Study of Some Key Issues for Applying LES to Real Engineering Problems

Abstract

Most of nature and industry flows are turbulence. There are three kinds of numerical simulation methods for turbulent flows (Lesieur 1990; Pope 2000; Sagaut 2000, 2006): direct numerical simulation (DNS), Reynolds-averaged Navier-Stokes equations (RANS) and large eddy simulation (LES). DNS is a straightforward way to simulate turbulent flows. Full Navier-Stokes equations are discretized and solved numerically without any model, empirical parameter or approximation. Theoretically speaking, results of DNS exactly reflect the real flow and the whole range of turbulence scales are computed. With DNS, people can compute and visualize any quantity of interest, including some that are too difficult or impossible to be measured by experiments. But as we all know the computation cost is very high. For high Reynolds number flow, even modern computer technology can not satisfy the computation requirement. In RANS, the flow quantities are decomposed into two parts: the average or mean term and the fluctuating term by applying Reynolds averaging. The effect of the fluctuating quantities on the mean flow quantities is described by the so called Reynolds stress tensor, which is must be modelled in terms of the mean velocities. Typical models can be grouped loosely into three categories: algebraic models, one-equation models and two-equation models. RANS is simple and robust. It is widely used in engineering problem. The general limitation of RANS is the fact that the model must represent a very wide range of scales. While the small scales tend to be universal, and depend on viscosity, the larger scales depend largely on flow condition and boundaries. So there is no one universal model for all flows. For different flows, the model must be modified to obtain good results. Another issue is that usually a time averaging is adopted in RANS. So RANS has difficult to handle unsteady flows. In LES, a filter is applied to separate the large scales from small scales. Then only the large, energy carrying scales (or called resolved scales) of turbulence are computed exactly by solving the governing equations. While the small, fluctuating scales are modelled, which is also called subgrid scales (SGS). Compared to RANS, LES has several advantages: 1) LES can capture the large scales directly which are the main energy container of turbulence and response for the momentum and energy transfer. 2) The dissipation of turbulence energy is believed to be done by small scales. Since small scales are thought to be homogenous,