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Nuclear Engineering and Design 241 (2011) 3824– 3838

Contents lists available at ScienceDirect

Nuclear Engineering and Design

jo u r n al hom epage : www.elsev ier .com/ locate /nucengdes

odeling pressure suppression pool hydrodynamics in the ABWR containment

ravin Sawant, Mohsen Khatib-Rahbar ∗

nergy Research, Inc., PO Box 2034, Rockville, MD 20847-2034, USA

r t i c l e i n f o

rticle history:eceived 11 January 2011eceived in revised form 25 June 2011ccepted 1 July 2011

a b s t r a c t

This paper focuses on the assessment of pressure suppression pool hydrodynamics in the advanced boil-ing water reactor (ABWR) containment under design-basis, loss-of-coolant accident (LOCA) conditions.The paper presents a mechanistic model for predicting various suppression pool hydrodynamics param-eters. A phenomena identification and ranking table (PIRT) applicable to the ABWR containment poolhydrodynamics analysis is used as a basis for the development of the model. The highly ranked phe-nomena are represented by analytic equations or empirical correlations. The best estimate and severalsensitivity calculations are performed for the ABWR containment using this model. Results of the sen-sitivity calculations are also presented that demonstrate the influence of key model parameters and

assumptions on the pool hydrodynamics parameters. A comparison of model predictions to the resultsof the licensing analyses shows reasonable agreement. Comparison of the results of the proposed modelto experimental data shows that the model predicted top vent clearance time, the pool swell height, andthe bubble breakthrough elevation are within 10% of the data. The predicted pool surface velocity andthe liquid slug thickness are within 30% of the measurements, which is considered adequate given thelarge uncertainties in the experimental measurements.

. Introduction

Following a postulated design-basis LOCA inside the ABWR con-ainment (see Fig. 1), the increase in drywell pressure results inuppression pool vent clearing and the rapid flow of drywell gasesprimarily nitrogen) through the suppression pool into the wetwellas space. The flow of drywell gases through the drywell to wetwellents creates large, expanding bubbles at the horizontal vent exits.hese bubbles expand against the suppression pool hydrostatic andhe gas space pressure, as the air/steam mixture flow continuesrom the pressurized drywell. As a result, the water ligaments (oriquid slugs) on top of the expanding bubbles accelerate upward,

hich give rise to the pool swell phenomena that typically last–3 s. During this phase, the containment wetwell region is sub-

ected to pressure loads on the suppression pool boundary, dragoads on structures initially submerged in the pool (due to theressurized and expanding bubbles), and pressure loads on the

Abbreviations: ABWR, advanced boiling water reactor; COL, combined oper-ting license; DBA, design-basis accident; DCD, design control document; FSAR,inal Safety Analysis Report; GE, General Electric; GOTHIC, Generation of Thermal-ydraulic Information for Containments; LOCA, loss-of-coolant accident; NRC,nited States Nuclear Regulatory Commission; PIRT, phenomena identification and

anking table; PSTF, Pressure Suppression Test Facility; RPV, reactor pressure vessel;TP, South Texas Project; SRV, safety relief valve.∗ Corresponding author. Tel.: +1 301 881 0866; fax: +1 301 881 0867.

E-mail address: mkr1@eri-world.com (M. Khatib-Rahbar).

029-5493/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.nucengdes.2011.07.002

© 2011 Elsevier B.V. All rights reserved.

wetwell gas space (due to the rising pool surface that compressesthe wetwell gas space). And finally, the rising pool surface canimpact and impose drag loads on structures that are located abovethe pool level inside the wetwell airspace.

Key wetwell airspace internal structures that will be subjectedto the pool swell loads (impact and/or drag loads) are the safetyrelief valve (SRV) discharge piping, catwalk structure, wetwell-to-drywell vacuum breaker, and access tunnel (ABWR DCD, 1997).To predict the pool swell hydrodynamic loads on these wetwellinternal structures, it is essential to determine various pool swellparameters such as the maximum pool surface elevation, peak poolsurface velocity, peak wetwell gas space pressure, and peak bubblepressure (before the bubble breakthrough) following a design-basisaccident (DBA) LOCA. The swollen level (or the maximum poolswell) determines the drag and hydrodynamic impact loads onwetwell structures that are initially above the pool surface. The poolsurface velocity determines the severity of the loads, and the gasbubble and wetwell gas space pressures before the bubble break-through determine the pressure loading on the wetwell gas spaceand the suppression pool structural boundaries.

Historically, ABWR vendors have used their proprietary modelsand computer codes for analysis of pool swell phenomena and asso-ciated hydrodynamic loads. The pool swell analysis presented in

the ABWR design control document (DCD) (ABWR DCD, 1997) wasperformed using the General Electric (GE) proprietary computercode PICSM. This code was validated against the Mark III PressureSuppression Test Facility (PSTF) data. PICSM is a newer version of

P. Sawant, M. Khatib-Rahbar / Nuclear Engineering and Design 241 (2011) 3824– 3838 3825

Nomenclature

Ab cross-sectional area of the bubble (m2)AHf total horizontal vent area available for the liquid

flow (m2)AHg1 area of the top horizontal vent available for the gas

flow (m2)AHg2 area of the middle horizontal vent available for the

gas flow (m2)ASP suppression pool surface area (m2)AV area of the vertical vent pipe (m2)CD drag coefficientD diameter of flow channel (m)Dpooli suppression pool annulus inner diameter (m)Dpoolo suppression pool annulus outer diameter (m)Dl length of the longer side of a rectangle (m)Ds length of the shorter side of a rectangle (m)DSP hydraulic diameter of the suppression pool (m)dHg1 hydraulic diameter of the top horizontal vent (for

gas flow) (m)dHg2 hydraulic diameter of the middle horizontal vent

(for gas flow) (m)dVg hydraulic diameter of the vertical vent pipe (for the

gas flow) (m)f wall friction factorg gravitational acceleration (m/s2)HS0 total suppression pool depth above the bottom of

the bottom horizontal vent (m)HPS suppression pool swell height (m)Hs top vent centerline submergence at the time of top

vent clearance (m)HSL thickness of the liquid slug on top of the bubble (m)kA effective gas phase vent form loss coefficient for the

top horizontal ventkd drywell connecting vent entrance loss coefficientke horizontal vent exit loss coefficientkfE effective liquid phase vent loss coefficientkgE effective gas phase vent loss coefficientkSP suppression pool loss coefficientkt 90◦ elbow turning loss coefficientkt1 standard tee loss (flow through branch)kt2 standard tee loss (flow through run)LH length of horizontal vent (m)LV total length of vertical and horizontal vents (m)mgb bubble mass (kg)N number of vertical vents (10 for the ABWR contain-

ment)P pressure (Pa)PB internal bubble pressure (Pa)P0

B initial pressure inside the bubble (Pa)PD drywell pressure (Pa)P∞ pressure outside the bubble (Pa)PWW wetwell gas space pressure (Pa)P0

WW initial wetwell gas space pressure (Pa)R time-dependent radius of the spherical bubble (m)RCAP radius of the cap bubble (m)Re Reynolds numberReb bubble Reynolds numbert time (s)TD drywell temperature (◦C)TSP suppression pool temperature (◦C)ub bubble rise velocity (m/s)ugs sonic velocity of gas phase (m/s)

ugv area averaged gas phase velocity in vertical vent(m/s)

uH area averaged velocity of water inside horizontalvent (m/s)

uSP area averaged suppression pool surface velocity(m/s)

utb bubble terminal velocity (m/s)utbCAP spherical cap bubble terminal velocity (m/s)utbSLUG slug bubble terminal velocity (m/s)u area averaged velocity (m/s)uV area averaged velocity of water inside vertical vent

(m/s)Vb volume of spherical bubble (m3)Vb volumetric growth rate of spherical bubble (m3/s)V0

WW initial wetwell gas space volume (m3)VWW wetwell gas space volume (m3)WgCR gas phase critical mass flow rate (kg/s)Wgb rate of change of the bubble mass (kg/s)Wgv mass flow rate of the drywell gas through the verti-

cal vent pipe (kg/s)x water level inside the vertical vent pipe (m)Zbubble elevation of the bubble above the top vent centerline

(m)Zpool elevation of pool surface above the bottom of the

suppression pool (m)

Greek symbolsˇ1 ratio of diameters for the top horizontal vent

(dHg1/dVg)ˇ2 ratio of diameters for the middle horizontal vent

(dHg2/dVg)� density of fluid (kg/m3)�f density of water inside the suppression pool (kg/m3)�g average gas phase density (kg/m3)�gB gas phase density calculated at the internal pressure

of the bubble (kg/m3)�0

gB gas density inside the initial bubble (kg/m3)

�gD drywell gas phase density (kg/m3)�w wall shear stress (kg/ms2)

� polytropic constant

the GE proprietary code PSAM which was developed for the MarkII containment design (NUREG-1503, 1994). Kukita et al. (1984)reported that PSAM models the pool swell as a one-dimensionalphenomenon. In this model, the air bubbles are assumed to occupyentire area of the pressure suppression pool forming a sheet ofuniform thickness. The pool of water above the air bubble is repre-sented by a one-dimensional water slug with a constant thicknessequal to the initial submergence height of the vent. Therefore, thePSAM model does not account for the rise of bubbles through pres-sure suppression pool water as observed in the PSTF experiments.Additional details about this model are not available in the openliterature.

The pool swell analysis presented in the Final Safety Anal-ysis Report (FSAR) (South Texas Project [STP] Units 3 and 4FSAR, 2007) submitted to the United States Nuclear RegulatoryCommission (NRC) in support of the combined license (COL)application utilized a methodology that is based on the Genera-tion of Thermal-Hydraulic Information for Containments (GOTHIC)

computer code. The GOTHIC-based methodology has also beenbenchmarked against the Mark III PSTF data (STP Units 3 and 4FSAR, 2007). Unfortunately, due to its proprietary nature, the addi-

3826 P. Sawant, M. Khatib-Rahbar / Nuclear Engineering and Design 241 (2011) 3824– 3838

R cont

to

mTaf(

hdDefmtiMaiStJ(pvo

Fig. 1. Schematic of the ABW

ional details about this methodology are also not available in thepen literature.

Yan and Bolger (2010) developed a three-dimensional CFDodel to simulate the pool swell process in the PSTF test facility.

hey reported satisfactory prediction of the vent clearance timend pool surface velocity. Sufficient details about the CFD problemormulation and setup have not been provided by Yan and Bolger2010), thus making it is difficult to reproduce the CFD results.

In the past, several experimental and theoretical investigationsave been performed to study the pool swell and associated hydro-ynamic loads in the Mark I and Mark II containments. Chen andhir (1982) studied the hydrodynamics of a bubble formed at thexit of a vertical pipe submerged in a pool of water. They per-ormed these experiments by injecting air through the pipe and

easured the bubble growth rate and the pressure histories insidehe pipe. They also studied the effect of presence of an orificenside the pipe on the growth of bubbles. Fernandez (1976), Lai and

cCauley (1978), Huber et al. (1979), Kiang and Jeuck (1980, 1981),nd Kiang and Grossi (1981) performed pool swell experimentsn scaled down test facilities simulating the Mark I containment.imilar scaled down experiments applicable to the Mark II con-ainment pressure suppression pool were performed by Kiang andeuck (1980) and Kukita et al. (1984). More recently, Gupta et al.

2011) obtained measurements of local dynamic pressure (at theool bottom, the pool walls, and the gas space) and high speed flowisualization which can be used for the development and validationf the CFD codes. The analytic models have been also developed for

ainment (ABWR DCD, 1997).

the modeling of pool swell in the Mark I and Mark II containment(Glenn and McMaster, 1978; Chan and Vander Vorst, 1978; Huberet al., 1979; Chambre and Nitao, 1981; Widener, 1986). However,these Mark I and Mark II related studies have limited applicabilityfor the ABWR pool swell analysis. Particularly the design of ventsystem and the pressure suppression pool in the ABWR contain-ment is quite different when compared to the Mark I and Mark IIcontainments.

The objective of this paper is to present analytic models basedon fundamental physical principles that are used for the confirma-tory prediction of suppression pool hydrodynamics and associatedfigures-of-merit (i.e., vent clearance, pool surface elevation, poolsurface velocity, wetwell gas space and the bubble pressure) underDBA LOCA conditions. A comparison of model predictions againstthe GOTHIC pool swell analysis results (STP Units 3 and 4 FSAR,2007) is intended to show the fidelity of the proposed model com-pared to other available studies. This paper also examines thesensitivity of key figures-of-merit to major model assumptions andgoverning model parameters. Finally, the paper presents the resultsof comparison of the proposed model to the BWR Mark III PSTFexperimental data.

2. Dominant phenomena

The highly ranked phenomena identified in the PIRT in Table 1are applicable to the ABWR containment suppression pool swelldynamic response. This PIRT identifies the dominant phenomena

P. Sawant, M. Khatib-Rahbar / Nuclear Engineering and Design 241 (2011) 3824– 3838 3827

Table 1PIRT for ABWR containment suppression pool swell dynamic response.

Phenomenon/process Importance ranking

Mass and energy release from RPV and piping sideStored energy in vessel and core assemblies and heat transfer to coolant LDecay heat to coolant (short- and long-term) LScram and core power during blowdown LRPV two-phase level swell (core and downcomer) and two-phase and single-phase blowdown intervals LTwo-phase and single phase critical flow HBreak flow flashing (generation of droplets and vapors) HInitial pipe inventory and double ended blowdown interval H

Drywell atmosphere mass and energy transferMixing and transport of non-condensable gases and water vapor HDroplet transport (break-up, coalescence, evaporation, and droplet suspension or fallout) HHeat transfer to drywell heat structures (steam condensation on surfaces) and wall heat transfer M

Flow in drywell connecting ventsTwo-phase flow regime through drywell connecting vents MFlow losses in drywell connecting vents MLower drywell non-condensable gas transportMixing and transport of non-condensable gases from lower drywell to wetwell gas space L

Flow in horizontal ventsVent clearance and fluid inertia MFlow through vent (perfect gas, steam, gas-droplet mixture, and choked flow) MFlow losses (bends, turns, geometric losses) HEffect of back pressure and clearing time, sequential H

Mass, energy and momentum transfer in suppression poolDirect contact condensation of vapors in suppression pool in presence of non-condensable gases MSuppression pool mixing and thermal stratification (pool heating) LGas bubble discharge HPool swell and height MBubble penetration M

Mass, energy, and momentum transfer in wet-well gas spaceGas sparging through the suppression pool HWetwell pressurization HPool surface rise and compression of gas HWetwell gas/vapor mixing and stratification LHeat transfer to wetwell heat structures LLong term pool heating of gas L

ttit(iTc

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Suppression pool bypass leakageFlow of vapor mixture directly from drywell to wetwell gas space

hat are modeled to analyze suppression pool hydrodynamics inhe ABWR containment, as described in Section 3 of this paper. Themportance rankings assigned in the PIRT were delineated based onhe expected impact of the phenomenon on pool swell parametersi.e., maximum pool surface elevation, peak pool surface veloc-ty, peak wetwell gas space pressure, and peak bubble pressure).he highly ranked phenomena can be broadly classified into fourategories based on what the phenomena affect:

(a) drywell pressurization rate;b) vent clearance time and flow rate;

(c) formation and growth rate of the bubble; andd) the rise and breakthrough of the bubble.

The drywell pressurization rate is a function of the rate of massnd energy release into the drywell from the reactor pressure ves-el (RPV) and the piping sides of the break. The break flow fromhe piping side of the break primarily consists of stored inven-ory of coolant inside the piping. The break flow from the RPVide is determined by the RPV thermodynamic conditions. Severalhenomena are identified in the PIRT that affect the RPV thermo-ynamic conditions and hence, the break flow rate. However, forhe present model, the transient drywell pressure and temperaturere specified as boundary conditions. Consequently, the phenom-na affecting the drywell pressurization rate are not formulated asart of this paper.

The vent clearance time is the time required for the transferf water from the drywell-to-wetwell vent system to the sup-ression pool after a LOCA. Predicting the vent clearance time isssential for modeling the pool swell phenomena because it deter-

L

mines the time required for the initiation of a pool swell followinga LOCA. Furthermore, the flow of the drywell gas mixture throughthe vents following the vent clearance determines the growth rateof the bubble and the magnitude of the pool swell parameters. Theparameters/phenomena affecting the vent clearance time includethe inertia of water inside the vent system and the suppressionpool, the hydrostatic head of water inside the suppression pool,the friction and form losses in the vent system (including the effectof flow regimes), and the back pressure at the exit of the horizontalvents (due to the expanding bubble and the inertia of the liquidslug following the clearance of the top vents).

The flow rate of the drywell gas mixture through the vents fol-lowing the vent clearance is mainly affected by various pressurelosses through the vent system, including the losses due to fluidinertia, spatial acceleration, gravity, friction, and form losses (dueto wall friction, flow area contraction/expansion, and bends/turns).Higher pressure losses through the vent system result in a lowervent flow rate and a relatively less severe pool swell response.Therefore, for the pool swell analysis, the assumption of a mini-mum pressure loss is bounding. Furthermore, the flow of drywellgases through the vent system could reach sonic conditions, thuslimiting the discharge of the drywell gas mixture through the ventsto the critical mass flow rate.

Predicting the growth rate of the bubble is important because itdetermines the magnitude of various pool swell parameters. Thisgrowth rate is governed by the difference in the pressures inside

and outside the bubble. In the present model, the growth rate of thebubble is calculated using the Raleigh equation (Carey, 2007). Thephenomena/parameters affecting the inside pressure of the bub-ble include the vent mass flow rate and the interfacial heat and

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828 P. Sawant, M. Khatib-Rahbar / Nuclear E

ass transfer at the bubble and suppression pool water interface.he interfacial heat and mass transfer at the interface of the bubbles due to the steam (which is part of the drywell gas mixture) athis interface and the cooling of the non-condensable gases in theubble resulting from the transfer of heat to the suppression poolater. If either the drywell gas mixture or the vent gas flow dis-

harge includes some percentage of steam, the growth rate of theubble will be lower. The higher growth rate is obtained by assum-

ng that 100% of the atmosphere in the drywell is only occupied byitrogen. Furthermore, the interfacial heat transfer between the gasubble and the suppression pool affects both the gas temperaturend the growth rate of the bubble. During a LOCA, the drywell airemperature is usually higher than the suppression pool tempera-ure. The reduction in the temperature of the gas in the bubble dueo the interfacial heat transfer to the suppression pool water willffectively reduce the growth rate of the bubble. An assumption of00% nitrogen in the drywell and the absence of the interfacial heatnd mass transfer would result in a higher growth rate of the bubblend more bounding predictions for various pool swell parameters.

The outside pressure of the bubble is affected by the hydro-tatic head and inertia of the liquid slug on top of the bubble.dditionally, the compression of the wetwell gas space due to aising suppression pool surface also influences this outside pres-ure. Pressurization of the wetwell gas space reduces the growthate of the bubble. Isothermal compression would result in a loweretwell gas space pressure and a higher bubble growth rate (hence,

higher pool swell height and pool surface velocity). On the otherand, adiabatic compression would result in a higher wetwell gaspace pressure and a lower bubble growth rate.

The bubble rise velocity and bubble breakthrough time deter-ine the termination of the pool swell transient. The bubble

ises through the suppression pool due to the combined effects ofuoyancy and drag forces acting on the bubble. These forces areunctions of the size and shape of the bubble. Therefore, the bub-le rise velocity depends on the size and shape of the bubble—ashe size increases, the buoyancy force on the bubble increases.owever, the shape of the bubble also changes with its size. Theubbles formed in the suppression pool during the pool swell tran-ient are relatively large in size (due to the large horizontal ventiameter of 70 cm). They do not exactly match any of the well-nown bubble types for which bubble rise velocity measurementsre available (see Figs. 11 and 12 of Lahey and Moody, 1993). Judg-ent is needed to predict the rise velocity of growing bubbles that

re being charged from the horizontal vents. Furthermore, the riseelocity of a slug bubble is affected by the presence (or absence) ofetwell gas space pressurization.

. Mathematical models

Based on the discussion of the dominant phenomena, this sec-ion presents the various mathematical models that are used toimulate suppression pool hydrodynamics in the ABWR contain-ent. Note that with the exception of specific geometrical aspects,

he proposed models are generally applicable to predictions ofydrodynamic loads in BWRs with different containment config-rations (e.g., Mark I and Mark II, etc.).

.1. Vent clearance

Fig. 2 shows a modeling approach used to simulate the ventlearance phenomenon. In this figure, x indicates the water level

nside the vertical vent pipe. AHf, Av, and ASP are the total horizontalent area available for the liquid flow, the cross-sectional area of theertical vent pipe, and the suppression pool surface area, respec-ively. kfE indicates the total effective vent form loss coefficient for

ring and Design 241 (2011) 3824– 3838

liquid flow (see Appendix A). Fig. 2 shows that the three horizontalvents (top, middle, and bottom vents) in the ABWR design (shownon the left side) are represented by a single horizontal vent by thepresent model (shown on the right side). This assumption elimi-nates the need of separate momentum equation for each horizontalvent leading to the simplification of the model.

The one-dimensional momentum equation is obtained by aver-aging the area of the three-dimensional momentum equation,namely:

∂�u

∂t+ ∂�u2

∂z= −∂P

∂z− 4�w

D+ �g (1)

Furthermore, it is assumed that:

a) The velocity of water inside the horizontal vent (uH) and thesuppression pool surface velocity (uSP) are related to the veloc-ity of water inside the vertical vent pipe uV through the masscontinuity equation:

uH = AV

AHfuV (2)

uSP = AV

ASPuV (3)

b) The suppression pool surface area (ASP) is very large comparedto the areas of the vertical vent pipe and the horizontal vent.Therefore, the pool surface velocity is negligibly small (uSP ≈0.0).

c) The rise in pool surface due to the transfer of vent system waterinto the suppression pool is accounted for by increasing thesuppression pool height (HS0).

d) The wetwell gas space pressure (PWW) is assumed to be constantat the initial condition.

e) Pressure drops due to inertia, special acceleration, gravity, andform and friction losses in the vent system are considered. Pres-sure drops due to inertia, special acceleration, and friction inthe suppression pool are neglected due to the negligibly smallsuppression pool surface velocity.

(f) Pressure at the water surface inside the vertical vent is assumedto be equal to the drywell pressure (i.e., before the vent clear-ance, the gas flow from the drywell to the vertical vent pipe isvery small).

Therefore, integrating Eq. (1) from the surface water inside thevertical vent pipe (point M in Fig. 2) to the suppression pool sur-face (point N in Fig. 2) results in the following ordinary differentialequation representing the water velocity inside the vent:(

�f x + �f LHAv

AHf

)duV

dt− �f u2

V = (PD − PWW ) − �f kfEu2

V

2

+ �f g(x − HS0) (4)

Subsequently, the water level inside the vertical vent pipe isrelated to the water velocity by:

−dx

dt= uV (5)

Eqs. (4) and (5) are solved numerically with the time-dependentdrywell pressure used as a boundary condition to calculate thewater level inside the vertical vent pipe. Furthermore, the totalarea of the horizontal vents available for the liquid flow (AHf) and

the effective liquid phase loss coefficient (kfE) are estimated fromthe water level inside the vertical vent. Appendix A presents theapproach for calculating effective vent form loss coefficients forthe liquid and gas flow phases.

P. Sawant, M. Khatib-Rahbar / Nuclear Engineering and Design 241 (2011) 3824– 3838 3829

lating the vent clearance phenomenon.

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Immediately after the clearance of the top horizontal vent, therywell air begins to flow into the suppression pool and createsn expanding air bubble at various vent exits. This expanding bub-le accelerates the pool surface and exerts a higher pressure onhe middle and the bottom vent exits, thus delaying their clear-nce (i.e., the backpressure effect). Therefore, the assumptions ofhe negligible pool surface velocity, the constant wetwell gas spaceressure, and negligible pressure losses in the suppression poole.g., pool inertia) are challenged as the water level drops below theop horizontal vent. Consequently, these assumptions are expectedo result in a faster prediction of the clearance of the middle andottom horizontal vents and in a more bounding estimate of theool swell parameters.

.2. Pool swell

The simulation of suppression pool swell behavior consists ofolving equations representing the vent system pressure drop (forhe gas flow) and the growth rate, rise velocity and location, outsideressure of the bubble; the pool surface velocity and elevation, theetwell gas space pressure, and thickness of the liquid slug on top

f the bubble. The pool swell calculations are initiated as soon as theater level inside the vertical vent pipe drops below the top eleva-

ion of the top horizontal vent. The models described below take thenput from the vent clearance model (Section 3.1) (effective ventorm loss coefficient and total horizontal vent area available for theas flow/flow of gas), while the drywell pressure and temperaturere supplied as boundary conditions.

.2.1. Vent pressure dropThe vent pressure drop equation is derived from the calcula-

ion of gas flow through the vent system following the clearancef the top horizontal vent. Similar to the vent clearance model,ll horizontal vents (top, middle, and bottom) are assumed to beepresented by a single horizontal vent. However, unlike the ventlearance model above, the elevation of the horizontal vent is fixedt the top horizontal vent elevation (see Fig. 3). This assumptioninimizes the thickness of the accelerating liquid slug thereby

esulting in more bounding estimates of the pool swell height andurface velocity.

The integration of the one-dimensional area averaged momen-um equation [Eq. (1)] from the entrance of the drywell connectingents to the exit of the horizontal vents by assuming:

(a) All horizontal vents are located at the elevation of the top hor-

izontal vents.

b) The total area of horizontal vents available for the gas flow (AHg)and the effective gas phase form loss coefficient (kgE) for ventsare obtained from the solution of the vent clearance model

Fig. 3. Estimate of pressure drop through vents.

presented in Section 3.1. A sensitivity analysis is consideredin Section 4 to study the effect of gas phase vent form losscoefficient (kgE).

(c) Only inertial and frictional pressure losses are accounted for(inertial pressure drop and wall friction losses in the horizontalvents are neglected). The pressure drops due to spatial acceler-ation and gravity are neglected. Since this assumption results ina lower pressure drop and hence, a higher gas phase mass flowrate through the vent system, it is considered bounding for thecalculation of pool swell parameters.

(d) The average gas phase density ( �g) is obtained by averagingthe drywell and bubble gas densities. The drywell gas density isobtained from the drywell pressure and temperature boundaryconditions. The bubble gas density can be calculated by assum-ing that either isothermal or adiabatic compression of an idealgas.

Therefore, the following equation represents the pressure dropthrough the vents:

�gLVdugV

dt+

(fLV

dVg+ kgE

)u2

gV

2�g = PD − PB (6a)

This is further simplified by neglecting the inertial pressure drop(due to a relatively small gas phase density) that leads to the fol-

lowing equation:(

fLV

dVg+ kgE

)u2

gV

2�g = PD − PB (6b)

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and associated top, middle, and bottom horizontal vents) is shapedas an approximately similar trapezoid.

A correlation for the terminal velocity of slug bubbles (utbSLUG)for a trapezoidal shape is not available in the literature. Therefore,

830 P. Sawant, M. Khatib-Rahbar / Nuclear E

.2.2. Growth rate of the bubbleThe submerged gas bubble that is formed at the exit of the

orizontal vents (following the vent clearance) is assumed to bepherical with a time-dependent radius R, internal pressure PB,xpanding against an outside pressure of P∞, surrounded by sup-ression pool water with a density of �f.

Assuming that:

(a) The pressure inside the bubble is uniform and equal to thepressure at the exit of the horizontal vent (PB).

b) Heat and mass transfers at the bubble interface are neglected.(c) The pressure outside the bubble is uniform around the bub-

ble and accounts for the liquid slug (which exists on top of thebubble) inertia and the hydrostatic head [see Eq. (31)].

d) The surface tension effects are negligible.

Therefore, the growth of an idealized spherical bubble is gov-rned by the Rayleigh equation (Carey, 2007) of the form:

d2R

dt2+ 3

2

(dR

dt

)2

= 1�f

(PB − P∞ − 2�

R

)(7a)

Even at the initial formation of the bubble, when the radius isinimum (i.e., equivalent to the radius of the horizontal vents), the

urface tension contribution is negligibly small (2�/R < 0.4) whenompared to the pressure difference (PB − P∞). The contributionrom surface tension continuously decreases as the bubble growsnside the pool. Therefore, the surface tension term can be neglectedo arrive at:

d2R

dt2+ 3

2

(dR

dt

)2

= 1�f

(PB − P∞) (7b)

Furthermore, the volumetric growth rate (Vb) and the rate ofhange of the submerged bubble mass (Wgb) are governed by:

dVb

dt= Vb = 4�R2 dR

dt(8)

nd

gb = dmgb

dt= �gb

dVb

dt(9)

The conservation of mass requires that the rate of change in theass of the bubble (Wgb) is the same as the mass flow rate of the

rywell gas through the vertical vent pipes (Wgv):

gv = dmgb

dt= �gb

dVb

dt(10)

Furthermore, the average gas phase velocity through the verticalent pipes is given by:

¯ gv = Wgv

AV �g(11)

.2.3. Bubble rise velocity and bubble breakthrough timeThe bubble rise velocity through a stagnant pool of water is

btained by accounting for the forces acting on the bubble due tonertia, buoyancy, and drag (Joseph, 2003; Wallis, 1969). That is:

gVbdub

dt= �f gVb − �ggVb − 1

2CD�f Abu2

b (12)

dub

dt= (�f − �g)

�gg − 1

2CD

�f

�g

Ab

Vbu2

b (13)

The drag coefficient (CD) depends on the relative velocity, size,

nd shape of the bubble and the fluid properties. The gas bubbleormed at the exit of the horizontal vent is assumed to rise at itserminal velocity (i.e., assuming that the bubble’s acceleration isegligible) through the suppression pool. Appendix B shows that

ring and Design 241 (2011) 3824– 3838

the bubble accelerates very rapidly and approaches the terminalvelocity in a negligibly small duration of time compared to the timerequired for a bubble breakthrough (i.e., the breakthrough time isseveral orders of magnitude longer compared to the characteristictime for the bubble to reach its terminal velocity). Consequently,the assumption that the bubble rises at its terminal velocity is justi-fied and appropriate. The terminal velocity of the bubble is obtainedfrom Eq. (13) by setting the inertia term to zero (i.e., dub/dt = 0.0).Therefore:

utb =√

2Vb(�f − �g)gCD�f Ab

=√

2Vbg

CDAb(14)

The gas bubble that is formed at the exit of the horizontal ventsappears to rise as a spherical cap bubble due to its relatively largesize. Therefore, a cap bubble drag coefficient (8/3) can be used. Thisis derived based on the theoretical analysis of a spherical cap bub-ble having an included angle of about 100 degrees and a relativelyflat tail (Clift et al., 1978; Wallis, 1969) and is applicable to the bub-ble Reynolds number greater than 150 (i.e., Reb = 2R�fub/�f > 150)of the bubble. Therefore, the terminal velocity of a spherical capbubble (utbCAP) of an equivalent spherical radius R is governed by:

utb = utbCAP = dz

dt=

√Rg (15)

The above equation can be used directly to obtain the rise veloc-ity of a bubble that is formed at the exit of the horizontal vents.However, the size of the bubble increases (due to the continuousflow of drywell gas and the bubble’s expansion) as it rises throughthe suppression pool. If the bubble grows and reaches the sup-pression pool structural boundaries, its shape will change from aninitial spherical cap to a slug bubble. The transition from the shapeof a spherical cap to a slug bubble and the terminal velocity of aslug bubble are governed by the geometry of the suppression pool.Similar to the terminal velocity relationship of the spherical capbubble [Eq. (15)], empirical correlations are available in the litera-ture for estimating the terminal velocity of the slug bubble (Wallis,1969). These correlations are dependent on the geometry of theflow channel. Wallis (1969) provides correlations for rectangularand circular geometries. Fig. 4 shows that each 10-degree sectorof the ABWR suppression pool (corresponding to one vertical vent

Fig. 4. Cross section of the ABWR suppression pool.

nginee

tr

u

a

k

f(

D

D

ptspTD

D

D

maetmel

2

aarw

R

iifbtbbbt

u

b

w

P. Sawant, M. Khatib-Rahbar / Nuclear E

he present model uses the following correlation based on tests inectangular geometry (Wallis, 1969):

tb = utbSLUG = k

√Dl(�f − �g)g

�f(16a)

nd

= 0.23 + 0.13Ds

Dl(16b)

Before the transition from a spherical cap to a slug bubble, theollowing equations are used to calculate the lengths of the shorterDs) and the longer (Dl) sides of the rectangle in Eq. (16):

s = �(Dpooli + Dpoolo)2 × N

(17)

l = (Dpoolo − Dpooli)2

(18)

After the transition from a spherical cap to a slug bubble takeslace, the slug bubbles from the neighboring sectors are assumedo coalesce and form a large slug bubble that spans the entire crossection of the suppression pool. Fig. 5 shows that the entire sup-ression pool cross section can be approximated by a trapezoid.herefore, the following equations can be used to calculate Ds andl in Eq. (16):

s = (Dpoolo − Dpooli)2

(19)

l = �(Dpooli + Dpoolo)2

(20)

The bubble rise velocity is calculated using the slug bubble ter-inal velocity correlation [Eq. (16)] as soon as the transition from

spherical cap to a slug bubble is predicted to occur. However, anstablished criterion for predicting this transition in a rectangularest section is not available. For the present pool swell evaluation

odel, the transition is assumed to take place as soon as the diam-ter of the cap bubble exceeds the average of the above estimatedengths of the longer and shorter sides of the rectangle:

Rcap ≥ Ds + Dl

2(21)

The cap bubble radius (Rcap) can be estimated from the equiv-lent spherical bubble radius R. For a spherical cap bubble withn included angle of about 100 degrees and a flat tail, the followingelation can be obtained that correlates the radius of the cap bubbleith the radius of the spherical bubble (Wallis, 1969):

cap = 2.26 × R (22)

The terminal velocity of the slug bubble is governed by Eq. (16)f the bubble is rising through a stagnant pool of liquid. However,f the channel top is open to the atmosphere (e.g., the PSTF testacility; Yan and Bolger, 2010), the liquid ahead of the rising slugubble is not expected to remain stagnant (Wallis, 1969). Underhis condition, the rise velocity of the slug bubble is augmentedy the velocity of the liquid ahead of the expanding and movingubble. Consequently, the effective slug bubble rise velocity wille equal to the sum of the terminal velocity of the slug bubble andhe pool surface velocity:

tb = utbSLUG + uSP (23)

After estimating the bubble rise velocity, the elevation of theubble is obtained using:

Zbubble =∫ t

0

dz

dtdt =

∫ t

0

utb dt (24)

here Zbubble is the bubble elevation above the top vent centerline.

ring and Design 241 (2011) 3824– 3838 3831

The bubble breakthrough time is defined as the time at whichthe bubble’s top surface penetrates the suppression pool surface.At the time of the bubble breakthrough, the thickness of the liquidslug on top of the rising bubble approaches zero. The liquid slugthickness is obtained by subtracting the elevation of the top surfaceof the bubble from the elevation of the pool surface (see Fig. 3 andEq. (28)):

HSL = (Hs + HPS) − (Zbubble + R) (25)

The bubble breakthrough is assumed to occur as soon as HSLreaches zero. The top vent centerline submergence height (HS)accounts for the rise in pool surface elevation due to the transfer ofwater from the vent system to the pressure suppression pool. Thesuppression pool swell height (HPS) is estimated using Eq. (27).

3.2.4. Pressure suppression pool surface velocity and elevationAs noted earlier, the pressure suppression pool surface velocity

and elevation are the most important pool swell parameters froma containment and structural design standpoint. The rising poolsurface will sweep out a volume that corresponds to the growthin volume of the submerged bubbles. For a total suppression poolsurface area of ASP, a total number of N vents feeding N submergedbubbles with a volume growth rate of Eq. (8) will result in a poolsurface rise in velocity of:

uSP = dHP

dt= N

ASPVb (26)

Eq. (26) is integrated to obtain the pressure suppression poolswell height (i.e., the pool surface rise above the initial pool surfaceelevation):

HPS =∫ t

0

dHP

dtdt (27)

The elevation of the pressure suppression pool surface abovethe bottom of the pool is obtained from the following equation:

Zpool = Hs + HPS (28)

3.2.5. Wetwell gas space pressurization and the outside pressureof the bubble

The pressurization of the wetwell gas space volume due to pres-sure suppression pool surface rise is calculated by assuming thepolytropic compression of an ideal gas:

PWW = P0WW

(V0

WW

VWW

)�

(29)

Wetwell gas space volume is obtained by:

VWW = V0WW − (Z0

pool − Zpool) × ASP (30)

The assumption of an adiabatic compression (� = 1.4) will resultin a relatively higher wetwell gas space pressure and a lower poolswell height and pool surface velocity. The assumption of isother-mal compression (� = 1.0) will result in a relatively lower wetwellgas space pressure and a higher pool swell height and pool surfacevelocity.

The equation to estimate the outside pressure of the bubble, P∞,is obtained by integrating the averaged area momentum equation[Eq. (1)] over the thickness of the liquid slug that is residing on topof the rising bubble:

du(

fH) u2

HSL�fSP

dt= (P∞ − PWW ) − (HSL + R)�f g − SL

DSP+ kSP

SP

2�f

(31)

3832 P. Sawant, M. Khatib-Rahbar / Nuclear Engineering and Design 241 (2011) 3824– 3838

er tran

o

P

tolp

33it

u

v

W

brc

3(

f

f

f

3t

�

wg

�

the drywell through the reactor coolant system break can also flowalong with the nitrogen into the pressure suppression pool. How-ever, the steam and water droplet content is expected to be verysmall during the time period of interest (i.e., 2–3 s). Furthermore,

Table 2ABWR containment initial conditions and key geometric parameters.

Geometric parameters/initial conditions Value

Initial drywell pressure, kPa 106.0Initial drywell temperature, K 330.0Drywell atmosphere composition (nitrogen), % 100Suppression pool water temperature, K 308.0Wetwell atmosphere composition (nitrogen), % 100Initial wetwell gas space temperature, K 308.0Initial wetwell gas space pressure, kPa 106.5Top vent centerline submergence, m 3.5Middle vent centerline submergence, m 4.85Bottom vent centerline submergence, m 6.2Initial wetwell gas free volume, m3 5958.0Total suppression pool surface area, m2 507.0

Fig. 5. Cross section of the ABWR suppression pool aft

Therefore, the pressure that is exerting on the bubble from theutside is governed by:

∞ = PWW + HSL�fduSP

dt+ (HSL + R)�f g +

(fHSL

DSP+ kSP

) u2SP

2�f

(32)

Even though this equation accounts for the frictional losses,hese losses are nonetheless negligible. Furthermore, since the areaf the pressure suppression pool remains constant, the pressureoss due to spatial acceleration is zero. Note that the gravitationalressure drop is calculated from the center of the expanding bubble.

.2.6. Closure relations

.2.6.1. Critical flow. The gas phase can approach the sonic velocitynside the vertical vent pipe. The sonic velocity of the gas phase athe drywell pressure is estimated using (McCabe et al., 1993):

gS =(

2� + 1

)�+1/2(�−1)√

�PD

�gD(33)

The critical mass flow rate for the flow of gas through the verticalent pipes at the drywell pressure PD is calculated by:

gCR = AV �gDugS (34)

If the gas flow rate through the vents calculated by Eq. (10)ecomes greater than the critical mass flow rate (WgCR), the growthate of the bubble is limited to the critical mass flow rate and isalculated using the following equation (instead of [Eq. (7)]):

dR

dt= WgCR

4�R2�g(35)

.2.6.2. Wall friction factor. The wall friction factor [in Eqs. (6) and32)] is calculated using the following relations:

= 64Re

for Re ≤ 2100 (36)

= 0.312(Re)−0.25 for 2100 ≤ Re ≤ 2 × 104 (37)

= 0.184(Re)−0.2 for Re ≥ 2 × 104 (38)

.2.6.3. Equation of state. The drywell gas density is obtained fromhe pressure and temperature of the drywell:

gD = �gD(PD, TD) (39)

The gas density corresponds to the inside pressure of the bubble,hich is obtained by assuming a polytropic compression of an ideal

as:

gB = �0gB

(PB

P0B

)1/�

(40)

sitioning from a spherical cap to a slug bubble shape.

The average gas density used in the vent pressure drop equation[Eq. (6b)] is obtained from:

�g = 12

(�gD + �gB) (41)

Furthermore, the pressure suppression pool density is calcu-lated as a function of the water temperature:

�f = �f (TSP) (42)

4. Application to the ABWR

The proposed model equations are solved numerically to ana-lyze the pressure suppression pool hydrodynamics in the ABWRcontainment, as discussed in this section. These analyses includebest estimate and sensitivity calculations (see Sections 4.2.1 and4.2.2). The sensitivity calculations are performed to study theimpact of key model assumptions on the pool swell parameters.Furthermore, the model predictions are also compared with com-parable results based on GOTHIC calculations, as documented inthe STP Units 3 and 4 FSAR (2007).

4.1. Initial and boundary conditions

Table 2 lists the initial conditions and key geometrical param-eters of the ABWR containment. Initially, the entire containmentatmosphere is assumed to be filled with nitrogen, which is alsoassumed to represent the composition of the gas that flows fromthe drywell into the suppression pool. During a LOCA, in additionto nitrogen, some steam and suspended water droplets that enter

Vent area of one vertical vent, m2 1.13Diameter of horizontal vent, m 0.7Total number vertical vents 10Total number of horizontal vents 30

P. Sawant, M. Khatib-Rahbar / Nuclear Enginee

0

50

100

150

200

250

300

350

32.521.510.50

Pres

sure

, kPa

300

320

340

360

380

400

420

Tem

pera

ture

, K

Drywell PressureDrywell Temperature

ted

otratbawwlip

4

4

ftcaesosv

isftta

TS

Time, s

Fig. 6. Drywell pressure and temperature boundary conditions.

he assumption of all nitrogen in the containment atmosphere isxpected to result in more bounding estimates of the pool hydro-ynamic response behavior.

Due to the short period of the pool swell dynamic, the impactf heat transfer from the suppression pool and wetwell gas spaceo the wetwell structures is considered to be negligible in the cur-ent analysis. As noted earlier in Section 3, the drywell pressurend temperature transients are supplied as boundary conditionso the model. Fig. 6 shows the drywell pressure and temperatureoundary conditions used in the current analyses. These bound-ry conditions are derived from the STP Units 3 and 4 FSAR (2007),hich provides pressure and temperature transient data in the dry-ell and wetwell for the design-basis feedwater and main steam

ine break accidents. The pressure and temperature curves shownn Fig. 6 are considered to represent the upper bounds of the drywellressure and temperature conditions.

.2. Results

.2.1. Vent clearance time sensitivity calculationsThe vent clearance equations presented in Section 3.1 account

or the pressure losses due to fluid inertia, spatial acceleration, fric-ion, and hydrostatic head. To assess the sensitivity of the ventlearance time to the contribution from various pressure loss terms,

series of sensitivity calculations was performed using the differ-nt forms of the vent clearance equation [Eq. (4)]. Table 3 shows theummary of these calculations. The first column tabulates the formf vent clearance equation that was used, and the second columnhows the corresponding vent clearance time predicted for the topents.

In Table 3, the results show that the vent clearance time is mainlynfluenced by the pressure losses due to fluid inertia and hydro-tatic head. The top vents clear very quickly if only the contribution

rom the hydrostatic head is considered. These results indicatehat the drywell pressure increases to the pressure equivalent tohe hydrostatic head of water inside the suppression pool withinpproximately 0.36 s following a large-break LOCA. Accounting for

able 3ummary of vent clearance time calculations for the ABWR containment.

Case Vent clearance equation assumption

1 Only hydrostatic pressure drop considered 0.0 = (PD − PW) + �fgz

2 Hydrostatic + inertial pressure drop considered(

�f x + �f L AvAH

)3 Hydrostatic + inertial + frictional pressure drop considered(

�f x + �f L AvAH

)duVdt

= (PD − PW ) − �f kfE

u2V2 + �f gz(x − HS0)

4 Hydrostatic + inertial + spatial acceleration + frictional pressure (�f x + �f L Av

AH

)duVdt

− �f u2V

= (PD − PW ) − �f kfE

u2V2 + �f gz(x − HS

ring and Design 241 (2011) 3824– 3838 3833

the inertia of the water column inside the vertical vent pipes and thehorizontal vents (the inertia of water inside the suppression poolis negligible due to the relatively large area) results in an increasein vent clearance time from 0.36 to 1.13 s. This increase shows theimportance of fluid inertia for an accurate prediction of the ventclearance time. As shown in Table 3, the pressure losses due to fric-tion and spatial acceleration have a negligible contribution to thepredicted vent clearance time.

4.2.2. Pool swell sensitivity calculationsBest estimate (base case) and sensitivity calculations were per-

formed for the ABWR containment to assess the impact of variousmodel inputs on the calculations of various pool swell parame-ters. The model input parameters/assumptions that were selectedfor the sensitivity calculations include (a) the pressure suppres-sion pool surface area, (b) the polytropic constant for wetwell gascompression, and (c) the effective vent form loss coefficient.

The best estimate values of these parameters were used for thebase case calculations. Fig. 1 shows that the horizontal vents in theABWR containment are located on the inner wall of the annularpressure suppression pool. Due to this configuration of the vents,the air bubbles that formed inside the suppression pool followingthe discharge of the drywell gas mixture through the horizontalvents do not extend uniformly across the entire pool, which leadsto the radially non-uniform swelling of the pool. Consequently, thepool swell has a higher rise near the inside radius of the suppressionpool. As a result, the thickness of the liquid slug on top of the bub-ble is also not uniform across the suppression pool cross section.The GE PICSM code (used for the ABWR DCD pool swell analysis) asstated in ABWR DCD (1997), does not account for the non-uniformpool swell due to its one-dimensional nature. Therefore, GE pro-posed the assumption of an 80% pool surface area for ABWR DCD(1997) pool swell analysis based on the results of a comparisonwith/against experiment data. The STP Units 3 and 4 FSAR (2007)GOTHIC pool swell analysis methodology is also based on a one-dimensional nodalization of the suppression pool. Therefore, theseanalyses also incorporate the 80% pool surface area assumption.For the current model, the best estimate (or base case) simulationsthat are presented in this section use the 100% value of the poolsurface area. However, similar to ABWR DCD (1997) and the STPUnits 3 and 4 FSAR (2007) pool swell analyses, in order to accountfor the effect of the non-uniform pool swell within the presentone-dimensional modeling framework, the results of a sensitivitycalculation that also assumes an 80% value for the pool surface areaare presented.

The polytropic gas constant used in Eq. (29) affects the wetwellgas space compression. As noted earlier, � = 1.4 is equivalent toassuming an adiabatic compression (for nitrogen gas) and � = 1.0is equivalent to assuming an isothermal compression. The adia-batic compression assumption (� = 1.4) results in a relatively higher

wetwell gas space pressure and a lower pool swell and pool sur-face velocity (due to a higher wetwell gas space pressure). Theassumption of isothermal compression (� = 1.0) results in a rela-tively higher suppression pool swell and pool surface velocity and

Vent clearance time, s

(x − HS0) 0.36duVdt

= (PD − PW ) + �f gz(x − HS0) 1.13

1.18

drop considered

0)

1.12

3834 P. Sawant, M. Khatib-Rahbar / Nuclear Engineering and Design 241 (2011) 3824– 3838

Table 4Results of best estimate and sensitivity case calculations.

Parameters Base case Sensitivity cases

1 2 3

Pressure suppression pool surface area, % 100 80.0 100 100Polytropic constant for wetwell gas compression 1.4 1.4 1.0 1.4Effective vent form loss coefficient

Top vent open 14.9 14.9 14.9 0.1Top and middle vents open 5.9 5.9 5.9 0.1All vents open 4.3 4.3 4.3 0.1

Calculated breakthrough time, s 1.7 1.8 1.7 1.8Calculated maximum pool swell, m 1.5 2.3 1.5 3.1

3 5.4 4.5 6.8158 148 184134 122 163

asbnt

lpisTfdfifivtFf

sstib

siiiFmiatwl8lttmr

c�(pri

Table 5Comparison with STP Units 3 and 4 FSAR (2007) results.

Pool swell model parameter STP units 3 and 4FSAR (2007)

Present model

Maximum pool swell height, m 8.8 8.7Maximum pool surface velocity, m/s 10.9 9.5

for the ABWR containment was performed using the GOTHIC code.Table 5 shows the comparison of peak values estimated for thepool swell height, pool surface velocity, wetwell gas space pres-

50

100

150

200

250

300

350

Pres

sure

, kPa

Current Model

STP Units 3 and 4 FSAR (2007)

Calculated maximum pool surface velocity, m/s 4.Calculated maximum bubble pressure, kPa 153Calculated maximum wetwell gas space pressure, kPa 129

lower wetwell gas space pressure. The time duration of the poolwell phenomena is about 2–3 s. Consequently, the transfer of heatetween the wetwell gas space and the wetwell heat structures areot significant. Therefore, for the best estimate (base case) analysis,he adiabatic compression (� = 1.4) is assumed.

The calculated effective form loss coefficients for the gas andiquid flows through the vent system use the modeling approachresented in Appendix A. The vent clearance analysis presented

n Section 4.2.1 shows that the vent clearance phenomenon is notensitive to the frictional and form losses inside the vent system.herefore, a sensitivity analysis using the liquid flow effective ventorm loss coefficient is not required. A sensitivity calculation usesifferent values for the effective gas phase vent form loss coef-cient. The best estimate values of the effective gas flow vent

orm loss coefficient are calculated using the approach presentedn Appendix A. The calculated effective vent form loss coefficientaries from 4.3 to 14.9 depending on the number of horizontal ventshat are open. These values are used for the base case calculation.or the sensitivity case calculation, a negligibly small (around 0.1)orm loss is assumed under all vent flow configurations.

Table 4 shows the results of the best estimate (base case) andensitivity case pool swell calculations and the values of the sen-itivity parameters used in each calculation. For each calculation,he table also shows the predicted bubble breakthrough time, max-mum pool swell height, maximum pool surface velocity, maximumubble pressure, and maximum wetwell gas space pressure.

The sensitivity case calculation with an 80% pool surface areahows a substantial increase in the maximum pool surface veloc-ty and pool swell height. The maximum pool surface velocitys increased by 25% and the maximum pool swell rise height isncreased by 53% compared to the predictions for the base case.urthermore, the maximum bubble inside pressure and the maxi-um wetwell gas space pressure remain relatively unaffected (an

ncrease of about 3%) by the reduction in the effective pool surfacerea. It should be noted that for the sensitivity calculation, evenhough the suppression pool surface area was reduced by 80%, theetwell free gas volume was the same as in the base case calcu-

ation. In summary, the uneven pool swell (as simulated by the0% pool surface area sensitivity calculation) results in a higher

ocal pool surface rise and pool surface velocity, but the effects onhe pressure of the wetwell gas space and the inside pressure ofhe bubble are negligible. Since this assumption would result in

ore bounding value of the estimated pool swell parameters, it iselevant for the design basis pool swell analysis.

The results of sensitivity case calculation with the isothermalompression of the wetwell gas space (i.e., polytropic constant,

= 1.0) show a small increase in the maximum pool surface velocity

4.5%). Furthermore, the maximum wetwell gas space and bubbleressures are reduced (−3 to −5%) when compared to the base caseesults. Therefore, for the design-basis analysis, the assumption ofsothermal wetwell gas space compression is more bounding in

Maximum wetwell gas pressure, kPaG 146 161Maximum bubble pressure, kPaG 195 179

terms of maximum pool surface velocity, and the assumption ofadiabatic wetwell gas space compression (same as the base case) ismore bounding in terms of maximum wetwell gas space pressure.However, the overall impact of this assumption is considered to benegligible.

The most significant effect on the all pool swell parameters isobserved in a sensitivity case with an effective vent form loss coef-ficient value of 0.1. Table 4 shows that the maximum pool swellis increased/increases by 106% in this sensitivity calculation. Sim-ilarly, the maximum pool surface velocity increases by 58%; andthe maximum wetwell gas space and bubble pressures increaseby more than 20%. The bubble breakthrough time for this sen-sitivity calculation also increases. The gas flow rate through thevertical vent pipes reaches critical condition due to the very smallvent system pressure drop assumed for this calculation. Therefore,the assumption of a smaller effective vent form loss coefficient ismore bounding for the prediction pool swell dynamics under DBAconditions.

4.2.3. Comparison to licensing analysesThe STP Units 3 and 4 FSAR (2007) pool swell licensing analysis

03.02.52.01.51.00.50.0

Time, s

Fig. 7. Comparison with STP Units 3 and 4 FSAR (2007) results: bubble pressure.

P. Sawant, M. Khatib-Rahbar / Nuclear Engineering and Design 241 (2011) 3824– 3838 3835

Table 6Comparison with PSTF experiment data.

Calculated model parameter Percentage of experimental data points predicted by model that are within:

<±10% ±10% < and < ±30%

Time of vent clearanceTop vent 100 0Middle vent 80 20Bottom vent 0 100

Liquid slug thickness Liquid slug thickness 44 51

sGgbta

4

toiect(tspa

F

Breakthrough elevation Breakthrough elevation

Pool surface elevation Pool surface elevation

Pool surface velocity Pool surface velocity

ure, and bubble pressure in the STP Units 3 and 4 FSAR (2007)OTHIC analysis and those based on the present model. Generally,ood agreement in the results is noted. In Fig. 7, time-dependantubble pressure predicted by the present model is compared tohe STP Units 3 and 4 results. This comparison shows a reasonablegreement.

.2.4. Comparison to experimental dataThe present model is also compared to the BWR Mark III con-

ainment PSTF experimental data. Fig. 8 shows a schematic of thene-third scale PSTF test section (Yan and Bolger, 2010). The facil-ty was designed and operated by GE and was used to generate thexperimental data in support of the Mark III pressure suppressionontainment design. The facility consisted of an integrated sys-em of the boiler or pressurizer, drywell, vent system, and wetwellsuppression pool and wetwell gas space). The pool and vent sys-

ems both represented one-third scale mockups of an 8-degreeector of the Mark III containment. The transient responses of theressurizer, drywell, vent system, suppression pool, and wetwellirspace were measured using instruments that included pressure

ig. 8. Schematic of the one-third scale PSTF test facility (Yan and Bolger, 2010).

100 0100 0

0 100

and differential pressure transducers, thermocouples, and conduc-tivity probes. The conductivity probes were used to monitor theliquid interface movement based on the difference in conductancebetween gas (air and/or steam) and liquid (water). These mea-surements were further analyzed to obtain data on pool swellparameters (i.e., pool surface elevation, pool surface velocity, andliquid slug thickness).

Three PSTF experiments were selected for the comparison. Theselected experiments used air as the blowdown fluid. Table 6 showssummary of the comparison results (detailed comparison could notbe presented here due to the proprietary nature of the experimen-tal data). As shown in Table 6, the vent clearance time for the topvent, pool swell height, and the bubble breakthrough elevation arewithin 10% of the experimental data. The liquid slug thickness andthe pool surface velocity are predicted within 30% of the experi-mental data.

Large deviation in prediction of the pool surface velocity canbe due to relatively large uncertainties involved in the measure-ment of this parameter. The pool surface velocity was not directlymeasured, instead it was calculated using the measured time forthe pool level or interface to travel from one conductance probe toanother conductance probe (located downstream) and the distancebetween the two probes. Therefore, the measurement of pool sur-face velocity involves uncertainties due to measurements of twoconductance probes and a distance between the two probes, whichare typically large.

The vent clearance times predicted for the top and middle ventsare close to those in the experimental data. However, the modelpredicted a very early clearance of the bottom horizontal vent com-pared to the experimental data. For the model, the vent clearanceis assumed to occur as soon as the water level inside the verticalvent pipe drops below the top elevations of the horizontal vents(shown by the dotted lines in the figure). The discrepancy betweenthe prediction and measurement of the vent clearance times can bedue to several simplifying vent clearance model assumptions (seeSection 3.1). These assumptions start to breakdown following theopening of the top horizontal vent. Immediately after the clearanceof the top vent, the drywell air begins to flow into the suppressionpool and creates an expanding air bubble at the exit of the vent. Thisexpanding bubble accelerates the pool surface and exerts a higherpressure on the middle and bottom vent exits, which delays theirclearance. Therefore, the assumptions of a negligible pool surfacevelocity and an inertial pressure drop inside the suppression poolmay not be fully applicable following the clearance of the top hori-zontal vent. Consequently, the model predicts an early clearance ofthe middle and bottom horizontal vents. Furthermore, as noted ear-lier, the model assumes the clearance of the horizontal vent as soonas the water level inside the vertical vent drops below the top ele-vation of the horizontal vent. However, the experimental data showthat after the water level drops below the top elevation of the hori-

zontal vent, the air–water interface enters into the horizontal ventand moves toward the exit with the increasing drywell pressure.Therefore, the air–water interface requires a finite time to travelfrom the entrance to the exit of the horizontal vent. The movement

3 ngineering and Design 241 (2011) 3824– 3838

oele

admcets

5

stpessbwtiTcsFttmpcCtms1am

A

FCiR

NN

A

lfvesf

v

tal vents are open (the middle vents are partially open). With themultiple vents open, the losses through the horizontal vents are

836 P. Sawant, M. Khatib-Rahbar / Nuclear E

f the interface through the vent is not included in the model. Thisffect is more pronounced in the PSTF experiments because of thearger length-to-diameter ratio of the horizontal vents in the PSTFxperiments as compared to the ABWR containment design.

In summary, the model prediction of the clearance for the topnd the middle horizontal vents is reasonable. The earlier pre-iction of the clearance for the bottom horizontal vent is due toodeling assumptions and limitations. Furthermore, this model

haracteristic of the pool swell analysis is bounding because thearlier clearance of the bottom horizontal vents would result inhe transfer of a larger amount of drywell atmosphere into theuppression pool, thus resulting in larger hydrodynamic loads.

. Conclusion

A PIRT applicable to the ABWR containment pool swell analy-is was used as a basis for the development of an analytic modelo predict important pool swell parameters. The highly rankedhenomena were represented mechanistically. The present modelnables the calculation of the vent clearance time and various pres-ure suppression pool swell parameters including the pressureuppression pool surface velocity, the surface elevation, the gasubble pressure, and the wetwell gas space pressure. The modelas applied to conditions of a large-break LOCA in the ABWR con-

ainment. Sensitivity calculations were performed to assess thempact of key model assumptions on various pool swell parameters.he vent clearance time sensitivity analysis showed that the ventlearance phenomenon is significantly influenced by the hydro-tatic head and the inertia of water residing inside the vent system.urthermore, the pool swell analysis sensitivity calculations showhat the assumption of a smaller pool surface area (to account forhe uneven pool swell) and reduced vent loss coefficients are the

ost bounding in terms of their impact on the calculation of sup-ression pool swell parameters. Finally, the model was applied toonditions corresponding to a LOCA inside the ABWR containment.omparisons of the calculated results to those of other studies ando the PSTF experimental data showed reasonable agreement. The

odel predicted vent clearance time for the top vents, the poolwell height, and the bubble breakthrough elevation are within0% of the experimental data. The predicted pool surface velocitynd the liquid slug thickness are within 30% of the experimentaleasurements.

cknowledgements

The authors acknowledge the significant contributions of Dr.redrick Moody (Consultant and formerly with General Electricompany) in preparing the PIRT used herein, and the valuable

nputs provided by Mr. Andrzej Drozd of the United States Nuclearegulatory Commission, Office of New Reactors.

This work was performed under the auspices of the United Statesuclear Regulatory Commission, Office of New Reactors (Contractumber NRC-42-07-483).

ppendix A. Effective vent form loss coefficient

The effective vent form loss coefficients for the flow of gas andiquid phases through the vent system are estimated by accountingor the geometry of the vent system and the water level inside theertical vent pipes. This section describes the methodology used tostimate the gas phase effective vent form loss coefficient (kgE). A

imilar approach is used to estimate the liquid phase effective ventorm loss coefficient (kfE).

Fig. A1 illustrates the scenario in which only the top horizontalents are partially open. The effective vent form loss coefficient for

Fig. A1. Estimate of the effective vent form loss coefficient: top vent open.

the gas flow (kgE) under this configuration is derived by summingup the drywell connecting vent entrance loss (kd), the vertical ventpipes to the horizontal vent turning loss (kt), and the horizontalvent exit loss (ke). As shown below, the effects of the flow areachange for the horizontal vents (due to a decreasing water levelinside the vertical vent pipe as the drywell pressure increases, anddue to differences in diameters) on the turning loss (kt) and theexit loss for the horizontal vents (ke) are also accounted for in thederivation (Crane, 1980):

kgE

A2V

= kd

A2V

+ kt + ((1 − ˇ21)/2ˇ4

1)

A2V

+ ke

A2Hg1

(A1)

Fig. A2 illustrate the scenario in which the top two horizon-

Fig. A2. Estimate of the effective vent form loss coefficient: top two vents are open.

ngineering and Design 241 (2011) 3824– 3838 3837

av

hti

b

o

(th

k

c

A

bast

u

w

a

a

b

a

odtbientTmTv

0

1

2

3

4

5

6

3.02.52.01.51.00.50.0

Time, ms

Bub

ble

rise

velo

city

, m/s

R = 0.1R = 0.35R = 0.5R = 1.0R = 2.0R = 3.0

P. Sawant, M. Khatib-Rahbar / Nuclear E

ssumed to be parallel. The loss coefficient for the top horizontalents is defined by:

kA

A2V

= kt1 + ((1 − ˇ21)/2ˇ4

1)

A2V

+ ke

A2Hg1

(A2)

As shown in Eq. (A2), the effects of the flow area change for theorizontal vents (due to a difference in the diameter of the horizon-al and vertical vent pipes) on the turning loss (kt1) is accounted forn the derivation (Crane, 1980).

The loss coefficient for the middle horizontal vents is definedy:

kB

A2V

= kt2

A2V

+ kt + ((1 − ˇ22)/2ˇ4

2)

A2V

+ ke

A2Hg2

(A3)

The effective horizontal vent form loss coefficient (kC) isbtained by:

AV√kC

= AV√kA

+ AV√kB

(A4)

The total effective vent form loss coefficient for the gas flowkgE) when the top two vents are open is obtained by summinghe drywell connecting vent entrance loss (kd) and the effectiveorizontal vent loss (kC):

gE = kC + kd (A5)

A similar approach is used to derive the effective vent form lossoefficient for the gas flow (kgE) when all three vents are open.

ppendix B. Bubble rise velocity

As presented in Section 3.2.3, for the present model, the gasubble formed at the exit of the horizontal vents is assumed to riset its terminal velocity (i.e., bubble acceleration zero) through theuppression pool. This Appendix presents the analysis to supporthe above modeling assumption.

The solution to Eq. (12) is:

b = a

(e2abt − 1e2abt + 1

)(B1)

here:

=√

2(�f − �g)Vb

CD�f Ab(B2)

nd

= 12

CDAb

Vb

�f

�g(B3)

The drag coefficient (CD) depends on the relative velocity, size,nd shape of the bubble and the fluid properties.

As noted in Section 3.2.3, the gas bubble that forms at the exitf the horizontal vents appears to rise as a spherical cap bubbleue to its relatively large size. Therefore, for the current calcula-ions, the cap bubble drag coefficient (8/3) is used. It is derivedased on the theoretical analysis that a spherical cap bubble has an

ncluded angle of about 100 degrees and a relatively flat tail (Clift

t al., 1978; Wallis, 1969) and is applicable to the bubble Reynoldsumber greater than 150 (i.e., Reb = 2R�fub/�f > 150). Fig. B1 showshe rise velocity of a spherical cap bubble calculated using Eq. (B1).he figure shows that the time required for a bubble to reach the ter-inal velocity increases with an increase in the size of the bubble.

he bubble accelerates very rapidly and approaches the terminalelocity. The maximum calculated characteristic time required for

Fig. B1. Rise velocity of the bubble through a stagnant pool of water.

the bubble to reach terminal velocity is less than 2 ms. This charac-teristic time is negligibly small compared to the time required for abubble breakthrough (i.e., the breakthrough time is several ordersof magnitude longer compared to the characteristic time for thebubble to reach its terminal velocity). Consequently, the assump-tion that the bubble rises at its terminal velocity is justified andappropriate.

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