Turbulence modeling for very large-eddy simulation

An approach is described that attempts to bridge the gap between the traditional Reynolds-averaged Navier-Stokes (RANS) simulation and the traditional large-eddy simulation (LES). This approach affords an intermediate resolution of turbulence scales relative to those of BANS and LES and has the characteristics of the very large-eddy simulation (VLES). The very large scales of turbulence are directly calculated, and the effects of the unresolved scales are accounted for by an eddy viscosity model that is evolved from state-of-the-art models used in the RANS approach. The dependent variables and governing equations are based on a temporal filtering with a constant filter width. The contents of both resolved and unresolved scales are regulated by the width of the filter. The dependent variables and governing equations will naturally evolve from RANS to VLES and further toward LES, when the width of the temporal filter is decreased from the turbulent integral timescale to its fraction and all of the way toward the Taylor microtimescale. The subscale model uses a resolution control parameter, which is a function of the temporal filter width, to regulate the content of resolved/unresolved scales. This approach is called the partially resolved numerical simulation. Its mathematical formulation is described. Also, a guideline is provided for selecting the resolution control parameter and the grid spacing that optimizes the accuracy of the numerical simulation. Results from validation studies are then reported.