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[rans] add density in all terms of the RANS models

Katharina Heck requested to merge feature/rans-include-density-changes into master

This is to include variable density in the the 1-2eq turbulence models.

Explanation, using the K-omega model as an example:

Previously implemented (K):

\frac{\partial \left( k \right)}{\partial t}
+ \nabla \cdot \left( \mathbf{v} k \right)
- \nabla \cdot \left[ \left( \nu + \sigma_\textrm{k} \frac{k}{\omega}\right) \nabla k \right]
- (2 \nu_t \mathbf{S} \cdot \mathbf{S})
+ \beta_k k \omega = 0 

Introduced in this MR (K):

\frac{\partial \left( \rho k \right)}{\partial t}
+ \nabla \cdot \left( \rho k \mathbf{v} \right)
- \nabla \cdot \left[ \left( \mu +  \rho \sigma_\textrm{k} \frac{k}{\omega}\right) \nabla k \right]
- (2 \mu_t \mathbf{S} \cdot \mathbf{S})
+ \rho \beta_k k \omega = 0 

Previously implemented (\omega):

\frac{\partial \left( \omega \right)}{\partial t}
+\nabla \cdot \left( \mathbf{v} \omega \right)
-\nabla \cdot \left[ \left( \nu + \sigma_{\omega} \frac{k}{\omega}\right) \nabla \omega \right]
-\alpha \frac{\omega}{k} (2 \nu_t \mathbf{S} \cdot \mathbf{S})
+\beta_{\omega} \omega^2
-\frac{\sigma_d}{\omega} \nabla k \nabla \omega = 0

Introduced in this MR (\omega):

\frac{\partial \left( \rho \omega \right)}{\partial t}
+\nabla \cdot \left( \rho \mathbf{v} \omega \right)
-\nabla \cdot \left[ \left( \mu + \rho \sigma_{\omega} \frac{k}{\omega}\right) \nabla \omega \right]
-\alpha \frac{\omega}{k} (2 \mu_t \mathbf{S} \cdot \mathbf{S})
+\rho \beta_{\omega} \omega^2
-\rho \frac{\sigma_d}{\omega} \nabla k \nabla \omega = 0

  • add density in production limiter term The production limiter is also modified from:
20 \beta_K k \omega \text{  to  } 20 \rho \beta_K k \omega

  • test how much that changes results
  • This shouldn't effect any of the isothermal single component tests. All ni or nc tests should be affected.
  • All of the ni and nc tests are effected.
  • Update reference solutions.

Introduce this additionally for the:

  • kepsilon
  • low re kepsilon
  • one eq models

Fix failing kepsilon wall function test

  • fix kepsilon wall functions

relevant documentation:

  • Check, if it is necessary to implement the additional term (MOVED TO #951 (closed))
- 2/3 \rho k \delta_{ij}

in the production term in the 2-eq models (see: Computational Fluid Dynamics, Versteeg& Malalasekera page 90)

\tau_{ij} = 2 \, \mu_t \, S_{ij} - \frac{2}{3}\rho k \delta_{ij}
Edited by Ned Coltman

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