Validation of homogeneous turbulence with constant shear for RANS models

GeorgS · August 24, 2018, 02:46

Hello,
i want to validate RANS models for homogeneous turbulence with constant shear. I share my case in the appendix. Simply modify the case settings and run the "./Allrun" script with OF5.X. The result is plotted into the "hit.eps" file on the "tmp" line. The target validation data is from the SSG models original publication.
NOTE: blockMesh must be run before, if modified.

Here a description:
I have created a 1 Cell sized mesh with cylic BCs to the sides and fixed velocities to impose the shear rate. Since all gradients vanish and so is the time dependency of mean U, the initial value of U is set the the mean of the imposed fixed veloceties at the boundaries. PimpleFoam is used and for solving; and the all different solvers for U,R,epsilon,p (PCG etc.) already tried out. Moreover, i have used a modified solver and turbulence model, where i have removed all gradient terms to ensure these terms are zero, same results here aswell. Also, the ddtSchemes Euler and CrankNicolson give the same.

I have also tried out other models, such as kOmegaSST and kEpsilon, which give the same (but the different to the ones shown in the figure) results, which is quite reasonable since kOmegaSST switches to full kEpsilon in homogeneous turbulence.
Note: chaning the BCs from cylic to zeroGradient gives the same results.

I hope someone can give me a little hint, i guess it is somewhere in the setup and hopefully quite easy to be solved.

Cheers, Georg

CASE: https://ufile.io/g4mdb

GeorgS · August 30, 2018, 12:08

To be more clear with the case description, the velocity gradients are uniform and contribute to the production of second moments. The mean velocity gradients are given with:
$\frac{\partial\overline{U_i}}{\partial x_j}= \begin{bmatrix} 0 & S & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$
Moreover, the equation of state for the TKE is given with:
$\frac{dk}{dt} = \underbrace{-\overline{u_{i} u_{j}}\frac{\partial\overline{U_j}}{\partial x_i}}_{P} + \underbrace{\nu \overline{u_j\nabla^2 u_i}}_{-\epsilon}$
In the case of the SSG model, the Production term is exact and the dissipation is constrained to be isotropic and modelled via an additional equation.
The whole case, however, should only depend on the choice of S, initial k and initial epsilon.
To ensure that the turbulence model is fed with the right velocity gradient tensor, i even hardcoded S = 1

Code:

    volTensorField tgradU
    (
    IOobject
    (
        "tgradU",
        this->runTime_.timeName(),
        this->mesh_,
        IOobject::NO_READ,
        IOobject::AUTO_WRITE
    ),
    this->mesh_,
    dimensionedTensor("default",dimensionSet(0, 0, -1, 0, 0),tensor(0,1,0,0,0,0,0,0,0))
    );

right into the turbulence model, which replaces the computed velocity fields gradient tensor. But, as aspected gives the same results as shown in the first post.

NOTE: I noticed that the SSG models implementation in version 5.X uses the wrong value for the model constant $C_{\epsilon2}=1.92$ , instead it should be $C_{\epsilon2}=1.83$ , according the models reference.

GeorgS · August 30, 2018, 15:11

SOLVED

Okay, the error was somewhat easy. The Reynolds stress tensors initial condition has to be purely diagonal, hence all off diagonal components are set to zero. Using the postpressing tool "R" computes the Reynolds stresses from k, which is what i used for computing k=0.5*tr(R). However, the tool "R" produces an off diagonal component which is the wrong initial condition for this case.
Moreover, i have added dependency of system rotation the the SSG model, where the magnitude of rotation is Omega. The results are given in the appended figure. Results shown with C_eps_2=1.83, for one ratio of Omega/S even with the old value of C_eps_2=1.92. Still, the results do not match the reference, but are kind of good. The error might be related to differing constants which i havent found yet.

August 30, 2018, 12:08		#2
GeorgS New Member Georg Join Date: Jun 2018 Posts: 7 Rep Power: 7	To be more clear with the case description, the velocity gradients are uniform and contribute to the production of second moments. The mean velocity gradients are given with: $\frac{\partial\overline{U_i}}{\partial x_j}= \begin{bmatrix} 0 & S & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$ Moreover, the equation of state for the TKE is given with: $\frac{dk}{dt} = \underbrace{-\overline{u_{i} u_{j}}\frac{\partial\overline{U_j}}{\partial x_i}}_{P} + \underbrace{\nu \overline{u_j\nabla^2 u_i}}_{-\epsilon}$ In the case of the SSG model, the Production term is exact and the dissipation is constrained to be isotropic and modelled via an additional equation. The whole case, however, should only depend on the choice of S, initial k and initial epsilon. To ensure that the turbulence model is fed with the right velocity gradient tensor, i even hardcoded S = 1 Code: volTensorField tgradU ( IOobject ( "tgradU", this->runTime_.timeName(), this->mesh_, IOobject::NO_READ, IOobject::AUTO_WRITE ), this->mesh_, dimensionedTensor("default",dimensionSet(0, 0, -1, 0, 0),tensor(0,1,0,0,0,0,0,0,0)) ); right into the turbulence model, which replaces the computed velocity fields gradient tensor. But, as aspected gives the same results as shown in the first post. NOTE: I noticed that the SSG models implementation in version 5.X uses the wrong value for the model constant $C_{\epsilon2}=1.92$ , instead it should be $C_{\epsilon2}=1.83$ , according the models reference.

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