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Thermoelastic Model Studies of Cryogenic Tanker Structures

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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 by 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 photo- thermoelasticity (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 atten- uated 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.
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