Theory and simulation of separated boundary layers and turbulence induced secondary motion
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Among the different types of flows encountered in practical applications, the physics of turbulent separated flows and turbulence induced secondary motion are not fully understood despite the large amount of previous experimental and numerical work. The objectives of this work are to study theoretically and computationally the conditions at the separation and reattachment point, the numerical simulation of turbulence induced secondary motion in non-circular ducts, and to provide a comprehensive test of different RANS models of these types of flow. In a theoretical study of flow separation, a Lagrangian approach was first used to derive an Eulerian criterion, which associates separation and reattachment points to a critical point in the eigenvalues of the Cauchy-Green tensor. A turbulent separated boundary layer under the influence of an adverse pressure gradient was simulated using DNS and LES techniques. A bootstrapping method was used to obtain high fidelity results at a relatively high Reynolds number with which the performance of some of the most commonly used eddy-viscosity turbulence models was evaluated. The DNS and LES results were used to assess the consistency of the different terms in the k−e , ζ −f , k −ω and Spalart-Allmaras models. Different wall-modelling techniques were employed for the calculation of separated boundary layers. The exact values of the modelled terms were calculated using the reference DNS and LES dataset. These results were used for both a priori and a posteriori tests. It was determined that the eddy-viscosity assumption works well, and that anisotropic effects are not significant in separated boundary layer. For the secondary flow calculation in non-circular ducts, direct numerical simulations of turbulent flow in square and skewed ducts were carried out to determine the effect of the duct (rhombus) included angle on both the mean and turbulence energy budgets. Two skewed ducts, with included angles of 30 and 60 degrees, were simulated. The capability of different turbulence models to predict the secondary velocity field was investigated. Results obtained from a non-linear stress-strain constitutive relation was found to be fairly accurate for the flows at the range of Reynolds number considered in this study.