SALSA turbulence models for OpenFOAM

Implementation of the strain-adaptive linear Spalart-Allmaras (SALSA) turbulence model in OpenFOAM. The repository provides:

• SpalartAllmarasSALSA: the RANS model.
• SpalartAllmarasSALSADDES: a conservative DDES model using SALSA as the RANS baseline.
• SpalartAllmarasQCR2020: the standard SA RANS model with the QCR2020 nonlinear stress relation.
• SpalartAllmarasComp: standard SA with the mixing-layer compressibility correction.
• SpalartAllmarasCompQCR2020: SA-comp with the QCR2020 nonlinear stress relation.
• SpalartAllmarasDDESQCR2020: the standard SA-DDES model with the QCR2020 nonlinear stress relation.

The repositories of TUFRG and mAlletto were used as template for the structure of this implementation.

Installation

To compile the SALSA turbulence models, execute:

./Allwmake

Once compiled, you should see libSASALSAIncompressibleTurbulenceModel.so and libSASALSACompressibleTurbulenceModel.so in $FOAM_USER_LIBBIN.

To remove the compiled model libraries and build files, execute:

./Allwclean

Setting up a case

To run a simulation with one of the SALSA models, first add the corresponding library to the controlDict. For compressible solvers:

libs    ("libSASALSACompressibleTurbulenceModel.so");

For incompressible solvers:

libs    ("libSASALSAIncompressibleTurbulenceModel.so");

RANS model

Choose the RANS model in constant/turbulenceProperties:

simulationType  RAS;

RAS
{
    RASModel            SpalartAllmarasSALSA;
    turbulence          on;
    printCoeffs         on;
}

There are three optional parameters: rhoInf, useRmod, and useSmod.

RAS
{
    RASModel            SpalartAllmarasSALSA;
    turbulence          on;
    printCoeffs         on;

    rhoInf              0.957837;   // required for useRmod = true
    useRmod             true;       // Edward's modification
    useSmod             true;       // strain rate instead of vorticity for Stilda
}

The parameter rhoInf denotes the free-stream density $\rho_\infty$ and is only required for useRmod true. The parameter useRmod activates Edwards' modification, and useSmod sets Stilda to be the strain rate instead of the vorticity. Setting both parameters to true results in the original SALSA turbulence model, linked in the references below.

Note on the diffusion coefficient: the $\tilde{\nu}$ transport equation uses the standard SA diffusivity $(\tilde{\nu} + \nu)/\sigma_{\nu_t}$, consistent with OpenFOAM's standard SA model. The original SALSA formulation writes the diffusion coefficient as $\nu + \tilde{\nu}/\sigma_{\nu_t}$ instead; this implementation deliberately retains the standard SA form. The influence was tested, the SALSA formulation leads to a smaller buffet amplitude and higher mean $c_L$ along with a slightly higher buffet frequency.

To use the standard Spalart-Allmaras QCR2020 model, select SpalartAllmarasQCR2020. This model is independent of SALSA and uses the standard OpenFOAM SA transport equation with the QCR2020 nonlinear constitutive stress relation.

RAS
{
    RASModel            SpalartAllmarasQCR2020;
    turbulence          on;
    printCoeffs         on;

    SpalartAllmarasQCR2020Coeffs
    {
        // QCR2020 defaults from Rumsey et al. (2020)
        Ccr1             0.20;
        Ccr2             2.150537634408602;
        Cfw1             2.0;
        Cfw2             0.3;
        Cqcr2            0.7;
        Cqcr3            0.9;

        // OpenFOAM's SA default is SA-noft2; set true for standard SA.
        ft2              false;
    }
}

For compressible mixing layers, SpalartAllmarasComp adds the SA-comp destruction term of Spalart (2000) to the standard SA transport equation. It is available only from the compressible library. The default coefficient is C5 3.5:

RAS
{
    RASModel            SpalartAllmarasComp;
    turbulence          on;
    printCoeffs         on;

    SpalartAllmarasCompCoeffs
    {
        C5               3.5;
        ft2              false;
    }
}

To combine that transport correction with the QCR2020 stress relation, select SpalartAllmarasCompQCR2020. Its coefficient dictionary accepts both C5 and the QCR2020 coefficients:

RAS
{
    RASModel            SpalartAllmarasCompQCR2020;
    turbulence          on;
    printCoeffs         on;

    SpalartAllmarasCompQCR2020Coeffs
    {
        C5               3.5;
        Ccr1             0.20;
        Ccr2             2.150537634408602;
        Cfw1             2.0;
        Cfw2             0.3;
        Cqcr2            0.7;
        Cqcr3            0.9;
        ft2              false;
    }
}

The implementation evaluates the local perfect-gas speed of sound as $a^2=\gamma p/\rho$, consistently with the assumptions stated by NASA/TMR for compressible SA. Setting C5 0 removes the additional SA-comp term.

DDES model

The SpalartAllmarasSALSADDES model is selected as an LES model:

simulationType  LES;

LES
{
    LESModel            SpalartAllmarasSALSADDES;
    turbulence          on;
    printCoeffs         on;

    delta               cubeRootVol;
}

The model uses the SALSA transport equation and source/destruction terms, but replaces the RANS wall-distance length scale with the DDES length scale. Optional DDES and SALSA coefficients can be supplied in the SpalartAllmarasSALSADDESCoeffs dictionary:

LES
{
    LESModel            SpalartAllmarasSALSADDES;
    turbulence          on;
    printCoeffs         on;

    delta               cubeRootVol;

    SpalartAllmarasSALSADDESCoeffs
    {
        // DDES settings
        CDES              0.65;
        shielding         standard;     // standard or ZDES2020
        lowReCorrection   true;

        // Only used with shielding ZDES2020
        Cd3               25;
        Cd4               0.03;
        betaZDES          2.5;
        usefP2            false;

        // SALSA settings
        rhoInf            0.957837;     // required for useRmod = true
        useRmod           true;
        useSmod           true;
    }
}

Note on useSigma: OpenFOAM's standard SpalartAllmarasDDES has a useSigma switch for a sigma-based grey-area enhancement. This implementation deliberately does not expose useSigma, because it changes the production measure and can conflict conceptually with SALSA's own useSmod strain-rate formulation. The first SpalartAllmarasSALSADDES version is therefore conservative: SALSA source/destruction terms plus DDES dTilda and standard or ZDES2020 shielding.

For the standard SA-DDES form with the QCR2020 stress relation, select SpalartAllmarasDDESQCR2020. The same standard DDES and QCR2020 coefficients can be supplied in SpalartAllmarasDDESQCR2020Coeffs.

QCR2020 compatibility

The QCR2020 equations were taken from the NASA/TMR Spalart-Allmaras model page: the stress relation, the wall-function-dependent Ccr1'' and Ccr2'' coefficients, the normalized rotation tensor, and the smoother QCR2020 Omega_s-based f_w path are all directly extractable there. No conflicting QCR2020 equations were found on that page.

QCR2020 is implemented here for standard SA RANS, SA-comp RANS, and standard SA-DDES, but not as a SALSA option. SA-comp and QCR2020 are compatible: the former modifies the transported-variable equation and the latter modifies the constitutive stress relation. QCR2020 should not be combined with another QCR variant. If a future base model includes a true modeled turbulent kinetic energy term in the Boussinesq relation, the QCR2020 isotropic approximation should be omitted to avoid double counting.

The source-code consistent equations for the standard SA, SALSA, and DDES variants are collected in equations.md.

You can find an example setup using the SALSA model here.

still TODO

• check if we can implement this more efficiently

References

• template / directory structure taken from TUFRG and mAlletto
• T. Rung, U. Bunge, M. Schatz, and F. Thiele, Restatement of the Spalart–Allmaras Eddy-Viscosity Model in Strain-Adaptive Formulation, AIAA Journal, Vol. 41, no. 7, May 2012, https://doi.org/10.2514/2.2089
• D.-M. Zimmermann, R. Mayer, T. Lutz, and E. Krämer, Impact of model parameters of SALSA turbulence model on transonic buffet prediction, AIAA Journal, Vol. 56, no. 2, pp. 874–877, December 2017, https://arc.aiaa.org/doi/10.2514/1.J056193
• C. L. Rumsey, J.-R. Carlson, T. H. Pulliam, and P. R. Spalart, Improvements to the Quadratic Constitutive Relation Based on NASA Juncture Flow Data, AIAA Journal, Vol. 58, no. 10, pp. 4374-4384, 2020, https://doi.org/10.2514/1.J059683
• P. R. Spalart, Trends in Turbulence Treatments, AIAA 2000-2306, June 2000, https://doi.org/10.2514/6.2000-2306