ML16256A283
| ML16256A283 | |
| Person / Time | |
|---|---|
| Site: | Waterford  |
| Issue date: | 08/25/2016 |
| From: | Entergy Operations |
| To: | Office of Nuclear Reactor Regulation |
| Shared Package | |
| ML16256A115 | List:
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| References | |
| W3F1-2016-0053 | |
| Download: ML16256A283 (9) | |
Text
WSES-FSAR-UNIT-36.2B-1Revision 10 (10/99)APPENDIX 6.2BEBASCO MODIFICATIONS TO THE CONTEMPT-LT MOD 26COMPUTER CODEThe containment pressure and temperature transient analyses are performed with an Ebasco modifiedversion of the CONTEMPT-LT Mod 26 computer code.In this computer code, the containment volume is divided into two regions, the atmosphere region (watervapor and air mixture) and the sump region (liquid water). Each region is assumed to be completely mixed and in thermal equilibrium. The temperature of each region may be different. Mass and energy additions are made to the appropriate region to simulate the mass and energy release from the Reactor Coolant System or Secondary System during and after blowdown with the contribution of the Safety Injection System (SIS) and Containment Spray System (CSS) water, and decay energy from the core.
Account is taken of boiling in the liquid region and condensing in the vapor region, and mass and energy transfers between regions are considered.The model represents the heat conducting and absorbing materials in the containment by dividing theminto segments with appropriate heat transfer coefficients and heat capacities. Thermal behavior is described by the one-dimensional, multiregion, transient heat conduction equation. The heat conducting segments are used to describe materials and surfaces in the containment which act as heat sources or heat sinks. The model includes provision for mathematically simulating cooling of the containment atmosphere by fan coolers and/or by water sprays, and cooling of the SIS sump water being recirculated to the CSS by the shutdown heat exchangers. The CONTEMPT-LT model and formulations have been shutdown to be applicable and conservative for the design of the containment vessel by simulated design basis accident tests such as the CVTR (see References 2, 3 and 4) blowdown experiment.Calculations are begun by computing initial steady state containment atmosphere conditions. Subsequentcalculations are performed at incremental time steps. Following the pipe rupture, the mass and energy addition to the atmosphere or liquid region is determined for each time interval. Heat losses or gains due to heat-conducting segments are calculated. Then the mass, and energy balance equations are solved to determine containment pressure, temperature of the liquid and vapor region, and heat and mass transfer between regions.The following modifications have been made to the CONTEMPT-LT code by Ebasco:a)An option has been added to calculate the condensing heat transfer coefficientbetween the containment atmosphere and the heat sink surfaces by using formulas based primarily on the work of Tagami (see References 5, 6 or 7). From this work, it was determined that the value of the heat transfer coefficient increases parabolically to peak value at the end of blowdown and then decreases exponentially to a stagnant heat transfer coefficient which is a function of the steam to air weight ratio.
WSES-FSAR-UNIT-36.2B-2Revision 10 (10/99)Tagami presents a plot of the maximum value of heat transfer coefficient (h) as a function of"coolant energy transfer speed," which is defined by: total coolant energy transferred into containment (containment free volume) x (time interval to peak pressure)
From this the maximum value of h is calculated by:
0.60 75=V t E h p maxwhere: hmax= maximum value of h (Btu/hr-ft 2-F)t p= time from start of accident to end of blowdown (sec)V= containment free volume (ft 3)E= initial coolant energy (Btu)The parabolic increase of h to its peak value is given by:
hh t t max p= o<t<t pwhere:h = heat transfer coefficient between heat sink and air (Btu/hr-ft 2-F)t P= Time period of blowdownt = time from start of accident (sec)The exponential decrease of the heat transfer coefficient is given by:
h = hstag + (hmax - hstag) exp (-0.05 (t-t p)) t>t pwhere: hstag = h for stagnant conditions = 2.0 + 50.0 X andX = steam to air weight ratio in containment WSES-FSAR-UNIT-36.2B-3Revision 10 (10/99)When the containment atmosphere is saturated or superheated and the heat sink surface is below thesaturation temperature, the sink heat flux is calculated using:
()w sat t T T A h q=.where: sink to flux heat t.q=A = heat sink surface area Tsat = containment saturation temperature T w = heat sink surface temperatureb) When either the Tagami of the Uchida (8) condensing heat transfer coefficient option is specified tocalculate heat transfer to heat sink surfaces, certain containment conditions can exist for which condensing heat transfer does not occur. For this situation, the CONTEMPT-LT Mod 26 computer code has been modified to calculate the sink heat transfer using the following free convection correlation (9): sat T w T or sat T v T for ()w T v T A fc h.t q=()L 1/3 f Pr L Gr f k 0.13 fc h=1/3 f f k pf Cf g 2 f 0.13=µ2where: T v= containment atmosphere temperatureg= gravitational constantf= 1/T f where T f equals the absolute temperature of T vT= T v - T w C pf= containment atmosphere specific heat at constant pressure k f= thermal conductivity of containment atmosphere
µf= containment atmosphere viscosity h fc= free convection heat transfer coefficient WSES-FSAR-UNIT-36.2B-4Revision 10 (10/99)L= characteristic length of heat sink surfacef= containment atmosphere densityG L= Greshof number at heat sink surfacePr= Prandlt number of containment atmospherec)When either the Tagami or Uchida (8) condensing heat transfer coefficient option isused and it is determined that steam condensation does occur on the heat sink surfaces, thesteam condensation rate is calculated using:
film h g h.t q.m=where: m.= steam condensation rate h g= saturated steam enthalpy at containment steam partial pressure hfilm = heat sink condensing film enthalpyThis approach is realistic for the following reasons:1)When condensation does exist on a heat sink surface, not all energy transferis due to condensation. The total heat transfer to the sink is actually the sum of a convection and a condensation term.(11) However, the assumption is made when usingthe Tagami or Uchida heat transfer coefficient options that all heat transfer is due to condensation. Therefore, a conservatively high steam condensation rate is calculated.2)Since the net condensation at the heat sink liquid condensate film is actuallythe difference between the simultaneous process of evaporation and condensation (10),saturation conditions exist in the gas at the interface of the containment atmospheregaseous boundary layer even if the bulk containment atmosphere is superheated. Ascan be seen in Figure 6.2B-1, a combination of the convective and diffusive effects in the gaseous boundary layer result in a gaseous interface temperature lower than the bulk containment atmosphere temperature. A 100 percent humidity or saturation condition must exist here since evaporation and condensation processes are simultaneously occurring at the gaseous-liquid interface. Since it is a complicated numerical procedure to calculate the gaseous interface temperature, and since the saturated steam enthalpy is not a strong function of pressure between 1 and 70 psia, it is assumed that the saturated steam enthalpy of the bulk atmosphere is equal to the steam enthalpy at the gaseous-liquid interface. This assumption will result in a maximum of eight percent error in thecalculated saturated steam enthalpy between 1 and 70 psia.
WSES-FSAR-UNIT-36.2B-5Revision 10 (10/99)3)The temperature gradient in the condensate boundary layer is small compared tothe gradient in the gaseous boundary layer (Figure 6.2B-1). In fact, the gradient in the condensate liquid boundary is small enough to be assumed negligible. The adequacy of this assumption can be shown by the following calculation. The total heat transfer rate from the bulk containment atmosphere to the heat sink surface is assumed to be calculated using the Tagami or Uchida condensing heat transfer coefficients:
()w T sat T A h t q=.The heat transfer rate in the condensate boundary layer from the gaseous - liquid interface to the heatsink wall is primarily due to conduction and can be written as:
liquid kA t q=.where k = thermal conductivity of condensatetherefore:
()liquid k w t sat t h=Assuming that the value of k is independent of temperature:
k.t qSolving for T ()liquid k w sat h=liquid k t q.=Using the typically most severe containment conditions resulting from a pipe break analysis whichmaximize the containment pressure and temperature, it can be shown that the temperature gradient across the condensate film is small and can be neglected. Assuming:
T sat = 280°F T w = 170°FA = 1.0 ft 2h = 200 Btu/(hr -ft 2 -F)
WSES-FSAR-UNIT-36.2B-6Revision 10 (10/99)Then a conservative maximum surface heat flux typical of the results expected following a pipe breakaccident can be calculated as:
Btu/hr.4 10 X 2.2 170)(280 200 t q==.A conservative approximation of the maximum condensate boundary layer thickness can be madeassuming the validity of the Nusselt condensation equation for a cool wall in the presence of pure steam(11), (12)
.The presence of noncondensible gas as air would actually decrease the heat flux and masscondensation rate and consequently decrease the boundary layer thickness. Therefore:
()()ft.0.0013 1/4 g f f fg h g w T gi T Z f k f 4 max==Assuming the following values:
sec)lbm/(ft 3 10 x 0.205 F)200 (at f=°F)ft Btu/(hr 0.394 F)200 (at f k=°Z (conservatively large heat sink height) = 150 ft.
Tgi (gas-liquid interface temperature) °T280F sat Note: Tgi is actually lower that Tsat due to the gas-liquid interface resistance which is large when anoncondensible gas as air is mixed with steam (13). hfg (represents the actual enthalpy drop from the gasto the liquid)=1173.8 - 138.08 = 1035.72f (at 200°F) = 1/0.01663 = 60.13 lbm/ft 3g(at 280°F) = 1/8.644 = 0.1157 lbm/ft 3Using an average value for y of 0.00065 ft., the value of T becomes 36
°F resulting in an averagecondensate film temperature of about 188
°F (conservatively assuming that the temperature gradient in thefilm is linear). Therefore, the assumption that the condensate film average temperature is 170
°F results ina conservative maximum error of about 10 percent at the time of peak heat flux. In reality, the heat sink surface heat flux and temperature gradient across the condensate film is a function of time and normally much less than these assumed maximum conservative values. Thus, the resulting error in the assumption of condensate film temperature is considerably less than 10 percent throughout the major portion of the transient.
WSES-FSAR-UNIT-36.2B-7Revision 10 (10/99)d)An option has been added to calculate the heat removal efficiency of the containment sprays when the containment atmosphere is saturated using:
e hh hh TT TT en fn en fn=where:e = spray system efficiency ratioT e= spray water temperature entering sump region, °F h e= spray water enthalpy entering sump region T n = spray water temperature at spray nozzle exit, °F T f = containment vapor region temperature, °Fh f= containment vapor region saturated liquid enthalpyh n = spray water enthalpy at spray nozzle exitSpray thermal efficiency data are taken from Reference 6. These efficiency data are specified as afunction of the steam/air mass ration in the containment. The data taken from Reference 6 are for a spray system with a mean spray drop diameter of 600 microns. A conservatively short drop fall height of approximately five meters is used. The spray efficiency is shown in Figure 6.2B-2.The energy removal rate from the containment atmosphere is then computed from the thermal efficiencyand energy transfer by
()n h f h.m e.q=where: q.= spray energy removal rate, Btu/sec m.= spray flow rate, lbm/secIf the containment atmosphere is superheated, the value of h e can be solved for using the efficiency dataand the definition of spray efficiency. Then h e and the containment partial steam pressure are used tosolve for the final quality (x) of the spray water after interaction with the vapor region. For this case, theenergy removal rate is calculated using:
)n h x)(l f (h.m.q=and the mass addition to the containment atmosphere and sump are calculated as:
WSES-FSAR-UNIT-36.2B-8Revision 10 (10/99) x m s m..=x)(1 m m 1=..where: m.s= steam addition rate to atmosphere m.l= liquid addition rate to sump regione)An optional method has been included that determines the steam condensationrate of the containment fan coolers by an interpolation in a table of containment atmosphere saturation temperature versus the fan cooler steam condensation rate.This additional table is merged with the existing CONTEMPT-LT Mod 26 input ofcontainment atmosphere saturation temperature versus fan cooler heat removal rate.If the values of fan cooler mass condensation rate input into the fan cooler table are zero,the code will calculate the steam mass condensation rate using the original CONTEMPT-LT Mod 26 assumption.Following the pipe break inside the containment, the mass and energy of the containmentatmosphere, and the mass of the containment sump are updated using the rates interpolated from the input table. Additionally, consistent with the assumptions of the CONTEMPT-LT Mod 26 code, the temperature of the fan cooler condensate is conservatively assumed to be at the containment atmosphere saturation temperature.Therefore, the condensate energy addition rate to the containment sump is calculated by:qmh.sump.condensate f=Where: q.sump=steam condensate energy addition rate to thesump region m.condensate =fan cooler steam condensate rate obtained fromthe table interpolation or calculated using theCONTEMPT-LT Mod 26 methods h f =saturated liquid enthalpy of containmentatmosphere WSES-FSAR-UNIT-36.2B-9APPENDIX 6.2B: REFERENCES1.Wheat, L. L., Wagner, R.J., Niederauer, G. F., Obenchain, C. F., CONTEMPT-LT - A ComputerProgram for Predicting Containment Pressure-Temperature Response to a Loss-of-CoolantAccident. Aerojet Nuclear Company, ANCR-1219, June, 1975.2.Norberg, J. A., Bingham, G. E., R. C. Schmitt, Waddoups, D. A., Simulated Design Basis AccidentTests of the Carolinas Virginia Tube Reactor Containment - Preliminary Results, Idaho NuclearCorporation, IN-1325, October 1969.3.Schmitt, R. C., Bingham, G. E., Norberg, J. A., Simulated Design Basis Accident Tests of theCarolinas Virginia Tube Reactor Containment - Final Report, Idaho Nuclear Corporation, IN-1403,December, 1970.4.Krotiuk, W. J., Rubin, M. B., "Condensing Heat Transfer Following a LOCA", Nuclear Technology,February, 1978.5.Tagami, Takshi, Interim Report on Safety Assessment and Facilities Establishment Project inJapan for the Period Ending June 1965 (No. 1)
.6.Fujie, H., Yamanouchi, A., Sagawa, N., Ogasuwara, H., Tagami, T., Studies for Safety Analysis ofLoss-of-Coolant Accidents in Light-Water Power Reactors, Japan Atomic Energy ResearchInstitute, NSJ-Tr 112, March, 1968.7.Slaughterbeck, D. C., Review of Heat Transfer Coefficients for Condensing Steam in aContainment Building following a Loss-of-Coolant Accident- Idaho Nuclear Corporation, IN-1388,September, 1970.8.Uchida, H., Ogama, A., Toga Y., "Evaluation of Post-Incident Cooling Systems of Light-WaterPower Reactors", Proceedings of the Third International Conference on the Peaceful Uses ofAtomic Energy held in Geneva, Switzerland, 7/31/64 - 9/9/64, Vol. 13, New York: United Nations,A/CONF. 28/P.436,1965.9.McAdams, W., Heat Transmission, New York, 1954.10.Minkowycz, W. J., Sparrow, E. M., "The Effect of Superheating on Condensation Heat Transfer ina Forced Convection Boundary Layer Flow", Journal of Heat and Mass Transfer, Vol. 12, GreatBritain, 1969, p. 147-154.11.Collier, J. G., Convective Boiling and Condensation, London, 1972.12.Rohsenow, W.M., "Film Condensation", Applied Mechanics Reviews, 1969.13.Slegers, L., Seban, R. A., "Laminar Film Condensation of Steam Containing Small Concentrationof Air", Journal of Heat and Mass Transfer, Vol. 13, Great Britain, 1970, P. 1941-1947.