4.11.1 Overview

Turbulent flows are characterized by eddies with a wide range of length and time scales. The largest eddies are typically comparable in size to the characteristic length of the mean flow. The smallest scales are responsible for the dissipation of turbulence kinetic energy.

It is possible, in theory, to directly resolve the whole spectrum of turbulent scales using an approach known as direct numerical simulation (DNS). No modeling is required in DNS. However, DNS is not feasible for practical engineering problems involving high Reynolds number flows. The cost required for DNS to resolve the entire range of scales is proportional to ${\rm Re}_t^{3}$, where ${\rm Re}_t$ is the turbulent Reynolds number. Clearly, for high Reynolds numbers, the cost becomes prohibitive.

In LES, large eddies are resolved directly, while small eddies are modeled. Large eddy simulation (LES) thus falls between DNS and RANS in terms of the fraction of the resolved scales. The rationale behind LES can be summarized as follows:

• Momentum, mass, energy, and other passive scalars are transported mostly by large eddies.

• Large eddies are more problem-dependent. They are dictated by the geometries and boundary conditions of the flow involved.

• Small eddies are less dependent on the geometry, tend to be more isotropic, and are consequently more universal.

• The chance of finding a universal turbulence model is much higher for small eddies.

Resolving only the large eddies allows one to use much coarser mesh and larger times-step sizes in LES than in DNS. However, LES still requires substantially finer meshes than those typically used for RANS calculations. In addition, LES has to be run for a sufficiently long flow-time to obtain stable statistics of the flow being modeled. As a result, the computational cost involved with LES is normally orders of magnitudes higher than that for steady RANS calculations in terms of memory (RAM) and CPU time. Therefore, high-performance computing (e.g., parallel computing) is a necessity for LES, especially for industrial applications.

The following sections give details of the governing equations for LES, the subgrid-scale turbulence models, and the boundary conditions.