Appendix K to Part 50 - ECCS Evaluation Models
10:1.0.1.1.30.0.117.88.33 : Appendix K
Appendix K to Part 50 - ECCS Evaluation Models
I. Required and Acceptable Features of Evaluation Models.
II. Required Documentation.
I. Required and Acceptable Features of the Evaluation Models
A. Sources of heat during the LOCA. For the heat sources
listed in paragraphs I.A.1 to 4 of this appendix it must be assumed
that the reactor has been operating continuously at a power level
at least 1.02 times the licensed power level (to allow for
instrumentation error), with the maximum peaking factor allowed by
the technical specifications. An assumed power level lower than the
level specified in this paragraph (but not less than the licensed
power level) may be used provided the proposed alternative value
has been demonstrated to account for uncertainties due to power
level instrumentation error. A range of power distribution shapes
and peaking factors representing power distributions that may occur
over the core lifetime must be studied. The selected combination of
power distribution shape and peaking factor should be the one that
results in the most severe calculated consequences for the spectrum
of postulated breaks and single failures that are analyzed.
1. The Initial Stored Energy in the Fuel. The
steady-state temperature distribution and stored energy in the fuel
before the hypothetical accident shall be calculated for the
burn-up that yields the highest calculated cladding temperature
(or, optionally, the highest calculated stored energy.) To
accomplish this, the thermal conductivity of the UO2 shall be
evaluated as a function of burn-up and temperature, taking into
consideration differences in initial density, and the thermal
conductance of the gap between the UO2 and the cladding shall be
evaluated as a function of the burn-up, taking into consideration
fuel densification and expansion, the composition and pressure of
the gases within the fuel rod, the initial cold gap dimension with
its tolerances, and cladding creep.
2. Fission Heat. Fission heat shall be calculated using
reactivity and reactor kinetics. Shutdown reactivities resulting
from temperatures and voids shall be given their minimum plausible
values, including allowance for uncertainties, for the range of
power distribution shapes and peaking factors indicated to be
studied above. Rod trip and insertion may be assumed if they are
calculated to occur.
3. Decay of Actinides. The heat from the radioactive
decay of actinides, including neptunium and plutonium generated
during operation, as well as isotopes of uranium, shall be
calculated in accordance with fuel cycle calculations and known
radioactive properties. The actinide decay heat chosen shall be
that appropriate for the time in the fuel cycle that yields the
highest calculated fuel temperature during the LOCA.
4. Fission Product Decay. The heat generation rates from
radioactive decay of fission products shall be assumed to be equal
to 1.2 times the values for infinite operating time in the ANS
Standard (Proposed American Nuclear Society Standards - “Decay
Energy Release Rates Following Shutdown of Uranium-Fueled Thermal
Reactors.” Approved by Subcommittee ANS-5, ANS Standards Committee,
October 1971). This standard has been approved for incorporation by
reference by the Director of the Federal Register. A copy of the
standard is available for inspection at the NRC Library, 11545
Rockville Pike, Rockville, Maryland 20852-2738. The fraction of the
locally generated gamma energy that is deposited in the fuel
(including the cladding) may be different from 1.0; the value used
shall be justified by a suitable calculation.
5. Metal - Water Reaction Rate. The rate of energy
release, hydrogen generation, and cladding oxidation from the
metal/water reaction shall be calculated using the Baker-Just
equation (Baker, L., Just, L.C., “Studies of Metal Water Reactions
at High Temperatures, III. Experimental and Theoretical Studies of
the Zirconium-Water Reaction,” ANL-6548, page 7, May 1962). This
publication has been approved for incorporation by reference by the
Director of the Federal Register. A copy of the publication is
available for inspection at the NRC Library, 11545 Rockville Pike,
Two White Flint North, Rockville, Maryland 20852-2738. The reaction
shall be assumed not to be steam limited. For rods whose cladding
is calculated to rupture during the LOCA, the inside of the
cladding shall be assumed to react after the rupture. The
calculation of the reaction rate on the inside of the cladding
shall also follow the Baker-Just equation, starting at the time
when the cladding is calculated to rupture, and extending around
the cladding inner circumference and axially no less that 1.5
inches each way from the location of the rupture, with the reaction
assumed not to be steam limited.
6. Reactor Internals Heat Transfer. Heat transfer from
piping, vessel walls, and non-fuel internal hardware shall be taken
into account.
7. Pressurized Water Reactor Primary-to-Secondary Heat
Transfer. Heat transferred between primary and secondary
systems through heat exchangers (steam generators) shall be taken
into account. (Not applicable to Boiling Water Reactors.)
B. Swelling and Rupture of the Cladding and Fuel Rod Thermal
Parameters
Each evaluation model shall include a provision for predicting
cladding swelling and rupture from consideration of the axial
temperature distribution of the cladding and from the difference in
pressure between the inside and outside of the cladding, both as
functions of time. To be acceptable the swelling and rupture
calculations shall be based on applicable data in such a way that
the degree of swelling and incidence of rupture are not
underestimated. The degree of swelling and rupture shall be taken
into account in calculations of gap conductance, cladding oxidation
and embrittlement, and hydrogen generation.
The calculations of fuel and cladding temperatures as a function
of time shall use values for gap conductance and other thermal
parameters as functions of temperature and other applicable
time-dependent variables. The gap conductance shall be varied in
accordance with changes in gap dimensions and any other applicable
variables.
C. Blowdown Phenomena
1. Break Characteristics and Flow. a. In analyses of
hypothetical loss-of-coolant accidents, a spectrum of possible pipe
breaks shall be considered. This spectrum shall include
instantaneous double-ended breaks ranging in cross-sectional area
up to and including that of the largest pipe in the primary coolant
system. The analysis shall also include the effects of longitudinal
splits in the largest pipes, with the split area equal to the
cross-sectional area of the pipe.
b. Discharge Model. For all times after the discharging
fluid has been calculated to be two-phase in composition, the
discharge rate shall be calculated by use of the Moody model (F.J.
Moody, “Maximum Flow Rate of a Single Component, Two-Phase
Mixture,” Journal of Heat Transfer, Trans American Society of
Mechanical Engineers, 87, No. 1, February, 1965). This publication
has been approved for incorporation by reference by the Director of
the Federal Register. A copy of this publication is available for
inspection at the NRC Library, 11545 Rockville Pike, Rockville,
Maryland 20852-2738. The calculation shall be conducted with at
least three values of a discharge coefficient applied to the
postulated break area, these values spanning the range from 0.6 to
1.0. If the results indicate that the maximum clad temperature for
the hypothetical accident is to be found at an even lower value of
the discharge coefficient, the range of discharge coefficients
shall be extended until the maximum clad temperatures calculated by
this variation has been achieved.
c. End of Blowdown. (Applies Only to Pressurized Water
Reactors.) For postulated cold leg breaks, all emergency cooling
water injected into the inlet lines or the reactor vessel during
the bypass period shall in the calculations be subtracted from the
reactor vessel calculated inventory. This may be executed in the
calculation during the bypass period, or as an alternative the
amount of emergency core cooling water calculated to be injected
during the bypass period may be subtracted later in the calculation
from the water remaining in the inlet lines, downcomer, and reactor
vessel lower plenum after the bypass period. This bypassing shall
end in the calculation at a time designated as the “end of bypass,”
after which the expulsion or entrainment mechanisms responsible for
the bypassing are calculated not to be effective. The end-of-bypass
definition used in the calculation shall be justified by a suitable
combination of analysis and experimental data. Acceptable methods
for defining “end of bypass” include, but are not limited to, the
following: (1) Prediction of the blowdown calculation of downward
flow in the downcomer for the remainder of the blowdown period; (2)
Prediction of a threshold for droplet entrainment in the upward
velocity, using local fluid conditions and a conservative critical
Weber number.
d. Noding Near the Break and the ECCS Injection Points.
The noding in the vicinity of and including the broken or split
sections of pipe and the points of ECCS injection shall be chosen
to permit a reliable analysis of the thermodynamic history in these
regions during blowdown.
2. Frictional Pressure Drops. The frictional losses in
pipes and other components including the reactor core shall be
calculated using models that include realistic variation of
friction factor with Reynolds number, and realistic two-phase
friction multipliers that have been adequately verified by
comparison with experimental data, or models that prove at least
equally conservative with respect to maximum clad temperature
calculated during the hypothetical accident. The modified Baroczy
correlation (Baroczy, C. J., “A Systematic Correlation for
Two-Phase Pressure Drop,” Chem. Enging. Prog. Symp. Series,
No. 64, Vol. 62, 1965) or a combination of the Thom correlation
(Thom, J.R.S., “Prediction of Pressure Drop During Forced
Circulation Boiling of Water,” Int. J. of Heat & Mass
Transfer, 7, 709-724, 1964) for pressures equal to or greater
than 250 psia and the Martinelli-Nelson correlation (Martinelli, R.
C. Nelson, D.B., “Prediction of Pressure Drop During Forced
Circulation Boiling of Water,” Transactions of ASME,
695-702, 1948) for pressures lower than 250 psia is acceptable as a
basis for calculating realistic two-phase friction multipliers.
3. Momentum Equation. The following effects shall be
taken into account in the conservation of momentum equation: (1)
temporal change of momentum, (2) momentum convection, (3) area
change momentum flux, (4) momentum change due to compressibility,
(5) pressure loss resulting from wall friction, (6) pressure loss
resulting from area change, and (7) gravitational acceleration. Any
omission of one or more of these terms under stated circumstances
shall be justified by comparative analyses or by experimental
data.
4. Critical Heat Flux. a. Correlations developed from
appropriate steady-state and transient-state experimental data are
acceptable for use in predicting the critical heat flux (CHF)
during LOCA transients. The computer programs in which these
correlations are used shall contain suitable checks to assure that
the physical parameters are within the range of parameters
specified for use of the correlations by their respective
authors.
b. Steady-state CHF correlations acceptable for use in LOCA
transients include, but are not limited to, the following:
(1) W 3. L. S. Tong, “Prediction of Departure from
Nucleate Boiling for an Axially Non-uniform Heat Flux
Distribution,” Journal of Nuclear Energy, Vol. 21, 241-248,
1967.
(2) B&W-2. J. S. Gellerstedt, R. A. Lee, W. J.
Oberjohn, R. H. Wilson, L. J. Stanek, “Correlation of Critical Heat
Flux in a Bundle Cooled by Pressurized Water,” Two-Phase Flow
and Heat Transfer in Rod Bundles, ASME, New York, 1969.
(3) Hench-Levy. J. M. Healzer, J. E. Hench, E. Janssen,
S. Levy, “Design Basis for Critical Heat Flux Condition in Boiling
Water Reactors,” APED-5186, GE Company Private report, July
1966.
(4) Macbeth. R. V. Macbeth, “An Appraisal of Forced
Convection Burnout Data,” Proceedings of the Institute of
Mechanical Engineers, 1965-1966.
(5) Barnett. P. G. Barnett, “A Correlation of Burnout
Data for Uniformly Heated Annuli and Its Uses for Predicting
Burnout in Uniformly Heated Rod Bundles,” AEEW-R 463, 1966.
(6) Hughes. E. D. Hughes, “A Correlation of Rod Bundle
Critical Heat Flux for Water in the Pressure Range 150 to 725
psia,” IN-1412, Idaho Nuclear Corporation, July 1970.
c. Correlations of appropriate transient CHF data may be
accepted for use in LOCA transient analyses if comparisons between
the data and the correlations are provided to demonstrate that the
correlations predict values of CHF which allow for uncertainty in
the experimental data throughout the range of parameters for which
the correlations are to be used. Where appropriate, the comparisons
shall use statistical uncertainty analysis of the data to
demonstrate the conservatism of the transient correlation.
d. Transient CHF correlations acceptable for use in LOCA
transients include, but are not limited to, the following:
(1) GE transient CHF. B. C. Slifer, J. E. Hench,
“Loss-of-Coolant Accident and Emergency Core Cooling Models for
General Electric Boiling Water Reactors,” NEDO-10329, General
Electric Company, Equation C-32, April 1971.
e. After CHF is first predicted at an axial fuel rod location
during blowdown, the calculation shall not use nucleate boiling
heat transfer correlations at that location subsequently during the
blowdown even if the calculated local fluid and surface conditions
would apparently justify the reestablishment of nucleate boiling.
Heat transfer assumptions characteristic of return to nucleate
boiling (rewetting) shall be permitted when justified by the
calculated local fluid and surface conditions during the reflood
portion of a LOCA.
5. Post-CHF Heat Transfer Correlations. a. Correlations
of heat transfer from the fuel cladding to the surrounding fluid in
the post-CHF regimes of transition and film boiling shall be
compared to applicable steady-state and transient-state data using
statistical correlation and uncertainty analyses. Such comparison
shall demonstrate that the correlations predict values of heat
transfer co-efficient equal to or less than the mean value of the
applicable experimental heat transfer data throughout the range of
parameters for which the correlations are to be used. The
comparisons shall quantify the relation of the correlations to the
statistical uncertainty of the applicable data.
b. The Groeneveld flow film boiling correlation (equation 5.7 of
D.C. Groeneveld, “An Investigation of Heat Transfer in the Liquid
Deficient Regime,” AECL-3281, revised December 1969) and the
Westinghouse correlation of steady-state transition boiling
(“Proprietary Redirect/Rebuttal Testimony of Westinghouse Electric
Corporation,” USNRC Docket RM-50-1, page 25-1, October 26, 1972)
are acceptable for use in the post-CHF boiling regimes. In
addition, the transition boiling correlation of McDonough, Milich,
and King (J.B. McDonough, W. Milich, E.C. King, “An Experimental
Study of Partial Film Boiling Region with Water at Elevated
Pressures in a Round Vertical Tube,” Chemical Engineering Progress
Symposium Series, Vol. 57, No. 32, pages 197-208, (1961) is
suitable for use between nucleate and film boiling. Use of all
these correlations is restricted as follows:
(1) The Groeneveld correlation shall not be used in the region
near its low-pressure singularity,
(2) The first term (nucleate) of the Westinghouse correlation
and the entire McDonough, Milich, and King correlation shall not be
used during the blowdown after the temperature difference between
the clad and the saturated fluid first exceeds 300 °F,
(3) Transition boiling heat transfer shall not be reapplied for
the remainder of the LOCA blowdown, even if the clad superheat
returns below 300 °F, except for the reflood portion of the LOCA
when justified by the calculated local fluid and surface
conditions.
c. Evaluation models approved after October 17, 1988, which make
use of the Dougall-Rohsenow flow film boiling correlation (R.S.
Dougall and W.M. Rohsenow, “Film Boiling on the Inside of Vertical
Tubes with Upward Flow of Fluid at Low Qualities,” MIT Report
Number 9079 26, Cambridge, Massachusetts, September 1963) may not
use this correlation under conditions where nonconservative
predictions of heat transfer result. Evaluation models that make
use of the Dougall-Rohsenow correlation and were approved prior to
October 17, 1988, continue to be acceptable until a change is made
to, or an error is corrected in, the evaluation model that results
in a significant reduction in the overall conservatism in the
evaluation model. At that time continued use of the
Dougall-Rohsenow correlation under conditions where nonconservative
predictions of heat transfer result will no longer be acceptable.
For this purpose, a significant reduction in the overall
conservatism in the evaluation model would be a reduction in the
calculated peak fuel cladding temperature of at least 50 °F from
that which would have been calculated on October 17, 1988, due
either to individual changes or error corrections or the net effect
of an accumulation of changes or error corrections.
6. Pump Modeling. The characteristics of rotating primary
system pumps (axial flow, turbine, or centrifugal) shall be derived
from a dynamic model that includes momentum transfer between the
fluid and the rotating member, with variable pump speed as a
function of time. The pump model resistance used for analysis
should be justified. The pump model for the two-phase region shall
be verified by applicable two-phase pump performance data. For
BWR's after saturation is calculated at the pump suction, the pump
head may be assumed to vary linearly with quality, going to zero
for one percent quality at the pump suction, so long as the
analysis shows that core flow stops before the quality at pump
suction reaches one percent.
7. Core Flow Distribution During Blowdown. (Applies only
to pressurized water reactors.)
a. The flow rate through the hot region of the core during
blowdown shall be calculated as a function of time. For the purpose
of these calculations the hot region chosen shall not be greater
than the size of one fuel assembly. Calculations of average flow
and flow in the hot region shall take into account cross flow
between regions and any flow blockage calculated to occur during
blowdown as a result of cladding swelling or rupture. The
calculated flow shall be smoothed to eliminate any calculated rapid
oscillations (period less than 0.1 seconds).
b. A method shall be specified for determining the enthalpy to
be used as input data to the hot channel heatup analysis from
quantities calculated in the blowdown analysis, consistent with the
flow distribution calculations.
D. Post-Blowdown Phenomena; Heat Removal by the ECCS
1. Single Failure Criterion. An analysis of possible
failure modes of ECCS equipment and of their effects on ECCS
performance must be made. In carrying out the accident evaluation
the combination of ECCS subsystems assumed to be operative shall be
those available after the most damaging single failure of ECCS
equipment has taken place.
2. Containment Pressure. The containment pressure used
for evaluating cooling effectiveness during reflood and spray
cooling shall not exceed a pressure calculated conservatively for
this purpose. The calculation shall include the effects of
operation of all installed pressure-reducing systems and
processes.
3. Calculation of Reflood Rate for Pressurized Water
Reactors. The refilling of the reactor vessel and the time and
rate of reflooding of the core shall be calculated by an acceptable
model that takes into consideration the thermal and hydraulic
characteristics of the core and of the reactor system. The primary
system coolant pumps shall be assumed to have locked impellers if
this assumption leads to the maximum calculated cladding
temperature; otherwise the pump rotor shall be assumed to be
running free. The ratio of the total fluid flow at the core exit
plane to the total liquid flow at the core inlet plane (carryover
fraction) shall be used to determine the core exit flow and shall
be determined in accordance with applicable experimental data (for
example, “PWR FLECHT (Full Length Emergency Cooling Heat Transfer)
Final Report,” Westinghouse Report WCAP-7665, April 1971; “PWR Full
Length Emergency Cooling Heat Transfer (FLECHT) Group I Test
Report,” Westinghouse Report WCAP-7435, January 1970; “PWR FLECHT
(Full Length Emergency Cooling Heat Transfer) Group II Test
Report,” Westinghouse Report WCAP-7544, September 1970; “PWR FLECHT
Final Report Supplement,” Westinghouse Report WCAP-7931, October
1972).
The effects on reflooding rate of the compressed gas in the
accumulator which is discharged following accumulator water
discharge shall also be taken into account.
4. Steam Interaction with Emergency Core Cooling Water in
Pressurized Water Reactors. The thermal-hydraulic interaction
between steam and all emergency core cooling water shall be taken
into account in calculating the core reflooding rate. During refill
and reflood, the calculated steam flow in unbroken reactor coolant
pipes shall be taken to be zero during the time that accumulators
are discharging water into those pipes unless experimental evidence
is available regarding the realistic thermal-hydraulic interaction
between the steam and the liquid. In this case, the experimental
data may be used to support an alternate assumption.
5. Refill and Reflood Heat Transfer for Pressurized Water
Reactors. a. For reflood rates of one inch per second or
higher, reflood heat transfer coefficients shall be based on
applicable experimental data for unblocked cores including FLECHT
results (“PWR FLECHT (Full Length Emergency Cooling Heat Transfer)
Final Report,” Westinghouse Report WCAP-7665, April 1971). The use
of a correlation derived from FLECHT data shall be demonstrated to
be conservative for the transient to which it is applied; presently
available FLECHT heat transfer correlations (“PWR Full Length
Emergency Cooling Heat Transfer (FLECHT) Group I Test Report,”
Westinghouse Report WCAP-7544, September 1970; “PWR FLECHT Final
Report Supplement,” Westinghouse Report WCAP-7931, October 1972)
are not acceptable. Westinghouse Report WCAP-7665 has been approved
for incorporation by reference by the Director of the Federal
Register. A copy of this report is available for inspection at the
NRC Library, 11545 Rockville Pike, Rockville, Maryland 20852-2738.
New correlations or modifications to the FLECHT heat transfer
correlations are acceptable only after they are demonstrated to be
conservative, by comparison with FLECHT data, for a range of
parameters consistent with the transient to which they are
applied.
b. During refill and during reflood when reflood rates are less
than one inch per second, heat transfer calculations shall be based
on the assumption that cooling is only by steam, and shall take
into account any flow blockage calculated to occur as a result of
cladding swelling or rupture as such blockage might affect both
local steam flow and heat transfer.
6. Convective Heat Transfer Coefficients for Boiling Water
Reactor Fuel Rods Under Spray Cooling. Following the blowdown
period, convective heat transfer shall be calculated using
coefficients based on appropriate experimental data. For reactors
with jet pumps and having fuel rods in a 7 × 7 fuel assembly array,
the following convective coefficients are acceptable:
a. During the period following lower plenum flashing but prior
to the core spray reaching rated flow, a convective heat transfer
coefficient of zero shall be applied to all fuel rods.
b. During the period after core spray reaches rated flow but
prior to reflooding, convective heat transfer coefficients of 3.0,
3.5, 1.5, and 1.5 Btu-hr −1-ft −2 °F −1 shall be applied to the
fuel rods in the outer corners, outer row, next to outer row, and
to those remaining in the interior, respectively, of the
assembly.
c. After the two-phase reflooding fluid reaches the level under
consideration, a convective heat transfer coefficient of 25 Btu-hr
−1-ft −2 °F −1 shall be applied to all fuel rods.
7. The Boiling Water Reactor Channel Box Under Spray
Cooling. Following the blowdown period, heat transfer from, and
wetting of, the channel box shall be based on appropriate
experimental data. For reactors with jet pumps and fuel rods in a 7
× 7 fuel assembly array, the following heat transfer coefficients
and wetting time correlation are acceptable.
a. During the period after lower plenum flashing, but prior to
core spray reaching rated flow, a convective coefficient of zero
shall be applied to the fuel assembly channel box.
b. During the period after core spray reaches rated flow, but
prior to wetting of the channel, a convective heat transfer
coefficient of 5 Btu-hr −1-ft −2- °F −1 shall be applied to both
sides of the channel box.
c. Wetting of the channel box shall be assumed to occur 60
seconds after the time determined using the correlation based on
the Yamanouchi analysis (“Loss-of-Coolant Accident and Emergency
Core Cooling Models for General Electric Boiling Water Reactors,”
General Electric Company Report NEDO-10329, April 1971). This
report was approved for incorporation by reference by the Director
of the Federal Register. A copy of the report is available for
inspection at the NRC Library, 11545 Rockville Pike, Rockville,
Maryland 20852-2738.
II. Required Documentation
1. a. A description of each evaluation model shall be furnished.
The description shall be sufficiently complete to permit technical
review of the analytical approach including the equations used,
their approximations in difference form, the assumptions made, and
the values of all parameters or the procedure for their selection,
as for example, in accordance with a specified physical law or
empirical correlation.
b. A complete listing of each computer program, in the same form
as used in the evaluation model, must be furnished to the Nuclear
Regulatory Commission upon request.
2. For each computer program, solution convergence shall be
demonstrated by studies of system modeling or noding and
calculational time steps.
3. Appropriate sensitivity studies shall be performed for each
evaluation model, to evaluate the effect on the calculated results
of variations in noding, phenomena assumed in the calculation to
predominate, including pump operation or locking, and values of
parameters over their applicable ranges. For items to which results
are shown to be sensitive, the choices made shall be justified.
4. To the extent practicable, predictions of the evaluation
model, or portions thereof, shall be compared with applicable
experimental information.
5. General Standards for Acceptability - Elements of evaluation
models reviewed will include technical adequacy of the
calculational methods, including: For models covered by §
50.46(a)(1)(ii), compliance with required features of section I of
this appendix K; and, for models covered by § 50.46(a)(1)(i),
assurance of a high level of probability that the performance
criteria of § 50.46(b) would not be exceeded.
[39 FR 1003, Jan. 4, 1974, as amended at 51 FR 40311, Nov. 6, 1986;
53 FR 36005, Sept. 16, 1988; 57 FR 61786, Dec. 29, 1992; 59 FR
50689, Oct. 5, 1994; 60 FR 24552, May 9, 1995; 65 FR 34921, June 1,
2000]