implementation of partially slip boundary conditionshani/kurser/os_cfd_2017/... · 2017. 12....

Background Slip models CFD Background Background Navier slip Model- Explicit formulation Navier slip Model- Explicit formulation Navier slip Model- Explicit formulation Navier slip Model- Explicit formulation Navier slip Model- Explicit formulation Navier slip Model- Explicit formulation Hatzikriakos slip Model- Explicit formulation Hatzikriakos slip Model- Explicit formulation Hatzikriakos slip Model- Explicit formulation Asymtotic slip Model- Explicit formulation Asymtotic slip Model- Explicit formulation Asymtotic slip Model- Explicit formulation Semi implicit Semi implicit Semi implicit Semi implicit Semi implicit Semi implicit Semi implicit Semi implicit Semi implicit Semi implicit Semi implicit Semi implicit Semi implicit Semi implicit Semi implicit Semi implicit Semi implicit Semi implicit Solving Verifying verifying verifying

Implementation of partially slip boundary conditions

Madhavan Vasudevan

Department of Applied Mechanics,Chalmers University of Technology,

Gothenburg, Sweden

22 Nov 2017

Madhavan Vasudevan Partially slip Boundary Conditions 22 Nov 2017 1 / 40


Partially Slip Boundary Conditions

High Knudsen Number Flows ( Rarefied flows and micro-nano channelflows)

Also in practical industrial applications - polymer extrusion

Analytical solutions exist based on simple Assumptions and complexrheology

CFD modelling of the same is of prime interest



Solution available to implement CFD

Poisuelle flow is assumed

Three major non-linear slip models are available

Navier slip model

uws = knl(µ(γ̇)du

dy)m

Hatzikiriakos slip model

uws = kh1sinh(−kh2µ(γ̇)du

dy)

Asymtotic slip law

uws = ka1log(1 − ka2µ(γ̇)du

dy)

These equations are referred to as transcendental equations from nowMadhavan Vasudevan Partially slip Boundary Conditions 22 Nov 2017 3 / 40


Building Blocks for CFD implementations

Explicit formulations- calculates from previous time step: more stable andneeds relaxation

(φ)n+1 = (φ)n + ∆t(dφ

dt)n

Implicit formulations- calculates from current iteration: less stable and norelxation

(φ)n+1 = (φ)n + ∆t(dφ

dt)n+1

We also employ a novel SIMPLE-Semi Implicit formulation

explicit, implicit and semi-implicit refer to the gradient term in thetranscendental equations



Strategy Deployed

The code provided for the Navier explicit formulation is studied

Explicit formulations of Asymtotic and Hatzikiriakos are developed

Implement Semi-implicit formulation of Navier slip model

Extend the semi-implicit formulation for Hatzikiriakos and Asymtotic



Navier slip Model- Explicit formulation

Figure: Directory structure for explicit Navier slip

options file shows the header files, libraries included for the compilation ofthe boundary condition: This remains the same for all models and bothformulations (semi-implicit and explicit)

files file shows the location where the boundary condition is appended alibrary for the cases to utilize it (This has to be particularly changed for all)



Navier slip Model- Explicit formulation- Member functions explained

line 134-139: used to update the wall slip velocity vectorField after eachiteration.

line 142 : this is a pointer. nf() refers to the normal vector. patch () refersto the boundary patch to which the boundary condition is being applied.

line 145: The gradient of the velocity is obtained for the previous iterationusing the same pointer ’this’ and the function snGrad(). could check itthis way in the member function.

// check grad

vectorField check_grad = (*this - pif )*this->patch().deltaCoeffs();

Info


Navier slip Model- Explicit formulation- Member functions explained

line 156: the patch is indexed

line 159-178: The dynamic viscosity is computed using the releantturbulence model. Since the mean flow is very Small in our case, it isideally chosen as a laminar model (described in ’case set up’)

line178: the value of the wall slip velocity is computed according to thetranscendental equation

line 184: As mentioned earlier, explicit methodologies are highly stable butsolutions could diverge. So relaxation of solution is performed for ensuringconvergence.



Navier slip Model- Explicit formulation- constructors explained

line 30: include the fvPatchFields class definitions

line 31 include the fixedValueFvPatchFields class definitions

line 32: include the transformFvPatchFields class definitions. This class isespecially used to compute the tangential components of the gradients ofvelocities from all the components included.

line 43: The nonLinNavSlipGenNewtonianRelaxationFvPatchVectorFieldclassbelongs to the base class namespace Foam.

line 45: The nonLinNavSlipGenNewtonianRelaxationFvPatchVectorFieldclass is publicly derived through the fixedValueFvPatchVectorField class



Navier slip Model- Explicit formulation- constructors explained

line 49-59: The member data of the class are constructed. These are thedensity, n (constant used for slip velocity calculations), slipFactor(constant used for the calculation of slip velocity) and the relaxationfactor(this is done for the explicit solver as explicit solving requires relaxation).All these member data that are initialized are private member data. Thiscould be realized with the help of the trailing underscores, which is theOpenFOAM standard.

line 64: The typeName is defined. This is the name of the class itself.This is the name by which the boundary condition class is identified fromthe set up case file.

lines 70-74 The constructor is used to initialize when the boundarycondition is set by the boundary patch properties and the internal field



Navier slip Model- Explicit formulation- constructos explained

lines 77-82 The constructor is used to initialize the member data when theboundary condition is set by the U file in the 0 directory in the case set up.The definition of the constructors could be seen in the Main file where thecorresponding keyword searched for the particular member data is defined.

lines 86-92: The construction through mapping

lines 95-98: Initialization of the copy constructor is done

lines 101-120: Initialization through other constructors

lines from 132: All the member data are by default initialized as privatemember data of the class. The member functions need to have haveaccess to their values and access change their values and hence thesemember data are returned.



Modifications to Hatzikiriakos

Directory Structure for Hatzikiriakos Explicit formulation

Figure: Directory structure for explicit hatzikiriakos slip

to set up the boundary condition: change the necessary member data,transcendental equation and the files file in the Make directory

--cp -r navier hatzikiriakos

--cd hatzikiriakos/

--mv myNLSlipGenNewtonianRelaxationV2/ myhatziSlipGenNewtonianRelaxationV2/

--cd myhatziSlipGenNewtonianRelaxationV2/

--OF22x

--wcleanMadhavan Vasudevan Partially slip Boundary Conditions 22 Nov 2017 12 / 40


Modifications to Hatzikiriakos - Explicit formulations

--cd Make/

--sed -i ’s/nonLinNavSlipGenNewtonianRelaxationFvPatchField.C/

hatziSlipGenNewtonianRelaxationFvPatchField.C/g’ files

--sed -i ’s/libmyNonLinNavSlipGenNewtonianRelaxation/

libmyhatziSlipGenNewtonianRelaxation/g’ files

--cd ..

--mv nonLinNavSlipGenNewtonianRelaxationFvPatchField.C

hatziSlipGenNewtonianRelaxationFvPatchField.C

--mv nonLinNavSlipGenNewtonianRelaxationFvPatchField.H

hatziSlipGenNewtonianRelaxationFvPatchField.H

--sed -i ’s/nonLinNavSlipGenNewtonianRelaxationFvPatchVectorField/

hatziSlipGenNewtonianRelaxationFvPatchVectorField/g’

hatziSlipGenNewtonianRelaxationFvPatchField.C


hatziSlipGenNewtonianRelaxationFvPatchVectorField/g’

hatziSlipGenNewtonianRelaxationFvPatchField.H

--vim hatziSlipGenNewtonianRelaxationFvPatchField.C

-- manually change the header file name

:wq!

-- manually chnage the name of the data members from slipFactor to kh1

-- manually change the name of the data members from n to kh2



substitute the Hatzikiriakos transcendental equation instead of the NavierTranscendental equation

vectorField u_wallslip = kh1_*(Foam::sinh(- kh2_*nuw*mag(gradient)))*

gradientDirection;

This also brings the necessity that the case files are supposed to be alteredto be looked up for the correct arguments expected here.



Modifications to Asymtotic- Explicit formulations

The Directory Structure for the Asymtotic Explicit formulation

Figure: Directory structure for explicit Asymtotic slip

--cp -r hatzikiriakos Asymtotic

--cd Asymtotic/

--mv myhatziSlipGenNewtonianRelaxationV2/ myasymSlipGenNewtonianRelaxationV2/

--cd myasymSlipGenNewtonianRelaxationV2/

--OF22x

--wclean

--cd Make/




--sed -i ’s/hatziSlipGenNewtonianRelaxationFvPatchField.C/

asymSlipGenNewtonianRelaxationFvPatchField.C/g’ files

--sed -i ’s/libmyhatziSlipGenNewtonianRelaxation/

libmyasymSlipGenNewtonianRelaxation/g’ files

--cd ..

--mv hatziSlipGenNewtonianRelaxationFvPatchField.C

asymSlipGenNewtonianRelaxationFvPatchField.C

--mv hatziSlipGenNewtonianRelaxationFvPatchField.H

asymSlipGenNewtonianRelaxationFvPatchField.H

--sed -i ’s/hatziSlipGenNewtonianRelaxationFvPatchVectorField/

asymSlipGenNewtonianRelaxationFvPatchVectorField/g’

asymSlipGenNewtonianRelaxationFvPatchField.C

--sed -i ’s/hatziSlipGenNewtonianRelaxationFvPatchVectorField/

asymSlipGenNewtonianRelaxationFvPatchVectorField/g’

asymSlipGenNewtonianRelaxationFvPatchField.H




sed -i ’s/kh1/ka1/g’ asymSlipGenNewtonianRelaxationFvPatchField.H

sed -i ’s/kh2/ka2/g’ asymSlipGenNewtonianRelaxationFvPatchField.H

sed -i ’s/kh1/ka1/g’ asymSlipGenNewtonianRelaxationFvPatchField.C

sed -i ’s/kh2/ka2/g’ asymSlipGenNewtonianRelaxationFvPatchField.C

vim asymSlipGenNewtonianRelaxationFvPatchField.C

----- manually change the header file name

:wq!

vim asymSlipGenNewtonianRelaxationFvPatchField.H

----- manually change the boundary condition name

:wq!

Again as in the case of Hatzikiriakos law, the U file in the case has to bealtered so that it gives the expected lookup variable for the member datainitialization



Semi-implicit formulations

No relaxation is required for this formulation

Consider the wall slip velocity from the current iteration

Consider the cell center velocity from the previous iteration

The explicit definition of snGrad() becomes useful here

Cannot apply boundary condition for the boundary patch at once

Bisection Method is used to solve the transcendental equation numerically

The Boolean might be satisfied on some faces and not on some other faces



Verify looping over the faces

forAll(cPatch,faceI)

{

vector nHat_face = nHat[faceI];

//Info


Navier slip - Semi-implicit formulations

The Directory structure of the Semi implicit Navier slip formulation

Figure: Directory structure for semi implicit navier slip

Note that the boundary condition class needs the same data members asthe explicit Navier slip boundary condition

procedure to set up the boundary condition

cp -r navier navier_semi

cd navier_semi/

mv myNLSlipGenNewtonianRelaxationV2 myNLSlipGenNewtoniansemiV2

cd myNLSlipGenNewtoniansemiV2/

wcleanMadhavan Vasudevan Partially slip Boundary Conditions 22 Nov 2017 20 / 40


cd Make/

--sed -i ’s/nonLinNavSlipGenNewtonianRelaxationFvPatchField.C/

nonLinNavSlipGenNewtoniansemiFvPatchField.C/g’ files

--sed -i ’s/libmyNonLinNavSlipGenNewtonianRelaxation/

libmyNonLinNavSlipGenNewtoniansemi/g’ files

--cd ..

--mv nonLinNavSlipGenNewtonianRelaxationFvPatchField.C

nonLinNavSlipGenNewtoniansemiFvPatchField.C

--mv nonLinNavSlipGenNewtonianRelaxationFvPatchField.H

nonLinNavSlipGenNewtoniansemiFvPatchField.H


nonLinNavSlipGenNewtoniansemiFvPatchVectorField/g’

nonLinNavSlipGenNewtoniansemiFvPatchField.C


nonLinNavSlipGenNewtoniansemiFvPatchVectorField/g’

nonLinNavSlipGenNewtoniansemiFvPatchField.H

--vim nonLinNavSlipGenNewtoniansemiFvPatchField.C

-- manually change the header file name

--:wq!

--vim nonLinNavSlipGenNewtoniansemiFvPatchField.H

-- manually change the name of the boundary condition class

:wq!



following member function has to be replaced

void nonLinNavSlipGenNewtoniansemiFvPatchVectorField::updateCoeffs()

{

if (updated())

{

return;

}

// obatin the viscosity

const label patchI = patch().index();

scalarField nuw = 1e-6*mag(patch().nf());

if (db().found("turbulenceModel"))

{

const incompressible::turbulenceModel& turbModel =

db().lookupObject

(

"turbulenceModel"

);

//Info



else

{

nuw = mag(patch().nf());

//Info



vectorField gradientDirection = gradient / (mag(gradient) + SMALL);

// obtain 1/del_y for the patch

scalarField invdelypatch = this->patch().deltaCoeffs();

//Info



forAll(cPatch,facei)

{

//obtain the nuw for the face from the patch

scalar nuw_face = nuw[facei];

//getting the 1/del_y for the individual face

scalar invdely = invdelypatch[facei];

//gradient of velocity in cell in previous iteration

vector gradient_prev_face = gradient1[facei];

//obtain the normal for the face

vector nHat_face = nHat[facei];

//gradient of velocty in the prev iteration---- only tangential

gradient_prev_face = transform(I -sqr(nHat_face),gradient_prev_face);

//initialise the guess limits for the bisection method

vector a(0,0,0);

vector b = pif[facei];

//introduce the guess function

vector guess_value = 0.5*(a+b);

//Info



vector guess_value = 0.5*(a+b);

//Info



pif_face = pif[facei];

gradient_face = (guess_value - pif_face)*invdely;

//obtain the normal for the face

nHat_face = nHat[facei];

//obtaining only the tangential components of the gradient

gradient_face = transform(I -sqr(nHat_face),gradient_face);

gradient_cellDirection = gradient_face / (mag(gradient_face) + SMALL);

//Info



}

vector u_wallslip_face = guess_value;

//tan_uws_func =mag(u_wallslip_cell.component(0));

//Info



void nonLinNavSlipGenNewtoniansemiFvPatchVectorField::write(Ostream& os) const

{

fvPatchVectorField::write(os);

os.writeKeyword("rho")


Hatzikiriakos slip - Semi-implicit formulations

The Directory structure of the Semi implicit Navier slip formulation

Figure: Directory structure for semi implicit Hatzikriakos slip

Note that the boundary condition class needs the same data members asthe explicit Hatzikiriakos slip boundary condition


cp -r hatzikiriakos hatzikiriakos_semi

cd hatzikiriakos_semi

mv myhatziSlipGenNewtonianRelaxationV2/ myhatziSlipGenNewtoniansemiV2/

cd myhatziSlipGenNewtoniansemiV2/

OF22x



--mv hatziSlipGenNewtonianRelaxationFvPatchField.C

hatziSlipGenNewtoniansemiFvPatchField.C

--mv hatziSlipGenNewtonianRelaxationFvPatchField.H

hatziSlipGenNewtoniansemiFvPatchField.H


hatziSlipGenNewtoniansemiFvPatchVectorField/g’

hatziSlipGenNewtoniansemiFvPatchField.C


hatziSlipGenNewtoniansemiFvPatchVectorField/g’

hatziSlipGenNewtoniansemiFvPatchField.H

vim hatziSlipGenNewtoniansemiFvPatchField.C

replace manually-- #include "hatziSlipGenNewtonianRelaxationFvPatchField.H"

by #include "hatziSlipGenNewtoniansemiFvPatchField.H"

:wq!

cd Make/

--sed -i ’s/hatziSlipGenNewtonianRelaxationFvPatchField.C/

hatziSlipGenNewtoniansemiFvPatchField.C/g’ files



--sed -i ’s/libmyhatziSlipGenNewtonianRelaxation/

libmyhatziSlipGenNewtoniansemi/g’ files

cd ..

Change the name of the boundary condition class name in the header file

wmake libso

Change the Transcendental equation

wmake libso



Asymtotic slip - Semi-implicit formulations

The Directory structure of the Semi implicit Asymtotic slip formulation

Figure: Directory structure for semi implicit Asymtotic slip

Note that the boundary condition class needs the same data members asthe explicit Asymtotic slip boundary condition


cp -r Asymtotic Asymtotic_semi

cd Asymtotic_semi

mv asymSlipGenNewtonianRelaxationV2/

myasymSlipGenNewtoniansemiV2/Madhavan Vasudevan Partially slip Boundary Conditions 22 Nov 2017 33 / 40


cd myasymSlipGenNewtoniansemiV2/

mv asymSlipGenNewtonianRelaxationFvPatchField.C

asymSlipGenNewtoniansemiFvPatchField.C

--mv asymSlipGenNewtonianRelaxationFvPatchField.H

asymSlipGenNewtoniansemiFvPatchField.H

--sed -i ’s/asymSlipGenNewtonianRelaxationFvPatchVectorField/

asymSlipGenNewtoniansemiFvPatchVectorField/g’

asymSlipGenNewtoniansemiFvPatchField.C

--sed -i ’s/asymSlipGenNewtonianRelaxationFvPatchVectorField/

asymSlipGenNewtoniansemiFvPatchVectorField/g’

asymSlipGenNewtoniansemiFvPatchField.H

vim asymSlipGenNewtoniansemiFvPatchField.C

replace manually-- #include "asymSlipGenNewtonianRelaxationFvPatchField.H"

by #include "asymSlipGenNewtoniansemiFvPatchField.H"

:wq!

cd Make/



--sed -i ’s/asymSlipGenNewtonianRelaxationFvPatchField.C/

asymSlipGenNewtoniansemiFvPatchField.C/g’ files

--sed -i ’s/libmyasymSlipGenNewtonianRelaxation/

libmyasymSlipGenNewtoniansemi/g’ files

cd ..

wmake libso

Change the Transcendental equation

wmake libso



Setting up the case

OF22x

cp -r /chalmers/sw/unsup64/OpenFOAM/OpenFOAM-2.2.x/tutorials/incompressible/simpleFoam/pitzDaily .

mv pitzDaily slipFlow

cd slipFlow

laminar in RASModels, switch off turbulence and printCoeffs

only µ is retained with 2e-6 in transportProperties

From this case, all the turbulent properties are neglected

The modifications to the respective files could be seen from the individualfiles attached

compile the code with simpleFoam command



Results



Questions?Thank You


BackgroundSlip modelsCFD BackgroundBackgroundNavier slip Model- Explicit formulationNavier slip Model- Explicit formulationNavier slip Model- Explicit formulationNavier slip Model- Explicit formulationNavier slip Model- Explicit formulationNavier slip Model- Explicit formulationHatzikriakos slip Model- Explicit formulationHatzikriakos slip Model- Explicit formulationHatzikriakos slip Model- Explicit formulationAsymtotic slip Model- Explicit formulationAsymtotic slip Model- Explicit formulationAsymtotic slip Model- Explicit formulationSemi implicitSemi implicitSemi implicitSemi implicitSemi implicitSemi implicitSemi implicitSemi implicitSemi implicitSemi implicitSemi implicitSemi implicitSemi implicitSemi implicitSemi implicitSemi implicitSemi implicitSemi implicitSolvingVerifyingverifyingverifying

implementation of partially slip boundary conditionshani/kurser/os_cfd_2017/... · 2017. 12....

Documents