Thermoelastic Model Studies of Cryogenic Tanker Structures

SSC-24 I

THERMOELASTIC MODEL STUDIES OF CRYOGENIC TANKER STRUCTURES

This document has been approved for public release and sale; its distribution is unlimited.

SHIP STRUCTURE COMMITTEE

1973 SHIP STRUCTURECOMMITTEE AN INTERAGENCY ADVISORY COMMITTEE DEDICATED TO IMPROVING THE STRUCTURE OF SHIPS ADDRESS CORRESPONDENCETO: MEMBER AGENCIES: SECRETARY UNITED STATES COAST GUARD SHiP STRUCTURE COMMITTEE NAVAt SHIP SYSTEMS COMMAND U.S. COAST GUARD HEADQUARTERS MIlITARY SEALIFT COMMAND WASHINGTON, D.C. 20590 MARITIME ADMINISTRATION AMERICAN BUREAU OF SHIPPING SR-191 1973

could arise in the Anticipating one ofthe problems which undertook tankers, the ShipStructure Committee design of LNG that would result studies to investigatethe thermal stresses occurred in the primaryLNG tank. if a sudden rupture theoretical consisted ofexperimental and One Droject analysis of LNG simplified thermal stress efforts to develop a condition, and toevaluate tankers under theemergency, rupture involved. the importanceof the parameters contains the resultsof this work. Comments The enclosed report on this reportwill be welcome.

W. F. REA, III Rear Admiral, U.S. Coast Guard Chairman, ShipStructure Committee - de SSC-241

t. FINAL REPORT - D AiUM on

Project SR-191, 'Thermal Study

to the

Ship Structure Committee

THERMOELASTIC MODEL STUDIES OF CRYOGENIC

TANKER STRUCTURES

H. Becker and A. Colao

Sanders Associates, Inc.

under

Department of the -Navy Naval Ship Engineering Center Contract No. N00024-7Q-C-5119

This document has been approved for publicrelease and sale its distribution is unlimited.

U. S. Coast Guard Headquarters Washington, D.C. 1973 ABS T R/\ CT

Theoretical calculations and experimentalmodel studies were conducted on the problem of temperatureand stress determination in a cryogenic tanker when a hold issuddenly exposed to the chilling action be the of the cold fluid. The initiation of the action ispresumed to sudden and complete rupture of the fluidtank.

Model studies of temperatures andstresses were performed on instrumented steel versions of a ship withcenter holds and wing tanks. Supplementary studies also were conducted onplastic models using photothermoelasticity (PTE) to reveal the stresses. Temperatures and stresses were computed using conventionalprocedures for comparison with the experimentally determined data. Simple calculation procedures were developed for temperature prediction andfor stress determination.

The highly simplified theoreticalpredictions of temperature transient stage were in fair agreementwith the experimental data in the reached peak and after long intervals. The temperatures and stresses values in every case tested andmaintained the peaks for several minutes during which time the behavior wasquasistatic. The experimental tem- models peratures were in good agreement withpredictions for the thin representative of ship construction.

Evidence was found for the importanceof convective heat cases transfer in establishing the temperaturesin a ship. In some this may be the primary process by which athermal shock would be attenuated in a cryogenic tanker. It also would influence thermal model scaling.

An important result of the project was thegood agreement of the maximum experimental stresses with theoreticalpredictions which were made from the simple calculations. This agreement indicates the possibility of developing a general design procedure which couldinvolve only a few minutes of calculation time to obtain the peak stressvalues.

-11- CONTENTS

PAG E

INTRODUCTION 1

HEAT TRANSFER THEORY 2

THERMAL STRESS THEORY 15

MODELS AND EXPERIMENTS 23

EXPERIMENTAL MECHANICS 34

TEMPERATURE INVESTIGATIONS 37

STRESS INVESTIGATIONS 52

OTHER SHIP PROBLEMS 56

CONCLUSIONS 60

RECOMMENDATIONS 61

ACKNOWLEDGEMENTS 61

APPENDIX I- EXPERIMENTAL TEMPERATURE DATA 62

APPENDIX II - EXPERIMENTAL STRESS DATA 68

REFERENCES 73

-111- LIST OF TABLES

PAGE NO.

4 I Dimensionless Groups Used in this Report

10 II Relative Heat Transfers, AT = 40°F

11 III Relative Heat Transfers, AT = 300°F

24 IV Model Descriptions

32 V Strain Gage Characteristics and Locations

45 VI Temperatures in Bottom Structure, °F

46 VII Simulated Wind and Sun Study, Model 2T2B-1

62 A-I Basic Calculation Data for Temperature Models

63 A-II Temperature Data for Theoretical Profiles,°F

64 A-III Experimental Temperature Summary, o = 1800 Sec - Alltemperatures °F

65 A-Iv J= (T- TF)/(Tw_TE) 65 A-V Temperature References for Thermoelastic Model

66 A-VI Normalized Temperatures for Thermoelastic Model

69 A-VII Thermoelastic Model Stresses (PSI)

-iv- LIST OF FIGURES

NO. PAGE

i Overall Convective Heat Transfer CoefficientBetween Two Walls 5 of an Enclosed Space 2 Cellular (Steady/State) Behavior in Horizontally Enclosed Space . . . 6 Heated from Below 3 View Factor for Radiation Between Parallel Plates Connected by . 7 Non-Conducting but Reradiating Walls 4 Plate Strip Element for Heat Transfer Analysis 12 5 Curves for R1 and R2 14 6 Range of Quasistatic Temperature Distributions Alonga Strip, 15 Shown Schematically 7 Effect of Biot Number on Thermal Shock Stresses 19 8 Schematic Representation of the Ship Cross SectionForce 20 Balace and Strain Equilibration 9 Cold-Spot Problem 22 10 Thermal Model Data 25 11 Ship Temperature Models and Experimental Equipment 26 12 Model for Heat Transfer Coefficient Tests 26 13 Cold-Spot Model 27 14 Photograph of Cold-Spot Model Test 27 15 PTE Ship Model 29 16 PTE Ship Model Photograph Showing General Experimental 29 Arrangement 17 Ship PTE Model Experimental Arrangement 30 18 Steel Ship Model Dimensions 31 19 Photos of Model at Different Stages of Construction 32 20 Thermocouple and Uniaxial Strain Gage Locations 33 21 Biaxial and Rosette Strain Gage Locations andThermocouple 33 Locations 22 Comparison of Theory with Experiment, 2T8,Between T = TE at s/L = O and T= Tw at s/L = 1. Path length from Bulkhead to Waterline 23 Comparison of Theory with Experiment, 2T8 BetweenThermo- 39 couples i and 4 Using Measured Temperaturesat Those Locations 24 Comparison of Theory with Experiment, 218, UsingExpanded Path 40 Length and T= TE at s/L = 0, T = T at s/L = i 25 Comparison of Theory with Experiment, 2T4,Between T = TE 40 at s/L = O and T= Tw at s/L = 1. Path Length from Bulkhead to Iaterlìne 26 Comparison of Theory with Experiment, 2T4,Between Thermo- 41 couples 1 and 4 Using Measured Temperaturesat Those Locations 27 Comparison of Theory with Experiment, 2T2,Between T= TE at 41 s/L = O and T at s/L = 1. Path Length from Bulkhead to Waterline = 28 Comparison of Theory with Experiment, 2T2, BetweenThermo- 42 couples 1 and 4 Using Measured Temperaturesat Those Locations 29 Comparison of Theory with Experiment, 3T12Between T = T 42 at s/L = O and T I at s/L = 1. Path Length from Bulk- head to Waterline= 30 Comparison of Theory with Experiment, 3112,Between Thermo- 43 couples 1 and 4 Using Measured Temperaturesat Those Locations 31 Comparison of Theory with Experiment, 316,Between T = TF at 43 s/L = O and T T at s/L = 1. = Path Length from Bulkhead to Waterline -v - LIST 0F FIGURES (Contd)

PAGE NO. T = T 44 32 Comparison of Theory with Experiment, 3T3, Between at s/L = O and T = T at S/L = 1. Path Length fromBulk- head to Waterline 45 33 Thermal Transient on 3T6B4 48 34 Temperature Response on the Insulated Side of aPlate When Chilled with Alcohol Mixed with Dr Ice. The Experimental Value of h was 22OBTU/Hr. Sq. Ft. °F 48 35 Temperature Response on the Insulated Side of aPlate When Chilled with Water. The Experimental Value of h was 125OBTU/ Hr. Sq. Ft. °F Plate Chilled 49 36 Temperature Response on the Insulated Side of a with Freon 114. The Experimental Value of h was 125OBTU/Hr. Sq. Ft. °F. Flat Plate 49 37 Temperature Response on the Insulated Side of a Chilled with Freon 12. The Maximum Experimental Value of h was 1625BTU/Hr. Sq. Ft. °F 50 38 Temperature History in the Cold-Spot Model 51 39 Temperature Measurement History in Ship PTEModel 51 40 Normalized Temperatures on Steel ThermoelasticModel 53 41 PTE Fringe Patterns in Cold-Spot Model 53 42 Comparison of Cold-Spot on Area Ratio Solutions Model at 5 Minutes . 54 43 Photoelastic Fringe Patterns in Simulated Shìp 57 44 Normalized Stresses on Steel Ship Model. A2/A1 = 0.92 During the First 59 45 Hold Pressure Versus Accessible Vent Area 10 Seconds of a Liquid Methane Accident for aShip with the Configuration Described in the Text Strain Gage Signal . . . 62 A-1 Correction Curve for Effect of Temperature on

-vi- NOMENCLATURE

Symbols

A area of cross section, in2 a,b radii in cold-spot problem,in. B Biot number, hL/k

C G/ctET

c specific heat- BTU/°F-l5. D thermal diffusivity, k/cp, ft2/hr

E Young's modulus,msi

e radiation constant, BTU/hr-ft24- F

F factor in radiation Eq.(13)

f material fringe value,psi-in/fringe G shear modulus, msi g coefficient, g2 = (1 +q/q)(h+.h)/kt1 ft2

depth of ship bottom,ft. h surface heat transfercoefficient, BTU/hr-ft2-°F J temperature ratio, see. Eq.(63)

k thermal conductivity, BTTJ/hr-ft-°F L general length, in. or ft.depending upon use n fringe order p pressure, psi

Q heat flow, BTU/hr. q heat flux, BTU/hr-ft2

R1, R2 parameters defined by Eqs.(31) and (32) r radius in cold-spot problem

S constant, see Eq. (28) distance, ft.

T temperature, °C or weighted temperature, see Eq.(34)

t thickness, in. or ft. u, y, w dimensionless lengths in Eq. (6) x, y athwartship and vertical coordinates, ft. thermal expansion, 1/°F temperature coefficient of volume expansion, 11°F

increment Stefan-Boltzmann constant, 0.1713 x1O8BTU/ sq. ft.-hr-°F4

E normal strain acceleration of gravity, ft/sec2

0,0 time, hr., also dimensionless time in Eq. (6)

P absolute viscosity, lb/ft. sec.

V Poissons ratio

P specific weight, ib/cuft

normal stress, psi

T shear stress, psi angle of principal stress, deg.

Subscripts

A Air

e Emissivity

F Fluid

H, V Horizontal, Vertical

h, k, r Convection, conduction, radiation

i Initial temperature of plate

L, R Left, right

m, p Model, prototype

o, u Total available, ultimate attainable (stresses, temperatures) -viii- s View

T Temperature

W Water w Wall x, y Coordinate directions

1, 2 Inner and outer (ship sections) (Radiative surface)

45 Rosette strain gage at 45 degrees to the orthogonal arms SHIP STRUCTURE COMMITTEE

The SHIP STRUCTURE COMMITTEE isconstituted to prosecute a research of knowledge program to improve thehull structure of ships by an extension pertaining to design, materials andmethods of fabrication.

RADM W. F. Rea, III, USCG, Chairman Chief, Office of Merchant Marine Safety U.S. Coast Guard Headquärters

CAPT J. E. Rasmussen, USN Mr. E. S. Dillon Head, Ship Systems Engineering Deputy Asst. Administrator for Operations an Design Department Naval Ship Engineering Center Maritime Administration Naval Ship Systems Command

Mr. K. Morland CAPT L. L. Jackson, USN Maintenance and Repair Officer Vice President American Bureau of Shipping Military Sealift Command

SHIP STRUCTURE SUBCOMMITTEE

The SHIP STRUCTURE SUBCOMMITTEE actsfor the Ship Structure Committee by providing technical coordinationfor the determination on technical matters the of goals and objectives of the program,and by evaluating and interpreting results in terms of ship structuraldesign, construction and operation. AMERICAN BUREAU OF SHIPPING NAVAL SHIP ENGINEERING CENTER

P. M. Palermo - Chairman Mr. S. Stiansen - Member Mr. L. Stern - Member Mr. J. B. O'Brien - ContractAdministrator Mr. I. Mr. G. Sorkin - Member NATIONAL ACADEMY OF SCIENCES Mr. C. H. Pohler - Member Ship Research Committee U. S. COAST GUARD Mr. R. W.Runike - Liaison E. Goldberg - Liaison CDR C. S. Loosmore - Secretary Prof. J. CAPT H. H. Bell- Member SOCIETY OF NAVAL ARCHITECTS &MARINE CDR E. L. Jones - Member CDR W. M. Deviln - Member ENGINEERS Mr. T. M. Buermann - Liaison MARITIME ADMINISTRATION BRITISH NAVY STAFF Mr. J.J. Nachtsheim - Member Mr. F. Dashnaw - Member Dr. V. Flint-Liaison Mr. A. Maillar - Member Mr. F. Seibold - Member WELDING RESEARCH COUNCIL MILITARY SEALIFT COMMAND Mr. K. H. Koopman -Liaison R. Askren - Member Mr. R. INTERNATIONAL SHIP STRUCTURE CONGRESS Mr. T. W. Chapman - Member CDR A. McPherson, USN - Member Mr. J. Vasta - Liaison Mr. A. B. Stavovy - Member

-x- INTRODUCTION

Purpose of Project This project was directed toward development of theoretical procedures for the calculation of temperatures and stresses in a cryogenic tanker when a tank ruptures and the liquid natural gas contacts the metal of the hold. The theortical procedures were to be substantiated through model studies.

It has been one aim of the project to reduce heat transfer and stress analyses to simple procedures. FDr this reason initial efforts have been devoted to application of simple engineering computation procedures although they may be lacking in fine detail and rigor. This has been done in order to assess the usefulness and limitations of the methods.

Approach to Project

The heat transfer investigations were performed ori model configurations which varied from a reasonably well scaled version of a ship to a model in which the walls were much thickér propor- tionately. Large variations in wing tank width were included. Both non-boiling and boiling chilling fluid experiments were conducted. Relatively simple heat transfer calculation procedures were developed and were used to compare theory and experiment.

The problems relevant to convective heat transfer analysis are identified and discussed, and the relative magnitudes of convective, radiative and conductive heat transfers are identified. The prevalence of convection in a ship is pointed out and substantiated.

An important aspect of the LNG tank failure is the prob- ability of generation of high pressure in a hold that is not vented properly. This would result from the vigorous boiling of the fluid as it comes in contact with the metal of the hold. A discussion is included on the character of this behavior and on the potential danger which it presents.

The literature on thermoelasticity and photothermoelasticity (PTE) contain sufficient data to allow the following two generalizations, which were used to design the approach to this project: -2-

Accurate information on temperature distributions will permit theoretical calculations of thermal stresses which will be of comparable accuracy and any loss of accuracy in a thermoelastic problemwill stem from inaccuracies in the computation of temperatures from heat transfer calculations. Peak thermal stresses almost invariably can be found, to engineering accuracy, from simple theoretical relations. These two observations were considered axioms for the present investigation, which concentrated ondetermining how simple the computation procedure could beand still yield good correlation with the experimental stress dataobtained during this project. The focus of the experimental stress phase wasthe steel model on which strain gages and thermocouples wereplaced to provide the required data. Effective data acquisition from that model depended upon placement of the strain and temperature sensors to provide peak values and toestablish the distributions reliably. This involved some prior knowledge of thecharacter of the stresses to be anticipated, for whichphotothermoelasti- city was used because of the total picture ofthe stresses which it provides. In addition, PTE experiments provided further checks with the simple calculation procedure for peakstress determination to supplement the experience with thesteel model.

HEAT TRANSFER THEORY

Introduction The theoretical bases for the temperaturecacuIations of this project are presented in thefollowing paragraphs. The various degrees of approximation for the heattransfer analysis are presented, from whichcalcu1atns are made subsequently for correlation with the experimental data. The three elementary equations of heattransfer per unit area are (Ref. 1),

conduction: q = k(T1 - T2)/L

convection: q = h(T1 - T2) 4 4 radiation: q =e(T1- T2) They were used to develop calculation methodsfor temperature as a function of time and position forcomparison with measured test data. .3 - Conductive Heat Transfer

The transfer f heat by conduction is usually considered to occur by diffusion of energy through the conductingmaterial. The material thermal conductivity depends primarilyupon temperature. In metals, it is essentially independent of strains. ne general expression may be written in the form

= kA(T1 - T2)/L (4) The numerical analysis of transienttemperatures in the plane of a thin plate with insulated faces is oftenaccomplished mathematically by writing Eq.(1) in difference form equivalent to the differential equation for heat conduction,

(cp 'k) aT/ao = a2T/ax2+ ä2T/ay2 (5) This relation is usable for general analysis and also for thermal scaling in heat conduction problems. It can be used to relate times ìn a model and prototype at whichthe shape of the temperature distribution in each wouldbe the saine provided convection is not a major consideration. This is done by nondimensionalizing Eq.(5) through the use of an arbitrary reference length, L, andan arbitrary reference, time, e,

u=x/L, v=y/L, w =

By substitution in Eq. (5)

(cpL2/k) &T/&w=a2T/au2 + 82T/,v2 (6) The temperature fields will have thesame shape when all the partial derivatives are in thesame proportion, or when

(cpL2/k)= (a2T/au2+ a2T/av2) a T/&w ) (7) both for the model and theprototype. Then the temperature scaling law becomes (using D= k/cr)

(Lm/Lp)2= (Dm/Dp) (/) (8) The choice of scaling lengthis arbitrary, as indicated above.

Representative values of diffusivityare shown in the following tabulation.

Table 1 - Diffusivities for Metals and Plastics Natcr ial Diffusivity Alum. Mag. Steel Titan Nickel Plastic

D=k/cp 1.97 1.60 0.45 0.24 0.24 0.005 ft2/hr (Approx.) -4- Consequently, the comparison of steeland plastic would involve times and lengths in the following relation

2 = 0.011 (L ¡L (9) steel'piastic steel plastic If a steel ship with a 60 foot beam iscompared to a plastic model with a 3.33 inch beam (which was used in the PTE experiments described below) ,then similar temperature distributions would be expected when the prototype timeis 520 times as long as the model time. Convective Heat Transfer In contrast to conductiveheat transfer the apparently simple relation of Eq.(2) actually involves some of the most complex phenomena in engineeringbehavior. They are all em- bodied in the convective heattransfer coefficient, h. Values for h have been determined by acombination of dimensional analysis and curve fitting to largequantities of data. Table i '(from Ref. 1) contains thedimensionless groups which appear in this report.

While k for a given metal may vary by percentages as afunction of temperature, h for a fluid may range over3 or more orders of magnitude as a functìon of temperature,pressure, velocity, viscosity, pathlength and several otherfactors including the state of the fluid and whetherit is quiescent or boiling. In the case of boiling, surfacecontamination is an important factor which can affect seriously the reproducibilityof data. The convective heat transfer relationis expressible as = hA(T1 -T2) (10)

TABLE J.- DimensionlessGroups Used in this Report

Name Group Symbol

Bìot number hL/k NB.. Fourier number D0/t2 N 2/2) Grashof number (L3 (ßt) NGr -5- The overall heat transfer coefficient,h, is given in Figure 1. It pertains to transfer between two parallelplates enclosed around the edges witha nonconducting material to form a box. The Grashof number is basedon the distance between the plates. The overall heat transfer coefficient forthis system is defined as

1 1 L h 1 A 2

where h and hare the unit surface coefficients for free convectionon he inner surfaces of the plates andL/kA represents the conduction through the air betweenthe plates.

The cell behavior (or convective flowpath) for the vertical plates consists ofone major cell which forms with flow down the chilled wall and up thewarm wall. There may be small corner eddies but the action is primarily uni-cellular.

Flow for the horizontal platearrangements is quite different. For laminar motion the cellular behaviorlooks hexa- gonal as depicted in Figure 2. This cell action can be biased by fin behavior induced by stiffeners. It will be affected strongly by the stiffeners as the motionbecomes turbulent.

The heat transfer per unitarea as given in Figure 1 would be independent of size until theplate separation is large with respect to the wall height (approximatley2-1/2 to 1) The equation using this heat transfercoefficient would then be used with the exterior surface heattransfer equations to complete the total heat flow analysis.

io2

VERTICAL

HORIZONTAL_L hL 10 kA JLE Q

106

GRASHOF NUMBER BASED ON L

FIGURE 1- Overall Convective Heat Transfer Coefficient Between Two Walls

of an Enclosed Space . (Ref. 1) -6-

FIGURE 2 - Cellular (Steady/State) Behavior in Horizontally Enclosed Space Heated from Below.

Radiant Heat Transfer (Ref. 1) Radiant heat transfer between any twosurfaces of an enclosure involves the view the surfaceshave of each other together with the emittirg and absorbingcharacteristics. This study treated the longitudinal girderand the side shell as the absorber and emitter. The connecting plating was considered to be non-conducting but reradiating. This is consistent with the convection analysis and adequately representsthe radiation effects at the mid-plane of the hold and wing tanks awayfrom the end bulkheads. The radiation equation can be written in the form

= hAr1 - T2) (12) for direct comparison with convective and conductive heat transfer rates. The heat transfer coefficient may be defined

h =FF F r seT contains the temperature factors for view, emissivity and radiation. The radiation temperature factor is

FT = 0.172 x10_8(T1 + T2) (T + T)

where T1 and T2 are in degrees Rankine. The emissivity factor is 1 Fe - 1/e1 + 1/e2 - 1 (15)

For rough steel plates the emissivity is approximately 0.95. This value drops to 0.80 when there is a coarse oxide layer on the plate. Painting the steel surface does not significantly -7- change that range. In fact, a variety of 16 different colors of the spectrum including white produced an emissivityrange on steel of 0.92 to 0.96. Some exceptions were black shiny shellac on tinned steel (e = 0.82) , black or white lacquer (e = 0.80) ,and the aluminum paints and lacquers (e= 0.27 to 0.67) Some red paints were as low as e 0.75.

The view factor, Fs, for this series ofexperiments ranged from 0.6 to 0.9as shown in Figure 3. The lower value represents the greatest wall separation.

Relative Magnitudes of Heat Transfer

From Eqs.(4, 10 and 12) ,it is possibleto estimate the relative magnitudes of the threetypes of heat transfer. For this purpose consider two walls ofsurface area Aconnected by steel plating with a cross sectionarea A. The relative heat flows between the walls, withone at T1 and the other at T2, would be

Qk:Qh:Qr = (kAk/L) : (hUAw) [Awse F F FT] (16)

Compared to conduction,

= B A /A = (hL/k)A,/Ak w k (17)

.9 LONG, NARROW RECTANGLES

.6 SQUARE PLATES

F5 .

r o o 2 3 4 5 o 7 SMALLER SIDE LENGTH

DISTANCE BETWEEN PLATES

FIGURE 3 - View Factor for Radiation Between Parallel Plates Connected by Non-Conducting but Reradiating Walls. (Ref. 1) -8-

(A /A rk= t.FFFTIJ/'k) w k = (FFFT/h) In order to obtain an estimateof the heat transfer ratios for a ship assume the wing tankdimensions to be 40 feet high, 60 feet long and 10 feet wide. Assume a constant plate thickness of l/20ft. which couldaccount for stif-feners and ribbing. Further assume that the hold walland the side shell are the two heat transfer surfaces forconvection and radiation. The plates that connect these two wallsconstitute the conduction path. The upper and lower plates (decks) areused at full material thickness for conduct'on. However, the si'fe plates, (fore and aft bulkhead) are used at 1/2 thematerial thickness for conduction heat transfer to thewing tank. This 1/2 thickness assumption allows 1/2 theconduction heattransfer to go to the wing tanks adjacent to thecompartment under consideration. This is not done with the lower plate (deck)of the compartment because it is assumed that all the heatconducted along that path comes almost directly from the water atthe connection to the outer hull. Assume a hull plating thickness of1/20 ft. The conduction expression of Eq. (4) is written

= (kAk/L)AT ( 2 0) where k = 25 BTU /hr.-ft2--°F L = 10 feet ft. Ak (1/20) (2x60)+(1/2) (1/20) (2x40) = 8 sq. This yields a conduction heat transferof = 20 AT BTU/hr-f t-F ( 21)

The convection relation of Eq.(10) can involve the establishment of a temperature differeiiceto determine the heat transfer coefficient from Figure1. Therefore, assume the hold wall temperature at -259°F(methane boilinq ooint) and (for convenience) an outer hull walltemperature of 41°F for a total temperature difference of 300°F. The above temperature difference and the assumed constants

kA = 0.013 BTU/ft±hrF

L = 10 feet

h= 1.2 BTU/fthr2.F yield u The convection heat transfer becomes

= 2880 AT BTU/hrF C22)

The radiation heat transfer isdetermined from Eqs. (12) through (14) -9-

= AFFETAT (23)

The constants are chosen as emissivity e9ual to 0.9,Fe = 0.82, FT 0.35 and F5 = 0.85 in this wing tank for the assumed temperature gradient. When combined above the radiation heat transfer equation is

= 580 AT BTU/hr°F (24) A comparison of the ship heat transfer magnitudes may be made with the aid of Eqs. (17) , (l8 , l9) , (21) , (22) arid (24).

= 144/29/1

= 144

= 29

+ r"k = 173 The ratios that would be obtained in the models used in this program for overall temperature changes of 40°Fand 300°F are given in Tables 2 and 3 which are based on models to be described subsequently.

General Equation for Thin Plates

A representtìon of a section of thinplate is shown in Figure 4. It is assumed to have unit depth perpenciicularto the plane of the paper. The stiffener web is shown at the midheight of the side. It is likely that little error would accrue if the stiffener total heat flow is assumedto be distributed over the length instead ofconcentrated locally provided the areas are taken into accountproperly.

The heat balance is obtained by relating theheat flows to the rate of temperature rise inthe element, AT/'LO,

As - (q2 - q t =C ptAs (AT/AG) (25)

The fluid end stiffener componentsare assumed to be constant in time and also over the length As. In general they may vary with respect to both.

If q - q is represented by Aq then the changein heat flow rataioAgthe element

+ q tAq/As = cpt(AT/A6) (26) -10-

Now employ Eqs.(1) through (3) and utilize thepartial derivative notation for the differentiallimits of time and length. Then if T is the only dependentvariable, the one-dimensional equation becomes(recalling the sign of ST/as) [(FFF) (T-T)+(FFF) (T-T)+h(T-T)+ s eT L L seTR R L L (27) hR(Tp_T)]/t +k(2T/3s? c (T/BO)

The analysis is eaily xter1dable to two dimensional heat transfer by adding k( T/v )to the left side cf Eq.(27).

TABLE II - Re'ative HeatTransfers, tT = 40°F

Model TF: TF Long )hort Path) Quantity 2T8 2T4 ZTZ 3T12 3T6 3T3 Path) 2/3 0.208 b)ft) 2/3 1/3 1/6 1 1/2 1/4

1 0 125 0.015625 0.296 0.0090 b3 0.296 0.0370 0.00463 26 26 k(BTU/hr-ft-°F) 26 ¿6 26 26 26 26

1 0.856 0.39 0.39 1 1 0.856 Ah(ft2) 0.39

0. 0139 0.0075 0. 0075 0.0075 0.0345 0. 0345 Ak(ft2) 0.0139 0.0139 0. 0080 b/k 0.0255 0.0128 0.00642 0.0385 0.0192 0.00962 0. 0255 133.3 133.3 133.3 24. 8 24.8 Ab/Ak 28. 1 28. 1 28. 1 1.28 0.633 0. 198 (b/k) (Ah Ak) 0.715 0.359 0. 181 5. 13 2. 56 0.371 h 0.43 0.395 0.36 0.44 0.405 0.379 0.43 u 1.04 0.485 0.272 0.0735 0h 'k 0.307 0. 142 0.065 2.26 0.92 0.92 0.92 0.92 0.92 FT 0.92 0.92 0.92

0.736 0.736 0.736 0.736 0.736 0.736 0.736 0.736 hr 0. 504 0. 585 0.538 0.490 0.60 0.55 0.516 0.584

0. 525 0.263 0. 133 3.77 1.89 0.94 0.464 0. 146

0.405 0. 198 6.03 2.93 1.43 0.736 0. 220 + 0.832 -11-

TABLE III - Relative Heat Transfers, T 300°F

MoeI TF (i.'ig Quantity ?LT4 Short 2T1 3T12 3 T6 3 T3 Path) Path)

b(ft) 2/3 1/3 1/6 1 1/2 1/4 2/3 0.208 b3 0.296 0.0370 0.00463 1 0. 125 0.015625 0.296 0.0090 k(BTtJhr-ft-°F) 26 ¿6 26 ¿6 26 26 26 26

Ah(ft2) 0.39 0.39 0.39 1 1 1 0.856 0.856

0.0139 00139 AkCft2) 0.0139 0.0075 0.0075 0.0075 0.0345 0.0345 b1'k 0. 0255 0.0128 0.00612 0.0385 0.0192 0.00962 0.0755 0.0080 Ah/Ak 28.1 28.1 28.1 133.3 133.3 133.3 24.8 24.8

b/k) )Ah/Ak) 0.15 0.359 0. 18 5.13 2.56 1.28 0.633 0.198 h 0.913 0.861 0.784 u 0.955 0.888 0.825 0.913 0.800

0.654 C. 309 0. 142 4.90 2.25 1.055 0.578 0. 158

F1. 0. 35 0. 35 0. 35 0.35 0. 35 0.35 . 0. 35 0. 35 hr 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 3.2( 3.08 2.90 3.41 3.17 2.95 3.26 2.86 0.200 0.100 0.049 1.43 0.71 0.36 0. 178 0.0554 0. 8c4 0.40) 0.191 6.33 2.96 1.41 0.7 0.213

In a transient the to peak at which time temperature often is observed the term on the rightwill vanish. Then Eq.(27) will have thecharacter of a steady which sorne useful state relation from calculation simplificationsare possible. situation is relevantto the present This temperatures an investigation since both stresses were observedto reach extreme values at approximately thesame time. Linearized Method

From the standpointof a designer, there considerable value in would be a reasonably reliabledesign temperature determination schemethat would require A straight line virtually no computation. temperature gradient mightbe possible if heat conduction predominatesand if a metal to the temperaturesof a liquid temperature would be close This may be inaccurate wherever the twoare in contact. depending upon theamount of convection and radiation whichis present. -12-

q2 = HEAT FLOW RATE AT 2

LEFT SIDE STIFFENER RIGHT SIDE FLUID WEB FLUID +

tsJ = R}, + q

HtH

q1HEATFWRATT i

IF s IS THE STIFFENER SPACING, L5, THEN AN EQUIVALENT STIFFENER HEAT FLOW, q5 MAY BE FOUND FROM sq t s SS

FIGURE 4 - Plate Strip Element for HeatTransfer Analysis.

This linearized method isprobably the simplest method. the experi- It was found to agreereasonably well with some of mental data of this investigation.

Quasistatic Method An improved method of temperaturedetermination (relative be achieved through useof the to the linear approximation) may observed quasistatic approximation, sT/3O = O. This condition was in the late stages of all theexperimental transients ofthis simple strip which relates project. The following is confined to a to two dimensional heattransfer, vertical andLthwartShip. From Eq.(27) with T/O = O, d2T/ds2=2eT4/kt + (hL+hR)T/kt - S (28) Where S =[ (FSFeFT)L + (FSFeFT)R]/kt+ (hLTL+hRTR)T/kt (29)

tf the radiation term is assumedto be a constantfraction of the convective term,then -13-

S=(1+ (hLTL+hRTR)/kt (30) If all the coeffic:ientsinEq. (23) are assumed constant, thc

T=(T1+T2)/2+ -T1)/2+R2 (31) where

R1=[sinh gs - sinh g (L-s))/sinh gL (32)

R2=i - [sinh gs+sinh g (L-s)J/sinh gL (33)

g2=(1+ (hL +hR) /kt (34)

=(1+q/g) (hLTL+hpTR)/(hL+Ì.) - (TL+TR)/2 (35)

The graphs of Rand R appear in Figure 5 in terms of s/L and gL. They showthatR1 ecomes linear and R2 becomes zero at very small gL which co±responds to prevalence of conductive heat transfer. For that case (Figure 6a)

T=T1+(T2 - T1) (s/L) (36) For large gL (which would be the case ina ship with a strong wind blowing across the deck) R, and R.) approachstep functions, convection controls, and T appróaches the form of Figure6c. Eq.(31) was compared with experimental data at long times for all temperature model tests conducted duringthis project. For those comparisons it was necessary to determine thetemperature of the air outside and inside the wing tank. This was done by assuming that the temperatureTL was that of the outside air, and that TR (for the air inside the tank)was the weighted aver'ge of the temperature of the metal surrounding thetank. It was also assumed that h =h =h with h determined as shown in the section on experiMenta data.

As for the weighted average of the metaltemperature, this was estimated for each test on the assumption ofa linear variation of temperature from that of the chilling fluidto that of the water. This estimate certainly is open to question. H.owever, it is consistent with the desire for simplicity incalculation.

Finite Difference Procedures

Eq. (27) may be written

2T/s =(l+q/q) (hL+hR)T/kt- (l+/q) (hLTL+

hRTR)/. +(1/D) (aT/ao) (37) The finite difference form is

Ts,t+Ts-11t n 2T51 - sTx,t+1 T,t D -14- 1.0 +1

g L 50 i +R R 0 0.5i gL

i + R1

0 0.5 s/I

g L=x

fi 0.5 gLO c/L FIGURE 5 - Curves forR1 and R2

2 As in Dusinberr (Ref. 2) assume (As) 2DAO. Then 2 (S - g2 Tt) (As) /2 (38) Tt+i =(1/2) (Tx+i t+Tx-1,t + When S = q /q = O4.t This is the strip tran3ientequation. Eq.r(3) becomes the Schmidt plot relation (Ref. 2). 'ias used to predict transient te"'poraturesfor comparison with test data at several locations on oneof the thermal models and at one point on the therinoelastic model. These calculations employed a typical value of D =1/2 sq.ft/hr. -15-

(1 + q/q)(hT-f hT)/(h1 + hR)

T+ T2)/2 T=Ti +(12T1)(VL)

T a.gL = O, CONDUCTION CONTROLS

T2 T '(12- T )/2

T = (T1 + T2)/2 +R1(T1 _T2)/2 -i- R ¶

b.INTERMEDIATE gL

T=(Tl+T2)/2+(hLTL+TR)/(hL±hR) T2

(IF q/ is negligibly small)

c. gL , CONVECTION CONTROLS

o s/I

FURE 6 - Range of Quasistatic Temperature Distributions Along a Strip, Shown Schematically.

THERMAL STRESS THEORY Nature of Thermal Stresses

Thermal stresses are mechanical stresses that arise from restraint of free thermal expansion. This is the generic term for dimensional changes due to either increasingor decreas- ing temperatures. The interaction between the thermally induced expansions and the restraint-induced stresses is thermoelasticity. The restraints may be external, or theymay be purely internal because of the inability of adjacent structural elementsat different temperatures to deform freely becausethey are attached. The general nature of thermoelasticity hasbeen delineated y Melan and Parkus (Ref. 3,

The emphasis of this project isupon the development of a theoretical procedure whichcan be used for reliable prediction of the thermal stresses ina structure which essentially is -16- comprised of numerous intersecting plates. The thermal field is to be assumed to originate fromthe sudden introduction of a mass of cold fluid into arelatively warmer region of that structure. That type of behavior commonly istermed "thermal shock". It is a loosely used term, as isdiscussed in Ref. 4. Furthermore, the theories for predictingtemperatures under thermal shock necessarily have had 1- assume specific forms of the initiating temperature transientin order to achieve a tractable closed form solution whichis often mathematically desirable. In this report, as was indicatedin the Introduction, thermoelastic theories are advanced which areof the utmost simplicity since experience has shown thatrelatively simple theories may be employed to predict stressesin a complex structural problem with reasonable accuracy.

Some Aspects of Thermal Stresses It is possible to approximate thesolutions to a thermal stress problem in various manners. A hypotietical maximum can be computed which would beindependent of all the shape and thermoelastic parameters of the problem exceptfor , E andT0. The quantity ctETQ may beused as an upper limit which may be approached rather closely undercertain conditions but would never be attained. (In a the:na1 stress fjeld wIth ox the quantity would be increasedby the rultiplying factor 1/Cl -V)). It would be the mostconservative estimated solution to the edge-heated planeproblem. A closer approximation maybe made through use of the Biot number, hL/k, as will beexplained later in this report. The magnitude of B depends uponproperties of the two media which come into contact to initiate thethermoelastic field in one of the media, such as liquid methane andsteel. A relation has been developed which delineates theultimate fraction of ETQ which can be attained no matter what theproblem geometry may be. conservatism than the This value would involve a lesser degree of first.(See Eq.(43) and ff below). Finally, the precise value of the thermalstress can be calculated from a knowledge of allthe geometric and thermoelastic aspects of the problem. This would involve no conservatism, of course. One of the directions of this investigationhas been to explore all three of these situations andascertain how they are related for the cases investigatedduring this project. The results of that comparison form an importantpart of the report and are discussed in theConclusions. Discussions of Related References Investigations of thermal stresses in shipshave been reported in the open literature (Refs.S through 8) . These studies relate to the generation of thermal stressesinduced in a ship by the external environment. They involved radiation from the sun, convection from the air, and primarilyconduction from the sea. The model studies have involved air convection and simulated sea conduction. -17- In all these studies, the ship structure was tacitly assumed to be a series of connected plates. No results were reported on the distributions of temperatures and stresses through the plating or across the stiffening systems in planes perpendi- cular to the stiffened plates. As a result, none of the theoretical procedures discussed in the references would be completely satisfactory in their present form for use in the analysis of ship therrnoelastic problems since the latter type of heat transfer (and the resulting thermal stresses) could be important for stiffened plate stresses. However, present theories could be modified and adapted to that purpose.

In general, the agreement of theory and experiment by Lyman and Meriam (Ref. R) was found to be good with deviations mostly in the order of a few percent for the ship measurements. However, it is surprising to observe that several experimental data differed by more than 10 percent from theoretical computer- ized predictions of thermal stress in the model studies conducted by Lyman and Meriam.

The most significant aspect of the cited references was the confinement of the problem to direct measurements of temperatures and of thermal stresses. Heat transfer calculations were not perfermed, nor were measurements made, to determine temperatures trom heat inputs.

In summary, therefore, it appears that the result of Ref.5 through 8 can serve only as a preliminary indication of the general nature of the stresses in a ship resulting from thermal shock. Basic Thermoelasticity

The basis for almost all thermoelasticity is the axiom that the total strain in a thermally stressed structure is the algebraic sum of the strains arising from unrestrained thermal expansion and from internal stresses,

= a/E + cET (39)

Eq.(3g) holds for uniaxial stresses because the mechanical stress ìs uniaxial. Otherwise it would be necessary to employ the three-dìmensional stress field relations, of which the total strain in one direction is expressed

E X=/E-L'r/E-i.'r/E+aTX y z (40) If we return to Eq.(39) and consider a situation in which the total strain is zero, then the thermal component bal- ances the mechanical component and if the minus sign is disre- garded, = aET (41) Eq.(41)is the simplest possible thermal stress theoretical relatìon of the induced stress to the average values of thermal expansìon, Youngs modulus and temperature change. In the case of a length of longìtudìnally restrained wire which has been chilled through a temperature change, T, ìt provides the precise solution in the region of the wire removed from the ends. -18-

Suppose, now, that a general three dimensionalstructure is subjected to action by a fluid mass initiallydifferent from the structure temperature by an amount, T0. If the structural material is homogeneous, and the structure is free in space, then it is possible to write the thermal stressrelation for any location at any time after application of the fluid mass

(o = aET (42) o- = C aET= C o 0 0 00 0 0 where the coefficient, co, contains all the complexityof the structural geometry and the character of the heat transferbe- tween the fluid mass and the structure. In fact, for initial estimates of the magnitude of severity of a thermalstress condition, Eq.(42) is often used with values of Cdictated by experience. For a large range of problems C may ge chosen to be1/2(a linear gradient across a restraine bar, for example) Stresses in a structure generally tend to peak at discontinuities.Mechanical stress concentration factors are well documented in the literature (for example, seePeter- son's compendium, Ref. (9). The situation with regard to thermal stress concentration ractors is radically different, as has been shown by Coiao, Bird and Becker inRef s.4, 10 and 11. One broad generalization relates to the maximum thermal stress in a structure of any shape, with or withoutdiscontin- uities. The basic study of Ref.4 showed theoretically and experimentally that there is an upper bound

0 (43) max o

while more recent studies by Emery, Williams and Avery (Ref.12) have added more substantiation to the prediction, also through both theoretical and PTE analyses. The simplest calculation of thermal stress can be made by substituting appropriate data in Eq. (43) ,which also will yield the most conservative estimate of thermal shock stress resulting from tank rupture. IfEis assumed to be 300 psi/°F then (44) 0o= 300T0 where T0 is the difference in temperature between the cryogenic fluid and the steel of the ship structure before the thermal transient begins. Actually, heat transfer considerations (as reflected in B) dictate the almost certain reduction of the largest usable temperature difference to some value less than the fluid-ship difference. In terms of maximum achievable thermal stresses, Emery, Williams and Avery have shown that for photo.a--c plastics the effective difference may be only about 60 to 65 percent of the maximum (Ref.12). Their results are displayed in rigure 7 which indicates that for the steel model of this investigation C would be less than1/2. The preceding relate to a rather simple type of structure and for a case in which the fluid temperature remains constant throughout the thermal transient. Actually, the chilling of the steel will be accompanied by warming of the fluid, thereby reducing the available temperature difference still further. -19-

ULTIMATE ATTAINABLE STRESS <1 a.,

q___ THEORETICAL CURVE (REF. 12 -- I I 7 I _-.. . I II. ui - i u mIrJiii!IIiÍi !i':

,L=O.27FTT

(h/k)L

FiGURE 7- Effect of Biot Number on Thermal Shock Stresses.

The coefficient, CO3 may be invested withthe role of reflecting this change.

These simple calculation methods representsteps in the approach toward determination of the precisevalue of thermal stresses in the steel ship model. One more factor is the relative cross section areas of the cold and warm regions of the ship imme- diately following chilling of the hold walls andbottom. If the longitudinal forces are balanced and thecross section strain is assumed to remain planar, then ( Figure 8)the force and strain relations are:

+ o2A2 - O (45)

+ czT1 = + T2 (46)

where T1is the average temperature of the Inner structurewhen the peak stress is reached, andT2 is the assumed uniform initial temperature of the ship steel before thetransient. That is not the type of initial distributionthat would exist at sea. The temperatures from the actual initial andtransient conditions would be additive if the superpositionprinciple is operative, which it would be if stresses remain elastic.The combination of inelastic thermal stress fields isa subject for a subsequent project.

It is a simple matter to combineEqs.(45) and (46) so that either°1 or o may be found. For example, for the model region outside the enter tank,

a = o(T /T - T /T )/(A /A 2 010 20 21+ 1) (47) -20-

EQUAL LENGTHS

CONTOUR FOR ___ A1

EQUAL - CONTOUR FOR LENGTHS A2

EQUAL LENGTHS- -

SHIP CROSS SECTION

a2 a1 .-._ a2 a2

FORCE BAIANCE DLAGRAM ASSUMING CENTROIDS OF A1AND A2 ARE COINCIDENT FIGURE 8 - SchematicRepresentation of the Ship Cross Section Force Balance andStrain Equilibration

the initial fluid temperatureand where T (the difference between normalizing factor. the iniìal model temperature)Is introduced as a (the initial temperatureof the If T.) represents room temperature chilling modet) and T1 is the devìationfrom room temperature due to egìon, then let T = T2-T , and the last terms in paren- in the tank relation. these's are the area correctionsfrom he force balance Consequently = (T/T)(A2/A1)/(l + A2/A1) (48)

(49) 02/O = (T/T)/(1 +A2/A1) factor of If A1 and A2 are nearly equal,then the above-mentioned 1/2 would apply as long as T isclose toT0. values for In any structure theselection of the proper would involve some judgementbased upon exper- A1 and A) normally first ince. Tn this effort the areas werechosen arbitrarily by of the anticipated meantempera- selecting the approximate location expected ture between the cold and warmregIons. Errors are to be throughout a structure and are sìnce the temperatures actually vary not so simply divided. -21- Cold Spot Problem

As a means of evaluating the general nature of the stress field in the ship, a relatively simple problem was chosen for an initial PTE investigation as shown in Figure 9. In order to compare the result with a classical closed form theoretical solution, it was assumed that the problem could be approximated by a cold spot in the center of a circular disk.

The general expression for thetangentialstress is (Ref. 13)

c/c = l/2 - (a/b)2[l + (b/r)2J/4 -(l/2)ln(b/r)/ln(b/a) (50) where e relates tQ the difeence in temperatu between the inner cold 8t and the disk exterior or the PTE study, one area of Tnterest is the outer boundaryQ the dìsk. mnce b at that location, then Eq.(50) becomes

c/c = (l/2)[l - (a/b)2j/ln(b/a) (51)

Out-of--Plane Behavior

The thermoelastic problem in a ship has been approached in this investigation mainly as the study of multiple-plateplane stress. However, the presence of stiffeners on one side ofa plate would induce heat flow normal to the plane of the plate. The consequence would be out-of-plane stresses anddeformations. If the stiffener flanges weresymmetric about theweb, then the deformations and stresses might be confined to bending. Angle stiffeners, however, might tend to bend and twist, andany tendency to buckle could be aggravated in certain cases. The buckling process would tend to relieve the thermoelastic field. However, it could lead to instability strength loss againstthe pressure- induced forces from the sea.

Angle-shaped longitudinal stiffeners were usedon the steel model to accentuate this effect in orderto assess the importance to ship design. In the current study, numerical values of stiffener stresses were obtained on the steel model. However, only a relative assessment was made of the stress levels compared to the maximum values in the model. A more det led evaluation of stiffener behavior was deferred to osile subsequent investigatIonsin which the possible significance to structural stabilitymay be considered. Thermal Stress Scaling

If two structures are identical in shape butdiffer in size and material, it isnecessary to utilize a theoretical relation to determine the nature of the stresses inone structure when the stresses in the otherare known in a given set of circum- stances. Rr mechanical loads the shapes of the stressdistributions in the two structures would be essentiallyidentical. Small differences may exist at discontinuities if Poisson'sratio is not the same for the two materials, but this is ucuallya negligible consideration. -22-

CRILLED ZONE

/o I T j EXPERIMENTAL MODEL CONFIGURATION

FIGURE 9 - Cold-Spot Problerrt.

COLD SPOT

EQUIVALENT COLD-SPOT CONIFIGURATION

The best means of relating thestiess fields is to develop the same a non-dimensional ratioof stresses which would have value for both structures. For example,it iSwell known that an appropriate scaling law for pressurevessels would be (52) °"model = 'prototype This means that the stress at agiven point and in a givendirection on a model would be exactlythe same on the prototypeif the pressures applied to each arethe same and that the prototypestress would be further increased beyond thatvalue as the pressure is increased. The relation in Eq.(52) applies to static pressures. Fbr transients a time factor mustbe considered. This is also the case for temperature transients. However, when the time factors are accounted for asdescribed for thermal scaling,then an appropriate scaling law for thermoelasticproblems would be

(53) =(o/cxET ) (ajaETo )model o prototype or, in the form of Eq.(42) and abbreviating the subscripts,

(54) Ccorn) = (Cop

I -23-

MODELS AND EXPERIMENTS

General Descriptions

Seven steel ship configuration models and two plastic models (Table 4) were designed and fabricated to acquire experimental data in this project. Three two-dimensional steel models and three three-dìmensional steel models were employed solely for temperature studies while the last steel model was used for both temperature and stress determinatìons. The two photoelastic models were tested to obtain supplementary thermal stress data.

The characteristics of all models appear in Figures 0 through 21 which depict the dimensional and material dataas well as the locations and types of instrumentation. Discussions of the models and test procedures appear in subsequent portions of this section.

A flat plate was employed to measure the surface heat transfer coefficients for the various fluids employed in these investigations. These tests are discussed below also. Temperature Models

Two models were designed and fabricated to represent a range of ship proportions and heat transfer characteristics. The cross-sections appear in Figure 10. A view of both ship models and the general experimental arrangement appear in Figure 11. Each temperature model consisted of one half of a ship region. It was rendered thermally symmetric about the vertical centerplane by 1 inch thick styrofoam plate cemented to the steel with RTV silicone rubber. In addition, styrofoam was cemented to the ends of each temperature model. As a result the 2D models were con- strained to essentially vertical and athwartship heat transfer where- as the 3D model was free to transfer heat longitudinally for one bay on each side of that into which the chilling fluid was'introduced. As is shown in Figure lO, each model was modified twice by halving the wing tank width so that three widths were available for study in 2D and in 3D. Since two non-boiling and two boiling runs were performed on each configuration, twelve pairs of tests were conducted to obtain experimental data for comparison with theory. Each experiment was performed by rapidly filling the center hold of the model with chilling fluid. Thermo- couple data were recorded for 1/2 hour after the start of the pour which required from 6 to 15 seconds depending on the model and the fluid.

Model for h

Part of the temperature investigation was assigned to measurement of surface heat transfer coefficients for the fluids whìch were used. The experIments involved rapid pouring of enough fluid into the square cavìty abovea plate (Thgure 12) to fill the cavity almost completely. Temperatures were recorded from the beginning of the pour which required only a second to accomplish. -24-

TABLE IV Model Descriptions

Model Figures Use

10 Two-dimensional temperature distribution.Large pro- Three portion of conductive heat flow compared toconvection Widths and radiation.Thick steel plates unreinforced.

3T, 10 Three-dimensional temperature distribution.Small Three proportion of conductive heat flow compared to convec- Widths tion and radiation.Thin steel plates reinforced against buckling.

3TE 18 Thermoelasticity in simulated ship.Conduction comparable to convection or radiation.Thick steel plates reinforced.

ZPTE 13 PTE local cold spot, two-dimensional problem.Single plastic plate.

3PTE 15 PTE ship simulation, three-dimensional behavior. Thick plastic plates.

Flat 12 Experimental determination of heat transfer coefficients Plate for non-boiling and boiling fluids.

Photothermoelastic Models PTE investigations were condu: ted on arectangular flat plate with a central chilled spotand on a plastic simulation of the steel model.One purpose was to determinehow closely Eqs.(4e) and (49) would agree withexperìmental data for these cases to provide a base forevaluating the steel modelresults. Another was to obtain a prelìmìnaryìndìcation of the usefulness of simple theoretical predictionprocedures for temperatures and stresses in the steel model.The PTE simulated ship experiment also provided data to aid strain gageplacement on the steel model. Cold-Spot Model The cold-spot model is a simplifieddelineation of the bottom plane of the ship.The region within the dam represents the hold floor and theexternal rectangular annulus corresponds to the remainder of the shipstructure at that level, except that the vertical walls of the shipintroduce the equivalent of additional cross section areas to the .tankbottom and the external regions. -25-

L3 - L4 4 3/ DEC K LA

SID ES H EL L IR ON/CO NSTANTAN

LONGITUD I NAL THERMOCOUPLE LOCATIONS BUL K H EAD

CENTER L MODEL DESIGNATION F WI NG TA N K 5 TAN K 218

L7 L DEGREES OF FREEDOM OF HEAT FLOW B' in.

MODEL USE L - fi (T = TEMPERATURE) L8 INNER BOTTOM

8 i OUTER BOTTOM

OVERALL HEIGHT, ALSO BAY LENGTH 21 MODELS, 8 IN. 3TMODELS, 12 IN.

M.ATERIALS: 2T MODELS, 1/8 IN. CARBON STEEL 31 MODELS, 0.032 IN. CARBON STEEL

ALL DIMENSIONS IN INCHES

MODEL LF LA Lw Lc Hw L1 L2 L3 L4 L5 L6 L7 L8

2 TB 7 12 3 1 4 115 80 400 3.40 4 0.5

214 7 8 3 1 4 74 40 20 0 3.4 0 1,8 05

2127 6 3 1 45520100 3401005

3 11210 18 4 2 6 173 122 6 3 0 5 1 0 6.11 0

3T6 10 12 4 2 6 1115.83.1 0 51 0 3.1 1.0

3T3 10 9 4 2 6 8.1 3.1 150 5.1 0 1510

FIGURE 10 - Thermal Model Datas -26-

CE WATER TEMPERATURE REFERENCE BATH II i m'i

THERMOCOUPLE LEADS

FIGURE 11 - Ship TemperatureNiodelsand Experimental Equipment.

5" ERMOCOUPLE S STYROFOAM 000000vçJI-, _5___ 00000000000000O0O 000000000 00000000000 00000000000 00000000000 J 00000000000 00000000000 00000000000 0000000000 00000000000 000000000 00000000000 000000000 00000000000 000000 00 00000000000 000000000 00000000000 0000000000 00000000000 00000000000 4 00000000000 00000000000 00000000000 00000000000 00000000000 00000000000 00000000000 00000000000 00000000000 00000000000 00000000000 0000000000 00000000000 00000000000 0000000000 00000000000 0 000000000 00000000000 00000000000 00000000000 STEEL 1/2 00000000000 ______00000000000 1020 00000000000 ______00000000000 000000000000 00000000k = 25 BTU/HR - FT - °F ______00090000 00000000 000000000 0 90 RTV SILICONE oocoo 000000000000 C EM E N T 4 0000000000000 0000000000000000000000000000000000000000000000 II00000000CC 0000000000000000000000000000000000000000000000 00000000 0000000000000000000000000000000000000V000800000000 00JIj000000 0 O0O0O00000000O00O0CÖ0O00000O00000O0f0O0 51/2' oaoc:-f00000000 SQUARE PLANFORM

FIGURE 12 - t1odel for HeatTransfer Coefficient Tests.

The model is shown in Figures 13and 14 together with the PTE material properties. It was important, in designing the experìment, to select a dam wallmaterial and joint which plate. Furthermore, would not resist the deformations in the walls. the joint had to prevent leakage of theethylene glycol under the Sone exoerimentation showed that theseconditions would be satis- fied with a fiberglas wall 0.064 in. thickand a silicone RTV rubber joint, as shown in Figure 13. The experiment was initiated by suddenintroduction of the chilled ethyleneglycol. Temperatures and fringe patterns were recorded at selectedintervals. SILICONE RIV CEMENT 10.18 H A H

,FIBERGLAS WALL

2.13 ETHYLENE GLYCOL 3.40 A-A A1/t

T A 0.132 A/t A 0- 340

MODEL MATERIAL, a, 37X10-ó/°F E,0.36MSI f, 40PSI-IN/FRINGE k/cp 0.005 (COMPARED 100.45FOR STEEL) ciE =13.32PSI/°F =0.60 FIGURE 13- Cold-Spot Model.

FIGURE 14 - Photograph of Cold-Spot Niodel Test. -28-

PTE Simulated ShipExperiment Before this project began asmall photoelastic model the general character of thermalstresses was built to reveal The in a ship with sudden chillapplied to the center hold. model details appear inFigure 15. During this current project the experiment was repeatedfor the reasons discussedpreviously. The model was fabricated fromflat plates of PSM-1, which was used for thecold-spot study also. They were cemented to the configuration shown in Figures 15and 16. The polariscope sheets model so as to reveal the stressfield in every were built into the quarter plate, although polarizingsheets were located only at one of the model and experimentsymmetries. of the model plates because This It was desirable to view allpolarìscopes sìmultaneously. the experimental arrangementshown in Figure was accomplìshed with fringe pattern 17 whìch enabled the camerafilm to contain all the images.

Therrnoelastic Model steel Thermoelastic studies wereconducted on a welded of a cryogenictanker model fabrìcated torepresent three bays in generalconfiguration. in Figures 18and 19. The size was The model is depicted complete between a small modelthat would permit a compromise hold in a short time,and a large enough filling of the central details reasonablyrepresenta- model to enablethe duplication of tive of an actualship. welding 1/8 inch thick The model wasfabricated by TIG The fabricationprocedure required coor- plates of T-1 steel. ii-i order dination of thewelding andinstrumentation processes installations of thestrain gages andthermo- to permit internal important to locatestrain gages close couples. Also, since it was gradients are greatest, to the plateintersections where stress final establìsh the minimumdistances from the it was necessary to located without damageby the welds at which straingages could be tests to establish process. These necessìtated heat of the welding provide a soundjoint, and experi- the smallest sizeweld which would to those survivability as afunction of proximity ments on gage precautions, a few gageswere lost welds. (In spite of all these during fabrication)

Welding studies wereconducted to design the welding procedure so asto maintain details of the model of adjacent plates. plate flatness andaccurate alignment These tests and themodel fabricationschedule portion of the project. However, the efforts consumed a large proximity resulted in a well-builtmodel, optimized the gage number of gages. to intersections,and minimized the -29-

SIDE VIEW TOP VIEW

t 0.135 TYP. r------i

0.50 DIA. I I II -- --- IITYP. II I

t 10 00 ______3.33 £ i I j

= LJL__aL I

= 5.00 I

L J LLJLI l's 3.33

END VIEW MODEL MATERIAL., PHOTOLASTIC PSM-1 TWTT 37 X I0-6/°F

li i E, 0.36 MSI I II f, 40 PSI-IN/FRINGE ii i

Il aE = 13.32 PSI,/°F i AilAi = 1.11 Lii__II JLJii

0.75 FIGURE 15 - PTE Ship Model.

FIGURE 16 - PTE Ship Model Photograph Showing General Experimental Arrangement. -30--

¡D

D j

FRONT VIEW L TOP VIEW L-LIGHT FIELD D-DARK FIELD

POLARISCOPE LOCATIONS

TOP AND VERTICAL BOTTOM WALLS

L 1G HT ING

FIGURE 17 - Ship PTE Model ExperimentalArrangement.

Instrumentation The temperature sensors werefashioned from 24 into gage iron-constantarithermocouple wire, beaded and wound a 3-turn spiral. The bead and the spiral were heldin close contact with the steel while the epoxycement bonding agent drieci adhered to the and hardened. The strain gages (Table 5) were steel with BLH SR-4 EPY-550 cement, Data wereobtained on a are depicted Visecorder. The applicatìons of the uniaxial qaqes ìn Fìqure 20 while the arrangementsof the others are shown in Figure 21. NOTES MATERIAL10 GA. (.135") T-1 TYPE A STEEL 4200 3, MENTSVIDEDTION1/4"1/16"L'S TO DIA. FEEBEND IN6E OF VENTALL D-THRUBENT MODELRADIUS CLOSED AND FROM HOLES HOLES INSTRUMENTA- COMPART-T-1 TO MATERIALTO BE 6E PRO- p a 6.5EPOSSIBLECONFINED X 10-6/°F TO ENDS OF MODEL WHERE A2/A1 = 0.92 29 ms \ = -, tr_flrr_ r = --=- I iL - a- -=--- FIGURE 18 - Steel Ship Model Dimensions ------.----- .T______j 4.00 --- -- 4---- J4e ----4------32-

I'- 4r

Thermocouples Attached to Plates BeforeWelding

Completed Interior Structure

FIGURE 19 - Photos of Model atDifferent Stages of Construction.

TABLE V - Strain GageCharacteristics and Locations

Type Shape Locations 9, 10, 11 BbH FAE-12-12S6 120 ohms, gage length =1 /8 in. Figure 20 6,7,8 Vishay Micro-Measurements WK-06-Z5OWT- 120 Figure 21 120 ohms, gage length =1/4 in. 3,4, Vihay Micro-Measurements WK-06-250WR- 120 Figure 21 120 ohms, gage length1/4 in. PMOBULKHEAD LOCATION T/C A BACK-TO-BACK,LONGITUDINALLONGITUDINAL SUM-PAIRED,TO MEMBRANEREAD WALL STRAINAVERAGE 4, LONGITUDINALINNEROUTS IDE BULKHEAD FACE CENTERLINEOF ON TRANSVERSE DIFFERENCE - PAIRED, I I TRANSVERSEBACK-TO-BACK, CURVATURE TO READ FLANGE SIDESHELL ALL ANGLES I X i X i/B END BAY -th---H----- CENTER BAY END BAY o. INNER WALL CENTER BAY LEFT SIDE 3;,4 STIFFENER IWO : OUTERBENDINGLONGITUDINAL FACE ONLY, DIFFERENCE TO READ VERTICAL - PAIRED, LONGITUDINAL BULKHEAD 21 F' I - '@:- i I + 7 I b. INNER WALL CENTER BAY RIGHT SIDE F OUTER BOTTOM FIGURE 20 - Thermocouple and Uniaxial Strain Locations Gage FIGURE 21 - Biaxial and Rosette Strain Locations and Thermocouple Locations. r--- Gage -34-

Experimental Procedure forThermoelastic Model chosen to receive thesudden The center bay was system was introduction of chilled fluid. A special pumping of the chilled designed and constructedfor rapid Injection denatured alcohol into thecenter bay. A MInneapolis-Honeywell used to record thedata throughout light beam oscìllograph was mInutes duration. each run, whìch wastypically of 6 to 7 denatured Each experimental run wasbegun by cooling the ice until a tempera- alcohol by immersing thetank ìn chopped dry had been reached. The recorder wasactivated ture of about -30°C gallons of chilled and then the pump wasstarted to ìnject 5 holds Injection was accomplished denatured alcohol into the center level of from i to 2 within 8 to 10 seconds,wìth a final fluid of the hold top.Appendices I and II con- ìnches below the undersurface obtained during all the runs. tain temperatures and stresses signals At the completion of thetests the thermocouple strain gage data were were converted totemperatures and the The culmìnation ofthe project was the converted to stresses. predictions of the comparison of the experìmentaldata with the theoretical procedures. Five runs were required toacquire all the necessary However, strain and temperature data. T0 varied from run to run. all the principal stresses werenormalized to

EXPERIMENTAL MECHANICS

Introduction temperature Thermocouples wereapplied to the steel used on the steelthermoelastic models while strain gages were Photothermoeiastìcity was model together withthermocouples. data from twosupplementary experi- employed to obtain pertinent simulation of the ments, one of which wasconducted on a plastic types togetherwith the theore- steel model. The three experiment planned to provide thedata on which tobase tical analyses, were this project. the prediction proceduressought as the goal of instrumentation are des- The properties of thesteel model relating to thoseexperiments. They are cribed ìn the sections architects and in broad use and arefamiliar to most naval in universal employment. Therefore, engineers. However, PTE is not a brief sketchof the technique ispresented.

PTE polarized light, When transparent structuresare loaded in observed, the nature ofwhich may be interference fringes are The basic related to stress through acalibratIon procedure. is more than 150 yearsold. tetailed character of the process textbooks and journalarti- descriptions are availablein numerous -35- cies. Two of the best known references are the treatises by Coker

and Filon (Ref. 14) and by Frocht (Ref. 15) . The basic relation between stress level and fringe order is shown to be

n = - c2)L/f (55) where i and 2 refer to the principal stresses and L is usually the thickness of the model. For a free edge, a = O. In all the work in photoelastic analysis of structural behavior the loading was a mechanical force system until about 15 years ago. At that time a series of investigations was initiated (Refs. 16 through 19 contain many of the results) in which the models were loaded by temperature fields, most of which were initiated by application of dry ice directly to the model surfaces. The resultant transient temperature fieids induced inge patterns which are related to stress in exactly the rame mar,ner as for mechanical loads. Although the stress distrihutions generally are different for the two types of loads, the usual calibration process and fringe interpretation of mechanical photoelasticity apply without modification to thermally loaded structures. It is only necessary to measure the relevant model material parameters as functions of temperature to obtain reliable data.

After a series of relatively simple investigations, experi- mentalists found that the achievable precision of a PTE investigation was as good as, or better than, that of a mechanical irives- tigation. Correlation with theory was found to better than 1 percent in almost every case. This success led to the use of PTE to evaluate the precision of thermoelastic theories, as was done by Becker and Colao on rectangular strips (Ref. 10) . It also was used to establish broad generalizations of thermoelastic behavior such as the lemma advanced in Ref.4 relative to the maximum attainable thermal stress in a structure, and the generalization that thermal stress concentration factors are not the same as mechanical stress concentration factors except possibly in a few special cases. This latter generalization was established by Becker and Bird (Ref. 11)in a study of holes in a plate.

Perhaps one of the most important aspectsof the PTE investigations to date is the observationthat a relatively simple theory may be found to predict theobserved stress maxima. In some cases it al.o was possible to predict thestress distributions reliably (ref. 4) . The experience with PTE has provideda part of the basis for the approachto this project which was focused on initially simple methods for calculationof thermal stresses and temperatures.

As was stated in the introduction, thereare numerous in- stances in the photothermoelastic literatureto demonstrate that excellent agreement of theory and experimentis achievable when the stress predictions proceed fromthe known temperature fields (Refs. 16 through 19). All the observed discrepanciesare directly traceable to the heat transferaspects o the problem. These lie either in the errors ofmeasurement of surface heat transfer coefficient or in the errors resultingfrom unwarranted simplifications in heat transfer analysismethods. These laLter often involve one dimensionalization of trulytwo dimensional problems, and the -36- assumption of temperature-independent properties when the properties really are temperature sensitive. The Biot number is in this cate- gory. Tramposch and Gerard (Ref. 17) showed the importance of these factors when analyzing a piate-type structure whIch is typical of aircraft wings and shìp structures. Strain Gage Data Reduction In terms of mechanical strains alone, the relations between plane stresses and strains are (Ref. 20, for example)

E(E +v)/(1_y2) (56) = E(e + )/(1 2)

G(E+ E - 2E45) (58) X y and the principal normal stresses and maximum shear stresses are obtainable from )2/ 1/2 (59) = ( + )/2 + - + 7 J 1 x y X y (60) )2/4 2 1/2 a- =(o- + a- )/2- - J 2 x y X y

)Z/ T2]1/2 T = [(a- - + (61) max x y The principal normal stress direction may be found from

tan24 = 2T/(o- - a-) (62)

In this investigation Eqs.(53)through(59)were utilized to

, yield the magnitudes of o , o and , and the magnitudes and directions of the principl nrmal stresses and the maximum shear stresses.

Experimental Errors The experimental data consisted of temperature and strain measurements. Generally, both of these measurements may be made to an accuracy of better than 1 percent. Another view of accuracies achievablewiththese types of Listrumentation s rzui identification of the magnitude of the smallest measureabie quantity. For strain gages read through a bridge balance :his can be as little as5microinches per inch under the conditions which existed in our laboratory during the testing phase. For the thermocouples the minimum measurable quantity would be 1/4°F. However, both these types of data were recorded on an oscillograph and then were deduced from the recorder traces. As a result the accuracy of reproducibility would control the accuracy of the data. For the Minneapolis-Honeywell recorder used in this project the strain scale was940nuicroinch/inch for 1 scale inch with a direct reading precision of 1/100 inch which indìcates a maximum precision -37- of 9.4 microinch/inch. The temperature correction chart was of comparable precisìon. For the thermocouples used on the thermoelastic model the scale was 705 millivolts/inch directly readable to 1/100 inch which corresponds to a precision of 1.4°C or 2.5°F. On the temperature models the scale was 0.67 millivolts/inch. The net precisìon was better than 05°F.

TEMPERATURE INVESTIGATIONS

Thermal Models

The six thermal model configurations, each tested twice boiling and twice non-boiling, provided24 runs with which to evaluate the theories proposed for determinationof ship structure temperatures under cryogenic shock. The ensuìng discussions have been designed to explore the correlation of theory and experiment. This was done by first examìnìng the temperatureson the deck and upper sidewall. After that the interìor plate temperatures were examined.

Attention is directed to the discussion of experimental errors which has been presented previously. The range of temperature error should be borne in mind when exploring the figures to be presented during this discussion.

Normalized Temperatures and Distances

The inìtial model, air and water temperatures were close to 70°F in every model test. However, the initial temperatures of the chilling fluid varIed from +40°F to -100°F. In addition, the most severe test of the usefulness of the calculation methods is the reliability with which they may be used to determine the distribution of temperature from one locatìon to another alonga plate. The absolute temperatures are of little importance in this type of evaluation. Only the change between locations is important.

For these reasons the portrayal of the temperatureson graphs was accomplished by normalizing them with respect to Furthermore, the lowest temperatures were reached when the quasistatic behavior was observed. This occurred at approximately 1/2 hour in every test on the thermal models. Consequently,the graphs display the 1800 second values of

J =(T - TF)/(Tw- TF) = (1-1-R1)/2+ R2/(Tw_TF) (63) as a percentage of the distance from the deck/girder joint to the total length between the waterline and the top of the longitudinal girder. This completely nondimensionalizes the data. In a few cases other lengths were employed as references. They are described subsequently. Tables Al through A4 display the theoreticaland experimental temperatures. Table A4 containsthe normalized experimentäl temperatures. The theoretical curves were plots from Eq.(31) using Figure 5to constructthe icjhest and 1owet curves only. -38-

Presentation of Data The theoretical and experimentalinformation appear in Figures 22 through 32. After preliminary examination of the experimental data, it was apparentthat there was enough scatter to invalidate a test-by-testcomparison of theory with all the infor- experiment. It appeared more reasonable to present matìon for one model on one graphand to compare scatter bandsin the manner shown on the graphs. This manner of presentationIs consistent with the scatter. It also permits a visualizationof the range of theoretIcal curves for eachmodel. Fin3lly, the clustering of the data permit a clearerobservation of the trends in the data. Discussion of Results The scatter of the experimental dataand the general agreement with theory are somewhat betterfor the 3D models than for the 2D models. However, there does not appear tobe a great deal of difference between them. In most cases the temperatures werehigher at the girder/ deck corner and lower at the waterlinethan the theory predicted based upon the use of TF and T as the referencetemperatures. This was probably the result othe details of the convectiveheat transfer process in these regions, The direct test of thepredic- tive power of the quasistatic 2D theory maybe seen in Figures 23, 26, 28 and 30 in which the plate wasanalyzed between thermocouples 1 and 4 instead of between the waterand the girder. The agreement with theory is considerablyimproved but there are still some The reference inexp1aFne large dvìatìons for these cases. length was changed to the distancebetween these thermocouplesand the reference temperature difference wasT - T so that J became Table A3 and (T -TA)/(T1-TA). The temperatures were tken rom the leigths were taken from Fìgure 10. The quasistatc theory was derived onthe basis of a model in which the plate length isthe distance between thelongi- tudinal girder (assumed to be at TF) andthe point of contact with the wetted surface (assumed to be at Tw) . In the cases of the 2D models however, conduction controlsand therefore these ref erencè surfaces would not be expected tobe isothermal. Gradients would be expected along them, as isverified by comparison of the temperatures at thermocouples 4,5 and 6 at the top, center andinner bottom of the bulkhead, respectively.(Table A3) The path length was increased 3.5 inches infront of thermocouple 4 and 2 inches beyond thermocouple 1 for model 2T8(Figure 24). The revised plots of meacured and calculated temperaturesdisplay a better matching of scatter bands than in Figure22. It is apparent that the fine details of radiation and convectionshould be corsidered if better agreement of theory and experimentis required.

Bottom Structure There is one thermocouple at the middleof the inner bottom (No. 7) and another at themiddle of the girder between the inner and outer bottoms (No. 8) . The temperatures at these locations appear to deviate radicallyfrom the average of the water and chilling fluid (Table A3). However, they do not depart -39- 1.0

5 PERCENT 8 -t-

e I s

0.5

THEORY EXPERIMENT NONBOILING o BOILING

o o 05

s/L

FIGURE 22 - Comparison of Theory with Experiment, 2T8, Between T =TE at s/L = O and T at s/L = 1. = Path Length fromBulkhead to Waterline.

1.0

5 PEENT o

0.5

THEORY EXPERIMENT NONBOILING o BOILING

0 / o 05 s/L

FIGURE 23 - Comparison of Theory with Experiment,2T8, Between Thermocouples i and 4 Using Measured Temperaturesat Those Locations. -40-

1.0

5 PERCENT . 4

0.5

J THEORY EXPERIMENT NON-BOILING o BOILING

o o 05 s/L

Expanded Path FIGURE 24 - Comparison ofTheory with Experiment, 2T8, Using Length and T = TE at S/L =0, T = TW at s/L = 1.

5 PERCENT -4-

0.5

THEORY EXPERIMENT NON-BOILING o BOILING

O o 05

/Theory with Experiment, 2T4,Between T = TF at sIL = FIGURE 25 - Comparison of Path Length from Bulkhead to Waterline. 0 and T = T at s/L = 1. -41- 1.0

I- 5 PERCENT

0.5

THEORY EX PER IM E NT NON-BOILING o BOILING

0 O 05 VI

FIGURE 26 - Comparison of Theory with Experiment, 214, Between Thermocouples i and 4 Usinq Measured Temperatures at Those Locations

1.0 k 5 PERCENT -f .

0.5

THEORY EX PE R IM E NT o NON BOILING o BOILING

o 05

s/L

FIGURE 27 - Comparison of Theory with Experiment, 2T2, Between T= TE at sIL = O and = Tw at s/L = 1. Path Length from Bulk- head to Waterline. -42- 1.0 I 5 PERCENT T

I I 0.5

J ° THEORY EXPERIMENT NONBOILING BOILING o/

0 05 s/L FIGURE 28 - Comparison of Theorywith Experiment, 2T2, Between Thermocouples i and 4 Using Measured Temperaturesat Those Locations. 1.0 i 5 PERCENT

-f-

o o

e o 0.5

THEORY EXPERIMENT NON-BOILING o BOILING s

o o 05 s/L

FIGURE 29 - Comparison of Theory withExperiment, 3T12 Between T = TF at s/L = O and T = Tw at s/L = 1. Path Length from Bulkhead to Waterline. -43- 1.0 ± 5 PERCENT T - . . o o

0.5

TI-IEORY EX PER IM E NT NON-BOILING o BOILING

o o 05 s/L

FIGURE 30 - Comparison of Theory with Experiment, 3112, BetweenThermocouples i and 4 Using Measured Temperaturesat Those Locations. 1.0 i 5 PERCENT

0.5

THEORY EXPERIMENT NON-BOILING o BOILING

o 05 I s/L FIGURE 31 - Comparison of Theory withExperiment, 3T6, Between T= TE at s/L = O and T l at sIL = 1. = Path Length from Bulkhead to Waterline. -44-

-i 5 PERCENTT

0.5 s J

o THEORY EXPERIMENT NON-BOILING o BOILING o

o 0 05 s/L T = TE at sIL = FIGURE 32 - Comparison ofTheory with Experiment, 3T3, Between Path Length from Bulkhead to Waterline. O and T = T at s/L = 1.

temperature and the temp- as greatly fromthe average of the water No. 6 as shown inTable 6. In these regions, erature at thermocouple reasonably then, the thermal gradientapparcnly is predictable between the fluid temperaturesat the ends of well by linear theory deck The problem (as in thecorresponding case of the the strip. the temperature and upper sideshell) liesin being able to predict at thermocouple No.6.

Transient Transient temperatures werecomputed theoretically from The choice of (38) for the first 180seconds of run 3T6B-l. Eq. temperature was made sincethat was the initial 70°F as the starting boundary value temperature of thermocoupleNo. 4 which was the controller for the analysis. data in The results are comparedto the experimental The early-time Figure 33 which shows areasonably good match. and experiment appearedto wash out quickly difference between theory been retained at thermo- for thermocouple No.3, but it seems to have couples 1 and 2. that the fine The general agreement isgood but it is clear transfer affected details of the characterof the convective heat the correlation atthermocouples i and 2. TABLE VI - Temperatures in Bottom Structure, °F 70 THERMOCOUPLE 4 T W T 6 T T 7 T 8 60 FAIRID CURVED 2T8-22T8-1 Run 7170.5 -4 1 3633 av 3934 4640 405° 2T4-12T8B-22T8B1 6771.573 -16 53521O 64603029 573027 424357 3080 1HERMOCOU1LE 3 T' 2T4B-22T4B..12T4-2 756768 48-5 5832 553760 5467 - 6070 TRANSIENT THEORY u 2T2-22T2-1 7274 5253 6363 5957 6057 ;50 I i i ZT2B-2ZT2B-1 7274 4443 5859 5354 5553 8070 THERMOCOUPLE 2 Li 3T12-1 75 45 60 61 58 3T1ZB-23T1ZB-13T12-2 7072 444248 575660 575661 585657 5060 1TRANSIENT THEORY 3T6-13T6-33T6-a 697173.5 464747 605859 565759 575660 8070 THERMOCOUPLE t 3T6B-23T6B-1 6868.5 4142 55 5254 5257 60 0 20 40 60 60 OtOO SEC 120 140 160 180 200 3T3B-23T3B-13T3-23T3-1 7271.57578 444549 58596264 555960 566061 FIGURE 33 - Thermal Transient EXPERIMENTALon DATA3T6B4. ) -46-

Effects of Wind and Sun A short run was madeafter 1800 seconds on model of wind and sun on the temperature 2T2B-1 to assess the influence 4-inch-diameter fan and in a ship. This involved the use of a a 150 watt lampIn a reflector. The lamp was 7 inches above the 11 inches forward of thefore-and- deck, 6 inches outboard and The fan aft centerplane, tilted toilluminate the model directly. It was aimed to was 6 inches above thedeck and 18 ìriches abeam. blow directly on the model. At 1800 seconds the Freon114 in the model was topped off (about one inch) and thelamp was turned on. The fluid temperature was 39°F and that ofthe water was 73°F at the startof this se- is shown in Table 7. Thermo- quence. The rest of the test sequence couples 1 and 2 were at locations'losest to the lamp and fan while thermocouples 3 and 4 were successivelyfarther away. During the test little heating orcooling penetrated to to the interior of the model. Only the deck and sideshell appear at thermocouple 2 where have responded. The largest change occurred the temperature rose 14°F underradìant heating alone and another 8 degrees while the fan was on. The total change of 22°F was 65 percent of T - TF. This result cannot be relatedquantitatively to the corresponding behavior of a ship at sea. Qualitatively, however, it indicates that the effectwould be large. Consider the convec- Assume again, a wingtank 40 feet high, 60 feet long tion alone. plate all over. If a 20 kE. and 10 feet 'i' with 1/20 feet thick the deck, so that a value wind at 8&° is assumed to blow acoss of h = 4 might be realistic,then g would be (4+1)/(25 x 1/20) = (34) is used to deter- 4 if h = 1 for the air in thewing tank and Eq. also that the steel girderis mine g2 AssumeT = 30°F and assume, at 50°F while the ìng tank air ìs at 0°F.' If radiative effects are neglected, then T = (-80x4)/5 - (50 +30)/2 = -104°F using Eq.(35). The path length would be 10ft. plus the height of the deckabove If this is 20 ft. then gL =2 x 30 = 60. The tempera- the water. (31) the ture would approach a stepfunction and according to Eq. steel temperature would beclose to T = (50 + 30)/2 - 104 =-64°F.

TABLE VII - Simulated Wind andSun Study, Model 2T2B-1

Time Thermocou1es Sec. i ¿ 3 4 5 6 7 8 Heat Lamp On 1800 67 51 46 40 39 43 54 55 1870 70 57 50 42 39 43 55 54 2100 73 64 56 46 39 43 55 55 ¿220 74 65 56 47 39 43 55 55 54 Fan & Lamp On 2400 75 65 56 48 39 43 55 2420 75 65 56 48 39 43 54 54 2430 76 65 57 49 39 43 54 54 2460 76 66 58 49 39 43 54 54

Fan On, Lamp Off¿700 76 73 63 49 39 43 54 53 2730 76 70 61 48 39 43 54 53 2760 75 70 59 47 39 43 54 52 3200 71 62 56 47 39 43 54 53 -.47 - Convective Heat Transfer Coefficients

The surface heat transfer coefficient between the fluid in the hold and the hold wall is of primeinportance for ihe determination of the temperatureas a function of position and time in the ship structure. It also is the factor which identïfies the energy transfer to the fluid to obtainthe boil- off rate.

Experiments were performed during this investigation to determine surface heat transfer coefficients forthe various fluids used. The determìnatìon employed the experimental model depicted in Figure 12 together with the theoreticalsolution for the temperature response ofa plate with an insulated back face when there is a step function changein the fluid in contact with the front face. The solutions were obtained from thecurves provided by Schneider (Ref. 21) . Three thermocouples were used for the test as shown in Figure 12. One was welded to each side of the plate while the thirdwas suspended ìn the fluid cavity just above the plate. The thermocouple on the chilled facewas used for qualitátìve data only becauseof uncertainties such as the fact that the leads were in the fluid.

The data are shown in Figures 34through 37. They represent the response at the Insulated face whichis sufficient to determine the Blot number by interpolation betweenthe theoretical curves. Figures 34 and 35 depict fluids whichdo not boil and will warm up as the plate cools downdepending on the relative masses and specific heats. Therefore, onlythe injti.l Dart of the experimental plotshows hbefore any appreciable warming of the fluid has occurred.

The Freon fluids boil atconstant temperature at room pressure. Figures 36 and 37 present thethermal responses obtained. Figure 37 indicates the effectof the surface-generatedgas on the heat transfer coefficient duringthe early stages of the event. When the fluid was first pouredinto the cavity it erupted. As time progressed andmore fluid met the surface the heat transfer coefficient rose. When the temperature of themetal approached that of the fluid the heattransfer coefficient dropped significantly. This occurred when the metalno longer provided enough energy for phase changeover tre total surface in contactwith the fluid. The boiling action stoppedwhen the metal was at the fluidtempera- ture. The only phase change occurringat this timewas at the interface of the fluid. 'ir

An interesting sidelightto these experimentswas a reduction below the boilingtemperature in eta1 surface temperature when total fluidevaporation was permitted.

The temperature approached theboiling point temperature coincident with the partialpressure of the Freon in the air. This was equivalent to evaporativecooling. Therefore, if liquid methane were to splash ontoany metal the interface temperature could fall well below the boilingpoint of the liquid methane.

The terminology usedon Figures 36 and 37 to describe the boiling action can be definedas: -48-

1.0 THEORY - EXPERIMENT 0.8

_:- 0.6

0.4 0.2

B - ht/ k 0.2

L 0.0- I I I Ê 100 1 5 10 50 0 01 0.050 1 0.5 i DB /t2

the Insulated Side of a Plate When Chilled FIGURE 34 - Temperature Response on The Experimental Value of h was with Alcohol Mixed with DryIce. 22OBTU/Hr. Sq. Ft. 0F.

1.0 THEORY - --EXPERIMENT 0.8

:-0.6

I- I 0.4

- 0.2 r

0.0 t I I liii 1 5 10 50 100 001 0.05 0 1 0.5 DB /t2 when Chilled FIGURE 35 - Temperature Response onthe Insulated Side of a Plate 125OBTU/Hr. Sq. Ft. with Water. The Experimental Value of h was °F. i -49-

ERUPTIVE ACTIVE BOILING AGITATION QUIESCENT

1.0 THEORY - -EXPERIMENT 0.8

4 2

0.6 u0.4

0.2

0.0 1.

0 01 0.050 1 0.5 1 5 10 50 100 DO /t2

FIGURE 36 - Temperature Response on the Insulated Side of a Plate Chilled with Freon 114. The Experimental Value of h was 1250BTU/Hr. Sq. Ft. °F.

EXPLOSIVE ERUPTIVE ACTIVE QUIESCENT BOILING BOILING AGITATION

1.0 THEORY - EXPERIMENT 0.8

:- 0.6

u-- 0.6 / 0.4

0.2 «NB-hi/k

0.0- I I 111111 0 01 0.05 0 1 0.5 5 10 50 100 D9 /t2

FIGURE 37 - Temperature Response on the Inslllated Side ofa Flat Plate ChÌled with Freon 12. The Maximum Experimental Value of h was 1625BTU/Hr. Sq. Ft. °F. -50- Explosive Boiling - Unable to maintain any appreciable fluid in the experimental cavity.

Eruptive Boiling - Violent action with excessive splashing. Active Boiling - Can be compared to boiling water.

Quiescent - Gentle boiling to none at all.

PTE AND TE Temperature records were obtained during the PTE and TE tests. The results appear in Figures 38 and 39. to attempt was made to analyze the PTE data. However, the TE results were analyzed for the thermocouple at gage i using the transient calculation procedure of Eq.(38) with the result shown in Figure 40. The convective and radiative heat transfers were asssumed to be 1/2 of the conductive, which is the average of the values shown in Tables 2 and 3. The differences are seen to be of the order of a few percent. The experimental temperatures at all the sta- tions of Figure 40 were used to compute stresses as shown in the following section.

70 END PLATE TEMP()

50 INITIAL TEMPERATURE OF ETHYLENE GLYCOL = -22°F T = -94°F

40 MID PLATE TEMP () o o-

FLUID TEMP

TIME (MINUTES) 4 2 3 -10 160 180 200 220 240 O 20 40 60 80 100 120 140 TIME (SECONDS)

FIGURE 38 - Temperature History in the Cold-Spot Model. -51-

INITIAL TEMPERATURE 0F ETHYLENE GLYCOL -22°F T0 = -94°F

TEMPERATURE °F

BOTTOM PLATE

TIME (MINUTES) -10 2 i I I 4 I J I 20 40 oc 80 100 120 140 160 180 200 220 240 TIME (SECONDS)

FIGURE 39 - Temperature Measurement Historyin Ship PIE Model

TIME- MINUTES

1 2 3 4 5 6 T o I00 200 300 400 TIME-SECONDS

GAGE I o 0f o 0.1- o o CALCULATED CURVE o o 0 0 0 0 0.2 GAGE 3 o o o o o T° 0.3 o 0 o o GAGE Il 0.4 o 0 0 THERMOCOUPLE 0 0 0 0.5 A o

0.6

FIGURE 40 - Normalized Temperatures on Steel ThernloelastiC Model. -52- STRESS INVESTIGATIONS

Introduction flat PTE investigations wereconducted on a rectangular plate with a central chilledspot and on a plastic imuiation One purpose was todetermine how closely of the steel model. these Eqs.(48) and (49.) would agreewith experimental data for cases to provide abase for evaluating the steelmodei results. Another was to obtain apreliminary indication of theusefulness of simple tneoretical predictionprocedures for stresses in the . t also provided data steel model. The PTE simulated ship experir to aid in strain gageplacement on the steel model. In the following descriptionseach study is discussed the PTE data with the separately. Comparisons have been made of simplified predictions which arediscussed in the Theory Section.

Cold Spot Model Figure 41. The photoelastic fringepatterns are snown in transient. The peak stress The results aretypical of a thermal 4 minutes afterinception of the test. occured at approximately field from 3 Actually, tnere was littlevariation in the stress minutes to almost 7minutes. solutions were The cold-spot and balancedforce theoretical The magnitude of thedifference compared to the experimentalresults. is shown in Figure 42. The nature of the between the two theories basically the expected since Ecr.(48) and (49) are agreement is to be for the result of a force balanceanalysis with consideration curvature of the disk. The relevant data for thecold-spot experiment appear The temperaturedifference, T, is the in the following summary. the temperature to thetemperature measured at change from room peak stress. center of the platemodel at the tìme of

Area ratio, A2/A1 = 0.60 T0=-92°F = 1200 psi Maximum model temperaturechange, T = 69 F aET = 920 psi Maximum fringe order, n =2. 03 (extrapolated) Location, centers of longedges Experimental thermal stress,Eq. 55 , o =613 psi C0 = 0.49 C = o-/a E T = 0. 67 Theoretical thermal stresses, Force balance, Eq. (4;),o- = 575psi Cold-spot analysis, Eq. o- 598 psi Percentage errors, theorycompared to experiment, Force balance, 6.6 percent Cold-spot analysis, 2.5 percent _53.

NOTE: These are doubling polari scope photographs. All fringe orders must be halved for stress calculation.

n 4.Oó (ExtpoIoted) At 5 Minutes

FIGURE 41 - PTE Fringe Patterns inCold-Spot Model.

0.8 - THEORIES EXPERIMENT ciEl

0.6

0.4 -t lo PERCENTAGE ERROR BETWEEN THEORIES O

0.5 LO 1.5 A/A1 (b/a - I) FIGURE 42- Comparison of Cold-Spot on Area Ratio Solutions. -54 - The correlation is in accordancewith numerous PTE investigations in which excellent agreementof theory and experiment have been obtained for problemsof equal or greater complexity (Ref s. 16 through 18, forexample). In the cold-spot problem the in error was slightly largerthan has been sustained in the past which accuracies of the order of 1percent were common. However, some portion of thedifference must be identified withthe approximate natures of Eqs.(49) and (51) as applied to theexperiment. In spite of the size of the errorfor the balanced force method, the utility of the procedure forLNtankers has received some support from this relativelysimple investigation.

It is instructive to examinethe various degrees of conservatism related to estimatingprocedures. C0 is seen to be the hypothetical upper bound for afinite Biot number, 0.49 while As a result the use c1, is seen tobe 0.57 according to Figure7. o o would have predicted atheoretical peak stress which would have0been more than twice as high as observed whileCuwould have been 17 percent too high.

The photoelastic fringe patterns appearin Figure . it The maximum follows that o = 1200 psi, as inthe cold-spot test. the inner wall. fringe order o 1.4 occurred at the lower corner of If the fringe order issubstituted into Eq.(55) the principal stress difference is found tohave been 1.4 x 303, or 424psi, and the principal shear stress was212 psi. The numerical value of ET (Figure 33) was 813 psi using thebottom plate temperature at 4mm- utes (11°F) sothat T = 61°F.

= .4

5 Minutes. FIGURE 43 - Photoelastic FringePatterns in Simulated Ship Model at -55.- At the centers of the inner andouter walls the peak fringe orders were 1.0 and 0.8, respectively.These are equivalent to 303 and 244 psi, respectively.If the inner and outer section areas are as shown in Figure15,then the application of Eqs.(48) and (49) (using the bottom platetemperature as a referenceso that T = 61°F)yield predictions ofthe longitudinal inner andouter thermal stresses of 426 psi and383 psi at those locations.It was not possible, in the currentPTE tests, to separate the prin- ciptl stresses and obtain thetwo values experimentally because of the manner in which thepolariscopes were built into themodel. As a result itwasnecessaryto assume values of in order to perform the correlation.Ifoere chcs ei1'o 1/4 of thenx would be404and 325 jïsi at the inner and outer respectively.The test data on the steel walls, this assumed order of the ratio fflOQi indicated that right not be improper. of vertical-to-horizontalstress The simulated ship experimentrevealed no stress concentration at any location.It did demonstrate the ficant shears since the principal presence of signi- normal stress. shear was 1/2 of the principal The results from this study aiding the selection of strain played an important role in in order to reveal the peak gage locations on the steel morel importantly, however, it normals and the corner shears.More the force balance relationsindicated the order ofaccuracy with which peak stresses in of Eqs.(48) and (49) can predict the in one hold. a shiplike structure subjectedto thermal shock Because of the uncertaintiesin the values of theseparated principal stresses, the followingsummary of the various stress bounds may be somewhat inaccurate.However, the exercise is felt to be important to the aspect of thisinvestigation which deals with approximation procedures.The results above show thatC0 = 455/1200= 0.38.Fer the ship PTE model,Figure 7 shows that for the pertinent Biot numberCu = 0.64.Therefore, use of instead of the observed valuewould have resulted ina predictiono of thermal stre?-s that would have beenabout 3 times as high whilethe attainable ultimate,Cu'would have been 87 percent toohigh. Steel Ship Model Investigations Thermoelastic studies steèl model described above. were conducted on the welded summarized in this section. The significant stressdata are of the inner Theand peak thermal stresseswere observed at the centers 44, the experimentalouter walls (gages 1 and11).As shown in Figure peaks were in reasonablygood agreement with the predictions ofEqs.(48) and (49).The locations of the were in the same placesas on the PTE ship model. peaks of C0 was5 The peak value 6 percent smallerpercent smaller than theoreticalon the inner wall and on the outer wall.The largest C0 was0.258 which means that theuse of as an estimate for thiscase would have been too largeby a factor of nearly 4.If the Biot number estimate of 0.43were to be used (Figure 7)then the prediction would have been 67percent too high. -56-

The point-by-point comparisonshows similarity of the close theory and experiment. However, the correlation becomes only at long times. ërtical shear was observed inthe corners, as in the case of the PTE model. The largest value of theprincipal shear was half of the peakprincipal normal stress. The peak stress on the innerwall was measured on the outstanding leg of the anglestiffener. As can be seen from Figure after about 44, the stress started ascompression and then reversed This may be explained by assumingthat the temperature on 5 seconds. stiffener and induced the wall plate causedshrinkage relative to the compression and bending with a nettension on the a combination of which it flange. Then the temperature reachedthe stiffener after began to act in concert withthe inner wall. The differentially connected strain gage at location9 revealed a small amountof vertical curvature which wouldhave inducec a rollingaction on compression in the flangebefore the stiffener. The relatively small reversal ¿oes not imply thatthis is a negligible problem in a full Because of the time scalinglaw of Eq.(8) the stiffeners size ship. after the plate is chilled. may not becomechilled for several minutes stresses and rollingaction could be As a result the compression This is an area much greater than observed inthis investigation. for possible future study. The minimumrincipal stress at the centerof the wall The minimum was oriented was approximately1/4 of the maximum. vertically and the maximum washorizontal. This result provided the for the PTE ship model toindicate basis for the assumption made be converted how the photoelastic principalstress difference could into separated stresses. Some other featuresof the steel model response For example, the plateau may warrantsubsequent investigation. may reflect thefinite injection time forthe at 10 to 20 seconds location 5 indicates chilled alcohol. The reversal in sign at gage model to the changingtemperature field. It the adjustment of the the time difference may be important toinquire into the reasons for the peaks at the innerand outer walls. in the attainment of require extensive However, the resolutionof that problem would theoretical analysis in asubsequent investigation.

Other Ship Problems

If the fluid boils after beingpoured from a ruptured tank into contact withthe hold the resultantpressure surge could lead to destruction of the ship. A large venting area must be available to avoid a largepressure surge.

In the case of a leak, instead ofa catastrophic tank failure, the chilledzone of the hold could be small in which case A,,/A1 would be large, and thethermal stress in the chilled zone w6uld approach ET0 if the fluidboils on contact with the steel of the hold. The influence ofpressure surgìng may modify this effect by rapidly enlargingthe leak in which case the time of the thermal transient willcontrol the stress level. RECOMMENDAT IONS Further studies should be performedon convective heat transfer in ship-detail configuratìonsto increase the accuracy of prediction procedures of thisreport and to help find reliable modeling laws for this mode of heattransfer.

Analyses, experiments and design studiesshould be conducted on the problem ofpressure surge. These should include measurements of the convective heat transfercoefficients of various liquid natural gases.

Local thermal shock problems shouldbe investigated experimentally and the data shouldbe compared to theoretical predictions (such as Eqs.(48) and (49)).

An examination should be made ofthe effect of ship motion on convective cell stabilityand the relationship to the heat transfer process.

One problem which in the past hasreceived considerable attention with little in theway of a satisfactory con- clusion is the behavior ofa structure when mechanical stressesare applied in conjunction with thermalstresses. The range of current practice extends from algebraicaddition of the two stresses in some cases to complete neglect of the thermalstresses in others. From the standpoint of stress analysis,the stresses should be added if superposition holds. Otherwise the addition fied. process must be modi- From the standpoint of failureof the ship structure theproper procedure probably would liebetween the two extremes mentioned It is suggested that here. an exploratory study be made to determinethe proper approach for ship design. Acknowledgements The authors wish to express appreciationto Messrs. Richard Goldman, John Pozerycki andRoger Milligan for work which they did in the thermoelasticphase of this project on model design and instrumentation, conductof the experiments and reduction of the data. -62-

APPENDIX I

EXPERIMENTAL TEMPERATURE DATA

The following pages contain the temperaturesfor all model experiments.

FIGURE A-1 - Correction Curve for Effect of Tempera- ture on Strain Gage Signal

TABLE A-I - Basic Calculation Data forTemperature Models

Model 2T8 ¿Th- ¿T2 .TTt 313

1.0 0.7 1 2/3 1/2 1.5 L (ft(

0.4 0.4 0. At400T. h1IBTU/hr-ft-°F) 0.4 0.4 0.4

0. 54 0. 54 At900T. h2(BTU/hr-ft-°F) 0. 54 0. 54 0.54 kBTU/hr-ft-) 25 ¿5 2 ¿5 25 0.00267 0. OCZo/ t (ft) 0.010 0.010 0.010 0.00267 2h1/kt ift2 3.2 3.2 3.2 12.1 12.1 12 i

¿h2/kt ft 4.32 4. 32 4.32 ié, Z. 16. 2 1 2

0. 3 0. 3 0. 3 0. 3 0. 3 0.3 Q r1Qcl 1.2 1.2 1.2 1.2 1.2 (Q r/Q cZ) 3.9b g1 (1t1 2.12 2.12 2.12 3.96 3.% g2 (ft') 3.08 3.08 3.08 5.97 5.7 97

3.b 2..97 g1L ¿.12 1.42 1.06 5.95 gL 3.08 ¿.06 1.54 .96 5.97 4.47 -63-

TABLE A-II - Temperature Data for Theoretical Profiles,°F

T tT T -T 1 T +T F W W F 1 A r g T T T T -T Run L F A W Z 2 1 2 - T. ZTS-1 3.08 -43 78 70.5 13.8 56.8 20.3 49. 1 35. 3 0.311 2 T8-Z 3.08 -27 74 71 22 49 26.8 50.4 28.4 0.292

2T813-I 3.08 -38 80 73 17.5 55.5 23.8 51.9 34.4 0.314 2T813..Z 3.08 -38 81 71.5 16.8 54.8 24.6 52.8 36.0 0.329 2T4-1 1.42 37 74 67 52 15 53.5 63ç8 11.8 2T4-2 1.42 0.393 42 74 75 58. 5 16. 5 58.3 66. Z 7.7 0.233 ZT4 13-1 2.06-fl 74.5 68 23. 44.5 24.9 49.7 2T4 R-2 1.42 26.2 0.285 38.8 72.5 67 53 14. 1 54. 1 63. 3 10. 3 0.365 2T2-1 1.06 43 76 74 58.5 15.5 57.9 67.0 8.5 2T2-2 1.06 43 75 0.274 72 14.5 57.1 66.1 8.6 0.297 2T2R-1 1.06 38.8 74 36.4 17.6 5.5 65.2 8.8 ZTZR-2 1.06 38. 8 72 72 0.250 55.4 16.6 54.3 63.2 7.8 0. Z35 3112-1 5.95 39 74 75 5? 18 58.2 66.1 9. 1 0.253 3112-2 5.5 3 72 72 54 18 55.5 63.8 9.8 0.272 3T12R-16.95 38.8 74 70 51.4 15.6 56.7 65.4 11.0 0. 353 3T12F3-25.95 38.8 73 70 54.4 15.6 56.5 64.8 10.4 0.334 3T6-i 3.96 39 73.5 73.5 Sij. 3 17.3 56.3 64.9 8.6 3T6-2 3.96 36 0.249 70 71 53 18 52.8 61.4 8.4 3T6-3 3.96 35 70 0.233 69 52 17 52.2 61.1 9.1 0.268 1T613-1 3.96 3. 8 71.0 68. 5 53.7 14.9 54.2 62.6 8.9 0.299 3T6B-2 3.96 38.8 73.0 68 53.4 l4. 54.6 63.8 10.4 0.359 313-1 2.97 34 77.5 78 56 22 54.4 66.0 3T3-2 2.97 10.0 0.227 36 75 75 55.5 19.5 54.2 64.6 9.6 0.246 2. ì7 38. 8 '5.5 71. 5 56.2 16.4 54.9 65.2 10.0 0. 306 31113-2 ¿.97 38.8 75 72 5S4 j 16.6 54.9 65.0 9.6 0.Z8' 1Wihtndaverage uf ta tmperatures ass1n1in and watr. linear variation hetwein chilling fluid -64-

TABLE A-III - ExperimentalTemperature Summary, o = 1800 Sec All Temperatures °F

7 8 Run 1 2 3 4 5 6 2T8-1 60 54 39 10 -16 -4 34 40 2T8-2 67 56 44 1 -1.1 1 39 46 2T8B-1 52 41 26 -6 -31 -16 27 43 2T8B-2 56 47 30 -4 -2 -lo 30 42 2T4-1 62 53 47 37 43 52 57 57 2T4-Z 68 59 53 45 45 53 60 67

¿T43-1 NG ¿6 7 -15-16 -5 37 12 ¿T4B-2 62 51 47 39 39 48 55 54

2T2-1 62 53 47 37 43 52 57 57 2T2-2 65 55 50 47 46 53 59 60

ZTZB-1 71 62 56 47 39 43 54 53 2T2B-2 65 50 45 40 39 44 53 55

3T12-1 66 64 58 37 37 45 61 58 3T12-2 67 64 61 39 39 48 61 57

3T1ZB-1 66 62 61 48 40 42 56 56 3T12B-2 65 62 57 40 39 44 57 58

3T6-1 70 62 55 34 36 47 59 60 3T6-Z 65 59 52 36 35 47 57 57 3T6-3 65 61 54 37 36 46 56 56

3T6B-1 65 59 53 40 40 42 54 57 3T6B-2 63 58 52 39 37 41 52 52

3T3-1 71 59 51 43 38 49 60 61 3T3-2 69 57 49 41 38 49 59 60

3T3B-1 67 57 53 47 40 45 55 57 3T3B-2 67 55 47 43 40 44 55 56 -65-

TABLE A-PI - J = (T- TF)/(Tw - TE)

Thermocouple T T Run 8L 1 2 3 4 5 6 7 8 - TF

2T8-1 3.08 0.907 0.855 0.722 0.467 0.238 0.344 0.678 0.731 0.311 2T8-2 3.08 0.959 0. 847 0.724 0.459 0. 163 0.256 0. 673 0.745 0.292

2 T8Ft-1 5.08 0.811 0.712 0. 577 0.288 0.063 0. 198 0.586 0.730 . 314 ¿T88-2 3.08 0.858 0.776 0.621 0.311 0. 119 0. 256 0.621 0.730 0. 529

214-1 1.42 0.833 0. 533 0.333 0 0.200 0. 500 0.667 0.667 0. 393 2T4-2 1.42 0.788 0. 515 0. 333 0.091 0.091 0.333 0. 545 0.758 0.233

2T4B- 1 2. 06 - 0. 528 0. 315 0.067 0.056 . 180 0. 652 0.371 0.285 2T4B-2 1.42 0. 823 0.433 0.291 0.007 0.007 0. 326 0. 574 0. 539 0. 365

2T2-1 i.06 0.613 0.323 0. 129 -0. 194 0 0.290 0.452 0.452 0.274 2T2-2 1.06 0.759 0.414 0.241 0.138 0. 103 0.345 0.552 0. 586 0.297 2T28-1 1.06 0.915 0.659 0.489 0.233 0.006 0. 119 0.432 0.403 0.250 2T2B-2 1.06 0.789 0.337 0. 187 0. 03 0. 00t 0. J57 0.428 O488 0.235

3 T 12-1 5.95 0.750 0.722 0. 528 -0.056 -0. 056 0. 167 0.611 0. 528 0.253 3T12-2 5. 5 0.861 0.778 0.694 0.083 0.083 0.333 0.694 0. 583 0.272

3T12B- 15. 0.872 0.744 0.712 0.295 0.038 0. 103 0.551 O.S51 0.353 3T12B-29.950.840 0.744 0.583 0.038 0.006 0. 167 0.583 0.615 0.334 3T6- 1 3.96 0.899 0.667 0.464 -0. 145 -0. 087 0.232 0. 580 0.609 0.249 3 T6-2 3.96 0.833 0. 667 0.472 0.028 0 0. 333 0.611 0. (1 i 0.233 3T6-3 3.96 0.882 0.765 0. 559 0.099 0.029 0.324 0.618 0.618 0.268

3T6B-1 3.96 0. 8l2 0.680 0.478 0.040 0. 04o 0. 108 0.512 0.613 0. 299 r6B-2 3.96 0. 829 0.658 0.452 0.007 -0. 062 0. 075 0.452 0.452 0.357

3T3-1 2.97 0. 41 0. 568 0.isq 0.205 0.091 0.341 0. Sfl 0.614 0. 227 iT3-2 2.9 .46 0.538 0. 333 0.128 0.051 0.333 0. 590 0.615 0.Z44 3T313-1 2.97 0. 862 0. 557 0.434 0.251 0.037 0. 190 0.495 0. 557 0.305 3TSB-2 2.97 0. 84 0.488 0.247 0. 127 0.036 0. 157 0.488 0.519 0.289

TABLE A-V - Temperature References for Thermoelastic Model

Location Model initial Temp. Fluid Initial Temp. T o °C °F °C °F °C °}' A +23.0 +73.4 -39.0 -38.2 62.0 111.6 1 +23.0 +73.4 -30.0 -22.0 53.0 95.4 2 +23. 0 +73.4 -23. 5 -10.3 46. 5 83.7 3 +23.0 +73.4 -39.0 -38.2 62.0 111.6 4 +23.0 +73.4 -39.0 -38.2 62.0 111.6 5 +23. 0 +73.4 -23. 5 -10. 3 46. 5 83. 7 6 +23.0 +73.4 -24.5 -12. 1 47.5 85.5 7 +23.0 +73.4 -30.0 -22.0 53.0 95.4 8 +24.0 +75.2 -32.5 -26.5 56.5 101.7 9 +23.0 +73.4 -24.5 -12. 1 47.5 85.5 10 +24.0 +75.2 -32.5 -26.5 56.5 101.7 11 +24.0 +75.2 -32.5 -26.5 56.5 101.7 TABLE A-VI - Normalized Temperatures for Thermoelastic Model A I ¿ 3 4 5 Sec.hme 0 TempModel 23 TI'T 0 o Temp.Model 23 T/1 0 o Temp.Mdei 23 T/T 0 o Temp.Model ¿3 T/T 0 o Temp.Model ¿3 T/T 0 o Temp.Model 23 T/T 0 o lO 1217 0.097 .171 23 00 ¿3 0 23¿3 0 23¿3 0 23¿3¿3 00 40¿0iS 3.5 89 .315.242.226 23¿3 0 23¿323 00 2221 .024.008 ¿Z¿1.5 .024.003 21.522.5 .011.032 loo 8060 -4-20.5 .444.411.363 22.5¿3 .009 0 ¿323 00 201819 .048.081.065 20IS19 .081.065.048 ¿0.519.5¿0 .065.054.075 IZO160140 7.-6.5 5-s.s .460.432.4Th 22¿2.5 .013.015.009 22.5¿3¿1 . Oli i j 15.16.5ii 5 ..105.089 121 15.5i?IS .121.097. 129 17.1818.5 5 ..108.097 118 ¿00180 -8.5-8 .508. 500 21.5¿ i. 5 .028 22¿2 .022. 022 14iS .145. 129 145 1412.513 .161. 145 iSl617 .172.131. 129 260240220 _9-9 ..516 516 21 ..038 038 047 ¿I21.5 .043. 043O2 1 13 .161. 161 11.512 .185..169 l77 ISiS .172. 172 280 -9.5-9 .524.516 20¿0.5 .057 21¿I .0-1 1212.5 -. 169 I?? 10.5iO .210.202 13.514 .204. i94 320340300 -9.5 .524.524 19.52019.5 .066.057 ¿020.5 .054.043.065 12II . 185 177 9 lO .218.210 1313.5 .215.204 400380360 9.5 1818.19 5 .075.084 085 ¿019.5 .065.O7S 075 12.512 .237.226 TABLE A-VI (Cont'd) - Normalized Temperatures for Thermoelastic Model Time Model 6 Model 7 8 9 I lO Sec. 0 Temp.23.0 T/T 0 ° Temp. ¿3 TÍT 0 ° Temp.Model24.0 T1T 0 O Temp.Model23 0 ° Temp.Model T/T 0 ° Temp.Model Il T/T 0 ISlO 5 23 00 ¿323 0 24 0 22.523 .011 0 ¿I21.524.0 .053.044 23.024.0¿4.0 018 0 4020 2223 .021 0 ¿I23 5 .028 0 0 2324 0 2021.5 .063.032 1719.5 .124.080 211419 .088.053 177 lOO 8060 20¿I .042 063 20 8.5 .057 085 20¿2 .071.055.0)8 lOISIb .274.202.147 II 4 7 .354.301.230 lO 7.5 .292.248 140120 1818.519.5 .095.074 IS17 5 .142.113 1718.5 .124.097 7.08.5 .305 337 01.5 .425.398 35 .336.372 180160 17 ..105 26 ISIi. 5 .189.170 ISIb .142 59 5.05.5 .379 368 -3.0-1.5 .478.451 ¿ .5 .416 389 220200 151616.5 .168.137.147 II 9.0.5 .236.217 1213 .230.212.195 2.534.0 .432.42).400 -4.0 45 .504.496 -I.0 -.5 .4.42.434 260¿80240 13.51414. 5 . 189 179 7.7.58 5 . 274..24 292 lOII 9 .265.248 I.¿ 5 .453 442 -6.0.5-5.0 5 ..513 52253) .3.25-2. .478 460460 320300 13 .221.211.200 56 .321.302 7 88.S .283.274 1.01.5 .463.453 -6.5 .540 -3 35 .487.478 360340 12 2.5 .232 ¿42 44.5 .358.349.340 66.S .3)0.30) 1.0 .463 463 -7.0 .549 -4 496 400380 IIILS . ¿53 ¿53 33.5 ..370 37 5 .336.319 01.0 5 .484 474 -7.5-7 5 ..558 558 -4.-4 5 5044%496 -68-

APPENDDC II EXPERIMENTAL STRESS DATA

The following pages containthe stresses for the triermoelastic model experiments. The strains were computed after the appropriate correctiorhad been made to the gage readings according to the curvesin Figure Al. The stress com- prop- ponents were derived fromthe strains and the mechanical T-1 steel utilizing theappropriate equationsshown erties o and in the previous section. The principal normal stresses maximum shears were thencalculated. All data were normalizedfor assessment of uniformity. discussing the steel Some of the results areplotted in the section of the printout of the computer model. The results are copies the raw data. The minimized stresses em- program used to convert C2 and C3 as the reference. The three coefficients Cl, ployed the normalized are the normalizedprincipal normal stresses and No significance should beattached to the relation maximum shear. normals and between the magnitudes ofthe normalized principal The directions and magnitudesof the the subscripts 1 and 2. through a sign maximum values wereidentified through logic and not convention. -69-

TABLE A-VII- ThermoelastjcModel Stresses (PSI)

LOCATION No.i o- = 18603 OUTPUT: SINESSE o STRAI NS: TENSILE S ,sX IN 4NULE IDE X Y 4 X Y loOX 60NÌ NUhi. IDEo) Ci C2 5 C.S -47 0 -1499-435 531 -435 -1419 0 -.0234-.0806 0 IO -57 0 -ISIS-527 645 -527 -18U) 0 - .0284- .0977 0 IS -66 0 -2105-611 746 -611 -21uÇ o -.0329 0 20 -66 -.1132 0 -2105-III 746 -614 -í.I0 0 -.0329 0 40 -.1132 -85 o -2710-7b 962 78o -2710 0 -.0423-.1457 0 60 -94 0 -2997-870 1063 -870 -2997 0 -.0468-.16)1 0 80 -94 0 -2997-80 1063 -870 -2995 0 .0468-.1611 0 10(1 -113 0 -3603-1045 1278 -1045-303 O -.0562-.1937 0 120 -123 0 -3922-1138 1392 -1138-3522 0 -.0612-.2108 0 140 -118 5 -3716 _-932 1392-932 -3710 0 -.050!-.1998 C 160 -127 5 4P03.-1015 1493 -1015-003 o -.0546-.2152 Ci 180 -136 5 -4290-1098 1595 -1098 200 -,290 O -.0591-.230V 0 -13V 5 -429(1 -1(198 1595 -I(19)Ç -4290 0 -.0591-.2306 0 220 -l36 5 -429(1 -1096 1595 -1(198-A$0 1) -.0591-.2306 0 240-146 5 -1191 1708 -1191 ..09 O -.064 -.2478 0 260-143 6 448s -1163 1708-1068 O 280 .4 -.0574-.2411 0 -150 lu - I 09 lElo -1(160 -4090 0 0 3(10 -.0575-.2521 -ISo io -4650-¡069 1810 -1CS-49 -.0575-.2521 0 320-150 ¡0 -4690 -1 08& 1810 -IU9 4890 O -.0575-.2521 0 340-ISo IO -69U -1069 IEIP-10s9 4SO 0 -.0575 .2521 O 36(1 -155 15 -4803-955 36(1 1924 $55 -403 (1 .0514 .2562 V IS -155 -4803 -(155 1524-955 -4803 0 -.0514-.2582 0 40(1 -155 15 4803 -955 Ii-24 -0)5 -480 O -.0514-.2582 0

LOCATION No. ¿ o- = 16322 o OUTPuX: ST%SS.S SIA8NS: IE.I4.1LE Sh4i ..X ¿(N .05 hic. X Y 45 X Y lMX NONI NOi1- (DL..) Cl C.. 0.5 5 -s -0 8 27 -247 5 45 -202 -293 II) 6 -It. -18-3-i. -066 4. .0144-.0175 .0027 158 194 -258 -64e 21.23.0158-.0397 .00Y7 .15 -8 -25 -IN 423 553 56 222 4I6 -56(1 2(1 -0 -25 --123 7.31.025)-.8527 .0034 -IS -853 55 222 -4.6 -00 737 -.055-. .i527 .0034 40 -16 -25 -18 -742 -945 -57 lIb -727 -560 0 -16 -35 -lO -b5 -14.53.0446 .05o8 .0035 -1264-170 273 -775 -1323-15.15.0475-.0811-.1.105 80 -(1.5 -35 -29-1121 I347_23 115 -IllS-1350 100 -5.68 -.Oobt. .0ö27-.0014 -25 -35 -29 -l1i-1347-23 -l30 .0Oo 12(1 -25 -35 -25 -5.68 .0827 .01.14 -II.l-I..7- ¡U) 1119 -1350-s. -.085V .0827-.0014 140 -35 -35 2) 1"O 14..0 I36 135 -130,- 107e 16G -35 -35 -39 -14..(1 -1440 -45.0 -.0799-.0988-.0084 90 90 13-.5 -1530 4(1. - .0827- .0936 .0055 loO -42 -33 -37-164)-1441-12 102 -I,u 1o4 20(1 -42 -33 -37-1645 3.17 -.0683-.100e .0007 -1441-12 132 -1,40-it.-.5 3.17 -.0603 .lûUo .0007 22O -50 -32 -58-1058-14o3-114 233 -I45 -1920 14.52-.0o91-.11l -.007 24(1 -49 -31 -35-184S-1442-114 233 -1413-IbiS 14.52-.0o06-.1151-.007 26(1 -49 -31 - -185-1442-III 233 -1413-U)79 I4.52.O8VS-.1151-.007 280-49 -40 -46-1933-1725 33 107 -1723-1536 -9.22 -.1056 .118o 301. -49 -40 -46-1533-172 33 .002 -47 107 -1723-1938 -5.22.1VS5 .I150 .002 320 -38 -44-1050-1647 33 lOI -1641-1850-9.22.1006-.1137 .002 340-45 -36 -42-1788-1564 33 ¿07 -1559 177A 5.22 -.0955-.1087 .002 3(1360 -55 -36 -42-20X7-1657-00 229 -1643-2101 10.1 1.IUO7-.1287-.0049 -4Y -30 -3v-1840-1410-80 229 -139V lo5 10.11.0855-.1136-.0019 400-49 -30 -36-1041 1410 -80 229 -1396-184 10.lI-.0855-.1136-.0049

LOCATION No. 3 o- = 21762 001Piili STMESSES O TENSILE SlIEAH iX ION .,NOLI. lii.. , Y 45 X Y lAX NOtti, NOMI-, (1h05 Ci 02 C3 S o.S-S -ii 197 -177 390 lO 25 432 443 -423 32.22.0203-.u19) .0179 25 '.2 565 S66 950 1106 1106-11(17 .0008 ¡5 5 -33 -SS 491 -821 29.81 -.0509 .0436 20 1241 1407 1242-1572 3I.O .0571-..23 .0572 25 -AP -8E 427 1045 ¡369 1054 40 30 -43 -71 ¿246-1863 3o7.0572-.0857 .0629 556 lP94 1160 1677 1410-1945 30.24.0643-.0894 .067 oO 35 -35 92 74 868 2048 6o 220X 2147 2271 34(101.0986-.1044 .0941 4 -33 104 971' 683 2433 2569 2713 242t. IOU 37 -20 -107 35.2 .1246 ..It) .1118 92G -551 2523 2628 2813-2414 36.57 .1293-.1123 .1159 ¡20 .57 -28 -115 920 -OSI 2704 14P 2803 2988-2619 37.39 .1373-.1204 .1242 29 -36 -124 591 -680 2727 2825 2681 160 34 -40 -2970 37.45.1232-.1365 .1253 -ils 714 -561 2625 2756 2632-2880 36.15.120V-.1324 .1206 180 34 -40 -119 640 -1216 2535 2699 2411 2(0 30 -43 -lUS -2988 34.94 .1105-.1313 .1164 555 -1094 2229 2377 2110 -2646 34.83 .09V9-.1216 .1024 220 (.1 -43 -89 271 -1177 1765 1908 240 21 1455-2361 33.84 .0669-.1065 .0811 -..3 -89 271 -1177 1765 1908 1455 íoO ¡5 -50 87 -2361 33.64.0669-. 1065 .0611 IS 1456 1573 1736 1016-2457 32.46.0467-.1129 .0722 bO 15 -50 -87 15 -1456 1513 ¡736 1016 3u0 Ib -47 -84 -2457 32.46 .0487-.1129 .0722 139 -1332 ¡573 1736 1140 -2334 32.46 .0524-.1073 .0722 320 Id -47 -84 139 -1332 1573 340 lb -47 1736 1140 -2334 32.45 .0524-.1073 .0722 -84 139 -l3Si 1573 ¿736 140 -23S4 32.46 .0524-.107.5 .0752 -70-

TABLE A-VII (Cont'd) - Thermoelastic Model Stresses(PSI)

¿1762 LOCATION No. 4 o OUTPIJTZ SJESS.S ç 4tLE 5ThA1IS1 TENSILE (DEo) Ct C2 DE X Y 45 Y ¿..l. 5oj, -13.29 5 ¿8 -lB s 407 -408 -204 455 .0205-.021 - -4.07 .0245 .Q47 ¿0 27 - 0 327 -102 720 3s Ou 36 -45 0 731 -1102 102 s.2 737 -jjo -3.18 .0336 -.0509 -.0047 IS .0303 -.0664 20 36 -55 0 639 -1421 -216 IO2 661 -5.9 -.0743 40 41 -59 ¿4 iSt -1502 -521 ¿245 75 -lj -12.3V .0402 -.024 .0583 -.0735 -.024 60 55 -63 ¿9 1170 -1501 -321 1433 ¿ -ls -1.65 .0641 -.0133 -.0333 60 56 -62 29 1212 -1459 -725 1519 ¿35> -14.24 -.0692 -.0237 ¿00 65 -62 29 1499 -l37 -623 l5 loZo -ISo!.-II.? j .0748 i .0748 -.0692 ¿20 65 -62 29 ¿499 -1376 -c3 ¿366 l6 -i5u -11.7 -.0257 -14.24 .0735 -.0661 -.0333 ¿40 61 -37 34 1417 -1254 -7:5 Ij9 ¿soi -i.s -.0661 160 61 -57 34 1j7 -1254 -7 1519 1601 -l.3 -14.24 .0735 -.0333 180 66 -61 39 ¿540 -1335 -57 1b57 1760 -150 -14.95 .0509 -0713 -.038 200 68 -59 32 ¿622 -1253 -623 ¿566 ¿75j -134i -It.7i.0804 -.0635 -.0287 220 87 -59 32 2228 -i01 -408 17Cl 2277 -ll/ -6.93 .1046 -.0518 -.018(1 240 90 -56 35 2351 954 -406 17(11 2401 -6.93 .1403 -.0461 -.0188 260 90 -56 35 2551 954 408 1701 24Cl -tOoj -6.93 .1103 -.0461 280 95 -SI 31 2537 -748 -204 1664 2509 ?ui 3.52 .115 .55 .(JO94 300 -9j 3I 2557-748 -204 ¿664 -ìj -3.52 .118 -.Osy -.0094 320 95 -60 31 2.473 -1035 -306 ¡730 2500 -l0l -4.95 .114! -.0488 -.0ji 340 100 -55 36 2679 -829 -306 ¿780 27(16 -63o -4.95 .1243 -.0394-.0141

LOCATION No. 5 16322

0tJ1lJ7tSISLSSEs ,..X II. .1 (lut.E SIR.SJNS, 11.8011.6 SME.4n Cl c 45 Y I4X UQH(. NUF COCO) cs t1lL X y x .0851 28 -13 52 753 _20 -1Q30 ¿139 ¿406 -872 -32.38 -.0335-053k -22(1 -1.o ¿5.38 ¿606 -l27 -35.7 lIOt-.073 .0á95 IO 28 -is 71 753 .1106-.07e -.0695 lI 753 -220 -l46. 1538 ¡806 -l27 -35.79 ¿5 28 -is .11(1(1 Ij 754 -1460 1338 130o -1272-35.7$ -.078 -.0895 20 25 -i -220 .1026-.1228-. I06 22 -3 7.3 42.4 -754 1743 1639 1675 -35.68 ¿132-2sy.-3533 .0693-.152t-. ¿345 U lu -43 5 -79 -127$ -1709 toit .061 ¡8 1u2 -I4Su -1483 1615 997 -2.3s-31.12 .l443-.1.905 5I 9 .11457 -. l56 100 ¡3 57 -1695 1449 1631 7s -255(1-30.67 .085 4 -113 .04 -. 14U -.1.76.3 ¿20 3 3t -1l5 -1245 l475 653 -2299-26.77 ¿5 5 .0422 -.1559 .0742 ¿40 9 O2 27 e7 189 -1212 t53 363 -28.22 -28.22 .0222 -.1S59 .(1.4O 9 7 -2o? -1654-1212 ¿45.3 363 -Cs.... b -27.97 .0034 -. ¿724 .0729 IbO O 89 ¡ -2I82-lIES (434 -2813 -2345 -1291 ¿516 iSo -301 27.4b .5(1o5 -.¡846-.U7j 200 5 -75 22 -535 -26.99 -. u0o -. ¿552-.0763 22(1 I -7 2551 -(245 ¿335 -lOo -3143 Q .UU$l .Qbub 240 0 IS -323 23 l34? 1681 145 3512 26.6l 1506 -3337 2i.3 .0199-.20.45-.06o. 260 (1 -89 5 -623 -2638-1121 -324 si -331.7-O6oI .003> -.2026 280 5 -64 Q -OIS -2632-1347 168I .04?4-.19,6 .054j -IO ß -9 -lb(. -2755 -883 ¿201 -773 -SIlo-23.65 .O424 .l69 .(15.4( 320 I0 7 1077 2707 063 ¿201 -651 4u5..,-23.S -23.53 -.0424 .2U7 .0604 .340 9 90 -(12(1 -2933 9b5 I35 651 -90 -6 -ItOu -2553-9 I.3.i5 -651 -23.53 .0424 -.061.4 -3156-861 ¿333 -806 -3wU.09 .0494-.2128-.0527 380 -7 97 -14 -ItOu .0494-.2128-.0527 4110 -7 14 -1120 -IE -661 1335 (1Os -3,72-20.09

LOCATION No,6 0 16673 0&1TP(Jj STIIESSE o S1kAI#s, TENSILE S¡*8 4X MIN ANGLE ¡DIE X Y 45 X y IAX NORM NORJ (060) C 3 5 -56 9 0 (703 -231 735 -231 -1703 -.0139-.1021 ¿0 -85 ¿8 0 -2544-213 1165 213 -2514 0 .0128 .1526 15 -65 18 0 -2544 -213 1165 -213 -2544 0 -.0123-. ¿326 20 -85 18 0 -2544 -213 ¿165 -213 -2544 (j -.0128 .1526 40 -90 22 0 -2666 -131 ¿267 -131 -2666 0 -.0079 60 -98 23 11 -2912 -173 ¿369 -173 2912 0 -.0104-.1747 0 -93 28 0 -2707 32 ¿569 32 -2707 0 .00(9 .1624 100 -103 23 0 -3025-60 1482 -60 -3025 0 -.0036-.1815 lOO -108 32 0 -3143 21 1364 21 -3116 o .0013 -. (88X ¿40 -IO? 24 0 -3190 -225 1482 -225 -3190 o -.013s -.1913 zo -106 25 0 -3149 -183 1482 -183 -3149 0 .01l .t889 loU -11(1 29 0 -3303 -t1 1595 -III -34.03 0 -.0067-. 200 -121 29 -3590 ¿691 -195 -3590 o -.6th -.2133 220 -II? 24 0 -Ssus -3i7 ¡593 -317 3509 -.019 -.2103 24(1 -116 23 0 -3468 -216 155 -216 -3466 0 -.0166-.203 IO 114 27 0 -335-194 I95-194 -3585 u .Olio-.203: OoO -119 29 0 3525 1i ¿675 -176 -3526 .0lD6-.2113 120 3(1 (1 -35q9 -13.4 ¡691-134 -3549 u -.0092-.2129 .320 -lOO 21 0 3632 -o 1)93 440 -3632 -.0204 -.2179 .4O -119 22 0 -3391 -399 ¿395 -599 -3591 -.024 -.2134 .360 127 24 0 -3628-410 1708 41P -3828 - .0246- .2296 .0i96 36(1 -LOS 26 ( -3745 -327 ¿706 -327 .224? 4(10 125 26 (1 -3745-327 ¿708 -327 -7 -.0190 .2247 -71-

TABLE A-VII (Cont'd) - Thermoelastic Model Stresses (PSI)

LOCATION No. 7 =16673 o UUIPUIa SIÑSE5 ST#AINSi Tk.NS1L S6EAN I.*X alti 4NtaL 11I. A Y 4 X Y L.X tioNi Nun, (08G) Cl C2 3 5 -71 0 0 -2264-651 0 8113 657 -2b.. O -.0394-. 1306

lu -6* 0 0 -2583 -149 U 916 -749 -58 I. -.045 -. 1549 ¡5 -9* 0 0 -2902-842 0 1Q29 -842 -25u U -.05115 -. 1741 20 -9. I. 0 -2902 -842 U 1029 -842 25u2 U -.UUOS -. 1741 40 -97 5 u -3047 -738 C 1154 138 30.il 0 -.0443-.1828 60 -102-2 -3211-1007 0 1131 -10?? -3271 0 -.0604 .1962 80 -97 -8 -3181-1152 0 ¡(07-1152-316. 0 -.0691-.19 lOO -95 -6 -30X5 -loll. U bOl-1010 -308 u .064 -. ¡85 20 -102-IS -3351 -141i2 0 984 -1422 -339* 0 -.0853-.2034 140 -97 -21 -3287-1567 U 860 -1567 -37 0 -.094 -.1972 160 -92 -16 -3082-*361 0 8611 -*361 -30 0 -.0817-.1848 ISO -89 -13 -2958-125o 0 880 1c38 -29)8 0 -.0743-.1774 200 -86 -22 -2946-1497 0 724 -1497 -9..b O -.C89X-.1167 220 -82 -lB 3 -2781 -1332 0 124 -1332 -2781 0 -.0799-.1668 40 -79 -20 u -2704-1369 3. 661 -389 ulU 0 -.0821-.1622 2611 -77 -24 -2677-1478 0 )95. 1478 -OuI. 0 -.0886-.1606 280 -75 -22 3 -2595 -139Y 11 59 -*350-2(.. 0 -.0837-.1551 .9111 -72 -3* - -2583-*654 1 464 -1854-2)63 0 -.0993 -.. 1549 32u -67 -26 0 -2371 -1449 484 -*449-c377 0 -.0869-.1426 34U -66 -25 - -2336 -l4O 0 464 -1..*8-.33. 0 -.0845-. l4P1 360 -62 -2ti . -2218 -14113 Q 407 -14.I.13 -2I8 (1 -.0841-.133 361 -62 -32 1 1 -2h13 -1594 399 -159m Q -.0956-.1363 4011 -59 -23 u -2o94 -1279 u 07 -1279 -2.9.. 0 -.0767-. 1256

LOCATION No. 8 a- =19832 o OUTPUT,ST*.SSf5 STRPINS, TFP4SIL $HF.AA !N 8IGLE 11Ml X , x y AX N0R NOW. CDEG Ci C2 C3 5 -29 9 0 -714 ss O 384 55 -714 0 .0028-.036 0 iO -33 9 0 -969 -19 0 475 -19 -969 0 - .001 -.0489 0 15 -33 9 0 -969 -lO 0 475 -19 -969 0 -.001 -.0489 0 20 -42 9 0 -1256 -102 0 977 -102 -1256 0 -.0052-.0634 0 40 -31 9 0 -1543 -189 0 679 .5 ..l543 0 -.0094-.0778 0 60 -Sl 9 C) -1943-*89. 0 619 -185 -1543 0 -.0094-.0776 0 80 -59 9 0 -179e-299 0 769 -259 -1798 0 -.0131-.0907 0 100 -59 9 0 -1798 -299 0 769 -2'9 -1798 0 -.0131-.0907 0 ¡20-63 lA 0 -1880-137 0 87* -*37 -*880 0 -.0069-.0948 0 180 -63 14 0 -1880-137 0 871 -137 -1880 0 -.0069 0 *60 -.0948 -63 lA 0 -*880-*37 0 871 -137 -1880 0 -.0069-.0948 0 ¡60-63 lA 0 -1680-*37 0 871 -137 -*880 0 -.0069-.0948 0 200-63 14 0 -*880-137 0 871 -137 -1680 0 -.0069-.0948 0 220 5 -63 0 -424 0 769 -424 -1963 0 - .0214 -099 O 240 -63 5 0 -*963-424 0 769 -424 -1963 0 --0214- .099 0 260 -63 5 0 -*963-424 0 769 -424 -*963 0 - .0214-099 O 260 -60 8 0 -1839 -300 0 769 -300 -*839 0 -.0*52-.0928 0 300 -69 -1 0 -22*0-670 0 769 -670 -2910 0 -.0338-.1114 0 320 -615 -I 0 -2178 -661 0 758 -661 -2*78 0 -.0334-.1098 0 340 -58 I O - 1840 -505 0 667 -505 -¡880 0 - .0255- .0928 0 360-58 i 0 -*840-505 0 667 -505 -1640 0 - .0255-.0928 0 360 -58 I 0 -1640 -505 0 667 -505 1840 0 -.0295-.0928 0 400 -58 I 0 -1640 -905 0 667 -505 -*840 0 -.0255-.0926 0

LOCATION No.9 16673 OUTPUTI SINESSE o SINAINS: TENSILE SEA PIAX 1,18 ANGLE TIlE X 45 X Y hAX 8ORta tiGRI, IDEO) CI CZ 3 S C O O O 0 0 0 -45.01 0 0 IO 0 1) 0 0 0 0 0 -45.010 0 IS O 3. 0 0 O 0 0 -45.01 0 0 211 0 U 0 0 O U u i-45.111 0 0 40 -II U -322 C *60 -. -322 -.000*-.0193 60 -II 0 -322 0 160 -1 -322 o -.11001 -.0193 20 -*7 u 0 -49' 0 248 1 -497 0 -.0001-.0290 lOO -17 0 0 -49 0 24$ -1 -497 0 -.0001-.0298 20 1 497 -Il 0 O £46 -1 -497 U - .0001 -.0298 141.1 -Il - 0 .497 11 24$ 1 -491 1 -.uuUi-.029ti 160 U U -497 0 -Il 24$ -I -497 11 -.11001 -.0296 lt&-Ii 0 0 0 -497 24$ -i -497 O -.uOOI-O,t96 200 U U -23 -672 0 3.39 -ì -612 0 -.OUU. -.11403 22u -23 0 0 -01e Q 335 -I 072 U -.0001-.0403 4l -23 U 0 -672 0 3.35 - -670. U -.Ul'Ul -.84113 bU -23 0 0 67. O 335 -1 -672 0 .UUilj -.04u3 bu-23 0 0 C -47e 335 -1 -672 U -.0001 .Q40 3vU - U 0 -672 0 3.35 -1 -672 -.0001-.0403 3 -2.3 u o -672 0 339 -1 -72 -.00-Ql 341 -.0403 -23 0 11 -672 0 Q .935 -I -672 -.0001-.841'3 36v -23 u 0 -662 0 0 .339 -* -612 -00iJl-.0403 36u -23 u 11 -672 C 3. 33) -1 -072 0 -.0001-.0403 4110 23 U 0 o -672 u 339 -I -41k 11 -.0001-.0403 -72-

TABLE A-VII (Cont'd) - Thermoelastic ModelStresses (PSI)

=19832 LOCATION No. 10 o-o OUTPUT, STRESSES STRAINSi 1E3*SILL SI4EAR MIN ANIU.! MX NOR! NOI (DEG) Cl 2 CS TIML X Y 45 X Y 0 0 0 0 0 S O O 0 0 0 -45.0*0 0 O O O 0 0 0 -45.0*0 IO O O O O O 0 0 0 O 15 0 0 0 0 0 0 0 0 0 0 -45.010 20 O 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 -45.010 0 0 0 0 60 0 0 0 0 0 0 -45.0*0 0 0 0 0 0 0 -45.01 0 10 O 0 0 0 0 0 0 0 0 0 -45.0*0 lOO O O O 0 0 0 0 O -45.0* 0 O O 0 0 0 0 120 0 -.0001-.0192 0 0 0 -380 0 0 *69 -1 -380 *40-13 0 -.0001-.0191 0 160 -*3 0 0 3!0 0 0 159 -1 -380 189 -1 -380 0 -.0001-.0192 0 180 -13 0 0 -380 0 0 -.0*92 0 0 -380 0 0 189 -1 -380 0 -.0001 200-*3 O 0 -.0001-.0*92 0 220 0 0 -380 0 0 189 -1 -360 -13 ¡69 -380 0 -.0001-.0192 0 240-13 0 0 -380 0 0 -I 0 0 *89 -1 -380 0 -.0001-.0192 260-13 0 0 -380 0 0 0 189 -1 -380 0 - .0001 -.0192 210-13 0 0 -380 0 0 0 0 189 -1 -380 0 -.000*-.0*92 300-*3 0 0 -380 -.0001-.0*92 0 0 -380 0 0 189 -1 -380 0 320-13 0 -.000*-1lQ2 O 0 -380 0 0 189 -1 -380 0 340-13 0 0 -.0001-.0*92 0 0 0 -380 0 0 189 -* -380 360 -13 0 0 -.0369 0 0 0 -730 0 0 365 0 -730 380 -25 0 0 -.0369 0 400-25 0 0 -730 0 0 365 0 -730

LOCATION No. 11 o- =19832 o (JtiTPUI: STN_58 T8NSIL.0 S)15Ar, ..X .i ,.r.tiLL CL C3 Y t..X iQ6I Nt»*t (bt.ti) *2 I1t. Y -.0001-.0*33 0 b3 i O 181 -1 -2b3 o 5 -, O .0073 0 0 l-.5 C C 72 14 o 1v 5 - C 0 0 u .025 0 0 0 496 0 0 2.8 '.96 1 17 .0471 0 0 34 U C '.07 C ¿ti 3 0 .106 0 0 21U2 C ti lti1 2Lu2 U O 40 72 0 i 0 O O O I32 24)7 0 .1339 Ci O O 257 0 0 0 0 1591 3*81. u .1604 tus u u 3182 0 0 0 0 1810 3620 ti ¡825 ltO 124 y Q 3620 0 0 2087 4*75 0 t_ .21ti, U (7 120 143 i 0 4*75 0 0 4233 0 0 21*6 4233 o .2*34 *40 *45 0 o .2252 0 u 4167 0 0 2233 4467 0 160 153 C .2325 0 0 4513 0 0 2306 46*3 0 *80 *58 0 0 0 0 0 2379 .759 0 e .2399 200 163 0 0 4759 C O 0 0 232* 4641. 1. .234* 220 *59 0 o 4642 0 0 47b8 0 0 2394 4788 U .2414 240 154 0 .2296 0 0 4555 0 0 1.277 655 C 0 260 156 0 o .2296 0 0 4555 0 0 2277 '.5 O o ObO 156 0 Ó .237 0 0 470* U 0 2350 470* Ct 0 300 IGl 0 0 .2237 0 0 320 4438 0 0 22*9 .438 0 o 152 0 .212 0 0 42i4 0 0 2*02 4204 0 u 340 144 0 .2*2 0 0 4204 0 0 2*02 4204 ti 0 360 *44 C .212 0 0 4204 0 0 2102 4204 u 0 380 *44 0 0 0 U 0 2175 4350 Ij .2*93 400 149 0 4850

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U= 5 p=0 Q1 W= 7 R2 X=8 sT43 Y= 9 -73- RE PERENCES

"Heat Transmission", Mci3raw-Hill, 1954 cAdams, W. H.) "Numerical Analysis of Heat flow", Mi3raw-Hill, 1949 (Dusinberre, G.M.) "Waermespannungen," Springer -ërlag, 1953 (Melan, E. and Parkus, H.) "An Exploratory Study of Stress Concentrations in Therma_ Shock Fields," Trans, AE, Journal of Engineering for Industry,Vol.84, Series B, No. 3,pp. 343-350, August 1962 (Becker, H.) "Temperature-Induced Stresses in Beams and Ships," Naval Ship Research and Development Center Report - DT4B No. 937, June 1955 (Jasper, Norman H.) "Service Stresses mnd Motions of the ESSO Asheville, A T-2 Tanker, Including a Statistical Analysis of Experimental Data," Naval Ship Research and Development Center Report - DIMB No. 960, September 1955.(Jasper, Norman H.) "Thermal Stresses in Ships," Ship Structure Committee Report SSC-95, October 30, 1956 (Hechtman, R. A.) "Temperature Distribution and Thermal Stresses," Ship Struc- ture Committee Report No. SSC-l52, June 1964.(Lyman, P. T. and Meriam, J. L.) "Stress Concentration Design Factors," John Wiley, 1963 (Peterson, R. E.) 'Photothermoelastic Investigation of Thermal Stresses in Fiat Plates," Trans. A9VIE, Journal of Basic Engineering, Vol. 85, Series D, No. 4, pp. 566-568, December 1963.(Becker, H. and Colao, A.) "Thermoelastic Stress Concentrations", 2merican Institute of Aeronautics and Astronautics Meeting, January 1966 (Becker, H.and Bird,F.) "Thermal Stress Concentration Caused by Structural Discan- tiriuities," Experimental Mechanics,bl. 9, No. 12, pp. 558-564, December 1969.(Emery, A.F., Williams, J. A., and Avery, J.) "Thermo-StruCtUral Analysis Manual", WADD-TR-60-5l7, vol. 1 (AD 286908), August 1962. (Switzky, A.,Forray, M.J. and Newman, 4.) "A Treatise on Photoelasticity,"Cambridge University Press, 1931 (Coker, E. G. and Filon,L.N.G.) "Photoelasticity," John Wiley, 1941 (Frocht, M. 4.) -74- "An Exploratory Study of Three-DimensionalPhotothermo- elasticity," Journal of Applied 'lechanics,vol. 28, No. 1, pp. 35-40, 4arch 1961.(Tramposch, H. and Gerard, G.) "Physical Properties of Plastics forPhotothermoelastic Investigations,' Journal of Applied Mechanics, Vol.25, No. 4, pp. 525-528, December 1958.(Trans. A9'E, Vol. 80, pp. 525-528, 1958(Tramposch, H., and Gerard, G.) "Photothermoelastic Investigation of TransientThermal Stresses in a Multiweb Wing Structure,"Journal of the Aero Space Sciences,Vol. 26, No. 12, pp. 783-786, December 1959 (Gerard, G., and Trarnposch, H.) "Photothermoelastic Investigation of a TrimetallicStrip," Part II New York U-niversity Report S'I60-4, July 1960. (Becker, H. and Colac, A.) "A Nomographic Solution to the Strain RosetteEquations," Proc. of the Soc. for Exper. StressAnalysis, Th1. 4, No. 1, 1946, pp. 9-26 (Hewson, T. A.) "Temperature Response Charts", Wiley 1963 (Schneider,P.J.) 'ririlvCtassificatio DOCUMENT CONTROL DATA - R & D S s-cur, (y classification of title, body of abstract arId indexing annotation n,ust be entered when RI eover all report is Classified,) 1, ORIGINATING ACTIVITY (Corporate author) Ga. REPORT SECURITY CLASSIFICATION Uncias s i fled Sanders Associates, Inc. 2h. GROUP Nashua, New Hampshire REPORT TITLE THERNOELASTIC MODEL STUDIES OF CRYOGENIC TANKER STRUCTURES

4 DESC RIPTI VE NOTES (Type of report and inclusive dates) FINAL 5. AU THORISI (First name, middle initial, last name) H. BECKER A. COLAO

8. REPORT DATE la. TOTAL NO. OF PAGES lb. NO. OF REPS August, 1973 74 21 sa. CONTRACT OR GRANT NO. Sa, ORIGINATOR'S REPORT NUMBER)SI N00024-70-C-5119 b. PROJECT NO. SSC-241

e, 5h. O TRER REPORT NOISI (Arty other numbers that may be assigned this report)

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Naval Ship SystemsConiiiand

3 ABSTRACT Theoreticel calculationsand experimental modelstudies were conducted on the problemof temperature and stressdeter- mination in a cryogenic tankerwhen a hold is suddenlyexposed to the chilling action of thecold fluid.The initiation action is presumed to be the of the fluid tank. sudden and complete ruptureof the Model studies of temperaturesand stresses wereperformed on instrumented steel versionsof a ship with center holdsand wing tanks.Supplementary studiesalso were conductedon plastic models using phutothermoelasticity(t'TE)to reveal thestresses. Temperatures and stresses werecomputed using conventional dures for comparison with the proce- Simple calculotion procedurecexperimentally determineddata. diction and for stress determination.were developed for temperaturepre- The highly simplifiedtheoretical predictions oftempera- ture wore in fair agreortlentwiSh the, experimental datain the transient stage and after longintervals.The temperatures stresseo reached peak valuesin every case tested and maintainedand the peaks for several minuteCduring which time the behavior quasiatatic.The experimental was with predictions for the thintemperatures were in goodagreement strUctiOn. models representative ofship con- Evidence was found forthe importance of convectiveheat transfer in establishing thetemperatures in a ship.Insome cases this may be the primary processby which a thermal shock attenuated in a cryogenic tanker. would be model scaling. It also would influencethermai. An important resultof the project was the goodagreement f the maximum experimentalstresses with theoretical predictions which wore made from the simplecalculations,This agreement indicates the possibility ofdeveloping a general designprocedure which could involve only a fewminutes of calculation time ..t,#l.,4-),. ,',t,..+.* to DDIFORNNOV 85I 1473 GPO 867-823 S/N 0101-807.6801 Security Classification