Transition Guidelines

A number of guidelines are advised when setting up simulations that use the Gamma or the Gamma ReTheta transition model. These guidelines concern mesh creation, the turbulence specification on inflow boundaries, and convergence.

Mesh Creation

Validation studies show that the Gamma ReTheta and the Gamma transition models require a high-quality, refined low-Reynolds number mesh:

Create a mesh with a wall-normal spacing that is fine enough to guarantee Wall Y+ values between 0.1 and 1.
Make sure that the streamwise mesh spacing near the transition region is fine enough to accurately capture the onset of transition.
Use either the all- $y^{+}$ or the low- $y^{+}$ wall treatment formulation.
If transition is induced by laminar separation, then refine the mesh to resolve the curvature of the body where the separation exists, and to capture the laminar separation bubble.

Inflow Turbulence Specification

The Gamma ReTheta and the Gamma transition models attempt to account for the effect of the freestream turbulence levels on the transition location. Therefore, pay proper attention to the turbulence specification on inflow boundaries to encounter realistic turbulence intensities in the boundary layers within the transition zone.

Whenever possible, provide experimental data that describes the behavior of the freestream turbulence. With three or more data points, you can determine the dissipation rate and subsequently the inflow turbulence values through a regression analysis of the data.

The freestream turbulence decay laws, which are derived from the SST K-Omega model transport equation, are as follows (using the default coefficients):

Figure 1. EQUATION_DISPLAY

k = k_{i n l e t} {[{1 + 0.0828 \frac{x}{U_{\infty}} ω}_{i n l e t}]}^{- 1.087}

(263)

Figure 2. EQUATION_DISPLAY

ω = ω_{i n l e t} {[{1 + 0.0828 \frac{x}{U_{\infty}} ω}_{i n l e t}]}^{- 1}

(264)

where $x$ is the streamwise distance and $U_{\infty}$ is the (assumed constant) freestream velocity.

Using the following relations for turbulence intensity $I$ and turbulent viscosity ratio ( $T V R = μ_{t} / μ$ ):

Figure 3. EQUATION_DISPLAY

I = \frac{\sqrt{(2 / 3) k}}{U}

(265)

Figure 4. EQUATION_DISPLAY

T V R = \frac{k}{ω μ}

(266)

you can transform Eqn. (263) and Eqn. (264) into:

Figure 5. EQUATION_DISPLAY

I = I_{i n l e t} {[1 + \frac{0.1242 x ρ {U_{\infty} I}_{i n l e t}^{2}}{μ T V R_{i n l e t}}]}^{- 0.5435}

(267)

Figure 6. EQUATION_DISPLAY

T V R = {T V R}_{i n l e t} {[1 + \frac{0.1242 x ρ {U_{\infty} I}_{i n l e t}^{2}}{μ T V R_{i n l e t}}]}^{- 0.087}

(268)

Care must be taken with the specification of turbulent viscosity ratio at the inlet because large values of effective viscosity cause excessive diffusion. The exponent in Eqn. (268) is small, so that the turbulent viscosity does not decay significantly, allowing the inlet values to propagate far downstream. Unfortunately, the smaller the value of the turbulent viscosity ratio, the faster the turbulence will decay. In the absence of measured data, the proper turbulent inflow boundary conditions become a delicate balance between an acceptable turbulent decay rate and an acceptably low turbulent viscosity ratio.

Since the turbulent viscosity ratio is, in effect, a turbulent Reynolds number, it is impossible to specify what an acceptable value is for any given flow. (Higher bulk Reynolds numbers would suggest higher turbulent Reynolds numbers, and hence higher levels of acceptable turbulent viscosity ratio.) However, a rough guideline is that the freestream turbulent viscosity ratio should be significantly lower than the turbulent viscosity that occurs within the boundary layer. For natural transition problems and lower freestream turbulence bypass transition, a desirable goal would be to have a TVR from 1 through 10. This prevents the high levels of effective viscosity from contaminating the laminar boundary layer and affecting the laminar skin friction prediction.

In some situations, such as wind tunnels with very low background turbulence, it might be a challenge to obtain a suitable compromise between these two variables. This issue is often exacerbated when a far-field boundary is specified a large distance away from the body.

High Reynolds Number Effects at Low Mach Number

The Gamma and the Gamma ReTheta transition models tend to predict an unexpectedly early transition for high Reynolds number flows at low Mach number, such as for wind turbine flows or transonic flows over aircraft wings. To overcome this issue, some correlation parameters of the models require tuning.

For the Gamma transition model, you are advised to rescale the correlation coefficients $C_{TU 1}$ and $C_{TU 2}$ and the transition onset parameter $C_{onset 1}$ according to Colonia and others [375].

The following table lists the suggested modifications:


$C_{TU 1}$	$C_{TU 2}$	$C_{onset 1}$
163	1002.25	Figure 7. EQUATION_DISPLAY $\min (4.84, \max (2.2, 1.388 \ln (Re \times 10^{- 6}) + 0.705))$ (269)

where the function for $C_{onset 1}$ is given in the range $1 \times 10^{6} \leq Re \leq 15 \times 10^{6}$ .

For the Gamma ReTheta transition model, you are advised to modify $C_{onset 1}$ according to Eqn. (269).

To calibrate the models:

For the Gamma transition model, select the Gamma Transition node and modify the following properties:
- CTU1
- CTU2
- Conset1
For the Gamma ReTheta transition model, select the Gamma ReTheta node and modify the Conset1 parameter.

See Gamma Transition Model Reference and Gamma ReTheta Transition Model Reference.

Convergence

Apart from the fact that the Gamma ReTheta and the Gamma transition models require the solution of additional transport equations, incurring an additional computational overhead as a result, an impact on solution covertness must be expected.

It has been noted that the interaction between flow, turbulence, and the transition model can increase the number of iterations to convergence significantly. Furthermore, the intermittency transport equation residuals are naturally noisy. This is attributed to the strong dependence of the source terms on higher powers of the mean flow strain rates, and the fact the source terms are not differentiable functions.