ML20210V083
| ML20210V083 | |
| Person / Time | |
|---|---|
| Issue date: | 09/30/1986 |
| From: | NRC |
| To: | |
| Shared Package | |
| ML20210V063 | List: |
| References | |
| NUDOCS 8610100495 | |
| Download: ML20210V083 (12) | |
Text
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d ENCLOSURE Topical Report Evaluation
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Report Titles and Dates:
I (1) FACTRAN - A Fortran IV Code for Thermal Transients in a UO 2Fuel Rod, WCAP-7908, July 1972.
(2) Proposed Appendix to WCAP-7908 transmitted by letter NS-CE-563 from C. Eicheldinger to D. B. Vassallo dated February 21, 1975.
(3) Additional'information transmitted by letters NS-CE-820 from C. Eicheldinger to D. B. Vassallo dated October 17, 1975.
(4) Additional information transmitted by letter NS-TMA-1872 from T. M. Anderson to J. F. Stolz dated July 20, 1978.
(5) Additional information transmitted by letter NS-TMA-2026 from T. M. Anderson to J. F. Stolz dated January 12, 1979.
(6) Additional information transmitted by letter NS-EPR-2856 from E. P. Rahe, Jr. to C. O. Thomas dated November 29, 1983.
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I.
SUMMARY
OF TOPICAL REPORT Topical report WCAP-7908, the proposed Appendix and the additional information transmitted by letters from C. Eicheldinger to D. B. Vassallo dated February 21, 1975, and October 17, 1975, from T. M. Anderson to J. F. Stolz dated July 20, 1978, and January 12, 1979, and from E. P. Rahe to C. O. Thomas dated November 29, 1983, describe the FACTRAN code used by Westinghouse to calculate fuel rod performance during the accidents and transients listed in Table 1.
The FACTRAN code is basically a fuel and thermal analysis code, and the coolant parameters are input as boundary conditions. The purpose of the code is to calculate the transient temperature distribution in a cross section of metal-clad U02 fuel rod and the heat flux at the surface of the cladding. The code can be used to calculate the transient temperature distribution for pre- and post-CHF conditions, provided that the mechanical behavior does not affect the calculations. It can be used to show compliance with the fuel melting or clad temperature criteria and with one of the coolable geometry criteria, i.e., limi-tatica of the pellet enthalpy. However, the code does not model time-dependent mechanical behavior of the cladding or fuel. Pellet-clad-interaction (PCI) or volumetric changes due to melting may be reasons for fuel failures and the code does not consider either of these failure mechanisms.
II. STAFF EVALUATION
- 1. Calculational Model A detailed fuel design modell including the effects of the fuel pellet densification and swelling, cladding creepdown, and fission gas release from the fuel is used to calculate the fuel volume-averaged and surface temperatures.
These temperatures form the basis for initial condition input into FACTRAN. If the calculated values of temperatures are input into the FACTRAN code, the code 1 Improved Analytical Models Used in Westinghouse Fuel Design Computations, WCAP-8720, October 1976.
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will calculate the initial gap heat transfer coefficient and conductivity. The initial gap heat transfer coefficient is calculated using the known heat flux, inner cladding temperature and the fuel surface temperature. The inner clad-ding temperature is calculated from initial heat flux, cladding geometry and properties and outer boundary conditions. It is independent of the gap heat transfer coefficient and fuel conductivity.
The fuel volume-averaged temperature or surface temperature can be chosen at a desired value which includes conservatisms reviewed and approved by the NRC.
If the fuel average temperature is input into the code, the code will perform iterations and will calculate a fuel conductivity multiplier (FCONC) to match the input temperature. If, in addition, fuel surface temperature is input into the code, the gap heat transfer coefficient is calculated first and then the conductivity iteration is performed.
The conservatisms of the input value to FACTRAN are identical to those used in the approved LOCA analysis method (WCAP-8218). This conservatism has been shown to bound calculational uncertainties. Since the initial value of gap heat transfer coefficient is dependent on the choice of fuel surface tempera-ture, the fuel surface temperature is chosen to bound uncertainties in initial value of the gap heat transfer such as due to different pellet sizes and uncer-tainties in cladding inner diameter. The average fuel temperature is chosen to bound uncertainties in the conductivity function, pellet density, cracked fuel, sintering temperature and flux depression. Table 2 presents the guidelines used to select initial temperatures.
During the transient, the value of FCONC, .he conductivity multiplier, remains constant. The gap heat transfer coefficient may be held at the initial con-stant value or can be varied as a function of time as specified in the input.
As described in E. P. Rahe's letter to C. O. Thomas dated November 29, 1983, i the choice is made such that the variation of the gap heat transfer coefficient is conservative for the transient analyzed. Table 2 also presents some infor-mation as to its choice in various applications.
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- 2. Heat Transfer Coefficients The heat transfer between the clad outer surface and the coolant is calculated using the Dittus-Boelter correlation in the forced convection single phase regime and the Jens-Lottes correlation in a two phase nucleate boiling regime.
DNB occurs when either the calculated time exceeds the input DNB time or the calculated heat flux exceeds the input DN8' flux. Once DNB occurs it is assumed to stay in effect throughout the transient.
The staff reviewed the~ report entitled " Analysis of Heat Transfer Burnout, Pressure Drop and Density Data for liigh Pressure Water" by W. H. Jens and P. A. Lottes, ANL-4627, describing the development of the Jens-Lottes correlation.
The data were obtained from electrically heated tubes. The experimental data indicate that the heat flux scatter for the same wall superheat can be as much as'i 60 percent. In addition, the scatter may be higher if the data were taken for the rod bundles. In the judgement of the staff there could be 1 75 percent scatter in heat flux data for the same wall superheat. Regarding the Dittus-Boelter correlation, the staff notes that the data may have a scatter of 1 20 percent and there may also be a bias in a rod bundle geometry on the order of 30 percent.
The staff performed some audit calculations to determine the sensitivity of the analyses using different multipliers in the Dittus-Boelter and Jens-Lottes cor-relations. The change in heat transfer from the fuel was within 1 percent for a multiplier of 0.7 in the Jens-Lottes correlation and a multiplier of 1.7 in the Dittus-Boelter correlation.
These calculations were performed for the loss of flow and rod assembly bank withdrawal from subcritical transients where the FACTRAN code is used. Because the results are insensitive over the range of uncertainties in the heat trans-fer correlations in these transients, these correlations are acceptable for use in the FACTRAN code.
The heat transfer coefficient, following DNB, is an input function (either a constant number or a function of time) or it is calculated using the Bishop-Sandberg-Tong (B-S-T) correlation. The staff reviewed the related 4
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information for the B-S-T correlation in the letter from T. M. Anderson to J. R. Stolz, NS-TMA-1872, dated July 20, 1978, and also the original paper
" Forced Convection Heat Transfer at High Pressure After the Critical Heat Flux" by A. A. Bishop, R. O. Sandberg and L. S. Tong, ASME, 65-HT-31, describing the development of the correlation. The correlation was developed from tube data.
The paper reports the experimental data, their range and uncertainties in the correlation. One of the important parameters is the wall temperature. The highest value of the wall temperature is 1109 F in these tests while the calcu-lated clad temperatures in the hot pin can be over 2000 F. To account for this limited data, Westinghouse in a proposed Appendix to WCAP-7908 which was sub-mitted in a February 21, 1975 letter, indicated that a factor of 0.84 provided a probability of 95 percent that the actual heat transfer coefficient will be larger than the calculated. However, more test data with higher wall tempera-tures subsequently became available and Westinghouse contended that the 0.84 multiplier was no longer necessary.
The staff extended the review to a larger data base. Idaho National Engineer-ing Laboratory presented comparative studies of post-CHF heat transfer correla-tions to existing tube data in Report SRD-134-76, dated July 1976. In this report, more than 4,600 post-CHF data points were compared with various corre-lations including Groeneveld 5.9. This data package included wall temperatures up to 1540 F. Based on this comparison, the Groeneveld 5.9 correlation cra-servatively predicts a majority of the data.
Based on the additional information* received during the re' view of ,
WCAP-8963(P), the Bishop-Sandberg-Tong correlation has a lower heat transfer coefficient than Groeneveld 5.9 for clad temperatures up to 1750 F. Hence, the Bishop-Sandberg-Tong correlation should predict the heat transfer for a majority of the 4600 post-CHF data points conservatively.
In letter NS-TMA-2026, NS-RPA II-3162 dated January 12, 1979, Westinghouse presented comparisons of the Bishop, Sandberg, and Tong and Groeneveld
- Letter from C. Eicheldinger to J. Stolz, NS-CE-1440 and NS-RPA II-2601 dated May 18, 1977.
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5.9 correlations to Westinghouse and Combustion Engineering rod bundle film boiling data. The Westinghouse data were obtained on a 336 rod heater bundle with an overall heated length of 164 inches, using a rod diameter of 0.374 inches and a square pitch of 0.496 inches. An axial profile of 1.66 was employed and there was no radial power profile in the bundle. The flow was downflow through the bundle with the rods-initially heated in steam to temperatures above the Leidenfrost point. The tests were transient in nature with the bun-die starting from a post CHF condition then eventually being quenched by the [
downflow of a two phase mixture. '.s A total of 5170 film boiling data points were available. Each data point represented an average film boiling heat transfer coefficient calculated from a sample of several rods. Westinghouse presented comparisons of heat transfer coefficients calculated using the Bishop-Sandberg-Tong correlation and these average measured heat transfer coefficients. The coefficients calculated using the Bishop-Sandberg-Tong correlation and these average measured heat transfer coefficients were lower for 4915 data points providing a 95.1 percent probability s that a lower heat transfer coefficient in rod bundles than those predicted did -
not exist for the same experimental range. The Groeneveld 5.9 percent correla-tion predicted 2977 out of 5170 data points (57.6 percent) conservatively. This substantiates the earlier finding that the Bishop-Sandberg-Tong correlation -
predicts lower heat transfer coefficients than those predicted by Groeneveld 5.9.
The use of these data which were obtained from experiments under downflow conditions to evaluate the film boiling coefficients is appropriate for this particular application.
In the M. S. thesis "Downflow Post-CHF Heat Transfer of Low Pressure," by P. Robertshotte, MIT, 1977, it is shown that the film boiling heat transfer coef-ficients in a downflow are lower than those in an upflow under the same condi-tions. Since the Bishop-Sandberg-Tong correlation predicts lower coefficients than those measured in downflow experiments, it should also predict lower coef-ficients for upflow conditions.
A further evaluation of the B-S-T correlation is provided by Westinghouse using the Combustion Engineering rod bundle film boiling tests which employed 21 and 25 rod heater rod bundles. The axial power distribution was uniform. The 6
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radial power factors varied from approximately 0.94 to 1.4. The tests were conducted in a steady-state fashion with the heater rods first starting in nucleate boiling, going through DNB and attaining stable film boiling as the power was increased. A steady state energy balance was calculated using the power and inlet flow to calculate quality at each instrumented elevation. The heat transfer information from the center rod was used to evaluate the heat transfer coefficient and evaluate the Bishop-Sandberg-Tong correlation. Com-parison of these coefficients for the available 139 data points indicated that the Bishop-Sandberg-Tong correlation without any multiplier predicted all of the data points conservatively, i.e., heat transfer coefficients from the Bishop-Sandberg-Tong correlation were lower than those calculated using measurements.
Groeneveld 5.9 correlation predicted 116 of the 139 points conservatively which substantiated the earlier finding.
One of the important parameters in film boiling is the wall (clad) temperature.
In Westinghouse rod bundle tests, the peak clad temperatures varied between 1300 F and 1000 F. In the Combustion Engineering tests, the peak clad tempera-tures varied between 1285 F and 1861 F. A test series performed at INEL's Power Burst Facility (PBF) has been performed and reported in an article entitled
" Response of Unirradiated and Irradiated PWR Fuel Rods Tested at Power-Cooling-Mismatch Conditions", Nuclear Safety, Vol. 19. The test data showed clad tem-peratures up to 2564 F. The P8F experimental data were evaluated using several film boiling correlations. The Groeneveld 5.9 correlation predicts 21 out of
- 26 data points conservatively; i.e., the calculated cladding temperature was higher than the measured for 21 out of 26 data points. Based on previous findings the Bishop-Sandberg-Tong correlation was more conservative than the Groeneveld 5.9.
, Reviewing this information we find that the Bishop-Sandberg-Tong correlation is sufficiently conservative and can be used in the FACTRAN code. It should be cautioned that since these correlations are applicable for local conditions only, it is necessary to use input to the FACTRAN code which reflects the local conditions. If the input values reflecting average conditions are used, there must be sufficient conservatism in the input values to make the overall method conservative.
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- 3. Heat Conduction Model The fuel rod is divided into a number of concentric rings. The maximum number of rings used to represent the fuel is 10. Based on our audit calculations we require that the minimum of 6 should be used in analyses. The gap, the clad and the film are r .ented using three additional rings. Two sets of finite difference equatic une for the energy balance and the other for the heat conduction, are solved to calculate heat fluxes and temperatures at the end of each time step. l Westinghouse noted that the FACTRAN code accurately predicted an analytical solution for the temperature due to a step change in power. The step change in power represents a severe transient, and the comparison demonstrates that; the i
mathematics are solved correctly. There is less than 1*F difference between the code-calculated and the analytical results during the transients. The staff finds that the mathematical model is acceptable and no margin for poten-l tial calculational errors is needed.
Since there is little suitable experimental data for code verification, the accuracy of this mathematical solution forms the basis for acceptance of the equations programmed in the FACTRAN computer program. The program can be used to analyze transients and accidents in Table 1 when properly used with other computer codes as part of an approved method.
- 4. Cladding Mechanical Behavior Althcogh time-independent mechanical behavior (e.g., thermal expansion, elastic l deformation) of the cladding are considered in FACTRAN, time-dependent mechani-cal behavior (e.g., plastic deformation) is not considered in the code. The effect of including time-independent mechanical behavior of the cladding would vary from transient to transient. For the loss-of coolant accident analysis (where the FACTRAN code is not applied) significant cladding strain and ballooning effects are possible. However, for those events in which the FACTRAN code is applied (see Table 1), significant time-dependent deformation of the cladding is not expected to occur due to the short duration of these events or low cladding temperatures involved (where DNBR Limits apply), or 8
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the gap heat transfer coefficient is adjusted to a high value to simulate clad collapse onto the fuel pellet. For these applications, we find the use of FACTRAN acceptable.
- 5. Zircaloy - Water Reaction The zircaloy-water reaction model developed by Baker and Just is used to calculate heat generation from this source in the cladding. This heat contri-butes to the total heat flux out of the rod and increases the fuel and clad temperatures. A telecon (F. Odar-M. Marion) on May 4,1978 confirmed that the FACTRAN code did not contain the error in programming of the zircaloy-water reaction similar to that reported in March 1978 for the codes used in the evalu-ation of postulated loss of coolant accidents. We conclude that the model developed by Baker and Just is acceptable for use in the FACTRAN code.
- 6. Flux Depression Approximate formulas are used to express the flux depression factor in terms of enrichment and pellet radius. Using these formulas and the power generation expression derived assuming a moncenergetic one group model, the power genera-tion rate for each concentric ring is calculated. This value is used to calcu-late the thermal power and subsequently the temperatures and heat fluxes using the finite difference equations mentioned above.
The one group diffusion theory model in the FACTRAN code slightly overestimates at beginning of life (BOL) and underestimates at end of life (EOL) the magni-tude of flux depression in the fuel when compared to the LASER code predictions for the same fuel enrichment. The LASER code uses transport theory. There is a difference of about 3 percent in the flux depression calculated using these two codes. When [T (centerline) - T (Surface)] is on the order of 3000 F, which can occur at the hot spot, the difference between the two codes will give an
. error of 100*F. When the fuel surface temperature is fixed, this will result in a 100*F lower prediction of the centerline temperature in FACTRAN.
- WCAP-6073, " LASER-A Depletion Program for Lattice Calculations Based on MUFT and THERMOS," April 1966.
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We have indicated this apparent nonconservatism to Westinghouse. In the letter NS-TMA-2026, dated January 12, 1979, Westinghouse proposed to incorporate the LASER-calculated power distribution shapes in FACTRAN to eliminate this noncon-servatism. We find the use of the LASER-calculated power distribution in the FACTRAN code acceptable.
III. STAFF POSITION i
, We reviewed the analytical methods and models presented in the subject documents.
We find that the FACTRAN code is acceptable for the analysis of the transients and accidents in Table 1.
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, Since the heat transfer correlations are applicable for local flow conditions only, the input to the FACTRAN code should reflect the local conditions. If the i core average conditions such as calculated from the LOFTRAN code are used, care j should be taken to ensure the overall input to the FACTRAN code is more conser-vative than those dictated by the local conditions. There must be sufficient conservatism in the input values to make the overall method conservative.
The FACTRAN code does not include a model for fuel mechanical behavior. Thus, fuel rod failure could occur even though the fuel rod did not approach thermal limits (such as DNBR = 1.3 or fuel melting). Therefore, the FACTRAN code can-not be used to predict such failures and another fuel code should be used to predict mechanical behavior. The FACTRAN code can be used to show compliance with a) DNBR, b) fuel melting, and c) pellet enthalpy criteria.
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Table 1 List of transients and accidents that use the FACTRAN program i
A. Uncontrolled RCC Assembly Bank Withdrawal From a Subcritical Condition. ,
D. Partial loss of Forced Reactor Coolant Flow.
i C. Complete Loss of Forced Reactor Coolant Flow.
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D. Single Reactor Coolant Pump Locked Rotor.
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E. Rupture of a Control Rod Drive Mechanism Housing (RCCA Ejection). I J
t FACTRAN is also used for transient analyses where it is suspected that fuel
!. temperature or clad temperature limits may be exceeded or to determine heat flux for reduced flow or loss of flaw type transients. It is not used for normal control studies.
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Table 2 FACTRAN Application Purpose to Initial Fuel fransient Be Used Temperatures gap
- 1) Heat Flux Calculation for DNB a) Loss of Flow *High Initial gap kept constant b) Rod Withdrawal -----
Initial gap kept constant from Subcritical
- 2) Compliance with *High Increase Suddenly PCT Limit to a high value
[ Locked Rotor]
- 3) Indication of Melt a) Rod Ejection *High Increase Suddenly at Power to a high value b) Rod Ejection *High Increase Suddenly at Zero Power to a high value Nominal
- The initial temperatures are to be increased as per the uncertainties in the approved LOCA analysis method refer to WCAP-8218.
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