Reply To: Unexpected composition fluctuations in a directional solidification problem with species transport

[vladr]

Dear Surya,nthanks a lot for your reply.nnFirst thing, to clarify better what am I trying to do: nnIdeally I would like to completely decouple the Temperature, Convection and Solidification from the Species Concentration. I.e. to have a problem of a solidifying pure material (InSb) with a single melting Temperature, without (or with minimal) 2-plase mushy zone, and to have the Species field as a Passive Scalar.nFrom playing previously with a pure material solidification problem I know that I still need (for some reason) to have Tsolidus and Tliquidus, which I made 0.0001 K apart, but still had a small mushy zone region. If there's no good workaround, I can live with that, provided that the mushy zone does not influence melt convection and convection-diffusion of the solute in the melt.nImportantly, I'd like to have the Species Concentration as a passive scalar field that obeys: n1) The partial rejection of the solute at the solid-liquid interface into the liquid and partial incorporation of it into the formed solid, that would be determined by the partition coefficient K;n2) Convection-Diffusion for the solute that's in the liquid (without solutal buoyancy) n3) No diffusion for the solute in the formed solid, so that once its in the solid it does not redistribute itself along the solid.nIdeally, I would also like not to have any mushy zone, like it is a sharp interface, to model the convective field/boundary layer at the interface influence on the solute incorporation in the formed solid. But for now I leave this question out, because at this stage I am trying to properly duplicate the diffusion controlled scenario described above (and to verify it with analytical solution). Though, I am also concerned with the mushy zone influencing the diffusion of of the solute away from the build-up region next to the interface, that may get in the way of matching the analytical solution, so If you can shed some light on it for me I would appreciate it.nnI would very much welcome any suggestions on if there is a better (more robust and less expensive) way to set this up compared to how I did it.nnNo to the answers to the rest of your questions:nnIs the problem now with convergence as you mentioned after a few time steps?nIt went like this: I would start the calculation in the evening and monitor the first few hundred timesteps, it would start by easily hitting the residual in few iterations, then after a few timesteps (probably when the solidification starts to progress) it would start to struggle to hit the prescribed concentration residual (10^-, though still coming pretty close to it in few iterations, while the temperature is doing OK. Then I would decrease the timestep and it starts to converge in few iterations again, and I leave it over night. nBut when I look at it the next day (when its already at ~80% of the process) I find that C residual does not fall much below 10^-3 in the prescribed iteration limit (100-200), it kind off levels out. The temperature residual is doing better, it still is much worse compared to what I prescribe (like 10^-6 instead to 10^-9). Unfortunately I was not saving the whole history to see when it starts to go wrong, I only could see this from the iterations displayed in the plot/terminal for the last stages of the computation. All this is speaking of the more problematic case (slower freezing, 2mm/hr). nFor the the less problematic one (faster freezing 1cm/hr) I think I was finding it doing OK on the last stages in the late stages of the process, but the concentration plot would display that the Initial Transient stage did not go well (the left side of the color plot and the first chart above).nnHow does the Temperature field look like?nFor the more successful (1 cm/hr) case the temperature field looks ok including the early phase (10 min into the process) resulting in problematic concentration section, see the plots below:nnnCould you also check the mass diffusivity of the species that you are using?nI am using the diffusion coefficient 10^-9 (m^2/s) for the solute (Te), and because I am using the dilute model I think its irrelevant for the Solvent.nnDo you take this diffusivity value from experimental/test data?nI took this value from the following paper:nModel of Tellurium- and Zinc-Doped Indium Antimonide Solidification in Space, Alexei V. Churilov and Aleksandar G. Ostrogorsky, Journal of Thermophysics and Heat Transfer 2005 19:4, 542-547, https://arc.aiaa.org/doi/10.2514/1.8463nThat in its turn is referencing the experiemtnally measured value reported here:nAleksandar G. Ostrogorsky, H.J. Sell, S. Scharl, G. Müller, Convection and segregation during growth of Ge and InSb crystals by the submerged heater method, Journal of Crystal Growth, Volume 128, Issues 1–4, 1993, Pages 201-206, ISSN 0022-0248, (http:/www.sciencedirect.com/science/article/pii/002202489390319R).nnnOverall I would be happy even If I could debug the more successful case (faster-freezing 1 cm/hr) , that had problems in the initial and final transients, but the steady-state middle section looked almost ok. I think it would provide me with clues on what is wrong in the slower-freezing case too.nIf you would need any more details please let me know.Thank you again.nnVladimirn