## 31 Introduction

Turbulence is difficult to define precisely, although any reactor engineer may intuitively understand the differences in laminar and turbulent flow processes. Fluid motion is described as turbulent if it is irregular, rotational, intermittent, highly disordered, diffusive and dissipative. Turbulent motion is inherently unsteady and three-dimensional. Visualizations of turbulent flows reveal rotational flow structures (so called turbulence eddies), with a wide range of length scales. Such eddy motions and interactions between eddies of different length scales lead to effective contact between fluid particles which are initially separated by a long distance. As a consequence, heat, mass and momentum are very effectively exchanged. The rate of scalar mixing in turbulent flows is greater by orders of magnitude than that in laminar flows. Heat and mass transfer rates are also significantly higher in turbulent flows. Because of such effective mixing and enhanced rates of mass, momentum and heat transport, turbulence is often employed in chemical reactors to enhance performance. Turbulent flows are also associated with higher values of friction drag and pressure drop. However, more often than not, advantages gained with the enhanced transport rates are more valuable than the costs of higher frictional losses. It can be concluded that for many (if not most) engineering applications, turbulent flow processes are necessary to make the desired operation realizable and more efficient. It is, therefore, essential to develop suitable methods to predict and control turbulent flow processes.

Turbulence is the most complicated kind of fluid motion. There have been several different attempts to understand turbulence and different approaches taken to develop predictive models for turbulent flows. In this chapter, a brief description of some of the concepts relevant to understand turbulence, and a brief overview of different modeling approaches to simulating turbulent flow processes is given. Turbulence models based on time-averaged Navier-Stokes equations, which are the most relevant for chemical reactor engineers, at least for the foreseeable future, are then discussed in detail. The scope of discussion is restricted to single-phase turbulent flows (of Newtonian fluids) without chemical reactions. Modeling of turbulent multiphase flows and turbulent reactive flows are discussed in Chapters 4 and 5 respectively.

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