Wall modeling for large-eddy simulation using an immersed boundary method

Orthogonal, structured grids allow flow simulations in simple geometries with high efficiency and accuracy. In contrast, complex and realistic flow problems have traditionally required the use of curvilinear or unstructured meshes, which require large computational costs and reduced accuracy due to limited grid smoothness and orthogonality. In recent years an alternative approach which combines the advantages of simple Cartesian grids with the ability to deal with complex geometries has been developed. In this technique, named the immersed boundary method (Fadlun et al. (1999)), the complex object is immersed in a regular grid and the body effect on the flow is accounted for by prescribing an appropriate body force in the momentum equations in the first computational cell outside the immersed body. This is a de facto grid-free numerical method in the sense that the time-consuming construction of the smooth mesh fitted to the body is avoided. Flows in industrially relevant configurations are often characterized by high Reynolds numbers. A Direct Numerical Simulation (DNS) which resolves all the time and length scales requires grid resolution and computational resources that will not be available in the near future. Turbulence models have to be used to make those simulations feasible. The immersed boundary approach has been used successfully in combination with Large-Eddy Simulation (LES) and Reynolds Averaged Navier-Stokes (RANS) techniques (Iaccarino & Verzicco (2003)). Accurate LES of wall bounded flows, however, requires a near-wall resolution comparable to that for DNS, thus limiting the use of LES to moderate Reynolds numbers. One way to overcome this difficulty is to replace the near-wall region with a wall model which provides the outer LES with approximate wall boundary conditions. In recent years wall models based on turbulent boundary-layer equations and their simplified forms (Balaras, Benocci & Piomelli (1996); Cabot & Moin (2000); Wang & Moin (2002)) have been developed and applied successfully in a number of flow configurations. The objective of this work is to study the applicability of a simple near-wall model, based on the local equilibrium hypothesis, in the framework of immersed boundary method for LES and to analyze its effect on the flow dynamics. The selected test case is the flow past a 25 degree, asymmetric trailing edge of a model hydrofoil. The Reynolds number based on free-stream velocity U∞ and the hydrofoil chord C, is ReC = 2.15×10 . The simulation is performed over the rear 38% of the hydrofoil chord, and the Reynolds number based on the hydrofoil thickness is Re = 1.02 × 10. The flow was investigated experimentally by Blake (1975) and numerically by Wang & Moin (2000), who reported that 200 CRAY C-90 CPU hours were needed to advance the simulation by one flow-through time for a fully resolved LES.