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.