Modeling Turbulent Heat Flux

The classical definition of heat flux in the energy equation is based on the Boussinesq approximation, where the heat flux is assumed to be proportional to the turbulent eddy-viscosity. This assumption fails either when buoyancy forces are dominant, or at locations very near the wall. A remedy proposed by Kenjeres and others [346] is to replace the Boussinesq approximation by an algebraic formulation for the turbulent heat flux itself. This formulation is a function of the Reynolds-stress anisotropy and the temperature variance, for which an additional transport equation is solved. The performance of the algebraic heat flux (or Temperature Flux) model is strongly linked to the correct approximation of the near-wall turbulent behavior, thus requiring a low-Reynolds number turbulence model.

Table 1. Temperature Flux Model Reference
Theory	See Theory Guide—RANS Turbulent Heat Transfer.
Provided By	[physics continuum] > Models > Optional Models
Example Node Path	Continua > Physics 1 > Models > Temperature Flux Model
Requires	Space: Axisymmetric, Two Dimensional, or Three Dimensional Time: Implicit Unsteady, PISO Unsteady, or Steady Material: Gas or Liquid Flow: Segregated Flow or Coupled Flow Optional Models: Segregated Fluid Temperature, Segregated Fluid Enthalpy, or Coupled Energy Equation of State: Constant Density Viscous Regime: Turbulent Turbulence: Reynolds-Averaged Navier-Stokes Reynolds-Averaged Turbulence: K-Epsilon Turbulence K-Epsilon Turbulence Models: Standard K-Epsilon Low-Re Wall Treatment: All y+ Wall Treatment or Low y+ Wall Treatment Optional Models: Gravity Optional Models: Boussinesq Model
Properties	See Turbulent Heat Flux Properties.
Activates	Initial Conditions	Temperature Variance See Initial Conditions.
	Boundary Inputs	Temperature Variance See Boundary Settings.
	Region Inputs	`Temperature Variance Source Option` See Region Settings.
	Solvers	Temperature Flux Solver See Temperature Flux Solver Properties.
	Field Functions	Temperature Variance See Field Functions.

Turbulent Heat Flux Properties

Convection

Controls the convection scheme.

1st-order: Selects the first-order upwind convection scheme.
2nd-order: Selects the second-order upwind convection scheme.

Ctu0

The coefficient

C_{{t u}_{0}}

, see Eqn. (1345).

Ctu1

The coefficient

C_{{t u}_{1}}

, see Eqn. (1345).

Ctu2

The coefficient

C_{{t u}_{2}}

, see Eqn. (1345).

Ctu3

The coefficient

C_{{t u}_{3}}

, see Eqn. (1345).

Ctu4

The coefficient

C_{{t u}_{4}}

, see Eqn. (1345).

R

The turbulent-to-thermal time-scale ratio

R

, see Eqn. (1350).

Secondary Gradients

Neglect or include the boundary secondary gradients for diffusion and/or the interior secondary gradients at mesh faces.

On: Include both secondary gradients.
Off: Exclude both secondary gradients.
Interior Only: Include the interior secondary gradients only.
Boundaries Only: Include the boundary secondary gradients only.

Sigma_Theta2

The coefficient

σ_{θ^{2}}

, see Eqn. (1347).

Theta2 Minimum

The minimum value that the transported variable

\overline{θ^{2}}

is permitted to have. An appropriate value is a small number that is greater than the floating point minimum of the computer.

Initial Conditions

The Temperature Flux model requires the temperature variance $\overline{θ^{2}}$ as initial condition. You can enter the corresponding value directly.

Temperature Variance: Scalar profile value to specify $\overline{θ^{2}}$ directly.

Boundary Settings

Inflow and Outflow Boundaries

Temperature Variance: Scalar profile value to specify $\overline{θ^{2}}$ directly.

Region Settings

Applies to fluid regions.

Temperature Variance Source Option

Controls whether you want to apply a source for the temperature variance.

Method	Corresponding Physics Value Nodes
Deactivated	None.
Activated	Temperature Variance Source Scalar profile value to specify a source for $\overline{θ^{2}}$ directly.

Temperature Flux Solver Properties

Under-Relaxation Factor: At each iteration, governs the extent to which the newly computed solution supplants the old solution. The default value is 0.8. For the theoretical background, see Eqn. (920).
Under-Relaxation Factor Ramp: The Temperature Flux Solver > Under-Relaxation Factor Ramp node allows you to set and control a linear ramp for under-relaxation. For details, see Under-Relaxation Factor Ramp Reference.
AMG Linear Solver: The Temperature Flux Solver > AMG Linear Solver node allows you to set the algebraic multigrid parameters for the turbulence solver. For details, see Algebraic Multigrid and AMG Linear Solver Properties.

Reconstruction Frozen: When On, Simcenter STAR-CCM+ does not update reconstruction gradients with each iteration, but rather uses gradients from the last iteration in which they were updated. Activate Temporary Storage Retained in conjunction with this property. This property is Off by default.
Reconstruction Zeroed: When On, the solver sets reconstruction gradients to zero at the next iteration. This action means that face values used for upwinding (Eqn. (905)) and for computing cell gradients (Eqn. (917) and Eqn. (918)) become first-order estimates. This property is Off by default. If you turn this property Off after having it On, the solver recomputes the gradients on the next iteration.
Solver Frozen: When On, the solver does not update any quantity during an iteration. It is Off by default. This is a debugging option that can result in non-recoverable errors and wrong solutions due to missing storage. See Finite Volume Solvers Reference for details.
Temporary Storage Retained: When On, Simcenter STAR-CCM+ retains additional field data that the solver generates during an iteration. The particular data retained depends on the solver, and becomes available as field functions during subsequent iterations. Off by default.

Field Functions

Temperature Variance: Scalar field that represents $\overline{θ^{2}}$ in Eqn. (1347).