*2.3.2.1 Langtry and Menter γ-Reθ model*

Langtry and Menter's formulation of the two-equation γ-Reθ model [11] is one of the most widely used transition models as far as general CFD applications in aeronautics are concerned. This model is formulated in such a way that allows calibrated prediction of transition onset and length that are valid for both the 2-D and 3-D flows. It uses the so-called local variables and thus applicable to any type of grids generated around complex geometries with robust convergence characteristics. As mentioned in the introduction part, this model is based on an important experimental observation that a locally calculated parameter called as the vorticity Reynolds number (Rev) and the momentum thickness Reynolds number (Reθ) where

$$Re\_0 = \frac{Re\_{v\text{max}}}{2.193} \quad \text{and} \quad Re\_v = \frac{\rho \, d\_w^2}{\mu} \, \Omega \tag{4}$$

are proportional in a Blasius boundary layer. For most of the flow types, the relative error between the scaled vorticity Reynolds number and momentum thickness Reynolds number is reported [1] to be around 10%.

The model solves for two additional equations besides the underlying two-equation k-ω SST turbulence model, an intermittency equation (γ) that is used to trigger the turbulence production term of the k-ω SST turbulence model and a momentum thickness Reynolds number transport equation (Reθ) that includes experimental correlations that relates important flow parameters such as turbulence intensity, freestream velocity, pressure gradients etc. and supplies it to the intermittency equation. The details of the model are available in the literature [1, 11].
