[navierstokes][nonisothermal] Implement effective thermal conductivity

dumux/discretization/staggered/freeflow/fourierslaw.hh

@@ -85,8 +85,8 @@ public:
         const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()];
 
         // effective conductivity tensors
-        auto insideLambda = insideVolVars.thermalConductivity();
-        auto outsideLambda = outsideVolVars.thermalConductivity();
+        auto insideLambda = insideVolVars.effectiveThermalConductivity();
+        auto outsideLambda = outsideVolVars.effectiveThermalConductivity();
 
         // scale by extrusion factor
         insideLambda *= insideVolVars.extrusionFactor();

dumux/freeflow/navierstokes/volumevariables.hh

@@ -326,6 +326,12 @@ public:
     Scalar thermalConductivity() const
     { return FluidSystem::thermalConductivity(this->fluidState_, phaseIdx); }
 
+    /*!
+     * \brief Returns the effective thermal conductivity \f$\mathrm{[W/(m*K)]}\f$.
+     */
+    Scalar effectiveThermalConductivity() const
+    { return thermalConductivity(); }
+
     //! The temperature is a primary variable for non-isothermal models
     using ParentType::temperature;
     template<class ElementSolution>

dumux/freeflow/navierstokesnc/model.hh

@@ -20,20 +20,7 @@
  * \file
  * \ingroup NavierStokesNCModel
  *
- * \brief A single-phase, multi-component isothermal Navier-Stokes model
- *
- * This model implements a single-phase, multi-component isothermal Navier-Stokes model, solving the <B> momentum balance equation </B>
- * \f[
- \frac{\partial (\varrho \textbf{v})}{\partial t} + \nabla \cdot (\varrho \textbf{v} \textbf{v}^{\textup{T}}) = \nabla \cdot (\mu (\nabla \textbf{v} + \nabla \textbf{v}^{\textup{T}}))
-     - \nabla p + \varrho \textbf{g} - \textbf{f}
- * \f]
- * By setting the property <code>EnableInertiaTerms</code> to <code>false</code> the Stokes
- * equation can be solved. In this case the term
- * \f[
- *    \nabla \cdot (\varrho \textbf{v} \textbf{v}^{\textup{T}})
- * \f]
- * is neglected.
- *
+ * \copydoc Dumux::NavierStokesModel
  *
  * The system is closed by a <B> component mass/mole balance equation </B> for each component \f$\kappa\f$:
  * \f[

dumux/freeflow/nonisothermal/model.hh

@@ -26,9 +26,18 @@
  * \f[
  *    \frac{\partial (\varrho  v)}{\partial t}
  *    + \nabla \cdot \left( \varrho h {\boldsymbol{v}}
- *    - \lambda \textbf{grad}\, T \right) - q_T = 0
+ *    - \lambda_\text{eff} \textbf{grad}\, T \right) - q_T = 0
  * \f]
  *
+ *
+ * For laminar Navier-Stokes flow the effective thermal conductivity is the fluid
+ * thermal conductivity: \f$ \lambda_\text{eff} = \lambda \f$.
+ *
+ * For turbulent Reynolds-averaged Navier-Stokes flow the eddy thermal conductivity is added:
+ *  \f$ \lambda_\text{eff} = \lambda + \lambda_\text{t} \f$.
+ * The eddy thermal conductivity \f$ \lambda_\text{t} \f$ is related to the eddy viscosity \f$ \nu_\text{t} \f$
+ * by the turbulent Prandtl number:
+ * \f[ \lambda_\text{t} = \frac{\nu_\text{t} \varrho c_\text{p}}{\mathrm{Pr}_\text{t}} \f]
  */
 
 #ifndef DUMUX_STAGGERED_NI_MODEL_HH