Turbulent Flows

Abstract

AbstractMost flows in our natural and technical environment are turbulent and it is for this reason that a more extended treatment of turbulent flow is presented in this chapter. The statistical treatment of turbulent flows is emphasized and appropriate mean flow and time-averaged turbulent properties are introduced. Probability density distributions of turbulent velocity fluctuations are introduced and are employed to explain isotropic and homogeneous turbulent flow fields. Correlations, spectra and time scales of turbulent flow properties are described. The turbulent flow fields are split into a mean flow and superimposed turbulent fluctuations, \(\widehat{U}_{i} = U_{i} + u^{\prime}_{i}\). Introducing these into the basic equation of fluid mechanics allows the Reynolds equation to be derived by time averaging the equations. In this way, unknown turbulence properties arise in these equations. It is necessary to develop turbulence models to yield additional equations to permit numerical solutions to the Reynolds equations to be obtained. This leads to the introduction of “turbulence models”, connected to a new sub-field of fluid mechanics, resulting in approaches to yield acceptable solutions to many fluid flow problems. Zero-, one- and two-equation eddy viscosity models have resulted from this work and the basics of their development are summarized in this chapter.