f},‘ "|‘§ w} o T ORNL-TM-31L45 Contract No. W-TUOS5-eng-26 Instrumentation and Controls Division THERMAL RADIATION TRANSFER OF AFTERHEAT IN MSER HEAT EXCHANGERS J. R. Tallackson LEGAL NOTICE— - _This . report was ~prepared as an account of work | | sponsored by the United States Government, Neither | the United States nor the United States Atomic Energy | Commission, nor any of their employees, nor any of - their contractors, subcontractors, or - their employees, i | ‘makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, com- pleteness or usefulness of any information, apparatus, product or process disclosed, or represents that its use - would not infringe privately owned rights, MARCH 1971 OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee | - operated by UNION CARBIDE CORPORATION - for the | U.S. ATOMIC ENERGY COMMISSION 1 PISTRIBUTION OF THIS DOCUMENT IS ...,\m. H_ \ (r P t 4y ‘w; 2 v "’ f;‘" i. (‘ by 111 CONTENTS Page Abstract —-cceccmm e ea 1 I. INLTOAUCHLON == emmeccmmc oo oo cmmSommm e mcccmmcmmmcmmmmmm D ITI. Conclusions and Recommendations =--eeweeecccccccccccccccaa- ———— 2 III. MSER Heat Exchanger Configuration eee---ece-ccccccccccaaaaa-. -- 3 IV. Afterheat Genefation and Distribution -—---ec-eccccmmmccmaccoo 6 V. Metallurgical Conéiderations ------------------------ ————————— 11 VI. Results —--recmcommmenccccnnan.. mmememmm e ae 14 Appendix A. Computational Model and Assumptions | | Governing the Computations -—ceececccmmcmmmmcccccmceee o 43 Appendix B. Directional Distribution of Radiation -~--eeccocmcacmoao. L5 Appendix C. View Factors --eweec-ecccceccaaa- me—m———- cemmmemcece————- Lo Appendix D. Shell Temperatfires'----_------_--;-- .................... 61 Appendix E. The Eeat Transfer — Temperature Equations ----; -------- 63 Appendix F. Computational ProCeduUre =--eemmmmmm-rmm-esmmme—e—---.-— 69 Appendix G. Thermal Radiation Characteristics of Hastelloy N ececcmemecmmcmcmcccmcccccccccmncc e e T1 Appendix H. Comparison - Experiments and‘Analyses ................. 75 Appendix I. Method Used to Estimate the Initial | | | Peak Temperature Transient in the ' : 563-Mw .Reference Design Heat Exchanger ~----emec-ceaa-- 93 *References ----;-----+---Q---;--;-- ...................... e —————— 103 = U s W o ffl x ,‘\..sv . 5 J lw: w) e). 1,.‘ ¥ U u;‘ 1[7 J THERMAL RADIATION TRANSFER OF AFTERHEAT IN MSER HEAT EXCHANGERS - J. R. Tallackson ~ ABSTRACT A fraction, estimated to be 40%, of the heat-producing noble-metal fission products--niobium, molybdenum, technetium, ruthenium, rhenium, and tellurium--is expected to deposit on the metal surfaces within the primery fuel-salt loop in a molten-salt reactor. Virtually all of this 40% will be in the heat exchangers. The normal means of afterheat re- moval is to continue to circulate the primary and secondary salts. The worst abnormal situation arises if the heat exchangers are quickly drained of both primary and secondary salts in circumstances such that all afterheat removal from the heat exchangers is, of necessity, by radiative heat transfer. Whereas such an event will rarely, if ever, take place, the primary system must accommodate the consequences, prin- cipally high temperatures, without compromising containment. Steady-state temperature calculations, based on radiative heat transfer in MSER primary heat exchangers, are presented. Several sizes with ratings from 94 Mw to 563 Mw and all with the same general configu- ration were considered. Radial tempersature profiles were computed for afterheat rates corresponding to elapsed times from 100 sec to 11 days after reactor shutdown. The effect of the emissivity of the internal radiating surfaces in the heat exchangers was included. The calculations show that the principal single barrier to heat removal is the inter- mediate shell surrounding the tube bundle. This shell is located just inside the outer shell and, unfortunately, becomes an effective thermal radisation shield. - It is shown that heat exchangers with but one shell. 1nstead of two as in the MSER reference design will achieve significant reductions in ‘peak temperatures, particularly in the larger sizes and at low emissivi- ties._ No transient case was computed but the upper 1imit of the initial - transient was estimated; the heat capacity of the exchangers affords a cushion which, with the exception of the 563-Mw unit, limits meximum temperatures to numbers that are high but not disastrous. Design changes to increase radiating surface areas and to shorten the radial transfer distance through the tube bundle should render the 563-Mw exchanger acceptable. | Keywords: thermal'radiatiCn; noble metals, heat exchangers, emergency cooling, deposition, afterheat. I. INTRODUCTION The afterheat problem in molten-salt reactors caused by the noble metals which plate out on metal surfaces during reactor operation has not gone away. Reliable, consistent data are scant, but, from MSRE dats, Briggs' has estimated that 40% of the noble-metal fission products might plate out on the metal surfaces in the primary salt circuit. These pro- duce substantial amounts of afterheat and virtually all of it will be developed in the heat exchangers. - Normally, afterheat in an MSER is easily removed by continuing the circulation of the primary.and secondary salts. The situation, albeit unlikely, may arise in which both primary and secondary salts are rapidly drained immediately after reactor shutdown. 1In these circumstances, afterheat removal is, of necessity, solely by radiative transfer and the maximum temperatures so developed are of considerable interest. In September 1967 the author® presented calculated estimates of temperatures produced by afterheat from noble metals plated on the sur- faces in an empty primary heat exchanger of & two-region MSER. It was assumed that all afterhesat rejection was by radiative transfer. These temperatures were distressingly high, due, in large measure, to the overly simplified computational model employed (see Appendix H). I am pleased, without benefit of rack and thumbscrew, to recant. More real- istic calculations based on the single-region "reference design"® MSER heat exchangers indicate that peak afterheat temperatures, while still uncomfortably high, will be much lower than originally anticipated. II. CONCLUSIONS AND RECOMMENDATIONS MSER "reference design" type heat exchangers can be designed to withstand the after-shutdown temperature rise produced by noble-metal ~ afterheat. This worst-case study indicates that the two larger sizes considered, 563 Mw and 281 Mw, may experience excessively high tempera- tures, but the excess is small. If the overall diameters of these ex- changers are increased, the peak temperatures can be limited to accept- able values without undue penalties in cost. The improvement obtained is twofold: (1) The reduction in annulus thickness decreases the radi- ation path through the tube annulus, and (2) the radiating areas of the outer and intermediate shells are increased. The additional intermediate shell between the tubes and the outside shell is an effective barrier to radiative transfer. This shell is required if the tube bundle is to be replaced in situ. Significant reductions in peak temperatures will be obtained if this shell is elimi- nated. Alternatively, if the effective emissivity of the surfaces of the intermediate shell and the outer shell can be made very high (5 0.8) so as to be nearly black, the peak temperatures will be appreciably lower. .y Ty "f } 0 N ) «) ‘[T h;‘Likr Calculated estimates of radiant heat transmission and resulting ~ temperatures may be extremely sensitive to the assumptions, approximations, and uncertainties on which the calculations are based. For example, earlier calculations on a not too dissimilar heat exchanger, using an oversimplified model, ¥ produced discouragingly high temperature forecasts; the temperatures estimated by these earlier computations were as much as 2500°F higher than the temperatures reported herein. The present compu- tational model is widely accepted and used. It contains no gross com- promises with respect to heat exchanger geometry. It does require that photons be emitted, reflected, and absorbed in a simple pattern, and that their behavior be unaffected by temperature. A casual literature search indicates that the errors produced by these simplifications may be relatively small and probably on the high side, but confirmation would be highly desirable. The variation of maximum temperature with emissivity is substantial. Generally, I conclude that these calculated temperatures may err on the high side but hesitate to enumerate the amount. It will not be worthwhile to use or develop more accurate and elegant computational approaches until reliable experimental evidence, aspplicable to this par- ticular type of problem, has been produced. Without the support of the experimental confirmation we can expect to produce a conservative and perhaps expensive design. If radiant heat transmission remains a domi- nant consideration, I recdmmend an experimental program to support and confirm the analyses. Such experiments are not uncomplicated; they must be carefully designed and well planned. III. MSER HEAT EXCHANGER CONFIGURATION Figure 1 is a vertical section through the "reference design"® MSER primary heat exchanger rated at 563 Mw. Four of these will be re- quired for a 2250-Mw(th) MSBR. This exchanger type was scaled down by rating factors of 1/2, 1/3, 1/k, and 1/6, thereby giving heat exchangers rated at 281, 188, 141, and 94 Mw. The dimensions and details pertinent to these heat transfer computations are on Fig. 2. It should be noted that the scaled-down dimensions of the four smaller exchangers do not follow any precise scaling{laW(s) based on stress or flow. For example, it is more realistic to choose nominal pipe sizes and plate thicknesses for the inner and intermediate shells instead of the non-standard diam- eters and thicknesses that would result from any exact scaling down. Also, it would be unwise to use thicknesses less than 1/2 in. for the outer shells. Therefore, the outer shells are-l/e,in. in all the ex- changers. '- S ' o ' A second set of calculations was made'for 563-Mw"exchangers having . larger outside diameters, thinner annuli, and therefore fewer tube circles than the "reference design." These exchangers are scaled-up versions of the 563-Mw unit which has 31 tube circles in the tube annulus. These calculations are discussed in Section VI. o ¥Each tube circle was presumed to be a continuous impenetrable-shell (see ref. 2). ORNL DWG. 69-6004R SEAL.WELD n B _’\/—fi ) \ e oD . SECONDARY = =i SALT S =11 = =i > | t | £ " . # I. . ‘ ) —Hl seconpury s 5 (— ) Aversge Tube / Iength: ~22 ft I ) / ( _F - — Tube Annulus: —i Contains 5549 Tubes, 3/8 0. Diam, in 31 ( S ) Concentric Circles. Radial Pitch = 0.T1T7 in. Circumferential —) (— Pitch = 0.750 in. / fl——\*_ “— g=v|f~=h “§h“~\““-20 in. sched 40 Pipe AT oot s | LT 1 b PRIMARY SALT 36 in. diam Fig. 1. MSER 563-Mw "Reference Design" Primary Heat Exchanger. b b e wiy ORNL DWG. T1-567 Material; Tubes and Shells: Hastelloy N: Density 0.320 1b/in.> Melting point 2470 - 2755 °F Thermal conductivity, 12.7 Btu/hr at 1300°F ' reEoF et cific heat 0.138 _Btu Spectfl To-°F Heat Exchanger Tubes _ External surface area = 0,0987 rt%/rt . Metal mrea, sectionsl = 0.0373 in.2 = 2.59 x 1074 rt# Weight = 0,143 16/t _ Effective tube length = 22 ft, all exchsngers Tube Geometry Circumferentisl pitch -« 0.750 in. Radial pitch -= 0.7T1T7 in. The fraction of cross sectional area occupied by tubes is seme as for triangularly pitched tubes having P/D = 2.1. HEAT EXCHARGER DIMENSIONS Tube Annulus Rating ' Intermediate Outer : Tube Totel {Mw) Inner Shell , Shell - Shell Dimensions Circles Tubes % g emetto Rerlomm fasisoty Roolgis. : 1 = 8.3 n. = 1, . “Ay = O, = . n. : Ay = 2.26 T18/1t :10 = '{g:;, 2’/1;: Ay e 8.36 rt¥/rt R = T.09 in, W 10, schealo Ry - 17.58 in, §3 - 19,38 1fi./ R, = ig;m in, 15 1% R; = 5.38 in, t = 1,38 in, = 10,13 fee/rt = 6.10 1n. Ay = 2,81 reB/rt Ay = 9.16 r18/es Ai = 10,39 fté/ft k = 10.0% in. Ay = 9.88 Tt8/y : 18 12 1n§, fie::a 40 Re = 19:50 in _— R = 2250 ::;/fi - 13.;58 1. 17 1853 = D, . = . n. o .- . - - Ne. A: = 3.34 Ft2frt A = 10.20 ft2/rt Af, = 11.51 ftR/re = 11.47 in, Ao = 1L.00 £E¥fre T 281 1 in., sched 40 - Rp = 23,00 i‘n; 7 Rs = 25,25 1in. = 22,59 22 2794 | Ry = 7.00 in. -t = 1.75 in. - Ay = 13,20 rt8/rt = T.53 Ay = 3.67 £t2/ry Ay = 12,02 £t2/ft A = 13.16 fre2/rt = 15,06 A 2 ° , = 12.9% reefrt 563 20 in., sched k0 Rg = 32.75 in. Rs = 35.75 in. = 32,12 31 5549 R1 = 10.00 in. t = 250 in. Ay = 18.80 12/t = 10.62 Ay = 5.2 re2/rt A, = 17.13 rta/ft Ay = 19.06 rie/ft = 21.50 A =18.15 1t /£t Fig. 2, Diagram, With Dimensions, of Transverse Cross Sections Through MSER Heat Exchangers IV. AFTERHEAT GENERATION AND DISTRIBUTION The smount of afterheat in the heat exchanger is based on Briggs' estimate! that 40% of the noble-metal fission products plate out on the metal surfaces exposed to the primary salt. The inside surfaces of the heat exchanger tubes provide 39,000 ft® of surface in a 2250-Mw(th) MSER system. This is a very large area compared with the shell and pipe surface areas in the primary salt circuit. It can be assumed, with negligible error, that the entire 40% is deposited on the inner surfaces of the exchanger tubes. The heat-producing noble metals are niobium, molybdenum, technetium, ruthenium, rhodium, and tellurium. The heat produced by the jodine deughters of tellurium is included. The heating by those noble metals produced in the drain tanks by the decay of non-noble parent nuclides is not included. Figure 3 shows the afterheat rate in the 563-Mw unit per foot of length of heat exchanger, .and Fig. 4 shows the rate per square foot of outside tube surface¥* in any MSBR exchanger of this type. The accumu- lated afterheat curve on Fig. 5 is the integral curve of Fig. 3. Table 1 gives numerical values of these data. | Heat exchanger temperatures were computed for two different distri- butions of heat generation in the exchangers. The simplest case, Type 1, is that in which all heat generation is assumed to be confined to the tubes and uniformly distributed. This, in effect, says that gamms radi- ation does not generate heat in adjacent shells nor is the total heat generation in the exchanger(s) reduced by gammas escaping to the outside world. The second case, Type 2 distribution, considers the effect of gamma radiation on the location of internal heat generation. Careful calcu- lations*’® of gamms heat generation in heat exchangers of this general design are available and from these the total heat generation rate was subdivided into four parts:¥¥ . the fraction in the inner shell, the fraction in the tube annulus (includes all B~ heating). the fraction in the intermediate and outer shells, the fraction escaping the exchanger. =W o~ *¥Since the outside of the heat exchanger tubes provides 0.098 ft2 per foot of length, the heat rate per foot of tube length is obtained, very closely, by dividing the data on Fig. 4 by 10. **These data were developed from ref. .1, Table 5.6, p. 63, and ref. 5, Fig. 4, p. 10. LY 1] im L.y "l Btu/hr £t of hel 2 W ) Heat Generation Rate in a 563-Mw Heat Exchanger - 100 w ORNL DWG. 71-5_58 2.78hr 27.8hr 11.64 1164 108 10 s 10° 2 104 a 10 3 10° a3 107 n 3 Q 10 2 102 ® 100 100 % 108 * 108 ® 107 - Elepsed Time After Shutdown - Seconds Afterheat Generestion Rate Per Foot of Height in a 563-Mw MSER ‘Heat Exchanger, Afterheat ie that produced by 40% of the total noble metal fission products (including iodine daughters of tellurium) which are assumed to plete out on metal surfaces. Refer to MSR-68-99 Rev., Fig. 9, Heat Generation Rate - Btu/hr ££2 of tube surface ORNL DWG. T1-569 2,78hr 27.8hr 11.6d 116d ] = o 1 3 3 3 3 10 10° 10° 104 108 10° Elepsed Time After Shutdown - Seconds 107 Fig. k. Afterheat Generation Rate Based on the Outside Surface Area (radieting surfaces) of MSER Heat Exchanger Tubes. Afterheat i that produced by 40% of all noble fission producte plus the iodine daughters.of tellurium (see MSR-68-99 Rev., Fig. 9). EHeat exchanger configuration per Fig. 1. LAY iy ‘) (‘\ by SNy wly r'j) " Btu ft of height Accumnlated Afterheat in a 563-Mw Hest Exchanger - ORNL DWG. T1-570 _ 2.75hr 27,6hr 11.63 _116d 3 10° 8 108 3 10t 3 105 8 108 8 107 o lo® 10t 10° ' ' Y108 10t 108 * 108 * 107 psed Time After Shutd = Seconds 10 10° Fig. 5. Accumilated Afterheat in a Perfectly Tnsuleted 563-My MSER Heat Exchenger per Foot of Heat Exchanger Length, - Afterheat - is that produced by LO% of all the noble metal fission pro- duets which are assumed to plate out on the heat exchanger tubes. Refer to MSR-68-99 Rev,, Fig. 10. Heat exchanger configuration per ORNL DWG 69-600L. Table 1. Total® Afterheat Generation by Noble Metals Plated on Tube Surfaces in MSBR Heat Exchangers Heat Generation Rates Elapsed Accumulated (Integrated) Time Per Foot of Height Per Square Foot of Per Foot of Length®? Heat Per Foot of Height After in MSBR 563-Mw Heat Outside Surface of of 3/8-in.-0D Heat in MSBR 563-Mw Heat ~ Reactor Exchanger Heat Exchanger Tubes Exchanger Tubes Exchanger Shutdown Btu[hr kw: tu[hr ' tuZhr tu hr (sec) £t ) (I"E) (Bfta) Q—;i;) (Bft ) Cf%:"') %3 @t) 0 2.52¢10% T7.39x10* L4.60%10% 1.35x10-1 4,52x10 1.33x10"2 0O 0 102 2.32x10% 6.82x10' L4.27x10° 1.25%10°* L.20x10! 1.23x10°2 7.00%10® 2.05 3102 1.94x108 5.69%x10* 3.55x102 1.04x10~} 3.48x10* 1.02x10°2 1.94x10* 5.68 102 =16.Tm 1.74x10% 5.12x10%* 3.20%10%2 9.38x10°2 3,12x10} 9.21x10"% 5.63x10% 1.65x10% 3x103 = 0.83 hr 1,24x10% 3.64x10% 2.27x10® 6.67x10°2 2.23x10' 6.55%107% 1,36%10® 3.98x10% 104 =278 hr T.36x10* 2.16x10* 1,35x107 3.96x10°? 1.33x10' 3.88x10"® 3.18x10% 9.32x10? 3x10% = 8.33 hr 5.63x104'1.65x101 1.03x10® 3.02x10°2? 1.01x10' 2.97x10°% 7.16x10% 2.10x10° 105 = 27.8 hr L.26x10* 1.25%10° 7.81x10! 2.29x107% 7.67 2.25%x107%® 1.59x10° 4.66x10% 3x10% = 3.7 a4 2.71x10* T.95 4,98%10 1.46¥1072 L.90 1.43x10°° 3.48x10° 1.02x10% 102 =11.64 1.24x10* 3.64 2.27x10* 6.67x107% 2,23 6.55x107% T.37x10® 2.16%10° 3¢10% = 34,74 6.58x10° 1.93 1.21x10* 3.54x10°% 1.19 3.48x10°%* 1.36x107 3.98x10° 107 =3.80mo 1.67x10° L.89x10°* 3.05 8.95x10~* 3.00x10°! 8.78x10"® 1.94x10” 5.68x10° 3x107 = 0.95 y 3.30x10% 9.66x10 2 6.05x107% 1.77x10°* 5.94x1072 1.74x10™% 2.36x107 6.93x10° 10° =3.1Ty 6.58x101 1.93x10=® 1.21x10-* 3.54x10°% 1.19x10°° 3.48x107% 2.64x107 7T.73%00° ®These rates and accumulated heat values include all gamma, energy and represent the afterheat pro- Heat generation by the iodine duction by 40% of the noble metal fission products at saturation levels. daughters born after shutdown from the tellurium is included. b Nominal height (length) of MSBR heat exchangers is 22 ft. o1 )} » l') ¢) 11 Figure 6 is a typical profile of the gamma heat deposition rate in an empty 563-Mw heat exchanger. Figure 7 shows curves of the fractions, (1) to (4) above, for the exchangers in the size range considered.¥ These distribution fractions do not show any large variations with elapsed time, particularly at the times of interest, from 10® to 10° sec (0.3 to 30 hours) after shutdown. These curves are based on averages of 10%- and 10*-sec data. Figure 6 shows that, of the two outermost shells, the thicker inter- mediate shell is the much larger heat source; also, note that gamma heat generation in these shells is attenuated very rapidly in the radial di- rection. For these reasons, with Type 2 distribution, all the gamma heat deposition in both outer shells was considered to be near thée inside sur- face of the intermediate shell. V. METALLURGICAL CONSIDERATIONS The primary concern of this study is to determine whether or not excessive heat exchanger temperatures will jeopardize the integrity of the Hastelloy N primary containment envelope. Because the event postu- lated seldom, if ever, would occur and because the resultant high tem- peratures would be of short duration, we are not concerned with the long-term creep-rupture behavior. We are concerned with the short-term physical properties of Hastelloy N at temperatures around 2000°F (~1100°C) and assuming that these temperatures are maintained for no more than 20 hours. Hastelloy N pressure vessels, piping, etc., are not expected to sustain serious damasge if held at low stress for short times (< 20 hr) at temperatures of 2150°F (1177°C).® A vessel subject to any substantial fluence will lose ductility. Ultimate strength at this temperature will be very low.” If a component is to survive at this temperature, we must ensure that the high temperature regions be virtually free of stress- producing imposed loads. It is appropriate to point out that it is rou- tine fabrication practice to specify a stress-relieving anneal at 2150 °F for welded Hastelloy N.pressure vessels. The foregoing suggests that ve evaluate preliminary designs using '2100°F as an upper temperature - limit for the unlikely events being considered here. ' This assumes that " the calculated or estimated temperatures tend to be on the high side and leaves a small margin for thermal stresses and other uncertainties " ~which will be evaluated with some care during gestation of & final design.. *These data were developed from ref. l, Table 5.6, p. 63 and ref. 5, Fig. 4, p. 10. HEAT DEPOSITION RATE {Btu/tt3-hr) Fig. 6. 12 ORNL-DWG 69-12604 INTERMEDIATE SHELL TUBE ANNULUS INNER SHELL TUBE DIAMETER: 0.375 in. WALL THICKNESS: 0.035 in. TOTAL NUMBER OF TUBES: 5910 OUTER SHELL 104 : ] ] ! 5 I’ / 2 103 ” e £ \ N\ . 5 2 10° 0 6 12 18 24 30 36 42 RADIUS (in.) Distribution of Gemms Heet Generation Produced by Tellurium* Fission Products in a 563-Mw MSER Heat Exchanger. Forty percent of all the tellurium is assumed to deposit uniformly on the inside surfaces of the tubes. ) *The energy spectrum of tellurium gammas is considered to be typical of the gammas produced by the other noble metal fission products. M .“‘ (i1 iy il Fraction of Total Afterheat Generation ORNL DWG. T1-5T1 1.00 o.8 0.6 0.4 Intermediate and Outer Shell 0.2 ° o 100 200 300 400 500 600 \ ' MSBER Heat Exchanger Rating - Mw Fig. 7. Type 1 Distributions of Noble Metel Afterheat in MSBR Heat Exchangers. €T 14 VI. RESULTS Figures 8 to 11 (incl.) are steady-state radial temperature pro- files in four sizes, from 94 to 281 Mw, of MSBR-type heat exchangers having the dimensions shown on Fig. 2. The heat generation rate is that predicted at 10* sec (2.8 hr) after shutdown and drain. These curves are based on the assumption of Type 1 distribution (see Section IV); i.e., all afterheat generation is uniformly distributed in the heat ex- changer tubes and no gamma energy escapes. It was also assumed that the emissivity of the outside surface of the outer shell was 0.8 and that this surface was radiating into infinite "black" surroundings whose tem- perature is 1000°F. The emissivity¥of the internal radiating surfaces, tubes and shells, is one of the larger uncertainties in a calculation of this type. Both tubes and shells will meet stringent quality assurance standards and we should expect them to have an excellent surface finish, perhaps appearing almost polished. Furthermore, after exposure to molten fluoride salts these internal radiating surfaces will be oxide free. All the factors tending to promote bright, low emissivity surfaces in a material tending toward low emissivity are present. For these reasons, nearly all the calculations were made at internal surface emissivities of 0.1, 0.2, and 0.3. The general subject of emissivity¥ is discussed in more detail in Appendix G. The data in Appendix G suggest that we can expect the internal Hastelloy N surfaces to have an emissivity of 0.2 to 0.3 and that we select an emissivity of 0.2 in evaluating heat exchanger performance in the situstion considered herein. The high emissivity (0.8) of the outer surface of the outer shell is justified by assuming that it is coated with one of the titanates® or, alterna- tively, deeply convoluted by fins or a gridwork. : : It is emphasized that these temperature curves are for steady- state conditions and do not take into account the rapid decrease with time of the heat generation rate nor the temperature reducing effect of heat capacity of the exchanger. These temperature profiles are, perhaps, higher than would be obtained should the situation postulated actually occur. The upper limits of the initial temperature transient in the 563-Mw unit have been estimated and are discussed in subsequent paragraph(s). The estimate indicates the temperature will reach its maximum in about 10* sec after reactor shutdown and an immediate drain; therefore, most of the data herein were calculated as if at steady state with the afterheat rate expected at 10* sec after shutdown. As the calculations proceeded, starting with the smallest, 94 Mw, unit, some trends became evident; (1) the effect of heat capacity of the exchanger cannot be ignored, (2) the variation of maximum internal temperature with emissivity is less at higher emissivities, (3) gamma *As this report was going to press, the writer's attention was directed to ref. 27, in which emissivity measurements of INOR-8 (Hastel- loy N) are reported. Bright and matte finished specimens showed an emissivity of 0.20 at 1000°F to 0.25 at 1830°F." Oxidized specimens had emissivities of approximately O.4 to 0.6. A value of 0.2 for the emissivity of Hastelloy N is therefore appropriate. - » k) 3) C i) ) x) Temperature, °F 15 ORNL DWG. T0-8546 3000 ‘Intermediate Shell ‘Outer e 2500 2000 1500 1000 500 0 > 1o 1L 20 : ' - Radius - Inches . Fig. 8. Steady-State Tbmperature Profiles in an Empty 94-Mw Heat Exchanger at Three Values of Internal Surface Emissivity. . \ . Heat Production: 12 300 Btu/hr-ft height; uniformly distri-. buted 1n tube annulus. Equivelent to afterheat rate 10% sec after shutdown produced by Lo of the noble metal fission products plated on tube surfaces._ Heat Transfer: By radiation only. Outer surface emissivity=0.8. Environment: "Black"” surroundings at 1000°F, ORNL DWG. TO-8542 3000 Intermediate _Shell ’ Outer Shell 2500 2000 1500 Temperature, °F : 500 5 10 15 20 Radius - Inches Fig. 9. Steady-State Temperature Profiles in an Empty 141-Mw Heat Exchanger at Three Values of Internal Surface Emissivity. Heat Production: 18,400 Btu/hr-ft height; uniformly distributed in tube annulus. Equivalent to afterheat rate 104 sec after shutdown produced by 40% of the noble metal fission products plated on tube surfaces. Heat Transfer: By radiation only. Outer surface emissivity = 0.8. Environment: "Black" surroundings at 1000°F, 4 ORNL DWG. T0-85k41 3000 Intermediate Shell ter - ofe g Temperature, °F 3 500 0 -5 o o100 15 20 ' 25 ' o ' Radius - Inches s “Fig. 10. Steady-State Temperature Profiles in en Empty 188 Mw Heat - Exchanger at Three Values of Internal Surface Fmissivity. Heat_Prbduction: o, 500 Btu/hr-ft height; uniformly distrlbuted in tdbe annulus. Eguivelent to afterheat rate 10* sec after shutdown produced by 40% of the noble metal : f1531on products plated on tube surfaces. " Heat Transfer: By radiation only ‘Outer surface emissivity 0.8. Environment: "Black" surroundings at 1000°F. 18 ORNL DWG. T1-572 3000 iate Outer Shell She 2500 Temperature, °F 5 3 : 500 0 5 10 , 15 20 25 30 Radius - Inches Fig. 11. Steady-State Temperature Profiles in an Empty 281-Mv Heat Ex- changer at Three Values of Internsl Surface Emissivity. Heat Production: 36,800 Btu/hr-£t height; uniformly distributed in tube - annulus. Equivalent to afterheat rate 10* sec after shutdown produced by 40% of the noble metal fission products plated on tube surfaces. ' Heat Transfer: By radiation only. Outer surface emissivity = 0.8. Environment: "Black" surroundings at 1000°F. 1 n 19 energy losses to the outside are insufficient to contribute materially toward reducing pesk internal temperatures, and (4) the maximum tempera- tures in the 563-Mw "reference design" exchanger may become unacceptably high. Finally, it developed that the time-sharing computational program used to obtain temperatures in the tube annulus (Appendix E) would not run if the number of tube circles in an exchanger exceeded 22, whereas the 563-Mw exchanger contains 31. There was not sufficient incentive to spend time in rewriting the program for a larger machine. Instead, it was decided to produce additional computations to indicate the changes in the 563-Mw "reference design" which will reduce the maximum internal temperature to acceptable values. Therefore, scaled-up versions of the 563-Mw "reference design" unit with larger outside diasmeters and a re- duced number of tube circles were programmed and the peak temperatures in the "reference design" were obtained by extrapolation. The effect of emissivity, number of outer shells, heat capacity, overall size and rating are considered in the paragraphs which follow. Temperatures in 563-Mw heat exchangers having larger outside diam- eters and thinner tube annuli than in the "reference design” (Fig. 1) model were computed. These computations served two purposes: (1) They indicated the minimum outside diameter of an exchanger which will limit the maximum temperature to the 1900°F—2100°F region, and (2) they pro- duced the basis for a good estimate, by extrapolation, of the peak tem- peratures in the 563-Mw "reference design" shown on Fig. 1. The dimen- sions of these exchangers and the computed temperatures therein are in Table 2 and on Figs. 12 and 13. The extrapolated temperature profiles, Fig. 1L, assigned to the 563-Mw "reference design" model which has 31 tube circles, are pre- sented with considerable confidence because the extrapolations involved only the temperature differentials in the tube annulus and thls repre- sents only about 25% of the total temperature above the 1000°F ambient. The remaining 75%, the temperatures of the outer and intermediate shells, has been computed accurately. It can be seen that if the outside diameter of the reference design heat exchanger is increased from 36 in. to approximately 50 in. so that "the tubes are arrayed in 17 to 20 tube circles, the peak steady-state internal temperstures will be in the acceptable 2000°F—2100°F region at 10* sec after shutdown when the internal surface emissivity is about 0.2. - A further lIncrease in diameter may be necessary if: (1) the internal surface emissivity turns out to be much less than 0.2; {(2) the "reference ~ design" model, with two outer shells, continues to be the required de- sign; and (3) if we use the steady-state temperature calculations at "flO* sec to guilde the design. It will be shown that eliminating one of ' the shells outside the tube annulus effects a very substantiasl reduction in peak internal temperatures should the internal surface emissivity be low (0.1). , Table 2. Temperatures Developed by Radiative Transfer of Noble Metal Afterheat in MSBR Heat Exchangers Rated at 563 Mw and Having Tube Annuli of Different Thicknesses Fo. Tube Ry R, Eniesivity Tewperatures, °F ((!1rc1es R R Rb’ of . . . o Total t Internal T 1 T Ts Tubes) in, ° AR::? Surfaces mex ° ann ? shells 17 2 50,50 44.65 0.1 Lol 2087 317 2019 1149 870 1140 (5542) 46 33.18 0.2 2059 1759 300 1691 1149 542 1140 3.50 11.47 0.3 1903 1607 296 1539 1149 390 1140 20 - 25 45,00 39.87 0.1 2495 2150 345 2084 1165 819 1155 (5540) 41 26.25 0.2 21hl 1807 337 172 1165 577 1155 3.00 13.62 0.3 1987 1648 339 1583 1165 418 1155 22 21.5 43.00 37.62 0.1 2541 2179 362 2111 1172 939 1161 (55u44) 39 22,56 0.2 2191 1831 360 1763 1172 59 1161 3.00 15.06 0.3 2035 1668 367 1600 1172 428 1161 24 18 40.75 35.80 0.1 2578 2208 370* 2142 1180 962 1169 (5544 37 19.38 0.2 220k» 1854 370* 1788 1180 608 1169 - 2,75 16.k2 0.3 205T* 1687 370% 1621 1180 L 1169 26 15 39.75 | 34,40 0.1 2619% 2229 390% 2155 1184 971 - 1172 (5538) 36 16.47 0.2 2262% 1872 300% 1798 1184 614 1172 2.75 17.93 0.3 209hL» 1704 390% 1650 1184 46 1172 31 10 36.00 32.12 0.1 2705% 2280 L2s* 2212 1198 101h 1186 (5549) 32.75 10,62 0.2 2336% 1911 L425% 1843 1198 6ks 1186 2.50 21,50 0.3 2162+ 1737 Los* 1669 1198 W1 1186 (1) Temperatures were calculated for steady-state heat rate of T7.36 x 10%* Btu/hr per ft height of heat exchanger uniformly distributed (Type 1) on the inside of the heat exchanger tubes. This 1s equivalent to 135 Btu/hr = 13.3 _BWL and 1s the heat rate expected st £42 tube surface £t length of tube 10* gec (2.8 hr) after shutdown. (2) Heat exchangers in "black, infinite” surroundings at 1000°F. (3) Fmissivity of outer surface of outer shell = 0.8. #Thege temperatures obtained by extfapolation. Oc 21 ORNL DWG. T1-5T73 , Reference Design € 15 _ 20 25 30 b Temperatures of Inner Surface of Intermediste Shell Temperature, °F _ Average* Temperature T _ ' Drop Across Tube 0 5 10 15 ° 20 35 30 : - Number of Tube Circles - Pig. 12. Internal Steady-State Temperatures in MSBR Heat Exchangers Rated at 563 Mw With Tube Annuli of Different Thicknesses and With the Emissivity, ¢, of All Internal Surfaces a Parameter. Heat exchanger con- figurations generally similar to Fig. 1. : . Heat Generation: T.36 x 10‘ Btu/hr-ft height; ell uniformly distributed (Type 1) in the tyube annulus and equivalent to the . afterheat rate 10* gec after shutdowvn produced by Lo of the noble metal fission products plated on the tube surfaces, Beat Transfer: _By redietion only, Envirorment: ~ "Black, infinite" surroundings st 1000°F | : (a) Emissiv:lty of outer surface of outer shell = 0. 8 - ' %For internal emissivities from 0.1 to 0.3 the variation, with emissivity, of the temperature rise in the tube annulus is negligible. Averaged values are 9 used. Peak Temperature, °F 22 "ORNL DWG. T1-5Th Reference _ ~ Design, Fig. 1 15 20 25 30 ‘Peak Temperatures (at innermost tube circle - 5 10 15 20 25 Number of Tube Circles Fig. 13. Peak Steady-State Temperatures Developed in MSER Heat Ex- changers Rated at 563 Mw With Tube Annuli of Different Thicknesses and with Eanissivity, €, of All Internal Surfaces a Parameter, Heat exchanger configurations generally similar to Fig. 1. Heat Gemeration: 7.36 x 10* Btu/hr-ft height; ell uniformly distributed (Type 1) in the tube snnulus and equivalent to the afterheat rate 10* sec after shutdown produced by Lo% of the noble metal fiesion producte plated on the tube suri_’aces. Heat Transfer: By rasdiation only. Environment: "Black, infinite" surroundinge at 1000°F ' (e) Emissivity of outer surface of outer shell = 0.8, 30 35 ORNL DWG. T1-575 3000 2500 - 2500 2000 2000 Ig,“‘l. "-’“.;3' - a o 3 1500 1500 £ _ HH Q) g Q e 1000 ° 1000 - 500 500 0 - 5 10 15 20 25 30 35 ko Radius - Inches Fig. 14 Steady-State Temperature Profiles in an Empty 563-Mw Heat Exchanger at Three Values of Internal Surface Fmissivity, Heat Production: 73,600 Btu/hr-ft height; uniformly distributed in tube annulus. Equivalent to afterheat rate 10* sec after shutdown produced by 40% of the noble metal fission products plated on tube surfaces. Heat Transfer: By radiation only. Outer surface emissivity = 0.8, FEnvironment: "Black" surroundings at 1000°F. £c 24 The estimated temperature transient in the 563-Mw exchanger is shown on Fig. 15. The estimate shows that the peak temperature, 2150°F, devel- oped in this exchanger borders on acceptablility if we can rely on an in- ternal surface emissivity of 0.2 or better.¥ The simplifying assumptions and approximations used in calculating this transient were made so that the results would tend toward the high side. A brief description of the method used to develop this transient is in Appendix H. Figure 16 shows the author's version of a similar transient in the 141-Mw unit. This curve was estimated by inspection using Fig. 15 as a guide. The transient peak, slightly above 1800°F, was located slightly below the intersection of the adiabatic temperature growth curve of the annulus and the steady-state peak temperature curve. This smaller unit can be expected to perform well in the stated situation. Figures 17 and 18 are temperature profiles in the 9&- and 281 Mw units at 10% sec after shutdown and for the nonuniform, Type 2, heat distribution, Fig. 7. All other conditions are the same as for Figs. 8 and 11, with which they may be compared to note the effect of making cal- culations using the simplifying Type 1 approximation. Table 3 provides a comparison of peak temperatures if calculated for both types of heat distribution at steady-state heat rates corresponding to those expected at 10* sec (2.8 hr) after shutdown. Noting that the more reallstic assumption, Type 2, gives lower tem- peratures, it 1s proper to query, "Why not use the nonuniform case entirely?"” The question is particularly appropriate because once the equations are programmed, there is little difference in the ease of obtaining numbers. The more exact nonuniform case, Type 2, requires a prior and not uncomplicated nor inexpensive computation of gemma heating.® During the early phase of a design study it will not be worthwhile to spend much time in this effort until a detailed design has been confi- dently established. The simple, uniform case, Type 1, requiring only a knowledge of heat exchanger geometry and afterheat genersation rate, is relatively easy to calculate and, as it seems to provide temperatures slightly on the high side, will tend to produce & conservative design. Figures 8 to 11 and Fig. 1k show inner shell temperatures slightly less than the temperature of the adjacent row of tubes. At first glance this seems contrary to all accepted laws governing heat transfer. 1In fact, and as will be seen, it is not true. However, if the assumption of zero heat generation in the inner shell were actually true we should expect this slight temperature depression at the inner shell. Because the tube matrix is quite open, the inner shell is in thermal equilibrium not only with the adjacent row of tubes but with the combination of several sets of tube circles at lower temperatures farther out in the tube annulus. On Figs. 17 and 18, in which the inner shells are generating 9% of the total afterheat, their temperature is the peak temperature as expected. *¥Refer to footnote on page 1k, -~ "l 25 ORNL DWG. T1-5T6 2.78h 27.8h 11.64 3000 2500 Fstimated Transient 2000 1500 Tempersture - °F Temperature 1000 3f Inf'j‘.nite Black® sur=- roundings, 1000°F 500 10° * 8 108 @ B 0% @ 8 10?2 3 5 10° ,Eflépsed Time After Shutdown - Seconds Fig. 15. Estimated Initial Temperature Transient Caused by Noble Metal Afterheat in an Bmpty 563-Mw MSER Heat Exchanger. - L - " Curve A: Pesk steady-state temperature computed for Type 1 afterheat rates at the indicated times (see Table 1) and with the emissivity of all internal surfaces = 0.2 and the emissivity of the outer gurface of the outer shell = 0.8, Curve B: ‘Temperature growth in the inner shell and the tube annulus computed as if , (1) the annulus and shell are perfectly insulated; (2) they have a total heat capacity of 129 Btu/°F-ft of height (based on Table 3); and (3) generate 77% of the total afterheat (see Table 1 and Fig. T). Curve C: Temperature growth in the intermediate shell computed as if: (1) the shell is perfectly insulated; (2) 1t has a heat capacity of 287 Btu/°F-ft of height, and (3) generates 23% of the total afterheat. 26 ORNL DWG. T1-57T7 2.76h | 27.8n - 11.64 Pransient: Temperature - °F Temperature of Infinite "Rlack" Sur- roundings 1000°F 1° 2 8 1 3 68 3¢ 8 & 308 3 5 308 Elapsed Time After Shutdown - Seconds Fig. 16. BEstimated Initial Tempersture Transient Caused by Noble Metal Afterheat in an Empty 1h41-Mw MSER Heat Exchanger. . Curve A: Peak steady-state temperature computed for Type 2 afterheat rates at the indicated times (see Table.l and Fig. 7) and with the emissivity of all internal surfaces = 0.2 and the emissivity of the outer surface of the outer shell = 0.8. Curve B: Temperature growth in the inner shell and the tube annulus computed as if: (1) the annu- lus and shell are perfectly insulated; (2) they have a total heat capacity of 32 Btu/°F-ft of heie);ht (based on Table 3); and (3) generate 70% of the total afterheat (see Table 1 and Fg. 7). . ‘ Curve C: Temperature growth in the intermediate shell computed as if: (1) the shell is perfectly insulated; (2) 1t has a heat capacity of 72 Btu/°F-ft of height, and (3) generates 23% of the total afterheat. 27 ORNL DWG. T1-5T78 3000 Intermediate Outer Shell Shell 2500 2000 Temperature - °F & 3 : 500 o > 10 © 15 20 , Radius - Inches - Fig. 17. Steady-State Temperature Profiles in an Empty 9h-Mw S MSER Heat Exchanger for Type 2 Heat Distribution Which Takes into Account the Effects of Gamma Energy losses and Distribution, Fig., 7. Upper (dashed) curve is profile for Type 1 distribution (see Fig. 11) end is shown for comparison. - _ Totel Heat Generation: 12 ,300 Btu/hr-ft height; equivalent to afterheat rate at 104 sec after shutdown. Heat Transfer: By radiation only. Outer surface emissivity = 0.8. Environment: "Black" surroundings at 1000°F, Temperature = °F & 8 28 " ORNL DWG. T1-579 Intermediate Shell 3000 2500 5 500 0 20 30 Radius ~ Inches Fig. 18, Steady-State Temperature Profiles in an Empty 281-Mw MSBR Heat Exchenger for Type 2 Heat Distribution Which Tekes Into Account the Effects of Gemms Energy Losses and Distribution, Fig. T. Upper (dashed) curve is profile for Type 1 distribution (see Fig. 11) and is shown for comparison. Total Heat Generation: 36,800 Btu/hr-ft height; equivalent to afterheat rate at 10* sec after shutdown. Heat Transfer: By radiation only. Outer surface emissivity = 0.8, Environment: "Black" surroundings at 1000°F. ‘Table 3. The Influence of Internal Afterheat Distribution and Heat Exchanger Size on Peak Steady-State Temperatures in Empty MSBR Heat Exchangers at the Heat Generation Rate® Expected 10* Sec (2.8 Hr) After Reactor ShutdownP 9h-Mw Heat Exchanger 141-Mw Heat Exchanger 188-Mw Heat Exchanger 281-Mw Heat Exchanger Assumptions ‘ ‘ - ‘ on Distribution = Internal Surface Internal Surface Internal Surface - Internal Surface of the ~ Emissivity® ~ Emissivity® | Emissivity® ~ Emissivity® Heat Generation . —s——————— u _ - — — . N . 61 02 03 01 02 03 01 0.2 03 0l 0.2 0.3 i ———— - | Peak Temperatures - °F Uniform, Type - RN — _ — . - ‘ 1 (100% con- 1995 1706 1577 2111 1810 1678 2231 1913 1771 - 2406 2075 1928 fined to the - = . , o ' | - | ) - tube annulus) Nonuniform, ‘ ' - . ' S . Type 2)(see 1908 1635 151k 2072 1776 1645 2183 1878 1733 2380 2050 1903 Fig. T - B - \ Difference, °F 87 7L 63 39 3% 33 18 35 38 26 25 25 13.3 Btu/(hr-ft length of tube), Heat generation rate | | - 135 Btu/(hr-ft® of outside tube surface). PHeat exchangers in infinite, "black" surroundings at 1000°F. _gEmissivity of outer surface of outer shell = 0.8. 62 30 A1l the preceding figures which show temperature profiles indicate one thing in common; namely, as in calorimeters and similar devices, the continuous intermediate shell, with low emissivity, is an efficient bar- rier to radiative heat transfer and is a large factor in producing higher internal temperatures. The reduction in pesk temperatures effected by eliminating one of these two shells was determined by calculations made for the same group of exchangers with the outer, 1/2 in.-thick shell re- moved. Table 4 provides a comparison of the pesk steady-state tempera- tures in exchangers of this type designed with one and two shells external to the tube bundle and at the heat rate expected at 10* sec after shut- down. Figure 19 shows curves of the data in Table 4 which have been extrapolated to include estimated pesk steady-state temperatures in the 563-Mw exchanger. Interest was expressed in the reduction of temperature attained by increasing the apparent emissivity of all surfaces of the outer and intermediate shells. A possible method would be to add fins or a gridwork so that these surfaces take the appearance of & continuous sheet of black body cavities. No effort was spent investigating the feasibility of this idea, but temperature profiles in a 281-Mw exchanger were calculated as if all the surfaces of the intermediate and outer shells, internal and external, had an emissivity of 0.8. A value of 0.2 for emissivity of the inner shell and tube surfaces was selected. No allowance was.made for the increases in shell diameters required. The results, calculated by using Type 1 heat generation at the rate expected at 10* sec after shutdown, are on Fig. 20. The temperature reductions so obtained are appreciable. ' Table 5 gives a comparison of maximum temperature in a 281-Mw - exchanger for four different cases described in the preceding paragraphs. The effect of internal emissivity on peak temperature is implicit in many of the preceding figures. Figure 21 shows, explicitly, the influence of emissivity on peak temperatures in the 94-Mw unit. It is apparent that we will get a worthwhile improvement in afterheat rejection by this heat exchanger if the emissivity of the Hastelloy N surfaces, after exposure to molten salts, is 0.3 rather than O.l. It is also apparent that. increasing the emissivity above 0.3 produces little additional benefit. - The transfer of radiant energy from surfaces far inside the exchanger will be strongly dependent on the combined effects, not separable, of internal geometry and emissivity. At low values of emissivity (high re- flectivity) a photon will have a higher probability of traveling farther from its point of origin via multiple reflections through the tube bundle before being absorbed. The surfaces will also be at a somewhat higher ' temperature if they are radiating at a rate which maintains temperatures constant at a constant afterheat generation rate. These are offsetting trends, but the fourth power effect of temperature on heat transfer sug- gests that higher emissivities may produce only fringe benefits in open tube lattices. The quantitive extemsion of data from Fig. 21 to other geometries is not recommended since this figure does not provide the interrelation between geometry and emissivity. ' 31 Table 4, Afterheat Temperature Reductions Attained by Removing the Outer Shell from Empty MSBR Type Heat Exchangers External surface emissivity = 0.8, Heat exchanger in infinite, "black" surroundings at 1000°F. m:d.mum Steady-State Temperatures Computed at Heat Generation : Rate® Equivalent to 40% of the Noble-Metal Afterheat 10* Sec Heat No, of Puissivity _ After Reactor Shutdown : Exchanger Tube of Internal Rating Circles Surfaces Reference Design Reference Design With (see Fig. 1) Outer Shell Omitted Difference 9 Mw 12 0.1 © 1995 1631 . 364 0.2 1706 : 1470 236 0.3 1577 1406 171 Wime 15 0.1 2111 1731 380 ' 0.2 1810 1566 _ 2k 0.3 1678 1501 177 188 Mw 17 0.1 2231 1822 . ho9 0.2 1913 1646 267 0.3 1771 1576 195 281 Mw 22 0.1 2ko6 1973 433 0.2 2075 1794 281 0.3 1928 1723 205 563 Mw 3 0.1 2t0s? 2365° | 34ad 0.2 2335: 21653 J"Qb 0.3 2162 2075 563 Mw 26 0.1 216 222 0.2 2262b g: 922 0.3 13k 563 Mw 2k 0.1 216 0.2 2221?; 1975°: ab 0.3 2057 1900 157 563 Mw 22 0.1 254) 2099 L2 0.2 2191 1920 271 0.3 2035 _ 1850 . 185 563 Mw 20 0.1 o 2hg5 - 2020 L75 R 0.2 - 23kh © 1Bz 1L 0.3 o987 1755 : 232 563 Mw - 17 0.1 a0k 193 468 0.2 2059 1747 ' ' 312 0.3 11903 _ 1672 o 231 At 10 sec heat generation rate = 13.3 —15[115 135 ——BEIL £t2 tube surface and is Type 1 generation. Indicates temperatureé obté:lned by éxfirapolation.. Peak Temperature - °F Fig. 19. 32 ORNL. DWG. 71580 One Shell 100 200 300 Loo 500 600 Heat Exchanger Rating - Mw | Moximum Internal Steady-Stete Temperatures in Single-Region MSER Heat Exchangers with One and Two Shells Outside the Tube Bundle. Elspsed Time After Shutdown --- 10* sec = 2.8 hr. . o Afterheat Rate ==« 13% Btu/hr-ft2 Tube Surface = 13.3 Foof t\l:;b = . Emissivity of Internal Surfacegs --- 0.1l to 0.3 as noted. Emissivity of Outer Surface --- 0.8, Surroundings --- Infinite, "black,” at 1000°F. 33 . ORNL DWG. T1-581 Intermediate Shell - Outer . 3000 2500 500 0 5. . 10 15 20 25 S - -Radius - Inches - : . Fig. 20. Temperature Profiles in a 281-Mw MSER Heat Exchanger Showing the Effect of Increasing the Emissivity of the Internsl Surfaces of the Outer and Intermediate Shells. "Heat Production: 36,800 Btu/hr-ft height, at lO‘sec after shutdown. Heat Transfer: By rsdiation only. - Environment: Infinite, "black" at 1000°F, o S S Cagce A Case B a) Emissivity of inner shell and tubes - 0. b) Emiesivity of intermediate shell surfaces : c¢) Emissivity of inner surface, outer shell (d) Fmissivity of outer surface, outer shell 000 @R 30 3k Table 5. The Effect of the Outer Shells on Maximum Steady-State Afterheat Temperatures in an Empty 281-Mw MSER Heat Exchanger A comparison of four cases at 10* sec. Reduction in Maximum Internsal. Steady- Maximum Tempera- State Temperature Calcu- Cases e ture Referred to lated for Heat Rate at ’ : "Reference - 10* Sec (2.8 Hr) After Design” Reactor Shutdown 1. "Reference design" per ' 2075°F Fig. 1. All intermal ' ' surfaces exposed to primary and secondary salts have an emissivity of 0.2. Type 1 heat distribution. 2. "Reference design," with 25°F 2050°F ' Type 2 heat distribution : which takes into account gamme, energy distribution. All other conditions as in in Case 1 (above). 3. "Reference design" with 281°F 1794°F outer shell removed. All other conditions as in Case 1 (above). i. "Reference design" in 381°F | 1694°F which emissivity of all surfaces of outer and intermediate shells is 0.8. Emissivity of tube and inner shell surfaces is 0.2. Type 1 heat distribution. ®Total afterheat load in exchanger (Type 1 distribution) = 8.1 x 10° Btu/hr at 10* sec after shutdown. Equivalent to: hr h (1) 3.68 x 104‘?%E%é5§53 5 (2) 135 _EWu/ - ; : ft® tube surface Btu/hr (3) 13.3 ¥t Tube Maximum Temperature - °F " Type 1 Heat Generation: . (a) At 10° sec -- 29,000 Btu/hr-ft height 35 ORNL DWG. T71-582 ® 10 sec- ® 10* sec Temp. of "black" surroundings 0 0.1 0.2 0.3 0.4 0.5 0.6 Emissivity of Intermal Surfaces Fig. 21. Effect of Internal Surface Emissivity on Peak Steady State Temperatures in a 94-Mw MSBR "Reference Design" Type Heat Exchanger (see Figs. 1 and 2), 3102 Btu(hr . | £t of tube n , — RPN Btu/hr (b) At 10* sec -- 12,300 Btu/hr-ft height = 13.3 — / . | | T | ft of tube = 0,8 | Emissivity of outer Sfiiface,router shell 36 The primary item of concern is peak temperature and its variation with heat exchanger size and the heat generation rate. Figures 22 to 26, incl., show peak temperatures in the five sizes of exchangers listed in Fig. 2 and how these temperatures vary with the hest generation rate. The temperature profiles inside the exchangers will have the same general - pattern as those shown on Figs. 8 to 11, incl., but with different grad- ients. As peak temperatures rise and/br as emissivity decreases, the radial gradients through the tube annuli will tend to flatten out. Temperature - °F ORNL DWG. T71-583 Elapsed Time After Shutdown - Seconds o 3X108 . 108 | 3x108 108 3x10* 10* 3x10% 108 10° 100 : 2 3 s & & 7 8 914 2 s 4 5 & 7 10 Heat Generation Rate,d Btu/hr-ft2 Fig. 22. Peak Steady=-State Temperatures in a 94-Mw MSBR Heat Exchanger vs Heat Generation Rate and Emissivity of Internal Radiating Surfaces, (a) Heat transmission: By thermal radiation only. b) Emissivity of outer surface of outer shell: 0.8, gc Surroundings: Infinite, "black" at 1000°F. d) Heat generation is Type 1 (all afterheat 1s generated in the tubes). e) Heat exchanger design and dimensions on Figs. 1 and 2. LE g 3000 Temperature = 10 10® Fig. 23. ORNL DWG. T1-58k Elapsed Time After Shutdown - Seconds 3x10® 3x10% 10® 3x10* 104 3x10® 10°® 10° 4 B 8 7 8 9 103 2 a 4 s Heat Generation Rate,d Btu/hr-£t? Peak Steady-State Temperatures in a 141-Mw MSER Heat Exchanger ve Heat Generation Rate a) b C a e). and Emissivity of Internal Radiating Surfaces. Heat transmission: By thermal radiation only. Emissivity of outer surface of outer shell: 0.8, Surroundings: Infinite, "black" at 1000°F. Heat generation is Type 1 (all afterheat is generated in the tubes) Heat exchanger design and dimensions on Figs. 1 and 2. 108 gt ORNL DWG. T1-585 Elapsed Time After Shutdown - Seconds , , . 3x102 10® 3x10®* 105 3x10* 10* 3x10® 103 10° 10 3 . 3 4 s 8’ 7 8 92 10 a 3. 8 8 108 'Heat Generation Rate,d Btu/hr-ft? Fig. 24. Peak Stesdy-State Temperatures in a 188-Mw MSBR Heat Exchanger vs Heat Generation Rate and Pmissivity of Internal Radiating Surfaces, _(a; Heat transmission: By thermal radiation only. Emissivity of outer surface of outer shell: 0.8. (c) Surroundings: Infinite, "black" at 1000°F. (a) Heat generation is Type 1 (all afterheat is generated in the tubes). (e) Heat exchanger design and dimensions on Figs. 1 an® 2, 6¢ 10® ORNL DWG, T1-586 Elapsed Time After Shutdown - Seconds ax108 3x108 105 3x10%* 10¢ | %10 10% 100 10 2 Fig. 25. 4 8 8 7 8 8 109 2 3 4 5 o Heat Generation Rate,d Btu/hr-ft2 Peak Steady-State Temperatures in a 281.Mw MSER Heat Exchanger vs Heat Generation Rate and Emissivity of Internal Rediating Surfaces, (a) (b e d e Heat transmission: By thermal radiation only. Fmissivity of outer surface of outer shell: 0.8, Surroundings: Infinite, "black" at 1000°F. Heat generation is Type 1 (all afterheat is generated in the tubes) Heat exchanger design and dimensions on Figs. 1 and 2. ‘10® Temperature = 10 ORNL DWG. T1-58T7 Elapsed Time After Shutdown - Seconds 3107 10% 3xl0® 10® 310 10% 3x10°® 10° 107 2 3 & 8 e 7 8 9 108 2 3 4 &8 Heat Ceneration Rate,d Btu/hr-ft? Fig ,26. Peak Steady-State Temperatures in a 563-Mw MSER Heat Exchenger vs Heat Generation Rate and Fmissivity of Internal Radiating Surfaces. (a) Heat tranemission: By thermal radiation only. (b) FEmissivity of outer surface of outer shell: 0.8. (¢) Surroundings: Infinite, "black” at 1000°F. id) Heat generation is Type 1 (all afterheat is generated in the tubes). e) Heat exchanger design and dimensions on Figs. 1 and 2. NOTE: These curves obtained by extrapolation. 102 o T 43 APPENDIX A COMPUTATTONAL MODEL AND ASSUMPTIONS GOVERNING THE COMPUTATIONS Geometry (see Figs. 1 and 2) All equations are written for infinite cylindrical geometry. Tube layout is assumed to be sn annular array consisting of an integral number of concentric circles of tubes. Tube spacing (pitch) is: circumfer- ential pitch -- 0.750 in.; radial pitch ~-- 0,717 in. In terms of space or volume occupied by the tubing in the annulus, these tube spacings are equivalent to triangularly-pitched tubes having P/D = 2.1. PhyS1cal Characteristics and Considerations The computational model is based on five assumptions or postulates?® involving the radiating surfaces and_the energy radiated; these are: (1) We are dealing with a multi-surfaced enclosure in which it is possible to construct a heat balance for each surface in the enclosure. Each surface in the enclosure is considered to be isothermal. Since radial symmetry obtains, each circle of tubes was considered to be a “single surface. (2) The surfaces of the enclosure are considered to be gray; i.e., absorptivity, o, is equal to emissivity, €, for all wave lengths of radient energy and is uniform on any particular surface. (3) The distribution of emitted radiation follows Lembert's cosine law. TLambert's law is outlined in the next appendix. (4) The distribution of reflected radietion also follows Lambert's ~ cosine law, (3) above; i.e., when a collimated beam or pencil of rays strikes the surface it is reflected diffusely. A consequence of (3) and (4) above is that, in considering the energy leaving an element of surface, no distinction is made between emitted and reflected radiation. The" resulting heat transfer — temperature equations - are linear and tractable., . -~ (5) The radiation incident on any particular_surface'in the enclosure is uniformly distributed on that surface. This assumption is required if the isothermal and gray conditions per (l) and (2) above are met. It is generally recognized that these postulates are simplifying assumptions which may deviate, sometimes quite substantially, from the actual physical situation. They receive wide use because of the tractable mathematical expressions resulting from their use. In most cases and 1n spite of their deficiencies, equations derived from these general uy assumptions usually produce satisfactory engineering answers. Insofar as these healt exchanger calculations are concerned, we cannot justify or favor any other set of assumptions unless we have reliable experimental date which enable us to evaluate: (1) emissivity, its: temperature dependence and the angular distribution of emitted radiation, (2) the degree to which reflected radiation is specular instead of diffuse and how specularity is affected by surface finish,. surface composition, and immediastely adjacent sub-surface structure, temperature, and exposure to molten salt. Even if we had these data the development of solvable equations would be ‘& formidable problem and certainly, during the development of a design, not worthwhile from the standpoint of cost and time. We would, perhaps, consider a calculation in which tube surfaces are divided in two parts [see (5) above], the inner and outer half circles. This would have, as its only effect, increasing the number of equations by a factor of almost 2 but would not increase the complex- ity of the equations. Such a step would, as of now, require programming for one of our local computers; our remote time sharing facility would not have the necessary capacity. b5 APPENDIX B DIRECTTONAL DISTRIBUTION OF RADIATION (Lambert's Law) Cénsider an elemental black surface; di, , radiating in accordance with Lambert's cosine law. The energy, 4Q, emitted from _ solid angle dQ centered about the direction (8,6), Fig. Bl, may be expressed, aQ(8,6) = aQ(B) = I, A cos B dq . I 1s the rate of emission per unit elemental area, into the elemental (B-1) » of emitting sur- face, into a unit elemental solid angle around the normal, (g = 0), to da, . /, Normal to . dAg | Normal to dA; - dAg at o distance B ro from dA, = 0 Fig. Bl 46 On s heflispherical surface of radius r, centered on dAE and in spherical coordinates ' r sin B dO r 48 an = z = sin 8 d6 dp (B-2a) _ =2 , | and B : _ : - - aq(se) = I, dA cos P sin B dedp. (B-2b) The solid angle, dQ, may also be specified in terms of another element of area and its location elsewhere in space; e.g., on Fig. El cos @ a0 = —— (B-2¢) T2 end from (B-1) - | I, dA, cos B dAg cos o ‘ . aq(p) = —— — —_ . | (B-2d) Tz The total energy emitted by dA, is obtained by integrating (B-2b) over the hemisphere, ' | on . /2 - Q = Io GT.%Y S S cos B sin B 46 df - (B-3a) , o 5 _ Q=rnI ay Btu/hr . (B-3b) The total energy emitted by dA1 as a black body is Q=dAp oT* | (B-L) in which o = Stefan-Boltzmann constant = 1730 x 1073 B (experimental value) hr-ft2-°R& | T = temperature, °R . k7 rTherefore, by equating (B-3b) and (B-4) | . 1, =5 Btu/ftd-hr (B-5a) for black body emission; correspondingly, if Lambert's cosine law is extended to non-black surfaces having hemispherical total emissivity, e€, | _egT¢ : I(e) = —— . (B-5b) The fraction of the tétal-energy emitted by dA; which is inter- cepted by dfs is, from Egs. (B-24) and (B-3b), .'Ié dA cos BiQAB cos a - (3-6a) F = B—a dfy =~ dhg m I da . O _ - dA; cos B cos ¢ dhy - dAs . | (B-6b) This equation defines the view factor of one differential element, dA,, radiating to another differential element, dAg, with the proviso that dA; is radiating diffusely in accordance with Lambert's cosine law. It is the basis for the view factor determination discussed in the next appendix. k9 APPENDIX C ~ VIEW FACTORS* General Considerations 1 In an enclosure made up of two or more surfaces the view factor¥* for any particular surface, the reference surface, to any surface in the en- closure is defined as the fraction of the total radiant energy leaving the reference surface which is transmitted directly (no reflections) to the viewed surface; obviously then, this fraction is dependent on the geometrical configuration of the surfaces in the enclosure and on the directional distribution of the radiant energy leaving the reference surface. "View fraction" would, perhaps, be more accurate terminology. References 11 and 12 provide excellent material on this subject. 1In this report view factors are represented thus: F is the view factor of m-n surface m looking at surface n. It is not difficult to show'! that for surfaces, all composed of infinitely long parallel elements, the view factor, assuming diffuse radiation, from a strip of differential width to a neighboring surface is given by Fig. Cl. ' ' At Surface o Surface A : B | Elements of surfaces A and B perpendicular to the plane of the to paper are infinitely long and parallel. dA Normal o )// todh, o =0 - o FdA'+'B = O.S_(sin ai -— s8in aa) : ' (C-l) ¥Also referred to as "configuration,"”" "angle factor,” "shape factor" in various texts and references. 50 ‘This is the situation which obtains in MSBR heat exchangers. Tubes and surfaces which see each other are separated at most by about 6 in., end since they are about 250 in. long, the infinite length model is appro- priate. Note that concave surfaces see themselves and that view factors of surfaces to themselves must be included. The relation in Fig. Cl, evaluated graphically and integrated, was used to determine a majority of the view factors required by this analysis. The reciprocity relation Fen® " Fnant _ (c-2) Am = area of mth surface A.n = aresa ofrnth surface was also used. View Factors, Tube to Adjacent Tube and Adjacent Plane The view factors for simple regular geometries can often be obtained anglytically and several references (13 to 20 incl.) are good sources of view factor formulas for a variety of geometrical shapes and arrangements. In these MSBR exchangers the unobstructed view factors for a tube to an adjacent tube, Fig. C2, were determined from 1/2 1/2 Fr L 17° % [(x2 - 1) - X + 121 - tan-l((xa— 1) / )] (c-3) X = p/D. NOTE: In some references this L P . view factor is referenced to one-half the perimeter of tube I since only one-half of tube D I sees tube II. The value of / / . will be twice that I- 1T obtained from the above formula. Also, cos *(1/X) may be sub- I I stituted for the tan™! term in some formulas. The tan ?® term is better adapted for some computers. Fig. C2 51 Each tube sees adjacent tubes on either side in the same row; there- fore, the view factor of a tube row to itself where a tube row is con- sidered to be 'a single surface, n, in an infinite planar array is Fn -n 2Ftube - adjacent tube (C h) 0.154% for P/D = 2.1. At the boundaries where the tubes see a continuous plane surface, the view factor of an infinite row of tubes to an infinite plane is determined thus: 1. Consider an infinite row of tubes bounded on either side by parallel, infinite planes, Fig. C3. ORNL DWG. T1~588 Ld L LLLLLLSLLLLLLL TSI, 7727 . _,_\ f | /_,_ 2 _—/// D _a’/, \\\~. 1777777777777 777777777777 7777777777777 Fig. C3 2. Since the total #iefi=factor for the tube row is 1.00, we can write 7 o : f _Fn-ejn f_2Fn.—'Plane =1.00 o | | - (C-5a) and. ' R | 1.00 = F - ' , , , n ~-n ' i - plane o L (c-5b) 0.423 for P/D = 2.1. 3. The view factor'fbrid'plane to the tubes is derived from the generally applicable reciprocity relation, : - 52 < A - Fplane -pn = [_Fn - plane :]K-piTm; | - (c-6a) = [Fn - plane ] (TT D/P) (C-—6b) 0.630 for P/D = 2.1. View Factors, Tube to Non-Adjacent Tube and Non-Adjacent Plane View factors from a tube or from an inner or outer shell which sees only portions of neighboring tubes through the gap(s) between tubes were determined graphically as illustrated by the next diagram, Fig. Ck, and the procedure which follows. ORNL DWG. T1-589 © O © Fig. C4. Graphic Integration of Tube-to-Tube View Factors | ( “ 1. 53 ‘Procedure for Calculating View Factors on a large-scale layout, determine graphically the arc,'fifi' the part of the periphery of the reference tube (1C) which sees the viewed tube, 3R2._'fifl'is deflned by MP tangent to 2R2 and NQ tangent to 3R2. Subdivlde'fifi‘into 1ncremental arcs, AA;, A, —.4.-7Qi. The number of subdivisions is a matter of judgment. Increasing the number of subdivisions. increases both sccuracy and labor. For these -computations the EE"fiére:typically 10° arcs. Determine the llmits of view of each incremental arc on 1C to viewed tube 3R2. On the diagram these view limits of AR, are denoted by lines OX and 0Y, making angles o+ and oz with the normal to AAl The average view factor of the element of surface represented “by arc AAi seeing 3R2 is given by The view factor of the'surface represented by arc MW 1is the simple integrated average of the view factors of the incremental arcs: Z(mixn—\ -+ 3m0) _i=1 ' I“m 332 —F (c-7a) )]’ 1= and if all Efii,arelequal; this is reduced to J | F -1 Z F ' m-sae J - 3R2 . L {Cc-Tb) | ahy ~ The view factor-of-tube:1C,'réferred to'its;tdtal surface, looking at tube surface 3R2 (or 4Ll, 4R1, or 2R3, etc.) is F1c - 3R - PR ¢ (c-Te) 5k This procedure is repeated to get the view factors from tube 1C to the other tubes seen differently by 1C until a catalog of view factors to all tubes seen by tube:-1C is complete. Because infinite geometry in all directions has been assumed, the sum of the view factors of tube 1C to all the tubes it sees in Row 2 is also the view factor of the surface represented by all tubes in Row 1 to all tubes in Row 2. As noted in Section III and Fig. 2, the assumed tube spacing with 0.750 in. and 0.71T7 in. circular and radiasl pitch, respectively, is equiv- alent, in terms of space occupied by the tubes, to triangularly pitched tubes having a pitch/diasmeter ratio of 2.1. Specifying an actual detailed tube sheet layout is beyond the proper scope of this investigation as it will depend on accepted fabrication practices, designers' preferences, the vendor's machine tools, etc. Also, it would be folly to believe that, regardless of tube sheet layout, 3/8-in.-diam tubes over 20 ft long will exactly reproduce the tube sheet layout at the midplane. We can only depend on the average tube density in the tube annulus. Since, from symmetry, each tube in any particular circle was assumed to be at the seme temperature, each circle of tubes was considered to be a single surface (see Appendix A). Ideally, view factors for each tube circle would be determined by a careful computation, and tube circle curvature would be taken into account. Nearly as good results would be obtained by getting view factors at several radii and interpolating. Either of these methods requires a tremendous expernditure of routine labor in graphic computations and piece- meal integrations -- awesome to contemplate and wholly impracticable. Therefore, view factors were determined as if the tubes were in infinitely wide and deep slab geometry, triangularly pitched (P/D = 2.1) end bounded on two faces by infinite planes. .This reduced the labor involved to an acceptable minimum. The view factors so determined were then modified by considering the view factor akin to conductivity and using conduction equations as a basis for computing a correction coefficient which will make the slab array view factors apply to cylindrical geometry. - Consider, for example, the effect of tube circle curvature. 1In a simple enclosure consisting of two infinitely long concentric cylinders, it is immediately apparent that the view factor from the inner cylinder to the outer cylinder is 1. However, the concave inner surface of the outer cylinder sees itself across the annulus, and the view factor from the outer to inner annulus will be less than 1. This, of course, is also evident from the reqiprocity relation, Fh - A.n =F on A . In these heat exchangers the ratios of the radii of tube circles which view one another are not sufficiently close to one to justify neglecting curvature by using a slab approximation. o An infinite, triangularly pitched array is completely regular, and view factors for a tube or row of tubes to other tubes or rows may be used repetitively throughout the array. An infinite array of uniformly spaced concentric circles of tubes will not be completely regular. The small local deviations from uniform geometry are expected to average out and hence were not considered in the determination of the view factors. 25 It will become apparent, by considering the equations in subsequent Appendix E, that system geometry enters the temperature — heat transfer equations only via the view factors; i.e., the use of slab array view. factors would be equivalent to solving this heat exchanger transmission problem in infinite slab geometry. For thin annuli having ID/OD ratios close to 1, the substitution of slab for cylindrical geometry is probably of little consequence. The MSBR heat exchangers do not meet this con- dition. It is easily shown that, for conductive transfer with internal heat generation, the substitution of an infinite slab having the same thickness as the tube annulus may produce a large error. For example, the temperature-drop equations for the two cases are:2® ORNL DWG. T1-590 Infinite Cylinder Infinite Slab | / ra ri s AT Cylinder b . H( Ar)® slab | kslab o @cy]., :_EEHQ-; E!r;_(Ar) + (ar)2 "_-'21.12. iog_e (1 + (Ar)/r;)] ' H = internal heat generation rate, . Btu/hr - - o3 ’ k = thermal conductivity, —2r/Br £t2-°F/rt 56 If we use the tube annulus dimensions, Fig. 2, of the MSBR 9563-Mw ex- changer in these equations, we get, for equal values of H and k: = 1.80 Hk . AT . = 1.28 H/k; AT cyl sleb The infinite slab equation, in this case, produces answers 40% higher (referred to the cylinder). Alternatively, if the conductivity of the slab material is increased by 40%, the temperature drops will be the seme. | It was decided--for two reasons: (1) intuition, and (2) the immedi- ate lack of a better proven approach--to use these conduction transfer equations to compute the correction coefficient gpplied to the slab array view factors. If the conduction transfer Equations (C-8) and (C-9) are rearranged to give the relative values of conductivity in a slab and a hollow cylinder which, all else equal, provide equal temperature differ- entials, we can write ' 2(Ar)° = = = . (c-10) 2r, (ar) + (&r)" - 2r] log, (14 I{) kslab = kcy]_ The bracketed expression is the ratio of conductivities that must exist if an infinite slab of thickness Ar is to transfer its internally generated heat across the same temperature differential as in an infinite hollow cylinder of inner radius r and annular thickness Ar. Equael values of heat generation per unit volume are assumed. This expression in brackets is always positive and greater than 1 (>1) if Ar is taken as positive in the radially outward direction. It can be regarded as the correction factor, applied to conductivity, re- quired to make a slab geometry computation produce results applicable to a hollow cylinder. It is again emphasized that the temperature — radiant heat transfer equations do not contain explicit terms based on system geometry; i.e., if the view factors in these equations are those of slab geometry, the results are correct for slab geometry. The view factors, for reasons noted in the preceding paragraphs, were obtained from a slab model and subsequent computations based on these view factors must be corrected so the results are applicable to hollow cylindrical geometry. View factors were regarded as analogous to conductivity and values obtained from the slab array calculations and graphics were corrected using a factor based on the bracketed term in Eq. (C-10). In detail, the corrections were made as follows: ' " 57 _ zlip(n+k) = view factor from afiy row of tubes, surface n, to | | another parallel row, the (n+k)th, where k = 1, 2, 3, --- etc; or, from a bounding plane, n = 1, to a row of tubes. Ffiyi (n{k = view fgctor from the nth cylindrical surface (circle T of tubes or a shell) to the (n+k)th surface; n = 1 “ is assigned to the outer surface of the inner shell of the heat exchangers. -rn7=_radius of nth surface. Ar = difference in the radii of nth and (n+k)th surface. Ar is slways positive since these corrections were applied by starting at the innermost radius where = k x (radiel tube pitch) = 0.717 k (see Fig. 2) Ah = area of nth surface. A ., = area of (n+k)th surface. n+k The view factors in the cylinder are: cyl _ 8lab 2(ar) n = (o) = Fn o (nex) (C-11) X _Erfi(ér) + (_Ar‘)s-- 2r; log, (14—?—2) With this expression (C-11), the corrected view factors were established gtarting with the innermost surface st the inner shell n=1), for all surfaces to other view surfaces located radially outward. Having ‘established the radially outward view factors, the view factors from all surfaces to other surfaces located radially inward were then determined from the reciprocity relation, viz.: o ' . A eyl = _ “nk/_cyl - o= (0k) T A \F(ox) - n) ‘ (c-12) , ' cyl o ' ‘ : S , becauserF(n;k)Fn-—u)Bn E 0Ty a. For T&pe 2 heat generation, in which the gamma heat generation rate in the inner shell is considered, the 1st equation is not set equal to zero, 9 18 then the heat generation rate in the inner shell per unit outer surface area of the inner heat exchanger sghell, For uniform heat generation rate in the tube annulus, Q2 = qa = .... qJ ser =Gy - Note that the cylindrical geometry is not explicit in these equations; it is implied by the view factors. Lo In matrix format, suitable for machine computation, these equations (1la) are written: p—— 01'1 cl,2 01’3 L BN BN N B BN} %2,1 ®2,2 ®2,3 (1lb) cn,l cn’a ......'..‘....‘.'..CC ,J cnl CH’a Y S 0 ee B e For surfaces having a lmown or prescribed rate of heat transfer: c = -F . n,J n-+} ’ an Cn,a = (I-Fn*J)-(l-FJ_'_J) ; J=n Rn,]. = % For surfaces having a known or prescribed temperature: c, ==(1=E)F ——J’; ’ n,§ 1-(1—En)Fn_'J.= 1—(1_-133)5",‘_,.‘j ; 4 .Rn,l * En"’,rn Tre radiosities, B,, are computed and surface temperatures, Tk' .obtained from Equation (93). et s d e cl,“—l Ca’h sresse 02’M_1 oooo.-noocn,M.l J£n i 0 > ¥ Cy,m o, JsM T.M 89 APPENDIX F COMPUTATIONAL PROCEDURE Calculations were made in sequence as follows: 1. View factors were determined as outlined in Appendix C. 2. Temperature profiles in the outer and intermediate - shells were calculated as outlined in Appendix D. The temperatures at the inner surface of the inter- mediate shell are the boundary values, TM, used in "Egs. (11c) in Appendix E. . 3. Having established the view factors, boundary values for temperatures, and heat rates, Eqs. (1lc) in Appendix E were solved for tube circle and inner - shell temperatures. The computations were made using Extended Basic (BII) programs with the Reactor Division's time-sharing computer facility. Several programs were written for the various aspects of the problem. It has been this author's experience that the inclusion of computer program lists without coplous explanatory notes and instructions is wasted effort. Should a ‘need develop, the programs will be reported separately. = T1 APPENDIX G THERMAL RADIATION CHARACTERISTICS OF HASTELIOY N The emissivity of Hastelloy N (INOR 8) is reported in reference 27. These data suggest that, for clean, unoxidized surfaces, we use an emis- sivity of 0.2 and, for oxidized surfaces, an emissivity of 0.5 or 0.6. The author did not become aware of reference 27 until this report was virtually completed. The remainder of this appendix is the result of my attempts to infer a value of emissivity from measurements on alloys composed of similar elements. Although the data and references which follow are not directly applicable, they are included since they may be relevant and useful to persons dealing with similar problems. There is considerable data on alloys containing nickel, iron, molyb- denum, and chromium. Table Gl lists values of emissivity for metals of this general composition. 1In general, the numerical values of emissivity for smooth, clean, unoxidized surfaces at temperatures in the region 1200°F-2000°F are from 0.1 to 0.3. In the absence of better information, similar values were assumed for Hastelloy N. Therefore, the temperature calculations were made for internal emissivities of 0.1, 0.2, and 0.3. In general, the data indicate, and theory substantiates, that emissivity increased with increasing temperature. This change is not large; within the temperature differences calculated in the tube annuli, it will be of the same order as the uncertainty in the value of the emissivity. No attempt was made to include a mild temperature dependence of emissivity in the temperature — heat transfer equations. These equations, linear . with T as the unknown, are easily solved by standard routine programs. We are dealing with conceptual designs, subject to change, and a physical system containing uncertainties other than emissivity. The incremental elegance of solution and the resulting improvement in accuracy are insuf- ficient to justify the very appreciable increase in cost and time re- quired to develop or adapt a program which allows the use of temperature- dependent emissivity in the system of equationms. In connection with the data from reference 22 in Table Gl, it is appropriate to point out that this report, NASA CR 1431, outlines a program now apparently under way at Purdue University to collect, evaluate, and present radiative properties data from all available sources. When suf- ficient evidence exists concerning a particular property of a particular material, such as the emissivity of stainless steel, broad band curves of "recommended” values are presented which enable the reader to get a general feeling for the tolerances or variations to be expected and the circumstances in which the "recommended" values are applicable. These data tend to develop more confidence in the user than anything this writer has seen heretofore in the readily available texts and references. It has been'pointed out that by assuming gray, diffuse conditions, no distinction is made between emitted and reflected radiation; both are assumed to have directional properties in accordance with Lambert's cosine law. There is evidence that, whereas the pattern of emitted radiation may and Various Alloys Containing These Elements Teble Gl. Emissivities of Molybdenum, Nickel, Chromium, Typel of : Condition Emittance | Material and/or Meagure- Emlssivities and Corresponding Emissivities at Treatment ment Temperatures and/or Wavelengths 1200°F 2000°F Rotes Source I. Molybdenum A. Polished HTE Iinear variation from 0.07540.02 0,110%0.02 0.190t0.02 Based on T references, Data Ref, (22) at 600°F to 0.25010.02 at 3500°F. 1s apparently consistent with NASA CR 1431, p. 26 . uniform scatter, B. Grit dlasted HTE 0.2840,05 at 1340°F; 0.3C a 0,26+0.05 ~0, 32% Based on 2 references. Rer, (22) 1T00°F. . NASA CR 1431, p. 26 C. Shot blasted HTE 0.22 at 1000°F to 0.40 at 2T00°F. 0.25 0.38 Based on 1 reference, Ref, (22) and etched . FASA CR 1431, p. 26 D, Etched and BTE 0.25 at 1340°F to 0.40 et 27T00°F. 0.125% 0.275 Baged on 1 reference. Rer. (22) flashed NASA CR 1431, p. 26 : Based on 1 reference. , E. Stably oxidized. HTE Approximately 0.82 at TOO°F. - - Curve sheet states that oxide Ref.. (22) : is volatile in & vacuum sbove NASA CR 1hk31, p. 26 1000°F (B11°K). II., Stainless steels, A, Clesned RTE 0.30:0.09 at 600°F; 0.35:0.09 0.35 Appears to be based on at Ref, (22) cleaned at 1000°F; 0.4110.09 at 1340°F; least 13 references. NASA CR 1431, p. M4~ 0O Eflm_'u_nf- 1700°F . B. N-155, as received NIE linear varistion from 0,10 at 0.16 - Based on 4 references. No- Rer. (22) or cleaned 350°F to 0.15 at 1160°F rising tation on curve sheet at NASA CR 1431, p. bb nonlinearly to 0.3 at 1580°F nonlinear portion of curve (see Note). reads "Oxidation Probeble.” C. As folled, clesped RIE 0.4T at 600°F; 0.5 at 1160°F. - - Based on 1 reference. Rer. (22) ' NASA CR 1431, p. ¥4 II, Stainless steels, A. Oxidized in air at NIE 0.15+0.06 at 260°F; 0.25+0.0T 0.3240.07 O.h7* Based on 6 references, Ref, (22) oxidized red heat for 30 min. at BOO°F; 0.29:0.0T at 1000°F; NASA CR 1431, p. 45 0.35+0.07 at 1340°F; 0.4l at YTO0®F; essentially linear vari- ation from 440°F to 1TOO°F. B. Buffed, stably NTE 0.40 at 620°F; 0.42 at 1OO0O°F; 0.46 - Pased on 1 reference, Rer, (22) oxldized at 1112°F 0.50 at 1340°F. KASA CR 1431, p. &5 (873°K). C. Shot blasted, 0.64 at BOO'F; 0.6T at 1160°F; 0.67 -- Based on 1 reference, Ref. (22) stebly oxidized at 0.70 at 1340°F. NASA CR 1431, p. 45 1112°F (873°K). D. Polished and oxi- RIE 0.67£0,02 at 980°F; 0.T0:0.03 0.6920,03 0.8110,06 Based on &t leagt 5 refer- Rer. (22) dized at high at 1340°F; 0.75:0.05 at 1TO0°F; ences (probably 7). NASA CR 1431, p. IS temperature., 0.8210,06 at 2060°F. E. As rolled, stably NIE 0.TT at TOOF; 0.8 at 980°F; 0.83 - ‘Based on 1 reference. Ref, (22) - oxidized at 1112°F 0.85 at 1340°F; 0.87 at 1450°F. RASA CR 1431, p. 45 (873°K). F. Stably oxidized NIE 0.83:0.05 &t TOO°F; 0.86+0.05 0.8820.05 - Based on 3 references, Ref. (22) at high tempera- at 980°F; 0.9:0.04 at 13%0°F. NASA CR 1431, p. &5 ture, . —-. _IIT. Stainless steels, A. N-155, polished_ __. NTE_ . 0.1 at 620°F; 0.13.at.980°F; __ __0.16 .. _ 0.28%.___ Based on.3 references. . Data__ Ref, (20) .. .. _ polished (oxtdation re- © 0.18 at 1340°F; 0.2320.03 indlcates scatter sbove RASA CR 131, p. 46 tarded), at 1700°F. 1340°F, ' . B. Various polished NTE 0.17+0.04 at 260°F; 0.19+0.0% 0.28+0,06 -- Based on § references, The Rer, (22) stainlegs steels at 620°F; 0.21:0.04k at BOO'F; curve rises rapidly at high NWASA CR 1431, p. 46 (oxidation re- 0.2310.0‘ at 980°F; 0.330.07 tempersture and carries no- tarded), at 13%0°F; 0.4330.10 at 1520°F; tation "Oxidation Probable,” 0.56£0.11 et 1T00°F (aee Note), ' IV. Tnconel A. As received Fot Constant at 0,25 from 300°F to 0.25 - Rer. (23) : stated 1200°F. ] B. As received and Kot 0.55 at hOO'F to 0.53 at 1100°F. 0.53* - oxidized at 1200°F stated Linear variation. for 48 hours. : C. Polished Rot 0.12 at 300°F to 0.20 st TOO°F. 0.30% - stated Linear variation. D, Polished end oxi- Kot 0.27 at 500°F to 0.30 at 1100°F. 0.31* - dized at 1200°F stated Linesr varjation. for 48 hours. V. Inconel X A. As received Fot 0.27 at 300°F to 0.23 at 1100°F. 0.23% - Ref. {p3) stated Linear variation. B. As received and Not Constant at 0.38 from 300°F to 0.38% .- oxidized at stated 1100°F. 1200°F C. Polished Not 0.18 at 300°F to 0.17 at 1100°F. 0.1T* - stated D. Folished apd Kot 0.29 at 300°F to 0.35 at 1100°F. 0.35* - ‘.{% oxidized at 1200°F stated ILinear variation, for k8 hours. VI. Monel A. As received Kot 0.10 at 200°F to 0.31 at 1100°F. 0.31% -- Rer, (23) e stated Linear variation, B. As received and Not 0.50 at 200°F to 0.T2 at 1100°F. 0.T5* -- — oxldized at 1200°F stated ILinear variation. for I8 hours C. Polished and oxi- Kot 0.65 at 4OO°F to 0.5T at 1100°F. 0.56% - dized st 1200°F stated Linear variation. for U8 bours. : VII, Rickel Polished TE 0.07 at 300°F to 0.16 at 2000°F. 0.11 0.16 Rer. (24) Rearly linear varistion. VIII. Chromium Polished TE 0.05 at 300°F to 0.h6 st 1800°F. 0.26 - Ret. (2b) Linear variation, IE .- Hemiepherical Total Emittance. l NTE -- Kormel Totel Emittance, TE -- Totsl Fmittance, ¥Extrapolated by suthor of this report. £ ¥ a_ * ¥ e 73 be well approximated by the cosine law, reflected radiation from the same surface can be highly specular, particularly when very smooth or palished surfaces predominate. Intultively, this is reasonable. No . attempt was made to estimate or evaluate the effect of a strong specular component on temperatures developed in these heat exchangers. Any effect of specularity would be more apparent at low emissivities when the energy content of the total radiation leaving a surface contains the largest fraction of reflected radiation. The literature contains comparisons of computations based on diffuse vs specular radiation emansted by relatively simple, regular cavity configurations such as continuous rectangular and V-shaped grooves, cylindrical and conical cavities, and spherical cavi- ties. The data are presented by plotting curves of apparent emissivity, “which is a measure of overall heat transfer capability of the cavity, as a function of cavity depth-to-opening ratio (L/R for a cylindrical cavity). Actual emissivity is a parameter. The effect of specularity -is to increase the gpparent emissivity and the effect is most pronounced in deep cavities of low emissivity. For example, reference 12, Fig. 6.2, p. 165, shows calculated curves of apparent emissivity of cylindrical - cavities having depth to radius ratios, L/R, from zero to 10. The data in Table G2 have been taken from this figure. Table G2 Calculated Apparent Actual | - Emissivities Emissivity _ - ‘ _ — of Cavity L/R Diffusely Specularly Surface Reflecting Reflecting 0.1 2 0.3k 0.34 0.1 6 0.48 0.59 0.1 10 0.49 0.72 0.2 2 0.53 0.56 0.2 -6 0.63 0.79 0.2 10 0.63 0.88 0.3 2 0.66 0.70 0.3 6 0.72 0.83 0.3 0.72 0.9k TS The degree to which the internal surfaces, tubes mainly, reflect specularly deserves consideration. Certainly the spaces between the tubes are not unlike deep cavities. If specular reflections will take place in the heat exchangers, it is reasonable to conclude that the diffuse calculations reported here give higher temperatures and may be regarded as conservative. | ' B ¥ " > APPENDIX H COMPARISON -~ EXPERIMENTS AND ANALYSES The calculated temperatures reported herein are not presented en- tirely unsupported by experimental verification. In November 1965, temperatures in a 9l1-rod bundle of 0.5-in.-diameter strajight stainless steel tubular electrical heaters were reported.25 Figure Hl is a photo- graph of a somewhat similar heater assembly. Figure H2 shows the essentials of the test setup. The information required to do tempera- ture calculations follows. ‘ : A. System Configuration 1. See Fig. H2 - 2. Rod pitch/diem = 1.25. 3. Rod diam --- 0.5 in. L. Rod surface area --- 0.131 fts/ft length. 5. Heated length of rod =-- 10 in. = 0.83 ft. 6. Rod array --- concentrlc, hexagonal rings formed by trlangu— larly pitched tubes. The single, central tube is considered to be ring No. 1. Thermal Conditions 224 w/rod = 91.7 Btu/hr-ft length of rod 700 Btu/hr-ft? rod surface 6780 Btu/hr for 90 active rods (1 rod not heated) I 1. Heat input --- I 2. Environment (a) Tube bundle hou51ng evacuated to a pressure of < 3 microns of mercury. (b) Housing in laboratory atmosphere, protected from drafts. 3. Emissivities No measurements were made of emissivity of the tube sur- faces or the internal surface of the housing. Based on the several-year-old recollection of a person somewhat familiar with the experiment, it can only be concluded that the stain- less steel surfaces were neither new, bright and polished, nor were they heavily and deeply oxidized. Between these extremes, emissivities from 0.2 to 0.7 are possible and values from 0.3 to 0.5 are likely. Tube surfaces displayed a dull, satiny gloss typical of stainless steel after long immersion in a high-temperature liquid metal (NaK, K, Na, etc.). _m o ik o0l tg § = 58 = wm M Q &g | r m 3 i oD i 2 -~ O ™o 88 33 Hl. Fig. ekiniine » ¥ ORNL DWG. 71-392 AON(romIACK) MO, °¢ 2 3 Radfus - Inches g " xAoweooe £ 2 3 € § & 7 .E— ! ¢ , : -] M e B SCH ¥D PFE i I _ e 30% 5T 5TL ! '5/ 70 : ‘ 4 = EXPERIVENTHL DPONT T I i : l | . . ¢ r2* ! R - BOTTON TG ! L _ FI-‘ N ~x y - ; $ k | Jwewreo ‘ - sacrron L TTTTZ7Z20777 2070 77 R £ Pani - > ' . 2w Pmicm KQowooL Coe STvrraxx’ Meocr ' ‘ : o 5 . . . { };’7_:5 o 5 uo - £ MERTEE LODS,) Joo ;‘4,‘:.32'0(04‘3: El Kreaad ” f s, LoD Mrpen” u L2555 o7 Test Setup and Hester Rod Geometry Curve Legend Radjiated Shell 8 in. ,nc;xed-ho, Curve Emissivity, Heat Rated 304 SS pipe Ko, 1 t:":fm" Btu/hr tof o0 a1l Batssivity Assmumed to be 0.8. A 0.10 82.9 B 0,15 82.5 725 = inside C 0,20 82.5 surface temp. D o.ho B2.5 B 0-'&5 m‘s r 0.50 82.5 G 0.60 82.5 * Thig 1s 90% of total hest imput. Fig. H2. Comparison of Experimental and Calculated Temperatures in 9]- Rod Array . LL 78 k. Temperature measurements Temperatures were measured by chromel-alumel thermo- couples embedded in the heater rods and placed on or in the housing. Temperature calculations were made using the same general method as that used to calculate heat exchanger temperatures. Because of the close spacing of the heaters (P/D = 1.25) the view of any rod is limited to ad- jacent rods and to rods in any second row distant. The central rod and each of the five hexagonal rings were considered to be an isothermal sur- face so that the "enclosure" consisted of a total of seven surfaces. This assumption is capable of producing some error since the corners of the hexagons are closer to the outer shell. This is particularly apparent on examining the corner rods in the outermost hexagonal ring. Each of these six rods sees only three adjacent rods instead of the four seen by the other rods in this ring. Everything else being equal, we should expect its temperature to be lower than the other rods in that ring since it has more surface directly viewing the heat sink (the outer shell). This has been borne out in the second experiment discussed subsequently, but it was not taken into account in the temperature computations for this test setup. The length of heated section in the rods was 10 in., giving the assembly an approximate L/D of 1.7. The one-dimensional infinite length computational model was used; it was recognized that, applied to this short assembly, accuracy would suffer. In an effort to compensate parti- ally for axial heat losses by conduction in the rods and by radiation, particularly from the outer ring to the shell, the radially radiated heat was assumed to be 90% of the total input. Since the actual emissivities of the surfaces were not known, it was decided to assume values for emissivity and attempt to match the experi- mental temperature data. The results of these calculations are on Figs. H2 to H5, inclusive. These figures are, for the most part, self-explana- tory, but in all cases note that the observed radial temperature gradient is steeper than the calculated values. The temperatures developed and measured in the rod array will be affected by axial conduction in the heater elements and thermocouples and by specular or other non-diffuse components in the emitted and reflected radiation. Any computation de- signed to obtain precise agreement with experiment must include these factors. They were not considered in the calculations reported herein. The calculations using emissivities in the neighborhood of 0.5 are in the best agreement with the experiment. This may be reasonable since the heaters had seen considerable use. Figures H6 and H7 are included to emphasize that radiative transfer in a bundle of rods should not be approximated by assuming that each ring of rods behaves as if a continuous, impenetrable shell. ' ¥ 1, d Temperature - °F 9 ORNL DWG. T1-593 1600 Peaks af /6%0°~c 7 1500 Curve Legend _ ' _ Radiated 1400 Emissivity, Heat Rate¥ All Surfaces Btu[hr _ , t of rod o.ig g.s . 00 05 1300 0.45 82.5 0.50 82.5 0.60 82.5 *90%k of total heat input. 1200 £ 1100 _ EXCELNTEN T 3 900 . Shell, 8 1in.,sched-ko, 30k 8S pipe 125 = inside - surface temp. o 1 2. 3 ' Radius = Inches Fig. H3. A Comparison of Experimentsl and Calculated Temperatures Required to Radi- ate 82.5 Btu/Hr-Ft of Rod in a 91-Rod, Hexagonal Array of ljg-In.—Diam Heater Rodsz Spaced 5/ 8 In. Apart Enclosed in an 8-In. Sched-40 SS Pipe (refer to CF 65-11-68). Calculations are shown with emissivity a parameter. ORNL DHG. T1-59% Fnissivities® Radiated Heat Rate Curve - Btu/hr-rt of Rod BT R e % % % & e M 0.60 0.55 0.50 O.45 0.0 0.35 0.30 82.5 X 0.50 0.50 0.50 0.50 0.h0 0.50 0.k0 82.5 P 0.52 0.50 0.h8 0.46 O.Bh 0.k2 0.50 8.5 Q o.50 050 0.50 0.0 0.B0 0.30 0.60 82.5 R 0.50 0.50 0.50 0.50 0.50 0.h0 0.80 82.5 #Subseripts refer to surface pumbers. Surface mmber 1 is centyal rod, surface muber 7 is inside of 8-im. sched-40 pipe. Experimental curve is from Fig. 12 in CF-65-11-68. Refer to Tig. B2 for details of rod geometry and test setup. Temperature « P Snell, 8 4n.,sched-ho 304 SS pipe T25 = inside surface temp 2 3 Radius - Inches Fig. B4, Temperature Profiles in 91 Heater-Rod Array in Which Rod Emissivities are Assumed to Vary With Their Radial Location. 1% " 81 ORNIL. DWG. T1-595 “Continuous Shell Model Experiment Multi-Surfece Enclosure Model o -z 2 3 - RROIVS ~ INCHES Fig. H5. A Comparison of Calculated Temperatures Required to Rediate 82.5 Btu/Hr-Ft of Rod in a 91-Rod, Hexagonal Array of 1/ 2-In.-Diam Heater Rods Spaced 5/ 8 In. Apart Enclosed in an 8-In. Sched-4O SS Pipe (refer to CF 65-11-68). Calculations are shown for emissivities (all surfaces) of 0.5 and 0.6. 82 ORNL DWG. T1-596 Thie curve indicates that, in celculeting the temperatures required to get rediant heat transfer from arrays of rods or tfibes, & continuous impenetrsble convex shell is & poor substitute for the open, convoluted geometry of the tube humdle., The curve was pre- pared &s follows: ' 1. Temperstures, Fig. E2, in the 9l-rod array were calculated by the method described in Appendix €, for several values of rod surface and outer ghell emigsivity and with a heat input estimsted at 82,5 Btu/hr-ft length of rod. 2. The 9l-rod arrsy was then represented, Fig. H5, as a series of continuous, concentric, closely spaced, infinitely long hexagonal shells surrounded by an outer cylindrical shell. For this configu- ration the radiative transfer from shell to shell is given by the sixple relation, ' ' ~ Fig. B6, Diagram of & Continuous Shel) Model of a Hexsgonal Arrey . . ' of 91 Heater Roda. Q=0cF, (n+1) An('l'n - T(n+1) ) (1) ' Fna(e) ™ o Se) @) An , n(n*'l) + I(IHI) !n (1 - E(IH'].)) ¢ = Stefen~Boltzmarn constant = 1730 X 10~% A = area of nth surface; A, , = erea of (n+1)th surface Q = beat trensferred, Btu/hr Tn = temperature of nth surface T _ = tempersture of (n+l)}th surface n+l r . (n+1) = iuterchenge factor from nth to {n+1)th surface En = emigsivity of nth surface E(m»}.) = emiggivity of (n+l)th surfece Using formula (1) and inserting therein the numbers from the more exact calculation per (1) above, & value of F, . (n+1) V28 calculated vhich produced the game total heat transfer at the same temperatures (see Fig. H2) as those computed by the more exact method per (1) above. The emissivity of the outer, (n+l)th, shell was assumed to be the game es that essumed for the more exact computation and,from formula (2), 2 & .6 & value of En wae egtablished, Thie value of En is the emissivity which . Actual Emissivity e continuous shell must have if it iz to rediete to an adjacent shell as effectively as a hexagonal tube arrey having an emissivity of E(n+i) Fig. H]. The Apparent Emissivity rgaiating to = continuous outer shell having the same emissivity, of a Hexagonal Array of Rods if Viewed E as & Single, Hexagonal Surface vs (n+l)° \ Actual nogs Emissivity., Rod Pitch/Rod For example, Fig. H7 indicates that if the rod surfaces in the Diam E 1. - hexagonel array have an actusl emissivity of 0.2, they eppear, to en adjacent plane, as much blacker plzne with an emissivity of 0.7. 83 A second experiment,arnot dissimilar from the first, involves a hexagonal array consisting of a central tube plus eight hexagonal rings of heated tubes surrounded by a close fitting hexagonal shell and a final, outer shell of 10-in. sched-40 pipe, Fig. H8. The data re- quired for the radisnt transfer calculations are: A. System conflguration _ -1 OV W o - » See Fig. H8 Pitch/dlameter ——- 1. 375 Tube diameter --- 0.25 in. Tube spacing (pltch) -=- 0.343 in. ‘Tube surface area --- 0.0654 £t3/ft length Heated length --- 48 in. Total number of tubes --- 217 Total number of heated tubes --- 205 (12 tubes used for thermocouples) Thermal conditiens' 1. Heat input --- 5.86 w/tube 1 47 w/ft of tube 5.0 Btu/hr-ft '76.5 Btu/hr-ft® tube surface 4100 total Btu/hr, for 205 active (heated) tubes. nfufin u -Environment The hexagonal, stainless sheet steel tube enclosure is protected from air currents and sudden transients by the outer housing, a 10-in. sched-40 pipe. The system was evacuated to 100 microns of mercury or less for the tests discussed herein. _ Emlssiv1ties 77 A somewhat ‘similar situation as with'the flrst experiment described in the preceding paragraphs - obtains, except that the 0.25-in.-diam tubes had not been 1mmersed in hlgh-temperature 1iqu1d metal. Ibmperature measurements Temperatures in the bundle are measured by thermo- couples inserted inside selected tubes. These tubes do not contain heaters and are located (see Fig. H8) at the - corners and in the centers of the flats of the hexagonal rings making up the bundle. ®This experiment simulates afterheat generation by IMFER fuel assemblies. b H. C. Young, private communicgtion. TE 10 ORNL DWG. T1-597 -~ TE 12 OO0 @ -0\ Thin, Stainless .Steel Shield 5.13 In, Across Flats (Typ.). @ TE 9 D () @ @DO® @/ . e CICICACRCACRCARVICAD - GRCLORCRACACLEACAENY | T 142 OO/ — = Fig. H8, Diagram of a Cross Section Through the Hexagonal Array of 217 Tubes. TE 8, Unheated Tube containing a Thermocouple Steinless Steel =~ Housing, 10-In. Sched LO Pipe Tubing Detail T8 85 Results The comparison of experimentala and computed temperatures, Figs. H9 and H10 showed the same general trend as in the previous experiment, namely, the observed temperature gradient was steeper. The use of un- heated tubes for the temperature measurements gives temperature readings below the average temperatures of similarly located heated tubes. This is borne out by the calculations, curves D1l and D2 on Fig. H1O. Curve D2 calculated with zero heat input to the central tube is depressed 23°F below the temperature computed as if the tube were heated. Note also that curves D1 and D2 show a temperature difference of 34°F at the outer ring. This is the computed difference in temperature between a heated tube centrally locested on a face of the outermost hexagonal ring and the unheated corner tube. This difference has two causes; (1) the corner tube is not heated and (2) by virtue of its location more of its surface views the adjacent hexagonal shield, a heat sink. It will be - shown that the local temperature depression of an unheated tube tends to go inversely with the third power of the local prevailing temperature surrounding the unheated tube and, at lower emissivities (<0.3), nearly inversely with emissivity. From this we should expect that the actual radial gradient across the bank of heated tubes will be less steep than indicated by thermocouples in unheated tubes. During these prellminary runs the temperature of the intermediate, hexagonal shield was not measured. This is the heat sink temperature and its value is required in the calculations (see Appendix E). The calculated temperature curves in Figs. H9 and H10 are based on hexagonal shield temperatures of TOO°F and 600°F. These temperatures were calcu- lated by assuming an outer shell temperature of 200 °F and emissivities of shell and shield surfaces of 0.30 and 0.b42. The experiment was in its initial startup phase when the data were taken, and plans were under way to obtain these temperatures in future tests. The degree to which hexsgonal shell temperature affects internal temperatures has not yet been determined experimentally. Two calculations, virtually identical but for ‘hexagonal shield temperatures, may be com- pared with the following table, Hl. Reducing the sink temperature from Table HlL. Effect'offlLowering the Heat Sink Temperature on Peak Temperature in the Hexagonal Array of 212 Tubes ' fHEXagonal Shell ' o Outermost Heat Input Emissivity - Temperature Peak Tube Ring (Btu/hr-ft of ~ (Heat Sink) Temperature Temperature Tube) All Surfaces "'{: (°F) - (°F) - (°F) 5 ok 600 o931 783 s ok koo B59 676 - = T8 AT = 107 84. C. Young, private communication _ . ORRL DWG. T1-598 | Redial Location™ of Centerlines ‘ ' of Hexagonal Rings of Tubes 1 2 » 5 6 71 8 , o Steinless Steel Shield, 5.13 In. Across Housing, 10-In. Steinless Steel Sched 4O Pipe. Tempersture . °F : Bousing, Temper= ature - 205°F. 0 1 2 3 5 6 Redius® - Inches ) Fig. B9 . Experimental and Caslculated Temperstures in a Hexagonal Array of 217 Heated, Stainless Steel Tubes (see Fig. H2). 1. FEnvironment -- 10-in. pipe housing evacuated to ~3 microns Hg. 2. Heat Input -~ 14T watts/ft tube = 5 Btu/hr-ft = 76.5 Btu/hr-rtZ, Enissivity, Tubes Temperature and Hexagonal Hexsgonal Shield Shield - Curves Al and A2 0.3 TOOF Tube temperetures from central tube across flat and to corner tubes of hex, respectively. . Curves Bl and B2 0.5 TOOF Tube temperatures from centrel tube across flat and to corner : ; 3 tubes of hex, respectively. ) g Curves Cl and C2 - - Experimental data, . Pube centerlines and shield locations showvn a8 in an elevetion (section) view across corners of hexagon. : M (k ' i Temperature - °F Fig. Heated, Stainless Steel Tubes (see Fig. H2), 1. Curves C1 and C2 Curve D1 Curve D2 Curve El Curve E2 Redial Location® of Centerlines of Hexagonael Rings of Tubes 1 2 3 L 5 6. 7T 8 9 87 ORNL DWG. T1-599 " Snield, 5.13 In. Across Housing, 10-In. Stainless Steel Sched LO Pipe. - Housing, Tempere- ture - 205°F. 3 Radius? - Inches H10. Experimental and Calcuhted Temperatures in a Hexsgonal Array of 217 Envirorment -- 10=~in, pipe nouaing evacuated to ~3 microns Hg. Fnissivity Temperature Hexagonal - Hexagonal Tubes Shield Shield 0.3 0.3 T00°F 0.3 0.3 T00*F 0.10 0.5 600°F 0.15 0.5 600°F 2. Heat Input -- 1.4T nt.ts/fi. tube = 5 'Btu/hr-tt 76 5 Btufhr-ft=, 11y determined tube temperatures from central tube {unheated) across flat and to corner ‘tubes of hex array, respectively. . ‘Temperatures calculated as 1f all tubes are heated - and as {f outermost corner tubes have same view factors as other tubes in the outer ring. : . Temperatures calculated as if centrel tube and outer corner tubes are ynheated and with corrected view factors for the cuter corner tubes. Temperatures calculated with ceptral tube unheated - and with no view factor correction for outer corner tubeg which are heated, %Tube centerlines and shield locations shown as in an elevation (section) view across corners of hexagon. 88 600°F to U4OO°F effected an appreciable reduction in the peak temperature and a slight increase in the radisl gradient. At higher heat inputs or in larger assemblies with more tube rings, the fourth power effect of temperature will dominate the fractional improvement obtained by lowering the sink temperature. It will be shown, subsequently, that there were axial heat losses in this experiment. The differences between observed and calculated temperatures are subject to the same general considera- tions mentioned in the previous discussion of the 9l-rod array. Conductive transfer effected by the spiral wire wrap around the tubes (see Fig. H8) was not considered. If any appreciable heat is trans- ferred by conduction, it will affect the radial temperature gradient. Figure Hll shows that there were axial heat losses, amount unknown. No really serious attempt was made to consider these in the computations. A few calculations for which the radiated heat was reduced by ~5% (from 5.0 to 4.73 Btu/hr-ft tube) were made using the same infinite cylinder model. The effect of this small heat reduction, credited to axial heat - flow, was negllgible. It has been noted that we should expect the corner tubes to have a lower temperature. If unheated, as these are, the effect will be more pronounced. The unheated tubes in the inner rings will also be at lower temperatures than their neighbors at or near the same radius. The amount by which they will be lower will certainly be dependent on emissivity. For example, the temperature depression can be approximated by using the differential of the heat transfer expression, Qfl. - i Fyoz 0 (T — 15) (B-1) in which Fy 5,5 = radiation interchange factor from area A to Ag, o = Stefan-Boltzmann constant = 1730 x 10 12, T, and T, = temperatures of A and Az, °R. Assume that the unheated rod of area A; is surrounded by other rods having a total area, Az, at the same or nearly the same temperature so that T, == T;; also, assume that T; doesn't change. By differentiating, AQ/A) =k F,, 0T ATy | (E-2a) e 89 ORNL DWG. T1-600 1000 Fifth Hex. TO00 600 500 Hegted oo L f L -3 -2 - 0 o 42 +3 - Distance from.Midplane - Feet Fig. Hll. Axiel Temperatures in HExagonal Arrey of Ihternally Heated Tubes (see Fig. H8). " 90 and _ A(Q/4,) - lg.—__.Q.l'_f.}_;a- (H-Qb) L F, ,, 0T, for small changes in.Tl. The single tube represented by and nearly completely surrounded by six tubes is approximated by two cylindrical surfaces having an area ratio, Ay = 0.5. If the emissivity, E, of both surfaces is the same, the interchange factor is then given by E E F Sg A = - (H-3) 1+ (1-E) 1.5-0.5E 2 Now, if we disconnect the power from this central tube, it is, in effect, operating as a thermocouple tube and &Q/A ) = - 76.5 Btu hr-ft* . ‘The expression, Eq. (H-2b) for AT, , the temperature depression in this tube, becomes _ : - (76.5) — 11 x 10° AT e Py o= . | (H-2c) hF_‘l_)a(l730xlO ) A F;-»a T: Table H2 gives values of AT for the temperatures in the range of the experiment and for emissivities considered reasonable. It would not and will not be correct to apply these approximate tabulated values to the experiment. They are listed to indicate that the temperatures measured in an unheated tube will be below that of the surrounding heated tubes in the bundle. Since this deficit is greater at lower temperatures, measurements so taken will indicate a gradient steeper than actually exists. : The infinite cylinder model was used and, taking the length equal to the length of the heated section of the tubes, 4 ft, we have an LD = 8--a better approximation than with the first experiment. After assessing the calculated and observed temperatures in these tube bundles, it was concluded that the agreement was satisfactory. Since the computed values tended to be higher, it was decided that this calculational approach is a suitable method which gives safe answers " 91 Table H2. Approximated Temperature Depression in a Single Unheated Tube in an Extensive Tube Array Location in Approximate Emissivity, AT, Tube Bundle Value, T, E °R or °F Center 1000°F = 1460°R 0.1 -55 002 "“'25 0.3 -16 0.4 -11 | 0.5 -9 Center ~ 900°F = 1360°R 0.1 —63° Edge of TL5°F = 1175°R 0.1 -106 0.3 -31 Ooh‘ —22 0.5 -17 ®The more exact calculation, curve El on Fig. HI1O shows a temperature depression of 39° at the central tube. - to use in estimating temperstures in MSBR heat exchangers whose internal configuration is, essentially, a bundle of parallel rods or tubes. & 93 APPENDIX I 'METHOD USED TO ESTIMATE THE INITIAI, PEAK TEMPERATURE TRANSIENT IN THE 563-MW REFERENCE DESIGN HEAT EXCHANGER The adiabatic temperature versus time curves "B" and "C" on Fig. 15 were plotted. The bases for these curves are: A. The total accumulated afterheat, Table 1 or Fig. 5, is de- posited thus (see Fig. T): (1) 77% in the annulus (inner shell and tubes) (2) 23% in the intermediate shell. This includes the heat deposition in the outer shell and the gamms heat lost to the outside. B. The annulus and intermediate shell are separated and both are perfectly insulated. C. The heat capacities of these regions are as listed in Table I1. Table I1l. Heat Capacity of Empty 563-Mw MSER Primary Heat Exchanger : Heat Capacity Per _ Metal ' Mw Rated Capacity, Fraction Regd Volume ; * Heat Capacity, (Btu/°F ft height) of gion £t3/tt height Btu/°F £t height M Total 1. Inner shell 20 in. sched L0 pipe 0'?5 - 19 0.03% 0.0k 2. Tubes 143 0 110 0.196 0.23 3. Intermediste shell 3 8T | 0.510 0.60 L. Outer shell 019 ; 61 ~ 0.109 - 0.13 Total 6.8 T 0.849 1.00° p = 0.32 Ib/ifi.s = 553 1S/rt° Cy -<>n;anvn» | 'C!olumetric heat capacity pC TT.I& Btu/fts F of Kssteuoy X oL The steady-state temperature profiles across the tube annulus, Fig. 1k, show 1little curvature. The profile for the case when internal surface emissivities are 0.2 was approximated, by inspection, with a straight line. . Using temperatures taken from this straight-line approximation, an average annulus temperature, 6 __, was computed as outlined on Fig. Il. ann D i temperature at R, Ri =R = R0 and - —t ] average temperature in the tube annulus radius at which BR = 0 eR V = volume, per unit height 9{———- \ S Ro g Ro 2 QR av. 2 ., BR RDR \ R - i i elz = 8 v B - o (’o - %) If the temperature varies linearly with radius, «— Annulus . ) Bi(R - RO) - BO(R - Ri) QR = (R; - R)) 1 2 2 2(R. 6 —R.8,) R 6. —R 5, s o0 11d° . (R, - R,) Fig. 11 The location of'fil was taken to be at R = 25 in. 3 ay 95 . Using this value of R = 25 in., a simple two-shell model of the heat exchanger, Fig. 12, was adopted 32.75 in. = 2.73 £t (see Fig. 2) 17.13,ft2/ft o 8 & o 25 in. = 2.08 £t (see Fig. Il) 13.1 ft3/ft II Il : ‘Annulus Shell (equivalent to tubes and inner shell) (a) Heat generation -- T7% of total in the heat - rate exchanger Btu F-ft of height (b) Heat capacity 129 = Intermediate Shell () Heat generation -- 23% of total in the heat rate - exchanger Btu ‘F-ft of height (see Table I1) (b) Heat capacity - 287 Fig. I2. Radiant transfer from the annulus shell, surface Ay, to the inter- mediate shell, surface Az, 1s evaluated with this equation: %Hj"flaaAlcw 9) Bwhm .o (1-1) = interchange_factor for radiation transfer from A, to A 7 N n | .9, = average annulus temperature, °R O = temperature of the inner surface of the intermediate shell, °R "~ | S B . 0 = Stefan-Boltzmann constant = 1730 ¥x 10”12 EEE/Pr ft °R* 96 The interchange factor, Fy_, g, for this model was estimated with fl } Eq. (I-1) by using the steady-state temperatures computed with the heat rates at 10* sec after shutdown and for the case when the emissivity % ‘of all internal surfaces is 0.2. The shell temperatures, 6, and &, were obtained from the averaged straight-line approximation and from Fig. 14, respectively. The computed value of F,_, 3 was O. 178 and Eq. (1-1) becomes Qo s = (0.178)(13.1) o (8¢ — &) = (h.o3 X ‘103)(9‘1‘ ~e) .« (I-la) 4, The heat balance equations involved in developing the peak temperature transient are: ts ta -t Total heat Heat capacit Average Heat transferred generated of the temperature from the annulus in the = (annulus change in +: 110 the intermedi- annulus the annulus ate shell t | ty | % , -tz - ta ta (I-2) rU1] = [Ua‘l + [Ual L4, t 1 and ta ta ts . Total heat Heat transferred| Heat capacity| |Average temp. generated in + from the annulus = lof the change in the the inter- to the inter- intermediate intermediate mediaste shell mediate shell shell shell tl tl —tl t2 t3 ta W], W] - [u] ta 1 1 , £y Heat transferred from the inter- | mediate shell to -+ | the outer shell and thence to the surroundings _ ty tz + (1-3) » ] ty ny 97 In the above, t1 and tz denote any arbitrary time interval. These equations, involving both temperatures and heat transfers, were satisfied by cut-and-try iteration. ' On Fig. 15 it can be seen that the transient peak occurs at slightly more than 10* sec (~ 3 hr) after shutdown and drain. This time period was subdivided into several increments and the manner in which the above equations were applled is descrlbed below. A. From O to 1000 Sec- _ 7 1000 . . _1lo00 Eq. (I-2): Uy = Ué] ' o 0 \ o o L 1000 1000 Eq. (1-3): : o Ug , | = Us - To | 0 1000 1000 and Ua = Ue = O o 0 During the first 1000 sec (17 min) after shutdown and drain, the tempera- ture differences between the annulus and the intermediate shell and the outer shell are small. In these circumstances, little heat will be trans- ferred and the pesk temperature in the annulus will tend to follow curve B in Fig. 15. At 1000 sec after shutdown the annulus is transferring to the intermediate shell -about 20% of the heat being generated within the annulus. - This approx1mate rate was computed with Eq. (I-la) with temper- atures taken from curves’ B and C on Flg 15 B. From 102, Sec to 5 x lOa Sec | B Sxioa o pX10* .5x10° Eq. (1-2): U?]' = U + Us T 10° 10*° 10® | © 0 a5%10° o5x10° w5x10° 108 - 10° - 10% o 45x10° _ | and UsJ = . 108 98 During this 4000-sec interval, subdivided into two equal intervals for the computations, the heat transfer from the annulus to the intermediate shell was taken into account. : It was assumed that the heat lost by the annulus is transferred to the intermediate shell. The peak temperature in the annulus will, therefore, become less than curve B, Fig. 15, by an amount proportional to the heat transferred from the annulus and the average temperature of the intermedi- ate shell will rise above curve C. Note that, because of its large heat capacity and lower internal generation rate, the average temperature of the intermediate shell rises quite slowly and it is incapable of trans- ferring appreciable heat to the outer shell. Therefore, during this period, it was assumed that all the heat transferred from the annulus to the shell is retained by the shell. €. After 5 x 10°Sec All the components of Eq. (I-2) and I-3) were considered. ‘The compu- 7 tations of heat transferred from the intermediate shell to the outer shell . included the simplifying assumption that the outer. shell temperature re- mained constant at 1200°F, the initial temperature of the system. The thick intermediate shell is & good heat sink and intercepts all the heat from the annulus. Moreover, it is a poor radiator and must develop an appreciable temperature increase over the outer shell temperature before it can transfer an accountable amount of heat. The outer shell, on the other hand, is thin (0.5 in.) and, with an outer surface emissivity of 0.8 it is a good transmitter and radiator of such heat that it receives on its inner surface. 1In an actual situation we would expect the outer shell temperature to decrease, beginning immediately at shutdown. It would not begin to rise until the intermediate shell outer surface temperature had increased to a level that transfers substantial heat outward. Note, on Fig. 14, that the steady-state temperature computatlon at 104 sec after shutdown shows adjacent surface temperatures of 1940°F and 1200°F for the intermediate and outer shells, respectively. From the transient calculation, the intermediate shell temperature is estimated to be from 1750°F to 1800°F at this time. This lower temperature will reduce the heat radiated to the outer shell and, therfore, the outer shell temperature will be less than the assumed value of 1200°F. From 5 y 10® to 1.1 x 10* sec the computations were based on time increments of 2 x 10® sec. At 1.1 x 10* sec the rate of change of heat generation had been reduced to a value for which a final time increment of one hour was reasonable. The computations were terminated at 1.46 x 10% sec (4 hr) at which time it was evident that the transient had turned over and system temperatures were beginning to decrease and approach the steady-state values. : . The generalized heat balance terms, U; to Us, incl., in Egs. (I-2) and (I-3), will now be specified in detail. U, and Uz are obtained from Table l and/or Fig. 5 with the fractional amounts, T7% and 23%, respectively, from Fig. 7. The remaining terms are established by iteration. o 9 Thelequations for Uz and Ug are simple and straightforward: _ ty Ca' = heat capacity of the annulus, A6, see Fig. I1, is the change in the average annulus temperature during time interval, tp - t;. Note that the peak temperature in the heat exchanger will be slightly above @ because of the gradient in the annulus. With the annulus trans- ferring heat at the generation rate existing 10* sec after shutdown the increase is approximately 75°F. ty _ ¢, = heat capacity of the intermedi- Us:) = Cis (A%)] : ate shell_. oty ty — _ o AB; = change in the average tempera- ture of the intermediate shell. The average temperature of the thick (2.5 in.) intermediate shell is, during the transient, appreciably dependent on both space and time. From Fig. 6 it is apparent that most of the gamma heat deposition takes ‘place near the inside surface. The radiant heat received from the annulus will be deposited directly on the inner surface. The net effect, of course, is to raise the temperature of the inner surface a- substant1al amount above the average value, &, that must be used to evaluate Ug. However, the inner surface temperature, @y, is the effective heat sink temperature used in Eq. (I-1) when radiant transfer from the annulus is being calculated. This difference between the average and inner surface temperatures was not caleulated directly as a function of elapsed time; instead, the approximate transit time for heat flow through the slab was estimated. Specifically, the case considered was an infinite slab, 2.5 in. thick, of Hastelloy N, with one face insulated. . The uninsulated surface sees a step increase in temperature. From Fig. 10-2, p. 235, and related text material in reference 28, it was estimated that the -average temperature will lag the. inner surface temperature by approxi- mately 1000 sec. This local transient effect in the 1ntermediate shell was con31dered during the computations. The total heat transferred from the annulus during any 1nterval, R -t;, is obtalned by integrating Eq. (I—l) Uaj" = amf'-@_e—_-"--m_;-m.g {t[“e;(t)]-_--[ea(fi)];}dt-: (1-4) th 100 As written, this expression presupposes the desired solution, 6 (t) and 6;(t). Therefore, it was assumed that, during each time interval, the temperature changes in both the annulus and the intermediate shell pro- gressed linearly, i.e.: 6 (t) 62 (t) A + Bt ' ; (1-5) fn M + Nt (1-6) Also, at the temperatures and temperature differences involved in this . calculation, the fourth power temperature difference in Eq. (I—l) can: be ‘approximated with negllglble* error, v1z. : {[a]- Leafifl}a-h e in which 1/2 (e;(t) + ea(t)> (z-7) G(t) — &,(t) . - (1-8) e avg A8 In terms of Egs. (1-5) and I-6) these can be written, ave =F + Gt ’ , - _(1_73) NS =J + Kt (I-8a) F=1/2 (A+M) = 1/2 [Sum of the surface temperatures at t;] G=1/2 (B + N) = 1/2 [Sum of the slopes of the surface temperature curves during the interval, (tz — t,). J=(aA-M = -[Temperature difference at t, ] "K=(B—-N) = Difference of the slopes of the temperature curveé"l during the intervel, (tz — t;). — and Eq. (I-4) becomes tz J_ 2 - 8 a U;J =P ,a M0 S E(F + Gt) + Kt(F + Gt)] at . (I-ka) ty , | _, *For exa.mple, if 91 and 6. are 1800 F and 1L00°F, respectively, the error introduced by using this approx1mat10n is 1%. "y " 101 After integration and somé algebra, Ua] =Lk TP, AlcE{T -EFGt +—F2Gt +F“t} +K{Gt +-EFGt +F2Gt +F3JG H (I-Ab) in which t = (tz — t,), hr. For the range of temperatures and the time intervals used in this problem the first two terms in each set of brackets in Eq. (I-Ub) are small enough to omit and tz Ua =L F s A o JEE‘QGtB + ffl+ K ‘:fifGta + Fagtaj . (1-ke) ta This equation was used to estimate the total heat transferred from the annulus during the time interval, tz — t,, if the temperature variations are lineasr during the interval as shown in Fig. I3. ORNL DWG. 71-601 Temperature, 8, °R ‘ Average temperature of annulus, Bl = A + Bt. T J 1 | Temperature of imner o o _ - surface of intermediate . ! e s shell, 92-M+Nt. =3 Elapsed time. tl e te, Fig. I3. 102 The heat transferred to the outer shell from the intermediate shell is estimated by the familiar equation, _ 4 4 Btu/hr-£t2 Us = A, Fo [e. ~ eos] , —=yar-Ib Ais A0 S eis Q8 i 18 ft of height 18.45 £t2/ft of height, the area of the outer surface of the intermediate shell. 18.80 £t3/ft of height, the area of the inner surface of the outer shell. the temperature of the outer surface of the inter- mediate shell, °R. 1660°R (1200°F), the temperature of the inner surface of the outer shell. € jf:?ffljf:r§7,= interchange factor for radiative transfer from an infinitely long convex inner shell concentric with an infinitely long outer shell, when the emissivities of both surfaces are equal. A'is/A'os emissivity c € = the Stefan-Boltzmenn constant. "y 10. 103 REFERENCES MSR Program Semiann. Progr. Rept Feb. 28, 1969, ORNL—h396, p. 60, Sect. 5.7.3 - Heat Removal Systems, and p. 62, Sect. 5.8 - Distri- bution of Noble-Metal Fission Products and Their Decay Heat. J. R. Tallackson, Estimated TEmperatures Developed by Af'terheat in MSER Primary Heat Exchanger, SK+E304 Rev. 3, ORNL CF 67-9-1 - (Bept. 27, 1967) E. S. Bettis and Roy C. Robertson, "The Design and Performance of a Single-Fluid Molten-Salt Breeder Reactor,” Nuclear Applications & Technology, Vol. 8, pp. 190-207, Feb. 1970. MSR Program Semiann. Progr. Rept. Aug. 31, 1969, ORNL-LLL9, p. 56, Sect. 5.7 - Gamma Heatlng in MSER Heat Exchangers. J. R. Tallackson, Calculations of Heat DepoSition in Empty MSER Primary Heat Exchangers by Gemma Radiation from Noble Metal Fission Products, ORNL CF 69-0-27 (Aug. 1k, 1969). H. E. McCoy, private communication. MSR Program Semianh;rPfogr, Rept.]Aug. 31, 1969, ORNL-4klhg, p. 183, Sect. 18.2 - Statistical Treatment of Aging Data for Hastelloy N, and p. 191, Fig. 18.10, R. E. Cleary, R. 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Kollic, "The Total Hemispherical Emittance of Platinum, Columbium—1% Zirconium, and Polished and Oxidized INOR-8 in the Range 100° to 1200°C," Measurement of Thermal Radi- ation Properties of Solids, Paper No., 38, NASA SP-31. A symposium held at Dayton, Ohio, Sept. 5-T, 1962. P. J. Schneider, Conduction Heat Transfer, Addison-Wesley Publishing ay - 1-2. O o= O\ =W 10. . 120 13. 1k, 15. 16. 17. 18. 19. 20. 21. 22, 23. 2L, 25, 26. - 27. 28. 29. 30. 31. - 32, 33.. 3k, 35. 36. 37. 39. Lo, Li. Lo, e Lk, 45, . L7. 48. 49, 107 INTERNAL DISTRIBUTION MSRP Director/'s Office, Bldg. 9201-3, BRm. 109 R. G. Affel J. L. Anderson C. F. Baes H. F. Bauman S. E. Beall M. J. Bell M. Bender C. E. Bettis E. S. Bettis D. S. Billington F. F. Blankenship R. Blumberg E. G. Bohlmann C. J. Borkowski G. R. S. W. R. C. E. J. J. F. J. S. W. J. D. A J. V. c. W 'I_ A. Ro P. -We. P. R. ,P. E. H. P. P. R. A. E. B. Boyd Briggs Cantor L. H. W. L. W. L. L. R. J. P. R. -E. P- Ho' .K. H. .Ro' G. H. H. o. N. E. G. 'C. W. P. R. J. R. Carter Chapman Collins Compere Cooke - Crowley Culler Distefano Ditto Eatherly Engel 'Férguson Fraas Frye, Jr.3 :1:=.._” Furlong 'Gabbard o Grimes o Grindell Guymon Harley Harms o Haubenreich Helms Herndon Hise Hoffman = Holz Kasten Kedl Kerr 50. 51. 52, 53. sk, 55. 56. 57. - 58. - 59. - 60, 61. 62. 63. 6L. 65. 66. 67. 68. 69. 70. - T1. T2. 73. - Th. 75 T6. . 78. 9. 80. 81. 82. 83 87. - 88. 89. 90. - ol. 92. - 93. ol 95. 96. 97-98. 99-100. 101-103. 104, - H. ORNL-TM-3145 S. 5. Kirslis H. W. Kohn R. B. Korsmeyer . T. S. Kress R. B. Lindauer M. I. Lundin R. N. Lyon H. G. MacPherson R. E. MacPherson H. E. McCoy C. K. McGlothlan H. A. McLain L. E. McNeese J. R. McWherter J. Metz R. L. Moore E. L. Nicholson L. C. Ozkes A. M. Perry B. E. Prince G. L. Ragan R. C. Robertson J. P. Sanders H. C. Savage Dunlap Scott J. H. Shaffer W. H. Sides E. G. Silver M. J. Skinner A. N. Smith 0. L. Smith I. Spiewak R. A. Strehlow J. R. Tallackson W. Terry - R. E. Thomsa D. B. Trauger G. M. 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