xr -- , svi7- c w 420 ASSIFIED K i t A 1 J UNCLASSIFIED CF-53-12-94 Subject Category: ENGINEERING UNITED STATES ATOMIC ENERGY COMMISSION CALCULATIONS FOR HRE NO. 2 HEAT EXCHANGER By C. L. Segaser December 16, 1953 Oak Ridge National Laboratory Oak Ridge, Tennessee Technical Information Service, Oak Ridge, Tennessee Date Declassified: December J, 1955 • This report was prepared asa scientific account of Govern- ment-sponsored work. Neither the United States, nor the Com- mission, nor any person acting on behalf of the Commission makes any warranty or representation, express or implied, with respect to the accuracy, completeness, or usefulness of the in- formation contained in this report, or that the use of any infor- mation, apparatus, method, or process disclosed in this report may not infringe privately owned rights. The Commission assumes no liability with respect to the use of,orfrom damages resulting from the use of, any information, apparatus, method, or process disclosed in this report. This report has been reproduced directly from the best available copy. Issuance of this document does not constitute authority for declassification of classified material of the same or similar content and title by the same authors. Printed in USA, Price 25 cents. Available from the Office of Technical Services, Department of Commerce, Wash- ington 25, D. C. CF-53-12-9 1 *- CALCULATIONS FOR HBE NO. 2 HEAT EXCHANGER By C. L. Segaser December ±6, 1953 Work performed under Contract No. W-7^05-Eng-26 OAK RIDGE NATIONAL LABORATORY Operated By CARBIDE AND CARBON CHEMICALS COMPANY POST OFFICE BOX P OAK RIDGE, TENNESSEE -2- C*l eolation* hare been made for the heat transfer aurface area, number of tubes, length of tubes, hold-up rolume In the tubes, and the pressure drop through the tubes for a proposed mala Ueat exchanger for the HRE Bo. 2. In general, the calculations for the required surface area were Bade In accordance with the method described in CF-49-8-231 «nd CF-52-IO-195. Engineering design data on which the calculations were based vere specified by V. Ft. Gall as follows: Fuel Inlet Temperature 300°C (572°F) Total heat 3000 kw Tube size 3/8 in. 0D (U-Tube) Fuel 20 g/llter UOgSO^ in HgO or D Fuel pressure 2000 psla Flow rate 220 gpm Steam pressure 520 psla Supplementary design data required for the determination of the film coefficient in the tubes of the heat exchanger were obtained from CF-52-1-124 and are listed as follows: Density of fuel solution 5* lb/ft 3 Specific heat of fuel solution 1.20 Btu/lb-°F Viscosity of fuel solution 0.270 lb/hr-ft Thermal conductlrlty of fuel solution. . O.35O Btu/hr-lb-°F/ft These properties of the fuel solution were eraluated at an arerage temperature I in the heat exchanger tubes of 527°F. The Heat Balance In order to determine the process temperatures at the entrance and exit of the heat exchanger tubes, a heat balance to transfer 3000 kw (1.025 x 1° 7 •tu/hr) as sensible heat from the fuel solution to latent heat of raporlzatlon -3- of water on the shell Bide at 520 peia vaa made. Q = WC p (T 1 - T Q ) where, 4 = Sensible heat given up by fuel, Btu/hr. W - Flow rate of fuel, lb/hr. C « Average specific heat of fuel, Btu/lb- F. o T. » Initial or entrance temperature of fuel, F. T « Final or outlet temperature of fuel, F. Since the circulating pump is assumed to deliver a fixed quantity of 220 gpa of solution, (220) (60) , . where, p = Average density of fuel, lb/ft . therefore, 4 = 1765 (0 C_)(T 1 - T ). P x o Ite product (p C ) must correspond to the average fuel solution temperature T Q + T« in the tubes, — » . Figure 1* shows that the density of the solution decreases and the specific heat increases with temperature, but that the product (p C ) does not have such a wide variation, In fact, having a fairly constant value between the temperatures of — 300 F and 500 F. By trial and error calculations, the temperatures at the entrance and exit of the tubes were determined such that the average temperature in the tubes coincided with an assumed value of the product (p Cp). The results of this calculation are tablulated as follows. Tj = 572°F T = Wl-5°F o 572 * U8I.5 o T avg " 2 Z '- 527 F T ■ V7I F (Saturation temperature of steam at 520 psia) B T, - T = 90.5°F T 1 - T B " 101°F T o - T B ' 10-5 f The Tubes The required wall thickness of a Type Jkf stainless steel 3/8 in. 0D tube at a design pressure of 2000 psia, a corrosion allowance of 0.030 in. and an allowable stress of 15,000 psi was calculated fron the equation, as reconmended in Section VIII of the 195? edition of the ASME Onfired Pressure Vessel Code. PR % = SE - 0.6P * C vhere t • thickness of wall, Inches. P ■ design pressure, psi. P ■ inside radius of tube, inches. S » allowable stress, psi. E = Joint efficiency ( E * 1 for seamless tubes). C - corrosion allowance, Inches. This equation shows that a 3/8 In. OD - 18 Ga (0.0^9 vt. ) tube is good for only 1590 psi. Therefore, a 3/8 'in. OD - 16 Ga (O.065 vt. ) tube, good for P - 3030 psi is specified. Tube Data 2 Flov area of 3/8" OD - 16 Ga(0.065 vt) tube - 0.000327 ft Outside heat transfer area per ft. of length ■ O.O982 ft Thermal conductivity of Type 3U7 stainless steel » 130 Btu/hr-ft 2 - F/ln. Wall coefficient of 3/8" OD - 16 Ga tube - 2000 Btu/hr-ft 2 -°F -5- Heat Transfer Surface Area In CF -49-8-231 It vaa shown that the surface area of an exchanger, in which there 1* a substantial variation in U (the overall heat transfer coefficient) with temperature from one end of the tubes to the other, nay be calculated from, C ° B d(T - To) A - WC PI U (T - Tb) *1 -*B Since, T - 1L » £A^ + At, + At o and Atj^ - A A l " *c hT /^ '* ^ h ft) At, ■ 4 ■ A. - *w *1 ftV Q n o g Q Q Substituting T - T B - A„ + A + /£ (IF" 15) ho -6- o where, A - outside tube surface area, ft V - flov rate of fuel, lb/hr C P specific heat of fuel, Btu/lb - F T - T_ - orerall temperature difference at cold end, F o .i*°-») {k) 2oo ° 100 At Q l'»2 j; = N) At o At, ■ »»&) 0.414 T - Tb l Q /Q 1650 ^ V* ( o.inu 0.778V ' 8 A Q Differentiating this equation, substituting in the Integral equation for surface area and integrating between the limits of heat flux at the hot end to heat flux at the cold end; the following equation was derired for calcu- lating the heat transfer area WC. O.778V 3 *■ - 0.105 . .-O.586 , „ -0.586 where, A - Outer tube surface area, ft 2 W - Weight rate of flow thru tubes, lb/hr Average specific heat of fuel, Btu/lb °F -8- Heat flux at hot end, Btu/hr-ft 2 CO, S_ ) - Heat flux at cold end, Btu/hr-ft 2 *o/ o V - Velocity thru tubea, ft/hr Thus, for a given flow rate and ateaa pressure, this equation shows that the surface area varies Inversely as the 0.8 power of velocity. ■umber of Tubes For a given flow rate of 220 gpm, the number of tubes required will vary Inversely as the velocity through the tubea. A flow rate of 220 gpn is equivalent to 0.»91 ft 3 /eec. Since the flow area per tube Is 3-27 x 10 ft , 0.»91 - 3.27 x 10 HV and I - O.I>91 3.27 x 10"* V Average Length of Tubes tmiltlplylng the outside surface area per foot of length, by the average length per tube and the total number of tubes will give the surface area as shown by the following equation Sj • O.0982 IL From which, L - B» O.O982 I Hold-up Volume of Tubes In a similar manner, the hold-up volume In the tubes may be shown to be V - 3.27 x 10 ~ k HL (Ft 3 ) Pressure Drop Through Tubes The pressure drop through the tubes was calculated by the familiar Fanning equation, AP„ l*fp V 2 L 2g Di Table 1 Tabulated Data for HRE Bo. 2 Heat Exchanger Velocity thru tubes, ft /sec 5 10 15 20 25 Flow Rate, gpm 220 220 220 220 220 Power (3000 Kw) 1.0< >5 x 10? B1 u'hr \ Temperature Surface Area (ft 2 ) T,, °F 572 572 572 572 572 S T , F 1*81. 5 1*81-5 U81.5 1*81.5 1*81.5 Clean 1*04 338 31* 298 290 Fouled 51*0 1*50 1*18 398 387 LKTD °F 1*0.1 1*0.1 1*0.1 1*0.1 1*0.1 Apparent Btu/hr-ft-°F Clean 633 760 811* 862 883 Fouled 1*73 570 610 61*6 662 Rumber of Tubes 300 150 100 75 60 Length of rubes, ft Clean 13-75 23.0 32.0 1*0.5 1*9.5 Fouled 18.3 30.6 1*2.7 51*. 66.0 Bold-up in Tubes (Liters) Clean 38.2 31.8 29-8 28.0 27.-* Fouled 51 1*2.5 39-7 37.1* 36.6 Pressure irop, psl Clean 1-95 11.20 32.8 68.2 123-0 Fouled 2.60 15.0 1*3.7 91.0 161*. -10- Results of Calculations The heat tranafer surface area based on the outside diameter of the tubes, the number of tubes, the length of the tubes, the hold-up rolume and the pressure drop through the tubes hare been calculated for fluid velocities from 5 ft /sec through 25 ft/sec using 3/8" 0D - 16 Ga (O.O65 wt) Type 3U7 stainless steel seamless tubes for a 3000 Kv vaporizing exchanger generating saturated steam at 520 pala pressure. The results are listed In Table 1. These results have been tabulated for both clean surface and fouled surface, where the fouled surface Is assumed to be U/j of the clean surface. Tbe results for the fouled surface account for scale build-up on both the Inner and outer surfaces of the tubes and provide a factor of safety for specifying the exchanger. Where an exchanger has a constant U, It is customary to calculate the surface area from the equation, Q = UAAT where AT Is defined as the logarithmic mean temperature difference as calculated from AT, - AT, AT * i £ ATi ta ATi Occasionally where there Is a substantial variation In U, this method Is still used. As a matter of record, some of the heat exchanger manufacturers contacted by ORNL have apparentlv used this method for specifying vaporizing heat exchangers for the ISHH using a constant U - /50 Btu/hr-ft 2 -°F. This coefficient was used for calculating the fouled surface area, based on 3A of an assumed U - 1000 Btu/hr-ft 2 -°F for clean surfaces. For purpose of comparison, the apparent overall U for the HRE Bo. 2 exchanger is shown. -11- This U vaa calculated for both the clean surface and the fouled surface using a logarithmic mean temperature difference based on the entrance and exit procesa temperatures and the saturated steam temperature. The LWD for this exchanger Is U0.1 F, hence, the apparent U Is, U - U0.1 A Q The results from Table 1 hare been plotted on Figures 1 through 7 for ease In Interpolating data for any velocity from up to 25 ft/sec. Figure 1 shows the required surface areas for both the clean and fouled tube surfaces. Figure 2 Is a plot of heat flux, Q/A Q , versus overall temperature drop T - T- for velocities from 5 through 25 ft/sec. Figure 3 shows the variation in outside heat transfer coefficient as a function of temperature difference betveen the tube surface and the saturated liquid for pressures of 1U.7 psia, 215 psla, 370 psia and 520 psia, from horizontal tubes. Figure k shova the variation of densitv, specific heat and the product of the tvo at Increasing temperatures for a 20 g/l solution of UOoSO^ in DO. Figure 5 glvea the number of tubes and average length of tubes as a function of velocity for the exchanger. Figure 6 shova the decrease in hold-up required as the velocity through the tubes is increased. Figure 7 shova that the pressure drop through the tubes of the heat exchanger Increases very rapidly with velocity and becomes exorbitantly high at 25 ft/sec. Preliminary Recommendations A meeting was held In the Conference Room of Building 920U-1 on Friday, December 11, 1953. between members of the REED Design, Development, and Operation Se-tlons to discuss a proposed design for the HRE No. 2 Main Heat Exchanger. Those present were Design Dev elopment. Operation W. R. Gall "• B. Graham S. E. Beall R. B- Brlggs W. T. Roes W. Terry L. F. Goode C. L. Segaser (1) The calculations presented in the enclosed memorandum were dis- cussed, and a sketch of a proposed heat exchanger made by W. Terry based on a velocity of 15 ft/se: through ICO 3/8" O.D. - 16 Ga. Type 3W stainless steel tubes was shown. At 15 ft /sec the average length of tubes required Is 32 ft. The exchanger surface shown was contained In a shell approximately 30-inches diameter by 15-ft long- This results in an exchanger shell which has a length to diameter ratio of 6:1, and the decision was somewhat arbitrarily made to reduce the velocity from 1=> ft 'sec to 10 ft/sec. This will result In increasing the number of tubes from IOC to 150 and decreasing the tube length from 32 ft to 23 ft with a consequent lower pressure drop and a better propor- tioned heat exchanger shell, but at the expense of approximately 2 liters of greater hold-up volume. (2) R. B. Brlggp recommends that the surface area of the exchanger should be specified on the basis of the clean surfaces rather than the fouled Burf*c«s. He bases this opinion on the performance of the existing HRE No. 1 heat exchanger which was specified neglecting scale build-up and which has apparently functioned satisfactorily during the relatively short time it has been operated. ■13- (3) The specifications of a vaporizing heat exchanger for the HRE Bo. 2 based on the above premises then may be tentatively listed as follows Fuel 20 g /l UOgSO^ - Dj.0 or HgO Fuel Preimire (lnle*) cOOO psia Heat transfer 3-00 kw Tube Bize 3/8" OD - 16 Ga (O.065) Flow ra-e 220 gpo Steam pressure 520 pela Steam temperature Fuel Inlet temperature Fuel outlet temperature Fuel velo:lty Heat transfer surfare area Number of tubes Average j.ength of tubes Hold-up volume In tubes Pressure drop *hru tubes (k) These spe : if 1 cations are based on the assumption that the bulk temperature of the boiler water is already at the saturation temperature of V71 F corresponding to the generated steam pressure of 520 psla. Actually, feedwater returned from the steam system will be considerably less than this temperature and means must be provided to preheat this water to saturation temperature. In normal power plant practice, part of this preheat Is provided by external feedwater heaters using steam bled from various stages of the turbine as the heating medium. In the HRE Ho. 1, boiler feedwater heat Is provided in part from the D.O cooler In the blanket system, and the U 7 1 °F 572 °F 481.5 °F 10 ft/sec 336 ft* 150 23 ft 31.6 liters 11.2 psl -14- remalnder la supplied through a feedwater heating element built Into the rapor space of the main hea" exchanger. Also, In the HHE No. 1 heat exchanger tvelre additional tubes were provided orer the calculated number as a safety factor to account for contingencies such as the above. (5) The fabrication problems of r he heat exchanger were discussed and the following decisions were tentatively proposed. 'ft) The tube-sheet to be of solid construction of Type 3W stain- less steel with the thl ;kaeas determined from the TEMA Standard Procedures using an allowable design stress of 15,000 psl. (b) The problem of leak-detection versus no leak-detection was presented. This problem Is *o be Investigated further before a final decision is made (c) The tube bundle doea not need to be removable from the shell. (d) An efficient entralnment separator Is desired for high quality steam. (e) A closure design Is desired which may be removed prior to final installation, tut which may be seal welded before the reactor system is made critical.- (f ) Feedwater surface area will be required for boiler water preheating. (g) The feedwater tempera" 'ire leaving the steam killer should be investigated. (h) A delivery late of January 1, l$F>k is desirable, (l) Type JOk L stainless dteel was discarded as a possible material of construction In favor of Type 31*7. -15- o o o o o o O O o o o O ? eg o a <0 * CM o CO (0 ♦ » * * n id tn IO IO CM N 2 U 'V3«V 3DVddnS -16- 200,000 1 00,000 10,000 5 o (,000 100 IN V»10ft/»ecv V»15 ft/iecx/^y V»_20 ^htcjy / 'S/' V ■ £3 IT/I e^ — ^ 1 1 1 1 . w 1 ■ — - Mf Mr 1 ff : g ' 1 i 1 1 1 i ' 1 (0 100 (T-T,) FIG 2 FLOW RATE OF 220 6PM; STEAM PRESSURE • 520 ptio 300 10,000 (000 100 (0 • IP'370 pile = 520 p»i0yt< gf p i / 1 / f 1 1 1 1 / / / - / / / | / | — i// / t— - - i / / 1 1 t t t / 1 | |_ / / f / f I I / j _ h,(520) 100 At,'** / / - h,(570) 90 At,'** / 11,(215) > 82 At,"'* / / hglatm) 42 At,* 4 * / t — — HORIZONTAL TUBES VERTICAL TUBES 10 At. fF) 100 FIG. 3. BOILING SIDE COEFFICIENT - HORIZONTAL TUBES -18- J.QI/n»8 '(do) 1V3H DIJlD3dS o II O IM Q i O* CO o tr o CO a. o a. z o o CO 6 -19- ro Mill Mill 1 1 1 1 1 1 1 1 ! I 1 1 ^7 *♦ •^ i jA X z UJ - 1 3«> UJ m => 30 __ i /^ n i- 3U 15 "^N // 5 t\ i i i 1 II 1 I l i i 1 1 1 1 i i i i 300 200 UJ m 3 UJ CD 100 z 5 10 15 20 VELOCITY, ft/sec FIG. 5. HRE No. 2 HEAT EXCHANGER - NUMBER AND LENGTH OF TUBES. 25 -20- » 1111 1 1 1 1 ~"i i i i ■ i i i?i i i i i 1 1 '! ! TUBE CD 1 3 1 *- I zf < 1 u. 1 6/ U.I -II ul / / J 1 / 1 ^ J / 1111- ki i i i i i i i I j/i i III! 1 1 1 1 en CD s _l o O in -* ^ a "- Z) m • O I cr UJ o z < I o X < UJ I (M O Z UJ cr z «0 6 •«»!i '3wmoA dn-aioH O lO eg -21- 200 40 15 VELOCITY, ft/sec 20 25 FIG. 7. HRE No. 2 HEAT EXCHANGER - PRESSURE DROP THROUGH TUBES. GPO 903639 UNIVERSITY OF FLORIDA 3 1262 08905 5452 I