Raju Ananth Structural Integrity Associates, Inc Hellyer Avenue, Suite 210 San Jose, CA

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1 Poceedings of the ASME 1 Pessue Vessels & Piping Confeence PVP1 July 15-19, 1, Toonto, Ontaio, CANADA PVP Flow Loads on the Shoud in a Boiling Wate Reacto Due to a Reciculation Outlet Line Beak - A Compaative Study between Potential Flow and Computational Fluid Dynamics Methodologies Raju Ananth Stuctual Integity Associates, Inc. 515 Hellye Avenue, Suite 1 San Jose, CA ananth@stuctint.com Sanda Sowah Stuctual Integity Associates, Inc. 515 Hellye Avenue, Suite 1 San Jose, CA ssowah@stuctint.com Jay Gillis Stuctual Integity Associates, Inc. 515 Hellye Avenue, Suite 1 San Jose, CA jgillis@stuctint.com ABSTRACT This pape compaes two methodologies fo estimating the flow loads on the shoud of a typical BWR caused by a Reciculation Outlet Line Beak. Fist, assuming an ideal and iotational flow field, the complex potential methodology is used to calculate a two dimensional appoximation of the flow field by ignoing vaiations along the adial diection. As a simplification fo the compaative study the annulus will be assumed to be devoid of any stuctual components such as the jet pumps. The flow field deived fom the potential flow appoach will be used to compute the total lateal and moment loads acting on the shoud. These load values will be compaed against simila values deived fom a thee dimensional and moe ealistic flow field computed by Computational Fluid Dynamics (CFD). The potential flow based method is computationally simple as compaed to the moe time consuming CFD appoach. Keywods: Loss of Coolant Accident; Flow loads; Boiling Wate Reacto (BWR); Potential flow; Computational Fluid Dynamics (CFD). NOMENCLATURE i Equal to 1, an imaginay quantity z( A complex vaiable that is equal to x + i. y m Sink stength associated with the eciculation dischage flow u( Fluid velocity in the x-diection at a point ( v( Fluid velocity in the y-diection at a point ( V (x) Geneal 3-D velocity field at an abitay location epesented by x Φ( Complex velocity potential at a point ( φ( Velocity field deived fom velocity potential, dφ( z) ϕ( z( ) = dz INTRODUCTION Flow loads on the shoud caused by a Reciculation Outlet Line Beak Loss of Coolant Accident (LOCA) ae a equied design basis event that must be consideed fo Boiling Wate Reacto (BWR) intenal components. Duing a LOCA, subcooled wate flows past jet pump assemblies located in the annula egion between the Reacto Pessue Vessel (RPV) and the shoud [Fig. 1] as it moves towad the beak location and is 1 Copyight 1 by ASME

2 subsequently dischaged fom the RPV though the eciculation opening. Loads due to the momentum tansfe fom the eacto coolant flowing acoss and along the sufaces of the jet pumps and aound and down the shoud suface, ae efeed to as the flow loads. These loads ae used in stess and factue mechanics evaluations of the jet pump assemblies and shoud assembly to detemine allowable flaw sizes. This pape descibes two appoaches in estimating the loads as a esult of the LOCA accident. In the fist appoach, an impotant assumption is made that the velocity field does not vay in the adial diection. Hence the velocity field becomes two dimensional. Theefoe, complex vaiable techniques can be used by making futhe simplifications about the fluid and the flow. Since the annulus width is typically five o six times smalle than the adii of the two cylindical shells making the annulus egion, it is justified to teat the poblem as two dimensional. By assuming the fluid to be ideal and the flow to be iotational, the velocity field can be obtained fom potential flow theoy [1]. The desied steady state flow load can be estimated fom the velocity field by applying the genealized Benoulli s theoem. The shea and the bending loads acting on the bottom ancho suppot obtained by such a simplified appoach is then compaed against those values computed using CFD involving moe ealistic thee dimensional annulus geometies and eal fluid. ASSUMPTIONS 1. In the simplified appoach, the flow velocity is assumed not to vay in the adial diection. The poblem then becomes a two-dimensional one with the azimuthal diection becoming the hoizontal (x) axis. The mean cicumfeence of the annulus is the extent of the domain of inteest in the x diection. In essence, the cylindical coodinates (, θ, z) ae tansfomed into x (hoizontal diection) and y (vetical diection) coodinates. 4. The annula space is assumed to be fee of jet pumps o any such components fo the pupose of this compaative study. To evaluate the flow with obstuctions along the flow path, the velocity field needs to be suitably adjusted in the potential flow appoach in ode to compute the foces. 5. The blowdown flow afte the eciculation line beak is assumed to be single phase and no steam bubbles ae assumed pesent in the egion fo both methods. Fom the guidance povided in [-4] it is assumed that wate is exiting the annulus at the satuation pessue of wate detemined by the pescibed unifom fluid tempeatue in the annulus. The exit pessue and the total pessue in the annulus at the exit elevation detemine the exit velocity and flow volume ate. 6. The static pessue head due to gavity is ignoed as the static head tems cancel out at any elevation as the pessues ae integated aound the shoud to obtain the loads. FORMULATION OF THE POTENTIAL FLOW PROBLEM Fom the assumptions of the flow being iotational and the fluid incompessible, the fomulation is as follows: A velocity potential Φ(x ) exists such that the velocity field satisfies: Fo iotational flow, V ( x ) = and hence V ( x) = Φ( x). The incompessibility and steady flow assumptions lead to the elationship V = to satisfy the consevation of mass. Thus the velocity potential Φ(x ) satisfies the Laplace equation:. Fo the potential flow method, the fluid is assumed to be ideal (non-viscous) and iotational. Hence, no fluid phenomena such as flow sepaation, bounday layes, votex shedding etc., ae pesent. Howeve no such assumptions ae made in the case of the CFD appoach. 3. The flow is incompessible and steady fo both the appoaches. The assumption of incompessibility is appopiate wheneve flow velocities ae small compaed to the acoustic velocity of the fluid. The acoustic speed in sub-cooled wate in the annulus is on the ode of 1 m/sec. The esults of this calculation show that the maximum flow velocities in the annulus away fom the sink locations ae on the ode of 5 m/sec, justifying the assumption of incompessibility. The steady state assumption implies unlimited supply of fluid fa away fom the exit. Copyight 1 by ASME

3 Φ = (1) Techniques have been developed fo such fluids to detemine the velocity field in two dimensions based on complex vaiable theoy [5]. These techniques, paticulaly the method of images, will be utilized in this pape. The flow goes out of one of the two eciculation outlets fom the eacto vessel afte the pipe line beak [Figue ]. In the complex plane, this outflow can be epesented using a supeposition of sinks as follows: Fist, a basic sink is located at the point ( = (, B) as shown in Figue 3. Next, using the method of images, an image sink is added at the point ( = (, -B). Similaly, image sinks ae added on eithe side of the bounding side walls at x = ± an, y = ±B whee a is the half cicumfeence of the annulus at a adius midway between the inne and oute walls. The index n anges fom 1 to infinity. The doubly infinite, peiodically spaced ows of sinks above and below the x-axis ae needed to ensue that the flow exiting though the basic sink at (, B) oiginates in the aea bounded by the walls at x = ±a and the planes y = and y = infinity as shown in Figue 3. The velocity potential can then be epesented as follows: Figue 1: TYPICAL JET PUMP ASSEMBLY IN A BWR ANNULUS AREA FORMED BETWEEN RPV AND SHROUD π π Φ ( = m ln(sin( ( x + i( y B))) + ln(sin( ( x + i ( y + B))) a a () whee i = 1, m is the sink stength defined as the volumetic flow pe unit thickness nomal to the ( plane divided by π i.e. m = (Exit flow volume/ (π Annulus width)). The sine tems in equation () epesent the just descibed doubly infinite peiodically spaced sink ows. The fist tem inside the paenthesis on the ight hand side of equation () coesponds to the sink ows located at y = B and the second tem coesponds to the sink ows located at y = -B. Let z = x + i y. The velocity field, namely u( and v(, espectively in the x and y diection, following the sign convention in [5], may be given as Φ( z) π π = m ln(sin( ( z ib))) + ln(sin( ( z + ib))), a a -u( + i v( = d dz π π π Φ ( z) = m cot( ( z ib)) + cot( ( z + ib)) a a a (3) Figue : PLAN VIEW OF THE ANNULUS REGION 3 Copyight 1 by ASME

4 The above equation defines the velocity field V ( = u( + i * v( fo the accident caused blowdown flow. pessue load is geneated ove the fluid exit aea, the integation in (7) needs to leave out the aea ove the exit hole. Unde an ideal fluid assumption, whee the viscosity of the fluid is ignoed, the equation of motion of the fluid may be given in geneal as V 1 + V + 1 p = f t ρ + V ω whee ω is the otation of the fluid in space and time, f is a consevative foce that may be given as the gadient of a quantity as f = U. (4) Unde assumptions of steady flow and absence of factos such as fiction, viscosity and fluid otation, equation (4) may be integated along any abitay steam line fo steady state conditions to get V p + = ρ which is a genealized Benoulli s equation that holds fo any abitay steam line, suface etc. Hence, knowing the velocity field on the suface of the shoud inside the annulus, the pessue field may be obtained which may be integated ove the aea to get the loads. Once the pessue p( values ae known at the suface of the shoud, x axis along the cicumfeence and y axis along the vetical axis in the view [Fig.3], the net foces along the hoizontal and vetical diections in the plan view of the annulus may be computed as follows: F M 1 = = π π sin( ϑ) = ysin( ϑ) = Due to the symmety of the pessue field with espect to the axis along diection 1 [Fig.] connecting the two eciculation exits, the net foce and moment along diection is zeo, whee ϑ is the angle between the nomal at any point to the shoud and the axis along diection 1. Howeve, along the line connecting the eciculation exits (Diection 1) the coesponding foce and moment expessions ae: 1 π F = M π = *cos( ϑ) * y *cos( ϑ) The foce computations may be made by discete summation of the pessue instead of the integations shown in (7). Since no (5) (6) (7) Figue 3: ILLUSTRATION OF THE POTENTIAL FLOW MODEL CFD COMPUTATION OF SHROUD LOAD A solid geometical model of the fluid domain, with the details povided in the table unde the example poblem section, was ceated to simulate the annulus egion of a typical BWR eacto vessel using the SolidWoks [7] softwae. The domain of inteest is the sub-cooled liquid egion in the annulus which begins about 51 inches wate level and extends vetically downwad to the shoud suppot plate (plane of y =). Since the annulus configuation is symmetic about a vetical plane passing though the eciculation openings, an appopiate halfmodel is ceated in the egion of inteest fo the CFD analysis. A thee dimensional half-model of the post beak flow in the annulus was ceated and solved using ANSYS Wokbench [8] fo meshing and ANSYS CFX [9] fo the CFD simulation. The thee dimensional meshing esulted in a unifom mesh of edge length.5 inches. The mesh was composed of 16,391,17 elements, mostly tetahedons. Figue 4 shows pat of a detail of the mesh chosen to illustate the mesh size esolution. The mesh typically had ove elements in the coss-annulus diection and thee wee 5 mesh layes in the vetical diection. The CFD model uses the mateial popeties of wate based on the Intenational Association fo the Popeties of Wate and Steam [1] in equation of state (IAPWS-IF97 database). 4 Copyight 1 by ASME

5 A steady-state solution using the shea stess tanspot (SST) tubulence model (a modified k-ω tubulent model) was used in the steady-state simulations with a fist ode high esolution advection scheme fo the fluid domain. The flow egime fo the simulation is in the subsonic ange (i.e., Mach <1) with the inheent assumption that the density of the fluid is elatively constant in the fluid domain and non-buoyant. The total enegy tanspot equation [1] that accounts fo enthalpy and kinetic enegy effects in the liquid egime fo the annulus egion was used. Figue 5: STREAM LINES CFD ANALYSIS Figue 5 shows the steam lines obtained fom the solution. As expected the steamlines convege on the beak simila to steamlines fom the potential flow solution. Figue 6 shows the pessue distibution contou on the Shoud. As with the potential flow solution, the gavitational pessue field has been neglected. The pessue diffeence ove the shoud is not lage, only about 3 psi, but lage loads ae accumulated due to the lage aeas involved. RESULTS An example poblem was solved using the potential flow and the CFD methods. The vaiables and thei values chosen fo the poblem ae shown in the table below. The velocity fields computed by both solutions wee used to calculate the asymmetic load on the shoud. The potential flow solution computes a load of 6557 N and a moment of m-n. Coespondingly, the CFD computes a load of 5657 N and a moment of m-n. Figue 4: CFD MESH OF THE FLUID DOMAIN At the top of the annulus the liquid mass flow ate was specified as a bounday condition. This total mass flow ate into the annulus egion is the same as the output though the nozzle. The shoud, RPV and nozzle sufaces wee specified as nonslip and adiabatic. At the nozzle beak plane duing the post- LOCA condition, the satuation pessue coesponding to the tempeatue of the subcooled liquid in the annulus just pio the beak is specified as a bounday condition. DISCUSSION The load calculation with the simple potential flow model in the example chosen agees to within 11% of that of the moe accuate CFD model. The moe ealistic velocity distibution in the annulus esults in lowe loads with the CFD calculation. The simple potential flow calculations will allow quicke estimates of the load and check the CFD esults as well. Figue 6: PRESSURE CONTOUR CFD ANALYSIS 5 Copyight 1 by ASME

6 EXAMPLE PROBLEM No. Vaiable Value 1 Vessel (RPV) ID m Shoud OD m 3 Annulus Width = ( )/ =.58 m Mean Radius of = ( )/4 = 4 Annulus.96 m Mean Half 5 Cicumfeence ( a ) π x.96 = m 6 Distance ( B ) [Fig.3] 1.51 m Annulus Fluid 7 Tempeatue 79 C Fluid Satuation 8 Pessue at exit MPa Pessue in the middle of the annulus at the 9 eciculation exit 7.35 MPa elevation Reciculation exit 1 diamete.5 m 11 Fluid density at 79 C kg/m 3 1 Blowdown exit velocity (m/sec) *( ) = Mass Flow ate at exit 13 pe unit aea 14 Blowdown Volume ate 15 Blowdown Sink Stength ( m ) 3.97*1 4 kg/m.sec 1.7 m 3 /sec (1.7*1 4 lite/s) =1.7 m 3 /sec x (1/(π*.58 m)) = 3.18 m /sec REFERENCES [1] Ananth, R., Fujikawa, K., Gillis, J., 9, Fluid Flow Field in the Annulus of Boiling Wate (BWR) Nuclea Reactos unde Nomal and Accident Conditions, PVP [] Lahey, R. T., and Moody, F. J., The Themal- Hydaulics of a Boiling Wate Reacto, Ameican Nuclea Society. [3] Suchanek, M. and Batak, J., Themo-hydaulic Behavio of the Coolant in the Initial Phase of a Loss-of- Coolant Accident, Multiphase Flow and Heat Tansfe, Second Intenational Symposium, Ed. Chen, Xue-Jun, Volume, pp , ISBN: , , Published by Taylo and Fancis, [4] Alamgi, Mohammed, and Lienhad, J. H., 1981, Coelation of Pessue Undeshoot Duing Hot-Wate Depessuization, Tansactions of the ASME, Jounal of Heat Tansfe, Vol. 13, pp [5] Milne Thomson, L. M., 1968, Theoetical Hydodynamics, Macmillan Pess, Fifth Edition. [6] Rolf H. Sabesky, Allan J. Acosta, Edwad G. Hauptmann, Fluid Flow, 1971; The Macmillan Co., NY, Second Edition. [7] Dassault Systems, SolidWoks 11 [Softwae]. Sevice Pack 5.. [8] ANSYS Inc. ANSYS Wokbench. Famewok (Vesion 13.. Sevice Pack ) [Softwae]. [9] ANSYS Inc. ANSYS CFX (Vesion 13., CFX-13., build ) [Softwae]. [1] ANSYS Inc. (1). ANSYS CFX Solve Theoy Guide, Release Copyight 1 by ASME