Simulation of magneto-hydrodynamic (MHD) flows in OpenFOAM

Transcription

1 Simulaion o magneo-hydrodynamic (MHD) los in OpenFOAM Sepember 1-15, 2010 NUMAP-FOAM, Universiy o Zagreb

2 Ouline Problem: magneohydrodynamic (MHD) lo Magneo-hydrodynamic equaions Opimizaion o presen solver Tess or soluion mehods, parameers... Non-orhogonal correcion Circular pipe example Implemenaion o hin all condiion FAM coupled ih FVM problem Firs approximaion or a boundary layer model

3 Magneohydrodynamic (MHD) equaions MHD Movemen o elecrically conducing luids in a magneic ield Conservaion o Momenum Mass & Charge Ohm s la 1 N j v Ha v v p v j B v 0, j 0 vb vb Lorenz orce Poisson eq. or 2 Induced elecric ield Dimensionless groups Fusion reacors Ineracion parameer N LB u 0 2 el.magn. orce ineria orce N 10 5 Harmann number 2 2 L B Ha 2 el.magn. orce viscous orce Ha 10 4

4 Opimizaion o presen MHD solver Developed mhdepofoam solver is saring poin or all he oher seps: Proper inerpolaion procedure o calculae he curren lux a cell ace o ensure divergence-ree curren densiy in CV non-orhogonal correcion j jn n n u B n n n ub

5 Opimizaion o presen MHD solver Developed mhdepofoam solver is saring poin or all he oher seps: Proper inerpolaion procedure o calculae he curren lux a cell ace o ensure divergence-ree curren densiy in CV non-orhogonal correcion j jn n n u B n n n ub z = 0.4 Circular pipe ih O-grid B Ha = 500, insulaing all y = 0.4 y x z

6 Opimizaion o presen MHD solver Insulaing circular pipe

7 Walls ih inie elecric conduciviy Thin all condiion Modeling assumpions: The all is much hinner han he luid domain << L j, uniorm in he all ( consan across all hickness) Elecric curren conservaion in a volume elemen o he all: V jdv 0 A A A j n j n j n j n da da da S l C A j j n l n l j da j, ds, da Fluid Tangenial curren in he all rom Ohm s la: j, = - S l j, C A n l jn Insulaing exernal surace: j n 0 n s n Wall n l j,, j n n luid all Thin all approximaion Curren enering he luid is aken rom he balance o he angenial curren in he all

8 Walls ih inie elecric conduciviy FVM FAM coupling Dirichle boundary condiions or a luid-side: Fixed value o he elecric poenial BC 0 1. Poisson equaion or is solved FVM problem in luid domain 3D Poisson solver v B 2. Calculaion o curren in he all FAM problem on all surace 2D Poisson solver n j 3. Wall elecric poenial used o updae luid-side BC coupling beeen FAM and FVM BC j j n j Wall elemen j

9 Walls ih inie elecric conduciviy FVM FAM coupling FVM problem in luid domain: vm and vc uncions o represen he dierenial operaors FAM problem on geomery surace am and ac uncions Variables deined in he volume have o be mapped o he surace maptosurace, boundaryfield Elecric poenial value calculaed on he surace (FAM problem) is ranserred (mapped) o he volume and used as Dirichle j boundary condiion or he soluion o he FVM problem in he luid j domain j j n j Wall elemen

10 Walls ih inie elecric conduciviy MHD ully developed lo Side all (II B) Harmann all ( B) y x z v B Side layers s ~ Ha -1/2 Tess Comparison Analyical or asympoic soluions Resuls rom conjmhdfoam solver Core Harmann layer Ha ~ Ha -1 L Conjugae MHD solver : conjmhdfoam Momenum Eq. solved on luid mesh and Eq. on boh meshes (combined marix or luid-solid coupledfvscalarmarix) Fluid j vb vb j n j n Solid / Wall j 0, elecric conduciviy o luid and all

11 Walls ih inie elecric conduciviy

12 Firs approximaion or a boundary layer model FVM FAM coupling B. Dirichle boundary condiions or a luid-side: Fixed value o he elecric poenial BC 0 1. Poisson equaion or is solved FVM problem in luid domain 3D Poisson solver v B 2. Calculaion o hickness o boundary layer: L ( n B) Ha* B 3. Calculaion o curren in he all and boundary layer correcion n 2. Wall elecric poenial used o updae luid-side BC coupling beeen FAM and FVM BC 0 ( )* FAM problem on all surace 2D Poisson solver j j j n Boundary layer Wall j

13 Firs approximaion or a boundary layer model Harmann all ( B) Side all (II B) y x v z B Free slip condion a Harmann alls

14 Oulook: problems o be solved Speeding up he convergence Convergence crieria (residuals, Couran number) Opimize he simulaion conrol Numerical model or boundary layers o B Implemenaion o suiable all uncions Coupling beeen MHD and buoyancy problems