CENTRAL Rpg DOCUM NARCH LIBRARY ENT COLLECTION e “ AEC RESEARCH AND DEVELOPMENT REPORT ... 02 & Features of Aircraft Reactors YA T | | !II.L_ er'.‘Jthli_.llhl_il.”lh. IR [l ANALYTICAL AND EXPERIMENTAL STUD IES OF THE TEMPERATURE STRUCTURE WITHIN THE ART CORE H. F. Poppendiek N. D. Greene L. D. Palmer G. L. Muller G. M. Winn OAK RIDGE NATIONAL LABORATORY OPERATED BY UNION CARBIDE NUCLEAR COMPANY A Division of Union Carbide and Carbon Corporation POST OFFICE BOX X - OAK RIDGE, TENNESSEE . - Sy Bl l : i Bty o Wk TP s A A h e e s s i e e g oy ORNL-2198 bz C-84 - Reactors-Special Features of Alrcraft Reactors This document consists of 106.pages. Copy & of 272 copies. Seriles A. Contract No. W-T4O5-eng-26 Reactor Experimental Engineering Division ANALYTICAL AND EXPERIMENTAL STUDIES OF THE TEMPERATURE STRUCTURE WITHIN THE ART CORE H. F. Poppendiek N. D. Greene L. D. Palmer G. L. Maller G. M. Winn DATE ISSUED JAN 31 1957 OAK RIDGE NATIONAL LABORATORY Operated by UNION CARBIDE NUCLEAR COMPANY » A Division of Union Carbide and Carbon Corporation Post Office Box X Oak Ridge, Tennessee R AT . RN Vr%?f&{v 2 t&:;}fi'xr ‘?y m MARTIN MARIETTA ENERGY SYSTEMS LIBRARIES A e = | IWIWI WHIWIIWIU I I Wlfl 3 445k 0350437 & -1~ ORNL-21 "y c-84 - Reactors-% Features of Aircraft Reactors INTERNAL DISTRIBUTION 65. W. K. Ergen 66. A. P. Fraas * ; 67. N Library 68. FAL : 69. ¢} g T0. & frds Department T1. B gords, ORNL R.C. 72. B34 grg 73. B.% i ({-25) Th, R Y-12) 75. T76. B.7 T7. §° 78. - HIN@18o1 79. C. Lind - 80. 36 F. L. Culler 81. 37. A. H. Snell 82. — '83. 8L, 85. 86. . 87 L. iM. ]3‘0 88. L.iB. Ho 89, E.: 90. 9l. 92, 93. ok, 95. 96. q7. 98. 99. 100. I.. T e s 101. 57T. D. P. Gregory 102. 58. G. L. Muller 103. 59. R. D. Pesk" 10L., €0. J. C. Amos 105. 61. W. B.: Cottrell 106. . 62. 5. J. Crémer 107. 63. C. W. Cunningham 108. 64. J. H. 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Gasser o - d) ‘ , o x 246, Technica& Research Group, New York P g 27, Division of Research and Development, AEC, O 248-272, Technical Information Service Extension, Oak Ridge TABLE OF CONTENTS Page SMARY '.‘.....l..lfl.......’..‘...l.......................I......... NOMENCLATURE 4. coeveesroneanssocososcoaceocoasoencenssesocososnesss INTRODUCTION .. cieiencoreancacsessrsasoeocensenensosensosoncnocsosss MATHEMATICAL HEAT TRANSFER ANALYSES +.veeveocconorcscaccccocnoeoseoss Uncooled Core Wall Temperature Structure ....,.}.....;........... A Cooling Analysis for Variable-Gap Channel (Idealized ART) ..... Radial Fuel Temperature Structure with Wall Cdoling cesesscenannse Transient Temperature Analyses ...............é.;....;........... EXPERIMENTAL SYSTEM Pe ettt eeaiteettenesntasesatseerecnrotnaeas Technique .......l....'.‘.i.........l.............";....l........... 30 BERERR ow - Electrode GEOMEtrY veveeeeeeeeeeroreonnssoosssaseccoccooscaneseos 31 Flow Clrcult v rtereeteeeeeeesoeonoeaososcosoneeoosnnonsenenes 33 Half-Scale Core Model Tececesirettestetestesesoscesoassasnsensnss 33 Power Circuit and Instrumentation ......ceeiveeeeseeneccooeeeeens 42 EXPERTMENTAL PROCEDURE .. .uiveuseercencocecaconoenoosnnnncconeoneses Lg Calibration ....covecuriiiiiieiieieeinerersronaccsosaonnannsansenss U9 Operational TechniqUe .iueeeeeeeeeeeesocecosecocesoooeososennsss.s 50 MEAN AND TRANSIENT TEMPERATURE RESULTS vvveveocecsccnsocsocecacoeens 53 SWIrl-Flow Case; TWO PUlDS tveeeeerereroroocascocenoesoosenonsses 53 Vaned-F1low Cas€; TWO PllIDS «eueeueesrosooeonosoonescsennennnennn, 59 Swirl-Flow and Vaned-Flow Cases; One PUmD ..eeeeeeesnn.. ceesssesses 1 GENERAL COMPARISON OF HYDRODYNAMIC AND THERMAL FIELDS .............. T3 CONCLUSIONS . 4ovcooesncsoneocncesacnsssneooereossosesssscosconnooses TT ART Core ....cc0ve ®erecesseessressrenscrsssastsresasccsrrosccnnce [T RefiectoreModerated Reactor Cores in General ...cceeeescoorcecees 79 New Core Configurations .vecieieeeeeereoeeseonsosssesoseocencnnesa 80 ACKNOWLEDGEMENTS « e vveuausennsnornennensosensesssnsonaonennenneas 81 -yil- Page P & = wlectrolysis Research ..eeceees.. Ceceseseseevsesescsscstasacscracnas 02 Physical Properties of Electrolyte ...e.ceececescsosesssssscssseans 85 Materials of Construction and Flow System Components .ceceeecesees 92 Calibrations weeeeeecerccesossosocosoccssscssssoscsssnssnsssnsoses I REFERENCES .eccovecccsssosoncssssasscessscsossscssssssnsscsssssansssesces I9 i SUMMARY This report is concerned with a series of studies which describe the temperature structure within the core of the ART for several different entrance flow conditions. Both analytical and experimental techniques of analysis are used in the investigation. Mean and transient temperature fields are predicted on the basis of the mathematical behaviour of ideal- ized cores; these results are compared with experimental temperature meas- ufements obtained in a half-scale model of the ART core, within which the volume heat sources are generated electrically. | The heat transfer studies presented here reveal the following facts about the ART core: 1) Unless the core shell walls are cooled, maximum wall temperatures ranging from 1750°F to 1850°F (depending upon the type of entrance flow) will exist near the core exit. About three per cent of the heat generated within the core must be extracted to accomplish the cooling task. 2) Unless the sodium coolant flows through the cooling annuli in a uniform fashion, hot and cold spots will exist in the core shells. 3) Peak fuel temperatures at the core exit, under wall cooling con- ditions, are from 100 to 170°F higher than the mixed-mean fuel temperature (depending upon the type of entrance flow). 4) The temperature structure within the core is significantly asym- metric with respect to peripheral position when one pump is not in operation. _— "2 L 5) The core shell interface afid fuel temperatures are transient in * nature (frequency spectrum ranges from about L/2 to 4 cycles per second). It is stiggested that a greater research effort is required to determine how seriously these temperature structures influence material strength and corrosion. Some of the general principles upon which circulating-fuel re- actors should be designed from the standpoint of heat transfer and fluid flow are discussed. Several reactor cores other than the ART are reviewed, eddy -3- ‘Ffigfififli NOMENCLATURE Letters cross sectional heat transfer area, ftz thermal diffusivity, £t2/hr fuel thermal diffusivity, £t°/hr Inconel thermal diffusivity, ft?/hr distance between coolant channel walls in Figure 3, ft distance between fuel channel walls in Figure 3, ft heat capacity, Btu/l1b °F coolant heat capacity, th/lb oF fuel heat capacity, Btu/1b °F Inconel heat capacity, Btu/lb °F frequency, cycles/sec coolant heat transfer conductance or coefficient, Btu/hr ft2 °F fuel heat transfer conductance or coefficient, Btu/hr £t° OF reciprocal of the thermal diffusion length, £t 1 thermal conductivity, Btu/hr £t° (CF/et) sum of turbulent and molecular conductivity, Btu/br £t° (CF/pt) fuel thermal or eddy conductivity, Btu/hr £1° (°r/ft) Inconel thermal conductivity, Btu/hr £t2 (°r/£t) channel wall thermal conductivity, Btu/hr £t° (°F/ft) total axial length of channel or core, ft coolant mass flow rate, lh/hr fuel mass flow rate, lb/hr q qcooling qfuel 4 r tey t, (¥) tinterface m g t mo e ‘I‘Efifil'7 total electrical power generated in the electrolyte in core, > Megawatts heat transfer rate, Btu/hr - channel or core cooling heat transfer rate, Btu/hr heat generation rate within volume of fuel, Btu/hr cooling heat transfer rate at interface 1 in Figure 3, Btu/hr distance from channel center, ft distance from channel center to where the reference temperature td is stipulated, ft one-half distance between channel walls, ft breadth of channel walls in Figure 3, ft temperature, °F a uniform step function temperature distribution, Op mixed-mean-coolant temperature, oF mixed-mean coolang temperature at entrance of channel, °F - fluid temperature at channel center,-oF °F a reference temperature at radius Ty mixed-mean fuel temperature, p mixed-mean fuel temperature at entrance of channel, °F initial temperature distribution, °F | fuel-Inconel interface temperature, p mixed-mean fluid temperature, °F mixed-mean electrolyte temperature at entrance of core model, 0F mixed-mean electrolyte temperature at exit of core model, °F * uncooled channel or core wall temperature, F fuel-wall interface temperature in Figure 3, °F coolant-wall interface temperature in Figure 3, F total temperature fluctuation, °F axial fluid velocity distribution, ft/hr mean fluid velocity, ft/hr mean vectorial fluid velocity, ft/hr radial volume-heat-source distribution, Btu/hr ft3 3 mean volume-heat-source, Btu/hr ft mean volume-heat-source of coolant, th/hr ft3 volume-heat-source of fuel at channel center, Btu/hr ft3 mean volume-heat-source of fuel, Btu/hr ft3 radial volume-heat-source distribution in fuel, Btu/hr ft3 radial volume-heat-source distribution in Inconel wall, Btu/hr ft3 mean volume-heat-source of channel wall, th/hr ft3 axial distance from core entrance, ft ¥y coordinate which is normal to the x coordinate, ft thickness of Inconel wall, ft weight density, lb/ft3 fuel weight density, lh/ft3 Inconel weight density, lb/ft3 channel wall thickness, ft eddy diffusivity, £t>/hr a mean eddy diffusivity of a high velocity fuel eddy, £t2/hr time, hr kinematic viscosity, fta/hr coclant kinematic viscosity, ft?/hr fuel kinematic viscosity, ft?/hr current density, am.ps/in2 Terms Wiid h 4r Nu, = fk , Fuel Nusselt Modulus for channels f yc_ v Pr = 2 Prandtl Modulus Y,C .V Pr, = —ELL | Fuel Prandtl Modulus hig u hro Re = v , Reynolds Modulus‘for channel ficab Re = v’ Coolant Reynolds Modulus for channel c ushro ReS = v , Vectorial Reynolds Modulus for channel or core fisfhro (Res)f = =5 , Vectorial fuel Reynolds Modulus for channel or core f T = (tf - tc) Ty (tfi' tci) N =5 lc “m 1c £ pf ¢ pc 2 o _ Wfbfs ] chcs ] Wwas Dp cpf o, cpc B, cpc U Overall heat transfer conductance or coefficlent, th/hr 't Normalized vectorial velocity profile Ko i 2 oF -7- Viod) r p = 0 W Wb il W c AtVHS - The wall temperature rise above the mixed-mean fluidotemperature ¢ that exists for the coolant with no wall heat flux, F AmVHS The wall temperature rise above the mixed-mean flgid temperature f that exists for the fuel with no waell heat flux, F //AthS Dimensionless wall-fluid temperature difference —}2 for a parallel plates system with a uniform \ ko uniform W(r) volume heat source and no wall heat transfer AmVHS£ Dimensionless wall-fuel temperature difference —> for a parallel plates system with a uniform w.r volume heat source and no wall heat transfer f o uniform W (reference 2) kf f A‘tVHSf Dimensionless wall-fuel temperature difference — for a parallel plates system with a nonuniform Wfro volume heat source and no wall heat transfer nonuniform W (see section on Mathematical Heat Transfer k f f Anslyses) to -t Dimensionless wall-fluid centerline temperature 7 r2 difference for a parallel plates system with no f o wall heat transfer n arallel plates T t -t m Wors parallel plates ke Dimensionless fluid temperature above the mixed- mean for a parallel plates system — 8- vi%d INTRODUCTION During the period 1953-1954, the ANP Project made the decision to de- sign and construct a 60-Megawatt circulating-fuel reactor of the reflector- moderated type which was named the ART (reference 1). The circulating fuel flows into a thick annular core whose flow cross-sectional area increases by a factor of four from the inlet to the equator, and then decreases by a factor of four from the equator to the core exit. A preliminary heat trans- fer analysis of the proposed core configuration was conducted at that time. It was shown that the ART core would have certain unique thermal character- istics which would perhaps be undesirable. These characteristics were identified as follows: 1. Large Radial Temperature Differences Within the Fuel Mathematical temperature solutions for a simplified flow system revealed that significant radial fuel temperature differences would exist in the reactor core primarily because the volume heat sources within the fuel were high and the mean thickness of the fuel annulus was great (reference 2). The core shell wall tempera- tures were so high that a wall cooling system capable of extract- ing several per cent of the heat being generated within the core was required. 2. Asymmetric Temperature Core Shell Structure From elementary fluid flow considerations, it became apparent that flow asymmetries could exist under certain circumstances in the fuel passing through the core or within the sodium flowing in the . 'k;_::i wall-cooling annuli that had been proposed (reference 3). Under s -9~ Nl such circumstances, asymmetrical core shell temperature dis- tributions would be established, giving rise to hot spots. 3. Transient Temperature Field On the basis of fluid flow phenomena, it was believed that the four-to-one area expansion ratio in the northern hemisphere of the core would, in general, create unstable flow within the ART fuel annulus. The combination of a nonuniform radial tempera - ture profile and an unstable velocity field would, of course, generate a transient temperature field that could initiate cyclic thermal stresses in core shell and heat exchanger tube walls. One of the first steps taken in evaluating the abeve problems vas to study the fluid flow in simple systems that in a sense approximated the actual ART fuel annulus. Nikuradse's classical experimental study of fluid flow in diverging and converging channels (reference 4) was used to describe the flow features in the northern and southern hemisphere of the ART core for the straight-through flow condition (reference 5). On the basis of Niku;adse's work, flow asymmetries and transients were predicted to be pre- sent in the core for this case. The investigation of fluid flow between curved channels by Wattendorf (reference 6) yielded fundamental information on velocity and eddy diffusivity distributions which was used to estimate the asymmetric hydrodynamic structure in the ART core for the case of super- posed rotational flow (reference 7). In 1954 the phosphorescent particle technique was first used to study the flow features in a quarter-scale model of an early version of the ART core. For stralght-through flow, large reverse-flow layers were found to exist on the outer core wall (reference 8); these were typical of the flow separations found by Nikuradse in large-angle diverging channels. When a significant rotational component was superposed on the axial flow, a reverse- flow layer next to the inner wall in thé northern hemisphere was observed (reference 9), These flow visualization studies as well as a quantitative investigation of the velocity structure in the core (reference 10) also demonstrated that the flow was generally transient in nature because of hydrodynamic instability. These data substantiated the earlier belief that flow transients would exist in the ART core and supported the prediction that corresponding temperature transients would also be present. Detailed information on this hydrodynamic research, chiefly with quarter-scale models, is to be summarized in ORNL-2199. Mathematical analyses of the temperature structuré in an idealized ART core with sodium wall cooling were carried out (references 11 and 12). De- terminations of cooling requirements and sodium flow rates were made. From these analyses maximum fuel-Inconel and sodium-Inconel interface temperatures at the core exit were calculated. The presence and magnitude of the high temperature peak within the fuel a short distance from the core walls was also described. Inconel-fuel interface temperature fluctuations in the ART core shell and heat exchanger tubes were considered. Estimates of interface temperature fluctuations under conditions of momentary flow stagnations and high-velocity flow instabilities were made. In order to determine information about the asymmetries in the mean temperature structure within the ART core and wall and fluid temperature “-“3 .‘i“ — LN £ - 1. W fluctuations, it was decided to obtain experimentally the core wall and fluld temperature structures. Several types of entrance flow conditions wvere studied in a hqlf-scale core model for the uncooled-wall case. The volume heat source was generated electrically within an electrolyte which circulated through the core model. The experimental mean and transient temperature fields determined in this system were generalized and compared with predicted temperature fields (references 13 and 14). After the detailed analytical and experimental descriptions of the mean and transient ART core temperature structures presented here, the in- fluence of the temperature field on structural integrity will be considered. Certain fundamental research on corrosion and material strength is suggested in view of these heat transfer studies. — -12- oA MATHEMATICAL HEAT TRANSFER ANALYSES 1. Uncooled Core Wall Temperature Structure It was determined from the ART hot critical experiment that, on the average, the volume heat source at the core wall was two times as large as at the centerline. Thus, a new radial temperature solution account- ing for the source variation in a parallel plates system was derived. An earlier analysis (reference 2) only accounted for a uniform radial source distribution. The boundary value problem is defined by the following equations: u(r) g& = 3 [a + €(u, r)] g% + Wy 7cp a9 (. - - (1) Th (r = ro) =0 t (r = rd) = t, From the activity data obtained in the hot critical experiment by A. D. Callihan et &l, it was determined that the averaged, ;adial power density distribution could be represented satisfactorily by a hyperbolic cosine function (see Figure 1). This power density function together with the generalized turbulent velocity profile was substituted into the above differential equation. The solution of this boundary value problem for established flow was obtained (reference,izj, and it was found that the resulting uncooled-wall temperature abovg the mixed-mean fluid tempera- ture was more than twice as great as the corresponding temperature differ- ence in a uniform volume-heat-source system. The two temperature profiles in dimensionless form afe shown plotted in Figure 2 for Re = 100,000 and - ¥Pr%=’§ which are representative of ART conditions. -13- ORNL=~-LR-DWG, 17989 LOCAL ACTIVITY/ CENTERLINE ACTIVITY AND W/ WE 2-6 I I o 2.4 2.2 o 2.0 {8 ° i ‘.6 — - - w_¢_ = cosh r k,p —\ OA {.49 4 L~ o A 2 P o A /o 10 pmo—"t"2T" o 08 RELATIVE ACTIVITY DATA (CALLIHAN ET. AL.) 0.6 A 10in. LEVEL O EQUATOR 04 0.2 o I 0 0.2 0.4 0.6 0.8 {.0 ¢ p WALL Fig. 1. Activity Data for ART Core and a Simplified Radial Volume - Heat - Source Distribution -14- ORNL-LR-D!/G. 17990 3.0 A 2.2 \ 2.0x 1079 \ C R _t-te 16 w_. cosh roKop wmroz wc K {4 \ ) {.2 N 10 xio"‘\ \ - AN L\ N N 0.2 N 0 1 1.0 0.8 0.6 0.4 0.2 0 WALL i ¢ ’ "o Fig. 2. Dimensioniess Radial Temperature Distributions in Parallel Plates Systems with No Wall Heat Transfer (Re=100,000 and Pr: 4) - ¥ : . ' - 2. -15- A Cooling Analysis for a Variable-Gap Channel (Idealized ART) A variable-gap channel representing the spiraling annular passage through which the fuel flows in the ART with the swirl-flow entrance was studied. The variable-gap channel was divided into a series of channels with parallel walls, having different wall spacings. The heat transfer analyses of these individual channels were performed as described previously in ORNL-1933. The idealized system shown in Figure 3 for each channel is defined as follows: a) b) c) d) e) £) Thermal and hydrodynamic patterns are established (long channels). Steady state exists. Volume heat sources exist in the fuel, wall, and coolant. Physical properties are invariant with temperature. The fuel channel is being cooled nonuniformly along its length by the coolant. The walls of the fuel channel are thin. The three equations describing heat flow from the fuel to the coolant can be expressed as, dg, = h.dA (AtVHS + tp - tl) f iz‘wa k_ Gy + g dh =g () - b)) dg, + W 5 dA = h dA (1:2 -t - AL, ) c From equations (2), (3), and (4) one can obtain, dql = Usdx (1;f -t + AtVHsf - AtV.Hsc - Atw) (2) (3) (%) (5) ORNL-LR-DWG. 17991 _]6.. COOLANT X 3 1 FUEL p A 1 COOLANT —— 8 — Ky % t t2 Q * Fig® 3. An Element of the Varioble-Gap Channel (Idealized ART) The two additional equations arising when making a heat rate balance on the two fluld streams in a length dx are, Wb dA m_c _ M Ml a9 =3 2 ©) dg, + W b dA = m.ccpcdtc - W b dA (7 From equations (6) and (7) one can obtain, dT = - Ndg, + M"dx (8) where, T = tf - tc N =2 lc T om i | I pf c pc 2 v Wobs _ Wébcs _ W bs ‘fi% mfcpf mccpc mccpc Upon substituting equation (5) into (8) and reducing, one obtains the solutions, | M", -NUsx M" T + AtVHsf- AtVHSC- at, = (T + AtVHSf- AtVHSc- oty - wo) e + TS (9)w 1 M" ~-NUsx M" 4 = § (To+ AtVHSf AtVHSc ot Img) (L -e ) + ¥ X (10) q, + W 8sx + W b sx 1 W ccC te " By < m (11) c pe Wfbfsx 94 b =Y “me T om,ec (12) £Opf “e Cpr 2 U ‘ £, = - B (T + Atmsf' AtVHSc-Atw) + AtVHSf+ t, (13) | N 18- v oL & w t, =t - U‘E-(T + AtVHSf- A“vnsc Axw) - on | (14) The fuel, wall, and sodium temperatures within the ART core as well as the sodium cooling requirements and flow rates were determined with the mathematical relations developed above for the following specific conditions that define the ART core with the swirl-flow entrance. Reactor fuel: Fluoride composition No. 30 with properties evaluated at 1425°F Coolant: Sodium with properties evalusted at 1125°F Wall material: Inconel Fuel power densities: Radial profiles obtained from "ART hot critical” experiment (see Figure 1) Inconel wall power density: A mean value of 5& watts/cc Beryllium power density in vicinity of sodium annuli: A mean value of 16.5 watts/cc Equivalent power density in sodium™: A mean value of 52,8 watfs/cc Mixed-mean fuel temperature rise:; About 350°F, depending upon the total reactor power and wall-cooling losses Gamma and neutron heat generated in the beryllium reflectors is carried away by sodium flowing through cooling holes and annuli. The heat gene- rated in the thin layers of beryllium (next to the annuli) flows into the sodium and hence raises its bulk temperature. In the anslysis, this heat flow was simply treated as an equivalent volume-heatesource term in the sodium itself. Although this technique correctly accounts for all the sodium heat transfer, the beryllium-sodium interface temperature is not explicitly determined. However, a separate calculation of the beryllium-sodium interface temperature shows that it lies only about 4°F above the bulk sodium temperature. gt -."i; m, = 2.25 x 10° 1b/hr (Res)f = 372,000 (footnote 2) Prf = 2.3 fi} = 60 MW per reactor core volume (3.23 ft3) Nuf = 1920 m, = 0.102 x 10° 1b/hr Rec = 125,000 From the fuel Reynolds and Prandtl numbers given above, the following uncooled-wall temperatures above the mixed-mean fuel temperatures were determined: Stymg_ . > = 4,5 x 10 7 (reference 2) Wf r, ' uniform W k f f “ves, . s — = (2.26) (4.5 x 10™7) = 10.2 x 10 W, r fk 2/ nonuniform W (footnote 3) £ £ 2. A mean vector Reynolds number for the fuel was uSéd in the analysis be- cause the maximum variation of the local vector Reynolds number was only + 12 per cent. 3. The analysis of the radisl temperature structure in the ART fuel under actual nonuniform radial power density conditions described above in- dicated that the dimensionless radial temperature difference for the nonuniform power density case was 2.26 times greater than the corres- ponding temperature difference for a uniform radial power density systenm. An entrance length analysis which is discussed in a later section of this report showed that the thermal and hydrodynemic flow layers are established by the time the fuel arrives at the exit of the idealized core. However, the whole northern hemisphere lies in the entrance region. The fact that both the local Nusselt number and A‘vns functions vary in compensating .H‘%fifirfashions in this entrance region validates the analysis there. o Rt The calculated temperature distributions in the fuel, wall, and sodium coolant streams are shown plotted in Figure 4. The sodium flow rates and cooling requirements in the variable-gap channel system per- tained to a passage having identical vall areas from which heat was transferred to the coolant streams. In the getual ART annulus systenm, the inner asnd outer wall areas are not ideatieal; thus, the results of the variable-gap channel snalysis were apportioned to account for the fact that the ART outer wall area was larger thaa the lnner wall area. The flow rates and cooling requirements so obtained follow: flow rate in inner sedium annulus: O0.071 x 196 1b/hr 6 1b/hr flow rate in outer sodium ennulus: 0,133 x 10 total cooling power capacity of sodium stream in Ipnmer annulus: 0,89 MW total cooling power capacity of sodium stream im outer amaulus: 1.65 MW total cooling power capaclty of both sedium streams: 2.54 MW TEMPERATURE (°F) 1600 / //“"‘__—_ i e 1400 / : - = // 1200 // —] 1, /// // B — 10000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 AXIAL DISTANCE (X/L) Fig.4. Temperature Structure Within Idealized ART Core. -lz_ 3. Radial PFuel Temperature Structure with Wall Cooling In order to illustrate the nonuniformity of the radial fuel tempera- ture profile at the exit of the reactor core, the following analysis is presented. The radial fuel temperature profile for the uncooled wall case, under the representative ART conditions of Re = 100,000 and Pr = 4, i1s graphed in Figure 5. 1In order to maintain the Inconel-fuel interface temperature at the core outlet at approximately SOOF below the mixed-mean fuel temperature, about 3 per cent of the heat generated in the core must% be removed by the wall coolant. The radial fuel temperature profile for this case was obtained by the superposition process described in reference 11 and is graphed in Figure 5 for purposes of comparison. Note that the peak fuel temperature above the mixed—mean fuel temperature in the wall-cooled case was still 62 per cent of the corresponding peak temperature difference . for the uncooled wall case. An enalysis of the degree of decay of the fuel temperature peak, for the wall-cooled case, in the short passage between the core exit and heat exchanger entrance will be discussed in a following section of this report. -23- ORNL-LR-DWG. 3.0 l - Re = 10° | Pr= 4 W= Wq:_ cosh roky p quoling —_— = 3. { PERCENT ] uneI 2.0 _——NO WALL COOLING t -1 i — 10 . Wil N k WALL COOLING 0 -1.0 - 1.0 0.8 0.6 0.49 0.2 0 P Fig. 5. Radial Fuel Temperature Distributions in a Parallel Plates System with and without Wall Cooling Ve - - 4. Transient Temperature Analyses The hydrodynamic studlies conducted with the quarter scale ART core models revealed that, under unstable flow conditions, a series of different - types of flow phenomena existed in the vicinity of the core-walls; high velocity layers, stagnant layers, and reverse flow or separation iayers could be identified at different moments during the complicated turbulent history. Two specific transient processes will be considered; namely, the cases of a momentary flow stagnation and a high velocity eddy for an Inconel- fluoride system will be analyzed. -a., Momentary Flow Stagnation Postulate that, at time equal to zero, the fuel contiguous to the Inconel wall remains perfectly stagnant for a short period of time (perhaps several tenths of a second). The problem is to determine the . transient temperature structure in the Inconel wall, in the adjacent fuel, and at the 1nterface between the two. The equations which definel this @oundary value problem follow: 2. W (y) gg = aI §;§-+ ;%E‘;? 0YI (Fuel) £ dy 7fcpf t(e = 0, y) = ti(Y) (15) “k g% (8, y = 0) =h, [t(e,y = 0) - tc] - -25- e An analytical solution of this set of equations would be 1aboriousu and was actually not required for this specific study; thus, a solu- tion was obtained very quickly by the graphical technique. A 0.2 second flow stagnation in the fuel with a volume heat source of 2 kw/cc created a 208°F temperature rise within the fuel at a sufficient dis- tance from the wall where heat conduction was no longer important. However, the Inconel-fuel interface only increased by 48°F during the seme time interval because of the transient conduction of heat into the Inconel. Thus, in the case of flow stagnation in an Inconel-fuel sys- tem, the wall-fuel interface fluctuation is only about one-quarter of the value occurring in the fuel at some distance from the wall. b. High-Velocity Eddy Consider the case of a momentary high-velocity eddy which flows past the core shell wall in the vicinity of the equator where the in- fluence of the divergent flow exists. The problem is to estimate the transient temperature structure in the Inconel and fuel for such a case. The mean boundary layer thicknesses and turbulent conductivities for the swirl-flow case were obtained from the fundamental velocity data for simple ducts and converging and diverging channels. Some of the results are shown in Table ;fi A mathematical solution to a slightly simplified boundary value problem was derived, however, which could be used to closely approximate the transient temperature behaviour of this system. - - TABLEH‘ Region Thermal or Eddy Conductivity’, Btu/hr £t (°F/ft) Inconel Shell 13 Laminar Sublayer 1.5 (0 < y<0.001) Buffer Layer 12.8 (a mean value) (0.001" < y < 0.0058") Turbulent Core y = 0.0058" 56 y = 0,182" (1/10 of mean radius) 1550 ¥y = 0.912" (1/2 of mean radius) 4270 5. The eddy conductivity of a fluid is the sum of the molecular and tur- € bulent terms, keddy = k(1 + v Pr). 'Ejfi&gi R - On the basls of the hydrodynamic research conducted in quarter- scale models of the ART, i1t is believed that the sudden high-velocity fluctuations observed near the core boundaries were due to momentary high-velocity eddies which greatly increase radiasl momentum and heat transfer during thelr existence. The following boundary value pro- blem represents an idealized description of the transient temperature structure during this event. xu _ Pt 3 "~ 8 32 y y - (16) 3 _ o 8 T °r 3 y £(y,0) = t_ y =0 lim t(y,8) = t, y——>= = Tt is assumed that the high-velocity eddy suddenly presents the Inconel and thin laminar sublayer and buffer layer with a new slab of fuel having a new higher or lower uniform temperature above the initial datum, ta' This new slab also has a higher eddy conductivity represent- ative of a region a short distance from the wall where the eddy originated. The source terms in both the Inconel and fuel have been neglected here. - -28- W : . -.4 A layer of Inconel having the same combined thermal resistance and capacitance as the thin laminar sublayer and buffer layers was added to the Inconel wall. The solution to this houndary value problem is proéaic and can be found readily in the literature (reference 15). The ratio of the actual Inconel-fuel interface temperature6 to the uniform fuel step function temperature, t g) Was evaluated for several dif- interfza.ce‘/t ferent eddy sizes. A typical one, which was defined by an eddy coming from 0.18 inch from the wall (a mean kf equal to sixty times the value for Inconel) was t = 0.79 in 0.2 second. interface/ta The high velocity eddy analysis presented above is based on a con- servative system. From photomicrographs of the surface of Inconel ex- posed to fuel, it was observed that the surface roughnéss was of the same size as the thickness of the calculated laminar sublayer. Many hydrodynamicists believe that if this is the case, then there would be no laminar sublayer. Further, the layer thickness used in the above analysis was calculated for the average flow condition; actually, it would be tfiinner because of the momentary higher local velocities. The thermal resistance and capacitance of the laminar sublayer as well as the buffer layer were so small that the calculated ratio, tinterface/ta’ given above would only increase 12 per cent if these two layers were neglected. It is also pointed out that in the analysis it was postulated The actual Inconel-fuel interface was located at y = - 0.009 inch; the . 9 mil layer represented the equivalent fuel laminar sublayer and buffer layer described above. - -29- LR that a slab of fuel was suddenly exposed to the boundary layers and the Inconel; however, the high-velocity eddy would continually supply new fuel, thus further raising the temperature ratio calculated above. Finally, calculations have been made which show that the thermal con- ductivity of a layer of Inconel, penetrated uniformly with subsurface corrosion volds, can suffer a significant reduction. For example, the reduction in conductivity of a uniformily pitted layer having a void volume of 30 per cent would be 38 per cent. The above calculations indicate that high velocity eddies of the type pictured here can transfer heat so effectively that Inconel-fuel- interface temperature fluctuations are not drastically reduced below the temperature fluctuations in the fuel, [ -30- sl EXPERIMENTAL SYSTEM l. Technique In order to determine a more detailed description of the mean and transient temperature structure within the ART core, it was decided to perform a heat transfer experiment in a half-scale model of the core. The most effective way of generating heat within the volume of an aque- T ous solution' flowing through the model was found to be the "resistance heating" technique, fising alternating currefit. This method was :found to possess the following advantages: a) High specific powers are attainable. b) Fluid and surface temperature measurements can readily be made. c¢) Proper electrode spacing and voltage regfilation yield control of the power density distribution. d) Power densities can be accurately determined from voltage and current measurements. In order to obtain sufficiently large temperature differences within the electrolyte flowing through the core, intense volume heat sources had to be generated. It was observed, hdwever, if the alternating current densities at the electrodes of the system were in excess of a certain value, then undesirable hydrogen and oxygen liberation would occur at the electrode surfaces. Hence, it was necéssary to so adjust the electrical 7. Other methods of generating volume heat sources were studied, but were not found to be readily applicable; they were induction, dielectric, ultrasonic, and radiant heating. | V . :;-‘:" St — }n F Ay e fi . — - resistivity of the electrolyte, by varying the specific gravity, so that a meximum current density just below the critical value for gas generation was obtained. It was also found that platinum electrodes made it possible to obtain higher current densities. Further details on electrolysis re- search can be found in Appendix 1. 2. Electrode Geometry It was found essentially impossible to create an electric flux field within the electrolyte flowing through the core which would generate g volume heat source that would peak sharply at the core wall as previously shown in Figure 1. It was possible, however, to create.an electric flux field which was nearly uniform throughout the whole core. It is possible to transform the experimental temperature profiles obtained in the uniform power density case to those corresponding to the nonuniform power density case (ART) with the aid of the mathematical temperature solutions carried out previously for these two systems, The electrode arrangement used in the experiment is shown in Figure 6. It can be shown that if the axial potential gradient is a uniform value throughout a conducting system (linear voltage drop), & uniform volume heat source will be generated. The electrode arrangement in Figure 6 Yielded a potential field that had an axial potential gradient that was within + 6 per cent of being uniform (excluding the extreme ends of the potential field); this means that the volume heat source was within + 12 per cent of being uniform. The potential difference of each electrode set was adjusted such that the potential drop between adjacent electrodes re- - mained constant. Aes v s . %.‘éa{!;’ ! v g ENTRANCE UNCLASSIFIED PHOTO 26304 EXIT Fig. 6. Electrode Arrangement, Voltages, and Potential Field for Half-Scale Core. sy —ze- — - A dilute solution of sulfuric acid (1% by weight) was used for the t circulating electrolyte. Some of the physical properties of this solution are presented in Appendix 2, 3. Flow Circuit A perspective drawing of the ART volume-heat-source system is shown In Figure 7. The components consist of an electrolyte reservoir, two centrifugal pumps, flow-control valves, and orifice meter, the half-scale core model, and a water-cooled heat exchanger. The entire flow system was enclosed by plywood and Plexiglas walls in order to protect the opera- tors from sulfuric acid in the event of a system leak. The electrolyte was pumped from the reservoir to the test section (where heat was generated within its volume) to the heat exchanger (where it was cooled) and finally back to the reservoir. Information on materials of construction and flow system components, excluding the core model which will be described next, can be found in Appendix 3. 4. Half-Scale Core Model Figure 8 shows a cross-sectional view of the core model including entrance and exit sections. A transparent Plexiglas pipe was located at the core entrance so that the presence of entrained gas in the electrolyte could be observed. A mixing chamber used to obtain a mixed-mean fluid temperature was also located in this pipe. The two flow control valves located above the pump volutes were used to simulate single and dual ART pump operation. A view of the pump volutes and the core entrance region 1s shown in Figure 9. The flow either spiraled through the core unguided (swirl-flow entrance) or was guided by a set of turning vanes (vaned-flow " Pl PFAND LIGHT ENCLOSURE HALF SCALE CORE MODEL — PIPE AND LIGHT SETwEE ORNL-LR-DWG. 17994 ORIFICE HEAT EXCHANGER ol |_———RESERVOIR - < PLEXIGLAS FRONT WALL -rg_ PUMPS MANOMETER Fig 7. ART Volume-Heat-Source Experimental System ORNL-LR-DWG 1CB19A t FLOW IN ENTRANCE TC MIXING CHAMBER THERMOCOUPLE THERMOCCUPLE PERFCRATED PLATES BOLTARON VALVE HONEYCOMB STRAIGHTENER PUMP AND HEADER MOCKUP ALTERNATE ENTRANCE SYSTEM THERMOCOUPLES LOCATED ON ISLAND AND SHELL WALLS ELECTROCES (24) {SLAND SHELL PERSPECTIVE VIEW CF MIXING CHAMBER BAFFLES (TYPICAL) EXIT MOCKUP THERMOCOUPLE ———— FLOW OUT THERMOCOUPLEJ EXIT MIXING CHAMBER Fig. 8. Cross-Section of Half-Scale ART Core Model Including Entrance and Exit Section. -gs... UNCLASSIFIED PHOTO 26251 ‘ ELEG D 41 12 | R AT oy . W T EE T e | Fig. ?. Top View of Pump Volutes and Core Entrance. — - entrance). The turning vanes in the core entrance are shown in Figure 10. #Wall temperatures within the core model were determined by forty No. 36 » W gauge copper-constantan thermocouples, located about 0.030 inch below the i, % Plastic surface, and twenty-four No. 30 gauge platinum-platinum + 10% rhodiumi’i thermocouples which were honed flush with the wall surfaces. In all cases, the junctions fiere of the butt type, and the couples were positioned in a plane parallel to the wall-fluid interface. Figure 11 shows a view looking down into the core from the entrance. This photograph was made after the first two sets of runs were completed. The simulated bellows on the island is observed in the center, and around it are seen the dark Platinum elec- trode rings in the outer wall of the core. Several copper-constantan ther- mocouples may be séen through their transparent Araldite resin coverings. The copper-constantan thermocouples were spaced st five axial stations; four were loecated 90o apart at each station on the inner and outer walls. The platinum-platinum + 10% rhodium thermocouples were spaced at four axial stations; three were located 120° apart at each station on the inner and outer walls. Table 2 gives the couple positions. Platinum tubes, 1/16 inch in dismeter, with platinum + 10% rhodium wires inside joined at the tips were fashioned into thermocouple probes whose Junc- tions were positioned in the flow stream L/8 inch below the exit plane (see Figure 12). The probe tips were rotated hSO from the vertical so that they faced in the general direction of the rotating flow from the exit of the core. An exit section similar to the ART exit can be seen in Figure 8; a mixing chamber to measure the exit mixed-mean fluid temperature iz also Do ly ol — Fig. 10, Pump Volutes and Core Entrance Region with Top Removed, Mounted on Core Test Section with Guide Vanes in Entrance. | PHOTO A -gE- i g‘ Fig..11. View of Inside of Core Through Entrance. B e e i e e e e e e = M b o e e -l Distance from Core Midplane (inches) TABLE 2 Copper-Constantan Thermocouples 'f. 500 6.000 3.375 1.500 0.000 -1.500 -3.375 -6.000 -7.500 X Platinum~-Platinum + 10% Rhodium Thermocouples -41- _ } ORNL-LR-DWG, 17995 / DIRECTION OF ROTATING FLOW | / THERMOCOUPLE PROBE (TYPICAL) 23/64" k A ) -/ k\___‘_/_.___ 'L: / 43/64" ///////// PLANE OF CORE EXIT / ts8" 4 + \\\\\:\\ { \¥¥¥§§<~45° N Q§:* \QF\\ N Z FLOW iy . SECTION A-A mii Section Through Core Exit Plane Showing Thermocouple Probe Lo ons. ~Lo- shown. A transparent pipe through which the solution could be inspected for gas generation followed the mixing chamber. A photograph showing the assembled core model with power leads and - thermocouple leads in place can be seen in Figure 13. 5. Power Circuit and Instrumentation Figure 14 shows a schematic diagram of the electrical power system. A saturable reactor shown in the diagram was only used to control the voltages of the end electrodes at certain times. The voltages of the intermediate electrodes (3 through 22) were controlled in pairs by vari- able autotransformers. The power level was controlled by varying the strength of the acid solution up to one per cent by weight, thus changing its resistivity. The maximum total power dissipated in the test section was about 125 KW. - Figure 15 shows a photograph of the control and instrument panels. The power control Variacs are on the panels at the right with their volt- meters and ammeters. An accurate voltmeter (less than one per cent error) with a selector switch so that any electrode potential could be measured was installed later and used throughout the experiments. Accurate ammeters (less than one per cent error) were used to measure the currents drawn by the electrodes. The total electrical power dissipated within the core model was obtained by summing the individual wattages consumed by the individual electrode pairs. Mean temperature measurements were obtained with the copper-constafi£an thermocouples. The voltages of these couples were recorded on four twelve- point recording potentiometers which are shown at the far left in Figure 15; -43- } ! -l i J -l e ‘-- UNCLASSIFIED PHOTO 25940 Fig. 13. Overall View of Core Model. -44- TD-E-4589 Rev. E UNCLASSIFIED gl E;l TEST SECTION N 3= oY =000 @ 230/15 -5 W PT- % e e AT4 T3 h ~YE SchLE 0500 W 4 — FET o=-3a0 # Ses s - 08GO O-55 - ", 48920 oy J00A, LINE Fig. 14. Schematic Diagram of Electrical Power System. _— - portable precision potentiometers were used most of the time to obtain these voltages, however. The platinum-platinum + 10% rhodium thermocouples, which were normally used to obtain transient data, were also used to determine méan voitages to verify the copper-constantan measurements, Two methods of measuring temperature fluctuations were used. One con- sisted of connecting a sensitive mirror galvanometer, made by the Hathaway Instrument Company, to the platinum-platinum + 10% rhodium thermocouples (see Figure 16). Galvanometer deflections were then calibrated in terms of couplé voltages or temperatures. Motion pictures were made of the gal- vanometer deflections. The second method of measuring transient tempera- tures involved using a Brush recorder with a special isolated preamplifiers. A photograph of this system is shown in Figure 17. To protect the test section and the people working with the experiment, several automatic safety controls were included in the electrical system. The power circuit to the core model was instantaneously opened by control equipment when the following events occurred: a) reduction of electrolyte flow rate below a preset value ‘b) - reduction of cooling water flow rate below a preset value c) opening of door to room containing the volume-heat-source experiment. An alarm system immediately made known the occurrence of any of the above events. 8. This amplifier had an input circuit which was isolated from the remainder of the circuit. This permitted the detection of small varying D.C. volt- ages in the presence of high A.C. potentials. The amplifier circuit was modified so that the range of flat frequency response was increased. PHOTO 25938 e UNCLASSIFIED iy .S A Fig. 15. Control and Instrument Panels. -47- ORNL-LR-DWG. 17997 Pt -Pt+ 10% Rh TRANSIENT THERMOCOUPLE /\ -_— —_—t —t = — = = e — —TEST SECTION LENS SYSTEM L o|-——-2F LIGHT SOURCE HATHAWAY GALVANOMETER SUSPENSION -+Vq— Fig. 16. The Hothawaoy Galvanometer System UNCLASSIFIED PHOTO 26252 !‘: ".l‘J‘ '.“-l - &a}s;. #5"1 _B :y_ Fig. 17. Components of Electronic Transient Temperature Recording System. 1. EXPERTMENTAL PROCEDURE Calibration a. Brush Recorder and Hathaway Systems When all the transient thermocouples within the core model were held at some lknown, uniform environment temperature, a zero reading was obtained on the Brush recorder. The environment temperature was then raised to some new uniform temperature level and the deflection of the Brush recorder again noted. The calibration constant was there- by derived directly in degrees centigrade per recorder scale division. An alternate method of calibrating the Brush recorder was used to verify the previous method. A direct current signal was applied to the Brush amplifier and then changed by a known increment. This increment was then convgrted to a temperature change, and the Brush recorder scale deflection was noted. The calibration constant so obtained was found to be within > per cent of the one determined by the previous method; The Hathaway system was calibrated in the following manner. The output of the platinum-platinum + 10% rhodium thermocouple was ifipreséed directly upon the galvanometer suspension. The light arm deflection was noted for a given thermocouple environment temperature. The temperature 1e§e1 was then raised a known numberrof degrees, and the deflection of the light arm recorded. b. Thermocouple Response An experimental and analytical study of the response of the tran- sient thermocouples under periodic and step function conditions was — -50- b conducted. It was found that the thermocouple response itself was far greater than those associated with the Brush recorder and Hathawasy gal- vanometer suspension systems. c. Frequency Response of Recorder and Galvanometer Calibration of the frequency response of the Brush recorder was accomplished by impressing a known signal of variable frequency on the system input. The amplitude of the output on the Brush oscil- lograph was measured, and the results appear in Appendix 4 in terms of percentage of D-C response versus frequency in cycles/sec. A similar calibration of the frequency response of the Hathaway mirror galvanometer was made. The results are also presented in Appendix k. Both of these Brush recorder and Hathaway response curves show that the 60 cycle per second response is very small compared to the low frequency spectrum. d. Orifice Meter The orifice meter was calibrated by measuring the weight flow rates and manometer deflections over the range of operating conditions. The calibration for a two-inch orifice is presented in Appendix 4; a graph of the mean Reynolds number as a function of manocmeter deflection can also be found there. 2. Operational Technique Four sets of volume-heat-source experiments were conducted during this investigation. Two sets of measurements were made with a swirl-flow en- trance; in one case, both simulated pump inlets were open, and in the other _— i _— - case, one inlet was closed. Two additional sets of measurements were obtained with vanes located at the core entrance; the one and two pump flow simulation was again examined. All heat transfer and fluid flow data were recorded only after the following steps were completed in the indicated sequence: a) The system was filled with the electrolyte. b) The electrolyte was circulated through the system by means of the two pumps. c) The datum temperature of the electrolyte was maintained by an automatically controlled cooling water flow rate in the heat exchanger. d) A predetermined voltage distribution for the electrode system . was established before the power was applied. e) Power was turned on. f) A final check was made on the desired electrode voltage dis- tribution as shown in Figure 6. g) Thermal equilibrium was established in the flow system. The external core model environment temperasture was matched to the mean fiall temperature within the core in order to establish the uncooled-wall condition. During the subsequent period of data recording, 1t was observed that the mean temperature and electric flux fields were extremely stable. For example,_the variation in the mean temperature structure was less than one-quarter of one per cent. Further, only negligibly small gaseous elec- f products existed in the exit flow as detected by the Tyndall light i - L, — 52 scattering effect. A minute amount of leakage current was conducted through the external flow circuit from the core (less than 0.001 amps). o -5 MEAN AND TRANSIENT TEMFERATURE RESULTS 1. Swirl-Flow Case; Two Pumps Fifteen complete power runs were made for the core model using the swirl-flow entrance. Both flow valves were open, thus simulating the ART flow with both pumps in operation. The ranges of parameters investigated follow: 66,000 < Re < 256,000 L f\. / — 1 N VN MID-STREAM BEYOND EXIT | | | 0 1.0 2.0 3.0 TIME (sec) = 0.18 ORNL-LR-DWG. 18000 Re W w 256,000 (UNIFORM) Transient Surface and Fluid Temperatures _89_ - -59- obtained. Typical measurements uncorrected for frequency response are shown plotted as a function of axial distance in Figure 21 for the uniform pover density case. These fluctuations would, of course, be larger the nonuniform power density case. Note that the outer wall temperaté?g fluctuations are greater than those measured at the inner well; this dif- ference appears to reflect the Rayleigh stability criterion. A detailed frequency response correction is laborious because of the difficulty in determining instantaneous frequencies for the complex fluctuation spectrum. However, on the basis of a mean fluctuation Prequency of about two cycles per second, one would expect to increase the magnitude of the fluctuations given in Figure 21 by a factor of about 1.5, 2. Vaned-Flow Case; Two Pumps Six complete power runs were made for the core model using the vaned- flow entrance. Agein, both valves were opened to simulate normal ART operating conditions. The ranges of parameters investigated follow: 60,000 < ReS < 180,000 L/ 11 n T —— OUTER CORE WALL — —t /| e N | /)/ 0.9 INNER CORE WALL — e _— 08 / - t =t /// / tl'l'n:."'vni 0.7 L / / /<—MIXED MEAN FLUID 06 / 0.5 // 0.4 / / / 0.3 Reg = 131,000 Pr = 4.0 0.2 / / 0.1 // ok | 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 E AXIAL DISTANCE, X/ L e _19_ Fig. 22. Mean, Uncooled Inner and Outer Core Wall Temperature Measurements for the Holf-Scaleg ART with a Uniform Volume Heat Source (Vaned Flow Entrance) m— - completely eliminated the flow separation in that region. However, the uncooled-wall temperatures in all other regions were higher for the vaned- y LN flow case than those for the swirl-flow case because the latter case was L% “ characterized by a significantly higher vector Reynolds number, A calculation revealed that the entrance length in a simple parallel Plates system corresponding to the vaned-flow case was about 29 diameters. Since the ph&sical vectorial channel length was only 16 diameters for this case, the thermal boundary layers were about 67 per cent of the fully estab- lished values at the idealized core exit. However, the analytical, uncooled- wall temperature profile for the southern hemisphere shown in Figure 22 was carried out for established temperature conditions. Peripheral variations in the experimental uncooled-wall temperatures were again observed. Hofiever, they were generally larger than those found in the swirl-flow case. For example, the uncooled wall-fluid temperature difference, on the inner wall in the equatorial region, varied by + 90 per cent from the mean temperature difference at that plane, The experimental temperature profiles obtained for the uniform pover density case were transformed to those corresponding to the nonuniform power density case as was done previouslyf The results can be observed in Figure 23 together with the analytical prediction. Note that wall tempera-~ tures as high as 18500F would result if the walls were not cooled. Typical trangient wall and fluid temperature data for the vaned-flow case are presented in Figure 24. The frequency spectrum of the temperature . fluctuation for this case was, in general, similar to the one found for the swirl-flow case. However, at certain flow conditions in the northern . s _63_ ORNL-LR-DWG. 18003 .8 1.5 _________’( A NEAUZED ART (THEORETICAL) OUTER CORE WALL \ 1.2 e T~ f/ ‘\ /| / INNER CORE WALL t = tmi — 09 / / — tmo— tmi 7/ / /7 / flxsn MEAN FLUID /S T~ o 03 / Reg = 431,000 Ve e as e 0 0.1 0.2 0.3 0.4 05 0.6 0.7 0.8 0.9 1.0 AXIAL DISTANCE, X /L Fig. 23. Mean, Uncooled Inner and Quter Core Wall Temperature Prafiles for the Hoalf-Scale ART with a Nonuniform Volume Heat Source (Vaned-Flow Entrance) -64- ORNL-LR-DWG. 18004 | I ~<—1{ S@ec » l A\ 1 At } \l — - 0.25 —— 7 - — = — tmo~— tmi INNER WALL - EQUATOR Re, = 131,000 W = W (UNIFORM) VANED ENTRANCE - { S@C / N 1. - T[— Atg - —_— = 0.18 trno' tmi \J X OUTER WALL - EQUATOR - { seC - A\ \ A/ | et MID-STREAM BEYOND EXIT L] 0 1.0 2.0 3.0 TIME, sec. Fig. 24. Typical Transient Surface and Fluid Temperature for the Vaned-Flow Case . — 55- hemisphere, some large amplitude, low-frequency fluctuations were note in the vaned-flow case, Maximum wall and fluid temperature fluctuations,ggi averaged with respect to peripheral position, are shown in Figure 25 aéj; function of axial position; frequency response corrections were not maégi The outer wall temperature fluctuations in the northern hemisphere were significantly lower for the vaned-flow condition than in the previous case. However, wall and fluid temperature fluctuations in the southern hemisphere were somewhat larger for the vaned-flow case. These increases in fluctu- ation magnitudes appear to correspond to similar increases in the mean radial temperature differences for the vaned-flow case. ‘ The four heavy platinum thermocouple probes located just beyond the core exit were used to obtein local fluid temperature fluctuations as well as a mean radial fluid temperature distribution in that region. The tran- sient temperature distribution within a platinum probe was calculated for the case of a sudden step function increase in the temperature of the elec- trolyte flowing past the probe. A similar calculation was made for the probe on the basis that it was made of Inconel rather than platinum;l. It was shown that shortly after the step function had been applied to the two systems (about 0.03 seconds), the fluid-metal interface temperatures of both probes increased almost by the same amount. The centerline temperature of 1l. A comparison of these two cases allows one to describe the probable transient temperature behavior in the Inconel heat exchanger walls under high frequency cycling. Note that the radial wall thickness of the Inconel tubes (25 mils) and the platinum probes (35 mils) were nearly equal. L i .:_’fr"-q 4} Voo ey e ORNL-LR-DWG. 18005 1.0 0.9 0.8 Re, = 131,000 0.7 W = W (UNIFORM) 0.6 Atg 0.5 tmo~ tmi 04 _—1 INNER WALL 0.3 —— X 0.2 MID-STREAM — PROBES 0o 2 49 6 8 10 {2 14 {6 {8 AXIAL DISTANCE FROM INLET (inches) Fig. 25. Peripherally Averaged Transient Temperature Fluctuations for the Vaned-Flow Cofi . -99- o - the platinum probe (where the thermocouple was located) had increased by an amount that was 88 per cent of the temperature rise at the probe-fluid interface. However, in the case of the Inconel probe, the centerline tem- perature increased by an amount that was only 61 per cent of the temperature rise at the probe-fluid interface; for this case, the centerline temperature had only increased by 18 per cent above the original initial temperature level as compared to a 52'per cent increase for the platinum probe. Further, more than one and one-half times as much heat was transferred to the platinum probe. These simple calculationslindicated that the temperature fluctuations measured in the center of the platinum probe would be at least as large as those which would exist at the surface of an Inconel tube located at that position under such rapid transient conditions. A graph of the mean radial fluid temperature distribution just beyond the core outlet in terms of the mixed-mean fluid temperature at core in- let and outlet can be seen in Figure 26. The uncooled core wall tempera- ture profile is not symmetrical about the channel centerlinelz; its shape is quite similar to the theoretical one shown previously in Figure 2. It is noted in Figure 26 that, upon the comparison of the measured fluid tem- perature distribution with the mixed-mean fluid temperature at exit, more area between the two curves lies above the mixed-mean temperature than lies below it. This is as expected, because the mixed-mean fluid tempera- ture is averaged with respect to velocity as well as temperature. Hydro- dynamic studies have shown that more fluid flows axially through the inner l2. The reason for thié temperature asymmetry will be more fully discussed in a following section of this report. ORNL-LR-DWG. 18006 ) / FLUID TEMPERATURE7 // y, 2 Z_MIXED-MEAN FLUID TEMPERATURE OUT 1 O~ o 1 0.2 0.1 7 4 /—MIXED-MEAN FLUID TEMPERATURE IN (ZERO) 0 4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. O INNER WALL OUTER NORMALIZED DISTANCE BETWEEN |INNER AND OUTER WALLS Fig. 26. A Comparison of the Rodial Fluid Temperature Profile with Inlet and Qutlet Mixed—Mean Temperaturj (Vaned-Flow Case) L -69- portion of the channel at exit than flows in the outer portion. It is also pointed out that the radial fluid temperature profile plotted in Figure 26 is based on only four thermocouple determinations; it would have been desirable to have had more data to establish a mean profile. It was of interest to determine what the peak fuel temperatures would be in the ART core exit. These temperatures were estimated for both the swirl-flow and vaned-flow cases as follows: a) The experimental radial temperature profiles for uniform volume- " heat-source conditions were transformed to profiles corresponding to an averaged nonunifofm volume-heat-source distribution (see Figure 1). b) The results of the wall cooling analysis described in the section on Mathematical Heat Transfer Analyses were ther used to determine the peak fuel temperatures. Local fuel temperatures so estimated ranged from 100°F to 170°F higher than mixed-mean fluid temperatures for the swirlfflow and vaned-flow cases, re- spectively. ' The complicated question of how much decay takes place in the fuel temperature peak (for the wall-cooled case as described in Figure 5) as the fuel flows through the short exit passage to the heat exchanger en- trance wfis investigated. This passage was divided into two regions. The First half of the passage was treated as a simple curved-wall channel sys- tem, and the second half was considered to be & simple straight channel. The decay of the turbulent thermal boundary layer in the curved channel t system on the convex side (where the high temperature peak exists) was oy S : el AR Y carried out by the usual Von Karman technique with the exception that, in this case, hydrodynamic data (velocity profiles and wall shear stresses) * characteristic of curved channel systems were used. The results for the first half of the passage showed that, on the convex side, the boundary layer would take about 80 diameters to become established (because of the great decrease in eddy diffusivity on that side of the chfinnel). As the physical length of that portion of the passage was only 9 diameters, a pegligible decay of the peak would occur in that region. Thermal boundary layer decay in the second half of the passage was calculated on the basis of the work of Latzko (reference 16) for straight ducts. The results in- dicatéa that it would take about 33 diameters for the thermal boundary layers to become established; the physical length of that portion of the - passage was oni& 9 diameters. On the basis of the functional relation- ship between boundary layer thickness with axial distance in the passage, this means that at the heat exchanger entrance there would be approximately a 36 per cent decay of the original fuel temperature peak. On the basis of these simplified decay analyses and the previous experimental and an- alytical studies of the fuel temperature structure within the core itself, it was estima.tedl3 that peak fuel temperatures at the heat exchanger en- trance will be about 90°F in excess of the mean fluid temperature for the 13. Peak fuel temperatures were calculated at the core exit in the manner outlined in the previous paragraph. However, the actual volume-heat- source distribution near the outer wall was used rather than the aver- . aged profile shown in Figure 1. \ s - AT [ “Tl- swirl-flow case and about 150°F in excess of the mean fluid temperature for the vaned-flow case. 3. ©Swirl-Flow and Vaned~-Flow Cases; One Pump buring both the swirl-flow and vaned-flow experiments, a series of runs were made for the simulated case of one-pump operation. In general, it was found that relatively large peripheral and axial asymmetries ex- isted in the uncooled-wall temperature distributions. The wall and fluid temperature fluctuations were also larger than had been found for the cor- responding two-pump experiments. Typical uncooled-wall temperature data are shown in Figure 27 for the swirl-flow case. The peripheral locations of individual temperature measurements are not indicated in the figure. Note that now, some points lie below the mixed-mean fluid temperature and other points lie far above. ' TR S t-tmi tmo— tmi 1.3 {.2 0.8 0.7 0.6 05 04 0.3 0.2 0.1 n ORNL- LR-Dag . 18007 Operation o 0 0 A ,/ T / A A 0 A~ 4 / 1 ~ N : . A ~—MIXED~-MEAN FLUID A A / 0 CORE WALL o A ISLAND WALL . / /) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 T’: X : L Experimental Uncooled-Wall Temperature Measurements for Swirl-Flow Case with One Pump . 13- GENERAL COMPARISON OF HYDRODYNAMIC AND THERMAL FIELDS It is obvious from analytical considerations that there is a direct relationship between the hydrodynamic and thermal fields for a given flow system. The forced con‘i@i@fii‘heat transfer equations contain heat flow functions that are uniquely defined in terms of the fluid velocity com- ponents. Several specific examples of how the steady velocity field influences the steady temperature field have already been mentioned in the past section; it may be of interest, at this point, to examine in more detail one such case. In Figure 18, it was observed that the uncooled outer core wall tem- perature at the core exit was significantly greater than the one at the inner wall. This feature can be explained by studying the vectorial veloc- ity distributions in the southern hemisphere shown in Figure 28. Note that these velocity profiles, which were determined from experimental axigl and tangential velocity measurements (reference 17), are asymmetric in shape. Consider the channel flow to be divided into a narrow inner layer and a wide outer layer, which possesses a somewhat lower velocify. From the pre- viously developed analyticael temperature solutions for a simple parallel plates system, it would be expected that the outer uncooled core wall tem- perature would be greater than the corresponding inner temperature. A comparison of the transient velocity and temperature fields was also made. A study of the fluctuating velocity structure in the vicinity of the core walls was carried out with motion pictures (reférence 18) of dye fila- ments in a full-scale plastic model of the core. Frequencies of the fluid -74- ORNL-LR-DWG. 18008 1.0 ~ N AT EXIT alfl | NN | \20L/D UPSTREAM \ FROM EXIT \ 0.4 Us max 0.2 0 0 0.2 0.4 0.6 0.8 1.0 INNER OUTER WALL WALL NORMALIZED DISTANCE FROM INNER WALL Fig.28. Vectorial Velocity Profiles in Reactor Core Exit (Swirl- Flow Case) — 75- velocity fluctuations as well as their angular displacements in the vicinity of the walls were determined by counting the total number of cycles a fluctuating dye filament underwent in a given unit of time as well as by observing angular displacements. Figure 29 shows a plot of the angular dye filament dis;_)l&moafl.tmentleL as a function of time, together with wall temperature fluctuation measurements obtained in the half- scale volume-heat-source system; both sets of measurements were determined for the outer wall in the equatorial region. The velocity data presented in Figure 29 suggests a mean frequency of perhaps one cycle per second, whereas, the wall temperatures appear to be varying with a frequency of about two cycles per second. This agreement is satisfactory because the fluctuation frequency in the half-scale model should be double that of the full-scale water model at the same Reynolds number. No attempt was made to compare the magnitude of the dye filament deflections with the temperature amplitudes chiefly because the exact locations of the dye filaments from the core wall were variable and unknown. 14. Note, since the temperature frequency spectrum was limited to l/é to 4 cycles per second, only the fundamental mode of the velocity data should be compared to the temperature date. ANGLE FROM HORIZONTAL PLANE (DEGREES) STATION#5- OUTER SHELL WALL 1" ABOVE MIDPLANE OF FULL-SIZE CORE AVG. HELICAL Re = 290,000 ORNL-LR-DWG. 18009 40 20 - FUNDAMENTAL MODE ] 77 UK Y Lasrny, 2O &V' - ‘\:\\A \ A AVERAGE -20 \/ L:I:'/"A Y ] L -40 -60 TRANSIENT TEMPERATURE MINUS MEAN TEMPERATURE OF CORE WALL Pt- Pt + 10% Rh THERMOCOUPLE AT STATION 4 {.500" ABOVE MIDPLANE OF HALF-SCALE CORE AVG. HELICAL Re = 256,000 0.2 | | . ~ T 0.1 / QDAMENTAL Mooer\ /.\ 0 AN \ _/ \ N / — N -0.1 ~—— < -0.2 0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 ELAPSED TIME (sec.) Fig. 29. Comparison of Transient Velocity and Temperature Data in the Swirl -Flow Case I -T7- bty CONCLUSIONS l. ART Core The following statements about the thermal structure within the ART core can be made on the basis of the results obtainéd from the heat trans- fef and fluid flow research presented here: a) Unless the core shell walls are cooled, maximum wall temperatures ranging from 17500F to 18500F (depending upon the type of entrance flow) will exist near the core exit. About 3 per cent of the heat generated within the core must be extracted to accomplish the cooling task. b) Unless the sodium coolant flows through the cooling annuli in a 15, hot and cold spots will exist which will in- uniform fashion fluence local shafie, strength, and corrosion of the core shells. c) Iocal fuel temperatures at the core exit, under wall cooling con- ditions, are from 100°F to 170°F higher than the mixed-mean fuel temperature (depending upon the type of entrance flow). Decay calculations indicate that peak fuel temperatures will not be at- tenuated markedly as the fuel flows through the short exit passage to the heat exchanger entrance. These nonuniform fuel temperature distributions must be taken into account in estimating heat ex- changer wall temperatures. 15. A study of the nonuniformity of the sodium flow through the cooling annuli for two types of eccentric flow conditions was conducted and the results reported in reference 19. = — — -7 d) The temperature structure within the core becomes significantly asymmetric with respect to peripheral position when one pump is not in operation. e) The core shell interface and fuel temperatures are transient in nature (frequency spectrum ranges from about L/2 to 4 cycles per second). Cyclic stress calculations, on the basis of these tem- perature fluctuations, indicate that stresses as large as + 13,000 psi will exist in the surface layers of the Inconel core shells if the metal is elastic. The influence of these temperature fluc- tuations on corrosion and material strength is unknown at present. It has been demonstrated that some hot spots as well as some high fre- Quency thermal cycling will exist in the ART system. This suggests that a greater research effort is required to determine how seriously these temper- ature structures influence material strength and corrosion. Some thermal cycling research has already been initiated by the Heat Transfer and Physical Properties Section. — 15 2. Reflector-Moderated Reactor Cores in General During the past several years, the heat transfer and fluid flow re- search on high-temperature reflector-moderated reactors has brought to light certain fundamental problems which prevent the attaimnment of opti- mum thermodynamic efficiencies. These problems are: a) High fuel temperatures exist at the core walls which must be reduced by substantial wall cooling. b) Radial fuel temperature distributions are normally so nonuniform in character that the highest mixed-mean fuel temperatures at the core outlets cannot be realized. c) Nonuniform radial fuel temperature distributions generate hot spots and significant temperature fluctuations if the fluid flow is asymmetrical and unstable in character. d) Complex moderator-cooling components are required to cool low- temperature moderators. In order to remedy problems a, b, and c listed above, it is necessary to develop a circulating-fuel reactor core whose fuel temperature distri- bution is nearly uniform with respect to radius. This can be achieved in two ways: 1) generate a high turbulence level within the fuel by mechani- cal means and 2) control the fuel velocity distribution so that very little radial heat flow occurs. - - 3. New Core Configurations One method of generating a high turbulence level within the fuel 1is to’ £11l a fraction of the core volume with packing such as screens; this configuration would destroy thermal boundary layers. The hydrodynamic studies describing this method will be repqrted in ORNL-2199, Two prob- lems associated with such a core would be the increase in the effective absorption cross-section of the reactor and the cooling of the packing, particularly under zero fuel flow conditions. It has recently been shown that the stabilizing effect of a forced vortex within a circular tube permits the generation of axial fluid ve- locity distributions of many desired forms. A unique tubular fuel element based on this principle has been developed (reference 20) which makes it possible to control the velocity structure so that a nearly uniform radial temperature distribution can be obtained. A reactor core utilizing this fuel element would have the following advantages: a) A separate core-wall cooling system is not required. b) An optimum thermodynamic efficiency can be achieved. c) Hot spot and thermal cycling problems would be greatly reduced. d) If a high-temperature reflector-moderator is used in the system, the fuel veloclty structure can be so controlled at the core walls so that "fuel cooling” of the moderator can be achieved. — - ACKNOWLEDGEMENTS A number of people played important roles in making the half-scale ART volume-heat-source experiment a success. The authors are indebted to the following people: J. M. Cornwell and his colleagues were responsible for carrying out the design work for the half-scale model. R. J. Pox and his associates in the X-10 machine shop constructed the complicated platinum-plastic core model. E. R. Baxter and other Y-12 craftsmen assembled the volume-heat- source experiment. G. W. Greene and J. A. Russell, Jr., designed the control and - instrumentation circuits of the experiment. R. T. Guice was responsible for the proper functioning of all the recording equipment. F. E. Lynch and R, M. Burnett assisted in assembling the compli- cated thermocouple system and in the reduction of the data. The authors also wish to thenk M. D, Eden, M. B. Arnold, and S. E. Wassom who typed the manuscript and prepared the 11lustrations. — - APPENDIX 1 Electrolysis Research An experiment was conducted to determine separately the effects of voltage, current density, frequency, electrode materials, and tempera- ture on electrolytic gas evolution. The results of this experiment in- dicated that current density, frequency, and electrode materials were significant. Faraday's law (the proportionality between liberated gas and current) was verified at bare electrode surfaces. Further, for a glven amount of gas liberation at an electrode surface,vthe amount of gas liberafed per unit surface area decreases as the total electrode area increases, During the search for electrode materials, it was found that platinum possessed the unique property of forming a finely divided platinum surface film, which materially reduced electrolytic gas liberation. This is the result of the recombination of oxygen and hydrogen due to the catalytic action of the film. Measurements were made with time of the 60 cycle cur- rent required to initiate gas liberation at the surface of a platinum elec- trode of known area. As a result of the surface film accumulation, the current was observed to increase with time and eventually level off at ap- pProximately 12 amps/ine. When this value was reached, the surface was con- sidered fully passivised. However, 6 am.ps/in2 was used conservatively as a design criterion. Since the liberation of gas may be considered an effect of polarization, & stu y, was also made of the influence of power source frequency on gas E— = generation. For a constant gas generation rate at a passivised platinum electrode surface in a 5 per cent Hesoh solution, determinations were made of the required surface current density with frequency to initiate gassing. These results are given in Figure 30, where it appears that the surface current density varies directly as the square root of the frequency; nemely, O'N‘/f (18) This expression is the well-known Warburg law, which relates pola?ization at electrodes to frequency. This study indicates that if one employs the resistance heating method of volume power generation, the following factors must be considered: | a) Platinum electrodes are superior to other types. b) High frequencj electric currents make it possible to attain higher power densities without gas liberation at the electrode. However, the frequency must not be so great that the "sk;n effect" becomes important. c) For é given system with a fixed electrical power frequency, the volume hea;ing intensity is proportional to the applied voltage, since the maximum surface current density is established. d) Electrode arrangements should be such as to distribute the cur- rent over the greatest electrode area. SURFACE CURRENT DENSITY (amps/in.2) -84- ORNL-LR-DW 60 55 50 45 40 OEXPERIMENTAL VALUES 35 30 :Ti_,2; 0 100 j ot a Passivised Platinum Electrode in an H, SO, $4 0 v 140 180 FREQUENCY (cycles/sec) 220 260 300 340 Fig. 30. Variation of Maximum Surface Current Density with Frequency Solution, I -85- * APPENDIX 2 * Physical Properties of Electrolyte ‘lfi%?fia The electrolyte employed in this experiment was a one per cent (by weight) HQSOu solution. Figures 31, 32, 33, 34, 35, and 36 show respec- tively the specific heat, thermal conductivity, viscosity, density, elec- trical conductivity, and Prandtl numbers of the sulphuric acid solution. 3R _86_ ORNL-LR-DWG, 18011 1.2 {.1 1.0 0.9 0.8 SPECIFIC HEAT (Btu/lb-°F) 0.7 / 0 0 10 20 30 40 350 60 TEMPERATURE (°C) Fig. 31. Specific Heat of a 4 Per Cent (By Weight) Aqueous HpSO4q Solution (Data from Int. Critical Tables) THERMAL CONDUCTIVITY Btu/ hr - f12(°F 7 ft ) ORNL-LR-DWG. 18012 0.50 0.45 0.40 0.35 — ...18_ 0.30 0.25 ¢ TEMPERATURE (°C) Fig. 32. Thermal Conductivity of a { Per Cent (By Weight) Aqu%__ Solution (Data from Int. Critical Tables) VISCOSITY (Ib/ft -hr) ORNL-LR-D&G. 18013 | l \. 0 | | 0 20 40 60 80 100 TEMPERATURE (°C) Fig. 33. Viscosity of a { Per Cent (By Weight) Aqueous H2S04 Solution (Data Taken from International Critical Tables) ?a&y}% _88_ DENSITY (Ib/ft3) ORNL-LR-DWG. 18014 66 I I 65 64 63 _68_ 62 \\ \ A | | 0 20 40 60 80 TEMPERATURE (°C) Fig.34. Density of a 1 Per Cent (By Weight) Aqueous H»SOg4 Solution (Data Taken from International Critical Tables) CONDUCTVITY {(ohm ¢m) ORNL-LR-DWG. 18015 0.04 / / / // 0.03 — // - 0.02 /ofi¢ 30 40 50 60 70 80 90 100 TEMPERATURE (°C) Fig.35. Electrical Conductivity of a 1 Per Cent (By Weightfifi Bl us Ho SO4 Solution (Data Taken from International Critical Table) -06... PRANDTL NUMBER e 'bfidmfifi' -9]~ ORNL-LR-DWG. 18016 10 [ | 8 6 \ * \\\;\\‘\\\\\ssmfifi 2 0 | | 0 20 40 60 80 Fig. 36. Prandtl H?_SO4 Solution. TEMPERATURE (°C) Number of a1 Per Cent (By Weight) Aqueous — -52- APPENDIX 3 Materials of Construction and Flow System Components - s r a. Ma%erf;iS“of Construction The materials directly in contact with the stou solution were Carpenter 20 alloy, platinum, Micarta plastic, Boltaron plastic, Araldite resin, Plexiglas, Pyrex, Teflon, and Neoprene. The pumps, heat exchanger, and flow regulator valves were also constructed of Carpenter 20 alloy. The core model (see Figure 8 for cross section) was made primarily of close-grain Micarta and platinum. b. The Half-Scale Core Model The exact half-scale model of the proposbd ART core was constructed of laminated Micarta sheets in which were imbedded platinum rings of the ) desired shape. Bus bars contacting the electrodes conducted the current radially outward. The thermocouples, which were in contact with the elec- trolyte between the electrodes, were composed of platinmum-platinum + 10% rhodium. ¢. System Components Two 20-h.p. Carpenter 20 single-stage centrifugal pumps withdrew the electrolyte from a glass-lined, 300-gallon reservoir. Carpenter 20 alloy globe valves regulated the electrolyte flow rates to a maximum of 200 gal/min at a 200-foot head. A thin plate VDI-type 2-inch diasmeter orifice in conjunction with a 50-inch manometer was used to measure electrolyte flow rates. The high resistance external electrical curcuit was insured e - ~93- t_,. R by means of Boltaron plastic piping in the flow system ducting electrolyte to and from the core. The Carpenter 20 alloy heat exchénger was of the cross-counter flow type having 50 one-half-inch tubes on three-fourth-inch centers in a tri- angular array. The outer diameter was 12 inches, with a total length of 12 feet, including the headers. The electrolyte temperature level was maintained by means of a 2-inch pneumatic valve, which controlled the flow rate of cooling water through the heat exchanger in conjunction with an automatic regulator. o ~oh- R APPENDIX 4 Calibrations Calibration curves for the Hathaway galvanometer and Brush recorder systems appear in Figures 37 and 38. The flow metering orifice coefficient versus the manometer deflection appears in Figure 39. The variation of the mean axial Reynolds number within the core is plotted with the manometer deflection in Figure 40. FRACTION OF D.C. RESPONSE ORNL-LR-DWG, 18017 1.0 1 T T T T [ [ ! T T \VINNER WALL 0.8 N\ UTER WALL 0.6 \ 0.4 ‘ INNER WALL THERMOCOUPLE EXTERNAL RESISTANCE =13 OHMS OUTER WALL THERMOCOUPLE EXTERNAL RESISTANCE = 4 OHMS \ 0.2 N \ 0 | I [ | ] | | ] | | 0.01 O.1 1.0 10 FREQUENCY (cycles/sec) Fig. 37. Freqency Response of Galvanometer 4036-2 ‘?413 _96_ FRACTION OF D.C. RESPONSE ORNL-LR-DWG, 18018 1.0 ! | l i T ! 0.8 0.6 0.4 0.01 0.1 FREQUENCY (cycles/sec) 10 _96- ORIFICE COEFFICIENTS 0.8 0.7 0.6 0.5 ORNL~-LR-DWG, 18019 _£6u 2 3 4 5 6 7 8 9 10 20 30 40 50 60 TOTAL MANOMETER DEFLECTION (in. of Hg) Fig. 39. Volume -Heat-Source Experiment Orifice Calibration (2in. Dia. Orifice in a 3in. Pipe) MEAN AXIAL REYNOLDS NUMBER ORNL-LR-DWG. 18020 AVG. CORE TEMP. 50°C 40°C 30°C \ \ U 10° /// 20°C = 1 A 8 — //// / 5 ,// A // ~ /// /,/ /// . = -~ pre - 7 T — _— H 4 10 { 2 6 8 20 40 60 % 10 100 TOTAL MANOMETER DEFLECTION (INCHES OF Hg) Fig. 40. Axial Reynolds Number Based on Mean Core Perimeter _86_ Iy | -99- $ .ol REFERENCES 1. Fraas, A. P., ANP Quarterly Progress Report, June 1954, ORNL-1729, p. 28. 2. Poppendiek, H. F. and Palmer, L. D., "Forced Convection Heat Transfer Between Parallel Plates and in Annuli with Volume Heat Sources Within the Fluids," ORNL-1701, May 1954. 3. Poppendiek, H. F. and Palmer, L. D., ANP Quarterly Progress Report, September 1954, ORNL-1771, p. 131 end, Bradfute, J. 0. et al, ANP Quarterly Progress Report, December 1954, ORNL-1816, p. 11k, 4. TNikuradse, Johann, "Untersuchungen Uber Die Stromungen Des Wassers In Konvergenten Und Divergenten Kanalen," Forschungsarbeiten, V. D.-I., Volume 289, pp. 1-49, 1929. : 5. Poppendiek, H. F. and Palmer, L. D., ANP Quarterly Progress Report, September 1954, ORNL-1771, p. 131. 6. Wattendorf, F. L., "A Study of the Effect of Curvature on Fully Developed Turbulent Flow," Proc. Roy. Soc., Vol. 148, 1935, pp. 565-598. 7. Poppendiek, H. F. and Muller, G. L., ANP Quarterly Progress Report, December 1955, ORNL~2012, Parts 1-3, p. 177. 8. Bradfute, J. 0., "Qualitative Velocity Information Regarding the ART Core," CF 54-12-110. 9. Muller, G. L. and Bradfute, J. 0., "Qualitative Velocity Profiles with Rotation in 18-Inch ART Core," CF 55-3-15. 10. Bradfute, J. 0., Lynch, F. E., and Muller, G. L., "Fluid Velocity Meas- ured in the 18-Inch ART Core by a Particle-Photographic Technique, " CF 55-6-137. 11. Poppendiek, H. F. and Palmer, L. D., "Application of Temperature Solu- tiong for Forced Convection Systems with Volume Heat Sources to General Convection Problems," ORNL-1933, September 1955. 12. Poppendiék, H. F. and Palmer, L. D., ANP Quarterly Progress Report, March 1956, ORNL-2061, Parts 1-3, p. 176. e % ST ey oy 13. 1k, 15. 16. 17. 18. 19. 20. 21. e :afifif e - e Greene, N. D. et al, ANP Quarterly Progress Report, June 1956, ORNL-2106, Parts 1-5, p. 222. " Greene, N. D. et al, ANP Quarterly Progress Report September 1956, ORNL-2157, Parts l -5, p. 227. - Churchill, R. V., "Modern Operational Mathematics in Engineering,” First Edition, McGraw-Hill Book Co., New York, 1944, p. 125, Latzko, H., "Der Warmeubergang an einen’ ‘Turbulenten Flussigkeits oder Gasstrom," Zeit. fur Ang. Math. und Mech., Vol. 1, No. 4, Auvg. 1921. Furgerson, W. T., Stelzman, W. J., Whitman, G. D., personal com- munication of unpublished velocity data. Stelzman, W. J, and Whitman, G. D., personal communication of photographic records. Copenhaver, C. M. and Lynch, F, E., "ART Reflector Sodium Annulus Study," CF 56-7-155. Poppendiek, H. F., Greene, N. D., and Palmer, L. D., ANP Quarterl Progress Report, December 1956, ORNL~-2221, Chapter 4.1, '"Heat Transfer and Physical Properties: Heat Transfer in Reflector- - Moderated Reactor Cores." Perry, A. M., "Core Power and Temperature Distribution,” ART Design v Memo No. 8-B-1, Add. 2, Feb. 17, 1956.