A non-linear k-ε model with realizability for prediction of flows around bluff bodies

The incompressible flow around bluff bodies (a square cylinder and a cube) is investigated numerically using turbulence models. A non-linear k-ε model, which can take into account the anisotropy of turbulence with less CPU time and computer memory than RSM or LES, is adopted as a turbulence model. In tuning of the model, the model coefficients of the non-linear terms are adjusted through the examination of previous experimental studies in simple shear flows. For the tuning of the coefficient in the eddy viscosity (= Cμ), the realizability constraints are derived in three types of basic 2D flow patterns, namely, a simple shear flow, flow around a saddle and a focal point. Cμ is then determined as a function of the strain and rotation parameters to satisfy the realizability. The turbulence model is first applied to a 2D flow around a square cylinder and the model performance for unsteady flows is examined focussing on the period and the amplitude of the flow oscillation induced by Karman vortex shedding. The applicability of the model to 3D flows is examined through the computation of the flow around a surface-mounted cubic obstacle. The numerical results show that the present model performs satisfactorily to reproduce complex turbulent flows around bluff bodies.