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.

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Transition modeling as applied to CFD methods has followed certain line of evolution starting from simple linear stability methods to almost or fully predictive methods such as LES and DNS. One pragmatic approach among these methods, such as the local correlation-based transition modeling approach, is gaining more popularity due to its straightforward incorporation into RANS solvers. Such models are based on blending the laminar and turbulent regions of the flow field by introducing intermittency equations into the turbulence equations. Menter et al. pioneered this approach by their two-equation γ-Reθ intermittency equation model that was incorporated into the k-ω SST turbulence model that results in a total of four equations. Later, a range of various three-equation models was developed for super-/hypersonic flow applications. However, striking the idea that the Reθ-equation was rather redundant, Menter produced a novel one-equation intermittency transport γ-equation model. In this report, yet another recently introduced transition model called as the Bas-Cakmakcioglu (B-C) algebraic model is elaborated. In this model, an algebraic γ-function, rather than the intermittency transport γ-equation, is incorporated into the one-equation Spalart-Allmaras turbulence model. Using the present B-C model, a number of two-dimensional test cases and three-dimensional test cases were simulated with quite successful results.

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