A correlation-based algebraic transition model

Abstract

A correlation-based algebraic transition model that relies on local flow information is proposed. The model is qualified as an algebraic model, or a zero-equation model since it includes an intermittency function in place of an intermittency equation that is found in one- or two-equation models. The basic idea behind the model is that, instead of deriving new equations for intermittency transport, existing transport terms of the Spalart–Allmaras (S-A) turbulence model can be used. To this end, the production term of the S-A model is multiplied with the proposed intermittency function γBC; thereby the turbulence production is damped until it satisfies some turbulence onset requirements. The proposed formulation also depends on local information that uses empirical correlations to detect the transition onset using less equations and less calibration constants than other higher order models. The model is first validated against some widely-used zero and variable pressure gradient flat plate test cases with quite successful results. Second, the model is employed for some low Reynolds number airfoil cases with very promising results. Third, the model is applied for a turbine cascade case with success. Finally, two different three-dimensional wing flow cases were calculated under transonic and low subsonic flow conditions. To this end, the DLR-F5 wing subject to a transonic Mach number of 0.82 and the low-speed NREL wind turbine flow case are simulated and good agreement with experiments are observed. The results indicate that the proposed model may become an alternative for other models as it uses less computational resources with equivalent or higher accuracy characteristics that is quite advantageous for the computational fluid dynamics design in industry.