OAK RIDGE NATIONAL LABORATORY | operated by UNION CARBIDE CORPORATION % for the U.S. ATOMIC ENERGY COMMISSION ORNL- TM- 78 ol MASTER THERMAL-STRE SS AND STRAIN-FATIGUE ANALYSES OF THE ' MSRE FUEL AND COOLANT PUMP TANK 'S C. G. Gabbard NOTICE This document contains information of a preliminary nature and was prepared primarily for internal use at the Oak Ridge National Laboratory. It is subject to revision or correction and therefore does not represent a final report. The information is not to be abstracted, reprinted or otherwise given public dis- semination without the approval of the ORNL patent branch, Legal and Infor- mation Control Department. LEGAL NOTICE This report was prepared as an account of Govarnment sponsored work, Meither the United States, nor the Commission, nor any person acting on behalf of the Commission: A. 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Contract No. W-7405-eng-26 Regctor Division THERMAL-STRESS AND STRATN-FATIGUE ANALYSES OF THE MSRE FUEL AND COOLANT PUMP TANKS C. H. Gabbarad DATE ISSUED OCT - 31962 OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee operated by UNION CARBIDE CORPORATION for the U. 5. ATOMIC ENERGY COMMISSION ORNL~TM-78 Abstract ....... Introduction ... iii CONTENTS B 8 5 5 ¢ 8 & 9 4 B ST D PSS B S PSS S et ess s S % 8 0 8 8 0 BB 4 S 6 S0 S &SN S N80 S AN TSNS eSS SE b Calculational Procedwes * % & 8 6 8 & 5 o ¢ 0 8 8PS S 0SS E SN G800 SRS StrainCyCleS ® 0 ® 5 5 % 0 0 8 0 aw e O b e s B s o s s OB s NS eR Temperature Distribulions cieeeeesssssssssccscescascscescssns Temperature Distribution Curve Fitting e..cceececiesssencncens Theml-stress Analysis ® 8 9 0 S 2 St et E R AP S SR B TS PEE S Strain-cyCle Ana.l'y'SiS S & 8 P B B e P GBS S S ES S EE S S SS eSS SEY OSSO Results ceeeeces a9 8 8 6 5 9 & B 8 PO P S S8 e ad b a S SV E S SEtE eSS eSS FE P e TemperatweDiStributiOns * 9 2 9 8 09 s b e s e b s S e ¢ s BSOS s eSS EE e Themal Stresses P & 8 0 8 % S 8 50 S 8 S0 0SS S8 e BT SR R P st StrainCyCleS ® ® & 9 P @ B B & B S S S A TSN O SN SO ST SR es b e e b Presswe andMechanical Stresses * ® ® & » ¢ 0 8 & @ 40 F S B e " T s PSS Recommendations Conclusions .... References veee. 29 BB S ST DS SRS E S S T ET PP E e s et et E S s Sese 8 & 5 85 & & 5 9 &8 5 0 88 R P e P eSS s b o e e s et h oo et s ¢ ® 5 0 ¢ a4 S8 P08 S0 0SSR R PO S PP RS ET RS AR EE TS e S sbee Appendix A. Distribution of Fission-Product-Gas Beta Energy .... " P s 5 9 0 8 P B U E 5 e 20N Rt e e e st S S E S S S SS S S S SES Energy Flux at Pump Tank Outer Surface ..c.cececesssossaccses Fnergy Flux at the Volute Support Cylinder Outer Surface .... Energy Flux at the Volute Support Cylinder Inner Surface .... Appendix B. Estimation of Outer Surface Temperatures and Heat Transfercoefficients o & % % * 0 0 % S 8 8 S 0 * S8 B S ST B PP EFS SRS Appendix C. Derivation of Boundary and Compatibility Equations for Thermal Stress Calculations s.eeeveecersescsscane Appendix D. Explanation of Procedure Used to Evaluate the Effects of Cyclic Strains in the MSRE Pumps cieveeecacenans Nomenclature .... ~ v B~ ~ B~ O 15 16 16 16 20 22 22 26 27 29 29 31 31 33 41 56 66 “l THERMAL-STRESS AND STRAIN-FATTIGUE ANALYSES OF THE MSRE FUEL AND COOLANT PUMP TANKS C. H. Gabbard Abstract Thermal-stress and strain-fatigue analyses of the MSRE fuel and coolant pump tanks were completed for determining the quantity of cooling air required to obtain the maximum life of the pump tanks and to determine the acceptability of the pump tanks for the intended service of 100 heating cycles from room temperature to 1200°F and 500 reactor power-change cycles from zero to 10 Mw. A cooling-air flow rate of 200 cfm for the fuel pump tank was found to be an optimum value that provided an ample margin of safety. The coolant pump tank was found to be capable of the required service without air cooling. Introduction The fuel pump for the Molteh Salt Reactor Experimentl (MSRE) is a sump-type centrifugal pump composed of a stationary pump tank and volute and a rotating assembly (see Fig. 1). The pump tank and volute, which is constructed of INOR-8 (72% Ni, 16% Mo, 7% Cr, 5% Fe), is a part of the primary containment system, and therefore the highest degree of reli- ability is required. The pump is similar to other high-temperature molten-salt and liquid-metal pumps that have accumulated many thousands of hours in nonnuclear tést-loop service,? Although these nonnuclear pumps have been highly successful, they have not been subjected to the degree of thermal cycling which may occur in a nuclear plant. It there- fore cannot be assumed from the operating records that pumps of this type will be adequate for the MSRE. Stress calculations* were completed in accordance with the ASME Boiler and Pressure Vessel Code for determining the wall thicknesses and nozzle reinforcements required to safely withstand an internal pressure *Performed by L. V. Wilson. UNCLASSIFIED ORNL- LR-DWG-56043-A SHAFT WATER COUPLING COOLED MOTOR SHAFT SEAL ST ————— =T 77 LEAK DETECTOR LUBE OIL IN LUBE OlIL BREATHER SHAFT SEAL GAS IN LUBE OIL OUT LEAK DETECTOR SHIELDING PLUG BUBBLER TYPE LEVEL INDICATOR GAS VENT XENON STRIPPER BUOYANCY LEVEL INDICATOR Fig., 1. MSRE Fuel Pump General Assembly Drawing. of 50 psi. In addition to these pressure stresses, the fuel pump tank will be subjected to relatively high thermal stresses because of the high thermal gradients which will be imposed by nuclear heating and the large temperature difference between the top flange, which will be at 250 to 300°F, and the pool of molten salt in the tank, which will be at 1225°F. Although the coolant pump will not be subjected to nuclear heating, there will be a large temperature difference between the top flange and the molten salt in the pump tank. Since the ASME Pressure Vessel Code and Code Case Interpretations do not adequately cover the design of a vessel at creep range tempera- tures under relatively high cyclic thermal stress, the thermal stress 3 The Navy evalvation was conducted under the rules of the Navy Code. Code covers the design of pressurized-water reactor systems. The problems of design in the creep range are not explicitly covered, but design cri- teria are established for vessels subjected to thermal stress and cyclic plastic strain. Thermal stresses are considered as transient in the Navy Code and must be evaluated on a fatigue basis using the estimated maximum numbers of various operational cycles and Miner's accumulative damage theorem as the design criteria.’> Automatic flow control of the cooling air to the upper pump tank surface was initially proposed so that the temperature gradient on the spherical shell would remain relatively constant at various opefating conditions. The complexity and possible lack of reliability of the auto- matic control system made it desirable, however, to determine whether a fixed air flow could be used for all the operating conditions of the pump. Calculations were therefore made for establishing the temperature distributions, thermal stresses, pressure stresses, and permissible num- ber of operational cycles for various modes of operation and various cooling air flow rates. From this information, it was possible to select operating conditions that would permit the maximum number of operational cycles and provide an ample factor of safety above the 100 heating and 500 power-change cycles anticipated for the MSRE. Calculational Procedures Strain Czcles Since thermal stresses are considered to be transient and in some cases subject to relief by stress relaxation at operating temperatures, they must be evaluated on a strain-fatigue basis, as required by the Navy Code. Two types of strain cycles will occur during normal operation of the pump: 1. heating and cooling when the reactor system is heated from room tem- perature to operating temperature and returned to room temperature, and 2. power-change cycles when the reactor power is raised from zero to 10 Mw and returned to zero. The change in strain must also be considered for a loss-of-cooling air incident in which the operating conditions would change from (1) re- actor power operation at 10 Mw with design air flow to (2) operation at 10 Mw with no air flow to (3) zero power operation with no air flow. Temperature Distributions The initial step in the thermal-stress and strain-fatigue analyses was to determine the temperature distributions in the pump tank for various operating conditions based on the effects of internal heat generation, conductive heat flow, convective and radiative heat transfer with the salt, and cooling of the shielding plug and upper pump tenk surface. The generalized heat conduction code” (GHT Code) was used to obtain the tem- perature distributions. During reaoctor power operation, the fuel pump tank will be heated by gamma radiation from both the reactor vessel and the fuel salt in the pump tank and by beta radiation from the fission- product gases. The maximum gamma heat-generation rate during reactor operation at 10 Mw was calculated* to be 18.70 Btu/hrein.? at the inner surface of the upper portion of the pump tank, giving an average heating rate through the 1/2-in.-thick pump tank wall of 16.23 Btu/hr.in.?. The gamma, heat-generation rate in the shielding plug above the pump tank *Calculated by B. W. Kinyon and H. J. Westsik. was calculated at increments of 1/2 in. based on an exponential decrease in the heating rate. The beta heating, which varied from 4.80 to 22.22 Btu/hr-in.?, was estimated by distributing the total beta energy emitted in the pump tank over the pump-tank surface exposed to the fission-product gases (see Appendix A). Preliminary calculations with the GHT Code indicated that controlled cooling of the upper pump tank surface was necessary, not only to lower the maximum temperature, but also to reduce the temperature gradient in the spherical portion of the pump tank near its junction with the volute support cylinder in order to achieve acceptable thermal stresses. These calculations also predicted excessive;y high temperatures in the volute support cylinder between the pump tank and the pump volute. These high temperatures were caused by a series of ports in the volute support cylin- der wall for draining the shaft labyrinth leakage back into the pump tank. The drain ports were originally located at the bottom of the cylinder and restricted the conduction of heat downward into the salt. The maxi- mum temperatures were reduced to an acceptable level by centering the drain ports between the pump tank and the pump volute so that heat con- duction would be unrestricted in the both directions. Final temperature distributions for zero power operation at 1200°F, zero power operation at 1300°F, and 10-Mw operation at 1225°F were obtained for various cooling- air flow rates by varying the effective outer-surface heat transfer coef- ficient. Temperature distributions were also calculated for 10-Mw opera- tion at 1225°F, zero power operation at 1200°F, zero power operation at 1300°F, and zero power operation at 1025°F without external cooling. The method of obtaining the effective outer-surface heat transfer coefficients for the various conditions is described in Appendix B. The pump tank and volute support cylinder geometry considered in these calculations is shown in Fig. 2. Temperature Distribution Curve Fitting Before the meridional and axial temperature distributions of the pump tank can be used in the thermal stress equations, they must be ex- pressed as equations of the following form (see p. 66 for nomenclature): UNCLASSIFIED ORNL—LR—-DWG 64491R TOP FLANGE I\ VOLUTE SUPPORT / % CYLINDER f,/ CYLINDER B 1 ; PUMP TANK % SPHERICAL % SHELL % % / \ CYLINDER / IIAIE / \ LIQUID % \ LEVEL\ | \ / SEF? d \\\\ ~ 4 \ ~ % 1/ »y N\ ~ /}»)) > \\ Q 00’ PUMP \\ e P vouuTe \ SS - LIQUID LEVEL Fig. 2. Pump Tank and Volute Support Cylinder Geometry. Internal Volute Support Cylinder "A" L2 + T L3 a g =T + Ta 4 a al L+ ?a 2 3 External Volute Support Cylinder "B" 6. =T. . +T L+ T L2+T L3+T e’bL b bl b2 b3 b4 b5 Pump Tank Spherical Shell ec - ?Ei * Tc2 * chYc * Tc4Y§ * TC5Y2 For the internal cylinder and the spherical shell, the GHT tempera- ture distribution data were fitted to the equation by the use of a least- squares curve-fitting program.5 For the external cylinder, manually fit equations containing only the exponential terms were found to fit ex- ceptionally well to within about 2.5 in. of the top flange, where exces- sive errors were encountered. On the other hand, the least-squares-fit equations containing all the terms fit very well in the vicinity of the top flange but deviated near the cylinder-to-shell junction. A comparison of the data obtalned with the two fitting methods and the GHT data for the external cylinder is shown in Fig. 3. Since the cylinder-to-shell Jjunction is considered to be the most critical area because of its high operating temperature, the manually fit equations were used for the ex- ternal cylinder. The points on Figs. 4 and 5 show the "fit" obtained for typical sets of GHT temperature-distribution data. Thermal-Stress Analysis In order to calculate the thermal stresses, the pump tank and volute support cylinder were considered to be composed of the following members, as shown in Fig. 2: 1. an internal cylinder extending from the volute to the junction with the spherical shell, cylinder "A," UNCLASSIFIED ORNL~LR-DWG 64490 1000 ! . [ | | | = | 1 , 800 ;;éL_mfi+f — — - [ ; -~ S| | @ POINTS PREDICTED BY "HAND FIT" EQUATION _ N | 0 POINTS PRECICTED BY “LEAST SQUARES" L i i EQUATIONS . 600 — | : . P L - Lt x i - — < o i 400 & [ SPHERE JUNCTION e 200 = TOP ' FLANGE 0 ! 5 0 { 2 3 4 5 6 7 8 AXIAL POSITION (in.) Fig. 3. Comparison of "Hand-Fit" and "Least-Square-Fit" Tempera- ture Data with GHT Data for Cylinder "B.” UNCLASSIFIED ORNL-LR-DWG 64492R 1400 T ] T VOLUTE SPHERE ‘ el 1 —e—— T JUNCTION | / \\ 1200 * -y e - — ~ \L\ \\\ | X e, N\ AN - N \ _ -~ FUEL PUMP, 10-Mw POWER, 1000 [ S — NN X" NOEXTERNAL COOLING _ ~ ~ N N\ FUEL PUMP, 10-Mw POWER, 200-cfm e AP & ~ \\ \ AIR COOLING A Ly \\\\ N\ \ = ~ \ \, ~FUEL AND COOLANT PUMP, ZERO 2800 - £uel pUMP, ZERO POWER, - L\ O\ POWER, NOEXTERNAL COOLING x 200-cfm AIR COOLING -~ \\ P\ Q. i i 3 1 i \ A\ W\ = : COOLANT PUMP, 10-Mw _>\\\ \\ 600 —— 1~ POWER, NO EXTERNAL COCLING T NNCN - - ' . QJI\\‘. \ | NN ‘ ’ N\ e ® ANC A INDICATE TEMPERATURES PRECICTED \\\.“ 406G i~ . BY THE TEMPERATURE EQUAT-ONS FCR THE AN SN Top | O-AND ‘0-Mw PCWER CASES W Th 200 cfm SR FLANGE COOLING AIR FLOW. N i N S 1 | 200 - 0 2 4 8 8 1C 12 14 16 AXIAL POSITION {in,) Fig. 4. Axial Temperature Distribution of Volute Support Cylinder at Various Operating Conditions. JNCLASSIFIED ORNL-LR-DOWG 644353R 2000 : : 1 ; | | | | © AND ® INDICATE TEMPERATURES PREDICTED BY THE TEMPERATURE EQUATIONS FOR THE O AND 10-Mw | | 1800 | . POWER CASES WITH 200-ctm COOLING AIR FLOW i o | ! ' ‘ CYLINDER | a JUNCTION FUEL PUMP, 10-Mw POWER, NO EXTERNAL COOLING 1600 /,’ffff“fi+ | ~ ' - : 7 I ‘\ I ! L // : i N = 4400 -~ A ‘] e I W i | ‘ | ; N 3 // | | 5 | \\ = ! G & / OWER o EXTERNAL COOLH N\ d 200} Lt ANT PUMPS, 2 ZERO POV T 2 / FUEL AND © COCLAT — - e fm AIR COOLING - —t POWER, ‘200-cim T L PUMP, 10- - 1000 : — — T T ER - NO EXTERN : 800 [~ 4 e g g - et e 87— FUEL PUMP, ZERO POWER, 200-cfm AIR COOLING ‘ | 600 : : - O 2 4 & 8 10 12 14 16 MERIDIONAL POSITION (in.) Fig. 5. Meridional Temperature Distributions of the Torispherical Shell at Various Operating Conditions. 2. an external cylinder extending from the junction with the spherical shell to the top flange, cylinder "B,” and 3. the pump tank spherical shell, An Oracle program* was used to obtain the pressure stresses, the stresses from the axial load on the cylinder, the thermal stresses re- sulting from temperature gradients in either or both cylinders, and any combination of these loadings. The Program assumes that the sphere is continuous (i.e., has no boundary other than the cylinder junction) and is at zero temperature. The zero-temperature assumption required that the temperature functions of the cylinders be adjusted to provide the proper temperature relationship between the three menbers. The boundary conditions for the ends of the two cylinders specified that the slope of the cylinder walls was zZero and that the radial displacements would be *¥The Oracle program for analysis of symmetrically loaded, radially Jjoined, cylinder-to-sphere attachments was developed by M. E. LaVerne and F. J. Witt of ORNL. 10 equal to the free thermal expansion of the members at their particular temperatures. It was recognized at the beginning that some degree of error in the thermal-stress calculations would be introduced by the ab- sence of a thermal gradient on the sphere; but in the cases where air cooling was used to limit the gradient, the results were believed to be reasonably accurate, ILater calculations showed, however, that the stresses were very sensitive to the temperature gradient on the sphere, and therefore the Oracle code was used only to evaluate the pressure stresses and the stresses from axial loads. In order to calculate the thermal stresses, including the effects of the thermal gradient on the sphere, it was necessary to substitute a conical shell for the sphere. The angle of intersection between the cone and cylinders was made equal to the equivalent angle of intersection on the actual structure. This substitution was required because moment, displacement, slope, and force equations were not available for thermal- stress analysis of spherical shells with meridional thermal gradients. Thermal stresses in the two cylinders and the cone were calculated by the use of the equations and procedures outlined in refs, 69, In order to evaluate the four integration constants required for each of the three members, it was necessary to solve the 12 simultaneous equa- tions which described the following boundary and compatibility conditions of the structure: Cylinder "A" at Volute Attachment. The slope of cylinder "A" was taken as zero and the deflection as —amez. Cylinder "B" at Top Flange. The slope of cylinder "B" was taken as zero and the deflection as -afi@z. Cone at Outside Edge. The slope of the cone was taken as zero and the meridional force was taken as zero. Junction of Cylinder "A," Cylinder "B," and Cone. The summation of moments was taken as zero; the summation of radial forces was taken as " and the cone were taken zero; the slopes of cylinder "A," cylinder "B, to be equal; and the deflections of cylinder "A," cylinder "B," and the cone were taken to be equal. 11 The following 12 equations, which are more completely derived in Appendix C, describe the boundary and compatibility conditions given above: 7 — Y C_ W/ = 279.04(T_, + 13.0420_, + 124.57T_,) , (1) where /7 _ ’ / / . 2: Cnéwn - Cléwl - C2aw2 ¥ CBQWB * C4éw4 ? 2 c. N =0 ; (2) 1 4a52 (EJ CnaMn U'zz Cnth) * 23 CnCM&n - 114'7(Ta3 - TbB) - b2 - 0.00?llJi — l.BJ2 - 122.82J3 - 324.9J4 - 229.41Tb5 fI ; (3) 1 ZEE (Z CnaQn * 2: Cann) ¥ 2 8% tan ¢ (sin ¢-9‘?L¢9)ZC Q 4+ sin nc nc 6.2094 (79,387, + 3.OJ3) — 2 b3 - 344.12(Ta4 + Tb4)_+ 229.41Tb5 —I 5 (4) Zc w'+zc W/ = 279.04(T . + T . ) — 1116.2T b . (5) na n nb n * a2 b2 5 Fl ? 2 ap Bc 2 —Yec w/ - = tan d)E C W/ = 1484.65T . + & na n tc nc nc a2l + 64.983(9.9225J2 ~ 10.100J; + 98.456J, + 976.937,) ; (6) 12 T v5 c N - Y C_ N =154.05(T , — T, ) — 616.21 ol (7) 2% c N+ sin” ¢ Yoc (v =W ) t na n tc Ccos 5 nc' nc ne C W/ = 0.0408J, — 24.503J nec nc 1 5~ 600.37J3 — 14710.6J L (9) Y, € Q. =196.027, + 37, ; (10) Y, W/ = 279.04(T, ) + 15.94T, 5 + 190.56T, ) — 1116.2T %; ;o (1) 4—F, ), C N, = 154.0T, = (12) In these equations, L= (/8" 44, F, =¥, & J, = 20,91 J, = 459.95T 5 — 11.555T_, , g, = 171831, 7, = 19.165T_, 13 Equations (1) through (12) are arranged so that the left side con- taining the unknown integration constants is dependent only on the specific pump tank configuration, while the right side containing the thermal- gradient terms will vary for each case. After obtaining the four integration constants for each menber, the bending and membrane stresses can be calculated using the following equa- tions for either cylinder or the cone: 6M $ O =% —— b t2 - _ ¢ =T md £ o -8 mp t For the principal meridional and circumferential stresses the applicable equations are: Q n o1 = “mo T %ve %% = pd T pp 2 %0 = %wp T “pe For cylinder "A," 1 . My = — ), C M - 2Dac (Ta3 + 3T, %) , bap 14 1 _ Y\ _ w2 ~-dy Mé_%zzcnan 2Dact (Tb3+3Tb4 B) Db°y e , P z: -dy d4 N, =-—) C.N —Etol , e , e nb n b5 d4 + 4 N@’:O - For the cone, = ! 5= ) CocMyn * TKp + 130, + 2.30P) + 2.20,P, = | =), C M, —JK, +1.37, + L.6J,P, + 1.2667J,P nc én A 172 2 371 3 7 = i 2 5 = B tan ¢ (_Z C Q. + 8P + 3J3) ; = i 2 , = B tan ¢ (—E C N, * BI,P5 + 3J3) : In order to facilitate the solution of several cases and to reduce the amount of time involved in calculating complete stress distributions, an IBM 7090 program was written for the MSRE pump configuration. The program calculates the temperature-dependent constants of the 12 simul- taneous equations, solves the equations for the 12 integration constants, and calculates the bending, membrane, and principal stresses at 65 loca- tions. Up to 25 cases can be solved, and the number of cases to be solved and the constants in the temperature distribution equations are included as input data. A set of general input data is also required 15 that contains the left-hand members of the simuitaneous equations and the position functions tabulated in refs. 7 and 9. A special test case with a uniform-temperature conical shell was prepared for the IBM 7090 program to check the validity of substituting the conical shell for the spherical shell and to obtain an over-all com- parison between the results of the IBM and Oracle programs, The compara- tive results are shown in Table 1 for the Jjunction of the three members. As may be seen, the cone stresses agreed satisfactorily at the junction where they were a maximum. Deviations between the results of the two programs at other meridional positions were not considered important for the cases of interest. Table 1. Comparative Results for Conical and Spherical Representation Axial or Meridional Principal Circumferentizl Principal Stress {psi) Stress (psi) IBM 7090 Program® Oracle Programb IBM 7090 Program Oracle Program Cylinder "A" -3 276 -3 374 -3 047 -3 351 Cylinder "B" 7 091 7 365 -4 018 -4 548 Cone or sphere -25 196 -25 1703 -3 572 -3 967 “For cylinder-to-cone Jjunction. bFor cylinder-to-sphere junction, Thermal-stress calculations were completed for the various operating conditions listed previously in the section on temperature distributions. Strain-Cycle Analysis In order to determine the optimum cooling-air flow rate and the life of the pump tank, it was necessary to determine the allowable number of each type of operational cycle (heating and power change) for each of several cooling-air flow rates. If P15 Pyy -e., P aTE the anticipated 1’ N2’ allowable number of cycles determined from the thermal-stress and strain- values for the various operational cycles and N “ony Nn are the fatigue data, the "usage factor" is defined as E: (pi/Ni). A design air 16 flow can then be selected to minimize the usage factor and give the maxi- mum pump=-tank life, The permissible number of each type of operational cycle is deter- mined by comparing the maximum stress amplitude for each type of cycle with the design fatigue curves. The maximum stress amplitude includes the thermal stresses caused by meridional thermal gradients, the thermal stresses caused by transverse thermal gradients, and the pressure stresses caused by the 50-psi internal pressure. A discussion of the various types of stresses (primary, secondary, local, and thermal) and the effects of each on the design of the pump tanks is given in Appendix D. A discussion of the procedure used in determining the allowable number of cycles is presented, and the design fatigue curves of INOR-8 are included. Results Temperature Distributions The results of the GHT temperature distribution calculations for pertinent operating conditions are shown in Figs. 4 and 5 for the fuel and coolant pumps. The spherical shell meridional temperature distribu- tions for the fuel pump at various cooling air flow rates and reactor power levels of zero and 10 Mw are shown in Figs. 6 and 7. Thermal Stresses Typical thermal-stress profiles of the fuel pump at a cooling-air flow rate of 200 cfm with the reactor power at zero and 10 Mw are shown in Figs. 8 and 9; similar profiles of the coolant pump are shown in Figs. 10 and 11. The relatively high stresses at the top flange are believed to be caused by the poor fit of the temperature equations in that area, as shown in Fig., 3. The stress at the top flange was calculated to be 15 000 psi when the least-squares-fit temperature equation was used. It was found, however, that this equation introduced stress errors at the cone-to-cylinder junction. Therefore, the actual stress profiles along the entire length of the external cylinder would probably be better 17 UNCLASSIFIED ORNL-LR-0OWG 64494R 1800 [ CYLINDER JUNCTION 0 COOLING AIR FLOW (cfm) 1600 - //- LT . _ / = 1400 ot 80 — % /- Z / a 100 o 4200 L vfluv_;;y__—-w,—" ! -1 = & " 150 ___,,:::::: 1000 /’:_:::—- 250 --flf'—-——_;/ —] 300" = 800 0 2 4 G 8 10 12 14 16 MERICIONAL POSITION (in.} Fig. 6. Meridional Temperature Distributions of the Torispherical Shell at a Reactor Power of 10 Mw and Various Cooling-Air Flow Rates, UNCLASSIFIED ORNL-LR- OWG 64495R T 1400 CYLINDER JUNCTION _ F cfm 1200 o . M_Q__SQQUNGAIR LOW (cfm) & / ! ‘ / 2 1000 <~ L - — § / /‘ i 100 / s ] : Z ‘ 800 [ — == T - 300 ; | | 1 600 ‘ 0 2 4 6 8 10 12 14 16 MERIDIONAL POSITION (in.) Fig. 7. Meridional Temperature Distributions of the Torispherical Shell at Zero Reactor Power and Various Cooling-Air Flow Rates. 18 UNCLASSIFIED ORNL-LR-DWG 64496R 30,000 VOLUTE o 20,000 / : — —-/7\ e 10-Mw OPERATION WITH 10,000 | - N 7" 200-c¢fm COOLING AIR — a INTERNAL CYLINDER EXTERNAL CYLINDER @ © / - )\ L o / = / w :’l % _/T—\ / e ;s 10,000 —— - - — ;",“// \_—T_\ _ £ 7ERO POWER OPERATION WITH 200-ctm COOLING AIR | -20,000 [~ — - TOP FLANGE ; ‘ i . -30,000 & | : ‘ -6 -4 -2 o 2 4 6 8 AXiAL POSITION (in.) Fig. 8. Fuel Pump Principal Thermal Stresses at Cylinders "A" and "B" for Operation at Zero Power and at 10 Mw with a Cooling-Air Flow Rate of 200 cfm. UNCLASSIFIED ORNL-LR—-DWG 64437 4000 2000 \\ — b e e ZERO POWER, 200 -cfm COOLING AIR 0 T~ “ CYLINDER N — | JUNCTION . —2000 f—---- e - S ‘@ (=% \ — '—-__—__ S —4000 | ] & 00 -cfm COOLING AIR b_ ¥ -6000 — - -8000 - + -10,000 , . ~12,000 5 5 0 1 2 3 4 5 MERIDIONAL POSITION (in.) Fig. 9. Fuel Pump Principal Thermal Stresses at Spherical Shell for Operation at Zero Power and at 10 Mw with a Cooling-Air Flow Rate of 200 cfm. 19 UNGLASSIFIED ORNL-LR-DWG 64498 f 30,000 / _ VOLUTE 20,000 _ 7ERO POWER,NO EXTERNAL COOLING \ 10,000 i~ | %7 \ . 7 T%&/ @ 10 Mw,NO EXTERNAL COOLING & 0 o % L 10 Mw,NC EXTERNAL COOLING ZERO POWER,NC EXTERNAL SPHERICAL SHELL JUNCTION COOLING I -20,000 \\ TOP FLANGE -30,000 | -6 -4 -2 0 2 4 6 8 AXIAL POSITION (in.) Fig. 10. Coolant Pump Principal Thermal Stresses at Cylinders "A" and "B" for Operation at Zero Power and at 10 Mw. UNCLASSIFIED ORNL-LR-DWG 64499R 60 1 | 40 3 10 Mw, NO EXTERNAL COOLING (ZERO POWER, NO EXTERNAL COOLING ::_r.; a o o e ~<\ o 20 |- < a N = CYLINDER @ JUNCTION ‘§=====:: -20 0 1 2 3 4 MERIDIONAL POSITION (in.) Fig. 11. Coolant Pump Principal Thermal Stresses at Spherical Shell for Operation at Zero Power and at 10 Mw. o, |9 20 represented by a composite of the two stress profiles; that is, 1t would be best to use the stress profiles from the manually fit temperature func- tions near the junction and from the least-squares functions near the top flange. Since the cone~to-cylinder Jjunction is the more critical area and since the stresses at the top flange do not limit the number of per- missible strain cycles, the stresses from the manually fit equations were used in completing the strain-cycle analysis. The cylinder is sufficiently long that the temperature error at the top flange has a relatively small effect on the stresses at the cylinder-to-shell junction. Strain Czples The results of the strain-fatigue analyses are presented in Tables 2, 3, and 4. A predicted usage factor of 0.8 or less indicates a safe Table 2. Fuel Pump Strain Data for Heating Cycle . Maximum Cycle Cycle Ffilr Stress Str§ss Allowable Fchtion Frac{ion in oW . Amplitude (cfm) Inten§1ty (psi) Cycles Per 100 Cycles, (psi) Cycle P. /N. 1771 Heating Cycle to 1200°F 50 31 124 15 562 700 0.00143 0.143 100 14 400 7 200 2 500 0.00040 0.040 150 14 143 7 072 2 500 0.,00040 0.040 200 16 095 8 048 2 100 0.00047 0.047 250 21 760 10 880 1 300 0.00077 0.077 300 26 955 13 477 880 0.00114% C.114 Heating Cycle to 1300°F 50 28 966 14 483 640 0.00156 0.156 100 19 104 9 552 1 300 0.00076 0.076 150 20 590 10 295 1 150 0.00086 0.086 200 23 811 11 905 900 0.00111 0.111 250 30 895 15 447 550 0.00181 0.181 300 36 099 18 049 420 0.00238 0.238 Loss-0of-Cooling-Air Accident 200 94 885 477 443 85 0.012 1.2 21 v Table 3. Fuel Pump Strain Data for Power-Change Cycle from Zero to 10 Mw . Maximum Cycle Cycle Total Alr Stress Str?SS Allowable Fraction Fraction in Usage Flow Amplitude (cfm) Range (psi) Cycles Per 500 Cycles, Factor, (psi) Cycle PZ/N2 SIE/Ni 50 37 971 18 985 520 0.00192 0.961 1.10 100 24 763 12 382 1 000 0.001 0.500 0.54 150 18 930 9 465 1 600 0.000625 0,312 0.352 200 18 814 9 407 1 600 0.000625 0.312 0.359 250 18 775 9 388 1 600 0.000625 0.312 0.389 300 18 639 9 320 1 600 0.000625 0.312 0.426 Table 4., Coolant Pump Strain Data for Heating and Power-Change Cycles Heating Cycles Power Change from Zero To 1200°F To 1300°F to 10 Mw Maximum stress intensity, psi 63 650 69 100 10 160 Stress amplitude, psi 31 825 34 550 5 080 Allowable cycles 4 400 Total relaxation 220 140 Partial relaxation 520 290 * Cycle fraction per cycle 0.0022%7 Total relaxation 0.00454 0.00714 . Partial relaxation 0.001.92 0.00344 Cycle fraction in 100 cycles Total relaxation 0.454 0.71l4 Partial relaxation 0.192 0.344 Cycle fraction in 500 cycles 0.114 Total usage factor?® Total relaxation 0.568 Partial relaxation 0.306 SFor 100 heating cycles to 1200°F and 500 power cycles from zero to 10 Mw, 22 - operating condition for the desired number of heating and power-change cycles. The results are based on the assumption of total stress relaxa- tion at each operating condition and are therefore conservative. The location of maximum stress intensity during the heating cycle is not necessarily the same as the location of maximum stress range during the power-change cycle. This also provides conservative results, since the maximum strains for each type of cycle were added to determine the usage factor, and the total strain at the actual point of maximum strain would be less than the strain value used. Since the pump tank will safely en- dure the desired number of heating and power cycles with this conservative approach, it was not considered necessary to locate and determine the actual maximum total strain. The coolant pump will operate at a lower temperature than the fuel pump, so the stress relaxation during each cycle will probably be incomplete and therefore a larger number of cycles will be permissible. As shown in Table 4, the assumption of partial re- laxation rather than total relaxation permits more than twice the number of heating cycles. For the fuel pump, thermal-stress and plastic-strain calculations were also made for the short 36-in.-diam cylinder connect- ing the two torispherical heads. The permissible number of cycles at this location was found to be greater than those shown in Table 2, and, therefore, the cycles in the cylinder do not limit the life of the pump tank., Pressure and Mechanical Stresses The results of the pressure stress calculations made with the Oracle program are shown in Figs. 12 and 13. The stresses, which include both primary and discontinuity stresses, are for a pressure of 1.0 psi and are directly proportional to pressure. The maximum stress from the axial load exists at the suction nozzle attachment and is equal to L.766 times the load in pounds. Recommendations The strain-cycle data of Tables 2, 3, and 4 indicate that the de- sired number of strain cycles on the fuel pump can be safely tolerated STRESS {psi) 100 23 UNCLASSIFIED ORNL-LR - DWG 64500 INTERNAL PRESSURE = (.0 psi — - | STRESS AT '#"PRESSURE = PxSTRESS AT 1.0 psi — | e TTTOP FLANGET 0,=MERIDIONAL STRESS -~ -1 O =CIRCUMFERENTIAL STRESS 7 =INSIDE L 0 =0UTSIDE SPHERICAL SHELL JUNCTION i . _ ) -4 -2 O 2 4 5 8 AXIAL POSITION {in.) Fig. 12. Fuel and Coolant Pump Pressure Stresses at Cylinders "A" a,nd_ HB . 1 UNCLASSIFIED ORNL-LR-DWG 84501 0 F | | | | "-.._._..- % \I__:o INTERNAL PIRESSURE =1.0 psi o S~ - STRESS AT'#"PRESSURE = AxSTRESS — - --@i__._____:"--..__ AT 1.0 psi 2 a0 % e == : é \% e R ST T e fe = o el :‘g g ,1/ 5 }/ 04 =MERIDIONAL STRESS 20 - / O'B—CIRCUMFERENTlAL STRESS‘ [ = INSIDE | : CYLINDER _ : ‘ JUNCTION 0 =0UTSIDE | 0 | I [ ] 0 i 2 3 4 5 6 7 8 MERIDIONAL POSITION (in.) Fig. 13. Fuel and Coolant Pump Pressure Stresses at Spherical Shell., 24 when any cooling air flow between 100 and 300 cfm is used; and, there- fore, the air cooling can be controlled manually by a remotely operated control valve, A cooling-air flow rate of approximately 200 c¢fm is recom- mended. for the following reasons: 1. The predicted usage factor is reasonably near the minimum value. 2. There is a wide range of acceptable flow rates on either side of this design air flow rate, 3. At alr flow rates greater than 200 cfm, the maximum stress in- tensity during zero power operation increases relatively rapidly and de- creases the permissible number of heating cycles. Since there is a possibility of error in the temperature distribu- tion calculations because of uncertainties in the heat generation rates and heat transfer coefficients, it is recommended that the temperature gradient on the spherical shell be monitored by using two thermocouples spaced 6 in. apart radially. This gives the maximum temperature dif- ference between the two thermocouples and therefore reduces the effect of any thermocouple error. Since the thermal gradient of the spherical shell near the Jjunction is of primary importance in determining the ther- mal stresses, the differential temperature measurements and the data of Figs, 6 and 7 can be used to set the actual cooling-air flow rate on the pump. This method has the disadvantage of requiring several adjustments as the temperature and power level are raised to the operating point. If direct measurement of the flow rate were possible minor adjustments could be made after the system reached operating conditions. ©Since no cooling-air flow measuring equipment is planned for the fuel pump at the present time, a preoperational calibration of the cooling-air flow rate versus valve position should be made to permit the approximate air flow rate to be set prior to high-temperature operation. The design temperature difference between the two thermocouples for monitoring the thermal gradient is 100°F at a power level of 10 Mw and a thermocouple spacing of 6 in. The maximum allowable temperature dif- ference is 200°F for 10-Mw operation. After the cooling-air flow rate has been set for 10-Mw operation, a readjustment of the flow should be made, if necessary, at zero power operation to prevent a negative thermal gradient on the sphere. This adjusted cooling-air flow should then become 25 the operating value. During the precritical testing and power operation of the reactor it should be kept in mind that any significant change in the fuel pump cooling-air flow rate will constitute a strain cycle and will represent a decrease in the usable life of the pump tank. Therefore, an effort should be made to keep the number of cooling-air flow rate ad- Justments to a minimum. The effect of heating the system to 1300°F is also shown in Tables 2, 3, and 4. The fuel and coolant pumps can safely endure only about half as many heating cycles to 1300°F as to 1200°F. For the coolant pump, 100 heating cycles to 1300°F would essentially consume the life of the pump tank., At 1300°F the assumption of total stress relaxation is realistic, and no additional conservatism should be claimed by its use. Therefore, it is recommended that the system not be heated to 1300°F on a routlne basis. Since the fuel and coolant pump tanks are primary containment mem- bers, the maximum value of the usage factor must not exceed 0.8, which is the acceptable upper limit. To avoid exceeding this limit, an accu- rate and up-to-date record should be maintained of the usage factor and the complete strain cycle history of both the fuel and the coolant pumps. In calculating the usage factor, partial power-change cycles in which reactor power is increased only a fraction of the total power should be considered as complete power cycles unless the number of partial cycles ig a large fraction of the total when a pump tank has passed through the permitted number of cycles. In this case, additional thermal stress calculations should be made to determine the proper effect of the partial cycles, Although the strain-cycle data indicate that the cooclant pump is acceptable for the specified number of strain cycles, the stress intensity is uncomfortably high. Thesé stressgses can be reduced by lowering the thermal gradient on the spherical shell by using a reduced thickness of insulation on the upper surface of the pump tank. Since nuclear heating is not involved in the coolant pump, the proper amount of insulation can best be determined on the Fuel Pump Prototype Test Facility, which is presently under construction. 26 Conclusions The strain-cycle analysis indicates that the fuel pump will be satis- factory for the intended life of 100 heating cycles and 500 power-change cycles if it is air cooled. No special cooling will be required for the coolant pump. A conservative design is provided by the use of standard safety factors in the strain-fatigue data and in the usage factor. Ad- ditional conservatlism of an unknown magnitude is provided by tThe assump- tion of total stress relaxation at each operating condition and by the fact that the actual maximum strain should be less than the calculated maximum strain. ‘ In addition to the safety factors outlined above, the fuel and cool- ant pump tanks are capable of exceeding their required service life by factors of 2.2 and 1.4, respectively, before the maximum permissible usage factor is eXceeded. 10. 11. 12. 13, 14, 27 References Molten-Salt Reactor Program Quarterly Progress Report for Period End- ing July 31, 1960, ORNL-3014. A. G. Grindell, W. F. Boudreau, and H. W. Savage, "Development of Centrifugal Pumps for Operation with Liquid Metals and Molten Salts at 1400—1500 F," Nuclear Sci. and Eng. 7(1), 83 (1960). Tentative Structural Design Basis for Reactor Pressure Vessels and Directly Associated Components (Pressurized, Water-Cooled Systems), ‘esp. p. 31, PB 151987 (Dec. 1, 1958), U. S. Dept. of Commerce, Office of Technical Services. T. B. Fowler, Generalized Heat Conduction Code for the IBM 704 Com- uter, ORNL-2734 (Oct. 14, 1959), and supplement ORNL CF 61-2-33 (Feb. 9, 1961). P. B. Wood, NLLS: A 704 Program for Fitting Non-Linear Curves by Least Squares, K-1440 (Jan. 28, 1960), O=k Ridge Gaseous Plant; SHARE Distribution No. 8371838. F. J. Witt, Thermal Stress Analysis of Cylindrical Shells, ORNL CF 59-1-33 (Mar. 26, 1959). F. J. Stanek, Stress Analysis of Cylindrical Shells, ORNL CF 58-9-2 (July 22, 1959). F. J. Witt, Thermsl Analysis of Conical Shells, ORNL CF 61-5-80 (July 7, 1961). F. J. Stanek, Stress Analysis of Conical Shells, ORNL CF 58-6-52 (Aug. 28, 1958). C. W. Nestor, Reactor Physics Calculations for the MSRE, ORNL CF 60-7-96 (July 26, 1960). T. Rockwell (ed.), Reactor Shielding Design Manual, p 392, McGraw- Hili, New York, 1956. M. Jakob, Heat Transfer, Vol. I, p 168, Wiley, 1949. A. I. Browvn and S. M. Marco, Introduction to Heat Transfer, p 64, McGraw-Hill, New York, 1942, Tbid, p °2l. 28 15. B. F. Lange, "Design Values for Thermal Stress in Ductile Materials," Welding Journal Research Supplement, 411 (1958). 16. S. S. Manson, "Cyclic Life of Ductile Materials,” Machine Design 32, 1394 (July 7, 1960). 29 APPENDIX A Distribution of Fisslon-Product-Gas Beta Energy The total energy that will be released in the fuel pump tank by the fission~-product gases has been reported10 by Nestor to be 15 kw. This energy will not be uniformly deposited on the surface area exposed to gas, however, so it was necessary to determine its distribution over the surfaces of the pump tank., The pump tank was assumed to be of straight cylindrical geometry, as shown in Fig. A.l, and the distribution of the energy flux at the cylindrical walls was calculated as outlined in the following sections. The distribution of energy to the upper surface was approximated by assuming a distribution similar to that for the outside wall. Energy Flux at Pump Tank Outer Surface It was assumed that there was no self-shielding or shielding from the volute support cylinder, and the line source (dy,dx) was integrated over the enclosed volume (see Fig. A.2)'! to obtain the energy flux ¢ at Pl: v j_yl j‘xl j, dy adx a se:2 e de . sec” B 2 yl X dy dx a sec” & db g - sec (A.1) o Yy 6 = L [f 1 j‘xl 11 L dy dx d@ (x2 + y2)_l/2 + dr LO 0 0 y e + j; 1 ngl jg 2 dy dx de (X2 + y2)'l/é] , 30 UNCLASSIFIED ORNL-LR-DWG 68993 36 in. DIA - e——-- {5 jn. DIA =] I 7 777777 N 1 \ N % 1 N C A . . 1 h,==8|n. N N \ \ ] N N M LIQUID LEVEL N N N 77 \ _'_‘w_‘—“ e = = = —.E'_—"_'E':'/’///l/ 7 =N = T e e e == ——= j—///////’ N — = — — = — T =NV NT—/— T Fig. A.1., Assumed Pump Tank Geometry. UNCLASSIFIED ORNL-LR-DWG 68994 ra’z = g sec® § 46 t—- 8 Fig. A.2. Surface., | | | | | | | | 1 |Ffi | [ f ! | | I ] eatf—————— /74——L/72—— Diagram for Determining Energy Flux at Pump Tank Outer 31 where ¥y = h2(x2 + yz)'l/2 , Sv = energy source per unit volume Energy Flux at the Volute Support Cylinder Outer Surface Figure A.3 and the following equation were used for determining the energy flux at the outer surface, P2, of the volute support cylinder: S Yy 0 ¢ = — [j‘ L j'xl j‘ L dy dx de (x2 + y2) 1/2 + 47T L0 0 0 y 6 ¥ jg 1 j;xl jg 2 gy ax 4o (x° + y2)-l/é] , (A.2) =8 TR x, =2 [fig - (y - Rl)z]l/2 s 0, = tan™T hl(x2 + yz)'l/2 , 6, = tan ™t h.2(x2 + y2)—l/2 Fnergy Flux at the Volute Support Cylinder Inner Surface The energy flux at P3, as shown on Fig. A.3, was approximated by calculating the flux at Pé using equation A.2 and the appropriate values of Rl and Ro' This value was then corrected for the additional volume visible to P, by the direct cross-section area ratio and the inverse 3 32 square ratio of the center-of-gravity distance: d(at PB) = 1,26 ¢(at Pé) . The values of ¢ at Py Py and, Pé were evaluated as functions of hy and h.2 by the Numerical Analysis Section of ORGDP. The beta-energy dis- tribution is shown in Fig. A.4. UNCLASSIFIED ORNL-~-LR-DWG 68995 VOLUTE SUPPORT CYLINDER PUMP TANK OUTER SURFACE OUTER SURFACE \ ; \ 2 X P} R - - - - R ‘ Fig. A.3. Diagram for Determining Energy Flux at Outer and Inner Surfaces of the Volute Support Cylinder, UNCLASSIFIED ORNL-LR-DWG 64502R 4000 T , : ‘ : I o ‘ : " TORISPHERICAL SHELL, INSIDE * 3000 L oy e;if__:_______--‘.".' ~ . \;CL; i } ,/I’ ' \\\ = VOLUTE SUPPORT CYLINDER 'A',OUTSICE ,a’ ! N o i -~ = T § 2000 S L LT NOTE: i _ — o > FACE 1. AXIAL POSITION OF CYLINDER"A > SHIELDING .E"EE-—--—- | 1S MEASURED FROM SPHERE -TO- & ' | CYLINDER JUNCTION = e ! & 000 \ : ' 2. RADIAL POSITIONS OF SHIELDING \ / : o i PLUG FACE AND TORISPHERICAL ! | VOLUTE SUPPORT CYLINDER AINSIDE i SHELL ARE MEASURED FROM 1 b | | § | PUMP CENTER LINE o l I ! | L I 0 2 4 6 8 10 12 14 16 18 POSITION (in.) Fig. A.4. Beta-Energy Distribution of Fuel Pump Tank, Volute Sup- port Cylinder, and Shielding Plug. 33 APPENDIX B Estimation of Outer Surface Temperatures and Heat Transfer Coefficients The GHT Code for calculating the complete temperature distribution of the pump tank couwld not consider the effects of the flowing air stream on the temperature distribution of the pump tank because of the tempera- ture rise of the cooling air along the pump tank surface. In order to obtain the temperature distribution, it was necessary to couple the pump tank surface with the surroundings by use of an effective heat transfer coefficient (hce) and the ambient temperature., It was impractical to obtain an effective coefficient at each point along the surface, and therefore the value of Ih.ce was calculated at the cylinder-to-shell junc- tion, where the thermal stress problem was most severe, and then applied over the entire upper surface of the pump tank. The air-cooled upper portion of the fuel pump tank is shown sche- matically in Fig. B.l. The pump tank is subject to thermal radiation and convection heating from the fuel salt, fission-product beta heating, and gamma-radiation internal heating. This heat is conducted to the UNCLASSIFIED ORNL-LR-DWG 68996 /COOLING-AIR SHROUD INSULATION N S A N A A N N N A O NN N S AN OIS N A AA N NSNS NSNS AN % COOLING - 4 _ AIR FLOW 73-5 %, Ya-s g,= g, t qB+qrf 93-4 9 9 q, = he (8, 6) e PUMP TANK WALL Fig. B.l. BSchematic Diagram of Cooling-Air Shroud and Pump Tank Wall. 34 pump tank surface where it is transferred to the cooling air by two paths: (1) direct forced convection to the cooling air and (2) radiation to the cooling shroud and forced convection to the same cooling air, Heat is also conducted parallel to the pump tank surface, but this heat transfer is assumed to be zero in estimating the surface temperature and heat transfer coefficients. The temperature distribution through the pump tank wall can be calcu- lated!? as outlined below, assuming a constant gamma heat-generation rate through the wall a-e — = —i!l ) (B.l) dx k ae q — ==L x+ Cl , (B.2) dx k dé q C, ==+ L x . (B.3) dx k 80 %4 3 dx k and therefore B ET Cl 5 35 and for any place within the wall, that is, x # O, —_—— L P (B.4) k 9=—-l-—~_(qf+q)+02 . (B.5) and 6 =86 —-q7 - (qf + qB) . (B.6) If the heat transfer from the outer surface is expressed by an ef- fective coefficient with respect to the ambient temperature rather than the actual forced-convection cooling system temperature, the outer sur- face temperature can be calculated as follows from Eq. (B.6) with x = t: q t2 t g, =90 -—"7—-'""( + ), (B.7) 37 % T T % T % where (6 I-EQ | © I \JQ t | _@19 1l ]__bD" 36 and qyt t = ——te — — -qt - + B.8 qyt2 t 6. =6.+ —_—— 3 (B.g) 3772 T T Tk % k k qyt c — g 4L (B.10) T2 T LT, U = Beef3 7 Beese (B.11) where 64e is the effective amblent temperature, and UG = Befy ~BFp + At * g (B.12) Solving Egs. (B.10), (B.11l), and (B.12) simultaneously for 6, yields the following equation: h ht +h k ce T ce 93 = 94e + hcehft + k(hce * hf) hfk k + el+ qB-i- .|. hcethG + k(hce * hf) hcehft + k(hce hf) t(h. .t + 2k) + £ o (B.13) hcethG * k(hce * hf) 2 Solving Eq. (B.13) for h,, and rearranging the terms gives & hfk(el - 93) + qu + t(hft + 2%) > h,= . (B.14) (thf + k)(63 - 646) 37 The difficulty in calculating the outer surface temperature (63) from Eq. (B.1l3) results from the fact that the heat transfer coefficients hce and hf are highly temperature dependent, and 93 must be known before accurate coefficients can be calculated. However, for a given set of re- actor operating conditions, it is evident from the preceding equations that the selection of an arbitrary value of 93 will result in a particular value of the total heat transfer across the outer surface, and a particu- lar value of hce is required to dissipate this dquantity of heat to the surroundings. Since the temperature drop across the pump tank wall is small for the cases of interest, 93 can be used to compute the value of the internal surface heat transfer coefficient (hf), and the value of h,_ can then be calculated by Eq. (B.14). The following procedure was used to estimate the effective outer surface heat transfer coefficients for various cooling-air flow rates: 1. Values of h_ versus inner surface temperature (92) were calcu- £ lated by Eq. (B.15), below, and plotted on Fig. B.2:17 e & o F F (6] —6]) T 91 - 92 + 1.5 . (B.15) 2. The total heat transferred (qt) was calculated versus the outer surface temperature (93) by Eg. (B.16), below, after first calculating UNGLASSIFIED ORNL-LR-DWG 64503 h, (Bfu/hr-f12-°F) 600 700 800 300 {000 1100 1200 1300 t400 SURFACE TEMPERATURE (°F} Fig. B.2. Pump Tank Inner Surface Heat Transfer Coefficient Versus Outer Surface Temperature. 38 h,. by Eq. (B.14): a =h _(65-6,) . (B.16) 3. The forced convection heat transfer coefficients for the pump tank outer surface and the cooling shroud were calculated as a function of air flow by Eq. (B.17) and plotted on Fig. B.3:1% B, = 0,0225 ¥ (pr)0* (re)?:8 . (B.17) g 4, The heat transferred to the cooling shroud by thermal radiation was calculated versus shroud temperature for each of several values of 93 and plotted on Fig. B.3. At equilibrium conditions, the heat radiated to the shroud (q3_4) Plus the heat transferred directly to the cooling air (q3_5) must equal the total heat transferred (qt), and the heat transferred from the shroud UNCLASSIFIED ORNL-LR-DWG 64504 COOLING SHROUD TEMPERATURE (°F) 1150 1050 950 850 750 650 550 450 350 8000 i 50C0 - 4000 - —- 3000 2000 1000 HEAT TRANSFERRED TO COOLING SHROUD (Bfu/hnf!z) A, CONVECTIVE HEAT TRANSFER COEFFICIENT (Bfu/hr-ft2-°F) Ty 40 C 400 500 COOLING AIR FLOW {cfm) Fig. B.3. Convective Heat Transfer Coefficient Versus Air Flow and Heat Transferred to Shroud Versus Shroud Temperature. 39 to the cooling air (q4_5) must be equal to the heat transferred to the shroud from the pump tank. Therefore, for each assumed value of 83, the heat transferred to the shroud is calculated versus cooling air flow rate from the expression 43,4 = % T 9325 where 9 = hce(93 - e4e) ? and The particular shroud tempersture required to accept the heat (q3_4) from the pump tank surface is obtained from Fig. B.3. The heat transfer- red from the shroud to the cooling air is then calculated: = hc(94 -8 U.-5 5) For each value of © q3_4, and q4_5 are plotted versus cooling-air flow 3.’ rate as shown on Fig. B.4, and the intersection of the two curves deter- mines the cooling-air flow rate that will produce the particular value of 6,. A plot of 0 3 3 in Fig. B.5, and the effective surface heat transfer coefficients hC versus cooling-air flow rate can then be made as e for use in the GHT Code can be calculated for any air flow rate using Eq. (B.14). 40 UNCLASSIFIED ORNL -LR-DWG 64505 6000 ) w Q 9 & 4000 3000 2 754 AND g,_; , TRANSFERRED HEAT (Btu/hr-ft S o o t000 100 200 300 400 500 600 COOLING AIR FLOW (cfm) o Fig. B.4. Shroud Heat Transfer Versus Cooling Air Flow, UNCLASSIFIED ORNL~-LR-DWG 64506 ~ 1200 L 1 < ] ) {0-Mw NORMAL POWER OPERATION | 2 <[ & 1000 G o s ul '— ul Q & T —— & \ ? — ZERO- POWER OPERATION 1300°F SALT TEMPERATURE I >~ = N x e - o S S — Z 800 t— LS — — | P ——— ZERO - POWER OPERATION ,1200°F SALT TEMPERATURE+—"" —~ —T=—~— | | | | 400 : : 0 100 200 300 400 500 600 700 AIR FLOW (cfm) Fig. B.5. Nominal Surface Temperature Versus Cooling Air Flow, 41 APPENDIX C Derivation of Boundary and Compatibility Equations for Thermal Stress Calculations The procedures for calculating thermal stresses in cylinders and cones are fully described in refs. 6 through 9. The general layout of the pump tank structure and the sign convention used in the stress analysis are shown in Fig. C.1. The cone-to-cylinder Joint is assumed to be rigid. It is necessary to evaluate four integration constants for each of the three members by solving 12 simultaneous equations describing the boundary conditions of the structure and the compatibility conditions which interrelate the three members at their junction, ©Since the posi- tion functions for cylinders are tabulated in ref. 8 only for positive values of L, the cone-to-cylinder Jjunction is made the origin and the cylinder axis is assumed to be positive in either direction., This UNCLASSIFIED ORNL-LR-DWG 64507 fi%%fi£=44 %fiflngOPFLANGE [ s Mg ' TN Ob M, CYL.B 'gii::: NN & c u Qa JOJNT M L M+ L+ /\\ DETAIL ? ~-7 T [ % CYL.A VOLUTE A Fig. C.l. Schematic Diagram and Sign Convention of Pump Tank Struc- ture., 42 assumption requires that the slope and the shear force equations be modi- fied by a sign change to compensate for the reversed sign on one of the cylinders. Derivations of the 12 simultaneous equations from the specific boundary or compatibility conditions are given below. The basic equa- tions for moment, displacement, slope, and shear force were obtained from ref. 6 for the cylinders and ref. 8 for the cone. The conical shell equa- tions differ somewhat from those presented in ref. 8 because a prelimi- nary version of the report was used that did not include the effects of a thermal gradient through the wall. All the terms considering the ef- fects of internal pressure and mechanical loading were omitted from both the cylindrical and conical shell equations. The following material constants, geometric constants, position con- stants, and auxiliary functions are used in the boundary and compatibility equations: 6 E = 26.3 X 10° , -6 a="7.81 x 10 5 p=0.3 , t=0075 3 3 D-—2 106 x10° 12(1 — p%) L s - 2 d4+4 Q I wmlo » 43 It was necessary to adjust the pump tank configuration slightly so that the boundaries of the separate members would coincide with tabulated values for the cone and cylinders: ™ i W W o x W | l_l K O - ¢ = 78.5 deg , Q O ct - il 0.2035 c c c X, = 2B,\Y,, = 6.2548 , X, = 28,4, = 9.84 a = '70125 ino » % Y, =—— =727 , sin ¢ Y ., =18.0 in. c2 4y The values of X . and Xc were adjusted to the nearest values tabulated cl 2 in ref, ©: Xcl = 6,30 , Xcl)fi Ycl = 'éE— = 7.376 , C XC2 = 9.90 . The cylinder mean radius 'a' was then corrected: a =Y, sin ¢ = 7.228 , 2 1.6523 _ 1.6523 e T E T TmEx o - 0T £ = 0.55207 , Vo1 = BLai = 3,588 , Ypi = BLbi = 4,416 L. =6.51dn., , al 8.0 in. . o The values of Vai and Vi were adjusted to the nearest tabulated values in ref. 7. y, = 3.6, L, = 6,521 , Y= b, 7.970 . o 45 The following cylinder position functions were taken from ref. 7: Volute, Junction, Top Flange, Function Y, = 3.6 Yo p = 0 yy = 4ot My 0.049 -2.0 0.007546 M2 ~-0.02418 ‘ C -0.02337 M3 -65.64 +2.0 ~-50.065 M, 32.39 ' 0 155.02 Ql 0.07319 -2.0 0.03091 Q2 0.02482 -2.0 -0.01582 Q3 33.25 -2.0 -104.95 Q4 -98.03 +2.0 -205.08 Ny -0.01209 O -0.01168 N2 -0.02450 +1.0 -0.00377 N, -16.19 0 -77.51 N4 -32.82 +1.0 -25.03 Wi -0.01241 1.0 0.00791 Wé 0.03659 -1.0 0.01546 Wé -49.02 1.0 -102.54 Wi -16.62 1.0 52.48 The following cone position functions were taken from ref. 9: Junction, Cone Outer Surface, Function X o =6.3 X, =9.9 cl c2 Myl 3.3798 M -1.0712 y2 M -0.000601 y3 M ~-0.0013052 T4 ch -0.45082 4, 4317 Qc2 1.0224 -2.2413 QcB -0.0004356 0.000010179 Q -0.00014553 -0.000003558 o ™ Function / Wcl W g W MW o The cone auxiliary temperature functions were obtained from the following exXpressions: —(Etca cot ¢) T . = 46 Junction, XCl = 6.3 10.1451 4,47331 -0,001444 0.004322 13.313 27 . 449 -0.01553 0.0051 0.10078 0.0071098 2.2948 1.9948 9.9225 19.845 147.684 19.691 cl 2 54 c ;. Etca cot ¢ (72Tc5 —2EtCOt cot ¢ J3 = — Tc4 = —17.183Tc 60 -3Et @ cot ¢ : J, = < T _ = ~19.165T7 4 8 c5 c B C 54 c —20.9T c Cone Outer Surface, X, =99 c2 -54,918 -108.588 -0.00008719 -0.0002494 0.04081 0.0011659 3.1988 2.8988 24,5025 49,005 900.559 120.074 2 -~ TC3) = 459.95T , — 11.555T_, , 4 2 5 47 The temperature distributions for the cylinders and cone were eXx- pressed in the following forms: Cylinder A" 2 3 _ Y L g 6a, - Tal * Ta2 8 * Ta3 (B) * Ta4 (6) * Cylindger "B" 2 3 = L L I -dy eb = Tbl + Tb2 5 + Tb3 (6) + Tb4 (B) + Tb5 e T cl 2 3 6, = + T * TC3YC * TC4YC * TC5YC At the pump volute (ya = 3.6), the slope of cylinder "A" = 0, and d.wa afB y y 2 — =0 = — CnéWQ —a T, + 2T 5 —+ 3T, |- , aL Et A & 2 ;. Bt L L E Cnawn TR [Ta2 * 2Ta3 B * 3Ta4 (B)] ? Y C_W/ = 279.04(T_, + 13.042T_, + 124.57T (c.1) na n al a a 3 4)' At the pump volute (ya = 3.6), the radial displacement of "A" = —a0eo ,, and a Vg T l_fichaNn_ 2 3 — g J I ack [Ta]_ * Ta2 B * TaB (B) * Ta4 (B):I ? and therefore ), C N =0 . (c.2) na n At the cone-cylinder junction, the summation of moments = O, that is, Ma —'ME * Mc =0, and 1 1 C__ M —2DadflT | — ———x C.M + 4352 na a3 4352 nb n 2 -dy + 2Daaf]?b3 + Dby e + 2: CncMyn + J'lK2 + + l.BJ2 + 2.3J3Pl + 2.2J4P3 =0 , 1 2: 1 23 — C M - 0— C.M + C M = 4a52 na n 4&62 nb n ne yn 2Daa(Ta3 - TbB) — 3K, + 1.30, + 2.305P) + 2 -d + 2.2J'4P3 — Dby e v s — (2 oty - 2 C M - C_M | + C M = 4aB2 ( na n nb g) ne yn 114.7(Ta3 -Tb3) — O.OO'?llJl - 1.3J2 — 102 - 122.82J3 - 324.9J4 - 229.41Tb5 o (C.3) 1 49 At the cone-cylinder junction, the summation of horizontal and vertical forces = 0, and therefore, for the vertical forces, i — Qc sin ¢ + Nc cos ¢ or Q = - cos ¢ e c sin ¢ For the horizontal forces, Qc cos ¢ + Nc sin ¢ = c052 o 2 _ . _ . _cos” ¢ Ncm—*'NCSlW*Nc(SlW sinqb)' For the summation of horizontal forces on both the cylinders and the cone, 2 . cos” ¢ U Y TN (;ln ¢ - sin ¢ ) =0 and 1 2ap 23 CnaQn * 6DaQT 4 ap El Cnb n + 6Daa.‘l‘b4 - Db37 e-dy - B? tan ¢ (%1n ¢ — ?) (Zc Q, + 87, +3J)=O , 1 _B(E Cna n Z Cnb n) 2 : +Bctan¢(81nd)_51n )Ecncncz 6.2094(79.38J, + 3.0J,) - W — 344.3_2(Ta4 + Tb4) + 229.41T (C.4) ‘filo" l._l b5 50 At the junction, the slope of Cylinder "A" = — slope of Cylinder "B," and dwa L dwb - J dL aL ap /7 _ - _2B ’ _ -dy Et Cran ~ 8Ty = ~ 8¢ Z Copiy + 80Ty — D7 € ’ EtQ Bt -dy / ! = === —_ Cnéwn * 23 Cnfiwn T B (Ta2 * Tb2) ap by e ’ Y o W+ ) W/ =279.04(T , + T ) - 1116.2T . = (c.5) na n nb n ’ a2 b2 "TTP5 F ’ . At the junction, the slope of Cylinder "A" = slope of the Cone 'GC,’ aw du 2 __¢c - J aL ay C ap e Cnéw, - aDflla2 - Et n 52 2P3 / — — Tt tan® ¢ ChoWpe — J1Kq + P 3 (J3 + 3,20 ap 62 — Ve w Lt ) c W = t na n nc nc 8 2p, a£bTa2 + E; tan” @ J‘lKl + JéPl + -;— (33 + Jg;l) , 2 B — /L 2 /= Z c_w’ : tan® ¢ Z C W7, = 1484657 + + 64.983(9.9225J2 —-lO.lOlJl + 98.456J3 + 976.93q4) . (c.6) 51 At the junction, the displacement of Cylinder "A" = the displacement of Cylinder "B," that is, Vo &% 7 and a _ _a W _ _ -dy Et Z CnaNn al = Et Z’ Cnan bl y € ? Z‘ CnaNn ZI Cnan - Eta(Tal Tbl) 2 | © 7 Tbs N - = - —~ =2 Y, Cpally = ), C_ N = 154.05(T_) =T, ) = 616.21 R (c.7) At the junction, the displacement of Cylinder "A" = the displacement of the Cone, and Wa=ucos¢»—V sin ¢ , 2 a - tan™ ¢ |\ ’ Et z CnaNn mal = cos ¢ E‘tc [ Cncwn P 2 3 - J.K, +J ]_oge SC + (3J2 + 2J3Pl + J4P3) — + C5c] - 13 1 9 —s:‘mqfitand) C V. —JK,+Jd log 52+ Etc nc nc 13 1 e "¢ P 3 + (]_3.6J4P1 + 2‘1J3)P1 + (3J2 + 2J3Pl + J4P3) 9— + C5c] — . 2 3 b — @ sin ¢ (Tcl ool * Teate * Tt * Tc5Yc) ? 52 a 51n _sin” ¢ B t Z CnaNn t_ cos ¢ Z wnc) - . 2 FaoT . — =2 9 (13 63 P. + 2.17 al tc cos ¢ 4 1. B)Pl - X 2 3 4 — Ex sin ¢ (Tcl + TC2YC + TCBYC + TC4YC + TC5YC) , . 4 . _ Fo sin ¢ (T . +T .Y + ... + TCEYC) = BoY | sin ¢ 6, = EaoT , cl c2' ¢ al therefore : Z cna n ¥ Sm Z Cnc(vnc - Wnc) - t:iiis¢ (13.63,P, + 2.13,)P, and %Z CnaNn :12 s¢¢ Z nc nc - nc) - —12895.87, — 200.687, . (C.8) At the outer surface of the cone, the slope = 0, and 7 —_ Coolne —Kydy + By - du 53 tan® ¢ [‘ dy Et c C i O - 2P, + —;— (53 + P1J4) 3 7 - - -2 Crcpe = 91Ky = 9P (35 + 3,B1) 53 ! ! _ - - - ), ©, W/, = 0.0408J) — 24.503J, — 600.37J, — 14710.6J, . (C.9) At the cone outer surface, the meridional membrane force = 0, and _fPtan ¢ [- Y ¢ +8P.J, +37) =0 C ne nc 174 3 ? ) €@, = 8Py, + 375 = 196.023, + 37, . (¢.10) At the top flange, the slope of Cylinder "B" = 0, and aw. af y y 2 b Z -dy —_—— = e C.W —ax |T , + 2T, ,— + 37T (—) + by e =0 , daL Tt nb n b2 b3 8 b4 5 Y, C W/ = 539- rosor Yo (IY] - Et e, oW = b2 b3 B b4 \ B apg 7 ) / _ ), C_ W/ = 279.04(Ty, + 15.94T, ; + 190.56T, ,) —1116.2T , > . (C.11) TS5 F i ’ 2 At the top flange, the displacement of Cylinder "B = —a0p ,, and J 12 2t L Cply — o |7, + T g " Tp3 (a) * 13 -dy +Tb4(§) -7 e = —al T,01+Tb2 v\’ y\ -dy +Tb3 (B) +Tb4 (6) +T_b5€ s a _ -4y gt L Sy T © i< + _dy aoch5 e s 54 _BL _-dy _ -ay ), C. N =—7e EtOT, ;€ , 4 —F Y C_N_ = 154.05T, ——= (c.12) nb n : b5 F2 * : The final forms of these 12 equations are arranged so that the left hand side containing the unknown integration constants is dependent only on the specific pump tank configuration, while the right side containing the temperature distribution terms will vary for each operating condition. The matrix of integration constant coefficients for the 12 equations is shown in Table C.1. 55 Table C,1. Simultaneous Equation Matrix Coefficients of Unknown Integration Constants C__, C ., and C na’ nb ne Equation e Cla Coa €3 Csa 1% Co Ca Can Cie Coc Cae Chc 1 -0,01241 -0.03659 =49.02 -16.62 0 0 0 0 | 0 0 0 0 2 -0.01209 -0.0245 -16.19 -32.82 0 0 0 0 0 D 0 0 3 -0.22696 O 0.22696 0 0.22696 0 ~0.22696 0 3,3798 -1.0712 -6.01 x 1074 -1.3052 x 1073 b -0.1253 -0.1253 -0.1253 0.1253 ~0.1253 -0.1253 0.1253 0.1253 -2.7993 6.3485 -2.705 x 1072 -9.03 x 1074 5 1.0 -1.0 1.0 1.0 1.0 -1.0 1.0 1.0 0 0 0 0 6 5.3205 -5.3205 5.3205 5.3205 0 0 0 0 ~919.2 ~290.69 0.009384 -0.28086 7 0 1.0 0 1.0 0 _1.0 0 1.0 0 0 0 0 8 0 9.637 0 9,637 0 0 0 0 128,212 ~264 .36 -0.14957 4,912 x 1072 9 0 0 0 0 0 0 0 0 -54.918 ~108.588 -8.719 x 1077 -2494 x 10~% 10 0 0 0 0 0 0 0 0 44317 -2,2413 1,018 x 107° -3.558 x 107° 11 0 0 0 Q 7.91 x 1073 1.546 x 1072 -102.54 52 .48 0 0 0 0 12 0 0 0 0 -1.168 x 1072 -3,77 x 1073 -77.51 -25.03 0 0 0 0 56 APPENDIX D Explanation of Procedure Used to Evaluate the Effects of Cyclic Strains in the MSRE Pumps J. M, Corum An essential difference in structural design for high-temperature operation as compared with design for more modest conditions is the need to consider creep and relaxation of the structural material. Many of the methods and procedures presently specified as a structural design basis in the ASME Boiler and Pressure Vessel Code, Unfired Pressure Vessels, Section VIII, and in the preliminary design basis developed by the Navy3 become meaningless at high temperatures. Thus a revised design basis must be formulated when high-temperature conditions are considered., The operating program of any component must be examined, and the design basis selected must be used to determine whether the number of operational cycles which can be safely tolerated exceeds the number of the cycles which is desired during the life of the component. If necessary, the nunmber of operational cycles of the component must be limited to the value which can be safely tolerated. As may be seen, the details of the operating program are extremely important and must be selected with considerable care. The concept of stress is used here as a convenience in discussing the effects of cyclic strains because it is the principal variable in : conventional problems of elasticity. Properly, however, the discussion | should be in terms of strains when dealing with high temperatures and, especially, in describing thermal effects in structures. With these factors in mind, four general types of stresses were considered in es- tablishing a design basis for the MSRE pumps which will operate at tem- peratures within the creep and relaxation range; these are primary, secondary, local or peak, and thermal. The primary stresses are direct or shear stresses, developed by the imposed loading, which are necessary to satisfy only the simple laws of equilibrium of external and internal forces and moments, When primary stresses exceed the yield strength of 57 the material, yielding will continue until the member breaks, unless strain hardening or redistribution of stresses limits the deformation. Secondary stresses are direct or shear stresses developed by the con- straint of adjacent parts or by self-constraint of the structure. bSec- ondary stresses differ from primary stresses in that yielding of the ma- terial results in relaxation of the stresses., Local or peak stresses are the highest stresses in the region being studied. They do not cause even noticeable minor distortions and are objectionable only as a pos- sible source of fatigue cracks. Thermal stresses are internal stresses produced by constraint of thermal expansion. Thermal stresses which in- volve no general distortion were considered to be local stresses. Thermal stresses which cause gross distortion, such as those resulting from the temperature difference between shells at a junction, were considered to be secondary stresses, In the present examination, four sources of stresses were considered. Pressure differences across the shells will produce membrane pressure stresses, These stresses are primary membrane stresses. The pressure differences will also produce discontinuity stresses, which are secondary bending stresses. Temperature gradients along the shells will produce stresses which are due both to the tempersture variations and to the dif- ferential ~expansion-induced discontinuities at the shell junctions. These stresses are secondary bending stresses. Temperature gradlents across the walls of the shells will produce thermal stresses which are assumed to be local stresses, The ASME Code is generally accepted as the basis for evaluating pri- mary membrane stresses, and the allowable stresses for INOR-8 at the op- erating temperatures of the pumps were obtained from the criteria set forth in the code, with one exception. A reduction factor of two-thirds was applied to the stress to produce a creep rate of 0,1% in 10 000 hr in order to avoid possible problems associated with the effect of irradia- tion on the creep rate.* The maximum allowable stress at 1300°F is 2750 psi, and the primary membrane stresses were limited to this value. The *Based on data from R. W. Swindeman, ORNL. 58 primary stresses were not considered further except from the standpoint e of excessive deformations produced by primary plus secondary stresses. In order to evaluate the effects of secondary and local stresses, repetitive loading and temperature cycles must be considered because fractures produced by these types of stress are usually the result of strain fatigue. Data which give the cycles-to-failure versus the total or plastic strain range per cycle may be used for studying cyclic condi- tions. The total strain range per cycle is defined as the elastic plus plastic strain range to which the member is subjected during each cycle. The plastic strain range per cycle is the plastic component of the total strain range per cycle. The strain-cycling information may be compared with the calculated cyclic strains in the member. ©Since most formulas express stress rather than strain as a function of loading or tempera=- - ture distribution, assuming elastic behavior of the material, it is con- venient, as stated before, to transform the test data from the form of strain versus cycles-to-failure to the form of stress versus cycles-to- failure by multiplying the strain values by the elastic modulus of the material, The resulting values have the dimensions of stress but, since the tests were made in the plastic range, they do not represent actual stresses. When the analysis of stresses in a member reveals a biaxial or tri- axial stress condition, it is necessary to make some assumption regarding the failure criterion to be used. In the plastic range, where most of the significant secondary and local stresses lie, there is no experimental evidence to indicate which theory of fallure is most accurate. There- fore, it has been recommended’® that the maximum shear theory be used, since it is a little more conservative and results in simpler mathemati- cal expressions. The following steps used in developing the procedure were taken from ref. 3: 1. Calculate the three principal stresses (o1, 0, 03) at a given point, 2. Determine the maximum shear stress which 1s the largest of the three quantities 59 1 5 (o —0y) 5 (o —03) or 1 5 (o —a5) . 3. Multiply the maximum shear stress by two to give the "maximum intensity of combined stress.” 4. Compare this quantity with the E Ae values obtained from uni- axial strain-cycling tests, Stated more simply, the procedure is to use the stress intensity representing the largest algebraic difference between any two of the three principal stresses. The procedure outlined above for evaluating the effects of cyclic loadings and cyclic thermal strains was used to examine the cyclic sec- ondary and local stresses which will be produced in portions of the MSRE pumps. The procedure is essentially that specified by the Navy Code; however, the Navy Code was developed primarily for applications in which the maximum temperatures would be below those necessary for creep and re- laxation of the material. Thus, several of the steps outlined in the Navy Code were modified for the present evaluation. The assumption was made that the temperatures were sufficiently high and that the times at these temperatures were sufficiently long for com- plete stress relaxation to occur. Thus the strains which the elastically calculated stresses represented were taken as entirely plastic. On this basis, strain cycling data in the form of plastic rather than total strain range per cycle versus cycles-to-failure were used. Figures D.1l and D.Z2, which give strain fatigue data for INOR-8 at 1200 and 1300°F, were ob- tained from a limited nunmber of strain-cycling tests performed by the ORNL Metallurgy Division. The dashed curves were obtained from the plas- tic strain range per cycle curves and represent a conservative estimate 60 UNCLASSIFIED ORNL-LR-DWG 64508 10° 5 - R - _ e ‘ 1 e STRAIN RATIO: #=—1 2 pr— L ; FREQUENCY : 2 cycles/hr - £ | £ =26.5x108 psi <. 10 £ T by = Y s N T O ‘ : e 2 ~—+~+_CONSERVATIVE ESTIMATE OF TOTAL STRAIN b, : RANGE PER CYCLE 10 s i g : g %z o i z H c 2 x PLASTIC STRAIN RANGE PER — 10 3 w w- — d 5 2 -4 . 10 5 ' 3 07 2 5 10 2 5 10 2 5 1000 2 5|032 5 10 2 5 1072 5 10 &, CYCLES TO FAILURE Fig. D.1l. Strain Fatigue Curves for INOR-8 at 1200°F. UNCLASSIFIED ORNL-LR-DWG 64509 G 10 T T T T e e ® Tl il + STRAIN RATIO: #=-1 -y - 2 - FREQUENCY: %3 cycles/min ———|_+ 1] £ £=25.5x105 ps; . i < o', b g et j = : ST f i L i d:fi Y o5 - T v L e 2 e o o e H © 2 _+~CONSERVATIVE ESTIMATE OF TOTAL STRAIN | 1+ & ' RANGE PER CYCLE “‘I‘J ‘ i 10 _ L 1 L.} 4 1l 260 YC BL e i Y c o (" 10.92 cot? \/4 Bc = —————F— C ., 4aaTb5 d4 + 4 e e 68 Constants in cylinder "B" temperature equation (n = l, ..., 5) Constants in cone temperature equation (n = 1, - 5) .., Wall thickness of cylinder Wall thickness of cone Thickness of cooling alr gap Displacement of cone perpendicular to surface Meridional displacement of cone 1 Displacement functions for cone (n =1, ..., 4) Radial displacement Displacement functions for cone (n =1, ..., 4) Slope functions for cylinder (n = 1, ..., 4) Slope functions for cone (n =1, ..., 4) Distance through pump tank wall Dimensionless coordinate of cone Dimensionless coordinate of cylinder Meridional position on cone from apex Coefficient of thermal expansion Characteristic length of cylindér Coordinate transformation parameter for cone Temperature Local temperature Subscrigts a b 69 One half of cone vertex angle Poisson's ratio Bending stress Membrane stress Principal meridional stresses inside and out- side Principal circumferential stresses inside and outside Stefan-Boltzman constant Cylinder "A" (internal volute support cylinder) Cylinder "B" (external volute support cylinder) Cone (substitute for pump tank spherical shell in thermal stress calculations) Meridional plane Circumferential plane 70 ACKINOWLEDGMENT'S The author wishes to acknowledge the work of J. M. Corum in the preparation of Appendix D, "Procedure Used to Evaluate the Effects of Cyclic Strains in the MSRE Pumps.' The Oracle Stress Analysis Program used to determine stresses produced by pressure and axial loads was prepared by M. E. LaVerne. The assistance of F. J. Witt in regard to the thermal stress calculations is also acknowledged. @OO.\'IO\W-I-\\,OI\JI—’ 25-39. 48. 49. 50. 51. 52. \ 31 W 100-101. 102. 103. 104, 105. 106-120. 71 Internal Distribution M. Adamson . E. Beall . Bender E. Bettis . 5. Bettis Blander . G. Bohlmann E. Bolt J. Borkowski F. Boudreau . A. Brandon B. Briggs Cantor . Cole Conlin Corbin Corum Cristy . Crowley DeVan Douglas . Dunwoody Engel Fraas . Gabbard Gallaher Greenstreet Grindell Guymon Harley Haubenreich Hise ' Hoffman Holz Kedl Lane . LaVerne Lundin Lyon ® * * o - ?U_ZZHWWMHFUFUEUPWBUOPV—!ZUQQQMfiLlFHUJWOE{OU)MZMOZU)Q ZHM?QWMQZMMQHWMWWM'J>iI€L‘“'fi>'SF3iJ> 54, 55. 56. 57. 58. 59. 60. 61. 62. 63. 64 . 65. 66. 67. 68. 69. 70, 71. 72. 73. T, 75. 76. e 78. 79. 80. gl. g82. 83. 84. 85. 86, 87-88. 89-90. 91-93. 94-98. 99. . G. MacPherson D, Manly . McDonald . McGlothlan . Miller Moyers . Northup . Parsly atriarca Payne Perry . Robertson Rosenthal . W. Savage . W. Savolainen Schneilder Scott J. Skinner N. Smith G. Smith . Spiewak Squires J. Stanek A, Swartout . Taboada . Tallackson Trauger . Ulrich Weinberg Westsik . Witt Wilson . Young Reactor Division Library Central Research Library Document Reference Section Laboratory Records Department Laboratory Records, ORNL-RC -~ o T QRId-HEBEQOQ p*?1}u>:2§jE:F1m1$=m:z e O Hag Qs = < g@nEQuw * = @] External Distribution Reactor Division, AEC, ORO Division of Research and Development, AEC, ORO F. P. Self, AEC, CRO W. L. Smalley, AEC, ORO J. Wett, AEC, Washington Division of Technical Information Extension