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Herve Bezard
Department of Modeling for Aerodynamics and Energetics, ONERA the French Aerospace Lab, 2 avenue E. Belin, 31055 Toulouse, France

Thomas Daris
Department of Modelling for Aerodynamics and Energetics, French Aerospace Research Agency (ONERA) 2, av. E. Belin, BP 4025, 31055 Toulouse, France


A new kθ − kθLθ two-equation turbulence model for heat flux predictions is described. This model is associated to a new k − kL two-equation turbulence model for Reynolds stress predictions, which forms a four-equation turbulence model. The method used to analyse existing four-equation models or to obtain a new model is presented. The model is expressed in terms of a generic k − φ / kθ − φθ model where φ = kaεb and φθ = kθpεθq can represent any type of turbulence scales. The transport equations include all diffusion and cross-diffusion terms. Relations on the model constants are derived to force the model to respect some basic physical features. It will be shown why existing models fail to reproduce the characteristics of heated APG boundary layer flows and how to build a new model that fulfils all requirements. Some applications of the new k − kL / kθ − kθLθ model are presented.