Numerical modelling of phase change processes in clouds. Challenges and Approaches. Martin Reitzle Bernard Weigand

Transcription

1 Institute of Aerospace Thermodynamics Numerical modelling of phase change processes in clouds Challenges and Approaches Martin Reitzle Bernard Weigand

2 Introduction Institute of Aerospace Thermodynamics The ITLR is part of the faculty of aviation and aerospace engineering and geodesy at the University of Stuttgart. Two professors are associated to the ITLR. The institute has about 39 research associates and about 22 non-scientific employees (technicians, designer etc). Research topics (numerical & experimental) of the institute are: heat transfer aerothermodynamics droplet dynamics hypersonic combustion shock tube research. Universität Stuttgart

3 Motivation Phase change processes in clouds Universität Stuttgart

4 Outline Motivation Introduction to multiphase code FS3D Numerical challenges for phase change problems Illustrative example Solution strategies Physical approach Numerical approach Universität Stuttgart

5 Introduction to multiphase code FS3D Universität Stuttgart

6 Introduction to multiphase code FS3D General information In-house CFD code of ITLR written in Fortran Finite Volume discretization of incompressible Navier-Stokes equations Marker-and-Cell scheme Conservation of mass u = 0 Conservation of momentum ρu t + ρu u = p + μ u + u T + ρg Conservation of energy ρc p T t + ρc p Tu = λ T + q Universität Stuttgart

7 Introduction to multiphase code FS3D Treatment of multiple phases - Volume of Fluid method (VOF) Volume tracking using an additional scalar field f 3 x, t = 0 0 < f 3 < 1 1 inthe continuous phase at the interface in the disperse phase Reconstruction of the interface (PLIC) liquid Additiondal conservation equation f 3 t + f 3u = m One-field formulation for material properties, e.g. ρ x, t = ρ s f 3 x, t + ρ l 1 f 3 x, t solid Universität Stuttgart

8 Introduction to multiphase code FS3D Numerical methods Finite Volumes discretization Convective terms: Diffusive terms: Fluxes: Advection: Poisson Equation: Time integration: 2nd order upwind scheme 2nd order central differences Godunov type schemes with TVD Flux Limiter Strang-Splitting or 3D unsplit Red-Black Gauss-Seidel multigrid Solver 1st order explicit Euler, 2nd order explicit Runge-Kutta MPI domain decomposition + OpenMP parallelization on loop level Universität Stuttgart

9 Solidification Numerical challenges for phase change problems Universität Stuttgart

10 Numerical challenges for phase change problems A closer look on the energy balance equation Phase 1 subscript s Conservation of energy V Γ Interface Γ Phase 2 subscript l ρc p T t + ρc p Tu = λ T + q Stefan condition local thermodynamic equilibrium V Γ ρ s L = λ l T l n Γ + λ s T s n Γ For the evaluation of the temperature gradients, the interface temperature T Γ is needed. Universität Stuttgart

11 Numerical challenges for phase change problems Interface Temperature Gibbs-Thomson effect Gibbs-Thomson relation With anisotropic mean curvature T Γ = T m 1 1 ρ s L σ 0H γ H γ = n i,j=1 γ pi p j v, 1 v xi x j Polar plot Shape of crystal in equilibrium Universität Stuttgart

12 Numerical challenges for phase change problems Reconstruct surface as a graph Use the height function method to parameterize the surface v x, y h f (x, y) Coordinate transformations depending on the main direction of the height functions Alternatively: locally fit parabola to surface Universität Stuttgart

13 Numerical challenges for phase change problems Summary Solution algorithm Calculation of normal vectors curvature Evaluate surface temperature Reconstruct surface as a graph Calculate temperature gradients at interface Solve heat conduction equation Advance interface Furthermore Asymmetrical and ill-conditioned matrices due to interface High spatial resolution small time steps Universität Stuttgart

14 Illustrative example Universität Stuttgart

15 Illustrative example Setup Solid seed embedded in liquid droplet T solid < T liquid < T gas Anisotropic phase change at solid-liquid interface Heat fluxes across all interfaces Universität Stuttgart

16 Illustrative example Tracing (Score-P + Vampir) MPI_PROC 0 MPI_PROC 1 MPI_PROC 0 MPI_PROC 1 MPI communication MPI PROC MPI_SENDRECV + MPI_ALLREDUCE [s] Percentage of walltime of timestep % % Universität Stuttgart

17 Solution strategies Universität Stuttgart

18 Solution strategies Physical approach Goal is to capture the true physics as closely as possible Evaluate temperature at interface T Γ Gibbs-Thomson equation Coupling of temperature fields at interface V Γ ρ s L = q s + q l Evaluate temperature at interface T Γ Use T Γ as a boundary condition in heat conduction equation Use these heat fluxes as source terms in the heat conduction equation Reduces number of inner iterations Especially at very fast transient processes better results are obtained Universität Stuttgart

19 Solution strategies Numerical approach Make use of highly optimized numerical methods e.g. UG4 multigrid solver (Pressure Poisson equation) Next step: reduce load imbalances Universität Stuttgart

20 Institute ofaerospace Thermodynamics Thank you! Martin Reitzle phone +49 (0) www. Uni-stuttgart.de/itlr University of Stuttgart Institute ofaerospace Thermodynamics Pfaffenwaldring Stuttgart