Carl Hamilton
Check out Sweden CFD-Lab in Sweden Uppsala

Benard-Marangoni Convection

I am trying to duplicate some results from a paper by Marc Medale and Pierre Cerisier called "Direct Numerical Simulations of Bernard-Marangoni Convection" (2001) using MGFlOW.

We are simultaing a coupled gravity and capillarity-driven thermoconvection of a fluid layer heated from below (Bernard-Marangoni convection).

In a small sqaure container that is heated from below.

Here are some of the results so far.

Movie 1) Four-Cells:Gamma = 5.86, Ma = 128, Ra = 33, Bi =0.16

This is a view from above looking down into the Z-plane
This is the first result that where we have achieved proper cell formation

Movie 2) One-Cells:Gamma = 1.82, Ma = 380, Ra = 228, Bi =0.16

This is a view from above looking down into the Z-plane

This result exactly matches Mark Medales results.

Movie 3) 2- cells:Gamma = 6.18, Ma = 82, Ra = 33, Bi =0.16

This is a view from above looking down into the Z-plane

This result is giving two cells now that Mark gave us the correct parameters

Movie 4) -should be 3 Cells:Gamma = 6.18, Ma = 96, Ra = 42, Bi =0.16

This is a view from above looking down into the Z-plane

This result does not match marks results and does not have previous state.

The Contours in this Movie have gone wrong but it gives you a general idea of the shape of the cells.

Movie 5) Four-Cells:Gamma = 6.36, Ma = 93, Ra = 38, Bi =0.16

This is a view from above looking down into the Z-plane

This exactly matches Mark Medales results.

Movie 6) Four-Cells evolving:Gamma = 6.36, Ma = 93, Ra = 38, Bi =0.16

This is a view from above looking down into the Z-plane

This result also exactly matches Mark Medales results.

Movie 7) Should be six cells evolving:Gamma = 8.08 , Ma = 86, Ra = 22, Bi =0.16, Mesh =10x10x5

I am begining to realise that you realy need fine meshes in these problems

This states evolves through several states with small cells before it reaches its final state.

Movie 8) Evolving from 2 cells to 3 cells:Gamma = 6.18 , Ma = 90, Ra = 42, Bi =0.16, Mesh =10x10x5

This state evolves to a two cell solution stayes there for 300 timesteps= a nonlinear time of 59,3 and then moves on to a pulsating three cell.

Movie 9) Transient solution at time 5.89 :Gamma = 8.75 Ma = 75, Ra = 16, Bi =0.16, Mesh =10x10x5

Movie 10) Transient solution at time 5.89

Movie 9 and 10 are an example of two runs with different meshes at the same nondimensional time.

They are clearly different but look similare. My conclusion from this is that either you have to run on the fine mesh or the tolerances change the solution

Note that none of the solutions have reached a steady state and might therefore still evolve to the same solution

Movie 10) Movie 11) Pulsating 3-cell that evolves to 4 -cell :Gamma = 6.18 , Ma = 100, Ra = 33, Bi =0.16, Mesh =16x16x5

Movie 11) Pulsating 3-cell that evolves to 4 -cell :Gamma = 6.18 , Ma = 100, Ra = 33, Bi =0.16, Mesh =16x16x5

Movie 12) Pulsating 3-4 Cells :Gamma = 6.18 , Ma = 90, Ra = 33, Bi =0.16, Mesh =16x16x5 elements

This is my first succesful triangle

Movie 13) Pulsating 2 Cells :Gamma = 6.18 , Ma = 90, Ra = 22, Bi =0.16, Mesh =16x16x5 elements

Last Updated: December 13, 2002 at 10:16:41 CST