Analysis and modelling of the relation between the shear rate and Reynolds stress tensors in transitional boundary layers |
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Affiliation: | 1. DIME Universitá di Genova, Via Montallegro 1, I-16145 Genoa, Italy;2. Warsaw University of Technology, Faculty of Power and Aeronautical Engineering, Institute of Aeronautics and Applied Mechanics, Nowowiejska 24, Warsaw, 00-665, Poland;3. Ghent University, Fluid Mechanics Research Group, St.-Pietersnieuwstraat 41, Gent 9000, Belgium |
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Abstract: | A non-linear eddy-viscosity transition model is presented, tuned by a large experimental data set describing transitional boundary layers. Data have been acquired by TR-PIV on a flat plate placed in a 2D converging-diverging channel with variable opening angle, allowing variation of the adverse pressure gradient, the free-stream turbulence intensity and the flow Reynolds number. Overall, 48 different combinations of these flow parameters encompass different modes of transition from bypass to separated-flow mechanisms, thus allowing fine tuning of the model, spanning significantly different conditions. The model is tuned locally as a function of the turbulent kinetic energy, a Reynolds number based on the wall distance and the ℓ2-norm of the shear rate tensor. A first correlation determines the rotation for alignment of the principal axes of the shear and stress tensors. By a second correlation, the eigenvalues of the stress tensor are obtained. The non-linear eddy-viscosity relation reproduces the anisotropy of the turbulence field observed for both bypass and separated-flow transitional cases. The relation has been applied to another experimental data set that did not participate to the fitting of the model and that is characterized by a different range of Reynolds number and turbulence intensity and a significantly stronger adverse pressure gradient with respect to the tuning dataset. Such application further strengthens the capability of the proposed correlations, that can easily be implemented in existing CFD solvers. |
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