Chapter 7 - Turbulence Modelling

Abstract

A relatively simple way of modeling the turbulence is offered by the so-called Reynolds-averaged Navier–Stokes equations (RANS). Reynolds stress models or Large-Eddy Simulation (LES) considerably enables more accurate predictions of turbulent flows. The various well-proven and widely applied turbulence models of varying level of complexity are presented in the chapter in detail. There is no single turbulence model that can reliably predict all kinds of turbulent flows. Therefore, it is important to determine whether the model includes all the significant features of the flow being investigated. The chapter discusses the basic equations of turbulence as they result from time and mass averaging of the governing equations. The chapter presents the Boussinesq's and the non-linear eddy–viscosity approaches, as well as the Reynolds–stress transport equation that forms the basis of the algebraic and differential Reynolds–stress models. The chapter also presents a few widespread one- and two-equation first-order closures. The first-order closures represent the easiest way to approximate the Reynolds stresses in the Reynolds-/Favre-averaged Navier–Stokes equations. They are based on the Boussinesq or non-linear eddy-viscosity models. From the large variety of first-order closure models, three widely used approaches, which represent the current state-of-the-art, are selected. All three models —namely, the Spalart–Allmaras one-equation turbulence model, the K-ɛ turbulence model, and the Shear Stress Transport (SST) turbulence model can be implemented easily on structured as well as on unstructured grids. LES, Detached Eddy Simulation (DES), and related approaches are discussed in the chapter in some detail because of the growing number of engineering applications.