MHD EFFECTS ON HEAT TRANSFER IN A MOLTEN SALT BLANKET. Sergey Smolentsev, Reza Miraghaie, Mohamed Abdou

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1 MHD EFFECTS ON HEAT TRANSFER IN A MOLTEN SALT BLANET Sergey Smolensev, Reza Miraghaie, Mohamed Abdou Universiy of California, Engineering IV, BOX , Los Angeles, CA (Sergey Smolensev): Sergey@fusion.ucla.edu Hea ransfer in closed channel flows of molen sals (MS)s, such as FLiBe or FLiNaBe, has been considered under specific reacor condiions. MHD effecs have been accessed for wo blanke conceps: self-cooled MS blanke, and dual-coolan MS blanke. The effec of hea ransfer degradaion due o urbulence reducion by a magneic field in he Firs Wall channels of he selfcooled blanke was analyzed wih he - model of urbulence. In he dual-coolan blanke, he MS flow is laminar. A -D MHD code was used o calculae he laminar velociy profile firs. Then, he emperaure field was calculaed using a 3-D emperaure code. Reasonable inerface emperaures below he maerial limi of 55 C, and low hea escape from he breeder zone have been demonsraed. Model limiaions and he ways of heir improvemen are also discussed. I. INTRODUCTION As a par of he US Advanced Power Exracion (APEX) program (1997-3) and recenly in he course of he US ITER TBM sudies (3-presen), a number of blanke design opions wih molen sal (FLiBe or FLiNaBe) as he riium breeder/coolan have been evaluaed. In he re-circulaing self-cooled blanke design [1], a re-circulaion flow scheme was uilized ha allows he coolan (high meling emperaure FLiBe) mass flow rae in he Firs Wall (FW) channels o be considerably higher han he flow rae in he power conversion sysem. This effec was achieved by employing a bypass o he flow in he large cenral channel. The disincive feaure of he concep is ha he flows in he FW channels are urbulen o provide a high hea ransfer coefficien, and hus o ensure allowable FW emperaures. More recenly [], anoher design opion was considered wih he helium cooled ferriic srucure and self-cooled breeder zone using eiher low meling emperaure FLiBe or FLiNaBe as a breeding maerial. In his dual-coolan design, he molen sal flows slowly (U~5 cm/s) hrough a large cenral poloidal channel wih a characerisic crosssecional dimension of abou.4 m. Such flow allows for a high MS exi emperaure leading o a reasonably high blanke hermal efficiency (~4%). Unlike he flows in he self-coolan blanke, flows in he dual-coolan blanke are laminar. Typical dimensionless flow parameers for he ouboard module are shown in Table 1: he Reynolds number, Re=UD/, Harmann number, Ha=B D(/).5, (boh buil hrough he hydraulic diameer, D), and heir raio, Ha/Re. Here B is he magneic field (oroidal), is he elecrical conduciviy, is he kinemaic viscosiy, and is he densiy. The parameer Ha/Re is he indicaion of he MHD flow regime. Usually, if Ha/Re>(Ha/Re) cr he flow is reaed as laminar. The criical value of his parameer for a flow in a ransverse magneic field is abou 1/=.5 [3]. TABLE I Typical dimensionless parameers in he MS blanke flows a he ouboard Opion Ha Re Ha/Re Self-cooled [1], FW flow Dual-coolan [].1 The main goal of he presen sudy is o access he MHD effecs on hea ransfer in he range of he flow parameers relevan o a fusion reacor. The imporan MHD effec in he urbulen flows in he self-cooled blanke is urbulence reducion by a magneic field hrough he Joule dissipaion, which can resul in hea ransfer degradaion. In he dual-coolan design, he MS flows are ypically laminar. The effec of he magneic field on hea ransfer appears mosly due o modificaions of he velociy profile caused by he Lorenz force. II. MODEL, CODE, AND RESULTS FOR THE SELF-COOLED MS BLANET The urbulence model used in he analysis is he - model, which was modified o incorporae MHD effecs [4]. The difference beween he presen model and he sandard - model is an addiional sink erm on he RHS of he equaion for he urbulen kineic energy () and a desrucion erm on he RHS of he equaion for he dissipaion rae (): v v i [( ) ] em ; x Dissipaion Producion Diffusion FUSION SCIENCE AND TECHNOLOGY VOL. 47 APR

2 MHD EFFECTS ON HEAT TRANSFER IN MOLTEN SALT BLANET v C v i x 1 [( ) ] C em. The correlaions in he equaions had been adused for hree magneic field orienaions: wall-normal, spanwise, and sreamwise [4]. The numerical code solves he flow equaions wrien in he boundary layer approximaion along wih he equaions for and using a non-uniform mesh, which clusers he mesh poins near he walls. The calculaed values of and are hen used o calculae he eddy viscosiy ( ) o close he model:. C /.16.1 /U k / U y / b B= B=5 T B=1 T The calculaions were conduced for high meling emperaure FLiBe ((LiF) (BeF ), T m =74 ). The channel characerisic cross-secional dimension is cm. The velociy is 5; 1; and 15 m/s. The channel lengh is 8 m. The surface hea flux a he FW is 1 MW/m. The magneic field is o 1 T. The calculaed resuls for he case of he wall-normal magneic field are shown in Fig.1. Nussel number B= B=1 T x / b Fig.. Nussel number disribuion along he channel wih and wihou a magneic field. The flow parameers are shown in Fig.1 / (Vis / Vis)max Nu/Nu Nu / Nu Magneic field, T Temperaure rise, B=1 T Liquid-wall emperaure Bulk emperaure B= Disance from he inle, m Fig.3. FLiBe emperaure rise a he heaed wall wih and wihou a magneic field. The flow parameers are shown in Fig Magneic field, T Fig.1. Effec of he wall-normal magneic field on he reference FLiBe urbulen flow: U=5 m/s, b=1 cm (channel half-widh). The plos are for: kineic energy, eddy viscosiy, and fully-developed Nussel number. One can see ha he magneic field growh resuls in pronounced reducion of boh he urbulen kineic energy and eddy viscosiy. I also reduces he fully-developed Nussel number by abou 5% when he magneic field changes from o 1 T. The Nussel number disribuion along he channel is shown in Fig.. Addiionally o hea ransfer degradaion, one can see ha in he presence of a magneic field he ransiion lengh becomes longer. 56 FUSION SCIENCE AND TECHNOLOGY VOL. 47 APR. 5

3 MHD EFFECTS ON HEAT TRANSFER IN MOLTEN SALT BLANET Figure 3 demonsraes he emperaure rise in he liquid a he heaed wall. I should be noed ha he wall-normal magneic field has he sronges effec on urbulence. Less effec is demonsraed in he spanwise magneic field, and he leas effec in a sreamwise magneic field. The sreamwise magneic field case corresponds o a oroidal blanke and is no relaed o he presen design. However, for he sake of compleeness we pu here daa for all hree orienaions of he magneic field. The endencies in urbulence reducion by a magneic field are demonsraed in Table II. One can see ha for he velociies of 15 m/s, he MHD effec on hea ransfer is insignifican for all hree orienaions of he magneic field. I is also insignifican if he liquid flows oroidally. channel walls. However he side-wall es are no very pronounced due o moderae Ha. TABLE II Temperaure rise () a he heaed wall in he reference MS flow for hree orienaions of he magneic field Case Wall-normal Spanwise Sreamwise 5 m/s, T m/s, 5 T m/s, 1 T m/s, T m/s, 5 T m/s, 1 T m/s, T m/s, 5 T m/s, 1 T III. MODEL, CODE, AND RESULTS FOR THE DUAL-COOLANT MS BLANET Deailed descripion of he design is given in []. The radial build of he blanke module wih basic dimensions is shown in Fig.4. Reduced Acivaion Ferriic Seel (RAFS) wih he allowable maximum emperaure of 55C is used as a srucural maerial. Two breeders were considered: low meling poin FliBe ((LiF)(BeF), T m =653 ), and FLiNaBe (T m =58 ). The calculaions were performed for he ouboard blanke segmen wih he maximum neuron wall loading 3 MW/m, and he maximum surface hea flux.4 MW/m. The poloidal flow lengh is 8 m. The calculaions ake ino accoun poloidal variaions in he hermal loads. Firs, he laminar velociy profile is calculaed using a -D code [5]. The flow is supposed o be fully developed and driven by a pressure gradien. The banana shape effec a he ends of he blanke segmen is presenly no aken ino accoun. Also, he effec of he spaial field variaions is no considered. The velociy profile is shown in Fig.5. The velociy profile demonsraes M shape due o elecrically conducing Fig.4. Radial build of he dual-coolan MS blanke. Fig.5. -D velociy profile in he reference FLiBe MHD flow in he dual-coolan MS blanke: Re=7, Ha=. The calculaed velociy profile was hen used as an inpu o a 3-D hea ransfer code. The hea ransfer code solves he energy equaion, which includes he diffusion and convecion erms as well as he source erm ha sands for he volumeric hea generaed by neurons: FUSION SCIENCE AND TECHNOLOGY VOL. 47 APR

4 MHD EFFECTS ON HEAT TRANSFER IN MOLTEN SALT BLANET C p T T T T ( U V W ) y z T T T ( k ) ( k ) ( k ) q'''. y y z z A special procedure was used o ensure energy conservaion in he calculaions, since he whole inegraion domain consiss of several sub-domains of differen physical properies. Wih his procedure he energy equaion was solved in a coninuous manner over he whole domain using conservaive finie-volume formulaion. Also, non-uniform meshes were used o concenrae mesh poins near he inerfaces Z= m Z=4 m Z=6 m X(oroidal),m X(oroidal),m X(oroidal),m Fig.6. Temperaure disribuion in he domain consised of he FliBe fklow and He-cooled walls a hree poloidal locaions: z= m (near he op); 4 m (middle); and 6 m (near he boom). The emperaure field calculaed wih he code in he domain consised of he large cenral channel wih FLiBe and He-cooled channel walls is shown in Fig.6 for hree poloidal locaions. The emperaure grows poloidally as he FLiBe moves down. The emperaure is disribued almos uniformly in he oroidal direcion, bu experiences significan variaions in he radial direcion. This can be explained by he fac ha volumeric heaing drops exponenially in he radial direcion and does no vary in he oroidal direcion. The maximum emperaure in each cross secion can be observed close o he channel side facing he firs wall. The maximum emperaure of abou 9C in he liquid is reached in he boom cross-secion. However he maximum wall emperaure is always below 55C due o effecive cooling by helium. I has also been observed ha he amoun of hea escaping from he breeder zone o cooling helium channels is no significan: only abou 7% of he oal volumeric hea generaed in he FLiBe channel. As a resul, he raio of power accumulaed in he molen sal o he oal power in he blanke module (MS power/oal power) is high, abou 8%. The regime parameers and he mos imporan calculaed resuls are summarized in Table III. TABLE III Resuls of he hermal-hydraulics analysis including MHD effecs for he dual-coolan MS blanke (ouboard module) Parameer FLiBe FLiNaBe He inle T, C 38 3 He oule T, C He Pressure, MPa 1 1 He mass flow rae kg/s He pressure drop, MPa.16.7 MS inle T, C 4 36 MS oule T, C MS mass flow rae, kg/s MS pressure drop, MPa.5.17 He power/oal power, % 3 3 MS power/oal power, % Maximum srucure T, C <55 <55 IV. CONCLUDING REMARS The mos criical issues relaed o MHD effecs on hea ransfer have been addressed for wo blanke conceps using molen sals. For he self-cooled blanke, he effec of hea ransfer degradaion has been assessed in a wide range of blanke relevan parameers and differen orienaions of a magneic field wih respec o he flow. For he dual-coolan blanke, full hermal-hydraulics assessmen was performed ha included MHD effecs hrough aking ino accoun modificaions of he velociy profile by a magneic field. The mahemaical models and 56 FUSION SCIENCE AND TECHNOLOGY VOL. 47 APR. 5

5 MHD EFFECTS ON HEAT TRANSFER IN MOLTEN SALT BLANET basic assumpions used in he analysis have been explained. Here, we would also like o menion some limiaions of he models used and discuss furher ways of exending hem. Firs, he - model of urbulence has been adused using experimenal daa for flows in nonconducing channels and sricly speaking should be applied o urbulen flows in conducing channels wih care. There are discrepan conclusions on he effec of elecrically conducing walls on urbulence [3]. Our opinion is ha urbulence damping in he presence of conducing walls will be more inensive due o sronger Joule dissipaion, especially in he case of a wall-normal magneic field. However reliable experimenal daa for urbulen flows in conducing channels have no been available. The applicabiliy of he model o flows in conducing channels should be verified and necessary readusmens performed once new experimenal daa appeared. Anoher way of adusing he model is erm-byem modeling using DNS daa. Unforunaely DNS daa for elecrically conducing channels have no been available eiher, bu could be available in he near fuure [6]. In he presen calculaions for he dual-coolan blanke, he effec of naural convecion was no included. Including his effec will require coupling beween he full se of 3-D MHD flow equaions and he energy equaion. The numerical resuls obained recenly for liquid meal flows under he fusion reacor condiions [7] show ha naural convecion is no negligible. One can also expec a pronounced naural convecion effec in he reference MS flows. This may cause, for example, more mixing in he MS and as a resul more uniform emperaures. The naural convecion phenomena under he dual-coolan blanke condiions will be a subec for fuure consideraions. Liquid Breeder Firs Wall and Blanke Opions for he Advanced Reacor Design, 6 h TOFE Conference. [3] H.Branover, Magneohydrodynamic Flows in Ducs, John Willey & Sons, New York, p.9 (1978). [4] S.Smolensev, M.Abdou, N.Morley, A.Ying, T.unugi, Applicaion of he - Model o Open Channel Flows in a Magneic Field, Inernaional Journal of Engineering Science 4, (). [5] S.Smolensev, A.Tananaev, Developmen of Compuer Code for Analysis of Hea Transfer in Liquid Meal MHD Flows in Ducs, Magneohydrodynamics 31, (1995). [6] Privae communicaion o Prof. S.Saake, Aug. 4. [7] A.haricha, S.Molokov, S.Aleksandrova, L.Buhler, Buoyan Convecion in he HCLL Blanke in a Srong Uniform Magneic Field, FZ 6959, p.11 (4). ACNOWLEDGMENTS We graefully acknowledge he suppor provided by he U.S. Deparmen of Energy hrough conrac DE- FG-86ER513. REFERENCES [1] C.P.C. Wong, S. Malang, M. Sawan, I. Sviaoslavsky, E. Mogahed, S. Smolensev, S. Maumdar, B. Merrill, R. Maas, M. Friend, J. Bolin, S. Sharafa, Molen Sal Self-Cooled Solid Firs Wall and Blanke Design Based on Advanced Ferriic Seel, Fusion Engineering and Design, o be published (4). [] C.P.C.Wong, S.Malang, M.Sawan, S.Smolensev, S.Maumdar, B.Merrill, D..Sze, N.Morley, S.Sharafa, M.Dagher, P.Peerson, H.Zhao, S.Zinkle, M.Abdou, Assessmen of FUSION SCIENCE AND TECHNOLOGY VOL. 47 APR