Eddy motions

Danckwerts [Jnd. Eng. Chem., 42, 1460(1951)] proposed an extension of the penetration theoiy, called the surface renewal theoiy, which allows for the eddy motion in the liquid to bring masses of fresh liquid continually from the interior to the surface, where they are exposed to the gas for finite lengths of time before being replaced. In his development, Danckwerts assumed that every element of fluid has an equal chance of being replaced regardless of its age. The Danck-werts model gives... 

Turbulent flow, by means of the chaotic eddy motion associated with velocity fluctuation, is conducive to rapid mixing and, therefore, is the preferred flow regime for mixing. Laminar mixing is carried out when high viscosity makes turbulent flow impractical. 

Wind speed has velocity components in all directions so that there are vertical motions as well as horizontal ones. These random motions of widely different scales and periods are essentially responsible for the movement and diffusion of pollutants about the mean downwind path. These motions can be considered atmospheric turbulence. If the scale of a turbulent motion (i.e., the size of an eddy) is larger than the size of the pollutant plume in its vicinity, the eddy will move that portion of the plume. If an eddy is smaller than the plume, its effect will be to difhise or spread out the plume. This diffusion caused by eddy motion is widely variable in the atmosphere, blit even when the effect of this diffusion is least, it is in the vicinity of three orders of magnitude greater than diffusion by molecular action alone. 

In Gaussian plume computations the change in wind velocity with height is a function both of the terrain and of the time of day. We model the air flow as turbulent flow, with turbulence represented by eddy motion. The effect of eddy motion is important in diluting concentrations of pollutants. If a parcel of air is displaced from one level to another, it can carry momentum and thermal energy with it. It also carries whatever has been placed in it from pollution sources. Eddies exist in different sizes in the atmosphere, and these turbulent eddies are most effective in dispersing the plume. 

Mixing is accomplished by the rotating action of an impeller in the continuous fluid. This action shears the fluid, setting up eddies w hich move through the body of the system. In general the fluid motion involves (a) the mass of the fluid over large distances and (b) the small scale eddy motion or turbulence which moves the fluid over short distances [21, 15]. 

In die streamline boundary layer the only forces acting within the fluid are pure viscous forces and no transfer of momentum takes place by eddy motion. 

Equation 11.12 does not fit velocity profiles measured in a turbulent boundary layer and an alternative approach must be used. In the simplified treatment of the flow conditions within the turbulent boundary layer the existence of the buffer layer, shown in Figure 11.1, is neglected and it is assumed that the boundary layer consists of a laminar sub-layer, in which momentum transfer is by molecular motion alone, outside which there is a turbulent region in which transfer is effected entirely by eddy motion (Figure 11.7). The approach is based on the assumption that the shear stress at a plane surface can be calculated from the simple power law developed by Blasius, already referred to in Chapter 3. 

If the motion of the fluid is turbulent, the transfer of fluid by eddy motion is superimposed on the molecular transfer process. In this case, the rate of transfer to the surface will be a function of the degree of turbulence. When the fluid is highly turbulent, the rate of transfer by molecular motion will be negligible compared with that by eddy motion. For small degrees of turbulence the two may be of the same order. 

Next, the buffer layer, in which molecular diffusion and eddy motion are of comparable magnitude. 

Finally, over the greater part of the fluid, the turbulent region in which eddy motion is large compared with molecular diffusion. 

Early studies of the transition to turbulence relied on flow visualization techniques for liquid flow through arrays of spheres. Jolls and Hanratty (1966) found a transition from steady to unsteady flow in the range 110<7 e< 150 for flow in a dumped bed of spheres at N — 12, and they observed a vigorous eddying motion that they took to indicate turbulence at Re — 300. In regular beds of spheres, Wegner et al. (1971) found completely steady flow with nine regions of reverse flow on the surface of the sphere for Re — 82, and similar flow elements but with different sizes in an unsteady flow at Re — 200. Dybbs and Edwards (1984) used laser anemometry and flow visualization to study flow... 

Though the sizes of particles which will be retained or lost by the separator can be calculated, it is found in practice that some smaller particles are retained and some larger particles are lost. The small particles which are retained have in most cases collided with other particles and adhered to form agglomerates which behave as large particles. Relatively large particles are lost because of eddy motion within the cyclone separator, and because they tend to bounce off the walls of the cylinder back into the central core... 

At an appropriate intensity level of ultrasound, intracellular microstreaming has been observed inside animal and plant cells with rotation of organelles and eddying motions in vacuoles of plant cells [9]. These effects can produce an increase in the metabolic functions of the cell that could be of use in both biotechnology and microbiology, especially in the areas of biodegradation and fermentation. 

The original eddy motion which sets up the chain of events leading to eruptions may be caused by forced flow of the bulk phases, density differences due to concentration or temperature gradients (B12), or earlier eruptions. Strong eruptions occur when a critical concentration driving force or a critical interfacial tension depression is exceeded (03, S8, S9). At lower concentration differences ripples may result (E4), eruptions may occur only over part of the interface (S8) with the jets taking some time to form (T9), or no interfacial motion at all may occur. Attempts to correlate the minimum driving force required for spontaneous interfacial motions have met with little success. 

The processes of transport at the atmosphere-water surface border have been well studied. The transport of moisture from the surface of a water body into the atmosphere is one of the complicated physical processes of mass and energy exchange across the water-air interface (Figure 4.12). These processes are functions of many climatic parameters and, to a large extent, are regulated by eddy motions in the surface layer of the atmosphere determined by the wind field. 

In polymer processing, because of the very high viscosities of polymeric melts, the flow is laminar and eddy motion due to turbulence is absent therefore, it cannot contribute to mixing. Similarly, molecular diffusion does not contribute much to mixing because it occurs extremely slowly. We are therefore left with convection as the dominant mixing mechanism.2... 

Diffusion Random migration of particles in a favored direction resulting from Brownian motion or turbulent eddy motion of the suspending gas. 

As velocity of flow increases, a condition is eventually reached at which rectilinear laminar flow is no longer stable, and a transition occurs to an alternate mode of motion that always involves complex particle paths. This motion may be of a multidimensional secondary laminar form, or it may be a chaotic eddy motion called turbulence. The nature of the motion is governed by both the rheological nature of the fluid and the geometry of the flow boundaries. 

Turbulent core 30 < y+, u+ = 2.51n y+ + 5.5 here turbulent flow and transfer by eddy motion dominate. 

The diffusion process involves substantial turbulent eddy motion so that the diffusion coefficient Dw may vary significantly with the height z. 

Figure 9-3. Steam rising from a leaf and a wooden fence post that are rapidly heated by the sun after a rainstorm. Moisture-laden air just outside the boundary layer next to the objects (cw = 1.05 mol m-3) is swept in an eddying motion into a cooler region, where the water vapor condenses.

Chilton-Colbum Analogy When a fluid moves over either a hq-uid or a solid surface, the eddy motion that causes mass transfer also causes heat transfer and fluid friction owing to the transfer of thermal energy and momentum respectively. This close similarity among the mechanisms for the transfer of mass, heat, and momentum was brought out in the Reynolds analogy (see Table 5-23-T), which stated that the following dimensionless ratios are equal ... 

Another approach that has promise for study of turbulence structure is the fluctuating velocity field (FVF) closure, adopted by Deardorff (D3). Using the analog of a MVF closure for turbulent motions of smaller scale than his computational mesh, Deardorff carried out a three-dimensional unsteady solution of Navier-Stokes equations, thereby calculating the structure of the larger-scale eddy motions. While it is likely that calculations of such complexity will remain beyond the reach of most for some time to come, results like Deardorff s should serve as guides for framing closure models. 

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