interphaschangefoam and pans

8/10/2019 InterPhasChangeFoam and PANS

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Abolfazl Asnaghi

Dec 2013

interPhaseChangeFoam PANS Turbulence Models


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Cavitation

A BC

D E F

Flow Direction

Pressure

A

B

CE

F

Liq.

Vap

D

Liq-Vap

Liq : Liquid

Vap: Vapor


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Cavitation


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Cavitation & OpenFoam

Available solvers in OF for multiphase simulations:

o cavitatingFoam

o compressibleInterFoam

o compessibleTwoPhaseEulerFoam

o interFoam

o

interPhaseChangeFoam

Find more information here:

http://www.openfoam.org/docs/user/standard-solvers.php

o multiphaseEulerFoam

o multiphaseInterFoam

o settlingFoam

o twoLiquidMixingFoam

o

twoPhaseEulerFoam


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interPhaseChangeFoam Solver

interPhaseChangeFoam

Solver for 2 incompressible, isothermal immiscible

fluids with phase-change (e.g. cavitation). Uses a VOF

(volume of fluid) phase-fraction based interface

capturing approach

interPhaseChangeDyFoam

Added in OF2.2.2 (since after will be called OF)

Providing optional mesh motion and mesh topology

changes including adaptive re-meshing


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interPhaseChangeFoam Structureo alphaEqn.H

o alphaEqnSubCycle.H

o createFields.Ho interPhaseChangeFoam.C

o pEqn.H

o UEqn.H

o phaseChangeTwoPhaseMixtures Folder

o Kunz Folder

Kunz.C

Kunz.H

o Merkle Folder

Merkle.C

Merkle.H

o phaseChangeTwoPhaseMixture Folder

phaseChangeTwoPhaseMixture.C

phaseChangeTwoPhaseMixture.HnewPhaseChangeTwoPhaseMixture.C

newPhaseChangeTwoPhaseMixture.H

o SchnerrSauer Folder

SchnerrSauer.C

SchnerrSauer.H

o Make Folder

files

o tions


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interPhaseChangeFoam Structure

o alphaEqn.H

o alphaEqnSubCycle.H

o interPhaseChangeFoam.C

o pEqn.H

o

UEqn.Ho phaseChangeTwoPhaseMixtures Folder

o phaseChangeTwoPhaseMixture Folder

phaseChangeTwoPhaseMixture.C

phaseChangeTwoPhaseMixture.H

o SchnerrSauer Folder

SchnerrSauer.C

SchnerrSauer.H


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User Input

o Initial time folder (usually zero folder)

U: velocity (m/s)

alpha1: liquid volume fraction (must be between zero & one

p_rgh = p-rho.g.h where p here is the thermodynamic pressure which comes

from intermolecular forces and you see it in the N.S. equations (pa)


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User Input

o constant folder: transportProperties file

Select the phase change model

Define the saturation pressure

Define the surface tension

Define the phases propertiesRemember for cavitation, the first phase is liquid

Define the phases change model propertiesn: number of nuclei

dNuc: average diameter of nuclei

Cc: condensation rate coefficient

Cv: vaporization rate coefficient


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Solver Flowchart

Reading maxCo, and maxDeltaT from controlDict

Calculates and outputs the mean and

maximum Courant Numbers

Calculates deltaT based on the

maximum Courant Number in the

flow, maximum allowed CourantNumber and maximum allowed deltaT

Calculates viscosity of mean flow

based on the each phase properties,

specified viscosity models for each

phase and alpha distribution. For

homogenous assumption:

lvvvm

lvvvm

)1(

)1(

In C file: #include "phaseChangeTwoPhaseMixture.H

And then in the above H file:#include "incompressibleTwoPhaseMixture.H"


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Solver Flowchart

Solves alpha1 transport equation, and

obtains new distribution

Correct the alpha boundary condition,

and also interface curvature.

PIMPLE loop to solve momentum, pressure

correction, and turbulence equations.


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UEqn

Keeping this term (which is the

continuity equation, and in converged

solution is equal to zero ) would increase

the stability of the solution considerably

gx

p

xgxg

x

gx

.

x

gxp

xgxg

x

p

.

This trick has simplified the boundary condition

implementation, and also increased the stability

when the gravity should be considered


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pEqn(just intrested parts)

Calling the source terms of pressure

correction equation, vDotP

C: stands for construction of liquid

V: stands for vaporization of liquid

Splitting the source terms in two termsSp as diagonal, and the other as Su

ghpSatVVpVV

pSatghghpVVpSatpVVU

vpcprghvpcp

vpcpvpcpf

..

...

* Look at the Jassak PhD thesis for further information about pressure correction equations


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alphaEqnSubCycle

Calling nAlphaSubCycles and

nAlphaCorr frompimpleDic

in system/fvSolution file

cAlpha(): two phase interface compression(relative velocity) coefficient, defined by

user at system/fvSolution:alpha Dictionary

Ref. Henrik PhD Thesis, Eq:3-58

rhoPhi is

set to zero


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alphaEqnSubCycle

Maximum allowed time step for alpha equation is much lower than the one that we can use for

solving momentum or turbulence equations.

Therefore, we consider deltaT as the main time step for momentum or turbulence equations,

and use deltaT/nAlphaSubCycle as the time step for alpha equation.

rhoPhiSum is set equal to rhoPhi equal to zero

Main time step used in other equations

subCycle.H is added to main .C file which

itself contains subCycleTime.H

In subCycle.H, runTime.deltaT() has been changed to

deltaT/nAlphaSubCycle or equivalently totalDeltaT/nAlphaSubCycle


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alphaEqn

l

i

rvl

i

illS

x

u

x

u

t

vvlli UUU

vl UUUr


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Importance of Turbulence Model

Twist11 HydroFoil - k Omega SST

A.Asnaghi, 16thNumerical Towing Tank Symposium, 2013


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PANS

PANS = Partially Averaged Navier Stokeso If all of the velocity disturbance specturm be solved that would be DNS:

very high precision but huge amount of computational cost

o If we use vaerage of all of the velocity disturbance specturm that would be

RANS: fair precision with acceptable computational cost

o In PANS, we are aiming to calculate some parts of unresolved velocity

disturbance specturm.

PANS

RANS DNS

PANS = Partially Averaged Navier Stokeso The main advantage of PANS (and other scale adaptive methods) is that it

switches depending on resolution, and can converges to DNS in the

resolution limit.

o Where can one use this in its work?

It is an attractive feature since it means that one could have primarily

RANS for the most parts of the computation domain and spend the

resources on the more importance parts where he/she needs the structures

and more detailed simulation.


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PANS

Starting point: defining the mapping functions:

o Where u stands for unresolved

o Unresolved means those parts of fluctuation spectrum band that instead of solvinghave been averaged

o This mapping functions have been proposed for k-epsilon model. However, they

can be extended to other RANS models, e.g. K-Omega


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PANS

k

ik

t

ii

immP

x

k

xx

ku

t

k

Transport Equations for standard k-Epsilon model

uu

i

u

ku

u

ii

uimumP

x

k

xx

ku

t

k

Transport Equations for PANS k-Epsilon model

Sk

Ck

PCf

xxx

u

tu

u

u

uu

k

i

u

u

u

ii

uimum

2

*

21

Sk

CPCPk

Cxxx

u

t bki

t

ii

imm

2

231


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Turbulence model Cd Cd Error (%) Strouhal number St. Error (%)

kEpsilon 1.67 -20.5 0.1348 2.12

OEEVM (LES) 2.05 -2.4 0.1333 1

PANS 2.139 1.8 0.1293 -2.04

Reference Value (Exp.) 2.1 ----- 0.132 -----

Flow Over a Square Cylinder

U = 0.54 m/s with 2% turbulence

Re = 22 000

Size of the square cylinder is 0.04 m wide and 0.392 m high.

Its situated in a tunnel with a width of 14D = 0.56 m

Primitive Results


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Thank you


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Backup Slides


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Turbulence Models

kEpsilon


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Turbulence Models

kEpsilon


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Turbulence Models

PANS

based on kEpsilon RANS Model

By defining the mapping functions:


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General Governing Equations

1

1

n

i

i

0

i

imm

x

u

t

g

x

u

x

u

xx

P

x

uu

t

u

m

i

j

j

i

m

jij

jimim

lvvvmvvvm )1(,)1(

SSDt

D

x

uS

x

u

tl

vl

m

m

mi

i

i

ivv

1,

To simulate phase change rate, few models are available: Sauer, Kunz, Singhal, ...


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PANS Implementation in OpenFoam

Create the initial files from original kEpsilon turbulence model

o Open a new terminal

o Load openfoam

o Copy kEpsilon turbulence model to your directory

o Rename the folder and its files (kEpsilon.C and kEpsilon.H) to kEpsilonPANS

o Replace all of the kEpsilon words with kEpsilonPANS in .C and .H files

o Go to Make folder, and then into the files

Replace kEpsilon with kEpsilonPANS, and also libkEpsilon with

libkEpsilonPANS

Debug the model (wmake libso)


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PANS Implementation in kEpsilonPANS.C

In the Constructors part of kEpsilonPANS.C, and between definitions ofsigmaEps_ and k_, define the following parameters: fEpsilon, and fK

fEpsilon_

(

dimensioned::lookupOrAddToDict

("fEpsilon",

coeffDict_,

1.0

)

),

fK_

( dimensioned::lookupOrAddToDict

(

"fK",

coeffDict_,

0.2

)

),


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eBtween definitions of epsilon_ and nut_, define the fields of kU_ andepsilonU_

kU_

(IOobject

(

"kU",

runTime_.timeName(),

mesh_,

IOobject::NO_READ,

IOobject::AUTO_WRITE),

autoCreateK("kU", mesh_)

),

epsilonU_

(IOobject

(

"epsilonU",

runTime_.timeName(),

mesh_,

IOobject::NO_READ,

IOobject::AUTO_WRITE),

autoCreateEpsilon("epsilonU", mesh_)

),



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After printCoeffs() add the following command. So you can be sure duringsimulation that an appropriate turbulence model has been called

Info


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In the kEpsilonPANS::correct section, do the following

1- Add definitions of C2U parameters

2- replace epsilon and k with epsilonU and kU in the section related to

creating equations

const dimensionedScalar C2U = C1_ + (fK_/fEpsilon_) * (C2_ - C1_);

// Unresolved Turbulent kinetic energy equation

tmp kUEqn

(

fvm::ddt(kU_)

+ fvm::div(phi_, kU_)

- fvm::laplacian(DkUEff(), kU_)==

G

- fvm::Sp(epsilonU_*fK_/kU_, kU_)

);

kUEqn().relax();

solve(kUEqn);bound(kU_, fK_ * kMin_);



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// Update unresolved epsilon and G at the wall

epsilonU_.boundaryField().updateCoeffs();

// Unresolved Dissipation equation

tmp epsUEqn

(

fvm::ddt(epsilonU_)+ fvm::div(phi_, epsilonU_)

- fvm::laplacian(DepsilonUEff(), epsilonU_)

==

C1_*G*(epsilonU_)/(kU_)

+ fvm::Sp(C1_*(1-fK_)*(epsilonU_)/(kU_), epsilonU_)

- fvm::Sp(C2U*(epsilonU_)/(kU_), epsilonU_)

);

epsUEqn().relax();

epsUEqn().boundaryManipulate(epsilonU_.boundaryField());

solve(epsUEqn);

bound(epsilonU_, fEpsilon_ * epsilonMin_);



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Calculate k, and epsilon based on the kU, and epsilon

// Calculation of Turbulent kinetic energy and Dissipation rate

k_ = kU_/fK_;

epsilon_ = (epsilonU_)/(fEpsilon_);

// Re-calculate viscosity

nut_ = Cmu_*sqr(kU_)/epsilonU_;



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Calculate k, and epsilon based on the kU, and epsilon

// Calculation of Turbulent kinetic energy and Dissipation rate

k_ = kU_/fK_;

epsilon_ = (epsilonU_)/(fEpsilon_);

// Re-calculate viscosity

nut_ = Cmu_*sqr(kU_)/epsilonU_;



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Add definition of fEpsilon, and fK to protected data:model coefficients

Add definition of kU, and epsilonU to protected data:Fields

In the Member Function, add definition of kU and epsilonU fields

Define DkUEff, and DepsilonUEff fields

PANS Implementation in kEpsilonPANS.H

dimensionedScalar fEpsilon_;

dimensionedScalar fK_;

volScalarField kU_;volScalarField epsilonU_;

//- Return the unresolved turbulence kinetic energy

virtual tmp kU() const

{return kU_;

}

//- Return the unresolved turbulence kinetic energy

dissipation rate

virtual tmp epsilonU() const

{

return epsilonU_;}


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interphaschangefoam and pans

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