An immersed boundary method for practical simulations of high-Reynolds number flows by k-ε RANS models

A combustion simulation software tool, “HINOCA”, has been developed for automotive engine analysis. HINOCA is based on fully compressible Navier-Stokes equations, which are Reynolds-averaged (RANS) or spatially-filtered (LES), and employs the Cartesian grid and immersed boundary (IB) methods to reduce the mesh generation cost. In the present paper, focusing on flow simulations using k-ε models, a robust and reliable IB method coupled with wall functions is proposed. One major aspect of the method is that different IB cell information is employed for inviscid and viscous flux evaluations at fluid-IB cell interfaces. To improve the evaluation of wall shear stress, the shear stresses on the boundaries of an IB cell are transformed into a body force acting on the adjacent fluid cell. The computational method for ε-equation and the source terms of the k-equation near IB cells are modified so that the development of the turbulent boundary layer on a flat plate is well reproduced. The effects of these modifications are validated by the 2D Zero Pressure Gradient Flat Plate problem. To improve the mass conservation property of the IB method, multiple geometric parameters are defined for IB cells; that is, different image point information is immersed on IB cell centers for evaluating the inviscid flux on each cell interface. Evaluation with the Steady State Flow Bench problem shows that the proposed method drastically improves the mass conservation property of simulations and is able with a coarse mesh to reproduce flow structures obtained by LES with a much finer mesh.