### 2.4.2. One Equation Intermittency Transition Model

The following topics are discussed:

- Overview
- Transport Equation for the Intermittency Transition Model
- Coupling to SST Model
- Intermittency Transition Model and Rough Walls

#### 2.4.2.1. Overview

The (intermittency) transition model [224] is a further development based on the - transition model. The transition model solves only one transport equation for the turbulence intermittency and avoids the need for the second equation of the - transition model. The transition model has the following advantages over the - transition model:

- It reduces the computational effort by solving one transport equation instead of two.

- It avoids the dependency of the equation on the speed . This makes the transition model Galilean invariant. It can therefore be applied to surfaces that move relative to the coordinate system for which the velocity field is computed.

- The model has provisions for crossflow instability that are not available for the - or - transition model.

- The model formulation is simple and can be fine-tuned based on a small number of user parameters.

Like the - transition model, the transition model is based strictly on local variables. The transition model is also only available in combination with the following turbulence models:

- BSL - model

- SST - model

- Scale-Adaptive Simulation with BSL or SST

- Detached Eddy Simulation with BSL or SST

Note the following limitations:

- The transition model is only applicable to wall-bounded flows. Like all other engineering transition models, the model is not applicable to transition in free shear flows. The model will predict free shear flows as being fully turbulent.

- The transition model has only been calibrated for classical boundary layer flows. Application to other types of wall-bounded flows is possible, but might require a modification of the underlying correlations.

- The transition model has not be calibrated in combination with other physical effects that affect the source terms of the turbulence model, such as:

  - Buoyancy

  - Multiphase turbulence

Guidelines on the use of the Intermittency transition model are similar to those developed for the - model as outlined in CFX Transition Model in the CFX-Solver Modeling Guide.

#### 2.4.2.2. Transport Equation for the Intermittency Transition Model

The transport equation for intermittency is the following:

The formulation of the source terms is similar in nature to the corresponding terms in the - transition model. The transition source term is defined as:

where is the strain rate magnitude.

The destruction/relaminarization source is defined as follows:

where is the magnitude of the absolute vorticity rate. The transition onset is controlled by the following functions:

| (2–156)

where is the wall distance and is a correlation used to trigger the transition model:

In this correlation, is the critical momentum thickness Reynolds number, and and are locally defined variables that approximate the freestream turbulence intensity and the pressure gradient parameter, respectively. A local formulation that provides levels in the middle of the boundary layer similar to the freestream turbulence intensity, , is expressed as:

The formula for reads as:

| (2–157)

For numerical robustness, was bounded as follows:

| (2–158)

The function accounts for the influence of the pressure gradient on transition, and is defined as:

The transition model has been calibrated against a wide range of generic as well as turbomachinery and external aeronautical test cases. While you should not have to adjust the model coefficients in most situations, the model provides access to the coefficients so that you can fine-tune the model. This should only be done based on detailed experimental data. You can adjust the following constants in the correlations: , , , , , , , , , .

The constant defines the minimal value of critical number, whereas the sum of and defines the maximal value of . The controls how fast the decreases as the turbulence intensity () increases. The and constants adjust the value of critical number in areas with favorable and adverse pressure gradient, respectively. The constant becomes active in regions with separation, correcting the value if necessary. Additionally, the size of the separation bubble can be tuned by another constant, , which enters the model through the source terms directly rather than the correlations (see Coupling to SST Model). The constants and define the limits of the function; while they typically do not need to be adjusted, it is possible to do so (for details, contact your support engineer).

For crossflow transition, a widely used experimental correlation is the C1 correlation proposed by Arnal (1984) [223]. According to that correlation, transition occurs when the following condition is met:

where

The crossflow Reynolds number is defined as:

In the previous equations, is the crossflow Reynolds number, the index refers to a coordinate system that is aligned with the freestream velocity (where refers to the boundary layer edge), is the crossflow velocity normal to the direction of the freestream velocity. The value of 150 is the calibration constant of the Arnal C1 criterion corresponding to a critical Reynolds number.

The transition model accounts for the crossflow transition through a separate correlation, which approximates the C1 correlation through a local formulation. The formulation uses only local information and has the following functional form:

The function accounts for the influence of pressure gradient (shape factor); the function accounts for the ratio of the crossflow strength relative to the streamwise strength; the Reynolds number effect is included through . The correlation can be adjusted by the constant . The transition location due to the crossflow instability will move upstream as increases.

The function is computed as follows:

where is a local variable used to approximate the pressure gradient parameter and is defined similarly to (see Equation 2–157 and Equation 2–158):

The crossflow indicator function is a non-dimensional measure of the local crossflow strength relative to the streamwise strength. It is computed based on the wall normal change of the normalized vorticity vector , which serves as a measure of the three-dimensionality of the velocity profile and which becomes zero for 2D flow.

Here, is the vorticity vector and is the wall normal vector.

The indicator function is proportional to the local change of the flow angle and therefore a measure of the overall crossflow strength.

The triggering function that accounts for the crossflow effects is defined as follows:

The source term in the equation is then triggered, either by the primary triggering function (see Equation 2–156) of the Intermittency transition model, or by : whichever has a maximal value.

The factor of 100 is used in in order to speed up the transition process.

The default values for the model constants are the following:

= 100.0, = 1000.0, = 1.0, = 14.68, = -7.34, = 0.0, = 1.5, = 3.0, = 1.0, = 1.0

#### 2.4.2.3. Coupling to SST Model

The coupling between the Intermittency transition model and the SST -, SAS with SST and DES with SST models is the same as for the - model and is accomplished by modifying the equations of the original SST model as follows:

where and are the production and destruction terms from the turbulent kinetic energy equation in the original SST turbulence model. The term is computed using Kato-Launder formulation:

An additional production term, , has been introduced into the -equation to ensure proper generation of at transition points for arbitrarily low (down to zero) levels. The additional term is designed to turn itself off when the transition process is completed and the boundary layer has reached the fully turbulent state. The expression for the reads as:

The constants and are adjustable. When the laminar boundary layer separates, the size of the separation bubble can be controlled by changing the constant . The default value of the constant is set to 1.0; a higher value results in a shorter bubble. This mechanism is different from the one used for the - model, where the effective intermittency, , is allowed to exceed 1.0 whenever the laminar boundary layer separates. It should be noted however, that the constant has an effect only for the bubbles developing under low conditions (<0.5%). It might also slightly affect the length of transition in attached boundary layers under very low freestream turbulence intensity.

#### 2.4.2.4. Intermittency Transition Model and Rough Walls

Note that the correlation does not include effects of rough walls. If you plan to include rough walls, it is recommended that you switch to the - transition model.

Release 18.2 - © ANSYS, Inc. All rights reserved.