Turbulent Flow processes

In the turbulent-flow region distinct fluid layers are no longer observed, and we are forced to seek a somewhat different concept for viscous action. A qualitative picture of the turbulent-flow process may be obtained by imagining macroscopic chunks of fluid transporting energy and momentum instead of... 

Horizontal In-Shell Condensers The mean condensing coefficient for the outside of a bank of horizontal tubes is calculated from Eq. (5-93) for a single tube, corrected for the number of tubes in a vertical row. For undisturbed laminar flow over all the tubes, Eq. (5-97) is, for realistic condenser sizes, overly conservative because of rippling, splashing, and turbulent flow (Process Heat Transfer, McGraw-Hill, New York, 1950). Kern proposed an exponent of -Ve on the basis of experience, while Freon-11 data of Short and Brown General Discussion on Heat Transfer, Institute of Mechanical Engineers, London, 1951) indicate independence of the number of tube rows. It seems reasonable to use no correction for inviscid liquids and Kern s correction for viscous condensates. For a cylindrical tube bundle, where N varies, it is customary to take N equal to two-thirds of the maximum or centerline value. 

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. 

In this approach, the unsteady processes occurring in turbulent flows are visualized as a combination of some mean process and small-scale fluctuations around it. The typical time variation of fluid velocity at a point in a turbulent flow is shown in Fig. 3.1. In the statistical approach, an instantaneous velocity, U, is visualized as a mean velocity, U (shown by a horizontal line in Fig. 3.1) and fluctuations around it, u. Based on such an approach, the statistical theory of turbulence flows has been developed (see Hinze, 1975 and references cited therein). It has been the basis for most of the engineering modeling of turbulent flow processes. Some of the key concepts of the statistical approach are discussed below. 

Direct numerical simulation, as the name implies, attempts to simulate all the dynamically important scales of turbulent flows, directly. It is based on the hypothesis that direct simulations may be carried out by artificially decreasing the Reynolds number to the point where important scales can be simulated accurately on existing computers. This is probably the most exact approach to turbulence simulation without requiring any additional modeling beyond accepting the Navier-Stokes equations to describe the turbulent flow processes. The result is equivalent to a single realization of a flow or a short duration laboratory experiment. It is also the simplest approach conceptually. In DNS, all the motions contained in the flow are resolved. 

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