Motion, turbulent, kinetic

The properties of the turbulence are different at the two extremes of the scale of turbulence. The largest eddies, known as the macroscale turbulence, contain most of the turbulent kinetic energy. Their motion is dominated by inertia and viscosity has little direct effect on them. In contrast, at the microscale of turbulence, the smallest eddies are dominated by viscous stresses, indeed viscosity completely smooths out the microscale turbulence. 

Now we turn our attention to flowing waters. Here the physics of the boundary is influenced by two kinds of motion, the motions induced by the wind and the water currents, respectively. The latter will be extensively discussed in Chapter 24. At this point it is sufficient to introduce the most important concept in fluid dynamics to quantify the intensity of turbulent motion and to assess the relative importance of several simultaneous processes of turbulent kinetic energy production. 

Recall our short discussion in Section 18.5 where we learned that turbulence is kind of an analytical trick introduced into the theory of fluid flow to separate the large-scale motion called advection from the small-scale fluctuations called turbulence. Since the turbulent velocities are deviations from the mean, their average size is zero, but not their kinetic energy. The kinetic energy is proportional to the mean value of the squared turbulent velocities, Mt2urb, that is, of the variance of the turbulent velocity (see Box 18.2). The square root of this quantity (the standard deviation of the turbulent velocities) has the dimension of a velocity. Thus, we can express the turbulent kinetic energy content of a fluid by a quantity with the dimension of a velocity. In the boundary layer theory, which is used to describe wind-induced turbulence, this quantity is called friction velocity and denoted by u. In contrast, in river hydraulics turbulence is mainly caused by the friction at the... 

Fluctuating components of gas velocity are selected from a Gaussian distribution with variance derived from the local value of turbulent kinetic energy. Integration of the particle equation of motion yields the particle position at any given instant in time. 

The classical turbulence models express the eddy viscosity algebraically in terms of a turbulence scale and intensity that are related, respectively, to the characteristic length dimensions of the flow field and the local mean velocity gradients. This implies an equilibrium between the local turbulence and the mean motion. This requirement of equilibrium has been relaxed in some eddy viscosity models where the intensity and scale of turbulence used to evaluate the eddy viscosity are expressed by partial differential equations for the turbulence kinetic energy and its dissipation rate. This latter class of models is presented in detail, for example, in Refs. 76 and 77. 

The most common way for turbulent kinetic energy to enter flow is by a shear layer. When we stir the soup, often we use a circular motion and induce a circular flow and/or circular eddies. This is also common in vessels with rotating mixers. But for flows in pipes, ducts, around airplanes or ships, or in... 

Fig. 2.26 Radial distributions of the axial turbulence kinetic energy for each turbulent motion...

Figure 2.27 compares the measured data on the contribution of each turbulent motion to the total turbulence kinetic energy in the axial direction with those in an... 

Fig. 2.27 Contributions of four turbulent motions to the axial turbulence kinetic energy...

Figure 2.28 illustrates the radial turbulence kinetic energy for each turbulent motion. The contribution of inward interaction is particularly large for rjh < 1.0 in spite of its lowest appearance frequency just like the axial turbulence kinetic energy. Meanwhile, in this radial region (r/i>u < 10), the contributions of sweep and outward interaction are hardly different from each other. 

Figure 2.29 shows the radial distribution of the Reynolds shear stress for each turbulent motion. The absolute values for the inward interaction and ejection are large, as suggested from the turbulence kinetic energies. 

The measured values of for each turbulent motion remain almost unchanged in the radial direction, but in a strict sense, those for ejection and sweep changed trend around r/b = 1.0. This implies that the Fle-Wood s metal bubbling jet has two large-scale coherent structures, the boundary being located around r/by = 1.0. This result is consistent with the above-mentioned findings on the appearance frequency and the contributions of each turbulent motion to the turbulence kinetic energies and the Reynolds shear stress. 

The pressure at every instant during an expansion or contraction of the working substance must be only infinitesimally greater or less respectively, than the external pressure, otherwise turbulent motions occur, the kinetic energy of which is ultimately converted into heat by friction, and this heat production is intrinsically irreversible. 

McKelvey, K. N., H.-N. Yieh, S. Zakanycz, and R. S. Brodkey (1975). Turbulent motion, mixing, and kinetics in a chemical reactor configuration. AIChE Journal 21, 1165-1176. 

The behavior of confined flames differs considerably from that of unconfined flames. Acceleration of the gases, caused by confinement, results in the generation of shear stresses and turbulent motions, which decrease the influence of approach stream turbulence and the effect of chemical kinetic factors. How the implementation of the ABC and the PPDF method helps to obtain the experimentally observed flow patterns and to understand the mechanism of flame stabilization and blow-off is demonstrated in this section. 

The eddies which give rise to short laminar motions along the wall are generated in the vicinity of the boundary in a region, located at the distance y0 from the interface, dominated by turbulence. The intensity of these eddies can be characterized by their kinetic energy E0 at that distance. The path length x is expected to depend on E0 and on the physical constants r and p. Consequently, dimensional analysis leads to... 

As a disturbance of laminar flow, which is exclusively caused by the elasticoviscous properties of the solution, is independent of the question, whether the external or the internal cylinder is rotating, one should not rely blindly on the criteria for the onset of turbulent motion, as given above on the basis of kinetic energy only. 

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