Evaluation of Turbulence Models for Unsteady Separation

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MacDougall, Claire
Computational Fluid Dynamics , URANS , Unsteady Separation , Turbulence Models
Unsteady separation occurs in many physical flows due to time-varying adverse pressure gradients. This phenomenon may result in increased drag, decreased lift, and loss of efficiency or failure in flow devices. It is, therefore, important to predict and analyze unsteady separation in the design of flow devices. Turbulence models in combination with the Reynolds-Averaged Navier-Stokes equations are commonly used in the industrial design process due to their low computational cost; however, their performance in predicting steady separations is unsatisfactory, and very few studies have investigated unsteady separation to date. This study uses high fidelity Large-Eddy Simulation (LES) of a flat plate boundary layer with unsteady separation to evaluate the accuracy of the K − ε, K − ω, and Spalart-Allmaras turbulence models in predicting flows of this type. Alternating favourable and adverse pressure gradients induce periodic acceleration and separation of the boundary layer (Case A, hereafter). Modelling errors are isolated by using an identical numerical scheme and consistent boundary conditions to the LES with a grid that has been validated in the LES study of this problem. The performance of the models is evaluated for three representative reduced frequencies k = 10, 1 and 0.2. An additional case is considered where separation is present throughout the entire oscillation cycle (Case B hereafter). All three turbulence models capture the general features of this complex unsteady flow correctly, with only small discrepancies from the LES. The largest errors occur closest to the wall, particularly in predicting the downstream shedding of the separation bubble. The models are most accurate during phases of the flow where the pressure gradients are mild, however, the maximum APG-FPG phases of the flow are predicted successfully. The cyclical alternation of the pressure gradients from FPG-APG to APG-FPG with intermediate phases of ZPG are shown to contribute to the success of the turbulence models. The performance of the turbulence models is significantly better in Case A than in Case B with integrated errors (IE) of 6.8 % and 16.7 % respectively.
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