[Fabio1893]

Hello dear community.

I want to implement an algebraic heat flux model, based on the one described in the StarCCM+ user guide, called Temperature Flux Model here, in OpenFOAM 8. The model is based on eddy viscosity models and needs to be implemented in a low-Re model. However, I start with an implementation in the standard k-epsilon model of OpenFOAM 8.

In OpenFOAM, if I understand correct, the heat flux is calculated, based on Boussinesq approximation, by:

(1)

In comparison for the Temperature Flux Model, the heat flux is defined as:

(2)

with being the turbulent heat flux, which is given as:

(3)

In order to calculate the turbulent heat flux , a third transport equation for the temperature variance needs to be solved. The transport equation for the temperature variance is very similar to the transport equation of the turbulent kinetic energy k and is defined as:

(4)


with the production term of the temperature variance:


(5)


Furthermore, the temperature variance dissipation rate is defined via the thermal time scale


(6)


and the assumption of a constant turbulent-to-thermal time-scale ratio:


(7)


I have almost finished the implementation of the transport equation (4). Only the production therm (5) of the temperature variance is missing:

// Temperature variance equation
    tmp<fvScalarMatrix> theta2Eqn
    (
        fvm::ddt(alpha, rho, theta2_)
      + fvm::div(alphaRhoPhi, theta2_)
      - fvm::laplacian(alpha*rho*Dtheta2Eff(), theta2_)
      ==
          // production of theta2 is missing
      - (alpha()*rho*theta2_)/(2*R_*turbTimeScale()) // epsilonTheta2
      + theta2Source()
      + fvOptions(alpha, rho, theta2_)
    );

My question now is quite simple: How can I get access to the temperature T in my turbulence model?


EDIT:


Access to T:

const volScalarField& T_ = this->mesh_.objectRegistry::template lookupObject<volScalarField>("T");

Furthermore, I am not sure, how I could implement equation (3). I have already defined model constants, but how can I get the Reynolds stress tensor and the thermal expansion coefficient here?



If any further information is needed, please let me know. Thanks a lot in advance!