ML19289C318
| ML19289C318 | |
| Person / Time | |
|---|---|
| Site: | Maine Yankee |
| Issue date: | 01/08/1979 |
| From: | Vandenburgh D Maine Yankee |
| To: | Office of Nuclear Reactor Regulation |
| References | |
| WMY-79-1, NUDOCS 7901110106 | |
| Download: ML19289C318 (7) | |
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ENGINEERING OFFICE YsESTBORO, MASSAtHUS ETr5 01531
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Q 617-366-9011
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January 8. 1979 B3.2.1 WMY 79-1 United States Nuclear Regulatory Cocaission Washington, D.C.
20555 Attention:
Office of Nuclear Reactor Regulation
References:
- 1) License No. DPR-36 (Docket No. 50-309) 2)
G. N. Lauber., "T00DEE2: A Two Dimensional Tine Dependent Fuel Element Thercal Analysis Program",
USNRC Division of Technical Review, May 1975.
~)
A. Husain e* al., " Application of Yankee-WREM-2 Based Generic PWR ECCS Evaluation Model to Maine Yankee", YAEC-1160, July 1978.
4)
XN-75-41, Supple =ent 1, " Exxon Nuclear Company WREM-Based PWR ECCS Evaluation Model, Further Justification to Reflood Heat Transfer Models",
August 14, 1975.
5)
XN-75-41, Supplement 5, Revision 1, " Exxon Nuclear Cocpany WREM Based Generic PWR ECCS Evaluation Model, Supplementary Information Relating to Blowdown and Heatup Analysis", October 3, 1975.
Dear Sir:
Subject:
Corrections to the T00DEE2 Computer Code Wa have addressed the errors in the T00DEE2 coeputer code (Reference
- 2) identified by NRC and have cade appropriate changes to YA J's version of T00DEE2 which is part of our UREM-Based Generic PWR ECCS Evaluation Model (Reference 3).
Our response.to each of the identified errors is as follows:
1.
Error in the Solution of the Axial Part of the Heat Conduction Ecuations The matrix solution of the axial part of the deat conduction equation is solved by a forward elimination, backward substitution method in the form:
T(I,J) = ABBTH(J) - AEMH(J)
- T(I,J+1)
For the coolant, I=IMAX, and with a positive flow direction, the tecperature at the point (IMAX,J) is not dependent on the coolant tenperature in the point (IMAX,J+1). Hence, the parameter AEMH(J) 7901110106
U.S. Nuclear Regulatory Commission January 8, 1979 Att: Office of Nuclear Reactor Regulation Page 2 must be equal to zero when I=IMAX.
The suggested change was implemented in subroutine RAT 2 as follows:
Paraneter ABLD Underdinensioned The dimensions for the parameter ABLD were not changed at this time.
YAEC curreatly employs a maximun of four material blocks and ABLD is dimensioned in our v*rsicn of T00DEE2 to handle twelve material blocks.
3+4. Errors in the Gap Conductance Calculation The suggested changes were made in the gap conductance calculation in subroutine CONDUC. They are:
- I CONDUC. 210 GVU = GW
- D CONDUC. 243 GW = GVU + GPGD
- D CONDUC. 245 RGAP =.1713D-8 *AFMG/(EIDID ^ AFC*(EMLD-0NE))
5.
Error in the Molecular Weicht of the Material in the Gas Gap This error is a FORTRAN error and was corrected in subroutine MADATA as follows:
- D MADATA.530 EMMIX = 18.
6.
Error in the Fluid Velocity Calculation The suggested correction to this error was not made since it is conservative to neglect it.
Leaving the calculation in its original form produces a lower fluid velocity at the given location and hence, a lower heat transfer coef ficient.
It is noted, however, that making the suggested correction for the fluid velocity results in a negligible change in calculated temperatures.
7.
FLECHT Correlation / Coolant Tenperature Error In our version of T00DEE2, the parameter Q(IMAX,J) is set to zero when Flecht correlation is used.
Since we do not use sube led water at the channel entrance, no additional corrections were made.
F
U.S. Nuclear Regulariry Comnission January 8, 1979 Att: Office of Nuclear Reactor Regulation Page 3 s
8.
Conplicated Errors From the errors pointed out for this item the only ones pertinent to the YAEC T00DEE2 model are the ones that deal with the calculation of coolant temperature.
The first change made in the code was:
- I RAT 2.290 IF(U(IMAX,J).LE.1.) GO TO 99 BZ=TP(IMAX,J-1)+(1.-l./U(IMAX,J))*(TE(IMAX,J-1)-TP(IMAX,J-1))
IF(AVAIL (25).LT.O.) BZ=TP(IMAX,J+1)+(1.-l./U(IMAX,J))*(TE(IMAX,J+1
+ )-TP(IMAX,J+1))
99 CONTINUE This change is made only in the radial part of the heat conduction equation and can be explained by a Von Neuman stability analysis.
This analysis is given in Appendix A.
The second change was made in both radial and axial part of the heat conduction equation. The change is:
- I PQSU.92 B = U(IMAX,J)/(PU(IMAX,J)*(AX(J)-AX(J-1)))
IF (AVAIL (25).LT.O.) B = U(IMAX,J)*(A(J+1)-A(J))/(AX(J+1)-AX(J))
IF B.GT.1) Q(IMAX,J) = Q(IMAX,J)/B The changes to our version of T00DEE2 as outlined in Itecs 1 through 7 above did not affect the calculation of peak clad temperatures (less than 1 F).
However, the incorporation of corrections outlined in Item 8 into T00DEE2 resulted in a 6 F lower peak clad temperature for 1.0 DECLG TOP PEAK Sample Problem Case (1.406 Fz TOP PEAK at 14.5 kw/ft Peak LHGR, see Section 3.2 and Figure 3.18 of Reference 3).
The peak clad temperature reported in Reference 3 for this case was 2070 F at the 9.22 ft. elevation occurring at 175 seconds. Using the corrected version of T00DEE2 outlined above for this case yielded a peak clad temperature of 2064 F at the 9.22 ft. elevation at 175 seconds.
Co=parisons have been made by Exxon Nuclear Company, Inc. (References 4&5) between predicted peak clad temperatures using the T00DEE2/ ENC steam cooling model and the FLECHT/ ENC-2 heat transfer correlations to FLECHT experimental data in order to justify the steam cooling model contained in our version of T00DEE2. YAEC intends to submit as soon as possible, the results of a study justifying the steam cooling model in our corrected version of T00DEE2. A direct comparison of clad temperature, predicted by the steam cooling model ir. YAEC's corrected version of T00DEE2 to the same lo'r flaod rate FLECHT expetiment results (used by Exxon in References 4 and 5 to justify the original steam cooling model) will be made.
U.S. Nuclear Regulatory Commission January 8, 1979 Att: Office of Nuclear Reactor Regulation Page 4 We. Just that the above information is satisfactory.
If any questions should arise, please feel free to call Dr. Ausaf Husain at our engineering office, 20 Turnpike Road, Westboro, Mass. 01581, Tel. 617-366-9011, Extension 219.
Very truly yours,
'tAINE YANKEE ATOMIC POWER COMPANY D. E. Vandenburgh Vice President WJS/wpc Enclosures
A1 APPENDIX A VON NEU11AN STAEILITY ANALYSIS OF CHANGES MADE TO 100DEE2 IDENTIFIED IN ITDI 8
" COMPLICATED ERP.0RS" The difference form of the heat conduction equation used in T00DEE2 is:
(I,J) - T"(I,J) = P(I,J)[T"(I+1,J) - T"(I,J)]
T
- Q(I,J)[T"(I,J) - T"(I-1,J)]
+ S(I,J)[T I,J+1) - T (1,J-1)]
- U(I,J)[7 (I,J) - T" (I,J-1)]
+ W(I,J)
(A-1)
T"+
(I,J) - (T (I,J) = P(I,J)[T (I+1,J) - T"+
(I,J)]
- Q(I,J)[T (I,J) - T (I-1,J)]
+ S(I,J)[T" (I, J +1) - T" (I,J)]
-U(I,J) [T (I,J) - T (I,J -1)]
+ W(I,J)
~
(A-2)
For the coolant channel P(I,J) = 0.0 S(I,J) = 0.0 U(I,J) = 0.0 For this stability analysis we choose the c se where:
Q(I,J) = 0.0 llence (A-1) and (A-2) will becomu:
T" (1,J) - T"(I,J) = -U (I,J) [T" (I,J) - T" (I,J-1)]
(A-3) and T"
(I,J) - T (I,J) = -U(I,J)[T" (I,J) - Tn+ (I,J-1)]
(A-4)
The stability analysis will be made only for forward flow. Same concepts are valid for reverse flow.
In equation (A-3) we express the exact solut2cn as T(cc=putcd) = T(cxact) + c(crror)
= a" e (A-5) i0 where t
where 0 = k0 (k: any Fourier code)
+
y
.s The analysis considers A-3 as a full tire step; same for A-4 such as U will be =
{
instead of V.At 2.4z (A-3) is the axial part of the heat conduction equaticn.
We introduce (A-5) in (A-3) to obtain:
,n+1,iJO = -U 4"+1 iJ O _,n+1,1(J-1)0) _,n iJe (A-6) c e
After simplification we obtain for "a"
(1 + U - Ucose). - Ui sine (A-7)
(1 + U - Ucos0)
+U sin 6 The condition for stability is (A-8)
/a/<1 (A-8) is equivalent with a.a* < 1 or:
<1 (A-Ba)
(1 0 - U cos0)
+U sin 0 (A-9)
From (A-8a) af ter sir.plification we get: (U + 1) (1 - cos0) > 0 Since - 1 < cos 0 < 1 we bound the error growth (A-8) by (A-8*)
/a/ < 1 (A-9) becomes:
(A-9*)
(U + 1) (1 - cose)
_ 0 (A-10) or U + 1 > 0 (A-10a) or U > -1 Since U is always positive the axial part of the heat conduction equation is valid for any U or in other words is unconditic: ally stable.
We do the same analysis for (A-4) and we will have:
- a"c ('I-1)e) i IJe n+1,iJe _ niJO= -U (a"e or (A-11) a - 1 = -U (1 - c~1 )
or n = (1 - U) + Uc'
~
'(A-12) but /a/<1 or a.a*<1 We obtain the condition for stability:
(1 - U + U cos0)
+U sin 0 < 1 or (A-13)
(U - 1) (1 - cose) < 0 therefore U<
1 The conclusion is that the equation in T00DEE2, for the radial part of the heat conduction is valid only for U < 1.
We will change (A-4) which is upstrean explicit finite differencing with (A-14) which is downstreas implicit:
T"+ (I,J-1) - T"(I,J-1) = - U (T"+ (I,J) - T" (I,J-1) )
(A-14)
Fron (A-14)
T +1(I,J) = Tel(7, J-1) (1 - f) + h T"(I,J-1) u The error equation is:
a"c (J~1)C i
1_
1 n+1 iJ0, n+1 1(J-1) 0 1,U),U a
(A-15) or 1
a=
U (e10_y, )
Eut for stability (A-16)
/a/ < 1 or aia* < 1 Introducing (A-15) into (A-16) we get:
(A-17)
(1 - cos0) (1 - h) > 0 Fron (A-17)
U>1 the change we r.ade in TOCDEE2, in the radial part of the heat llence:
conduction equation will r.ake the calculation si cble for any value of U.
9