Free Surface Flow Simulations

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1 Free Surface Flow Simulations Hrvoje Jasak Wikki Ltd. United Kingdom 11/Jan/2005 Free Surface Flow Simulations p.1/26

2 Outline Objective Present two numerical modelling approaches for free surface flows Topics Surface tracking method Surface capturing method Implementation in FOAM Examples: bubble DNS and jet breakup LES Free Surface Flow Simulations p.2/26

3 Background Why free surface flows? Large number of industrial interests: Liquid sloshing in LNG tankers Chemical and food industry Diesel injectors, atomisation, droplet-wall interaction, cavitation Ink-jets and similar devices Complex physics = demanding models Pretty pictures! Free Surface Flow Simulations p.3/26

4 Mathematical Model Two fluids with a sharp interface Two fluids = two continua Free surface represented by a boundary Compatibility condition + mesh motion Single continuum with a jump in properties: Step-change for density, viscosity How to deal with surface effects: free surface = Dirac function Free Surface Flow Simulations p.4/26

5 Free Surface Free surface effect Moving; position part of solution No mass flux through surface Momentum compatibility (normal + tangential) Pressure jump (surface tension), turbulence? Description of the free surface depends on the selected modelling framework Free Surface Flow Simulations p.5/26

6 Surface Tracking Model Two-fluid approach Separate mesh for each phase Motion obtained from boundary conditions Mesh adjusted for the motion of free surface Can handle only one phase: light fluid can be omitted from simulation Free Surface Flow Simulations p.6/26

7 Solution Algorithm Fluid flow SIMPLE-based segregated FVM fluid flow solver with mesh motion Double boundary condition on free surface Fixed pressure + position compatibility No mass flux through surface Compatibility in tangential velocity Transfer pressure/position between phases and adjust mesh for zero mass flux Free Surface Flow Simulations p.7/26

8 Automatic Mesh Motion Automatic moving mesh Need to determine vertex positions given boundary vertex motion Moving mesh solver in FOAM Formulation guarantees mesh validity (Vertex-based) Finite Element solver for polyhedral meshes Solving Laplace equation for vertex motion Variable diffusivity controls mesh quality Free Surface Flow Simulations p.8/26

9 Surface Tension Handling surface tension Specifies pressure jump on free surface Depends on local curvature and coefficient σ Curvature calculated from vertex position σ may depend on surfactant concentration Variable σ significantly changes behaviour Solving species transport on a 2-D curved surface in 3-D Free Surface Flow Simulations p.9/26

10 Example: Hydrofoil Flow coming in from left Mesh lines coloured by pressure Free Surface Flow Simulations p.10/26

11 Example: Bubble FVM fluid flow + automatic mesh motion (FEM) + Finite Area Method for surfactant transport Free Surface Flow Simulations p.11/26

12 Surface Tracking Model Advantages Precise modelling of free surface Sharp interface Compatibility through boundary conditions Can solve extremely high surface tension Drawbacks No change in interface topology! Problems for low density ratio Free Surface Flow Simulations p.12/26

13 Surface Capturing Single continuum approach Both (all) fluids treated as single continuum Indicator variable γ determines position of interface γ = 0 air γ = 1 water 0 < γ < 1 cell contains interface γ defines jump in properties Free Surface Flow Simulations p.13/26

14 Surface Capturing Single continuum approach Interface is not discrete but needs to be reconstructed from γ... in fact, interface is distributed Numerics challenge: preserving sharpness of interface in solution Volume-of-Fluid: planar reconstruction Compressive differencing Eulerian two-fluid derivation Free Surface Flow Simulations p.14/26

15 p-u Coupling Flow solver Based on segregated PISO solution algorithm Using unstructured staggered algorithm: cell centre velocity reconstructed from the fluxes Implementing surface tension Curvature calculation from γ Distributed surface source in p-equation For small droplets, surface tension totally dominates - problematic! Free Surface Flow Simulations p.15/26

16 Surface Tension Parasitic currents Interface compression = noise in γ Free Surface Flow Simulations p.16/26

17 Example: Dam Break Collapsing column of water Free Surface Flow Simulations p.17/26

18 Example: Bubble Bubble, surface capturing Free Surface Flow Simulations p.18/26

19 Example: Jet Breakup LES of a Diesel Injector d = 0.2mm, high velocity and surface tension Free Surface Flow Simulations p.19/26

20 Surface Capturing Advantages Natural handling of interface breakup Static mesh, efficient simulations Drawbacks Imprecise handling of interfacial properties: parasitic currents, surface tension balance Limited density ratio and surface tension Always requires all phases in simulation Free Surface Flow Simulations p.20/26

21 FOAM: CCM in C++ FOAM: Field Operation and Manipulation Natural language of continuum mechanics: partial differential equations k t + (uk) [(ν + ν t) k] = [ ] 2 1 ν t 2 ( u + ut ) ɛ o k k o Free Surface Flow Simulations p.21/26

22 FOAM: CCM in C++ Objective: Represent equations in software in the natural language solve ( fvm::ddt(k) + fvm::div(phi, k) - fvm::laplacian(nu() + nut, k) == nut*magsqr(symm(fvc::grad(u))) - fvm::sp(epsilon/k, k) ); Free Surface Flow Simulations p.22/26

23 FOAM: CCM in C++ Object Software representation C++ Class Space and time Mesh + time (database) polymesh, time Tensor (List of) numbers + algebra vector, tensor Field List of values Field Boundary condition Values + condition patchfield Geometric field Field + boundary conditions geometricfield Field algebra + / tr(), sin(), exp()... field operators Interpolation Differencing schemes interpolation Differentiation ddt, div, grad, curl fvc, fec Matrix Matrix coefficients ldumatrix Discretisation ddt, d2dt2, div, laplacian fvm, fem, fam Model library Library turbulencemodel Application main() Free Surface Flow Simulations p.23/26

24 FOAM: CCM in C++ Main characteristics Wide area of applications: all of CCM! Shared tools and code re-use Versatility Unstructured meshes, automatic mesh motion + topological changes Finite Volume (2nd and 4th order), Finite Element and Finite Area solvers Efficient: massive parallelism Free Surface Flow Simulations p.24/26

25 Summary Summary Presented two approaches to free surface flow simulations Surface tracking: mesh deformation Surface capturing: indicator variable Methods are complementary; choice depends on the problem under consideration FOAM Implementation: easy experimenting with numerics and algorithms Free Surface Flow Simulations p.25/26

26 Acknowledgements Acknowledgements Surface tracking simulations: Zeljko Tukovic, FSB Zagreb Bubble DNS, surface capturing: Dr. Henrik Rusche Spray breakup: Eugene de Villiers, Imperial College Free surface algorithm development contributions: Dr. Onno Ubbink, Henry Weller Foam and OpenFOAM are released under GPL: Free Surface Flow Simulations p.26/26

Object-Oriented CFD Solver Design

Object-Oriented CFD Solver Design Hrvoje Jasak h.jasak@wikki.co.uk Wikki Ltd. United Kingdom 10/Mar2005 Object-Oriented CFD Solver Design p.1/29 Outline Objective Present new approach to software design