Continuous casting - comparison between numerical simulation and experimental measurement EPM-MADYLAM Y.Delannoy, O.Widlund, J.Etay Presented by Y.Fautrelle

Continuous casting : simulation / experiment 2 EMBR for steel C.C.  Continuous casting of steel  Vertical pulling velocity ~1-2 m/mn (2cm/s)  Nozzle with two ports  jets ~ 1m/s  Control of temperature and inclusions  electromagnetic actuators  Electromagnetic brake (EMBR)  Transverse DC magnetic field to slow down the jets  Positioned at the surface level to damp level fluctuations  Numerical model + validation  MHD model added to Fluent® + MHD k-  model  Velocity measurements in a Mercury model Copper mould bending & cooling Submersed entry nozzle liquid steel pulling

Continuous casting : simulation / experiment 3 Mercury model  Design principles  Reduced typical slab caster (scale 1/3)  Froude similar flowrate (~casting 1m/mn)  No thermal effects, no solidification  Horizontal DC magnetic field up to 0.47T (centre)  Available measurements  Surface level fluctuations (not used here)  Vertical velocity profiles v z (z,t)  velocity fluctuations (not used here)  mean velocity profiles V z (z) Iron yoke Hg container Horizontal DC field DC coil Hg in Hg out Nozzle

Continuous casting : simulation / experiment 4 Experimental profiles Vz(z)  Measurement conditions  In the midplane (y=0) – 2D flow if B>0  Near the nozzle  jet position (V z max)  Near the small face  impact (V z =0)  Effect of B  Fluctuation reduction (in general)  Apparent acceleration of the “mean” jet (due to stabilization?) then braking  Increase of downward flow near the nozzle  Raise of the jet position and “impact” (gradient of V z ) poles of electromagnet Free surface z,V z x Measurement lines

Continuous casting : simulation / experiment 5  Fluid flow model  Reynolds Averaged Navier-Stokes (RANS) + Lorentz force f=jxB  K-  turbulence model + source terms due to anisotropy (  )  2-layer wall functions on walls, free slip on surface, V z imposed at outlet  Electromagnetic model  No convection of B (R m <<1)  B imposed from measurements  Electrical current from potential: j=  (-  +UxB)  Potential equation from current conservation: 0= .(  )- .(UxB)  Neuman conditions on  (insulating walls) + reference  =0 at inlet  Turbulence anisotropy equation  Deduced from transport of triple correlations  Source term due to B  Transport by the flow and turbulent diffusion  Non linear sink (return to isotropy)  Domain and mesh  MHD interaction: internal / external flow around nozzle  Whole domain (no symmetry), cells Numerical model

Continuous casting : simulation / experiment 6 MHD bidimensionnalisation B=0 B max Vertical vortices stagnation line 2D flow 3D jet flow Impact point Impact line

Continuous casting : simulation / experiment 7 Jets and recirculations  Effect of B  “Brakes” the jet because of 2D spreading  Symmetrisation of the upper loops  Raise the level of jets  Importance of the internal flow  No Hartmann flow in the nozzle because of a leak of current across the ports  High current flowing to the external flow  Current closure  increase the downward velocity around the nozzle  Asymetry  Always present even if fine convergence  More pronounced with the real nozzle (“conical” bottom)  nozzle with hole used in the calculations B=0 B max No vector drawn if |V|>0.5m/s

Continuous casting : simulation / experiment 8 Comparison  Quantitative aspects  Differences num-exp even without field  Real geometry of the nozzle to be introduced  Effect of B well reproduced  Raise the jet  Deforms the profile near the small face  Increase the downwards velocity near the nozzle B=0 B max x=4cmx=20cm

Continuous casting : simulation / experiment 9 Conclusion and perspectives Experimental results available for validation Numerical model available for MHD in complex geometry Validation of the numerical model for the effect of B  Real geometry of the nozzle to be introduced  Stable and unstable asymetry to take into account  Prediction of fluctuations with and without B?