IMPACT OF PRESSURE EQUALIZATION SLOT IN FLOW CHANNEL INSERT ON TRITIUM TRANSPORT IN A DCLL-TYPE POLOIDAL DUCT. H. Zhang, A. Ying, M.

Transcription

1 IMPACT OF PRESSURE EQUALIZATION SLOT IN FLOW CHANNEL INSERT ON TRITIUM TRANSPORT IN A DCLL-TYPE POLOIDAL DUCT H. Zhang, A. Ying, M. Abdou Mehanial and Aeropae Engineering Dept., UCLA, Lo Angele, CA 90095, USA, zhjboo@gmail.om A SiC-baed flow hannel inert (FCI i ued a an eletrial and thermal inulator in the Dual Coolant Lead Lithium (DCLL blanet. To redue the tre of the FCI trutural material, the preure equalization lot (PES i implemented in the FCI wall. However, the PES affet the tritium tranfer behavior and lo rate. Therefore it i important to examine the tritium lo rate and enure it remain below an allowable limit. In the preent tudy, we analyze tritium tranport and quantify the tritium lo rate in a front dut of the DCLL-type outboard blanet where PbLi move poloidally. Three type of poloidal dut have been onidered: one without the PES, one with the PES in the wall parallel to the magneti field and one with the PES in the wall perpendiular to the magneti field. Tritium onentration field are obtained by olving a fully 3-D problem with appropriate boundary ondition at variou interfae. Reult how a high tritium onentration at the loation of revered flow when a PES wa loated in the wall parallel to the field. Furthermore, when any PES wa introdued, the PES hanged the veloity profile and thu hanged the tritium onentration in the ore and gap, whih inreae the tritium loe from 1.244% to 1.413% under the alulation ondition. I. INTRODUCTION Proper ontrol of tritium tranport and permeation in fuion blanet are important feature ontributing to the ahievement of tritium elf-uffiieny a well a being neeary to aurately haraterize tritium inventory and loe. In the liquid metal (LM blanet, multiple tritium tranport proee have to be onidered imultaneouly beaue of the multi-material domain. The proee inlude: tritium diffuion and onvetion in the flowing LM, tranfer aro the liquid/olid interfae, and diffuion through the truture. Tritium tranport i alo ombined with magnetohydrodynami (MHD effet, whih aue flow reditribution. Any flow reditribution affet the tritium onentration profile and thu the permeation rate. To redue the tre in the FCI truture material, a PES i utilized at the FCI wall to balane the preure inide (ore and outide (gap of the FCI. However, the PES affet the tritium tranfer behavior and lo rate. Firt, it provide a path for tritium to migrate between the ore and the gap. The eond i that the PES hange the loal MHD veloity ditribution that in turn affet tritium diffuion and onvetion. The purpoe of thi paper i to develop mathematial and omputational model for tritium tranport in multi-region liquid PbLi DCLL blanet onfiguration and evaluate the effet of PES on tritium permeation and ditribution. Currently, TMAP7 (Ref. 1 i the referene tool for the imulation of the permeation phenomenon in ITER. Unfortunately it ha an important diadvantage: TMAP7 i only a 1D program. That mae it not ompletely adequate for the 3D blanet geometrie and alo mae it diffiult to etimate tritium tranport in flowing liquid metal that i an inherently three-dimenional flow. In thi tudy, we formulate the problem in 3D and numerially olve the omplete et of governing equation with appropriate boundary ondition at variou interfae. The tritium tranport i imulated for a front dut in a DCLLtype outboard blanet where PbLi move poloidally. Tritium onentration and permeation flux are preented and the PES effet are evaluated. II. FORMULATION OF THE PROBLEM The tritium tranport model preented in Fig. 1 inlude the multiple tritium tranport proee: Tritium generation in LM ore and gap Tritium onvetion and diffuion in flowing LM Tritium movement through the LM/FCI interfae Diffuion tritium in FCI Tritium migration through PES Tritium movement through the LM/ferriti teel (FS truture interfae Diffuion of tritium through the FS truture. Tritium deorption and reombination at FS/He oolant interfae Tritium tranfer & trapping into He bubble In any given ituation, the proe that ontribute the mot to the tritium tranport within the LM blanet depend on the peifi material propertie (e.g. tritium FUSION SCIENCE AND TECHNOLOGY VOL. 64 SEP

2 Zhang et al. olubility and diffuivity, operating temperature range and the flow ditribution under onideration. Let define T_LM, T_FS, T_FCI and T2_HC a the tritium onentration in the LM, FS truture, FCI and He oolant, repetively. In doing o, the following ma balane equation an be formulated in thee domain: / u + S (3 t = ( DLM T _ LM LM t = ( D (4 T _ FCI / FCI T _ FCI t = ( D (5 T _ FS / FS T _ FS / U (6 T 2 _ HC t = ( DHC T 2 _ HC HC T 2 _ HC T Fig. 1. The hemati of the tritium tranport model how all the oure and tranportation mode of tritium in a liquid metal breeder blanet unit. For tritium tranport modeling in the liquid PbLi, we aume tritium doe not alter liquid metal propertie nor flow behavior. Hene, general paive alar tranport equation for the onentration of peie, (mol/m 3, an be expreed a: 1 ( x, t / t = J( x, t + S( x, t + t t + + m + ( / t ν ν ν ( m m t m (1 Where S i the loal oure rate per unit volume (mol/m 3, The uperript t repreent trapped atom, denote different ind of trap ite, ν i the radioative deay frequeny of peie atom, ν m i the radioative deay frequeny of peie, m, atom that deay to peie,, and J i the flux of diolved atom, whih i given by * 2 J = D ( T ( D( T Q / T T + u Where D i the diffuivity, u i the advetion peed, Q* i Soret oeffiient, and T i the loal temperature. The firt term repreent the flux of peie due to onentration gradient; the eond term repreent the flux of peie due to temperature gradient and the third term reult from the effet of bul flow. In the preent tudy, the radioative deay, the trap, and the flux aoiated with temperature gradient are aumed to be muh maller ompared to thoe due to onentration gradient and are therefore omitted. We alo ignored the helium bubble effet beaue thi phenomenon i not onfirmed in DCLL blanet onept and a la of experimental data. (2 Where D LM, D FS, D FCI, and D HC are the diffuivitie (m 2 / in the repetive region, u LM and U HC are the veloitie (m/ in the LM and He oolant, t i time ( and S T i the tritium generation rate (mol/m 3. To obtain the onvetive part of the flux in the PbLi region, the equation for the teady tate, laminar, inompreible, viou, MHD flow are given by: 2 u = 0 (7 ρu 2 + u ρu = μ u p + j B t (8 j = 0 (9 j = σ ( φ + u B (10 By ombining equation (9 and (10, a Poion equation for the eletri potential i obtained: ( σ φ = ( σu B (11 Where the variable B, j, φ, ρ, σ and μ denote the magneti field, urrent denity, eletri potential, denity, eletri ondutivity and the vioity, repetively. To upplement the tranport equation, a et of boundary ondition expreing peie flux and hemial potential balane are applied at material interfae. At the LM/FS and LM/FCI interfae, we apply Sievert law and impoe ontinuity of partial preure. Thi lead to the onentration diontinuitie at interfae. T _ FS = _ FS _ LM T _ FCI _ FCI = (12 _ LM Where S _, LM S _ and FS S _ are the olubility of FCI tritium in LM, FS, and FCI. To enure ontinuity of fluxe, we alo apply ( _ ( LM LM FCI T _ FCI D LM T _ LM + T _ LMu LM n = ( DFS T FS n (13 D + u n = ( D n ( FUSION SCIENCE AND TECHNOLOGY VOL. 64 SEP. 2013

3 At FS/HC interfae, the peie flux i determined by the urfae reombination rate: 2 ( D FS T _ FS = rt _ FS n (15 Where r i the reombination oeffiient (m 4 /. III. NUMERICAL RESULTS AND DISCUSSION Zhang et al. In thi wor, we analyzed tritium tranport in a front dut of a DCLL-type outboard blanet where PbLi move poloidally. 3 Three type of poloidal dut have been onidered: one without the PES, one with the PES in the wall parallel to the magneti field and one with the PES in the wall perpendiular to the field. A eth of the roetional area of the liquid metal blanet hannel with FCI i hown in Fig. 2. the ore and very low veloitie in the left and right gap. For the ae of a PES opening perpendiular to the field, the veloity i not ymmetri. It i higher in the right gap than left gap, and a veloity drop in the ore near the loation of PES i oberved. Thee veloity profile math earlier obervation for variou FCI flow reported in. 4 A full three dimenional plot of the reult from the ro-etion at x=0.5 i alo given in Fig. 4 for larity. u/u Gap Core PES Veloity at y=0 and x=0.5m NoPES PES perpendiular to B Gap z/b (a Along y=0 1 Gap Core PES Ga p u/u0 0.1 Veloity at z=0 and x=0.5m NoPES PES perpendiular to B Fig. 2. The ro-etion drawing of the blanet dut how the PES opening. Here the PES i opened from x=0.1m to 0.9m and with 2a=0.06m, 2b=0.06m, RAFS wall 0.002m, FCI 0.002m, PES 0.003m, Gap 0.002m The veloity field i obtained by performing a 3D imulation with magneti field trength of1.852t. The eletrial ondutivity σ LM= Ω -1 m -1, σ FS= Ω - 1 m -1, σ FCI= Ω -1 m non-uniform mehe are ued to diretize the geometry with 216 nonuniformly ditributed in the x-diretion. A uniform veloity of U0=0.0675m/ i given a inlet boundary ondition, and the preure at outlet i peified a zero. Non-lip boundary ondition are applied on the olid wall. Veloity ditribution at the ro-etion of x=0.5m are plotted in Fig. 3. In Fig. 3(a for the ae of no PES, when we et y=0, we ee the veloity profile ha a relatively high veloity in the gap parallel to the magneti field and a very low veloity in the gap perpendiular to the field. When any PES i introdued, the high veloitie in the front and ba gap diappeared. Figure 3 alo how that when a PES i opened parallel to the field, we ee a trong revered flow at the loation of the PES due to a large omponent of Lorentz fore along the negative main flow diretion. In Fig. 3(b, we have et z=0. In the figure we ee flat-haped veloity profile in 0.01 y/a (b Along z=0 Fig. 3. Veloitie at the ro-etion of x=0.5m. (a Along y=0, it how a trong revered flow near the inert for the ae of PES i opened parallel to the field. (b Along z=0, it how flat-haped veloity profile in the ore and very low veloitie in the left and right gap. Fig. 4. Veloity profile at aro etion of x=0.5m for variou PES onfiguration. The omputer ode to olve the FCI flow field ha been validated by olving Ming-Jiu Ni ae. 4 In Ni ae, PES i opened parallel to the magneti field and GaInSn wa eleted a the liquid metal with 2a = 34mm and 2b = 40mm. The veloity profile at the ro-etion FUSION SCIENCE AND TECHNOLOGY VOL. 64 SEP

4 Zhang et al. of x=0.5m a een in Fig. 5 how good agreement with Ni olution. wall. Alo, beaue of the high veloity jet found in the front and ba gap, tritium onentration near the front wall i redued. With a PES in a wall perpendiular to the magneti field, the onentration in the right gap beame lower than in the left gap, whih refleted the nonymmetri veloity profile deribed in Fig. 3(b. Alo, a wea onentration jump wa formed around the PES a een in Fig. 7(b. With a PES in a wall parallel to the magneti field, uh a in Fig. 7(, we ee a high tritium onentration in the bul area near the loation of the PES, whih i due to the revered flow at that loation. Fig. 5. Comparion of veloity at y-z ro-etion. Tritium onentration field are obtained by our reently developed ode, whih ha been validated with ome experimental data. 5 It olve a fully 3-D problem with aforementioned boundary ondition at variou interfae. Additionally, zero onentration i given at inlet and onvetive flux boundary ondition i given at outlet. Tritium generation rate 6 i plotted in Fig. 6. Fig. 7. Tritium onentration at aro etion of x=0.5m for variou PES onfiguration. Figure 8 alo demontrate the feature een in Fig. 7(. In Fig. 8, we are eeing the tritium ditribution at the ro-etion of y=0 along the flow diretion. Tritium aumulated in the ore area above the PES. It i alo intereting to notie that tritium aumulated near the ba wall behind the PES end a mared by the yle region and reulted in loal tritium permeation jump a howed in Fig. 11(. Thi i due to very low veloitie in that area a hown by the arrow plot of veloity in Fig. 8. Fig. 6. Tritium generation rate how a non-uniform profile along the radial ditane from FW. Tritium diffuion oeffiient and Sievert ontant are dependent on temperature and ativation energy. There i a dramati direpany between the value omputed by data preented in variou referene. 7 Thi tudy ued the following value, D LM = m 2 /, _LM = mol/m 3 Pa 1/2. Figure 7 how the tritium onentration profile at the ro-etion of x=0.5m for the three different PES onfiguration. Without a PES opening in FCI, the tritium onentration in thoe gap aligned perpendiular to the magneti field are higher than the other two gap and the ore a een in Fig. 7(a. Tritium onentration inreaing in the poitive z diretion of the gap reflet the dereaed tritium generation rate away from the front Fig. 8. Tritium onentration near the outlet (bottom and at the ro-etion of y=0 (top with PES wall parallel to the field. Here Tritium aumulated in the ore area above the PES and in the ba gap behind the PES end. When we plot the tritium onentration at the ame ro-etion a Fig. 3, we ee the intereting oupling between veloity and tritium onentration. Thi i done in Fig. 9 and 10 where the tritium onentration are 654 FUSION SCIENCE AND TECHNOLOGY VOL. 64 SEP. 2013

5 plotted along y=0 and z=0, repetively, at the roetion of x=0.5m. Thee tritium onentration urve orrepond to the veloity profile een above. The important onluion i that high tritium onentration are alway aoiated with low-peed veloitie. For example, in the front and ba gap, a een in Fig. 9, the ae of no PES (whih had a relatively high veloity profile give the lowet tritium onentration. The highet onentration are oberved when the PES i opened parallel to the field and our omplementary to the veloity dereae hown in Fig. 3. T onentration (mol/m 3 1x10-4 1x10-5 T onentration at y=0 and x=0.5m NoPE S PES perpendiular to B z/b Zhang et al. Fig. 9. Tritium onentration along the line of y=0m at the ro-etion of x=0.5m how a high tritium onentration in the bul area near the loation of the PES for the ae of PES i opened parallel to the field Figure11 how the tritium permeation per unit length through the front, ba, left and right LM_FS wall. For the ae of no PES in the FCI, Fig. 11(a, tritium permeation i higher through the left and right wall than the front and ba wall due to high onentration in the left and right gap, a highlighted in Fig. 7(a. Tritium permeation through front wall i higher than the ba wall beaue of the high tritium generation rate in the front gap. With a PES opening in the right wall, whih i perpendiular to the magneti field, Fig. 11(b, the front wall ha the highet permeation flux and ba wall ha the lowet value. There i alo a differene between the left wall and right wall. Tritium permeation i lower through the wall on the PES ide beaue of lower tritium onentration in the right gap. With a PES opening in the ba wall parallel to the magneti field, tritium permeation i higher through the front wall a een in Fig. 11(, while the permeation through the ba wall (where the PES i loated inreae ompared to the other two ae. It i alo intereting to notie that there i a tritium permeation jump through ba wall behind the end of PES. Thi i attributed to high tritium onentration in that area due to low veloitie a deribed with Fig. 8. Along z=0, a hown in Fig. 10, tritium onentration in the left and right gap are higher than in the ore for all three ae. The ae of no PES give a higher tritium onentration and the ae of the PES opening parallel to the field give a lower onentration. When the PES i opened perpendiular to the field, it reult in the highet tritium onentration in the left gap and a lowet onentration in the right gap ompared to other two ae. Fig. 9 and 10 howed that the tritium tranport aro the PbLi i not only governed by diffuion but an be dominated by the advetive movement of the bul PbLi. T onentration (mol/m 3 1E-4 T onentration at z=0 and x=0.5m NoPES PES perpendiular to B 1E-5 y/a Fig. 10. Tritium onentration along the line of z=0m at the ro-etion of x=0.5m how higher onentration in the gap than in the ore. Fig. 11. Tritium permeation per unit length through the LM_FS wall (the front, ba, left and right wall. FUSION SCIENCE AND TECHNOLOGY VOL. 64 SEP

6 Zhang et al. Figure12 how the total tritium permeation through the four LM-FS wall. It an be een that tritium permeation i higher when PES i opened in the wall parallel to the magneti field. The overall permeation loe for the three different PES onfiguration are ummarized in Table I. For the ae without a PES under the given ondition, tritium lo i 1.244% of the tritium prodution, whih onfirm earlier reult (tritium permeation lo i le than 2% of the total tritium prodution for a DCLL dut flow without PES. 8 When the PES i opened perpendiular to the magneti field, it reult in a higher tritium lo of 1.321% of the tritium prodution. The ae of PES opening parallel to the field give a highet tritium lo of 1.413% of tritium prodution. The amount of inreae in tritium permeation i minimized beaue the PES i loated in the ba wall where tritium generation rate i lower. Fig. 12. Total tritium permeation per unit length through LM-FS wall TABLE I. Tritium Loe for Three PES Configuration T generation (mol/ T permeation (mol/ Lo perentage IV. CONCLUSIONS No PES PES in the PES in the wall // B wall B % 1.413% 1.321% In thi paper, we developed the framewor of the preditive apability for tritium tranport in a multi-region liquid PbLi DCLL blanet onfiguration. The preene of PES on tritium permeation and ditribution are invetigated numerially. Reult how that PES in the FCI hanged the veloity profile and thu hanged the tritium onentration in the ore and gap. High tritium onentration are alway aoiated with low-peed veloitie. With a PES in a wall parallel to the magneti field, reult how a high tritium onentration in the bul near the loation of the PES due to the revered flow. Under the given ondition, the ae of without PES give a lowet tritium lo of 1.244% of the tritium prodution, while tritium lo inreaed nearly 14 perent for the ae of PES opening parallel to the magneti field. It reult in a highet tritium lo of % of the tritium prodution. ACNOWLEDGMENTS Thi wor wa upported by the U. S. Department of Energy Contrat DE-FG03-ER REFERENCES 1. G. R. LONGHURST, TMAP7 Uer Manual, Idaho National Engineering and Environmental Laboratory Behtel BWXT Idaho, LLC, ( C. MISTRANGELO and L. BUHLER, Eletri Flow Coupling in the HCLL Blanet Conept, Fuion Eng. De., 83, ( P. NORAJITRA, L. BUHLER, et al., Coneptual Deign of the Dual-oolant Blanet in the Frame for the EU Power Plant Coneptual Study (TW2-TRP- PPCS12D, Forhungzentrum arlruhe Report FZA, 6780 ( M. Ni, S. XU, Z. WANG and N. ZHANG, Simulation of MHD Flow in Liquid Metal Blanet with Flow Channel Inert, Fuion Si. Tehnol., 60, ( H. ZHANG, A. YING, M. A. ABDOU, Integrated Simulation of Tritium Permeation in Solid Breeder Blanet, Fuion Eng. De., 85, ( P. BATISTONIA, U. FISCHERB,. OCHIAIC, L. PETRIZZIA,. SEIDELD, M. YOUSSEFE, Neutroni and Nulear Data Iue in ITER and Their Validation, Fuion Eng. De., 83, ( E. MAS DE LES VALLS, L.A. SEDANO, L. BATET, I. RICAPITO, A. AIELLO, O. GASTALDI and F. GABRIEL, Lead-lithium Euteti Material Databae for Nulear Fuion Tehnology, J. Nul. Mater., 376, ( M.J. PATTISON, S. SMOLENTSEV, R. MUNIPALLI, M. A. ABDOU, Tritium Tranport in Poloidal Flow of a DCLL Blanet, Fuion Si. Tehnol., 60, 809 ( FUSION SCIENCE AND TECHNOLOGY VOL. 64 SEP. 2013