Gamma ReTheta Transition Model

The Gamma ReTheta transition model is a two-equation, correlation-based transition model that provides a semi-local approach to predict the onset of transition in a turbulent boundary layer.

Most transition models are based on the concept of intermittency—a measure of the amount of time during which the flow is turbulent. An intermittency value of 1 corresponds to a fully turbulent flow (100% percent of the time) and an intermittency value of 0 corresponds to a fully laminar flow. Traditional correlation-based intermittency models, such as that by Abu-Ghannam and Shaw [374], require the evaluation of non-local quantities, which can not be evaluated at cell centers directly, such as momentum thickness Reynolds number. However, for complex geometries, or for flow conditions where free-stream conditions are not easily identifiable, these quantities are difficult to evaluate, which precludes the practical application of these intermittency models in modern CFD codes.

The Gamma ReTheta transition model [378], [380] is a correlation-based transition model that has been specifically formulated for unstructured CFD codes. An intermittency transport equation is used in such a way that the source terms attempt to mimic the behavior of the algebraic engineering correlations. The evaluation of momentum thickness Reynolds number is avoided by relating this quantity to a vorticity-based Reynolds number. In addition, a correlation for transition onset momentum thickness Reynolds number defined in the free-stream is transported (by solving a separate transport equation) into the boundary layer.

The Gamma ReTheta transition model was incomplete, as published, since two critical correlations were proprietary and hence omitted. A justification for such an omission is that the model provides a framework for users to implement their own correlations. The implementation of the model in Simcenter STAR-CCM+ is thus done in such a way as to allow the custom specification of correlations using field functions. Recognizing, however, that the process of calibrating the needed correlations is complex and time-consuming, generic correlations are provided by default within the model. These correlations are different from those that have since been published by the original authors [380].

Furthermore, the original Gamma ReTheta transition model does not account for an important type of transition mechanism—the cross-flow instabilities. Langtry et al. [379] proposed to add an additional source term in the transported transition momentum thickness Reynolds number to account for such instabilities. This correlation is optional in Simcenter STAR-CCM+.