[david112]

Dear Foamers,

for my masterthesis I tried to change the pimpleFoam solver to make the temporal boudary-layer development comperable to the spartial.

As base I used the ideas which MAEDER, ADAMS and KLEISER used for their DNS computation called ETDNS and appled them in LES. They compute seperated blocks of the boundary layer (principleOfETDNS). With the help of forcing terms the solution in a block reaches a steady-state. The forcing terms are defined by the downstream history of the flow with the help of the previous computed blocks (principleOfETDNS.png).

I added the forcing terms to the momentun equation (equations.png). To start simple I chose only the incomplessible and laminar part of the forcing terms without a pressure gradient in the boundary layer (forcingTerm.png).
By choosing equidistant block spacing xi_(n+1) - xi_n = xi_n - xi_(n-1) the second oder backward differnce formula (A8 in forcingTerm.png) becomes => 2ndOrdeBackward.png.

Now the UEqn.H file in the clone of pimpleFoam looks like:

// Solve the Momentum equation

MRF.correctBoundaryVelocity(U);



tmp<fvVectorMatrix> tUEqn
(
    fvm::ddt(U) + fvm::div(phi, U)
  + MRF.DDt(U)
  + turbulence->divDevReff(U)
// first additional term for the laminar flow stabilisation
  + (3*U.component(vector::X) * U - 4*Ul1.component(vector::X) * Ul1 + Ul2.component(vector::X) * Ul2) / (2*dxi)  
// end of the first additinal term
 ==
    fvOptions(U)
);
fvVectorMatrix& UEqn = tUEqn.ref();

UEqn.relax();

fvOptions.constrain(UEqn);

if (pimple.momentumPredictor())
{
    solve(UEqn == -fvc::grad(p));

    fvOptions.correct(U);
}

In the createFields.H file I added the Fields for dxi (the blockdistance in the streamswise coordinate xi), Ul1 and Ul2 which were the velocityfields of the 2 previous Blocks.

I am sorry that I am not able to upload the whole paper about the ETDNS because auf the file size limit. If you are interested and think the whole paper will help you to understand what I am working on just write me an email: david.kinast@gmx.de

The case setup and the results I present in the next post.

[david112]

Hello agian,

for the laminar case a simple rectangular 2D-domain is simulated with cyclic inlet and outlet conditions. A noSlip condition is used at the wall and on the top boundary it is zeroGradient for the velocity and fixedValue=0 for pressure.

The initial conditions for the first block the upstream history velocities Ul1 and Ul2 were taken from a RANS solution. Ul1 is also used for the initial condition of U.
The Freestream velocity is 1m/s. And I computed 10 blocks between x=0.2m and x=1.2m.

If someone wants to check out the case I appended the case of epsilon=4 (epsilon4.tar.gz). With OpenFoam4.1 on Ubuntu 16.04 the temporalTransitionScript file shoud run the case. I used the ppcfTemporal.m file in GNUOctave 4.0.0 for postprocessing.

But now the cool part: the results! I tried different blockdistances and different values for epsilon (the scaling between x and the slow streamwise coordinate xi). Surprisingly I got good results with an epsilon=4 (dx0.1.png and dx0.05.png). But the paper says 0<epsilon<<1 (previous post forcingTerm.png line 1).

And now finally my question: Has anyone an idea what I am doing wrong? Or any experience with related cases?

I noticed that in the paper they use the normalized version of the Navier-Stokes-Equations and OpenFoam deals with dimensions. But can that cause a problem when my freestream velocity is 1m/s and the resolved area is 1m? The normalization wouln't change anything, would it?

Hoping for any help, ideas or comments I whish you a nice day and good convergence in any simulations !