Dong-Yuan Sheng Westinghouse Electric Sweden AB 72163, Västerås, Sweden

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1 DETERMINATION OF THE PRESSURE LOSS COEFFICIENT AT CONTROL-ROD GUIDE TUBE FLOW-HOLE FOR A PWR NUCLEAR FUEL ASSEMBLY BY USING CFD AND BERNOULLI SOLUTIONS ABSTRACT Dong-Yuan Sheng Wesinghouse Elecric Sweden AB 72163, Väserås, Sweden shengd@wesinghouse.com Marcus Seidl E.ON Kernraf GmbH Trescowsrasse 5, Hannover, Germany marcus.seidl@eon.com For accurae predicion of he margins o boiling inside he guide ube of a PWR fuel assembly he bypass mass flow and he guide ube hea source has o be deermined. Hisorically due o a lac of numerical soluion mehods a conservaive approach based on one-dimensional fluid analysis (e.g. Bernoulli principle, sudden conracion and epansion pressure loss) has been used. In realiy he fluid moves in a complicaed, hree-dimensional way in he viciniy of he flow-hole: here is a sharp flow area change from fuel channel hrough he flow-hole ino he guide ube ogeher wih wo sharp 90 degree bends. In his sudy, a hree-dimensional CFD model wih full channel lengh has been developed o have a numerical deerminaion of he flow-hole pressure loss coefficien. The ISO 5167 sandard small sharpedged cylindrical orifice was seleced o validae he CFD model. The calculaed values for he pressure loss coefficiens (K in ) are in good agreemen wih he ISO sandard. The developed model has been applied o calculae he pressure loss under differen process parameers, such as: 1) Conrol rod posiion o sudy he effec of conrol rod posiion on he mass flow in he guide ube; 2) Space grid o sudy he guide ube mass flow influence on he effec of he pressure drop in he fuel channel; 3) Mass flow -- o sudy he relaion beween K in and channel flow Reynolds number. KEYWORDS PWR, CFD, pressure loss coefficien, bypass, flow-hole 1. INTRODUCTION In he design and safey analysis of a PWR, i is imporan o accuraely predic he margins o boiling inside guide ubes (GT) under normal and abnormal operaing condiions in order o eclude he possibiliy of sress corrosion cracing on insered conrol rod fingers. The coolan mass flow from he fuel channel (FC) o he GT hrough he GT flow-hole ogeher wih he GT hea source are he main parameers o deermine he margin o boiling. The pressure loss in a fuel assembly is an imporan parameer for his analysis because i conrols he flow redisribuion beween FC and GT. To evaluae he mass flow hrough he flow-hole, measuring of he pressure loss would be he mos commonly used approach. However he full scale real geomery measuremen is difficul o se up due o he comple consrucion deails. In hese radiional designs, he few available conservaive eperimenal correlaions from he open lieraure or handboo for he maimum pressure loss coefficien a he GT inle flow-holes were used. [1-2] 1303

2 The radiional, conservaive approach is based on one-dimensional (1D) fluid analysis (e.g. Bernoulli principle, sudden conracion and epansion pressure loss) o evaluae he pressure loss coefficien a GT inle flow-holes. In realiy he fluid moves in a complicaed, hree-dimensional (3D) way in he viciniy of he flow-hole: here is a sharp flow area change from fuel channel hrough he flow-hole ino he guide ube (GT) ogeher wih wo sharp 90 degree bends. This moivaes our analysis o re-evaluae he value derived from he 1D mehod wih modern compuaional ools. Pressure loss coefficiens of he cross flow beween flow channels of nuclear fuel bundles have been sudied by using heoreical and eperimenal analyses [3,4]. Compuaional fluid dynamics (CFD) offers a hree-dimensional mehod for predicion of he pressure loss hrough flow-holes and has been widely used in recen years o model pressure loss hrough sandard orifices [5-10]. Their resuls showed a good agreemen beween eperimenal daa and CFD predicion viz. velociy/pressure profiles and discharge coefficiens. The published resuls showed ha he difference beween simulaed discharge coefficien C D and values epeced from he ISO 5167:2003 sandard is lower han 5%. The reliabiliy of predicing pressure loss coefficiens wih CFD mehods in he above sudies means ha hey poenially can be used as an alernaive ool o deermine bes-esimae GT flow hole pressure loss coefficiens insead of conducing ime consuming eperimens wih a full lengh fuel assembly inside a flow channel es rig. The obecive of his sudy is o develop a 3D CFD model o ge a numerical deerminaion of he flowhole pressure loss coefficien (K in ) a he guide ube for a PWR fuel assembly. The CFD model is validaed wih ISO 5167 measuremens of fluid flow by means of pressure differenial devices insered ino circular-cross secion conduis [11]. The developed model has been applied o calculae K in a a GT inle flow-hole under differen process parameers, such as: 1) Conrol rod posiion o sudy he effec of conrol rod posiion wih regard o he mass flow in he guide ube; 2) Space grid o sudy he guide ube mass flow influencing he effec of pressure drop in he fuel channel; 3) Mass flow -- o sudy he relaion beween K in and channel Reynolds number. The numerical prediced pressure loss coefficiens can be used as inpu for analysis he flow redisribuion in he FC and GT based on Bernoulli s principle. 2. 1D MODEL AND 3D CFD MODEL D model-- Bernoulli principle The Bernoulli equaion from flow hole inle posiion o ei a guide ube op is wrien as (Figure 1): + + = (1) Where is he pressure loss due o he fricion on he inner GT channel surface and on he conrol rod surface, is he pressure loss hrough he GT inle flow-hole. The mass balance equaion gives: = (2) Combining eq. (1) and (2) yields a relaionship for he ei velociy: = ( ) / (3) 1304

3 The oal pressure loss from guide ube flow-hole, along he conrol rod unil he oule is calculaed as: + = ( ) + (4) I can be found ha K in in Equaion 3 and 4 is a ey coefficien o deermine he oal pressure drop and mass flow in he GT channel. Figure 1 Geomery region of guide ube applied for Bernoulli principle D CFD model Governing equaions The calculaion of single-phase incompressible flow is accomplished by solving he mass and momenum conservaion equaions given as: Coninuiy equaion: () + ( )=0 (5) Momenum equaion: ( )+ ( )= + + (6) where i are he Caresian coordinaes; u i are he corresponding average velociy componens; is he i are sress ensor componens; S Fi are he source erms for momenum equaions. The success of numerical predicion mehods depends o a grea een on he performance of he urbulence model used. From he lieraure review in secion one, i can be seen ha he Realizable - and SST - model in he simulaion of he flow hrough small holes. The Realizable -separaed flow [12]. SST - separaed or swirl flow [13]. In his sudy, he wo urbulence models are seleced and compared wih he ISO 5167 sandard. 1305

4 Realizable - M b S Y G G u (7) S G C C v C C S u b (8) Where is is urbulen viscosiy; G represens he generaion of urbulen ineic energy due o he mean velociy; Y M represens he conribuion of he flucuaing dilaaion in compressible urbulence o he overall respecively. SST - Y G u (9) Y G u (10) represens he generaion of urbulen ineic energy due o mean velociy gradiens; G Y and Y represen he dissipaion of a Though some oher urbulence models (Reynolds sress model, RSM and Large eddy simulaion, LES) have been repored o be superior o ohers in some flow scenarios, here is no universal urbulence model ha is bes for all flow condiions. Considering he compleiy of he geomery, he oal number of elemens is epeced o be large and urbulence models ha require fine meshes were ruled ou in he firs sep of his sudy Compuaional deails The CFD calculaion domain is buil for four fuel sub-channels (22), and one GT channel. The geomery is shown in Figure 2. The simulaions are performed wih he commercial CFD code -- Sar-CCM+ v A hree dimension, seady sae and segregaed solver was used. The second-order upwind scheme is used o calculae he convecive flu. The discreized equaions were solved in a segregaed manner wih he semi-implici mehod for pressure-lined equaions (SIMPLE) algorihm [14]. The soluions were considered o be converged when he sum of he normalized residuals for all he cells became less han 10-4 for he variables: = (12) p nb are he variable of he presen and neighboring cells, respecively, a p is he coefficien of he presen cell, and a nb are he coefficiens for he neighboring cells, b is he conribuions of he consan par of he source erm and boundary condiions Mesh and boundary condiions

5 The compuaional domains were discreized wih an unsrucured polyhedral mesh wih a prismaic elemens layer in he region near he walls in order o adequaely capure he flow gradiens in such areas. Meshes are refined in he flow-hole region. Mesh erusion is used for inle and oule pars in order o simulae he full flow channel. A mesh independency sudy was performed o find a mesh ha was sufficienly fine o provide an accurae soluion. The geomeries are impored from a CAD model creaed by Pro/Engineer. In order o creae a high qualiy CFD mesh he de-feauring echnique was used o remove hose small feaures in he CAD model (such as smaller filles, smaller faces/edges, small holes), which have lile effec on he resul. The miing vanes, grid srap, spring and dimple in fuel channel are simplified by using he porous media model. The compuaional domain is shown in Figure 2 and he CFD mesh is shown in Figure 3. The rod pich is 14.3 mm. The ouer and inner diameer of GT are 13.8 mm and 12.4 mm. Bypass flow-hole diameer is 2.6mm. 8 porous media regions were defined o simulae space grids. Grid span lengh is 534 mm. The isoropic inerial (quadraic) and viscous (linear) resisance are defined as source erms in he momenum equaion. The coefficiens for inerial and viscous resisance are 6300 g/m4 and 6000 g/m3-s. The polyhedral mesher, wih he embedded prism layer mesher, was used o build he volume mesh in he region close he bypass hole. The eruder mesh was used o generae he volume mesh in he channel in order o produce he orhogonal eruded cells (Figure 3). Mesh independency sudies have been performed wih he focus on he bypass mass flow. Mesh independence occurred a approimaely 6 million volume meshes. The surface average y+ is around 60 and maimum y+ is around 110. a) flow channel b) flow boundary Figure 2 Geomery of flow calculaion domain 1307

6 Figure 3 CFD compuaional meshes In all simulaions, a velociy inle boundary condiion is used a he inle of he fuel channel (V in in Figure 2b). A wall funcion is applied o bridge he viscous sub-layer and provide near-wall boundary condiions for he mean flow and he urbulence ranspor equaions. The wall condiions are conneced by means of empirical formulae o he firs grid node close o he solid surfaces [15]. The inpu parameers for simulaion are lised in Table 1. Pressure oule boundary condiions (P ref =0) are se up a he op plane of boh fuel channel and GT channel. Symmeric boundary condiions are applied a he rod gap. Table 1 Process parameers and physical properies Parameer Dimension Value Inle velociy m/s 1,2,3,4,5,6 Densiy g/m Viscosiy Pa s 9.24 *10-5 Pressure Bar 155 Inle Temperaure o C 290 GT inner diameer Mm 12.4 CR ouer diameer Mm VALIDATION OF CFD MODELS The ISO sandard 5167 is seleced o validae he CFD model. The principle of his ISO sandard is based on he insallaion of an orifice plae ino a pipeline in which a fluid is flowing. This sandard gives he deailed geomery design, insallaion and operaion condiions. The presence of he orifice plae causes a saic pressure difference beween he upsream and downsream sides of he plae. The mass flowrae, Q m, can be deermined using he following equaion = 2 (13) Where C D d is differenial pressure, d is orifice hole diameer, D is pipe l is epansion facor, for liquids i is consan one. The discharge coefficien C D relaes he acual flow-rae o he heoreical flow-rae hrough a device. I is relaed wih he urbulence of he flow and he resricion he device maes o he flow. To calculae he discharge coefficien from empirical daa, ISO 5167 gives he large Reader-Harris/Gallagher formula [16]. For each orifice plae, a leas one upsream pressure and one downsream pressure aps are insalled in one or oher of sandard locaion, i.e. as D and D/2, flange or corner appings. The corner apping resuls are used o validae he CFD resuls. 1308

7 d by Equaion (14), = (14) d. Figure 4 shows he pressure and velociy conour in he cener cross secion based on he CFD simulaion. a) Velociy conour b) Pressure conour Figure 4 Velociy and pressure conour in he middle cross secion While flowing hrough he orifice plae he fluid undergoes a flow conracion ha is followed by a flow epansion. During flow conracion he flow velociy increases and he saic pressure decreases (Bernoulli). Here, he poenial energy is ransformed ino ineic energy wihou significan energy losses. During flow epansion afer passing hrough he hole, he flow velociy decreases and he saic pressure increases (Figure 4). Fluid flow in he direcion of increasing pressure resuls in a significan pressure loss. Figure 5 shows he pressure loss hrough he orifice plae along he cener sreamline. The differenial pressure a he orifice plae is KPa and he pressure loss d (permanen pressure loss) is KPa. The comparison beween CFD predicions and ISO sandard is shown in Table 2. The Discharge coefficien can be used o direcly compare he resuls and he difference is smaller han 3.1%. 1309

8 Figure 5 Prediced pressure hrough orifice plae along cener sreamline Table 2 Comparison of CFD and ISO 5167 Discharge Coefficien (C D ) Difference (C D ) ISO CFD % % The urbulence model sudy was compleed by using wo differen urbulence models described previously, namely Realizable --Figure 6 shows he pressure loss hrough he orifice plae along he cener sreamline wih he wo differen urbulen models. The Realizable -- models predic nearly he same differenial pressure a he orifice plae. A sligh difference is observed a he downsream of orifice plae. The Realizable - ne secion. Figure 6 Pressure losses hrough he orifice along sreamline wih he differen urbulen models 1310

9 4. RESULTS AND DISCUSSION The CFD model was applied in predicing he pressure loss for a PWR fuel assembly using he same procedure as in he previous sub-secion. To sudy he pressure loss hrough he GT flow-hole, he CR posiion, he FC mass flow and he spacer grids were used as geomery srucure and process parameers. Based on he CFD resuls, he effecs of differen geomeries and process parameers on he pressure loss coefficiens of he GT flow-hole was prediced. 4.1 CR posiion In he following wo limiing cases for he conrol rod posiion are analyzed. In he firs case he conrol rod is fully insered and eends beyond he flow hole o he boom of he GT. In he second case he conrol rod ip is sanding us above he flow-hole posiion. The firs case is limiing wih regard o he maimum hea source wihin he GT. The second case is limiing wih regard o he minimum mass flow wihin he GT because in his case he pressure loss hrough he flow whole will be maimal. Figure 7 shows he velociy conour a wo differen cross secions for boh cases: conrol rod close o channel boom, and close o channel oule. The inle velociies are se o 5 m/s a he boom plane of he fuel channel and i is uniformly disribued a his plane. The blue color in he GT channel means a low velociy and sagnaion region below he flow hole. To he region close o he oule, i shows a fully developed channel flow paern in he fuel channel. The increase of velociy in he GT means he bypass flows hrough he flow hole. Figure 8 shows he pressure drop along sreamlines in he differen cases. Two ypical sreamlines are seleced: one is in he cener of fuel channel and he oher is in he cener of flow hole. The inle pressure drop (a Y= 0.0 posiion) is calculaed from he epored CFD daa. The flow-hole s pressure drop is mared by he red arrow in he figure. The pressure loss a inle flow-hole can be wrien as Equaion 15: = (15) The calculaion parameers of he pressure loss coefficien K in are lised in Table 3. The velociies of he inle hole (v) is calculaed by he using he GT oule velociies. The resuls of he wo CFD simulaion cases show ha: 1) The inle velociies hrough he flow hole are quie similar for he wo cases. 2) The pressure drops hrough he flow hole are similar. The pressure curves show same endency in he GT. 3) The calculaed pressure loss coefficiens is 2.8 (CR fully insered) and 2.9 (CR 1 cm above flow hole). The inle pressure loss coefficiens hrough he flow hole are no sensiive o CR posiions in he GT which indicaes ha he movemen of CR in he guide ube has a minor effec o he inle pressure loss. Tradiionally boh cases were analyzed o deermine he minimum mass flow hrough he GT. In mos of hese analyses he second case urned ou o be he mos limiing one because by using sandard, conservaive formulas for he pressure loss hrough he epansion of he fluid from he small flow-hole area o he full GT area he minimum mass flow occurred. CFD analysis indicaes ha a fully insered conrol rod is he limiing case for he margin o boiling safey analysis because i has he maimum possible hea source. 1311

10 Table 3 Calculaed pressure loss coefficien by using CFD resuls Parameer Annular Flow CR 1cm above hole GT oule velociy (m/s) Hole inle velociy (m/s) Densiy (g/m 3 ) Pressure Loss (KPa) Pressure Loss Coefficien Boom (CR fully insered) Boom (CR 1cm above flow-hole) Oule (CR fully insered) Oule (CR 1cm above flow-hole) a) Annular Flow b) CR 1 cm above hole Figure 7 Velociy conours on wo differen cross secions in channel 1312

11 a) CR fully insered b) CR 1cm above hole Figure 8 Pressure drop along sreamlines 4.2 Space grid The CFD simulaion region consiss of wo parallel channels (FC and GT) wih differen geomerical configuraion and hydraulic diameer. There is a pressure equalizaion process for FC and GT channels due o he bypass flow hrough GT inle hole. The spacer grids and fuel rod fricion deermine he pressure drop in he fuel channel, while he GT inle hole and he CR fricion deermine he pressure drop in he GT channel. As shown in Figure 2b, here are eigh spacer grids above he GT inle flow-hole in his design. The spacer grids have many small componens wih hicness of 1-2mm. The geomeric compleiy requires he adopion of a finer mesh. To reduce compuaional ime and effor, he porous media approach for he spacer grids is applied in his sudy. Porous media are modeled by he addiion of a momenum source erm o he sandard fluid flow equaions. The source erm is composed of wo pars: a viscous erm and 1313

12 an inerial loss erm. The spacer grids are simplified solid maerial wih uniformly dispersed in he flow domain. The porosiy and flow resisance replicae he volume-average characerisics of heir real geomerical domain. Figure 9 Calculaed pressure drop in he fuel channel (wih 8 spacer grids) and GT channel Figure 9 shows he CFD calculaed pressure drop in he fuel and he GT channel. The pressure drop along he fuel rods is considered o be due o fricion and he pressure drop in he spacers is calculaed by using he porous medium model. The oal pressure drop increased in he fuel channel due o he spacers compared wih he case wihou spacers (Figure 7). The higher pressure drop in he fuel channel leads o an increased mass flow hrough he GT inle hole. The calculaed pressure loss coefficiens is 2.3 which is 0.5 lower han he case wihou spacer grids (Kin=2.8). One eplanaion o he lower Kin wih spacer grid is ha he firs spacer grid is abou 7 cm above he GT inle hole. The closed disance beween spacer grid and GT inle hole will change he local flow paern, flow angle o GT inle and urbulence srengh near he GT inle hole. 4.3 Mass Flow Parameric sudies were done which characerize he pressure loss coefficien K in as he Reynolds number changes. Si differen cases were se up wih he fuel channel inle velociies as 1,2,3,4,5,6 m/s. The mass flow hrough he GT inle hole is increased when increasing he fuel channel inle velociy. The resuls show ha he pressure loss coefficien remains essenially consan across he range of Reynold number beween and CONCLUSIONS A 3D CFD model o predic he flow-hole pressure loss coefficien (K in ) a he guide ube for a PWR fuel assembly has been developed in his sudy. The validiy of he developed CFD model was evaluaed wih he help of he ISO 5167:2003 sandard. A comparison of he Realizable - and he SST - urbulence models have been done. The wo urbulence models predic nearly he same differenial pressure a he orifice plae in he ISO reference. A sligh difference is observed downsream of he orifice plae. The discharge coefficien is smaller han 3.1% by comparing CFD resuls and he ISO sandard resul. The resuls of he CFD simulaions on differen conrol rod posiions show ha he GT hole inle mass flow and pressure drops are quie similar. The calculaed pressure loss coefficiens is 2.8 (CR fully insered) and 2.9 (CR 1 cm above flow hole). The inle pressure loss coefficiens hrough he flow hole are no sensiive o CR posiion which indicaes ha he movemen of he CR in he guide ube has a minor effec o he inle pressure loss. Tradiionally, in mos of hese analyses he second case urned ou 1314

13 o be he mos limiing one because, by using sandard, conservaive formulas for he pressure loss hrough he epansion of he fluid from he small flow-hole area o he full GT area, he minimum mass flow occurred. This analysis shows ha a fully insered conrol rod (he firs case) is he limiing case for he margin o boiling safey analysis because i has he maimum possible hea source. The oal fuel assembly pressure drop is increased due o he flow resisance of he spacer grids. The higher pressure drop in he fuel channel leads o an increased mass flow hrough he GT inle hole. The calculaed pressure loss coefficien is 2.3 which is 0.5 lower han he case wihou spacer grids. Si differen cases (wih space grids) were done wih channel inle velociies as 1,2,3,4,5,6 m/s. The resuls show ha pressure loss coefficien remains essenially consan across he range of Reynold number beween and REFERENCES 1. I. E. Idelchi: Handboo of Hydraulic Resisance, 3 rd Ediion, Boca Raon, CRC press (1994) 2. J. Sichlmair: Drucverlus bei der Durchsrömung von Lochplaen, VDI-Wärmealas (2006) 3. J. Weisman, Cross flow resisance in rod bundle cores, Nuclear Technology, 15(9),pp (1972) 4. C. H. Shin, T. H. Chun, D. S. Oh and W. K. In, Evaluaion of loss coefficien for an end plug wih side holes in dual-cooled annular nuclear fuel, Journal of Mechanical Science and Technology, 26(10), pp (2012) 5. M. K Roul and S. K. Dash, Numerical modeling of pressure drop due o single phase flow of waer and wo-phase flow of air-waer miures hrough hic orifices, In. J. of Engineering rends and echnology, 3 (4), pp (2012) 6. Erdal and H. I. Andersson, Numerical aspecs of flow compuaion hrough orifices, Flow Meas. Insrum., 8(1), pp.1-11(1997) 7. J. Q. Chen, B. Wang, B. Wu and Q. D. Chu, CFD simulaion of flow filed in sandard orifice plae flow meer, J. of Eperimens in Fluid Mechanics, 22(2), pp (2008) 8. F. H. J. Imada, F. Salara and J. L. Balino, Numerical deerminaion of discharge coefficiens of orifice plaes and nozzles, Proceedings of 22nd Inernaional Congress of Mechanical Engineering, Riberirao Preo, Brazil, pp (2013) 9. M. S. Shah, J. B. Joshi, A. S. Kalsi, C. S. R.Prasad and D. S. Shula, Analysis of flow hrough an orifice meer: CFD simulaion, Chemical Engineering Science, 71, pp (2012) 10. V.V. R. Kaushi, S. Ghosh, G. Das and P. K. Das, CFD simulaion of core annular flow hrough sudden conracion and epansion, J. of Peroleum Science and Engineering, 86-87, pp (2012) 11. ISO 5167, Measuremen of fluid flow by means of pressure differenial devices insered in circular-cross secion conduis running full, In. Sand Org. (2003) 12. T.H. Shih, W. W. Liou, A. Shabbir, Z. Yang and J. Zhu, A new - high Reynolds number urbulence flows- model developmen and validaion, Compuers Fluid, 24(3), pp (1995) 13. D. C. Wilco, Formulaion of he -omega urbulence model revisied, AIAA ournal, 46(11), pp (2008) 14. S. V. Paanar and D. B. Spalding, A calculaion procedure for hea, mass and momenum in hree-dimensional parabolic flows, Inernaional Journal of Hea and Mass Transfer, pp.15 (1972) 15. B. E. Launder and D. B. Spalding, The numerical compuaion of urbulen flows, Compuaioinal Mehods in Applied Mechanics and Engineering, 3(3), pp (1974) 16. M. J. Reader-Harris and J. A. Saary, The orifice plae discharge coefficien equaion he equaion for ISO , Proceedings of 14 h Norh Sea Flow Measuremen Worshop, Scoland, pp. 24 (1996) 1315