晶体生长建模软件FEMAGDS法定向凝固法模拟.ppt

晶体生长建模软件FEMAG Numerical simulation of Direct Solidification (DS) processes FEMAGSoft ? 2013 Very accurate and efficient 3D prediction of the melt flow and the global heat transfer DS process simulation FEMAGSoft ? 2013 Direct solidification of multi-crystalline silicon with a square crucible Method: 1. Mapping of the square cross-section onto a circle 2. Use of a particular expansion technique for all fields (velocity, pressure, temperature) in the transformed domain Hypothesis: square symmetry of all averaged fields Objective: global, quasi-steady or time-dependent calculations at a reasonable cost DS process simulation (cont’d) FEMAGSoft ? 2013 y Y x X z = x + iy Z = X + iY Real square cross-section Transformed circular cross-section DS process simulation (cont’d) FEMAGSoft ? 2013 Next steps Write Z = X+iY = r eiq in the transformed domain and expand all unknown fields as Fourier series of cos q and sin q Then put all equations in a weak form and make the problem discrete using a mixed spectral – finite element technique (using a 2D mesh) This results in a system whose size is that of the 2D system multiplied by the number of Fourier modes considered and hence in a dramatic system size reduction. DS process simulation (cont’d) FEMAGSoft ? 2013 Time-dependent simulation of DS process Filling of a 20 cm side square crucible (“Minicaster” furnace) Evolution of the temperature, velocity, oxygen and carbon concentration fields. DS process simulation (cont’d) FEMAGSoft ? 2013 Evolution of temperature distribution DS process simulation (cont’d) FEMAGSoft ? 2013 Evolution of oxygen distribution Oxygen in the melt Oxygen in the crystal DS process simulation (cont’d) FEMAGSoft ? 2013 Evolution of carbon distribution Carbon in the melt Carbon in the crystal DS process simulation (cont’d) FEMAGSoft ? 2013 Comparison of 3D FEM-spectral and 3D Cartesian simulations DS process simulation (cont’d) FEMAGSoft ? 2013 Same isosurfaces : - Colo