Assessment of intermittency transport equations for modeling transition in boundary layers subjected to freestream turbulence

The γ–Reθ transition model of Menter et al. [Menter, F.R., Langtry, R.B., Volker, S., Huang, P.G., 2005. Transition modelling for general purpose CFD codes. ERCOFTAC International Symposium Engineering Turbulence Modelling and Measurements] is a highly generalized transport equation model in which it has been developed based on the concept of local variables compatible with modern CFD methods where the unstructured grid and the parallel computing technique are usually integrated in. To perform the prediction with this model, two essential parameters, Flength which is used to control the length of the transition region and Reθc which is used to control the onset of the transition location, must be specified to close the model. At present, both parameters are proprietary and their formulations are unpublished. For the first time here, the relations for both parameters are formulated by means of numerical experiments and analysis under the assumption of Reθc = Reθt corresponding with the bypass transition behavior. Based on this analysis, the optimized values of the parameters are found and their relations can be constructed as follows: Reθc = 803.73(Tu∞,le + 0.6067)−1.027 and Flength = 163 ln(Tu∞,le) + 3.625. The performance of this transition model is assessed by testing with the experimental cases of T3AM, T3A, and T3B. Detailed comparisons with the predicted results by the transition models of Suzen and Huang [Suzen, Y.B., Huang, P.G., 2000. Modeling of flow transition using an intermittency transport equation. J. Fluids Eng. 122, 273–284] and Lodefier et al. [Lodefier, K., Merci, B., De Langhe, C., Dick, E., 2003. Transition modelling with the SST turbulence model and intermittency transport equation. ASME Turbo Expo, Atlanta, GA, USA, June 16–19], and also with the predicted results by the k–ε model of Launder and Sharma [Launder, B.E., Sharma, B., 1974. Application of the energy dissipation model of turbulence to the calculation of flow near a spinning disk. Letters in Heat and Mass Transfer 1, 131–138] and the SST model of Menter [Menter, F.R., 1994. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA 32, 1598–1605] are presented here. Results show that the proposed relations for Flength and Reθc can work well with the model to give good agreement in predicting the transition.