , " '""a and interactin' •. : •g wit• „h ambien• . - t ' wind' s to . 254 cause wake vortices, and (2) by the ascending cooling tower plume con- densing into cumulus clouds, developing to cumulonimbus stage and pos- sibly generating vortices, such as tornadoes. 10.10 BOUNDARY CONDITIONS 0 "' The ambient vertical-wind profile can have a significant influence V , on the type and intensity of fire.11 Although strong convection over a fire is favored by low wind speeds both at the surface and aloft, the energy criterion (Eq. 1) shows that the rate of heat output, or fire intensity, is equally important. For a stationary fire to develop a convection column, the only restriction on the wind profile is determined by the condition that P^ must exceed Pw for some 300 m a"bove theafire.° Ordinarily, the wind speed increases with height, so that Pw in- creases very rapidly with height. For fires spreading before a strong wind, P^ will exceed P^ and may tend to limit the ultimate intensity. These fires are dominated by the energy of the wind and form smoke plumes rather than dynamic convection columns. a A moving fire, in order to survive, must continuously-travel into new fuel to maintain its energy output. For a moving fire to build up ' a high intensity (masst> fire) and establishja vertical structure, P^ must exceed P^ at the higher levels. The vertical wind„profiles that meet these requirements are showiKsin'Fig. 10.4. Generally, a wind speed max- imum is located at or slightly above the elevation of the fire with a zone of decreasing wind speed just above the maximum speed. This type c, of vertical wind profile permits a low-intensity forced-convection fire (1 (i , 1 1 1 i'i -i'- ^ , to overcome the wind-field barrier and convert toTa free-convection fire of much higher intensity. , ! Plumes from cooling tower systems are generally dominated by the ambient wind and turbulence. .Possibly, P_ will^normally exceed P >t> 1 , • ' h a ' , • ,, • f f 1 J • W during alight winS conditions. Strong winds and turbulence have a ten- dency ito^entrain ambient air into plumes, causing the plume to dissi- pate; especially if the air is not humid. Thus, cooling tower plumes are usually wind dominated, while in the case of4 fires the wind profile maye '' • •. ... „: - • v * " - ... n. 255 ORNL-DWG 78 8335 TYPE 1 - a TYPE 1 - b J 2 ! on ££ UJ O > z O < ) ( CO CO C 3 I— O o • X y \ 0 \ 0 10 20 30 40 50 0 10 20 30 40 50 WIND SPEED (MILES PER HOUR* WIND SPEED (MILES PER HOUR) TYPE 2 - a - TYPE 2 - b / / <* LL£I st— cL U cn u_ tn u_ LU Q > z (N s < £ as tn oq tn •< 3 3 t— O m n: i- O \\ o t— o t— 0 10 20 30 40 50 010 20 30 40 50 WIND SPEED (MILES PER HOUR) WIND SPEED (MILES PER HOUR) TYPE'3 - b TYPE 3-c * f! '' c 0 10 20 30 40 50 0 10 20 « 30 40 50 WIND SPEED (MILES PER HOUR)" 1 WIND SPEED (MILES PER HOUR) Fig. 10.4. Six types of wind profiles that have potential for causing fires to transform from forced-convection.systems to free- convection systems (after Byram, Ref. 12). " . c actually assist in transforming,a fire plume into a strong convection column. ,";', " > , a. ; a a «> Large fires often occur in mountainous terrain where topography can, have a direct and indirect effect on fire behavior. Fires spread more " rapidlyAipslope than on level ground because fuels upslope from Jthe fire are exposed to greater heating from radiation and convection^and because upslope winds are generated by the firesof natural heating.25' 256 !i « . Topography affects fire behavior directly through its effects on local weather and microclimate. Channeling of windflow by topography is an important indirect effect of topography on fire behavior. In addi- tion, topography may effect the generation of fire vortices in and near (I - the fire environment.25 As the result of these topographic effects and others, it is unlikely that a ldrge fire ,in rugged terrain would serve as an adequate model for a cooling tower system. ~ " Atmospheric stability affects fire plumes in a like manner to cooling L tower plumes. - Under unstable lapse rates, vertical motions will be accel- erated in both plumes. Stable lapse rates will suppress the vertical de- velopment of the .plumes, and elevated stable5" layers will limit^the ver- tical growth of both plumes. 10.11 CONCLUSIONS \ * , ' 1 - - if Fires with their associated smoke plumes or convective columns exist • - <5 . ; 0 on a wide range of intensities, depending,on, burning rate of fuel, size I . ' O of fire, meteorological conditions, and^other factors. The energy re- {i lease or power of larger fires varies from 102 to 107 MW with an energy . .. • . _3 2 ° » flux between 10 , and 1 MW/m . The power from single to groups of cpol- c .. -x ' U ' • & " ' ing towers varies from, 10^ to 5 x 10 MW with an energy flux between 5"K 10_lt and 1 MW/ra2., Since fires have such a wide spectrum of,, energy - releases and areas, it is possible that a fire could be matched up to some;, cooling tower grouping — energywise. However, energy release does not always delineate the physical differences between the energy release r 1 1 n 1 ,, 6 r *' ... ; , » ' ' q systems. This is the weakest aspect of6a fire analog concept. » There are important physical differences between cooling tower was^te heat plumes and the larger fire plumes. Fires, depending on burning rates and .other conditions,, are transient.phenomena that, can go through a trans-** formation in fire behavior from nonviolent to violent. This transforma- 1 ' ' '' ' 14 • ' Vt ' (i tion generates^strong inflow,?winds and updrafts: turbulence, concen- trated vortices, convective columns, and large quantities°o£ smoke and particulates. These characteristics are not observed with cooling towers or groups of^cooling towers, at least to date. " .. ,«* 257 Cooling tower plumes are generally dominated by the ambient condi- tions of wind, turbulence and stability. Fires — mass fires — can gen- erate intense convective columns which may or may not be^dominated by ambient conditions. For intense convective columns, interactions with VI ambient wind conditions may create significant/ciownwind effects such as wakes and concentrated vortices.26 ^ Some initial estimates on large energy Releases from proposed energy centers indicate that the addition of the energy to the atmosphere could result in increased cloudiness and^fog, changed precipitation patterns,, decreased daytime and increased nighttime temperatures, early3initiations of convective clouds, and increased frequency of hail, lightning, and convective vortices. Much of this impact^s due to the anticipated large releases'of water vapor to the atmosphere.21 Whether an energy-center thermal plume could become so concentrated as to resSmble a fire's convective column depends on several factors. It has been speculated'that this might happen if an energy center was located°on a small area around 106m2: According to Fig. 10.3, this may be possible if only the energy flux (MW/m2) is considered, since an energy center with an energy flux of about 10-2 MW/m2 would place it more&in the range of mass fi,res. However, it is still questionable whether an "energy , center plume would be as concentrated as a, convective column from a mass fire. Further research is needed on this aspect." The French Meteotron fire"experiments and some of the small con- trolled mass fire burns appear to exhibit similar general thermal and dynamic characteristics as compared to single or small groups of coolings towers. Since obtaining data from large mass fires is expensive and ; o dangerous, a research project on collecting data from smaller;, control , fires may still provide important information on thermal plumes. Upper- alevel data on temperature, humidity, turbulence, and vertical motion,,ap- pear to be lacking from past projects, and this type of data is needed to understand the nature of thermal plumes better. 258 References . ' b 1. C. M. Countryman, Project Flambeau — An Investigation of Mass Fire (1964—1967), Final Report, Vol. 1, Pacific Southwest Forest and Range Experiment Station, Berkeley, Cal. (1969). 2. J. Dessens, "Man-Made Tornadoes," '^Nature 193, 13-14 (1962). r - v. I'y , , 3. B. Benech, "Experimental Study of an Artificial Convective Plume Initiated from the Ground," J. Appl. Meteor. 15(2), 127-37 (1976). 4. E. Gaines et al., Broject Flambeau, DASA 1949, DASIAC Special Re- .. port 59, Mass Fire "Research Symposium, February 6—9, 1967, Wash- ^ ington, D.C. (1967). -. . . . O . I , 6. D. W. Williams et al., Operation Eur oka3 An Australian Mass Fire Experiment, Report 386, Australian Defense Scientific Service, 0 Defense Standards Labs, Maribyrhong, Victoria (1970) . ^ 7. H. E. Anderson, "Sundance Fire," USDA Forest Service Research Paper INT-56, 1968, Intermountain Forest & Range Experiment Station, Ogden, Utah, 1968. , 8; D. D. Wade and D. E. Ward, "An Analysis of the Air Force Bomb Range 0 Fire," USDA Forest Service Research, Paper SE-105, Southeastern Forest*1 c Experiment" Station, Asheville, N.C., 1973. 9. A." G. McArthur, "The Tasmanian Bushfires of 7 February 1967, and Associated Fire Behavior," Mass Fire Symposium, Canberra,, Aust.3 ' February 10—123 1969. Collected Papers, Vol. 1: Sessions A and c B? Paper A7, 1969., , = , ; , ° - 10. R. J. Taylor et al., "Convective Activity Above a Large-Scale Bush- f fire," J. Appl. Meteor. 12(7), 1144-50 (1973). ]Jl. G. M. Byram, Forest Fire Behavior, Chapter"4, "Forest Fire: Control and Use," pp. 90-123, McGraw-Hill, New York, 1959. 12. G. „ ^Forest Service, Southeast For. Exp. ,Stu. Paper 35, 1954,, 34 pp. 0 13. M. M.j Orgill, The Fire Analog: A Comparison Between Fire Plumes () ® and Energy Center Cooling Tower Plumes3 PNL-2453, Battelle, Pacific " .Northwest Laboratories, Richland, Wash. (1977). „ " ^ , ; .jr 1 • , 1 , .. ° , ' 1 ,1 14. B. R. Morton, "Buoyant(Plumes in a Moist Atmosphere," J. Fluid Mech., ' 2(Part 2), s 127—44 (1957). o , « , ^ ,. 15. " J. C.Weill, "The?fRise of Moist, Buoyant Plumes," J. Appl. Meteor. 1 ; S , 13 (4), 435-^3'(1974). qQ ^ \ ,' \ . . ,, "V' 16. S. R. Hannaj! "Rise and Condensation of Large Cooling. Tower Pliiines," ; - Appl. Meteor. 11(5), 793-^99 (1972),. » "„ , ' , • . • ' . ',:.V\ • -R.-; • • r • • • • : • •• . , OVJ -. \ J. E. Carson, "The Atmospheric Consequences of Thermal Discharges from Power Generating Stations," Radiological Physics Division An- nual Report —1971, pp. 250-69, ANL-7680 (PT3) (1971). R. M. Rotty, Waste Heat Disposal from Nuclear Power Plants, ERL ARL- 43, NOAA Technical Memorandum, Air Resources Laboratory, Silver Springs, Md. (1974). L. R. Koenig and C. M. Bhumralkar,On Possible Undesirable Atmos- pheric Effects of Heat Rejection from Large Electric Power Centers, R-1628-RC, Rand Corp., Santa Monica, Cal. (1974)o . , „ S. R. Hanna^arid F. A. Gifford, "Meteorological Effects of Energy Dissipation^of Large Power Parks," Bull. Amer. Meteor. Soc. 56(10), 1069-1076 (1975). J. V. Ramsdell et al>., Postulated Weather Modification Effects of Large Energy -Releases, BNWL-2162, Battelle, Pacific Northwest Labora- tories, Richland, Wash. (1977).° S. R. Hanna, "Predicted Climatology of Cooling Tower Plumes from Energy Clusters," J. Appl. Meteor. 16(9), 880-87 (1977). G. M. ^Byram, "Scaling Laws for Modeling Mass Fires," Pyrodyncorrlcs 4, 271-84 (1966). »Bi E. Boyach and D. W. Kearney, Plume Behavior and Potential Environ- mental Effects of Large Dry Cooling Towers, Final Report, Gulf-GA- °A12346, Gulf General Atomic Co., San Diego, Cals (1973). °C. M. Countrymsn, "MasscFires and'Fire Behavior," U.S. Forest Ser-^ vice Research Paper PSW-19, Pacific Southwest Forest and Range Ex-! periment Station, Berkeley, Cal., 1964. S. L. Lee, "Fire Research," Appl. Mech. Rev: 25, 503-509 (1972). PREDICTIVE METHODS 263 11. LOCAL PRECIPITATION INCREASES CAUSED BY SCAVENGING OF COOLING TOWER PLUMES L."R. Koenig* ABSTRACT {gus. •, • < . ' Quantitative estimates are provided of the^recipitation• ^increase in the vicinity ofovet cooling towers as a result of plume-droplet scavenging by natural rain. Rain rates from 1,, to 5 mm/hr and wind speeds of 1 toi10 m/s are considered with source strength equal to moisture flux from a 1000-MW(e) power w capacity. ;< & Q c ' The increase in precipitation strongly depends on dis- tance from the tower, wind speed, natural precipitation race, source strength, and horizontal angle of plume spread. Under favorable conditions of 1 ight iwinds" and steady^ rainfall, pre- cipitation increases due to scavenging up to about 25% of the natural rate should occur as far as 1 km ferom plants as small 'as 1000 MW(e). • , . ^ " , c 11.1 INTRODUCTION „ ' " " 9 - !leat re jection from cooling towers causes perturbations oh the at- mosphere that alter cloud and precipitation patterns., Asfh'eat burdens" increase, the reffectSj may become,, safficiently "objectionable-, to . create J ' , 1 • " 0 i demands for reducing industrials capacity on particular sites. Preferr- ably, planners1 would limit growth before atmospheric response reaches , ~J "untenable levels. ° . , Local, rain rate5 increases" due to scavenging is one. possible ^effect because rain tailing through plumes from wetj, cooling towers captures; » -droplets and carries their, to the ground. This work is intended torspro- vide information on the question of whether or not thiSJprocess is meas ibTe and of concern. „ ' ru •> " , • 1 ! , t, a, 1 ' ^ • . , • „, a, , . i, • , ii : . ; Ai/ t vj >' ~ . i ., 1 : eS" •• ' • ' ^ • ' • ' • "4" '"' • ' ° ' : ' * ' > . . The ""addxjion to the rainfall rate® caused b3y scavenging is given by the rate of plume "depletion divided by the areaj'over which it occurs. - h !.f , , , - ^ . , ,' „. ,i> *i 11 ,, , - 0 The-Rand' Corporation". . ,, O" 264 The normalized rate of depletion is given by the fraction of condensate mass that is swept out per unit^of time, '/i'hus, depletion rate (kg/s) depends on the amount present and is expressed by a first-order reaction: £ - • . a • <" where m is the mass of condensate in a given volume, kg; t is the--time, s; and A is a rate constant, s-1. The ambient air is assumed saturated ° "a' 1 0 with water ,vapor so evaporation is excluded. i. A question .. arise" s with respect to the 0 effect of the horizontal and vertical spread of a plume element as it expands while moving downwind. ' - , 1 u , '.a Regardless of scavenging, this changes the droplet concentration and mass per unit volume. However, this expansion is accompanied by pro- li -- _ ' , ! - portionally more scavenging particles falling through it, because the ^ '' i , o raindrop concentration remains constant in space. Accordingly, the rate of depletion (the fraction of condensate mass swept out per unit of time) remains constant (equal to A)'; and the rate1 of reimoval based on the num- ' •' ' * d • > . •• . • „ - " .P •• 1 < 1 ber of0 particles or, mass present in a given plume element movin g downwin1 5 d ' 0 >• • , '' o . a . ., ' " • vi < ' i Q.remains independent of its downwind mixing and dilution. ,„" Equation (lj is equivalent to the rate of change (kg/s2) in the flux tt, of& condensate^,as it moves downwind: ° tt, ' ' , ,'-.?* •« " ' , " i. < 1 • • where F is the flux of plume condensate passing through a cylindrical;sur- face centered at the source (kg/s)tand A is a rate constant (s-1). ' v ^ Often referred to as a "washout coefficient" (for example, Engelman, * ,, 6 01968), the rate constant A expresses the efficiency of the collection \ , process in which raindrops overtake and^capture smaller plume droplets. q c Its value depends.on the size of the collected plumeVdroplets and both: j1 the 'size.)and ^concentration , of collector rain, drops; the, latter depends on ram rate. , , ^ , r • , ' 1 11 '•>'. I ' » ' - ,0 "ii, . ',0 c - ' r/ 265 Assuming constant wind speed of u (m/s), Eq. (2) may be transformed to space coordinates which after rearrangement yields dF _ —A_ = fr. F, dx ~ u > W where x is/'distance downwind of the source, m. Integration of Eq. .;(3) leads to F = F exp (—) m"1 , u (A) X t S \ U /q where F is the flux at the source (kg/s) and F is the flux x meters s 0 s ° x downwind of-the source (kg/s). „,' Mixing characteristics are assumed to produce a plume that spreads with'a constant horizontal^angle 9 [radians]; accordingly, the area over which the precipitation falls ,,between locations Xj and x2 meters ' downwind of the source is a sector.of an annulus with the value (m ) A = 1/2 9(xf- x?) .6 , p " (5) '• I ' 1 . • . o Q, - • ' , . - • . / » »' • ' a • ti .y, " 1 ., j Assuming a",point source of emission, the rainfall increase, 2 -1 AR [kg m~* s ]i , over : this area is P o " ..'-'' 0 " > . ., * U * ,, - „ . ' o..„.' . ,0. " / . v-, : , ' Ct exp (6) P 1/2 0(x2 - xf) The* point source,, assumption can be improved .by using C.>iyirtual point source to account for the tower exit.diameter. Its upwind location «is specified so that the plume.width equals'the diameter of the1real .•source'after this travel distance: ',' , '•„;'•• . '••.„ * ' • P ' •"'Xv = 1/2° tan 0 ' ""„• ;'''•' n 1'7 ' ,« ' • •1 : V '! W^.7^ ..";.' • • - " ' 'V, 1 . H " • •.. " . • ':'• . '••>,> o.w-' :„;".,•.'.', where x is; „ vy\ ..v-v 4•'"', \ f.'-y V, " ° 'V, -„•*J t 'I (m);; andr is the radius of the .source (m) .' ;„.-' v/..;' 266 Since the pseudoplume is subject to depletion while moving from the virtual to the real source, a correction to the source strength over this distance should, in principle, be made. A source strength coefficient Cv equal to the inverse of the fractional depletion, exp (x A/u), modi- fies the (virtual source rfcrenKtti so that the flux at the real source equals the true source strength. The numerical value of the distance used in Eq. (6) must be adjusted for x . The rain rate, due to scavenging using the dispersed source esti- 2 — i mate, iAR* .d [kg m" s ], becomes -A(x + Xj) [--A(x + x2?l( v v > exp F I exp exp —^-J AR, = (8) d 1/2 01(x + x,)? - (x +x.)2] v ^ • v l ' A second correction accounts for the displacement of the raindrops 11 a as they are carried with the wind under the.plume. This displacement causes an "effect shadow" immediately downwind of the tower and tends to increase the distance to which the effect may be significant. The approximation that all raindrops fall at the speed v (m/s)°of the mass median drop leads to the> length of the effect shadow, x li[m] , < being o ' * j hu_ (9) v •9 a t> where h is the effective height (m) of the plume at the real source. Fallowing Kessler (1969) and assuming the Marshall-Palmer, raindrop dis- tribution with a zero diameter,, intercept equal toa10 (m ), the fall speed,(m/s) of the median mass drop is , ' v = 3.7AR1/9 ,' 'n (10) /where R is "the rain rate (mm/hr)I Adding x to the distance from theitower. for a^given rain rate in- ".'1 • . ' • • a: , 0 o. crease ^approximately accounts for the underplume trajectory! of the rain"; Accordingly, the: rain rate increase at/a point on the ground^designated AR (kg m~2 s-1), has the value of AR'(the rain rate increase at the 267 height of the plume base) at a distance xs upwind. At a given location beyond the effect shadow, che net effect of che underplume movement is to increase the rain rate immediately downwind but, to decrease the lateral extent of fallout. . yp) This treatment does not consider diffusion under che plume." If this is assumed to occur at the same rate as in-plumti r e diffusion,' a final,cor- rection for this spread can be made: ARf = ARg | • . 1 , \ (ID (X + Xv + 0 ' o where AR^"(kg m s ) is the rain rate increase at the ground x«meters downwind of the tower. 11.3 APPLICATION A Estimates of scavenging effects using the methodology developed in D the previous section can be easily programmed on a pocket calculator., 0 In this section, a limited set of input condiEions are used to "suggest ? " > ti« , <5 * , '' i the scope of environmental impact caused by scavenging. Table 11.1 summarizes the initial conditions of the sample calcula- 1 tions. Four rates of natural rainfall two wind speeds with constant , 0 " " " , „ • • v • source geometry, ,source strength, and plume-^spread were ..used. " co 0 ' , - o "' ' L" : 1 " ' n' r a • 1 1 .* ' 1* " „ 0" - '>- 43 t. -' ' ' 1 , , ' 0 Table 11.1. Initial conditions for sample calculations^ " ' a n 0 , jt4}T|fall Washout Rain & irat'e coefficient failspeed , 1 (s- ) (m/s) & , i'S? 31 74 n % i'i / jli * \\ • i 6; 7 X 10"" " : 4. 47 -id.. , • °Plume droplet radius, 4 ym (mono- , ^dispersed);, plume'angle of spread, '15° = 0.26 radian. Source: , strength,: 420 kg/s; iidiameter^, 60 m; height, 150 m. ^ 0 o. • S ' ;„/ei it . The source strength was choacn as appropriate for a wet tower op- erating In conjunction with a lOOO-MW(e) power generating capacity < (Kadel, 1970). The sd'urce geometry approximates dimensions of a large cooling tower (for example, that dt-Higned for the Forked River Plant; DeVine, 1975). The plume droplet size approximates the peak droplet size measured in the Centralia power plant plume (Wolf et al., 1977). \j-s~ -I " The plume spread angle, while arbitrary, Is In the range of'observed values, and direct scaling can be used to modify the results for other angles. Washout coefficients taken from Fig. 5.-4. ofjEngelmann (1968) are due to Chamberlain. Additional quantitiejs^derived from the input con- o ditions are shown In Table 11.2. Figure 11.1 shows plume element de- pletion as a function of time and rain rate. Figures 11.2 and 11.3 sum- marize the estimates of raiin rate increase as a function of distance and input conditions. The curves show AR^ [from Eq. (8)], the dispersed source estimate; AR , which additionally accounts for subplume r^in drop trajec- 1 ^ O ^ -- tories; and AR~, which modifies AR to account for diffusion under the 1 f 0 g • » " ' , plume. J , 1 : 0 0 " - > , i r Differences in the estimates are minor with 1-m/s wilSds but are con- sidered significant at 10 m/s. It is probable that rain drops diffuse at a slower rate than plume droplets; therefore, the best estimate For the,, V. '' a 1 . ' ' ' ' "-a - ' ' • • - • • «' . .-• ' ' • . 0 .. * ' ' ^ : ' ' '' Table' 11.2. Additional pairameters derived 0 " f ; e from input condit ions ^ ''. rt. c > * Rainfall rate (mm hr )* Wind speed (m/s) Source strength coefficient, C 1 1 a. t. • . ' u V 1.04 ,1.08 , 1.11 11 1.17 10 1.004. 1.007 c. 1.010 1.016 (.Effect shadow, x^ (m) •O 40.1 37.1 ;<>,: 35'i 5 33.6 , o 10 401 ' 371 355 336 Oo ' •V, - ,d .V ' <3> -fa.. Q M ''a 269 OF)NIL-DWG 78- 8336 1 2 3 Jiroe Uiloitconas) or diitance/wind sp«rfl Fig. 11.1. Depletion of a plume as a function of time and rain rate (R) 0 ORNL-DWG 78-8337 1000 J I I I I I I I I |I LI I | I I M_ Fig. 11.2. Percentage and absolute value of increase in rainfall • as a function of distance"from cooling tower for rain rate ,of 1 mm/hr. Solid line is' ARg, broken line is|ARf, and dotted line ^s'ARj /which is indistinguishable from ARf b^ond i|the ^shadow effect at» the resolution ofi 0 this figure)^. 1 '£ ' ' . 1"*, ;>v £ * ' - « o •9 ', £> -i • ' a. - au-r & " <0. £ ' V HcavenginK effect probably lieu Konevhert- ber-x-cn the /.H and /.K est. i- m/ites (I.e., In the shaded regions of Fi;;n. 11.2 and 11.3). // .Some selected values of rainfall Increase are shown in Table 11.3. Values are those of c-Hiitnat.es based on no diffusion o:'? rain under the OHNL UV.'C 7<4 H-iVi 1000 10.0 ,w. J i i f | I 1 I I | i l : i | yr* c\ Natural ramtall h-V 1 nm hr ' 5 100 \ 1.0 e —. Wind 1 m j-' E A n a <> v ,9 -A 5? N 10 0.1 .nEj Q£ X. SX - Wind 10 n S-1 ' M ' ' 'I ''I "Hi H 1 ! .01 I 2 3 Distance (kilometers) 'Ci \\ ft «Fig. 11.3: ^Percentage and absolutg value of increase in rainfall' as ia| function of "distance from cooling t;6wer for rain rate U 1 f? - « o ff= Tcible 11.3. Selected values of rainfall, increases caused a' by scavenging (with conditions in Table 11.1) ' o " , : • V. Maximum range of -rjjin increase (km) Natural . Wind For For absolute value rain rate' speed percentage of of increase 3 1 2.5 0.7 >4 0.7 a i© 0.7 ' a i'-^'v 1.3 r-m • H, it 10 ' a.a1 n a'' 1'V 1.1 - •<• 0.31^ 3.3 1V3 . 0.1 10 0 SU, • a' 3 . 0.5 ' . ' a /A • >• 'S'alue does""not occur. 0. si'-"0 ' A,'... • "i - .. 0 a i •, * *. r • . i < •0- , >1 rt «' ' jf tiffi;i, • \v - " ' " IT"'* 'S2-so ' • g 271 plume and, therefore, tend to be maximum distances for a given impact for the stated initial conditions. If one considers rain rate increases cf less than 1 ccn/hr as of no consequence, then for the prescribed source characteristics, one can conclude that effects of potential, concern are generally confined to distances within about 1"km'from the tower. 13.4 CONCLUDING REMARKS Thes& estimates indicate that precipitation increases due to the scavenging of plume condensate by rain should be measurable at afwet tower serving a lOOO-MW(e) facility but not at great distance nor easily under conditions other than light wind speed. By superimposing individual effects, estimates for effects at larger facilit ies with multiple towers can be prepared using the methodology dis- cussed. Simple"scaling, ignoring the placement of the towers, exaggerates the effect but suggests that a 5000-MW(e) facility would cause measurable precipitatflbn increases ats, distances somewhat greater than 1 km, even o '" s with moderate wind speed. .•' ,, n " The term "measurable precipitation increases" is used loosely; whether or not,this is true depends on the variability of the wind and natural precipitation both in(time and space. Warm-frontal situations having steady rain rates and°weak winds would reveal scavenging effects more easily tha0 n convective situations with greater variability in pre- '' " vS ' • , • p. _ & cipi?tation rat& and plume direction in both time and space. ai? • o ° A« 0 a References^) DeVine, Jr., C. J., 1975: "The Forked River Program: A Case Study in' Saltwater Cooling,'.' in Cooling Tower Environment —,1974 (compiled by 0 S. R.,Hanna and J. Pell), C0NF-740302, National Technical Information " Service, Springfield, Va. , ^ „ " '% ' •<• ' ^ %>* o " 1 ' ° Engelmann,,R. S.,"l968:o "The Calculation of precipitation Scavenging," Section 5-4 ot Meteorology and Atomic Energy — 1968 (Dv H. Slade, „ Editor)., TID-24190, National Technical Information Service, Springs" © field, Va. '„"'"•, . " „ . .0; " " * I •''ST Kadel, J. 0., 19/0: ° "Cooling Towers — A Technological Toolto Increase Plant Site Potentials," paper presented to American'Power Conference, 1 X'pril t23, 1970, Chicago, 111. Reprint'available frcSn ; the Mar ley Co., . Kansas? CityV'flo. ' r «. • ^ / • ' 'U , • ' " " • yjf - • a »• • « • 1 • • „ 1 „ •• - . KeH.nler, E., 1069: "On the lil Uolf, M. A., C. K. Hane, and K. I.. Drake, 1077: "Cooling lover Fit-Id Studies," in Atmospheric Effect;; of Nuclear- Energy Center:: (AF.UEU) Program, Annual Technical l*ro-jvntm Report for Period -July 737L-Cepierrber 1376 (romp I led by A. A. i'atr 1 m>s and H. V. Hoffman), 0KN1./TM-57 7H, Na- tional Technical Information Service. Springfield, Va. 12. KAINTALI. ENfiANX'EMKN'T HL"K TO SCAV;..\V.!N<, or COOLING TOVKR CONDENSATE >'.. T. Dana" M. A. Wolf" 12.1 INTRODUCTION The recent Increase in the number of electrical generalfng plants l.hat use cooling towers and projections for further expansion have prompted considerable concern about the environmental impact of large releases of energy and water effluent. One aspect of a comprehensive research program. Meteorological 'Effects of Thermal Energy Releases (METER), sponsored by the Enerpv Res-earrh and Hovelnpment Admini * 1 cinity. One question concerns" -the effect on "natural precipitation —0 namely, the potential for significant enhancement of precipitation (rates c and amounts in the sector traversed by the condensate plume. 6 In (this chapter, we consider theoretically the question of precipi- _ 1 it. ' tt „ Q V . ' 1 , 'J tation scavenging^) f condensate droplets b^natur£-lu p^ecipitat-iori and the resultant enhancement of precipitation under the plume. Scavenging of0 the vaptjr component of effluent is not considered, nor are thfe scavenging processes occurring purely as a result of cloud droplet—water vapor interactions (nucleation, droplet growth by accretion, etc.), which, are commonly referred to as "in-cloud" scavenging proces^es^ or "rainout." We do, however, consider the interaction between raindrops and condensate cloud droplets, generally called "below-cloud" scavenging or'"washout" (althoifgh, of course, these interactions do occur within clciids as well as outside them)., The approach is to use the currently accepted belo'©- cloud scavenging theory to estimate" for somewhat ideal cases the dekr(W . ' , - ' • vv, , - .. » ,, v .. - & , •^ U 1 ' -m , ' fl ' • , 0 Ct Atmospheric Sciences Department, - Battelle, Pacific Northwest Labora- tories,®Richland, Wash'.1 '•* • ••• -A,*1' . ' o» ~ " »V ' f ' • . ~ • " « ft' ' -3 • : . . ' . - .. Air Resources Center, Oregon State University, Cprvallis,0Ore. , 0 • of potential rainfall i.-nh/mcwat; corssents regard 1 n?, the efficacy of thin approach and reconssendai ions far exper loental evaluations and other calculations appear in the concluding nertlon. i) 12.2 AEROSOL SCAVENGING THEORY ' v • » ^ In treat inK\thfc of water drop! et«7 f roa a plurae by rainfall, we will tuie the traditional concept of a scavenging (washout) coefficient, or fraction of the emitted liquid water which is removed per,'unit tine. This removal may be expressed as an exponential decay process, O'r) - O0 exp (- kt) • * o , - ,, . (I) o C? where Q0 and Q(t) are the .source terms (mass/time) at times t = 0 and t, respectively^ The theoretical derivation of k for,the removal of aerosol 1 particles by raindrops is treated in detail elsewhere; for presen1 t pur1 - asi O " 1 ° O i " .' (7 poses, it is-useful"to consider the case where monodisperse particles are scavenged by a distribution of raindrop sizes. A simple^geometrical , argument leads to the familiar form for the differential scavenging co- efficient corresponding to a given single particle size: 2 J L k(a,R) = f TTR E(a,R) F(R) dR '„, ' t » (2) 4 J : ' - o • . • - • • -f ' ' • . , - 0 1 . .. , , " , . ^ 0° ,ljT , . it where a is the particle radius, E(a,r) is thcrcollectign efficiency {frac- o c. * 1 ! 1 ' i 1 • Sf tion of the particles encountered by the falling raindrop which is re-© • " ° . v • ' {1 : ° % " ' ;, moved*), and,F(R) dR is the flujl (number/area time) of raindrops^with «, radii,1 R to. R +, dR. s • • • . • fy(i . • ,.• * . • s ' , , • p .• , •• -A'/ ' " ' 4:1 " . ' J0:'" M- Polydispersity 6'f 'the parficle sizes car.8 be treated through a second integration, but for reasons listed* below we will approximate the^par-i ticle size spectrum by a mean radius and use the:monodisperse form;for » (5 p ' , sample calculations. (,viV.. > • ^ ,, o . a; For simplicity, we are assuming -perfect retention of particles ' / ,: scavenged^by raindrops. Thus the theoretical^,efficiencies, which; are , 3 actually coZ-Z-ision efficiencies, are equated to and called coVLeot-Con _ ^efficiencies. r ^ ^ ^^ 7 • ^"' : Theoretical est ir:.»t v.s based on evaluation ot" tlq. f.') thus require - the specif icatiors of a rsatheaat ical :'ors for the <*Bl led ion efficiency o as a function of a and R and a .suitable raindrop sire distribution or probability density function. An vi]] be shewn below, the important con- densate droplet si^es are in the several-micrometer range, u" i) ,, '0 of particles larger-'than about 1 radius. 0 Slinn2 has delved a convenient for% for the inertial collection ef- " . - v/ a ficiency, :a seraierapirical expression fitted5 to experimental) resujt=s of (j- 1 " p ^ - < : . ' Walton and Woodcock3 and the numerical ..calculations'of Fonda and Home."* The form is fr 3/2 0 E(a,R) - (s±miA r „ (3) U) \SOf 7/12/ ' 3 , Q where S is the Stokes parameter, ••//'' » 0 ^ r ' • , ' si a a . , a (i 'I n • .. ' . , • ri . ' s/ 1 O - 0 1\ I „ „ 2 • ' • 2a pv'vL ,.. , , • , ' o. ,0" r,;-" ; • - • ? j ; ^ 0 b : / • - • , . * In Eq. (4), p and p> are the mass densities of the particles and*air, respectively; V is the raindrop terminal velocity; and V is the kinematic ; viscosity of- air. ' • 1 ^ 1 , .1L- J' ' • " ' . D ' '•• ; „15 • u' • : ' "' „ •••• V ; 1 V •» • ' .o , • % : O 12.3 CALCULATION OF RAINFALL ENHANCEMENT - '.;' ' , 1 r '« - , :" - -s t • " ",. ' • rt - ' * . • "• - • * ® •• - ® - •• o-' > i " <; Evaluation of Eq.^(2) with the substitution of a suitable raindrop . " c flux ^distribution and collection efficiency given by: Eq. (3) cannot ^gen- ,r ° ' erally" be«done analytically; .numerical integration1 has lseen performedV. using log-not:nial raindrop distributions .ti For present purposes, however, < 1 r a computer program ' 0which utilizes a discrete raindrop spectrum to r '--1 ," . „fy,,.- «« 1 ; •'""'oi -'Vj-. i ^"'V;,.'!(*.,': i provid' ' ' e 1 ' accurat/'is"e ' approxdmations'u ' ' 0 M was use' d Foi' r «a give' n raindroi i - '"'s'p 1-'^size' -> if--^-'R. , \0; 1 , 1 I ^characterizing'a discrete size interval Eqi 0(2) reduces to , i > b : s- ' 1 ",'M, e " - '' • •• - ' i.-fjK; ' 10' (' ^V-"'"'' ... - ,.r," . /•; , . . " •. ' " - ..•>• v 27fi -h<-r<- J Jr. t h«- r-iinf/t 1 1" r:ii <• ' 1 <-r!grh/r ) for r.« 1 r.d rojin of H!?.*- , g£ v«-n by - " ; L Oo 'i\ o y _ -I / ... wh'i'V'- F,?!>» the flux of raIndropH of radius ". . . " >- I0 i o . " a -•<> S£nce ve are interested" in the enhancc-Kent of rainfall by scavenging 41 ••",* . ' , " V P 0 : {if- VSHT drov-letH, it i-i useful to consider the sass 'fluxi of water to the 1 ' 1 ' *•>1 ^ 'i ground (masK/area, !. ime or 1 <-ngth/t ltfl-t) afc a result of, scavengi ng. The * - ° n " " u a flux at appoint on the ground (x,y) for the raindrops R is given by k -jh C*°.y). wh»?re - * * . J, . a « u ftry, ^ (S " \(x,y) - J - /^y.'i) dp „ o (7), 'w (1 0 i? ft®> sS ' « is the integral of* the air concentratioxvpf water droplets X(x*y»z) along 1 1 •— - n 3 ^ £5 ^ i , • - 0 , . • ©'•»•> ® the path p of the raindrop. _ That is, the total mass of plume droplets in a 5 a^unit area column along the paGh of the raindrop is y °d k is thedfrac- tion per cuni t^time removed, so t|je flu* to the ground is kx • But the®, Jp ' o ' ;' - a , " ' ® ' " o • •flux is also jC.J., where C. is'the concentration, (ma§s/volume) ,of scavenged , water in the raindrop. Thus,, at a point°on the 4 • ij" - ®^ o •. ° , . "si i-'-i i - - : c. o • «b •« • o , _ .''' oo The enhanoement of rainfall, or vfractional increase incmass 'of water o 5 , deposited on the ground, is 6qualonumerically „to ther, concentration ,of ue 0 // scavenged.water in "g/cm units, since the concontra?2ion of;water"in the?° • , ^ ^raindrop® alohe (p ) is 1 g/^m3:^" '-'Jv v V .TA •V, f !' ' •-i J v 1 ' .-so/ , .••„=• v-v - • : fractional enhancement C./p (dimenslonless) . » : 0 ^ (9)« c ; The" evaluation of Che ne'ts enhancement "of rainfall" due to; scavenging' .: >f 5: A'by "thpfwhble raindrop spectijum, at a point t(x,y) is the mass weighted^sum J ;'•'•' 1 mi i .-vi, -'> ..." ,u.'.,. •, ' A • ^ ^ -- .-I1*-, 4'' '•' 1 .0'-O - " ,1 ."• -v^''IV'.",', ? .wl" v'ir". '''.V;1'"' He : of the individual consent ra: ion* C$ : C < x, v) - Yi C ^x.yK.Hj / ff (10) i" i i-1 / i-r O whore f is" the fraction of the "total *:zr~j > r of raindrops residing in ft I « ti r. the interval i, n is the total number.of intervals, and C (x.v) is Riven . T ij • i , i by Eq. (8). , . ' o " " a , ^ ' o O ? 0 « Evaluation of Eq. (-10) at a point on the plume centerl l»e (x,0) gives the peak rainfall enhancement; a subsequent integration o r sutamti&n 1 J of ! -- • a . CS C(x,y) in the cross-plume direction y leads to- a cross-plume integrated'1 ennanccacnt. This, divided by an effective^ total'vidth of the pd'ume (or scavenging deposition pattern) , gives an estim;ite0of the average ^rainfall. ' o ~ ~ i11 n „ ' ^ ' enhancement at a distance >:: ' J • 'c.<" "- . a 0" ;> o C(x,y) dy rJ — 00 . C(x) (11) 0 i, 0:, : 0The following calculations of cross-plume average enhanced|ht,were doriebby a.,summation over disegsete points y. similar ^in form to Eq. (10).? The", ef- £ ' ' " • 0 * ' 11 C1' ff p' ' • €1 ' ? q • • . 0 fective total width" of the deposition pattern was taken as six times the;r s." 1 1 J1 " v^ i 1 ^ 1 ^ 1' ^^ " • ' ' 'r ' ' xa /'' ^ standard deviation inothe y direction of .the plumgomodel chosen (see • 5 ' j/s 3 ' . .. ,, ' ^ 'd' >'«* ' TO below) at the appropriate downwind distance >v * ? i „ « • • ' (? • "4 - ' "v" ^ .."„ , ' "."-J5 . --•••IO' The mathematical form for the air concentration of condensate drop •• • ti, Of? - ,, • a- , IxCx'.y,?-) - „ exp, '.'a •, 1 2Tra o. u "1' 'ii ° (t'o, ' , " A o. 'Si a 1 fl t> a'- ' + exp o'-fi" \ & M « :: I o VP A , "ei fiWJii 'C?' •^'fc'^C.'Affl-'f 'where O.' 0 ifh a 'h A- '. , ,o ,0 = standard deviations fof " plume- spreads idthe.. cr o ss plume4«xl.vi# " : » a •I'"..'; y "•' •'V'. "•-" "-'J-'/ 2 -'4'''^M^Plk^^i San,and : verticaverticall zzidirection ^directions(cms (cm)) . , - C ,'A 278 u = wind speed (cm/sec), h = source height (cm). The standard deviations of plume spread used are those of Smith and Singer8 for neutral conditions, which best approximate conditions during frontal (nonconvective) rainfall: o = 0.69x° *85 y 8b az = 0.63X°- , (13) with CT y , a z,' and x in centimeters. The use of this point-source model directly for a cooling tower plume is inappropriate, since the source (the cooling tower mouth) is far from being a point. To approximate the area source of the cooling tower exit, a virtual source point as illustrated in Fig. 12.1 was de- termined as follows. At the real source, the plume was assumed to have diffused from a point at x = 0 to x = x^., where the mouth diameter W en- compasses 6a of the plume. Thus, W = 6a (x ) = 4.116x°*86 . (14) y r r ORNL-DWG 78-82.39 Fig. 12.1. Schematic of plume and raindrop trajectory geometry. 279 In addition, the plume is assumed to be rising linearly at an average velocity V^ such that the virtual source height is defined by x V H* = H --S-i , (15) where H is the true height of the cooling tower. Combining Eqs. (14) and (15), / „ \1.16 V H = H ~ (dti?) IT ' (17) The lofting plume is assumed to rise to an elevation H + AH at down- wind distance x , where it levels off. AH is evaluated9 as a function of temperature lapse rate, condensate exit temperature, and wind speed u. Thus, using Eq. (12) to describe the plume involves the definition of x as the downwind distance from the virtual source (where the real sampling distance of interest, the distance from the real source, is x, — x ) and ' A r use of a plume height which increases with x as follows: xV h = H" + —- x < xT , u L h = H + H x > x . (18) L The plume-derived quantity of interest for scavenging calculations [cf. (8)] is X^B-j)» fche raindrop-path integral of (12). For vertically ^lling raindrops, this is expressed by the vertical integral But raindrops never fall vertically if the wind speed is above zero. The trajectories of raindrops are approximated here as merely the resul- tants of the wind speed and terminal velocity (a function of raindrop 280 size) vectors (Fig. 12.1). The paths of a collection of raindrops of various sizes, all of which fall at the sampling point xA, thus cross the plume at various distances from the source, "seeing" different plume shapes and total mass of cooling tower droplets. Indeed, some of the raindrops close to the real source will pass under the source and be de- posited at x without scavenging anything. A Evaluation of the raindrop path integral x^ can be done analytically10 for the paths as defined in Fig. 12.1, but a good approximation to that rather complicated process involves use of Eq. (19) to derive x^ where the distance x involved is different- from the sampling distance x^. The value of x used is that distance where the raindrop crosses the plume centerline on the way to deposition at xA> The vertical integral at that point is a generally close approximation to the integral along the slanted path passing through that point. The plume centerline crossing distance x"* is defined by the plume geometry and the trajectory as fol- lows: (20) In the calculation process used here, Eq. (19) is evaluated at x" for each R^, the concentration derived from Eq. (8), and the subsequent rain- drop spectrum-mean concentration and cross-plume average concentration (en- hancement) by Eqs. (10) and (11). When x' < x^, the drop is assumed to have missed the source and the concentration is set to zero. If x" > xT, y/ is constrained by holding the corresponding plume elevation to H + AH. The terminal velocity expression used is an empirical expression11 fitted to the data of Gunn and Kinzer.12 12.4 SAMPLE CALCULATIONS The geometrical, meteorological, and source data listed in Table 12.1 were used to make sample calculations of condensate droplet scavenging and estimates of rainfall enhancement. The model cooling tower used is a typical modern natural draft tower; the source term for condensate was 2 281 Table 12.1. Input parameters used in calculations of rainfall enhancement Item Value 5 Source Liquid water source, g/'sec 1.7 x 10 Cooling tower height, m 150 Cooling tower mouth diameter, m 80 Loft velocity (average), m/sec 2.5 Plume droplet radius (mass mean), m 5 Meteorology Wind speed, m/sec 1, 5, 10 Rainfall rate, mm/hr 1, 5 derived from thermodynamic considerations detailed in Appendix A, and the mass mean droplet radius taken from measurements described in Appen- dix B. For a particular tower and source term Qq, the major meteorological variables are wind speed, rainfall rate, and raindrop size spectrum. Three choices of u and two of J were chosen to test; only one raindrop spectrum was used, that of a typical Pacific Northwest frontal rain. This spectrum (Table 12.2) was derived from numerous measurements in prefrontal rains of low to moderate rate (<5 mm/hr). For heavier rains and/or convective showers, a somewhat different spectrum may apply; however, the raindrop size dependency of the inertial collection efficiency is weak for most drop sizes encountered naturally.1 Thus, for rain spectra with a different overall mean radius than that used here (mass mean radius M).045 cm), one may apply the R-1 dependency of Eq. (5) to make estimates of departure. Table 12.3 is a list of the plume parameters derived from the input data for the various wind speed cases. These and the other data were used to estimate centerline rainfall enhancement, cross-plume average enhancement, and plume depletion at downwind distances (actual) ranging from 100 m to 50 km. These are expressed as percentages and plotted in Figs. 12.2 to 12.11. Because of the rather high rate of removal of water from the plume in all cases, it was necessary to account for depletion of 2 282 ORNL DWGTS-aUQ Fig. 12.2. Rainfall enhancement (concentration of scavenged conden- sate) at the plume centerline vs true downwind distance: u = 1 m/sec and J = 1 and 5 mra/hr. ORNl-OWG 16 SMl H Fig. 12.3. Rainfall enhancement (concentration of scavenged con- densate) at the plume centerline vs true downwind distance: u = 5 m/sec. 283 0"Nl D* Fig. 12.4. Rainfall enhancement (concentration of scavenged con- densate) at the plume centerline vs true downwind distance: u = 10 m/sec. ORNl-OWG 78 8313 DOWNWIND DISTANCE - X^ m Fig. 12.5. Cross-plume average rainfall enhancement: u = 1 m/sec and J = 1 and 5 mm/hr. 284 Fig. 12.6. Cross-plume average rainfall enhancement: u = 5 m/sec. S lS S DOWNWIND DISTANCE X^ - Xf. m Fig. 12.7. Cross-plume average rainfall enhancement: u = 10 m/sec. 285 OMtL-OMS IMM SLANTED RAINDROP PATHS VERTICAL RAINDROP PATHS -25 -20 -15 -10 -S 0 5 10 15 20 25 AZIMUTH, DEGREES FROM PLUME CENTERLINE Fig. 12.8. Examples of cross-plume rainfall enhancement patterns when calculation is done using either slanted raindrop or vertical rain- drop trajectories. U'lmtac ai 100 DOWNWIND DISTANCE XA - X,.. ID Fig. 12.9. Cumulative removal of condensate by scavenging: u = 1 m/sec and J = 1 and 5 mm/hr. 286 omiL-owG n~s>«a Fig. 12.10. Cumulative removal cf condensate by scavenging: u 5 m/sec. ORNL-DWG 7S-SM9 Fig. 12.11. Cumulative removal of condensate by scavenging: u 10 m/sec. 287 Table 12.2. Discrete raindrop spectrum used in calculations of rainfall enhancement Radius Fraction of total (cm) number in interval 0.0095 0.18 0.013 0.14 0.0175 0.18 0.0235 0.20 0.032 0.14 0.0435 0.09 0.059 0.05 0.080 0.013 0.1075 0.006 0.1475 0.001 Table 12.3. Plume parameters derived from input data of Table 12.1 and geometry of Fig. 12.1 Value (m) for wind speed u Parameter 1 m/sec 5 m/sec 10 m/sec H" -13.2 117 134 x 65.3 65.3 65.3 r 308 900 1430 *L AH 770 450 350 the plume by scavenging as x was increased. This was done using the ex- ponential decay expression Eq. (1). If x^ is the 1th sampling distance considered, Q(XAi) = Q(XAi-l) e*P Ai) ' , <21> o where Ax^ = Although the actual distance at which scavenging 288 takes plac1. is some mean tl" [cf. (19)], the x^'s were used since the dif- ference in distance between the i and i-1 points are nearly the same for each. In Eq. (21), k is a simple mean scavenging coefficient [(k + nl k^_^)/2] where the k^ values are derived from the cross-plume integrated concentrations. In practice, these are constant for all x^ large enough so that all raindrops are involved in the calculation (no undercutting of the real source). This follows from the fact that k is not a function of Q, nor does it vary as long as the raindrop spectrum and particle size are fixed. As Figs. 12.2 to 12.4 show, the plume centerline rainfall enhance- mer values are clearly significant close to the source for all three wind cases and both rainfall rate cases. For u = 1 m/sec, the highest centerline enhanc iment occurs within the starting sampling distance (100 m) and is apparently very large. The peak values for u = 5 and 10 m/sec are 46 and 17%, respectively. These peaks occur near the value of x where all the raindrops are involved in the calculation- According to Eq. (8), it should be noted that the removal rate i3 greatest for the smallest values of R^. The effect of wind speed here, of course, is just that more time is allowed in reaching a given distance, so that more water droplets are removed by that point. The variation as a func- tion of rainfall rate J arises solely from the inclusion of depletion of the source by prior scavenging. In the absence of- depletion, there would be no difference in the concentrations for different J input. It should be noted that the scavenging and resulting rainfall en- '.r* hancement calculated at the plume centerline is often sufficiently large to imply an actual growth in the mass of the raindrops. This apparent growth , in principle can increase the size of the raindrops to such an extent that the collection efficiency is changed [cf. (3)1. However, the raindrop, size is related to the one-third power of the mass, so a considerable mass increase is required before this effect becomes signifi- cant, especially since, through the btokes parameter S, the collection ef- ficiency dependency on R is rather weak. In fact, in none of the calcu- lations done here was this apparent growth great enough to warrant ac- counting for the change in the collection efficiency due to raindrop growth. - : 289 The cross-plume integrated rainfall enhancement (Figs. 12.5 through 12.7), or overall average enhancement at the given distance, generally reflects the character of the centerline value. In fact, the use of a bivariate normal plume allows the cross-wind value for each R^ to be proportional to the product of the centerline concentration and a (x"). However, each raindrop size considered has a different x' value (x' < x.); A thus, the cross-plume deposition pattern for the whole raindrop spectrum is not Gaussian. Figure 12.8 compares the cross-plume rainfall enhance- ment profile for one case (u = 5 m/sec, J = 1 mm/hr, x, — x = 400 m) n r with that which would result if all the drop size categories were assumed to be falling vertically. The curve for the case where slanted raindrop trajectories are considered is more peaked because the raindrops cross ' the plume at a point where it is less diffuse than it is above the point where they land. Correspondingly, the edge values are reduced because of the narrower plume seen. The areas under the two curves of Fig. 12.8 are identical, since the integral of the plume over both vertical and horizontal dimensions is Q(x^)» and the distance of plume travel for de- pletion purposes was defined as'x. — x in both cases for convenience. ,, A X The cumulative removal of cooking tower condensate as a function of distance downwind (Figs. 12.9—12.11) is significant for all cases, with plume half-distances ranging from about 600 m to 25 km. It should be noted that the decay shown is essentially exponential [cf. (21)] with time constant k (k being proportional to J). The value of k/J, or frac- tion of the source removed per unit depth of rainfall, for ..the present « -1 rain spectrum and droplet size is about 1 mm . ^ j( 12.5 CONCLUSIONS AND RECOMMENDATIONS j/ The integral process of removal of cooling towsr condensate by // scavenging, leading to depletion of the plume in time downwind, is essen- tially independent of plume or raindrop trajectory geometry .J) This fol~ I| lows from the basic premise that the scavenging rate k is a function of1 . 5 1 " - " -V •" " .'"''PV. only the raindrop and condensate droplet size spectra. ^Integration overf^l both these spectra leads to a fixed mean removal rate when the spec&a it 290 are considered constant in time. The condensate size spectrum was repre- sented by a single mean radius in the estimates made here; this was justi- fied on the basis of the Gaussian appearance of the measured spectrum. Other spectra, typically log normal, may be treated explicitly by the model.- Although measurements and suppositions about the sizes (particu- larly the sizes containing the greatest mass of water) of cooling tower droplets vary, most point to a predominant size in the micrometer range. The 5-ym radius used here is probably a good average value for cooling tower droplets in general. It should also be noted that the mean col- lection efficiency for this size of droplet (and for typically sized raindrops) is about 0.75. In the absence of extreme electric fields or other exotic scavenging mechanisms, the collection efficiency for drop- lets should not exceed 1.0. Thus, for spectra with a scavenging-effective radius of 5 ym or larger, estimates made using inertial scavenging theory should not exceed those herein by a factor of 1.5 or so. The effects on plume depletion of using different rain spectra should be less significant; the inertial collection efficiency is essentially independent of raindrop size, and the scavenging rate is in- versely proportional to raindrop radius. For^rainfall rates exceeding about 5 mm/hr, and for convective showers, the raindrop size spectrum may differ significantly from that used here.' In general, larger rain- drops will result in smaller collection efficiencies [cf. (3) and (4)] and a slower rate of removal [cf. (5)] per unit rainfall rate. The plume and raindrop trajectory geometries will, on the other hand, affect the pattern of deposition of condensate droplets. In par- ticular, the plume shape near the cooling tower mouth and the character of the plume rise will profoundly affect the location and magnitude of the maximum rainfall enhancement. Use of more sophisticated cooling tower condensate plume models will probably result in better estimates of rainfall enhancement near the source. Much of the information about plume configuration and, indeed, at- mospheric conditions such as temperature profiles, turbulence, and con- densate droplet spectra come from fair weather measurements by necessity. Complicating factors, such as low ceilings (plume disappearing into nat- ural clouds)(and stormy conditions, make measurements under actual 291 precipitation conditions difficult if not impossible. Therefore, it is questionable at this time whether it is useful to refine the model to include more detailed plume descriptions, because of the lack of experi- mental guidance under precipitation conditions. Since there are normally considerable uncertainties in raindrop and condensate droplet spectra, turbulence (affecting the raindrop trajec- tories), and plume behavior, the deposition patterns estimated here should be considered order-of-magnitude. The two significant results, and those which should be measurable in the field, are the overall sig- nificant rainfall enhancement and resultant rapid depletion of the plume; and the peakedness of the rainfall enhancement relatively near the cooling tower due to raindrops traversing a more concentrated, narrower plume than that directly above their deposition point. We suggest two types of field experiments to examine the two fea- tures of the scavenging process noted above. The first involves a con- centrated network of precipitation collectors deployed on a short-term, precipitation-event basis and arrayed in lines or arcs under the plume to detect the cross-plume shape of the deposition pattern near the cooling tower. For the situation illustrated in Figs. 12.6 and 12.8, about 20 collectors at 2 1/2° spacing at each of several distances downwind should be sufficient to detect the peakedness of the rainfall enhancement pat- tern. Given a rain of sufficient depth and relatively constant wind speed and direction, this could be done using ordinary buckets or funnel- and-bottle collectors. Many similar experiments detecting scavenging of S02 and other pollutants from power plants have been done successfully and practically.5'6 A second type of experiment could detect the degree of overall rain- fall enhancement in the downwind area by monitoring precipitation over a longer period with an array of recording rain gages. Given a fairly con- stant wind direction during precipitation, the typical situation of Fig. 12.6 could be examined by using about 40 such gages. This experiment probably would require data from a number of rainstorms in order to catch the proper conditions several times. Selection of a proper site for these experiments is a very important practical consideration. Sufficient rainfall, preferably mostly of a 292 frontal variety, is a requirement, as is a dependable wind direction during precipitation (the second experiment in particular would probably not be practical if more than an approximately 90° sector needs to be monitored). Also important are accessibility, reasonably flat terrain, and dependable operation of the cooling towers. References 1. M. T. Dana and J. M. Hales, "Statistical Aspects of the Washout of Polydisperse Aerosols," Atmos. Environ. 10, 45—50 (1976). 2. W. G. N. Slinn, "Below Cloud Scavenging of Particles," Pacific North- west Laboratory Annual Report for 1974 to the USAEC Division of Bio- medical and Environmental Research3 Part Zy Atmospheric Sciences, BNWL-1950 PT3, pp. 87-90 (1975). 3. W. Walton and A. Woodcock, "The Suppression of Airborne Dust by Water Sprays," Aerodynamic Capture of Particles, p. 129, Pergamon Press, Oxford, 1970. 4. A. Fonda and H. Heme, The Aerodynamics Capture of Particles by Spheres, National Coal Board Min. Res. Est. Rep. No. 2068 (1957). 5. M. T. Dana et al., Natural Precipitation Washout of Sulfur Compounds from Plumes, EPA-R3-73-047, Battelle, Pacific Northwest Laboratories, Richland, Wash. (1973). 6. J. M. Hales, M. A. Wolf, and M. T. Dana, "A Linear Model for Pre- dicting the Washout of Pollutant Gases from Industrial Plumes," AIChE J. 19(2), 292-97 (1973). 7. D. H. Slade, Ed., Meteorology and Atomic Energy, USAEC 68-60097, pp. 403—4 (1968). 8. M. E. Smith and I. A. Singer, "An Improved Method of Estimating Con- centrations and Related Phenomena from a Point Source Emission," J. Appl. Meteorol. 5, 631-39 (1966). 9. A. A. Patrinos and H. W. Hoffman, Atmospheric Effects of Nuclear Energy Centers (AENEC) Program. Annual Technical Progress Report for Period July 1975-September 1976, 0RNL/TM-5778 (1976). 10. M. T. Dana, "Below Cloud Precipitation Scavenging of Pollutant Plumes: u Effect of Nonvertical Precipitation on Deposition Patterns," Pacific Northwest Laboratory Annual Report for 1974 to the USAEC Division of Biomedical and Environmental Researcht Part 3j Atmospheric Sciences, BNWL-1950 PT3, pp. 91-98 (1975). 293 11. A. N. Dingle and Y. Lee, "Terminal Fallspeed of Raindrops," J. Appl. Meteorol., 11(5), 877-79 (1972). 12. R. Gunn and G. D. Kinzer, "Terminal Velocity of Fall for Water Drop- lets in Stagnant Air," «7. Meteorol. 6, 246 (1949). 294 Appendix A DETERMINATION OF APPARENT CONDENSATE FLOW RATE FROM A TYPICAL, LARGE NATURAL-DRAFT COOLING TOWER The behavior of a saturated, heated plume relative to its liquid water content as it mixes with the ambient air is determined by the en- thalpy, which is conservative. The wet bulb temperature completely de- fines the enthalpy and, under saturated conditions, the water vapor mixing ratio as well. Thus, two saturated air masses at different tempera- tures are completely defined by their wet bulb temperatures and the proper- ties of their mixture are defined as well. In practice, the enthalpy (EN) of the mixture is determined and this in turn specifies the wet bulb temperature. The wet bulb temperature (T ) defines the water vapor mixing ratio of the mixture, which is sub- w tracted from the mixing ratio determined as the mean of the mixing ratios of the two air masses to give the liquid water content (LWC). An example is provided in Tables A.l and A.2 of mixing a saturated plume at 34°C with ambient air saturated at 10°C. Table A.l. Conditions for example, condensed water calculation Ambient Plume Wet bulb temperature T , 8C 10 34 Enthalpy EN, cal/kg W 6939 27507 Mixing ratio MR, g/kg 7.76 35.13 The product of AMR and the total mass of the mixture containing 1 kg of the effluent yields the total liquid water (CW) in the mixture for each kilogram of effluent (last column of Table A.2). i. Except in the early stages of dilution when temperatures are quite elevated, the amount of condensed water is fairly constant. For a typical 295 Table A.2. Condensed water calculations for example cooling tower plume Ratio of ambient- T„ MR AMR I.WC 2 ENmix MRmix CW to-plume masses (cal/kg) <°C) (g/kg) (g/kg) (g/kg) (g/m3) 1 17223 24.55 19.89 21.44 1.55 1.83 3.10 2 13795 20.55 15.49 16.88 1.39 1.67 4.17 5 10367 15.75 11.38 12.32 0.94 1-15 5.64 10 8809 13.30 9.69 10.25 0.56 0.69 6.16 15 8224 12.30 9.07 9.47 0.40 0.49 6.40 20 7918 11.80 8.77 9.06 0.29 0.36 6.09 30 7602 11.25 8.45 8.64 0.19 0.24 5.89 40 7441 10.90 8.25 8.43 0.18 0.22 7.38 50 7342 10.72 8.15 8.30 0.15 0.19 7.65 60 7276 10.60 8.09 8.21 0.12 0.15 7.32 80 7193 10.45 8.01 8.10 0.09 0.11 7.29 100 7143 10.35 7.95 8.03 0.08 0.10 8.08 200 7041 10.20 7.87 7.90 0.03 0.04 6.03 aCondensed water in the mixture, grams per kilogram of effluent. effluent flow of 2.5 * 10** kg/sec, the condensed water flow would be ap- proximately 1.7 x 10s g/sec under the assumed conditions. This is the condition which is of maximum interest in regard to the washout of cloud droplets by natural precipitation. 296 Appendix B PLUME DPOPLET SIZE DISTRIBUTION USED IN SCAVENGING ESTIMATES A series of plume traverse measurements were made at Trojan Power Plant in northwest Oregon in May 1976. The results of these and others are described in more detail elsewhere;9 for purposes of the scavenging calculations, a spectrum measured on May 13 was chosen. On one traverse, where the plume width was about 250 m, the mean liquid water content (LWC) was 0.15 g/m3. The droplet size spectrum, measured with a laser spectrometer, at the parent center of the plume (LWC = 0.22 g/m3) is shown in Table B.l. Both the number and mass (LWC) distributions appear nearly Gaussian, though slightly offset in size. Because of the general characteristics Table B.l. Plume droplet spectrum used in scavenging estimates measured at Trojan Power Plant on May .13, 1976 Fraction of total in Radius interval interval (ym) (%) Number Mass 0.5-1.5 3 0 1.5-2.5 11 1 2.5-3.5 25 9 3.5-4.5 30 24 4.5-5.5 20 30 5.5-6.5 7 19 6.5-7.5 3 11 7.5-8.5 1 6 8.5-9.5 0 0 9.5-10.5 0 0 10.5-11.5 0 0 11.5-12.5 0 0 12.5-13.5 0 0 13.5-14.5 0 0 14.5-15.5 0 0 2 97 of the measuring instrument, there may be a tendency for a small de- ficiency in the numbers reported in the first two intervals (0.5—2.5 ym radius); thus, the actual distribution may b" *nore log normal in character. However, this correction shou i not signific ' affect the mass mean droplet radius (V? ym). The near-Gaussian nature of the droplet size distribution in this case simplifies the plume droplet size input to scavenging calculations. Such calculations for non-Gaussian, or, in general, polydisperse aerosol spectra, require integration over the aerosol spectrum or at least a strong knowledge of the scavenging-effect mean r.idius. These are related to the moments of the distribution or mean length radius, mean area radius, etc. In the case of the inertial scavenging scheme used for estimation here, the area mean is of importance. However, approximation of the spec- trum as a Gaussian one where all the mean radii are the same allows the specification of a single parameter to describe the scavenging character- istics of the spectrum. We have chosen in this case 5 ym, or the approxi- mate mass mean radius. SUPPORT ACTIVITIES 13. THE METER INVENTORY R. L. Miller A.A.N, r.triuos dcvoIopine.it of an inventory of U.S. power plants usin^ cot 1 in., towers • • cooling pon.I.s resulted primarily from the need tt) obtain knowl- edge of all potential sites for METER field studies. Selection of ; ' •.s would be enhanced through examination of the inventory. Additionally, n directory emphasizing the details of the cooling systems at eleetricn! generating stations would be useful to others outside the METER Provt-im. MLTLIl ^.'iVli.LuI' . 1-ri.Li lU^ Ui-1 L.S. |AJrtCC lJjuwL:-> It'cil , j . and geothermul) having a nameplato generating capacity of at least 25 'T which employ cooling towers, cooling ponds, or a combination involving on or more of these systems. Any power plants that are planned or under L:on struction and meet these requirements are also included. The specLfi'1 information provided for each plant is as follows: plant name, utility, location (city, county, and state), type of fuel, present and pro^ef'tod plant capacity, type of cooling system, water source, type and number oi cooling towers, number of cells per tower, tower dimensions, water cool in range, surface area and total volume of cooling pond, and date of initial operation. Several listings are contained within the inventory to iacilitace the need of the individual user. One listing includes all available in- formation on all plants;, while the others stratify the plants according to type of fuel, location by state, and cooling system. In all cases, power plants within a given heading are listed in order of decreasing electrical capacity. Plants which are planned or under construction are listed after the existing plants in order of decreasing projected capacity. Table 13.1 presents a typical display of all information avail able in the directory for a single power plant. The principal source of information for this directory was a mag- netic tape which contained the complete collection of the Federal Power Commission's Form 67 for 1973. Other references which proved valuable included the FPC Projected Generating Units directory, the NRC Insite Code, an EPA listing, and several documents from the Nuclear Safety Table 13.1. METER (AENEC) Inventory State GA ' Fuel F Plant name Bowen Plant capacity 3160 MW(e) Utility name Georgia Power Co. Projected capacity 3160 MW(e) County Bartow Cooling system NT Location 10 mi W Cartersville No. of cooling towers 4 Latitude ** deg ** min Water source Etowah River Longitude *** deg ** min General information Type Cells Tower Tower base width Tower top width Tower Water cooling Tower thermal . ^ length or diameter or diameter height range discharge & no. per tower (£t) (ffc) (ft) (f*; (0p) {w) Details of cooling system NT1 ** **** 276 **** 389 25 **** NT2 ** **** 276 **** 389 25 **** NT3 ** **** 317 **** 389 28 **** NT4 ** **** 317 **** 389 28 **** Surface area Total volume Date of initial of pond of pond operation Remarks (acres) (acre-ft) Year Month ***** ******* 71 10 ***** ******* 72 9 • ***** ******* 74 12 ***** ******* 75 11 303 Information Center at ORNL. The cooling tower manufacturers and the utilities were helpful in providing supplemental details. There are 416 power plants in the inventory, of which 326 are pres- ently in operation. All but 20 of the operating plants utilize fossil fuels; 17 of these are nuclear power plants, 2 employ a combination of fossil and nuclear sources, and the remaining one is geothermal. The cooling systems of the 416 current or future power plants are categorized as follows: 50 with natural-draft cooling towers, 206 with mechanical- draft cooling towers, 13 with towers of an undetermined type, 75 with cooling ponds, and 72 with combination systems. Table 13.2 displays a further stratification of the operating plants according to state, type of cooling system, and generating capacity. Over 57% of the operating plants in the table use mechanical-draft cooling towers, with the vast majority of these plants being less than 500 MW(e), and 20% utilize combination cooling systems. Cooling ponds are employed by 17% of the plants, while natural-draft cooling towers account for only 5%. Note the absence of plants under 500 MW(e) using natural-draft cooling towers or combination systems involving natural-draft towers. Texas has 68 operating plants — more than any other state. Table 13.3 presents the analogous v'.hart for those future power plants with known cooling systems. The fraction of plants utilizing mechanical- draft cooling towers has dropped significantly to 27%; conversely, the percentage of plants with natural-draft cooling towers has risen dramati- cally to 45%. Power plants with cooling ponds comprise 26% of the table. Combination cooling systems appear less frequently in future plants, com- prising only 1% of the total. (Note the trend toward plants with larger generating capacities.) Texas has the largest number of future plants, . and, along with Illinois, commonly utilizes cooling ponds in both current and future plants. Since the primary source for the directory was several years old, revisions are almost a certainty for the near future. Even so, the in- ventory forms <=\ comprehensive base of information providing the specifics of the cooling systems at U.S. power plants with cooling towers or cooling ponds. Table 13.2. Operating power plants according to state, type of cooling system, and generating capacity Natural draft Mechanical draft Cooling ponds CoiaMnation systems NT MT CP States £500 MW(e) <500 MW(e) £500 <500 ^500 <500 £500 <500 tMW(e)] [MW(e)] [MW(e)] tMW(e)] [MW(e)] [MW(e)l NT MT CP NT MT CP AL 2 AK AZ 1 c 1 AR 3 CA 3 11 CO 1 5 1 CT 1 DE u> o DC 1 FL 1 GA 1 HI ID IL 2 1 IN 3 IA 1 8 1 KS 2 11 1 KY 2 2 1 LA 1 12 ME MD 1 MA 2 1 MI 2 2 1 MN 2 3 3 1 MS 4 2 MO 7 MT NE Table 13.2 (continued) ' i Natural draft Mechanical draft Cooling ponds Combination systems NT MT CP States £500 MW(e) <500 MW(e) £500 <500 £500 <500 >500 <500 [M(e) ] [M(e) ] [MSf(e) ] (MW(e)] f MW(e)] [m(e)j NT MT CP NT MT CP NV 1 3 1 1 NH 1 NJ 1 NM 11 1 1 1 NY NC 1 2 2 1 1 ND 1 1 OH 2 1 2 2 OK 3 6 1 1 2 OR 1 PA 6 3 1 2 RI SC 7 1 1 1 1 2 2 SD 3 TN TX 3 29 14 11 1 4 2 1 3 UT 2 VT 1 VA 1 1 WA 1 WV A 1 WI 1 2 j>Total 17 35 151 33 23 5 16 3 16 26 Table 13.3. Listing of future power plants with known cooling systems Natural draft Mechanical draft Cooling ponds Combination systems NT MT CP States — : >500 MW(e) <500 MW(e) £500 <500 £500 <500 >500 <500 [MW(e)] [MW(e) ] [MW(e>] [MW(e)] [MW(e)] [MW(e)] NT MT CP NT MT CP AL 3 AK AZ 2 AR 2 CA CO 1 CT DE DC FL 1 GA 1 2 HI ID IL 1 1 IN 1 2 IA KS 1 KY 2 LA 1 ME MD 1 MA 1 MI 1 MN MS 1 MO 1 MT 1 NE Table 13.3 (continued) Natural draft Mechanical draft Cooling ponds Combination systems NT MT CP States >500 MW(e) <500 MW(e) 2500 <500 £500 <500 £500 <500 [MW(e)] [MW(e)] [MW(e)] [MW(e)] [MW(e)] [MW(e)] NT MT CP NT MT CP NV 1 NH NJ 1 NM NY 2 1 NC 1 1 1 ND OH 4 o OK OR 2 PA 4 RI SC 1 1 SD TN 2 TX 1 5 UT VT VA WA 2 1 WV 1 WI 1 2 WY Total 32 1 20 18 (73) J''- " • ' T> ** ' 1 . - ','* •>11