implementation of turbulent viscosity usin earsm -...

CFD with OpenSource Software 2015

Implementation of Turbulent Viscosity from EARSM for Two-Equation Turbulence Model

Thejeshwar Sadananda

Chalmers University of Technology

December 8, 2015

Order of Presentation

• Motivation

• Algebraic Reynolds stress model

• Explicit Algebraic Reynold stress model

• Solution of simplified ARSM for 3D mean flows

• Axially rotating turbulent pipe flow case setup

• Implementation of turbulent viscosity using EARSM in OpenFOAM 2.4.X.

• Run and post-process using paraview and sample utility

• Learning during the implementation

• Conclusion and Future work

2015-12-08 CFD WITH OPENSOURCE SOFTWARE, 2015 2

Motivation


• Standard two equation turbulence model are used in industrial flow computations

• It is roboust and takes less computational effort

• The Reynolds stress is computed based on the modellededdy viscosity

• Rotation part of the velocity gradient is not considered in computing the Reynolds stress

• Unable to accurately predict three dimensional flowfeatures

Algebraic Reynolds Stress Models

• ARSM is developed from the modelled Reynolds stress transport equation

• They have implicit relation between stress components and mean velocity gradient field

• ARSM includes the effect of rotational part of meanvelocity gradient tensor.

• The model considers the three dimensionality of the flow

• Need not model the production term


Explicit Algebraic Reynolds Stress Models

• Reynolds stress are explicitly related to the mean flow field

• It is numerically robust

• Negligible effect on the computational effort

• The Reynolds stress anisotropy term is expressed as

𝑎 = 𝛽1𝑺 + 𝛽2 𝑺2 −1

3𝐼𝐼𝑆𝑰 + 𝛽3 𝜴2 −

1

3𝐼𝐼Ω𝑰 + 𝛽4 𝑺𝜴 − 𝜴𝑺 +

𝛽5 𝑺2𝜴− 𝜴𝑺2 + 𝛽6 𝑺𝜴2 − 𝜴2𝑺 −2

3𝐼𝑉 𝑰 + 𝛽7 𝑺

2𝜴2 −


Solution of simplified ARSM for Three Dimensional

Mean Flow

𝛽1 = −𝑁 2𝑁2−7𝐼𝐼Ω

𝑄; 𝛽3 = −

12𝑁−1𝐼𝑉

𝑄; 𝛽4 = −

2 𝑁2−2𝐼𝐼Ω

𝑄;

𝛽6 = −6𝑁

𝑄; 𝛽9 =

6

𝑄; 𝜏 = 𝑚𝑎𝑥

𝑘

𝜀, 𝑐𝜏

𝜇

𝜌𝜀

𝑄 =5

6𝑁2 − 2𝐼𝐼Ω 2𝑁2 − 𝐼𝐼Ω ;

• Solution of Simplified ARSM two dimensional mean flow

𝑁 =

𝐶1′

3+ (𝑃1 + 𝑃2)

1 3+(𝑃1 − 𝑃2) 1 3

𝐶1′

3+ 2(𝑃1

2 − 𝑃2) 1 6cos

1

3cos−1

𝑃1

𝑃12− 𝑃2

, 𝑃2 ≥ 0

, 𝑃2< 0

𝑃1 =𝐶1

′2

27+

9

20𝐼𝐼𝑆 −

2

3𝐼𝐼𝛺 𝐶1

′; 𝑃2 = 𝑃12 −

𝐶1′2

9+

9

10𝐼𝐼𝑆 +

2

3𝐼𝐼𝛺

3


Case: Axially Rotating Turbulent Flow in a Pipe


• Boundaries• cyclicAMI patch type

• Mesh

• Boundary conditions• codedFixedValue

• turbulentIntensityKineticEnergyInlet

• kqRWallFunction

• turbulentMixingLengthFrequencyInlet

• omegaWallFunction

• k-ω Turbulence Model

• simpleFoam

side1

Side2

Wall

Inlet

Outlet

Implementation of Turbulent Viscosity in OpenFOAM 2.4.X.

𝜇𝑇 = −1

2𝛽1 + 𝐼𝐼Ω𝛽6 𝜌𝑘𝜏

cd $WM_PROJECT_DIR

• Copy the kOmega directory from src with the same directory structure

cp -r --parents src/turbulenceModels/incompressible/RAS/kOmega $WM_PROJECT_USER_DIR

cd $WM_PROJECT_USER_DIR/src/turbulenceModels/incompressible/RAS

mv kOmega/ earsmImpkOmega

•Create a new Make directory and include the below lines in to Make/files

mkdir Make

vi Make/files

earsmImpkOmega/earsmImpkOmega.C

LIB = $(FOAM_USER_LIBBIN)/libMyIncompressibleRASModels


Implementation of Turbulent Viscosity in OpenFOAM 2.4.X. •Create a new file Make/options and include the below links in the OpenSOURCE directory

vi Make/options

EXE_INC = \

-I$(LIB_SRC)/turbulenceModels \

-I$(LIB_SRC)/transportModels \

-I$(LIB_SRC)/finiteVolume/lnInclude \

-I$(LIB_SRC)/meshTools/lnInclude \

-I$(LIB_SRC)/turbulenceModels/incompressible/RAS/lnInclude \

-I$(LIB_SRC)/sampling/lnInclude

LIB_LIBS =

•Remove .dep file and rename the file name and the functions from kOmega to earsmImpkOmega

cd earsmImpkOmega; rm kOmega.dep

mv kOmega.C earsmImpkOmega.C; mv kOmega.H earsmImpkOmega.H

sed -i s/kOmega/earsmImpkOmega/g earsmImpkOmega.*



• Add the data members in the declaration file earsmImpkOmega.H

vi earsmImpkOmega.H

// Model Coefficients

dimensionedScalar c1_;

dimensionedScalar C1_;

dimensionedScalar cTau_;



•Add tau volScalarField before Reynolds stress tensor R() member function in the declaration file earsmImpkOmega.H//- Return the time scale

tmp<volScalarField> tau() const

{

return tmp<volScalarField>

(

new volScalarField

(

IOobject

(

"tau",

mesh_.time().timeName(),

mesh_

),

max(k_/epsilon(), cTau_*sqrt(nu()/epsilon()))

)

);

}


Implementation of Turbulent Viscosity in OpenFOAM 2.4.X. •Add invar2s volScalarField in the declaration file earsmImpkOmega.H

//- Return the invariant invar2stmp<volScalarField> invar2s() const{

return tmp<volScalarField>(

new volScalarField(

IOobject(

"invar2s",mesh_.time().timeName(),mesh_

),tr((tau()*(symm(fvc::grad(U_)))) & (tau()*symm(fvc::grad(U_))))

));

}


Implementation of Turbulent Viscosity in OpenFOAM 2.4.X. •Add invar2r volScalarField in the declaration file earsmImpkOmega.H

//- Return the invariant invar2rtmp<volScalarField> invar2r() const

{return tmp<volScalarField>(

new volScalarField(

IOobject(

"invar2r",mesh_.time().timeName(),mesh_

),tr((tau()*skew(fvc::grad(U_))) & (tau()*skew(fvc::grad(U_)))))

);}


Implementation of Turbulent Viscosity in OpenFOAM 2.4.X. •Add P1 volScalarField in the declaration file earsmImpkOmega.H

//- Return the coefficient P1tmp<volScalarField> P1() const


new volScalarField(

IOobject(

"P1",mesh_.time().timeName(),mesh_

),(sqr(C1_)/27 + (9/20)*invar2s() - (2/3)*invar2r())*C1_

));

}


Implementation of Turbulent Viscosity in OpenFOAM 2.4.X. •Add P2 volScalarField in the declaration file earsmImpkOmega.H

//- Return the coefficient P2tmp<volScalarField> P2() const


new volScalarField(

IOobject(

"P2",mesh_.time().timeName(),mesh_

),sqr(P1()) - pow((sqr(C1_)/9 + (9/10)*invar2s() + (2/3)*invar2r()),3)+SMALL)

);}


Implementation of Turbulent Viscosity in OpenFOAM 2.4.X. •Add N volScalarField in the declaration file earsmImpkOmega.H

//- Return the coefficient Ntmp<volScalarField> N() const


new volScalarField(

IOobject(

"N",mesh_.time().timeName(),mesh_

),C1_/3 + pow((P1() + sqrt(P2())),(1/3)) + pow((P1() - sqrt(P2())),(1/3))

));

}


Implementation of Turbulent Viscosity in OpenFOAM 2.4.X. •Add Q volScalarField in the declaration file earsmImpkOmega.H

//- Return the coefficient Qtmp<volScalarField> Q() const


new volScalarField(

IOobject(

"Q",mesh_.time().timeName(),mesh_

),(5/6)*(sqr(N()) - 2*invar2r())*(2*sqr(N()) - invar2r())+SMALL)

);}


Implementation of Turbulent Viscosity in OpenFOAM 2.4.X. •Add beta1 volScalarField in the declaration file earsmImpkOmega.H

//- Return the coefficient beta1tmp<volScalarField> beta1() const


new volScalarField(

IOobject(

"beta1",mesh_.time().timeName(),mesh_

),-N()*(2*sqr(N())-7*invar2r())/Q())

);}


Implementation of Turbulent Viscosity in OpenFOAM 2.4.X. •Add beta6 volScalarField in the declaration file earsmImpkOmega.H

//- Return the coefficient beta6tmp<volScalarField> beta6() const


new volScalarField(

IOobject(

"beta6",mesh_.time().timeName(),mesh_

),-(6*N())/Q())

);}



•Add the data members in the source file earsmImpkOmega.C before k_

vi earsmImpkOmega.C

c1_(

dimensioned<scalar>::lookupOrAddToDict(

"c1",coeffDict_,1.8

)),C1_(


"C1",coeffDict_,1.8

)),



•Add the data member in the source file earsmImpkOmega.C before k_

cTau_(


"cTau",coeffDict_,6.0

)),

• Replace the effective turbulent viscosity at two locations in earsmImpkOmega.C

//nut_=k_/omega_;

nut_ = -(1/2)*k_*tau()*(beta1()+beta6()*invar2r());

wmake libso



$FOAM_RUN

•copy the case from PingPong and extract it in your home directory

tar -xf testCaseEarsm.tar.gz

rm testCaseEarsm.tar.gz

cd testCaseEarsm

•Change the turbulence model in RASProperties dictionary to

RASModel earsmImpkOmega

• Include the dynamic library in controlDict file

"libMyIncompressibleRASModels.so" // under libs();


Implementation of Turbulent Viscosity in OpenFOAM 2.4.X. • Add the following to the controlDict to find the average and RMS velocity

functions

(

fieldAverage1

{

type fieldAverage;

functionObjectLibs ("libfieldFunctionObjects.so");

enabled true;

outputControl outputTime;

fields

(

U

{

mean on;

prime2Mean on; //RMS

base time;

}

);

}

);


Implementation of Turbulent Viscosity in OpenFOAM 2.4.X. •Copy and modify the sampleDict dictionary from the tutorials directory to sample the line

cp $FOAM_TUTORIALS/compressible/sonicFoam/laminar/shockTube/system/sampleDict ./system/.

//- sampleDict

interpolationScheme cellPoint;

setFormat xmgr;

sets

(

line

{

type face;

axis z;

start ( 0.5 0 0 );

end ( 0.5 0 0.05 );

nPoints 10;

}

);

fields (Ux Uy Uz U UMean UPrime2Mean);



•Mesh the computational domain and run simpleFoam solver

blockMesh

simpleFoam

•Post-process the results using paraFoam and sample Utility

paraFoam

foamCalc components U

sample -case testCaseEarsm

xmgrace testCaseEarsm/postProcessing/sets/xx/line_U_Umean.agr //replace xx with time directory


Post-Processing using paraview


Figure: Velocity Contour(no convergence in the Solution)

Post-Processing using Sample Utility


Figure: Velocity Profile of the inlet and Mean velocity

Learning during the implementation

• The data members using IOobject class has to be placed in the source (.C) file in the same order of declaration in .H file.

• It is not possible to compute volScalarField if the computed value arisesto be a complex number or a negative number

• The dimension set of the functions used for computing volScalarFieldshould match

• When the conditional statements are used in theIOobject class, a temporary dimensioned scalar has to be introduced to accept the value.

• The truncation error can be rectified by adding a very small value to the computed volScalarField

• Implement the source code in small steps in an thereby easy to identify and debug errors


Conclusion andFuture Work

• Effective turbulent viscosity from EARSM is implementedfor two equation turbulence model

• Tested the rotating pipe flow case using the implementedmodel

Improvement

• Include the anisotropy term in the production and turbulent diffusion term to implement EARSM completely

• Use perturbed solution of three dimensional equation of N in computing anisotropy term.


Thank You

implementation of turbulent viscosity usin earsm -...

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