free surface flow simulations - powerlab -...

Free Surface FlowSimulations

Hrvoje Jasak

[email protected]

Wikki Ltd. United Kingdom

11/Jan/2005

Free Surface Flow Simulations – p.1/26

Outline

Objective

• Present two numerical modelling approachesfor free surface flows

Topics

• Surface tracking method

• Surface capturing method

• Implementation in FOAM

• Examples: bubble DNS and jet breakup LES


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!


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

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


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 beomitted from simulation


Solution Algorithm

Fluid flow

• SIMPLE-based segregated FVM fluid flowsolver 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 phasesand adjust mesh for zero mass flux


Automatic Mesh Motion

Automatic moving mesh

• Need to determine vertex positions givenboundary 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


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


Example: Hydrofoil

• Flow coming in from left

• Mesh lines coloured by pressure


Example: Bubble

FVM fluid flow + automatic mesh motion (FEM)+ Finite Area Method for surfactant transport


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


Surface Capturing

Single continuum approach

• Both (all) fluids treated as single continuum

• Indicator variable γ determines position ofinterface◦ γ = 0 → air◦ γ = 1 → water◦ 0 < γ < 1 → cell contains interface

• γ defines jump in properties


Surface Capturing

Single continuum approach

• Interface is not discrete but needs to bereconstructed from γ

• . . . in fact, interface is “distributed”

• Numerics challenge: preserving sharpness ofinterface in solution◦ Volume-of-Fluid: planar reconstruction◦ Compressive differencing◦ Eulerian two-fluid derivation


p-U Coupling

Flow solver

• Based on segregated PISO solution algorithm

• Using unstructured “staggered” algorithm: cellcentre velocity reconstructed from the fluxes

Implementing surface tension

• Curvature calculation from ∇γ

• Distributed “surface” source in p-equation

• For small droplets, surface tension totallydominates - problematic!


Surface Tension

Parasitic currents

• Interface compression = noise in ∇γ


Example: Dam Break

Collapsing column of water


Example: Bubble

Bubble, surface capturing


Example: Jet Breakup

LES of a Diesel Injector

• d = 0.2mm, high velocity and surface tension


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


FOAM: CCM in C++

FOAM: Field Operation and Manipulation

• Natural language of continuum mechanics:partial differential equations

∂k

∂t+ ∇•(uk) −∇•[(ν + νt)∇k] =

νt

[

1

2(∇u + ∇u

T )

]2

−εo

ko

k


FOAM: CCM in C++

Objective: Represent equations in software inthe 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)

);


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() –


FOAM: CCM in C++

Main characteristics

• Wide area of applications: all of CCM!

• Shared tools and code re-use

Versatility

• Unstructured meshes, automatic meshmotion + topological changes

• Finite Volume (2nd and 4th order), FiniteElement and Finite Area solvers

• Efficient: massive parallelism


Summary

Summary

• Presented two approaches to free surfaceflow simulations◦ Surface tracking: mesh deformation◦ Surface capturing: indicator variable

• Methods are complementary; choice dependson the problem under consideration

• FOAM Implementation: easy experimentingwith numerics and algorithms


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: http://www.openfoam.org


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