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Hydraulic Modft,T,Ing of Circulation in Reservoirs HYDRAULIC MODFT,T,ING OF CIRCULATION IN RESERVOIRS An experimental study of jet-induced circulation in water-supply reservoirs. by Stephen John Robinson B. Sc. (Eng.) London. Thesis submitted to the University of London for the Degree of Master of Philosophy in the Faculty of Engineering, and to Imperial College of Science and Technology for the Diploma of Membership. Submitted March, 1979 ABSTRACT HYDRAULIC MODELLING OF CIRCULATION IN RESERVOIRS BY S. J. ROBINSON At certain times of the year large volume water supply reservoirs can become thermally stratified due to an increase in solar energy and a decrease in the natural mixing and circulation induced by wind action at the water surface. Since thermal stratification can cause serious water quality problems artificial circulation and mixing is often induced by introducing the inflow through nozzles which form momentum jets. This thesis describes an experimental study of jet-forced circulation in reservoirs. Since it is virtually impossible to study prototype reservoir circulation, hydraulic models are often used to investigate this phenomenon. A major problem encountered when using hydraulic reservoir models is the measurement of the extremely low water velocities which occur. This difficulty has been overcome in this research by the development of a simple method in which photogrammetry is used to determine the deflection (and hence the velocity) of a:number of tethered buoys. The velocity measuring technique has been used to study the circulation in several model reservoirs by the determination of the velocity fields and circulation parameters for various geometric and dynamic parameters. The aspect ratio has been shown to be very important for reservoir circulation suggesting that the use of vertically exaggerated reservoir models could produce misleading results. TABLE OF CONTENTS PAGE ABSTRACT i TABLE OF CONTENTS ii LIST OF FIGURES vi LIST OF TABLES xiv LIST OF SYMBOLS xv ACKNOWLEDGEMENTS xx CHAPTER 1 STATEMENT OF PROBLEM 1 1.1 INTRODUCTION 2 1.2 WATER QUALITY IN RESERVOIRS - TEE PROBLEMS 5 1.2.1 Algal Growth 5 1.2.2 Thermal Stratification 6 1.2.3 Stagnation 9 1.2.4 Short-Circuiting 10 1.3 WATER QUALITY CONTROL - REMEDIAL METHODS 13 1.3.1 Selective Withdrawal 13 1.3.2 Artificial Destratification by Vertical Mixing 14 1.4 WATER QUALITY CONTROL - PREVENTIVE METHODS 17 1.4.1 Multi-Inlet Systems 17 1.4.2 Momentum Jet Inlets 17 1.5 BACKGROUND TO THE USE OF JET INLETS 21 1.5.1 Early Research 21 1.5.2 Current Use 21 1.5.3 Economic Considerations 24 1.5.4 Further Investigation 24 CHAPTER 2 RESERVOIR AND ASSOCIATED FLOW-LifERATURE SURVEY 25 ii INTRODUCTION 26 2.1 RESERVOIR FLOW SYSTEMS 27 2.1.1 Laboratory and Mathematical Studies 27 2.1.1.1 The Generation of Circulation by Throughflow 27 2.1.1.2 The Generation of Circulation by Wind 33 2.1.1.3 Other Studies 34 2.1.2 Field Studies 36 2.2 ANALAGOUS FLOW SYSTEMS 47 2.2.1 Lake Flows 47 2.2.1.1 The Generation of Circulation by Wind 47 2.2.1.2 Laboratory and Mathematical Studies 52 2.2.1.3 Field Studies of lakes 5.9 2.2.2 Other Studies 60 2.3 THE NECESSITY FOR RESEARCH 63 CHAPTER 3 THE HYDRAULIC TURNTABLE MODEL 65 INTRODUCTION 66 3.1 MODEL ROTATION 69 3.1.1 Ring Beam and Rollers 69 3.1.2 Levelling of Turntable 70 3.1.3 Model Bed and Basin 73 3.1.4 Turntable Drive Unit 75 3.2 PUMPED SUPPLY 80 3.2.1 Water Circuit 80 3.2.2 Flow Measurement and Control 80 3.2.3 Inlet and Outlet 84 3.3 AIR-PRESSURED SUPPLY 87 3.4 PROVISIONS FOR INSTRUMENTATION 88 3.4.1 Photography 88 iii 3.4.2 Grid 90 3.4.3 Photogrammetric Control and Survey 91 CHAPTER 4 THE VELOCITY MEASURING TECHNIQUE 92 INTRODUCTION 93 4.1 PREVIOUS METHODS USED 94 4.2 THE TETHERED SPHERE METHOD OF S'1'tAN AND • SCHIEBE 96 4.3 AN ALTERNATIVE BUOY 99 4.4 POLYETHYLENE BUOY - DESIGN AND CALIBRATION 102 4.5 POLYETHYLENE BUOY - THEORETICAL ANALYSIS 110 4.5.1 General Analysis 110 4.5.2 Deflection-Velocity Relationship for the particular Buoy geometry 116 4.6 MEASUREMENT OF THE BUOY DEFLECTION IN THE HYDRAULIC MODEL 121 4.6.1 The Photography 121 4.6.2 Photogrammetric Control 125 4.6.3 Interpretation of negative observations 131 4.6.4 Photogrammetric Errors 134 4.7 TEE COMPLETE PROCESS 148 CHAPTER 5 THE JET-INDUCED CIRCULATION IN SEVERAL MODEL RESERVOIRS 150 INTRODUCTION 151 5.1 DIMENSIONAL ANALYSIS OF RESERVOIR CIRCULATION 152 5.2 A DYNAMIC RESERVOIR MODEL 158 5.2.1 Dynamic Similarity 158 5.2.2 Model Considerations 162 5.2.3 A Circular Reservoir Model 166 iv 5.3 INVESTIGATIONS OF A CIRCULAR RESERVOIR MODEL 169 5.3.1 Tangential Jet and Central Outlet Model 171 5.3.2 Radial Jet and Diametric Outlet Model 190 5.3.3 Asymmetric Jet and Outlet Model 205 5.3.4 Comparison of the three types of circulation 209 5.3.5 Unsteady Flows 212 5.3.5.1 Short Term Stability 212 5.3.5.2 Long Term Stability 215 5.3.5.3 Decay of a Velocity Field 216 5.3.6 The Influence of the Earth's Coriolis Acceleration 220 5.3.7 Influence of Bed Topography 225 5.4 INVESTIGATION OF A MODEL OF TURRIFF RESERVOIR 228 5.5 INVESTIGATION OF A MODEL OF RESERVOIR 4 (ALI, HEDSRS AND WHITTINGTON, 1978a) 235 CHAPTER 6 CONCLUSIONS AND SUGGESTIONS FOR FURTHER RESEARCH 251 6.1 CONCLUSIONS 252 6.2 SUGGESTIONS FOR FURTHER RESEARCH 262 APPENDICES A VELOCITY FIELDS'FOR THE RESERVOIR MODELS 265 B THE SPIN-UP TIME OF A SHALLOW CIRCULAR BASIN 330 C PHOTOGRAMMETRIC CONTROL DATA 338 D COMPUTER PROGRAM USED TO DETERMINE THE VELOCITY FIELDS 342 REFERENCES 352 V LIST OF FIGURES FIGURE PAGE 1-1 (a)- Section of a lake or reservoir during summer stratification. 8 (b)Section of a lake or reservoir with full circulation and mixing during autumn. (c)Typical summer stratification in a lake (Thompson, 1954). 1-2 Schematic diagram of momentum jet action 19 1-3 The inlet arrangement at Queen Mother Reservoir, Thames Water Authority. 23 2-1 Summer Energetics of King George VI and Queen Elizabeth II Reservoirs during March-August, 1965, (Steel, 1972). 41 2-2 Wind-driven circulation in a long, deep, unstra- tified lake. 50 2-3 Wind-driven circulation in a shallow circular lake. 51 3-1 General view of experimental turntable (1973). 67 3-2 General view of experimental turntable (1978). 68 3-3 Roller elevations before and after levelling. 72 3-4 Model bed levels in contour form. 74 3-5 Calibration graphs for rotation controls. 78 3-6 Turntable rotation control unit with avometer and oscilloscope. 79 3-7 Delivery side of pumped supply. 82 3-8 Rotameter calibration graphs. 83 3-9 Outlet arrangement. 86 3-10 Scaffolding bridge above turntable. 89 4-1 The Tethered Sphere of Stefan and Schiebe (1968) 97 vi -FIGURE PAGE 4-2 The wax sphere/glass rod buoy. 100 4-3 The low-density polyethylene buoy. 104 4-4 Buoy in flume with cathetometer above. 105 4-5 Graphs used for selection of gradient change point. (a)Correlation coefficient v gradient change point. (b)Degree of agreement v gradient change point. 107 416 Data sample, regression lines, 5% confidence limits for calibration experiments of the poly- ethylene buoy. 108 4-7 Forces acting on the polyethylene buoy. 111 4-8 Surface tension forces acting on the polyethylene buoy. (a)with no flow. (b)with a flow. 115 4-9 Theoretical and experimental calibrations for the polyethylene buoy. 120 4-10 Pye Universal Measuring Microscope. 122 4-11 Zeiss Jena Stecometer. 123 4-12 Schematic diagram of the photogrammetric control. 127 4-13 Threaded post for theodolite and surveying target. 128 4-14 General view of turntable showing theodolite and subtense bar. 129 4-15 Subtense bar and surveying target. 130 4-16 Definition sketch for negative centre co-ordinate determination. 132 vii FIGURE PAGE 4-17 Enlarged photograph of test field used for camera calibration. 135 4-18 Plot of lens distortion vectors. 136 5-1 Definition sketch for dimensional analysis. 153 5-2 Components of the Coriolis force due to the Earth's rotation. 161 5-3 Definition sketch for azimuthal velocity profiles of Sobey (1973a). 176 5-4 Definition sketch for wall jet flowing over a surface in still surroundings (Newman, 1969). 177 5-5 Sample velocity profile at a representative section, tangential jet inlet Ko=3.66 x 106m4s-2. 178 5-6 Sample velocity profile at a representative section, tangential jet inlet Ko=28.25 x 10 6m4s 2. 179 5-7 Graphs of Qc and Vm against Kol, L/h = 62.5 and Qc against Kol., L/h = 18.75 for tangential inlets. 184 5-8 (a) Graphs of Qc/Ko1L and Vm/(ghA against Fr., L/h = 62.5 and Qc/Ko2L against Frj, L/h = 18.75 for tangential inlets. (b) As (a) but against Rej. 185 5-9 Graphs of Qc and m against Kol, L/h = 62.5, radial jet with diametric and asymmetric outlet. 195 5-10 (a) Graphs of Qc/Ko L and Vm/(gh)1 against Frj, L/h = 62.5, radial jet with diametric and asymmetric outlet. (b) As (a) but against Re.. 196 viii FIGURE PAGE 5-11 Definition sketch for the equations of motion of an axisymmetric turbulent jet.
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