ML17179A890

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Validation of Loss of HPCI Room Cooler Analysis at Dresden Station
ML17179A890
Person / Time
Site: Dresden  
Issue date: 09/14/1992
From: Kong, Kovan K, Ramsden K
COMMONWEALTH EDISON CO.
To:
Shared Package
ML17179A889 List:
References
RSA-D-92-05, RSA-D-92-05-R00, RSA-D-92-5, RSA-D-92-5-R, NUDOCS 9305120193
Download: ML17179A890 (34)
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ENCLOSURE 1 CECo Calculation RSA-D-92-05 Validation of Loss of HPCI Room Cooler Analysis at Dresden Station

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Documellt Number RSA-D-92-05 September 11, 1992 Kevin B. Ramsden Nuclear Fuel Services Department Commonwealth Edison Company Chicago, lllinois Date: '7/11/?-z_

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Statement of Disclaimer RSA-D-92-05 Rev.O This report was prepared by the Nuclear Fuel Services Department for use internal to Commonwealth Edison Company as applicable to the Dresden Nuclear Generating Station. It is being made available to others upon the express understanding that neither Commonwealth Edison Company nor any of its officers, directors, agents, or employees makes any warranty, representation, or assumes any obligation, responsibility with respect to the contents of this report, its accuracy, or completeness pertaining to any usage other than the originally stated purpose.

Abstract jj

Abstract RSA-D-92-05 Rev.O The purpose of this calculation is to validate the analytical methodology employed in the calculation of HPCI room heatup at Dresden Station. Previous analyses have employed the RELAP 4 Mod 6 computer code to calculate the transient bulk temperature that would result from the loss of room coolers during LOCA events. In this calculation, an exact analytical representation of the wall heatup is provided for comparison to the RELAP calculations, confirming the applicability of the code and models for this analysis.

Abstract iii

RSA-D-92-05 Rev.0 Table of Contents Statement of Disclaimer................................................................................... ii Abstract..................................................................................................... iii Table of Contents......................................................... ;................................ iv List of Illustrations......................................................................................... v

1. Introduction............................................................................................. 1
2. Description of Analysis.................................................................................. 2 2.1 Analytical Solution of Transient Heat Conduction Problem................ 2 2.2 RELAP4 Mod 6 Calculation.................................................... 2 3.0 Results of Calculations................................................................................ 4 3.1 Integral Transform Solution..................................................... 4 3.2 HPCI Room Heatup with RELAP 4 Mod 6................................... 6 4.0 Conclusions...................... *...................................................................... 10 References............ ;..................................................................................... 11 Listing of Computer Cases............................................................................... 12 Appendix................................................................................ *.*................... 13 Table of Contents iv

List of Illustrations RSA-D-92-05 Rev.O Figure 1 HPCI Room Model............................................................................ 3 Figure 2 Analytical Solution of HPCI Room Heatup................................................. 7 Figure 3 RELAP 4 Solution of HPCI Room Heatup................................................. 8 Figure 4 Comparison of Analytical and Numerical Solutions....................................... 9 llb1~tratioos v

1. Introduction RSA-D-92-05 Rev.0 The purpose of this calculation is to respond to questions raised during the review of previously submitted calculations [References 1,2]. Specifically, the use of the RELAP 4 Mod 6 computer code was questioned, and a validation study was suggested. This calculation has been prepared to document analyses performed in response to these requests.

Introduction 1

2. Description of Analysis 2.1 Analytical Solution of Transient Heat Conduction Problem*

RSA-D-92-05 Rev.O An analytical solution of the HPCI room heatup problem was developed. It was recognized that the HPCI room heatup is primarily dictated by the heat transfer characteristics of the concrete walls.

The choice of surface heat transfer coefficients affects the temperature difference between the room* bulk air temperature and the surface of the wall, but once the temperature difference is established (establishing the heat flux into the walls), the rate of heatup of the room is solely dictated by the concrete thermal behavior. The analytical solution developed utilizes integral transform methods to solve the Fourier heat conduction equation for a slab.

The boundary conditions selected for this calculation were a constant flux to the concrete and a constant temperature boundary on the outside surface of the walls. A linear temperature variation from the interior to the exterior of the walls was utilized as an initial condition. The solution yields the transient temperature distribution in the slab.

The surface temperature for a slab with surface area and heat flux equal to that of the HPCI room was calculated. A slab thickness of three feet and outside temperature of 65 F were used.

Since the choice of surface heat transfer coefficient establishes the temperature difference between the bulk air and surface, the bulk air temperature was calculated based on the temperature differences for surface heat transfer coefficients ranging from the most conservative (natural convection only) to the design value used in HVAC calculations.

2.2 RELAP4 Mod 6 Calculation A RELAP model was set up that paralleled the conditions of the hand calculation described above. Two cases were run, using a surface heat transfer coefficient of 5 BTU/HR-FT2-F, and 1 BTU/HR/FT2-F.

These were run to confirm the hypothesis that the heat transfer coefficient was of secondary import, and to provide a.basis for direct comparison to the hand calculation. A diagram of the model is shown in Figure 1.

Description or Analysis 2

Description of Analysis Room Heat Source Two sided Heat Slab SINK 65 F Figure 1 Room Model RSA-D-92-05 Rev.0 3

3.0 Results of Calculations 3.1 Integral Transform Solution The solution of the heat conduction equations yields a series solution of the form:

T(x,t)=Tss (x) +I: Vn(t)

  • Kn(x)/Nn Where:

Tss (x) = Steady state temperature distribution = Tout+ Q/k*(a-x)

Kn(x) =cos[(2n-l)7tx/2a]

2 Vn(t)=Vn(O) e-aA.t V n(O)=[To-Tout -Qa/k]*4a/(2n-1)27t2 N=(2n-l )7t/2a and To= initial surface temperature (120 F)

Tout= outside boundary temperature (fixed at 65 F) a= wall thickness (3 feet) x = position in slab (feet)

RSA-D-92-05 Rev.O Q= average flux to inside wall (31.382 BTU/ft2) based on 200000 BTU/hr total heat input and wall area k= 1.05 BTU/hr-ft-F Thermal conductivity a=k/cp*p =0.038 ft2/hr The detailed derivation of this solution is presented in its entirety in the Appendix. This expression can then be evaluated numerically at T(O,t) to determine the wall surface heatup versus time for comparison to RELAP calculations. The heat transfer coefficient can then be used to determine the temperature difference between the slab surface and the room bulk temperature~ which is the figure of merit with respect to equipment qualification issues.

Results of Analysis 4

RSA-D-92-05 Rev.0 The impact of selection of overall heat transfer coefficient on the room side can be investigated as follows:

Q=UA(Troom*Twall)

Q/A=31.382 BTU/FT2 = U(Troom*Twall) therefore Troom = Twall + 31.382/U Note Twall = T(O,t) previously determined This leads to the following table of temperature differences:

Overall Heat Transfer Coefficient Temperature Difference (Troom-Twall)

(BTU/hr-ft2-F)

(Degrees F) 5.0 (RELAP default minimum) 6.277 1.46 (AHSRAE typical-includes radiation) 21.5

0. 7 (typical convection -only) 44.8 The above table shows the minimum temperature difference required to obtain the stated heat flux value with the given heat transfer coefficient.

If the heat transfer coefficient were recalculated based on the temperature differences in the table for the last two entries, a higher value would result, indicating a conservative treatment with respect to the temperature differences predicted. (i.e. the temperature differences for higher heat transfer coefficients would be less) Figure 2 illustrates the analytically derived wall surface temperatures and the resultant bulk room air temperatures for this transient.

Results of Analysis 5

3.2 HPCI Room Heatup with RELAP 4 Mod 6 RSA-D-92-05 Rev.O The RELAP model was exercised at the conditions described previously for comparison to the analytical solution. The results of the RELAP calculations are shown in Figure 3. Note that the air temperature rises faster than shown in these figures.

The temperature difference is normally established within 30 minutes or less. Figure 4 provides a comparison of the wall surface temperature generated by analytical and numerical methods.

As can be seen, the solutions agree virtually exactly, to within 0.1 degree F.

Results of Analysis 6

Dresden HPCI Room Heatup Calculations HPCI Room wall heat transfer problem Integral Transform Solution Wall and Room Temperatures u..

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Dresden HPCI Room Heatup Calculations HPCI Room wall heat transfer problem RELAP4 Mod 6 Results for U=5(B) and U=1 (C)

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4.0 Conclusions RSA-D-92-05 Rev.0 The HPCI room heatup due to loss of room coolers has been determined by purely analytical methods for comparison with the numerical methods previously utilized.

This comparison demonstrates the validity of the numerical methods utilized to date. It should be noted that the solution generated here employed a constant temperature boundary condition on the outside surface of the walls, selected for the convenience of the analyst.

The actual analysis performed previously applies more restrictive boundary conditions on the outer surfaces of the walls to ensure conservatism in the solution. The solutions generated here are intended to demonstrate the basic physics of the problem and validate the numerical solutions, but are not intended as replacements for them.

Coucl1L~ions 10

RSA-D-92-05 Rev.O References

1. "ECCS Pump Room Transient Response to Loss of Room Cooler for Dresden Station Units 2 and 3", RSA-D-90-01.
2. "An Evaluation of Loss of HPCI Room Cooler at Dresden Station", RSA-D-92-04.

References 11

Listing of Computer Cases Job Identifier Job Number NFSKRB JO 7978 NFSKRC JO 9619 Listing of Computer Cases RSA-D-92-05 Rev.O Case Description Single Slab Constant Sink T HTC=5.0 BTU/HR/FT2-F Single Slab Constant Sink T HTC=l.O BTU/HR/FT2-F 12

Appendix RSA-D-92-05 Rev.O The following pages provide the detailed analytical solution of the transient heat conduction equations summarized in Section 3.1. The numerical evaluation of the series solution is also attached at the end for reference. This evaluation was performed both by Mathcad as well as via a BASIC program written and executed on the author's Apple Ile. The Mathcad results are based on the first 50 series, while the Apple results use the first 25 series.

The convergence is very good.

Appendix 13

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Numerical Evaluation of Analytical Solution The analytical solution of the HPCI room heatup problem is evaluated using Mathcad to provide a table of time and temperature at the wall surface. The number of series terms is large to minimize error.

Otot. -

200000 Area.-

2*52*25 + 2*24.5*25 + 2*52*24.5 Area = 6.373

  • 103 O := Otot Area Q

31.382 a := 3 p

140 k := 1.05 cp -

0.2 k

0.038 a

a

=

p*Cp 0, 4.. 72 t* -

i I

x -

0 n -

1.. 50 Kn cos( ( 2* n -

1 n

X ]

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TS -

0*~)*4*

a k

( 2*n -

1 ) 2 *n 2 V

VOn*e i, n.-

TSS ( x )

TS + ~ * ( a -

x )

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140 135 Ttoti

/

---t--

/

130

/

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125 t* I 0

120.14

- 34.524 4

125.05

- 29.614 8

127.141

- 27.523 12 16 20 128.746 130.099 131.291

- 25.918

- 24.565

- 23.373 24 132.369

- 22.295 28 133.36

- 21.304 32 134.282

- 20.382 36 135.146

- 19.518 40 135.963

- 18.701 44 136.737

- 17.927 48 137.474

- 17.19 52 138.176

- 16.488 56 138.847

- 15.817 60 139.489

- 15.175 64 140.104

- 14.56 68 140.693

-13.971 72 141.257

- 13.407

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ENCLOSURE 3: HEAT LOADS; ECCS ROOMS COOLER HEAT LOAD CAPACITY STATION ROOM (BTU/hr)

(BTU/hr) ***

CALCULATION Dresden 2HPCI 194,013

  • 200,000 DR-721-M-004 3HPCI 194,013
  • 200,000 DR-721-M-004 2A LPCI 391,102 440,000 DR-721-M-001 28 LPCI 391,102 440,000 DR-721-M-001 3A LPCI 391, 102 440,000 DR-721-M-001 38 LPCI 391'102 440,000 DR-721-M-001 Quad Cities 1 HPCI 206,054
  • 200,000 QC-716-M-005 2HPCI 206,054
  • 200,000 QC-716-M-005 1ARHR 474,000 **

570,000 S & L 1968 18RHR 474,000 **

570,000 S & L 1968 1A LPCS 247,000 340,000 QC-716-M-001 18 LPCS 247,000 340,000 QC-716-M-OO 1 2ARHR 474,000 **

570,000 S & L 1968 28RHR 474,000 **

570,000 S & L 1968 2A LPCS 247,000 340,000 QC-716-M-001 28 LPCS 247,000 340,000 QC-716-M-001

  • Transient Calculations/Heat Load based on 130 degrees F ambient room temperature. Design temperature of room is 150 degrees F.
    • Heat load/heat removal is bounded by QC-716-M-001.
      • Cooler capacity is based upon an entering air temperature of 150 degerees F.
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