ML20216F234
| ML20216F234 | |
| Person / Time | |
|---|---|
| Site: | Yankee Rowe |
| Issue date: | 06/03/1992 |
| From: | DUKE ENGINEERING & SERVICES |
| To: | |
| Shared Package | |
| ML20216F193 | List: |
| References | |
| YRC-991, YRC-991-R00, NUDOCS 9909210221 | |
| Download: ML20216F234 (152) | |
Text
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4 YANKEB ATOMIC ELECI'RIC COMPANY ANALYSIS / CALCULATION FOR , k I TITLE ESTIMATION OF SPENT FUEL PIT MRAT-UP RATE INCORPORATING AUTuAL PLANT DATA AND THERMAL LOSSES r 1 PLANT YANKEE ROWE CYCLE t e ', i -
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_s, YANKEE ATOMIC ELECTRIC COMPANY ANALYSIS / CALCULATION FOR '. t e _j , F' . TITLE ESTIMATION OF SPENT PUEL PIT NRAT UP RATE INCORPORATING , j AtzruAL PLANT DATA AND THERMAL LOSSES
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YRC 991 !p ) Page 2 of 34 Pages y TABLE OF CONTENTS ;I v b t " y' Cover Page M .!
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i, Table of Contents . . . . . . . . . . . . . . . ..... 2 Y [ Calculation Documentation . . . . . . si t . . . . . .. ... 3-13 4 . References J
. . . . . . . . . . . . . . . .. . . ... . . 14 tj.
Figures . . . . . . . . . . . . . . . . . . . . ... . . 15-34
- .h Attachment 1: SFP Heat-up Test Data r
^ . . . . . ... . . 1-8 #;
Attachment 2: Thermocouple Locations For SFP ?
, Heat-up Test . . . . . . . . . . . . . . . 1 Attachment 3: :b SFP Heat-up Analysis Results . . . . . . . 1-44 y
'{' Attachment 4: SFP Cooling Pump Performance Curve . . . . 1 2 a
Attachment 5: l( Comparison of SFP Room Temperature g{ on Heat-up Rate . . . . . . . . ... . . 1-6
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Attachment 6A Detailed HEATUP. BAS Output, 6/15/92 ... 1-19 jj dt Attachment 6B: Detailed HEATUP. BAS Output,.6/15/93 ... 1-23 d i
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, Attachment 7: Sunnary of SFP Disrensions . . . ... . . 1 f '
p$ Attachment 8: Thennal Loss as a Function of Temperature . . . . . . , . . . ..... 1 ( Attachment 9: g Heat-up Rate Correction For Low W Temperature Data . . . . . . . . 4
..... 1-4 ;
- y. Appendix A SFP Heatup Prediction Method . . j) w . .... 1 *2 ' '
l Appendix B: Convnctive Heat Transfer Coefficient 1 p, Prediction . . . . . . . . . . . . . . . . 1-3
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e se a Om)3 YRC 991 Page 3 of 34 Pages ESTIMATION OF SPENT FUEL PIT HEAT-UP RATE INCORPORATIHQ -j ACTUAL DATA AND THERMAL _ LOSSES 1 a
- 1. CALCULATION NUMBER : 991 4
- 2. SYSTEMS AFFECTED BY ANALYSIS:
This analysis encompasses the spent fuel pit (SFP),
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2.1 # including the water inventory and surrounding environs :. 3 (i.e. wall, floor, and air). t b g 2.2 The SFP structure is not safety related. The SFP 3 g, cooling system is Safety Class 3. ; ik c
- 3. PROBLEM DESCRIPTION: ]>
3.1 The SFP cooling system is designed to maintain the SFP d {( at a constant temperature by removing energy that would j 4 heat wt t otherwise generated by accumulate the fuel.asThe a result SFP of decay $33 contains fuel :?
! assemblies that have been used for one or two cycles in j the reactor (Reference 6). Each assembly contains 7' ia'ioa'ctive d isotopes pfoduced by eithe'r fissi~n o or k(F neutron capture. The radioactive decay of these nuclides releases heat into the SFP water. '.
g. 3.2 SFP temperature will increase if cooling is terminated.
- f. The temperature increase is limited by either the onset of boiling in the SFP (210*F) or the establishment of
)*
b4 thermal equilibrium when thermal losses to the V environment equal the decay heat rate. g. h 3.3 The purpose of this calculation is to estimate the SFP gr heat-up rate for a variety of cases. The calculation
=W. includes the effect of thermal losses from convection, 3#
- conduction, and evaporation. In addition, the b calculation incorporates a decay heat rate that is 1 b determined from data collected during a plant test j g(: (Reference 1). j 4
{ 3.4 The following methodology will be used: 4 M 3.4.1 Determine the decay heat rate using data k _a 4+h gathered during a recent plant test. lh w.
-(t, 3.4.2 Compare measured decay heat rate with values from alternative analytical methods.
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YRC 991 Page 4 of 34 Pages 3.4.3 Predict SFP temperature as a function of time for several cases to determine the time for SFP temperature to increase from 100*F to 150*F and 180*F.
- 4. DETAILS OF ANALYSIS: [.
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4.1 The decay heat rate of the fuel in the SFP can be determined by evaluating data collected during a plant test completed during~ April, 1992 (Reference 1 and 7). l Attachment 1 presents a tabulation of these data. The i test used twelve thermocouples at different locations
, in the SFP to measure the temperature of the water.
f Attachment 2 presents a map of the thermocouple
'? locations.
4.2 Figures 1-11 present heat-up rate versus SFP temperature for each thermocouple location. Heat-up
!, rate is the ratio of temperature change to time 1 L; interval between sequential data points: i !
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F Where: T is SFP Temperature, 'F l PJ t is time, hr p i is occurrence , f g 4.3 Each heat-up rate plot has a similar shape. The j .. initial heat-up rate is higher due to the transition to j e natural convection cooling following termination of
- - forced convection. After several hours, the heat-up i; rate becomes relatively constant. In this regime 4 thermal losses,are low and decay heat predominates. j k The heat-up rate is directly proportional to the decay i heat rate. This can be seen in the following energy <
? balance for the SFP -
Ehergy Accumulation = Decay Heat-Thermal Losses (3) '
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Omsr) YRC 991 P:ge 5 of 34 Pages 4.4 SFP inventory mass does not incorporate the mass of fuel, racks, and other components. The mass calculation assumes that the SFP only contains water. 1 Attachment 7 sunnarizes SFP dimensions; SFP dimensions are approximately 33.7 ft x 16.5 ft x 36 ft (LxWxD). }' The total volume of the SFP is about 150,000 gal. The 1 incremental volume at the surface is about 346 gal /in. f (16.5 ft) (33.5 ft) (7.48SUd) Incremental Vol= ,, =346 ,"* (4) - it 4.5 Therefore, the volume of water when the level is 12 inches and 16 inches from the top is 145,800 gal and 144,500 gal, respectively. , { 2 4.6 Adjusting the inventory mass for fuel, racks, and other l t components reported in Reference 2 results in a small ,
& decrease in the estimate of the decay heat rate. The j lower estimate reflects the lower volumetric heat ; capacity of the components:
y y Water 62 Btu /f t /*F (Reference 4) j Zirconium ~30 Btu /f t /*F (Reference 8) e UO ~40 Btu /f t /'F (Reference 8) Aluminum ~35 Btu /ft /*F (Reference 9) b (144500-14100 gal) (62 Bru ) + (14100 gal) (35 #U" ) X= IU #U
/ =0.96 (5) h, w
(144500 gal) (62 Stu ) ft**F k* F *. Where: X is the ratio of decay heat calculated by incorporating fuel, racks and other .' R corponents to the decay heat calculated g by, incorporating only water. .
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3 [ 4.7 This correction is not i;scessary if the same basis is used in the deca 3 3 h.. up calculations.y heat This rato normalises determination the heatand up the heat-gc. calculations to plant perfotmance. ) 4'- t g M 4.8 As water tangerature increases above 100*F, the heat-up rate begins to decrease. This is caused by the q; _h5 increased thermal losses at the higher temperatures, t 9: Thermal losses are predominated by evaporation from the 4. l surface of the SFP. Evaporation rate is a function of s
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'k,.f( the difference between the partial pressure of water at the SFP temperature and that of the air at the SFP gh
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00tiG YRC 991 Page 6 of 34 Pages building air temperature and humidity. As temperature increases, water partia1' pressure increases rapidly (doubles every 30*F). Figure'20 illustrates the magnitude of each of the heat transfer modes (i.e. evaporation, convection, and conduction) incorporated into the calculation. 4.9 The impact of changes in air temperature are mininal. At lower SFP water temperature, the temperature driving force is low, changes in air temperature have no impact on the heat-up rate. At higher SFP water temperature, the partial pressure of water at the SFP water temperature is much greater than that of the air. At a SFP water temperature of 150*F, the SFP water partial pressure is five times greater than that of the air at 90*F and 100% relative humidity. Changes in air temperature have minimal impact on the partial pressure driving force for vaporization. 4.10 Figure 19 and Attachment 5 present a comparative case of the effect of increasing SFP air temperature from 85'F/70%RH to 100*F/100%RH. The time to heat the SFP . . - - to 150*F and 180*F is increased by 3 hr and 6 hr, respectively. The equations and a computer program (HEATUP. BAS) used to calculate thermal losses are presented in Appendix A. 4.11 Attachment 8 presents predicted thermal losses, based on conditions measured during the SFP test, for SFP water temperature betseen 84*F and 100*F. These data were evaluated to determine the apparent decay heat
, rate of the fuel in the SFP. This regime was chosen t
because of the low thermal losses compared to decay heat rate: V h Thermal Losses 0.04 - 0.09 MBtu/hr j, Decay Heat Rate >1.0 MBtu/hr D 4 When thermal losses are low, decay heat rate is nearly b proportional to the rate of temperature increase. A line is drawn on Figures 1-11 to indicate the average value of the heat-up rate for.the data between 84*F and h({ n
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l 0007 : YRC 991 Page 7 of 34 Pages 4.12 The following is a listing of the average heat-up rate values: 7 { Thermocouple # Average Heat-up, *F/hr " ( (84 - 100*F)
,i ~ 2 0.81(1) 3 0.79 5 0.81 6 0.81 7 0.83 9 0.92 10 0.82 j 11 0.82 r 12 0.81 j 13 0.81
- t 14 0.80
[ Average 0.81 Std Dev 0.014 n Notes: 1. Lowest data point was eliminated. ,,.
;; 2. Overall average is 0.81*F/hr f
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- 3. Overall Std dev is 0.081*F/hr - ~ ~"-- ' ' - * & -"' ~
h f 4. Number of points is 131 t' 4.13 Figure 12 and Attachment 9 presents all of the data from Figures 1-11 that are between 84'F and 100'F. c[..' Figure 13 highlights the small decreasing trend
;;l' indicated on Figure 12 (i.e. the heat-up rate is higher at lower temperature). The trend is expected as the therinal losses are lower at lower temperature resulting ,0 in a higher heat-up rate than measured at higher b.: temperature, q t },j.-
4.14 Figure 14 presents the same data as shown on Figures 12
- f. . ~ and 13 with an adjustment to correct the data for i f thermal losses:
z; e corrected Heatyp Rate = Actual Heatup Rate + Factorc (G) j? g, rector *,, Thermal Losses at Teatperature y, (c,) (SFP Inventory Nass) 3 "4:; <l c: Where: Thermal Losses At Temperature are determined ,
- i. - using the equations'and calculation presented a.
g , in Appendix A. y [ f[ m
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- YRC 991 Page 8 of 34 Pages 4.15 The corrected tient-up rate is the rate of SFP temperature increase that would occur if there were no thermal losses. The thermal' loss values were calculated assuming the following conditions, measured during the plant test:
SFP Air Temperature 80*F SFP Air Relative Humidity 65% Outside Air Temperature 55'F Ground Temperature 50*F Mass of SFP Inventory 1,213,000 lb (-12 inches) cp 'l Btu /lb/*F 4.16 The thermal losses at 84'F and 100*F are 0.04 MBtu/hr and 0.09 MBtu/hr, respectively. The correction factors for the temperature range were determined by correlating the results of HEATUP. BAS (Attachment 8) for the conditions above: Thermal Losses =-7 0 02 -14 3 3 ( T,,,) +2 3,47 5 ( T,,,) * (8) Where: Ts ,, is t.he SFP temperature (limits: 84- ' 100*F), 'F 4.17 Incorpotation of thermal losses into the data presented on Figures 12 and 13, using Equations 6 and 7, eliminated most of the trend indicated on Figure 13. Figure 14 presents the results of the correction. The average and standard deviation of these data are as follows: Average Value 0.86 'F/hr Standard Deviation 0.080 'F/hr Number of Observations 131 4.18 The average corrected heat-up rate is used to determine I- the apparent decay heat rate of the fuel in the SFP. I The heat-up rate will be increased to account for data
} scatter and instrument uncertainty (Reference 10):
995 Confidence Interval =2.33 (Std Dev) { / Number of Observations 99% Confidence Interval =2.33 0.080 =0.016 (10) er r p
,;c 4.19 AJbounding value for instrument uncertainty of lot (per RJR evaluation), will be applied direct.ly to the heat-up rate.
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I YRC 991 1 Page 9 of 34 Pages 4.20 The decay heat rate is calculated from an energy balance on the SFP using the corrected heat-up rate. The corrected value accounts for thermal losses, qw,y=(SFP Inventory Mass) (c,) (Adj Heatup Rste) (11) ,, Where: q ,, is decay heat rate, Btu /hr c, is SFP water heat capacity, Btu /lb/'F Adj Heatup Rate =(F,,,,,) (Corrected Heatup Rate +CI) (12) , Where: F CE, is instrument uncertainty, 1.10 ' is confidence interval, 'F/hr b 4.21 Using Equations 11 and 12, the following decay heat rate corresponds to the plant heat-up data:
#UU qw,y= (1,213,000 lb) (1 y ,7) (1.:10) ( (0. 86) + (0. 016) ) I13I t )Q qway=1.2 NBtu/hr (14) a j' 4.22 A similar calculation can be completed to verify the P decay heat determined above. The calculation uses the 1 observed heat-up rate and increases it to account for '
5
' the maximum thermal losses in the data range (0.1 MBtu/hr).
- 1) 15) q,/, w,,,= (1. 213 #1b) (1 lb 'F) (1.10) (0.'81+2.33 (0 qway=q,,,w ,,,+0.1 NBtu/hr=1.2 NBtu/hr (16)
.? 4.23 The calcul'ated value of decay heat differs from that
- estimated using the ANS correlatione (Reference 2).
The decay heat predicted using the ANS correlations is about 2.0 MBtu/hr (580 kW from Figure 15) . This is
..if about 1.8 times greater than the value measured during i j" the plant heat-up test. The ANS results also were f compared against three ORIGEN runs, supplied by Yi Yu .
(RPG). ORIGEN predicts an isotopic brealtdown of the fuel'in the assembly and the decay heat associated with the radioactive decay of those isotopes. ;
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YRC 991 Page 10 of 34 Pages 4.24 The following is a comparison of ANS and ORIGEN predictions: Assembly ORIGEN Calculation ANS Ratio of ANS Thernal Power + Actinides Correlation to ORIGEN A-801 2489 + 143 - 2632 W 4300 W 1.6 B-748 1157 + 65 - 1222 W 1900 W 1.5 B-822 1832 + 9 - 1841 W 3500 W 1.9 4.251he ORIGEN results are significantly lower than those predicted using the ANS correlations. The ORIGEN results approach the decay heat rate measured during the plant test. The calculation method using the ANS correlations incorporates several conservative assumptions: e The decay heat calculation assumes an average power level of 600 MWt from the cycle start-up date to the shutdown date. This does not account for any in-cycle shutdowns, outages, or coastdown. Incorporation of these effects reduces the predicted decay heat rate. e The calculation uses a simplified ANSI /ANS correlation that attributes all fissions to U-235. The standard indicates that this assumption overpredicts decay heat compared to a more detailed method : hat separately accounts for i fissions from each fissile isotope. e The calculation uses maximum correction factors to account for neutron capture and actinide decay. Actual contributions from these effects would be lower, decreasing predicted decay heat rate. 4.26 A decay heat rate consistent with a conservative evaluation of the plant data will be used in the SFP heat-up calculations. The plant data allows a direct determination of the decay heat rate, eliminating the need to rely on unnecessarily conservative
,.. correlations.
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0r.1 I YRC 991 Page 11 of 34 Pages 4.27 HEATUP. BAS (Appendix A) was used to predict the SFP temperature as a function of time for several cases. The following input data were u' sed: e Initial SFP temnerature of 100*F - This corresponds to the upper SFP temperature administrative limit (Reference 11). SFP buildino of 85'F - Increasing the temperature has a minor. impact on the heat-up rate (Note: Attachment 5 presents the effect of higher temperature).
- Relative humidity of 701 Increasing the humidity has a minor impact on the heat-up rate (Note:
Attachment 5 presents the effect of higher humidity). Outside air temnerature of 88'F - This corresponds to the general plant design maximum air temperature (Reference 12). Ground temnerature of 59'F - This corresponds to the maximum expected ground temperature for Ithaca, NY f rom the 1987 HVAC handbook;* -'This""is '"-~ " ~ ~ - - ' the closest location to Rowe for which data are available. SFP volume of 144.500 cal - This corresponds to the low level alarm setpoint of -16 inches in the SFP. 4
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0;. ; 2 YRC 991 Page 12 of 34 Pages 4.28 The following cases were performed and are presented in Attachment 3: Case Date Reference 2 Decay Hours to Hours to
' Decay Rate, Heat, Reach Reach l kW MBtu/hr 180*F 150*F 1 4/8/92 580, Fig 15 1.2 108 58 2 6/15/92 483.26 1.0 142 73 3 9/15/92 410.15 0.85 189 90 4 12/15/92 366.41 0.76 241 104 5 3/15/93 336.06 0.70 305 118 6 6/15/93 312.59 0.65 442 131 7 9/15/93 293.51 0.61 ---
143 8 12/15/93 276.94 0.57 --- 157 y , 9_ -
.3/.15/94 263.36 0.54 ---
170- - - --- - 10 1/1/95 231.27 0.48 --- 214 11 1/1/96 206.48 0.43 --- 269 ; 12 1/1/98 182.01 0.38 --- 372 . 1.3 1/1/00 168.76 0.35 --- 498 { 4.29 The decay heat rates beyond 4/8/92 were calculated by using a ratio'of the decay rate values in Reference 2 to the decay heat rate corresponding to 4/8/92 (580 kW). The 4/8/92 test data decay heat rate (1.2 MBtu/hr) was adjusted by this ratio. 4.30 A lower SFP volune than assumed in the calculation above could occur following a loss of integrity of the ' SFP cooling system. The following assumptions were l
, used to determine the lower volume:
The break flow is terminated within 30 minutes of i the annunciation of the SFP low level alarm. The SFP cooling pump operates at run out condition before it is isolated. Review of the pump curve (Attachment 4) indicates,that the average flow j rate at run-out conditions is about 600 gpm. s t 4.31 The SFP volume following isolation of the leak is the y difference between the volume following the low level 1 alarm (144,500 gal) and the inventory loss (18,000 it , S
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0.51.5 YRC 991 Page 13 of 34 Pages gal): 126,500 gal. This increases the heat-up rate by about 15%. This case was not used as the design case. Following isolation of the break, the operators would inject cooler make-up water to the SFP to re-establish inventory. If the SFP is refilled with water that is less than 100*F, the heat-up times will not be less than the cases presented above.
- 5. RESULTS/ CONCLUSION:
5.1 Figure 16 presents the SFP temperature profile for several of the cases presented above. The results are tabulated in Attachment 3. The rate of SFP heat-up decreases as the decay heat rate decreases. The equilibrium temperature also decreases as the decay heat rate decreases. These both occur because the difference between the decay heat and thermal losses decreases, decreasing the driving' force to heat the SFP. When the decay heat rate equals the thermal losses, the pool heat up stops.
- - - r/2-'Fipr~es ~17 and 18 IEefent graphs 'ortTie tee requireli~~"~ '
to heat-up from 100*F to 180*F and 150*F versus the dates corresponding to the cases above. Figure 17 shows that, by mid-1993, decay heat rate will not be great enough to cause SFP temperature to exceed 180*F. Figure 18 shows that, decay heat rate will not be great enough to cause SFP temperature to exceed 150*F until after 2000. This may be confirmed by collecting additional plant data with additional ~SFP heat-up testing. h s [ h-i t 4 i
0G14 YRC 991 Page 14 of 34 Pages
- 6.
REFERENCES:
- 1. RE 92-034, Results of the Spent Puel Pit Heat-up Test, April 15, 1992.
- 2. TAG-YR-92-013, YNPS Spent Fuel Pit Loss of Cooling Evaluation for Permanent Shutdown, May 8, 1992.
- 3. Kent's Mechanical Engineering Handbook, 12th Edition, Section 17.
- 4. Steam Tables, C-E Power Systems, Reprinted from 1967 ASME Steam Tables.
( 5. Heat Transfer, J. P. Holman, Fourth Edition. 4 6. YRP 174/92, Inventory of Puel in the YNPS Spent Puel Pool, April 24, 1992.
- 7. OP-7000.046, Spent Puel Pit Heat-up Rate Measurement.
-- w - --' - r- Tullalta from computer models analyzing reactor--thermal - - -
hydraulic transients, telecon with R. C. Harvey, May 11, 1992.
! 9. Mark's Mechanical Engineering Handbook, p. 6-10.
f 10. Statistics for Business and Economics, West Publishing
- i. Company.
- 11. OP-2164i Operation of the Spent Puel Pit Cooling and
,y Purification System. . j,, 12. Systematic Evaluation Program, Meteorology, Topic II- ?~ 2.A.
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- yte41 0;.'4!) /oFg, Attachroent 5: Comparison of SFP Room Temp on Heatup Rate Date 4/8/92 4/8/92 Decay Heat. MBlu/hr 1.2 1.2 ;
SFP Air Temp,'F 85 100 l Relative Humidity. % 70 100 Outside Air Temp. 'F 88 88 Ground Temp, ** 59 59 SFP Water Vol, gal 144500 144500 Hours 0 100.00 100.00 1 100,95 100.99 2 101.89 101.98 3 102.83 102.96 l 4 103.77 103.94 5 104.71 104.92 . 6 105.64 105.89 7 106.57 106.86 8 107.50 107.83 9 108.42 108.80 10 109.35 109.76 . . . . . - - . . . . - - - - - . . - . . . . . . 12 111.18 111.67 ; 13 112.09 112.63 1 14 113.00 113.58 ~ j 15 113.91 114.52 l 16 114.81 115.47 ) 17 115.71 116.40 l 18 118.81 117.34 l 19 117.50 118.27 20 118.39 119.20 l 21 119.28 120.13 i i 22 120.16 121.05 23 121.04 121.97 24 121.92 122.88 25 122.79 123.79 26 123.66 124.70 27 124.53 125.60 28 125.39 126.50 29 126.25 127.39-30 127.10 128.29 31 127.95 129.17 32 128.80 130.06 I 33 129.64 130.93
- 34 130.48 131.81 !
35 131.32 132.68 36 132.15 133.65 1 I l l
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.2 of Attachment 5. Comparison of SFP Room Temp on Heatup Rate 37 132.98 134.41 38 133.80 135.26 39 134.62 136.12 40 135.44 136.97 41 136.25 137.81 42 137.05 138.65 43 137.86 139.49 44 138.66 140.32 I 1
45 139.45 141.14 46 140.24 141.96 47 141.02 142.78 48 141.81 143.59 49 142.58 144.40 50 143.35 145.20 51 144.12 146.00 52 144.89 146.79 53 145.64 147.58 54 146.40 148.36 55 147.15 149.14 56 147.89 149.91 57 148.63 150.68 58 149.37 151.44 59 150.10 152.20 l 60 150.82 152.95 l 61 151.54 153.70 62 152.26 154.44 63 152.97 155.18 64 153.68 155.91 65 154.38 156.63 66 155.08 157.35 67 155.77 158.07 68 156.45 158.78 69 157.14 159.48 70 157.81 160.18 71 158.48 160.88 72 159.15 161.56 73 159.81 162.25 74 160.47 162.92 75 161.12 163.60 76 161.76 164.26 77 162.41 164.92 l 78 163.04 165.58 79 163.67 166.23 80 164.30 166.87 81 164.92 167.51
Y#d-99/ O. .;) l 36P( Attachment 5: Comparison of SFP Room Temp on Heatup Rate 82 165.53 168.14 83 166.14 168.77 84 166.75 169.39 85 167.34 170.01 86 167.94 170.62 87 168.53 171.22 88 169.11 171.82 89- 169.69 172.41 90 170.26 173.00 91 170.83 173.58 92 171.39 174.16 93 171.95 174.73 94 172.50 175.29 95 173.05 175.85 96 173.59 176.41 97 174.13 176.95 93 174.66 177.50 99 175.18 178.03 L _ 100 175.70 178.56 101 176.22 179.00 102 176.73 179.61 103 177.24 180.13 104 177.74 180.63 105 178.23 181.14 I' 106 178.72 181.64 107 179.20 182.13 108 179.68 182.62 109 180.16 183.10 110 180.63 183.57 111 181.09 184.04 112 181.55 184.51 l 113 182.00 184.97 f 114 182.45 185.42 115 182.90 185.87 l 116 183.34 186.32 117 183.77 186.76 118 184.20 187.19 119 184.62 187.62 120 185.04 188.04 121 185.46 188.46 122 185.87, 188.87 1 123 186.27 189.28 4 124 186.67 189.68
; 125 187.07 190.08 ) 126 187.46 190.47 2
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N .'iQ p Anachment 5: Comparison of SFP Room Temp on Heatup Rate 127 187.84 190.86 128 188.22 191.25 129 188.60 191.62 130 188.97 192.00 131 189.34 192.37 132 189.70 192.73 133 190.06 193.09 134 190.42 193.44 135 190.76 193.79 136 191.11 194.14 137 191.45 194.48 138 191.79 194.81 139 192.12 195.14 140 192.45 195.47 141 192.77 195.79 142 193.09 196.11 143 193.40 196.42 144 193.72 196.73 145 194.02 197.04 146 194.32 197.34 147 194.62 197.64 -r - 148 194.92 197.93 149 195.21 198.22 150 153.50 198.50 151 195.78 198.78 >- 152 196.06 199.06 153 196.33 199.33 154 196.60 199.60 155 196.87 199.86 156 197.14 200.12 157 197.40 200.38 158 197.65 200.63 159 197.91 200.88 160 198.16 201.12 161 198.40 201.37 162 198.64 201.60 163 198.88 201.84 164 199.12 202.07 165 199.35 202.30 166 199.58 202.52 167 199.81 202.74 168 200.03 202.96 169 200.25 203.17 170 200.46 203.38 171 200.68 203.59
YRe +1/ 4 ;:);5 CW4 Anachment 5: Comparison of SFP Room Temp on Heatup Rate 172 200.83 203.80 173 201.09 204.00 174 201.29 204.20 175 201.49 204.39 176 201.69 204.58 177 201.89 204.77 178 202.08 204.96 179 202.27 205.14 180 202.45 205.32 181 202.63 205.50 182 202.81 205.67 183 202.99 205.85 184 203.17 206.01 185 203.34 206.18 186 203.51 206.34 187 203.68 206.51 188 203.84 206.66 189 204.00 206.82 190 204.16 206.97 191 204.32 207.13 192 204.47 207.27 l 193 204.63 207.42 194 204.78 207.56 195 204.92 207.71 196 205.07 207.85 197 205.21 207.98 198 205.35 208.12 199 205.49 208.25 200 205.63 208.38 201 205.76 208.51 202 205.89 208.63 203 206.02 208.75 , 204 206.15 208.87 205 206.27 208.99 206 206.40 209.10 207 206.52 209.21 I
' 208 206.64 209.32 209 206.76 209.43 210 206.87 209.53 211 206.99 209.64 212 207.10 209.74 213 207.21 209.64 214 207.32 209.93 215 207.43 210.03 216 207.53 3
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Attachment 5: Comparison of SFP Room Temp on Heatup Rate 217 207.64 218 207.74 219 207.84 220 207.94 221 208.03 222 208.13 223 208.22 224 208.31 225 208.40 226 208.49 227 208.58 228 208.66 229 208.74 230 208.83 231 208.90 232 208.98 233 P09.06 234 209.13 235 209.20
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236 209.27 237 209.34 238 209.41 239 209.48 240 209.54 241 209.61 242 209.67 243 209.73
,244 209.79 245 209.85 246 209.91 247 209.97 248 210.02 i:
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YA!HP9/ - U i;V1' soft ATTACIDENT 7 BUMMARY OF SFP DIMENSIONS Location' Dimension Reference Top of SFP 1045 ft Dwg. FM 19B Normal Water Level 1044 ft OP-3615 Low Level Alarm Setpoint 1043 ft 8 in OP-3615 SFP Cooling Pump Suction 1031 ft 3 in Dwg. FP-54B Top of Top Rack 1027 ft 9 in Dwg. 60-0014 5/10 Bottom of SFP 1008 ft Dwg. FM 19B SFP Width 16 ft 6 in Dwg. FM 21A SFP Length 33 ft 8 in Dwg. FM 21A
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/ OFI 1 ATTACEMENT_8 TEIRMAL LOSS AS A FUNCTION OF TEMPERATURE I 1
Temnerature, *P Thermal Loss,' MBtu/hr 84.4 0.038 85.3 0.041 , t 86.1 0.043 87.0 0.045 87.9 0.048 88.7 0.050 89.6 0.052 90.5 0.055 91.3 __ 0.057 q .- . . 92.2"*
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\
97.3 0.075 l , 98.1 0.078 - 99.0 0.080 99.8 0.083 - Note: The thermal losses reported above were calculated from k- a HEATUP. BAS run at the test conditions: E Decay Heat, MBtu/hr 1.1
@ SFP Air Temp, 'F 80 f* Relative Humidity, % 65 ji. Outsida Air Temp, 'F 55 1:. Ground Temp, 'F 50 SFP Water Vol, gal 145800 i j' > The'following empirical equation was regressed to
'y relate thermal losses to SFP water temperature:
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YM/ 0 $ s*IU /bN l Attachment 9: Heat-up Rate Correction For Low Temperature Data Thermall.oss Corrected 1 7 Thermoco'u ple Temperature Heat-upRate OTemperature Heat-up Rate identifier 'F 'F/hr MBtu/hr 'F/hr TC-2 85.0 0.86 0.040 0.89 TC-2 86.2 0.73 0.043 0.77 TC-2 87.4 0.71 0.046 0.74 70-2 88.9 0.92 0.050 0.96 TC-2 90.4 0.92 0.054 0.96 TC-2 91.6 0.71 0.058 0.75 TC-2 93.0 0.86 0.062 0.91 TC-2 95.0 0.76 0.068 0.81 TC-2 96.4 0.87 0.072 0.93 ' TC-2 97.8 0.86 0.077 0.92 TC-2 99.0 0.73 0.080 0.80 TC-3 85.1 0.92 0.040 0.95 TC-3 86.4 0.80 0.044 0.83 . . . _ , . . . . _ . . .TC-3 . 87.7 0.76 0.047 . _.0.80. _. . . . . . , _ . . TC 3 89.0 0.80 0.051 0.84 TC-3 90.5 0.32 0.055 0.96 TC-3 91.7 0.71 0.058 0.75 TC-3 90.1 0.86 0.062 0.91 TC-3 94.1 0.62 0.065 0.67 TC-3 ' 95.3 - 0.70 0.069 0.76 TC-3 96.6 0.80 0.073 0.86 TC-3 98.0 0.86 0.077 0.92 TC-3 99.3 0.80 0.081 0.86 TC-5 85.2 0.92 0.041 0.95 TC-5 86.5 0.80 ' O.044 0.83 TC-5 88.0 0.88 0.048 0.92 TC-5 89.4 0.86 0.052 0.90 TC-5 90.6 0.73 0.055 0.78 TC-5 92.1 0.88 0.059 0.93 ," TC-5 93.4 0.80 0.063 0.85 TC-6 94.4 0.62 0.066 0.67 TC-5 95.8 0.82 0.070 0.87 .g TC-5 97.0 0.74 0.074 0.80 ,' TC-5 98.5 0.92. 0.079 0.98 o~ TC-5 99.8 0.80 0.083 0.86 , TC-6 85.0 0.98 0.040 1.01 I TC-6 48.8 0.80 0.043 0.83 h):'s:2. t ' TC TC-4 87..
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Ytt-49 i Oi10 aor54 Attachment 9: Heat-up Rate Correction For Low Temperature Data - 1 k i
. ThermalLoss Corrected q Thermocouple Temperature . Heat-up Rate @ Temperature Heat-up Rate j Identifier 'F *F/hr MBlu/hr 'F/hr TC-6 94.3 l
0.80 0.066 0.86 . TC-6 95.7 0.82 0.070 0.87 l TC-6 97.0 0.80 0.074 0.87 l TC-6 98.3 0.80 0.078 0.86 l TC-6 99.5 0.73 0.082 0.80 l TC-7 84.6 0.86 0.039 0.89 i TC-7 86.3 1.04 0.043 1.08 TC-7 , 87.6 0.76 0.047 0.80 TC-7 89.2 0.98 0.051 1.02 TC-7 90.3 0.67 0.054 0.72 1 TC-7 91.7 0.82 0.058 0.87 TC-7 93.2 ' O.92 0.063 0.97 TC-7 94.6 0.87 0.067 0.92 TC-7 95.6 0.50 0.070 0.84
. . .TC-7,. . 96.9 .0.80 . 0.074 . . ... 0.86 l
TC-7 99.5 0.57 0.062 0.74 TC-9 84.4 0.80 0.038 0.83 TC-9 85.8 0.86 0.042 0.89 l
- TC-9 87.4 0.9 t 0.046 0.98 TC-9 88.7 0.80 0.050 0.84 TC-9 90.0 0.80 0.053 0.84 TC-9 91.4 0.82 0.057 0.87 TC-9 92.6 0.73 0.061 0.78 , i TC-9 94.0 0.87 0.065 0.92 1 TC-9. 95.4 0.82 0.069 0.87 :I TC-9 96.9 0.93 0.074 0.99 ;
TC-9 98.0 0.67 0.077 0.74 '
.TC-9 99.3 0.80 0.081 0.86 .
TC-10 84.2 0.80 0.038 0.83 : TC-10 85.7 0.92 0.042 0.95 . TC-10 87.2 0.88 0.046 0.92 TC-10 88.6 0.80 0.049 0.84 TC-10 89.9 0.86 0.053 0.90 TC-10 91.2 0.76 .0.057 0.81 TC-10 92.6 0.86 0.061 0.91 70-10 93.9 0.80 0.065 0.86
.l TC-10 98.8 0.82 0.069 0.87 ,k TC-10 ~96.6 0.80 0.073 0.86 h 70-10 .98.0 0.86 0.077 0.92
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*a a 9: Heal-ep Rate Correcelon For Low Temperature Data Thermal Lo:s Corrected Tncemoconda Temperature Heat-upRate @ Temperature Heat-up Rate Idenfit;st *F *F/hr M8tu/hr 'F/hr TC-11 85.9 0.92 0.042 0.95 TC-11 87.3 0.82 0.046 0.86 TC-11 88.6 0.80 0.050 0.84 TC-11 89.9 0.80 0.053 0.84 TC-11 91.4 0.88 0.057 0.93 TC-11 92.7 0.80 0.061 0.85 TC-11 94.2 0.93 0.066 0.98 TC-11 95.4 0.70 0.069 0.76 TC-11 96.9 0.93 0.074 0.99 TC-11 98.1 0.73 0.078 0.80 TC-11 99.4 0.80 0.082 0.86 TC-12 84.1 0.73 0.038 0.77 TC-12 85.5 0.86 0.041 0.89 TC-12 87.0 0.88 0.045 0.92 TC-12 88.4 0.86 0.049 0.90 TC-12 49.6 0.7 '. O.052 0.78 70-12 91.0 0.82 0.056 0.87 TC-12 92.4 0 86 C.050 0.91 TC-12 93.7 0.00 0.064 0.86 TC-12 95.2 0.8
- 0.060 0.93 TC-12 9C.6 0.87 0.073 0.93 TC-12 97.9 0.80 0.077 0.66 .
TC-12 93.0 0.67 0.080 0.74 . 70-13 84.4 0.70 0.038 0.77 TC-13 85.8 0.86 0.042 0.89 TC-13 87.3 0.88 0.046 0.92 TC-13 88.6 0.80 0.050 0.84 TC-13 89.9 0.80 0.053 0.84 TC-13 91.2 0.76 0.057 0.81 1
- TC-13 92.7 0.92 0.06t 0.97 )
TC-13 93.9 0.74 0/A5 0.80 TC-13 95.4 4.47 0.069 0.93 TC-18 96.8 0.87 0.073 0.93 70-13 98.0 1K73 0.077 0.80 70-13 99.2 0.73 0.081 0.80 TC-14 84.4 0.73 0.038 0.77 TC-14 85.7 0.80 0.042 0.83 TC-14 87.2 0.88 0.046 0.92 TC 88.5 0.80 0.049 0.84 TC-14 89.7 0.73 0.053 0.78 ' 70-14 91.1 0.82 0.056 0.87
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- l YRC 991 ,' i Page 1 of 7 APPENDIX A !
SFP HEATUP PREDICTION METHOD l l l This appendix documents the methodology.used to calculate SFP l heat-up as a function of time. The calculation uses an energy balance on the SFP that accounts for thermal losses to the environment and decay heat generation. Decay heat that is not lost to the environment increases the SFP water temperature. A QuickBASIC computer program, called HEATUP. BAS has been written to facilitate the calculation. , 1 The following method is used to calcalate the SFP heatup rate for i each time increment:
- 1. Determine energy loss from evaporation by the following equation:
(Evap) (Ares,agu..) (Hg,)
***" hr (17)
( Vg ) Up..3 inch) (24 day "- Where: q,,, it. energy loss from evaporation, j Btu /hr Evap is rate of evaporation from the SFP surface, in/24 hr Area,,,,, is SFP water surface area, ft,
. H,, is latent heat of vaporization at SPP temperature, Btu /lb V, is specific volume pf SFP water at SFP temperature, f t /lb Evap=0.771 (1. 46 5-0. 0186
- P,e ) (0. 4 4 +0.118
- W) ( VPm-VP,e.) (18) i Where: P,,, is barrometric pressure, in. Hg I W is wind speed, sph 7P,,, is water vapor pressure at SFP temperature, in. Hg VP,,, 'is water vapor pressure at SPP building temperature and humidity,
,; . in. Hg VP,,,= (VPm,j,) (Relative Humidity) (
100 v.- w. S j ?,1, Whers: VP,,, 9 is water vapor pressure at SFP l y building temperature, in. Hg l
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YRC 991 l Page 2 of 7 Equation 18 is from Kent's Mechanical Engineering Handbook (Reference 3) -Two other methods of predicting evaporation ratea were investigated: - Buffalo Forge Company Fan Engineering Manual (Eq 5.25). Calculation of mass transfer coefficient from Nusselt number for free convection from a horizontal plate. Equation 16 was chosen because it was developed explicitly for reservoirs. Also, Equation 16 predicted the lowest evaporation rate, and therefore, resulted in the highest SFP heat-up rate.
- 2. Determine steady Otate energy loss from convection from the surface of the SFP using the following equation:
%nv" th s,,) (Areasurrac,.) ( Ts,,- T,,, ,,,) (20)
\
Where: q,. is enerqy loss from convection, Btu /hr hs ,, sfer is convectiveBtu coefficient, heat trap
/hr/ft /*F Area,urg,J- in SFP water surface area, ft, Ts ,, is SFP water temperature, *F Ts ,, ,i, in SFP building air temperature, 'F A heat transfer coefficient of 1 Btu /hr/f t /*F was used in the calculation. This value is based on a calculation from a correlation of Nusselt number for free convection from a flat plate. The calculation of the heat transfer coefficient is included as Appendix B.
- 3. Determine steady state energy loss from conduction through the walls and floor of the SFP. Two equatic,ns were used to estimate the thermal loss from conduction, one equation for walls above ground level and one equation for walls and floor below ground level:
(k,,,,,,,,) (Area u j,,,) (T,,,-Tuso,,)
**""'**'" '2" Wall Th1ckness (k,,,,,,,,) (Area,u.) ( T,,,-T u.)
Wall Thickness Q2)
. Where: q,,n, is energy loss from conduction above and below ground level, O Btu /hr k,,,,,,,, is thermal conductivity of 1,i. -
T., concrete, Btu /hr/ft/*F
- Area is SFP wall and/or. floor area above
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- YRC 991 .
Page 3 of 7 l and below ground level, ft' Ts ,, is SFP water temperature, 'F !< T is outside air temperature for above ground level case and ground ' temperature for below ground level case, 'F The SFP dimensions are approximately 33.7 ft x 16.5 ft x 36 : ft (LxWxD). The wall area above ground was determined by ,) evaluating drawings 9699-FM-p1A and 9699-FC-45B&C. The : below gyound area is 2115 ft and the above ground area is ! 2053 ft. The wall thickness is 6 ft. A thermal ' conductivity of 0.75 Btu /hr/ft/*F was used for concrete. ' This value is based on the average of several sources. J
- 4. Calculate the total thermal lor,ses from the sum of the j individual losses: j 72 eu.
- 7.v.p+ 7eonv+ ( 7c ) ,3.,,+ (Ocond) 3,3,,
(23) i
- 5. Calculate the energy that..is accumulated during the time ~ ~ ~ -~ ~ '-
interval from an overall energy balance: ~ ~ ~ ' )
- e. _ .-e - .,-e,..... (24>
l Where: q m ,y is decay heat rate, an input parameter to the calcul'ntion, Btu /hr.
- 6. Determine the temperature rise from the accumulated energy during the time interval:
#***"" (25)
T "**"= (c,) (SFP Inventory M&BB) A Where: T w ,,,,, is SFP temperature increase over the time period, 'F
;. c, is the heat capacity of the SFP water, Btu /lb/*F SFP Inventory is the mass of water in the SFP.
? This is calculated based on the water volume and the density at the
@ initial SFP temperature, lb Determine the SFP temperature at the end of the time
~
h,k 7 increment by adding the temperature increase to the SFP temperature at the beginning of the time increment. This calculation ~ method.is completed for each time' increment until either;the temperature reaches 210*F or it reaches an Luy,
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4. YRC 991 Page 4 of 7 equilibrium value (less than 0.01*F increase from the beginning
,, of the time increment).
HEATUP. BAS performs the calculation outlined above. The program uses the following default values: Barometric Pressure 29 inches Hg Time Increment 1 hour Wind velocity 0 mph Concrete Thermal Conductivity 0.75 Btu /hr/ft/'F SFP Wall Area Above Ground 2053 ft SFP Wall and Floor Area Below Ground 2115 ft Concrete Thickness 6 ft Convective Heat Transfer Coefficient 2 1 Btu /hr/ft 7.p The following are input values to tha program: Initial SFP Water Temperature Decay Heat Rate SFP Building Air Temperature SFP Air Relative Humidity Outside Air Temperature Ground Temperature
, SFP Water Volume The program uses saturated water properties from a file containing. steam table data from Reference 4. At the beginning of each time increment the program assumes the properties are equal to those corresponding to the initial temperature. Once the fins 1 temperature is calculated, the calculation is re-executed.using an average of the properties at the initial and final temperatures. The programs continues to iterate until the final temperature is within 0.01*F of the previously assumed temperature.-
Input parameters and the following output values are printed in a file called SFP.DAT: Time SFP Tenqperature .
,. Thermal Losses A listing of the program is appended to this appendix.
Attachment 6A and 6B present a detailed output from two runs corresponding to the cases developed for 6/15/92 and 6/15/93, respectively. The detailed output was developed to facilitate
^- Program verification activities.
e
- = ~~ o e - -
"w 9p g s p ~p e r
stetAtt rt'WCTION interpoletet (svalt, al(1. yl(). mustI sin toepdatet100) vpreedata(100). Wadste(100), speevoldata(190)
- Input dets for entculatten OPtN *c:geb45tdatatproperty.dat". Wee INrVT AS $1 IMPUT 41, duenyt
, INrtff fl. duesy4 ie8 ~
30 intf 8L 80F(1) ie i e1 INPUT 41. tempdatati) wpreedatati), hiedstati), speevoldatafi) LOOP CtOS$ 81 mundsta e i IMPUT *Imput Initial STP Toeperature, d (Di44)*3 toepinit INPVF " Input Decay West Este. MBfv/hr (Del.fi)*; deceyheet INPUT " Input srP Svilding Air Toeperature, af 19s0S]"; eYpairteep IMPUT " Input selatswo Numidity 1 (Ds50)"; rethumidity [ INPUT " Input Outside Air Toeperature, d 10 55)*; outaf s t ep INPUT *Imput Cround Temperature, d (De50)"i steundteep INFL'T
- Input SFP Initial Volume, sal (Dal37570]"; sfpal
- If toepinit e TO TMEN tempinat a 80 IT dese W at <s 0 TutN decayheat 1 IF erpairteep a 40 TNEW ofpairteep e 80 It relhumidity <s 0 THEN rethumidity a so IF outairteep as 0 THEN outalrteep S3 IF gesundtsap ts 0 THEN groundteep a 50 f.". IF afpvol a $0000 TNEN ofyvel a 137510 D
;f
- Initialise pereestore M-r-
*j eastlee e See 'llazieus ties for trenelent. hr tioe e 8 ' Initial ties he I - thselec e 1 'Taes increment, hr
. basemeter a 28 'Basemetric preneure in 5g
{h , erled e e ' Wind speed, ash
*. ha - *ete e .1$ ' Concrete easspmat sonductivity. BTU /ft/hr/ d fs, es.dereen e e n u *.r,e.n e.e. ano .re d lov.i. fin Q3 esadareebelev e till - 'stP es11/ fleer area belev ground level, f t2 M evegerse s $55.5 art meter eerfees area, ft2 f eenethick e S 'str eenerete 90itekeese, f t j k htestp e 1
'convoeties Est. BTU /hr/ft2/d apsip e 1 '8PF enter heet sepacity, BTV/lb/af
- , ,evepfester a 3 'Facter to leeresse eveperstlen rete 1
e 9stereine ester partial pressere la a&r g;}
=yg. -
- mer , setpresseb e &aterpolate(efpsitteep.' h.eproedata(),ausdata) ,
---,h,opecesch,e*estpreemd*peltaald&ty/30$
d #
'4 9 < - t . .i _ ., -
a .k ,, d s .-,; .* ,f6 , ' , , W"7,,;j. iw .. . Detereise h w.ww.8ett)st ester peepepttes l W ' < . , ,'P .. > :d ~ r: M 7 a ^:' w,W C ) ? "..s.. n M .' sL ,. p n. &, u,p.t. A. e %p;;1., . .: m ,. M., % ,. 4, M .9...be ,gygepdate(q),,dts)1
'Q s
- 9 h, i Tr EEIO O $ '8 .
Altg} . , J- i t.
l
'stp.m.se e of6*w l / Cpecselinit a .13348 gg4g 8 OF I !
' Initsalise pareesters far leep cals (0 e start of time tr6ttrv21)
* (1 e end af time ixtseval )
vpreso e vpresinit hfs0 i hfginit speese10 s specvelinit tonce e.tempinit tempt a tempo f toepheld e toopt print out inittal data
.( . '
M. OPEN *c \qb4$1detagefp.dat" pot OUTpVT AS 41 . u pSfpf fl. "' Decay 5*et. ISTV/hr'"3 decayheat palNT el. "'8Fp Air Tempe aF'"3 efpairtoop ptINT $1. ** Relative N e idity. S'"3 relhueidity PRINT fl. "'Outside Air Temp af'"3 outairteep
- ptINT 01. **Creund Toep af'"3 groundteep h,; PRINT $1. "'8Fp Water Vel, gal'"3 ofyvel e
U-1 time e time e tieeinc f.: tops
- r. -
-1
., toepheld a toep!
g.
- Determine average pawporties k -
toegeva e (toepe e toept) / 2 ( 4- {. ' vprest e interpelate(toepte tempdate(), vpreedatat). nundate) hfst e interpelatettempt, toepdatat), hrsdatat), nadate) [}.! epeevell e laterpelatettempt, taopdata() speeveldatat). andata)
*i .
a ti verosegg e (vpreso e vprest) / 2 hisevs ? (htg4 e higt) / 3' , j} speevelava e, (opeeve10 e speevell) / 2
. 0, jc
- Calculate evaporative heat less L. ,
k eva , 771'* (1.465 . 9104 e bareseter) e (.44 e .118 e wied) e (vpreeave - vprosesh) e 3 034 deltaheves e everfector e evey / speovelays e evapaces a hfgavs / 12 / 24 d.I Calculate eenductive losses through es11e B4 .
- d ,
D detteht a hennerete e condarembelev e (temperg . groundtemp) / eenethiek ? e (tempovs . entairtemp) / eoecthick l h,] deltabt a keenerete e seedereeabove
. detteheend e deltaat e deltaht .,
yg,,,', .. celeulate soevective heet lees Ydeltaheenv e hteefp's evepares e (tempaws ofpairtemp)
- f,; .
..s. .,
- Qi . .: hh.*/.}{,h', ,
r,)l,*- ', t
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'W'$
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- 4estseeps - toseheld) f ew-t it, ,
ir test > .81 intu C0to top OEt& prixt recults PalWT el, tiet; toepli detteheut
.Palprf time; toept; deltaheet i
l
- Initialise enesket iteralien
[ deltateep
- tempt
- tempe t j. ;
I f- time e time e timoinc
- y. vprest a versal l hfg8 e hfst l l 4 st xve80 e specvell tempe e tempt
\
IF toept a 210 TERN C0f0 theemd 4
'.'t.
- If ttee e samtise AND deltateep 9 .01 THEN COTO top tl' it
([ theend! 5k C10st 41 L' h, " p.
,i. - , r- - - -- - . . . . . _, ..
r g;
- FUDCTION interpolate (sval, su , y(), mus)
F08 i e 2 70 eue O.
#' IF wat's s(1) THEN C0f0 interp m,..
l
- - .,3:37 8 1>. ...
Tj , interpt. pr g~ g twel * (yta) - vf1 - 1)) / (sti) - sti - 1)) e (sval - a(1 - 1)) e y(4 . 1) m..' Q i'.-laterpelote e Yvel l t- ? -
= S?' aus remet 0m ,
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Owganha.swadduNesm* sm.tw wa
e 4 YRC 991 Page 1 of 3 APPENDIX B CONVECTIVE HEAT TRANSFER COEFFICIENT PREDICTION This appendix', documents the methodology used to calculate the heat transfer coefficient used for convective heat. transfer from the surface of the SFP. The calculation uses a methodology outlined in Reference 5. The heat transfer due to convection is small compared to the evaporative losses, the effect of changing conditions of the air are not considered. The calculation uses properties at an average temperature between 85'F and 140*F, properties were also taken from Reference 5. 1 Use the follow'ing equation for Nusselt number as a function of Grashoff and Prandtl numbers from Table 7-1 of Reference 5: Nu=0.54(GrPr}:Is [or ogpg,px30s.ex30s (26) Nu=0.15 (GrPr) 1/2 for GrPr=8x10 -1x2 0 8 11 (27) 2 Nusselt number (Nu) is defined as follows: Nu = ---- (28) Where: h is heat transfer coefficient, Btu /hr/ft2/*F D is a charact<ristic dimension, Area / Perimeter (Reference 5), ft k is thermal conductivity, Btu /ft/hr/*F 3 Prandtl number (Pr) is defined as follows:
#E (29)
Pr= k Where: c, Btu /lb/*F lo is heat capacity Ib /ft/sec y viscosity, k is thermal conductivity, Btu /ft/hr/*F 1 i '4 Grashoff number (Gr) is defined as follows: Gr=- 8' (30) gtZ k' em R$j Where: D is a characterist'ic dimension,
- a Tc
/,1 * ' hh k h:
- f.i *
~
s
* .h :
;W
, ^[l 4 J h 4 f / ., ,e 1
l u ' - - - _ _ _
0i.>1 l 1 YRC 991 Page 2 of 3 Area / Peri:reter, ft p is density, Ib/ft3 g is gravitational acceleration, ft/sec2 8 is thermal coefficient of volumetric expansion, 1/T, *R AT erature, *F p is is viscosity, Ib/ft differential temp /sec D, the characteristic dimension is the area of the surface of the SFP divided by the perimeter. The length and width 5 of the SFP are 33'8" and 16'6*.
- p. (33.7) (16.f.) =5.54 f t (31) 2 (3 3.7 +16. 5).
6 The following properties and constrnts were used to complete the calculations -(an average ten:petature of 113*F was used): 4 p(viscosity) - 1.3103x10 lb/ft/sec (~ c heat capacity).- 0.2405 atu/3b/*F , ' ~ ~ ~ ~ - -- k,-(thermal ( conductivity) = 0.01595 Btu /ft/hr/'F g(gravitational acceleration) =J2ft/sec2 R(ideal gas constant) = 1.544x10 ft-lbf/lbmole/*R MW air (molecular wt of air) - 29 lb/lbmole 7 The density of air was calculated from the ideal gas law: 8 8 p, (14.0 psla) (144 in /fi ) (29 lb/lbmole) =0.0661 N# i (1544 lbmole *R) (113 +460 *R) j 1
'8 The thermal coefficient of volumetric. expansion is the inverse of absolute temperature for an ideal gas:
1 (33)
= 0. 0017 45
$ = 113 +46 0 9 Calculate Grashoff numbers 58
- Gr= (5.54)8(0.0661)8 (32) (0.001745) (140-85) =1.329x10 (34)
(1. 3103x2 04)
- g ,
e > t.> r6,. 10 Calculate Prandt1 numbers , . (35) fij? Pr= (0.2405) (1.3103x10~5) (0.01595) (3600 sec/hr)) =0.71 : 9e "- e P
- ' eg g 3 , , _ ,
%1
M' . .. .a..
h g* b.[ .aChk_i.3,.m
. ,..>.%s f.,. k. m c.y.. n..,u;c.dNJ,h{3,;.
.'- U[ E,hfe; a s-#'./ .e. shS $9
,m
,...,r... . .'..
.;. .j l:i:,z E;).ff^::. ?Rg:%%:29:1.; . pp;4. cy. . . 'n wig a .5 - .: c.
l O}02 YRC 991 Page 3 of 3 11 Calculate Nusselt number: Nu=0.14 ( (1.329x2 010) (0.71) ) 1/8 =296 (36) 12 Calculate heat transfer coefficients h= Nu, (296) (0.01595) =0.85 Beu/f t2/hr/'F
-- (37) o (5.54) i; ' ' * * ' ' * ' * * * * **P.* u. . . . . . . . . . , , ...
k . 1 O hr s E
.c.
f
.P.
0-E Vp k.;,-.
,t-
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xf.,J . Uli [y'e R 7, 6 ' lt. b', . '. ~ ,
' . ,5.
.l$. . ; Il; , , , ,
pyy. _g f?; t' t. . 'r,',,
- )..',f . ' .3
.l, A ?. , , ., ,
, L.
t , s .
~k . p ', -'* ;y
~gj g e . ~.c i, . g p. ;. .,, ,; . . ,. . .,
~,
b,;g. , s # i-( r .; ,
- '~,
1 r g Olish A ry of calculation Review YEC 991 w 0 ; 1 sa The following attributes, methods and results were reviewed,and/or verified:
- 1. Calculation of decay heat level using the data obtained during SPP heatup test on April 7-11, 1992.
- 2. Use of reference 2 results to predict future decay heat ,
levels.
- 3. Verification of LOWS spreadsheet calculations of average heatup rate and standard deviation. l
- 4. Verification of all physical data and g'=*4ans used in the_.
i HEATUP. BAS 1
- 5. Verification, by hand calculathn, . of HEATUP. BAS results !
reported on attachment 6a for the 6/15 2 case. 1 l a - - - - P. SheldonT.__.1 . . . _ _ Yankee Project 1 d 0 40
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