A question about Numerical simulation of vertical Bridgman crystal growth using enthalpy-porosity method I¡¯m writing my code to simulate the CdTe growth process, and yesterday I encountered a hard nut to crack. I employ a traditional method, enthalpy-porosity formulation with fixed-grid, which has been implemented in Fluent. From several prior papers, I knew that the increasing ampoule pulling rates have the impact on the solid/liquid interface shape. But, I have no idea how to incorporate the pulling rate V into the governing equations. The computation is assumed in the steady state where the pulling rate equals to the crystal growth rate. Please give me a hint or some valuable references. Thanks. BTW, my technique comes from Pro. Shyy Wei¡¯s books and papers.

My first question is are u modelling a pure substance or a binary substance modelling.

You cannot implement stefan condition along with pulling rate in in Enthalpy porosity technique. Bcos it relaxes some dT over few grid cells and the result is affected in the source term of the Energy equation. In short the interface is not sharp (in numeric sense it does not pass through single cell) to implement Boundary conditions on the interface.

If u are using pure substance then there is a solution. You have to ALE(Arbitrary Eulerian and Lagrangian Techniques) where you can explicitly track the interface using lagrangian technique and solve it in Eulerian fashion.

You may also look up 'Journal of Crystal growth'

Thanks for your reply , Santhanu. My concern is an isotherm phase change problem about a pure substance, CdTe.. You said, "You cannot implement stefan condition along with pulling rate in Enthalpy porosity technique." I found some papers using Enthalpy porosity technique to simulate CdTe vertical Bridgman always give a pulling rate. I think it must be an influencing factor. In fact, I want to reveal the pulling rate's impact on the interface shape, however, as you said, the pulling rate generally is implemented by explicitly tracking the interface. I'm afraid I have to change my method.

However, in Shyy Wei¡¯s Computational Fluid Dynamics With Moving Boundaries Taylor & Francis (1996) PP164

¡°Source term in momentum equation is A(u-u(cast)), A=C(1-f^2)/(f^3+q). u(cast) denote the prescribed velocity at which the solid phase is moving, say, for example, in a crystal growth or a casing process.¡±

It appends a u(cast) while the source term in energy equation is common latent heat update. I have ever thought u(cast) is what I want, but the result is disappointing.

Hi,

In the momentum equation in the Enthalpy porosity technique uses a darcy's type law to suppress velocities in the solidified part. and a Ucast is supplied there to take care of the pulling velocity(to take care of the relative movement). It can be a way to do it. It is an easier way of treating the interface. But if u are able to get your results closer to experiments then everything is perfect.

I have never done any Vertical bridgeman modelling but as far as i know it is the ampoule which is given a velocity but not the solidified itself as in Czochralski Process

It is also possible that thermophysical properties such as thermal conductivity of solid vs. the melt, as well as flow conditions and pulling rates affect the interface shape. We did those calculations many years ago, but, I remember thermophysical properties having a significant impact on the interface shape.

Are you trying to compare the computations with measurements?

Best wishes,

Madhukar M. Rao

Nouri sabrina Attached of research to the unit of search for develop technological silicon in Algerie. Adress: udts 02 Bd frantz fanon, Bp 399 Alger-gare (algerie). Fax: 213/21/43/35/11 Télé: 213/21/27/98/80 research topic:Numerical analysis of the transfer of heat and momentum in a vertical system of growth of Bridgman

I do not have a clear idea in connection with this subject, which relates to: equations which govern the physical phenomenon, the boundary conditions in a vertical growth which occurs in the furnace of Bridgman. I ask you for illustrations is by e-mail or it is possible some articles. I do not have a clear idea on the method of enthalpy