Generalized turbulence

For a very thin liquid film, the value of 3 cannot be evaluated, and it should be replaced by a new parameter 3, using the generalized turbulent boundary-layer profile in an adiabatic flow as in Reference (Levy and Healzer, 1980). GF can be solved stepwise along the pipe until the G value goes to zero, where dryout occurs. This analysis was performed to compare the calculated g"rit with Wurtz data (Wurtz, 1978) and also to compare with the predictions by the well-known Biasi et al. correlation (1968), as shown in Figure 5.90. For the limited data points compared, the agreement was good. 

Interfacial transfer of chemicals provides an interesting twist to our chemical fate and transport investigations. Even though the flow is generally turbulent in both phases, there is no turbulence across the interface in the diffusive sublayer, and the problem becomes one of the rate of diffusion. In addition, temporal mean turbulence quantities, such as eddy diffusion coefficient, are less helpful to us now. The unsteady character of turbulence near the diffusive sublayer is crucial to understanding and characterizing interfacial transport processes. 

CHEMICAL VARIABLES. In general, turbulent burning velocity rises to a maximum rich of stoichiometric, and then declines, in a manner similar to that of laminar flames. Figure 10 shows the typical behavior (8). The maximum does not shift with changing Reynolds number some data do show a slight shift to richer mixtures at higher turbulence levels 78). 

Analysis of equations for second momenta like (SNA5NB), (5Na)2) and (5NB)2) shows that all their solutions are time-dependent. In the Lotka-Volterra model second momenta are oscillating with frequencies larger than that of macroscopic motion without fluctuations (2.2.59), (2.2.60). Oscillations of k produce respectively noise in (2.2.68), (2.2.69). Fluctuations in the Lotka-Volterra model are anomalous second momenta are not expressed through mean values. Since this situation reminds the turbulence in hydrodynamics, the fluctuation regime in this model is called also generalized turbulence [68]. The above noted increase in fluctuations makes doubtful the standard procedure of the cut off of a set of equations for random values momenta. 

Irregular behaviour of concentrations and the correlation functions observed in the chaotic regime differ greatly from those predicted by law of mass action (Section 2.1.1). Following Nicolis and Prigogine [2], the stochastic Lotka-Volterra model discussed in this Section, could be considered as an example of generalized turbulence. 

Finally, the most important problem is whether one can draw any conclusions for the general three-dimensional problem. Can one, for example, in the absence of helicity transfer directly to the case of isotropic three-dimensional general turbulence the concepts of diamagnetism of a turbulent plasma and of temporary growth of fields with a simultaneous decrease of the scale. These concepts can be applied not only to an infinite medium, but also to situations with boundary conditions at finite distances. But this problem is only posed here—its solution is a matter for the future. 

Gas-phase reacdotis are carried out primarily in tubular reactors where the flow is generally turbulent. By assuming that there is no dispersion and ttiere are no radial gradients in either temperature, velocity, or concentration, we can model the flow in the reactor as plug-flow. Laminar reactors are discussed in Chapter 13 and dispersion effects in Chapter 14. The differential form of the design equation... 

The various methods of agitation to produce emulsions have been described recently (18). In addition, the emulsions of smaller droplets can be produced by applying more intense agitation to disrupt the larger droplets. Therefore, the liquid motion during the process of emulsification is generally turbulent (9) except for high viscosity liquids. 

The GDE (Chapter 11) describes the basic processes that modify the particle size distribution. Because the atmosphere is generally turbulent, it is appropriate to time smooth the GDE which then takes the steady-slate form ... 

Pressure drop Because of the change in direction, impact of particles against bend walls, and general turbulence, there will be a pressure drop across every bend in any pipeline. The major element of the pressure drop, however, is that due to the re-acceleration of the particles back to their terminal velocity after exiting the bend. The situation can best be explained by means of a pressure profile in the region of a bend, such as that in Figure 4.29. 

Muffler geometry and residence time distribution. The diameter of the converter is larger than the diameter of the exhaust pipe. In the exhaust pipe, flow is generally turbulent, and the turbulent fluid enters the converter trough a short divergent inlet. Due to the divergent flow and to the backpressure induced by the monolith a complicated flow pattern develops and results in a non-uniform radial velocity distribution at the monolith scale. Presently, it is not possible to calculate the velocity distribution, and experiments are required. 

Now consider a stationary particle held in position by a stream flowing upward at just the terminal velocity of the particle, as shown in Figure 2-8. The fluid far away from the particle is in laminar flow, but in the wake of the particle, eddies form. A two dimensional slice of the flow provides a picture that is similar, in our intuitive context, to the surface currents behind a rock in a flowing stream. The eddies are relatively stationary in space and are easy to observe. They are typically round (or elliptical) in cross-section and maintain their size, which invites our intuition to jump to the idea of a coherent spherical (or ellipsoidal) eddy. We need to examine a general turbulent flow more carefully before making that assumption. 

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