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Development of a coupled heat and gas flow model for crystal growth

Abstract

Crystal growth simulations involve a variety of physical phenomena, e.g., heat transfer, gas and melt flows, electromagnetism and thermal stresses. The Finite element (FEM) and Finite volume methods (FVM) have been selected as the main simulation tools for a new crystal growth model. Currently, 2D axisymmetric heat transfer including radiation, phase change and inductive heating are implemented using FEM in Elmer and FEniCSx. The FVM solver OpenFOAM has been chosen for gas flow simulations. In this contribution, the coupling strategy between Elmer-OpenFOAM / FEniCSx-OpenFOAM using preCICE library is discussed. First test cases are evaluated for both couplings, and requirements for future development are analyzed. --- A recording of the talk is available here: https://youtu.be/8ivCDyz2FlI
vMax-Born-Str. 2 v12489 Berlin vGermany vwww.ikz-berlin.de v
LEIBNIZ -INSTITUT FÜR KRISTALLZÜCHTUNG
Development of a coupled heat and gas flow model for
crystal growth
Arved Enders-Seidlitz
Max Schröder
Iason Tsiapkinis
Kaspars Dadzis
Leibniz Institute for Crystal Growth
preCICE workshop 2022
February 22, 2022
vArved Enders-Seidlitz vDevelopment of a coupled heat and gas flow model for crystal growth v2
22.02.2022
Motivation
Software and coupling strategy
preCICE adapters
oOverview
oTest: FEniCSx-OpenFOAM coupling
oTest: Elmer-OpenFOAM coupling
Conclusion
Content
vArved Enders-Seidlitz vDevelopment of a coupled heat and gas flow model for crystal growth v3
22.02.2022
Motivation
Time lapse video of model experiment: duration 20 min
Heat
transfer &
phase
change
Electro-
magnet-
ism
Gas flow Melt flow
Stresses
Crystal
Melt
vArved Enders-Seidlitz vDevelopment of a coupled heat and gas flow model for crystal growth v4
22.02.2022
Motivation
Numerical challenges
oComplex coupled physics
oMoving geometries
oDifferent timescales
o
Goals in NEMOCRYS Project
oOpen source implementation
oValidation: Using model experiments
Heat
transfer &
phase
change
Electro-
magnet-
ism
Gas flow Melt flow
Stresses
Crystal
Melt
vArved Enders-Seidlitz vDevelopment of a coupled heat and gas flow model for crystal growth v5
22.02.2022
Motivation
Software and coupling strategy
preCICE adapters
oOverview
oTest: FEniCSx-OpenFOAM coupling
oTest: Elmer-OpenFOAM coupling
Conclusion
Content
vArved Enders-Seidlitz vDevelopment of a coupled heat and gas flow model for crystal growth v6
22.02.2022
Software strategy: FEM solvers
Heat
transfer &
phase
change
Electro-
magnet-
ism
Gas flow Melt flow
Stresses
Crystal
Melt
oVarious solvers for the selected physics available
oCoupling in between the solvers already implemented
oLacks some features, implementation in Fortran would
be difficult
“Multiphysics simulation toolbox”
oEasy implementation / adjustment of solvers
oFEniCSx required for complex numbers (advantageous in
electromagnetism)
oAll solvers have to be written by ourselves
oFEniCSx still under development (alpha-release available)
“Customized FEM solvers”
vArved Enders-Seidlitz vDevelopment of a coupled heat and gas flow model for crystal growth v7
22.02.2022
Software strategy: FVM solvers
Heat
transfer &
phase
change
Electro-
magnet-
ism
Gas flow Melt flow
Stresses
Crystal
Melt
oVarious flow solvers including turbulence
modeling available
oEfficient calculation of melt and gas flow possible
oMulti-region simulations difficult
vArved Enders-Seidlitz vDevelopment of a coupled heat and gas flow model for crystal growth v8
22.02.2022
Software strategy: coupling
How to bring these tools together?
vArved Enders-Seidlitz vDevelopment of a coupled heat and gas flow model for crystal growth v9
22.02.2022
Coupling: internal
Heat
transfer &
phase
change
Electro-
magnet-
ism
Gas flow Melt flow
Stresses
Crystal
Melt
FEM Solver (with internal coupling)
Electro-
magnet-
ism
heat source
(in volume) Heat
transfer &
phase
change
temperature
(in volume)
oGas flow modeled with heat transfer coefficients
oMelt flow modeled with increased heat conductivity
oImplemented in Elmer and FEniCSx
oValidated in model experiment
vArved Enders-Seidlitz vDevelopment of a coupled heat and gas flow model for crystal growth v10
22.02.2022
Coupling: with gas flow
FEM Solver (with internal coupling)
Electro-
magnet-
ism
heat source
(in volume) Heat
transfer &
phase
change
temperature
(in volume)
temperature
FVM Solver
Gas flow
heat flux
Dirichlet-Neumann
coupling on surfaces
Coupling scheme similar to
flow over heated plate!
Heat
transfer &
phase
change
Electro-
magnet-
ism
Gas flow Melt flow
Stresses
Crystal
Melt
vArved Enders-Seidlitz vDevelopment of a coupled heat and gas flow model for crystal growth v11
22.02.2022
Melt flow
temperature
Coupling: with gas and melt flow
FEM Solver (with internal coupling)
Electro-
magnet-
ism
heat source
(in volume) Heat
transfer &
phase
change
temperature
(in volume)
FVM Solver
heat flux
temperature
heat flux
FVM Solver
Gas flow
heat flux
Lorentz forces
(in volume)
Dirichlet-Neumann
coupling on surfaces
One-directional
volume coupling
Heat
transfer &
phase
change
Electro-
magnet-
ism
Gas flow Melt flow
Stresses
Crystal
Melt
vArved Enders-Seidlitz vDevelopment of a coupled heat and gas flow model for crystal growth v12
22.02.2022
Melt flow
temperature
Coupling: complete model
Electro-
magnet-
ism
heat source
(in volume) Heat
transfer &
phase
change
temperature
(in volume)
FVM Solver
heat flux
temperature
heat flux
FVM Solver
Gas flow
heat flux
Lorentz forces
(in volume)
Dirichlet-Neumann
coupling on surfaces
Stresses
temperature
(in volume)
Heat
transfer &
phase
change
Electro-
magnet-
ism
Gas flow Melt flow
Stresses
Crystal
Melt
FEM Solver (with internal coupling)
vArved Enders-Seidlitz vDevelopment of a coupled heat and gas flow model for crystal growth v13
22.02.2022
Motivation
Software and coupling strategy
preCICE adapters
oOverview
oTest: FEniCSx-OpenFOAM coupling
oTest: Elmer-OpenFOAM coupling
Conclusion
Content
vArved Enders-Seidlitz vDevelopment of a coupled heat and gas flow model for crystal growth v14
22.02.2022
Available preCICE adapters
OpenFOAM FEniCS FEniCSx Elmer
Surface coupling
Yes Yes Adjustment required Yes
Volume coupling
Yes, in PR (not merged)
Yes Adjustment required No
Coupling scheme
Explicit / implicit Explicit / implicit Adjustment required Explicit
Parallelization
Yes Yes Adjustment required No
Status
Official support Official support Experimental Experimental
Conclusion (so far)
oOpenFOAM adapter brings all that we need
oElmer adapter works only explicit
oFEniCSx adapter brings main infrastructure but is incomplete
Implement the flow over heated plate tutorial case
forked
vArved Enders-Seidlitz vDevelopment of a coupled heat and gas flow model for crystal growth v15
22.02.2022
FEniCSx adapter
General experience
oDifficulties due to alpha-stadium of FEniCSx
oDevelopment version required (for bugfixes)
oThere are still changes in the API
oIssues in linking with preCICE (PETSc version)
oDocker image with working configuration:
https://hub.docker.com/r/nemocrys/dolfinx-openfoam
Adjustment of the adapter (together with Benjamin Rodenberg)
oUsing partitioned heat conduction tutorial case (FEniCSx-FEniCSx)
oAdjustment to the new API of FEniCSx
oTests currently not working
oParallelization not tried
oPull request open: https://github.com/precice/fenicsx-adapter/pull/1 Partitioned heat conduction, t = 1 s
Error computation missing, but results look good!
FEniCSx
Solver 1
FEniCSx
Solver 2
Dirichlet-Neumann
coupling
vArved Enders-Seidlitz vDevelopment of a coupled heat and gas flow model for crystal growth v16
22.02.2022
FEniCSx adapter
Flow over heated plate (FEniCSx-OpenFOAM)
oStarting point: preCICE tutorial case for FEniCS
oAdjustment to the new FEniCSx API
(and quite some debugging)
Works immediately
Smooth isothermals over the interface
Fluid domain (OpenFOAM)
Solid domain
(FEniCSx)
t = 10 s
Dirichlet-Neumann
coupling
https://github.com/nemocrys/dolfinx-openfoam
vArved Enders-Seidlitz vDevelopment of a coupled heat and gas flow model for crystal growth v17
22.02.2022
Elmer adapter
General experience (Elmer-Elmer)
oEasy to set up: just compile the adapter (“coupler solver”)
oGood documentation for partitioned heat conduction
oBackground information in thesis [Saeed2021]
Flow over heated plate (Elmer-OpenFOAM)
oDiscrepancy in variable names
temperature flux vs Heat-Flux
Solved by hard-coded renaming in the Elmer adapter
oElmer uses lower case letters only
Adjusted preCICE config required
[Saeed2021] H. Saeed, Elmer Adapter for Precice, Master‘s
Thesis, Technical University of Munich (2021). Steps in isothermals due to explicit coupling
Flow over heated plate, t = 10 s
Partitioned heat conduction, t = 1 s
vArved Enders-Seidlitz vDevelopment of a coupled heat and gas flow model for crystal growth v18
22.02.2022
Motivation
Software and coupling strategy
preCICE adapters
oOverview
oTest: FEniCSx-OpenFOAM coupling
oTest: Elmer-OpenFOAM coupling
Conclusion
Content
vArved Enders-Seidlitz vDevelopment of a coupled heat and gas flow model for crystal growth v19
22.02.2022
Conclusion
Crystal growth simulation strategy
oFEM for electromagnetism, heat conduction, and stress
oFVM for gas and melt flow
Analysis of preCICE adapters (for coupling to OpenFOAM)
oFEniCSx adapter works well in flow over heated plate
oElmer adapter provides only explicit coupling
oParallelization missing in Elmer / FEniCSx adapter
Outlook
oNew test case: steady-state buoyant flow over heated plate
(for both adapters)
oCrystal growth simulation including gas flow with best
candidate
oValidation with PIV measurements
Collaborative
development?
20
vArved Enders-Seidlitz vDevelopment of a coupled heat and gas flow model for crystal growth v
22.02.2022
We’d like to thank the whole preCICE team, especially Benjamin Rodenberg and Gerasimos Chourdakis
for their advice and support and Hisham Saeed for the development of the Elmer adapter.
This project has received funding from the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme (grant agreement No 851768).
Acknowledgements
Thank you for your attention!
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