1. Ilmenauer MHD-Woche - vom 20. bis 24. September 2004 7th MHD-Days (20. - 21. September 2004) Numerical modelling of an MHD flow in the presence of transverse non-uniform magnetic field F. DUBOIS*, J. ETAY*, O. WIDLUND** and Y. DELANNOY* *EPM-Madylam ENSHMG BP95 38402 S t Martin d'Hères Cedex (FRANCE) ** CEA DER/SSTH/LDAS (Bat. 10.05) Rue des Martyrs 38000 Grenoble (FRANCE)

2. Tool : Fluent + MHD module + wall functions Goals: Compare numerical results with Ilmenau experimental results

3. At each iteration of the flow calculation with boundary conditions on  chosen on  -  o 1 1- solve the problem 2 2 - then calculate j and F MHD modulus

4. MHD modulus MHD modulus - tricky points 1 - calculation of gradients is done using a self-developed subroutine sensitivity to the mesh 2 - calculation of near the wall term is reconstructed MHD modulus MHD modulus - validation analytical solution of a Hartman flow : Ha = 10, 30 and 100 discrepancy 2%, 2.2% and 1.2% axial velocity current density parallel layer

5. Wall functions for laminar MHD flow wall B U n Hyp : - elec. insulating wall - solid wall - Ref : O.Widlund/Eur. J. Mech B/Fluids 22 (2003)

6. Geometry Ilmenau loop Honey comb 20 mm 100 mm 30 mm x y z Galinstan flow

7. Grid Refined grid Refined grid (no wall function) Hartman layer : first cell = 8.82  m 10 cells // layer : first cells = 16.07  m 10 cells total = 79 650 Coarse grid Coarse grid (+ wall function on Ha) Hartman layer : first mesh = 1 mm 1 cells // layer : first mesh = 16.07  m 10 cells total = 31 860 100 mm30 mm200 mm 100 mm x y magnet Top view

8. Inputparameters magnetic field x y

9. Results hyp : laminar particles path e.m. forces x elec. currents on symmetry face x y x

10. Results  Are identical for both grids, thanks to the use of wall functions  Are in conformity with phenomenology  Magnetic field acts as a “semi-permeable body”  2 wall jets developed at the vertical walls  Elec. Currents paths are different upstream and downstream of the magnet

11. Comparison with experimental results 1/4 voltage voltage on x=0, on symmetry plane shapes and level are similar difference near the // walls built with  num.

12. Comparison with experimental results 2/4 voltage voltage on symmetry plane

13. Comparison with experimental results 3/4 on ∆  y - in the centre : identical level - near the side wall : num M / exp no M proposed explanation in experiments in the center u x weak j y high in the M u x high j y weak when B->0 then ∆  y ->0

14. Comparison with experimental results 4/4 velocity - in the centre : same level - in the M-jet : different level and width - lower velocity at the border of the jet proposed explanation - calibration ? - size of the probe ? - in exp. no flow conservation u x (z)? calculations experiments z u x (m/s) - symmetry plane - x=19,5 mm probe

15.  Comparison of numerical results with Ilmenau experimental results are satisfactory.  Wall functions effective in reducing the cost of gridding in boundary layers  Discrepancies can be explained  Turbulence is weak => the turbulence model can not be checked in optimal conditions. Conclusions

16. Results x elec. potential