熱物質移動を含むプロセスへのオープンCAEの活用
大阪大学大学院基礎工学研究科
高木 洋平
オープンCAEシンポジウム2012@岐阜
Chemical engineering process
Ex. Chemical Vapor Deposition (CVD)
Heat, Mass and momentum transfer
Transport phenomena in melt
Governing equations in melt
• Navier-Stokes eq.
• Energy eq.
• Diffusion eq.
Common operator: Gradient, Divergence, Laplacian, Time Advancement
u: vector T: scalar C: scalar
Advantage of open source
• OpenFOAM – Object Oriented
Programming
• Fortran code – Procedural
Programming
grad(T) grad(U)
call grad(T,dTdx,dTdy,dTdz) call grad(u,dudx,dudy,dudz) call grad(v,dvdx,dvdy,dvdz) call grad(w,dwdx,dwdv,dwdz)
Operator overload Class module
Easy extension
Mixture of scalar, vector and tensor
Crystal growth of compound semiconductor
• Silicon germanium (SiGe) – (SixGe1-x) – High performance, high efficiency – Lattice mismatch in Si+SiGe
• Property of SiGe
Use of solution growth
Segregation
Traveling Heater Method (THM)
Heater
Ge rich
SiGe crystal
Si dissolution
Melt convection with heat and mass transfers
Objective
• Convection control in THM – Magnetic field – Crucible rotation
• Convection suppression effect with external forces
• Operating condition for high quality crystal – Si concentration near growth
interface
OpenFOAM
Governing equations in melt
• Navier-Stokes eq.
• Induction eq. of magnetic field
• Energy eq.
• Diffusion eq.
Boundary condition
• Velocity: no-slip condition, rotating wall velocity • Magnetic field: static vertical • Temperature and concentration:
• Not considered: moving boundary of crystal-melt surface, heater movement
5% Si
1% Si
Z
T Tmax Tmin
Si concentraDon [%] 1.0 5.0
M.F. Rot. Case1 × × Case2 ○ × Case3 × ○ Case4 ○ ○
With Magnetic field
No control
5 min
With Magnetic field
M.F. Rot. Case1 × × Case2 ○ × Case3 × ○ Case4 ○ ○
With Magnetic field
Si concentraDon [%] 1.0 5.0
No control
Vmax=1.04 m/s VZmax=0.07 m/s
M.F. Rot. Case1 × × Case2 ○ × Case3 × ○ Case4 ○ ○
With Magnetic field
With rotation Si concentraDon [%] 1.0 5.0
Vmax=1.04 m/s VZmax=0.07 m/s
M.F. Rot. Case1 × × Case2 ○ × Case3 × ○ Case4 ○ ○
With Magnetic field
With rotation
Vz = 6.4×10-3 m/s
Si concentraDon [%] 1.0 5.0
With rotation & Magnetic field
M.F. Rot. Case1 × × Case2 ○ × Case3 × ○ Case4 ○ ○
With Magnetic field
With rotation Si concentraDon [%] 1.0 5.0
M.F. Rot. Case1 × × Case2 ○ × Case3 × ○ Case4 ○ ○
With rotation & Magnetic field
Si concentraDon [%] 1.0 5.0
C ave. of S
i [%]
0.0
3.0
2.0
1.0
0 M.F. Rot. M.F. & Rot.
M.F. Rot. Case1 × × Case2 ○ × Case3 × ○ Case4 ○ ○
Combination of M.F. and rotation
Rich Si near growth interface
Si concentraDon [%] 1.0 5.0
Reω [-]
Cav
e. o
f Si
[%]
2.4
2.6
2.0 800 400 500 600 700
2.2
Combination of M.F. and rotation
Rich Si near growth interface
7 rpm 8 rpm
70 mT(Ha=40)
7 mT(Ha=10)
103 mT(Ha=60)
0 mT(Ha=0)
Toward smart control
Fluid dynamics
Heat transfer
MagneDc field
Chemical reacDon
・・・・
OpenFOAM
CondiDon 1
CondiDon 2
CondiDon 3
Result 1
Result 2
Result 3
OpDmal control (Nonlinear opDmal control)
First step for smart control:Adjoint method
Adjoint method formulation for ducted flow • Adjoint N-S equations:
• Adjoint BCs for the wall and inlet:
• Adjoint BCs for the outlet:
Ex. 1: Dissipated power Cost funcDon: DerivaDves for BCs:
Adjoint BCs for the wall and inlet:
at wall
at inlet
Adjoint BCs for the outlet:
adjointShapeOptimization.C // Adjoint Pressure-velocity SIMPLE corrector { // Adjoint Momentum predictor
volVectorField adjointTransposeConvection((fvc::grad(Ua) & U));
zeroCells(adjointTransposeConvection, inletCells);
tmp<fvVectorMatrix> UaEqn ( fvm::div(-phi, Ua) - adjointTransposeConvection + turbulence->divDevReff(Ua) + fvm::Sp(alpha, Ua) );
Result: adjoint velocity
Summary
• The simulation including heat, mass and momentum transfers is carried out by using OpenFOAM.
• OpenFOAM is suitable for multi-physics problem.
• Simulation code for optimization is now developed.
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