Turbulent structure

The averaging time of the rapid-response record [Fig. 4-1 (a)] is an inherent characteristic of the instrument and the data acquisition system. It can become almost an instantaneous record of concentration at the receptor. However, in most cases this is not desirable, because such an instantaneous record cannot be put to any practical air pollution control use. What such a record reveals is something of the turbulent structure of the atmosphere, and thus it has some utility in meteorological research. In communications... 

A reduced scale of the model requires an increased velocity level in the experiments to obtain the correct Reynolds number if Re < Re for the prob lem considered, but the experiment can be carried out at any velocity if Re > RCj.. The influence of the turbulence level is shown in Fig. 12.40. A velocity u is measured at a location in front of the opening and divided by the exhaust flow rate in order to obtain a normalized velocity. The figure show s that the normalized velocity is constant for Reynolds numbers larger than 10 000, which means that the flow around the measuring point has a fully developed turbulent structure at that velocity level. The flow may be described as a potential flow with a normalized velocity independent of the exhaust flow rate at large distances from the exhaust opening— and far away from surfaces. 

An appropriate model of the Reynolds stress tensor is vital for an accurate prediction of the fluid flow in cyclones, and this also affects the particle flow simulations. This is because the highly rotating fluid flow produces a. strong nonisotropy in the turbulent structure that causes some of the most popular turbulence models, such as the standard k-e turbulence model, to produce inaccurate predictions of the fluid flow. The Reynolds stress models (RSMs) perform much better, but one of the major drawbacks of these methods is their very complex formulation, which often makes it difficult to both implement the method and obtain convergence. The renormalization group (RNG) turbulence model has been employed by some researchers for the fluid flow in cyclones, and some reasonably good predictions have been obtained for the fluid flow. 

In relatively low-reactive fuel-air mixtures, a detonation may only arise as a consequence of the presence of appropriate boundary conditions to the combustion process. These boundary conditions induce a turbulent structure in the flow ahead of the flame front. This turbulent structure is a basic element in the feedback coupling in the process by which combustion rate can grow more or less exponentially with time. This fundamental mechanism of a gas explosion has been described in Section 3.2. 

Experimental research has shown that a vapor cloud explosion can be described as a process of combustion-driven expansion flow with the turbulent structure of the flow acting as a positive feedback mechanism. Combustion, turbulence, and gas dynamics in this complicated process are closely interrelated. Computational research has explored the theoretical relations among burning speed, flame speed, combustion rates, geometry, and gas dynamics in gas explosions. 

The values of Gy and Gz vary with tlie turbulent structure of the atmosphere, tlie height above the surface, tlie surface rougluiess, the sampling time over wliich tlie concentration is to be estimated, tlie wind speed, and tlie distance from tlie source. For tlie parameter values tliat follow, the sampling time was originally assumed to be about 10 minutes, tlie height to be tlie lowest several hmidred meters of tlie atmosphere, and tlie surface to be relatively open country. The parameters are estimated from tlie stability of the atmosphere. 

Chemiluminescence images of a turbulent CH4/H2/N2 jet flame (Re = 15,200) measured with two different exposure times. The long-exposure image (far left) indicates the mean flame structure, and the six shorter exposures to the right illustrate the instantaneous turbulent structure. 

D.R. White, Turbulent structure of gaseous detonation, Phys. Fluids, 4(4), 465-480,1961. 

Almost all flows in chemical reactors are turbulent and traditionally turbulence is seen as random fluctuations in velocity. A better view is to recognize the structure of turbulence. The large turbulent eddies are about the size of the width of the impeller blades in a stirred tank reactor and about 1/10 of the pipe diameter in pipe flows. These large turbulent eddies have a lifetime of some tens of milliseconds. Use of averaged turbulent properties is only valid for linear processes while all nonlinear phenomena are sensitive to the details in the process. Mixing coupled with fast chemical reactions, coalescence and breakup of bubbles and drops, and nucleation in crystallization is a phenomenon that is affected by the turbulent structure. Either a resolution of the turbulent fluctuations or some measure of the distribution of the turbulent properties is required in order to obtain accurate predictions. 

The theory of bulk liquid turbulent structure control in combination with the transverse lift force (Drew et al., 1978 Lahey, 1988)... 

Serizawa, A., I. Kataoka, and I. Michiyoshi, 1975, Turbulence Structure of Air-Water Bubbly Flow— II, Local Properties, Int. J. Multiphase Flow 2 235 246. (3)... 

Figure 21. Examples of the stationary patterns observed in the CIMA reaction (a) Hexagonal structure (b) lamellar stripe structure (c) irregular (turbulent structure).

However, it is not likely that all of the air entrained will react with the fuel. The turbulent structure of the flame does not allow the fuel and oxygen to instantaneously mix. There is a delay, sometimes described as unmixedness . Hence, some amount of... 

The mechanism is essentially a combination of the deformation of a round liquid jet by aerodynamic forces and the instability of the deformed jet. The liquid jet is first accelerated rapidly in the high speed air stream (Fig. 3.3b). The jet diameter is thus significantly reduced as it interacts with the surrounding air stream. The direction of the thinning capillary liquid jet is influenced by the interaction between the liquid jet and the turbulent structures of the surrounding air stream. The formation of... 

Pulsation in a spray is generated by hydrodynamic instabilities and waves on liquid surfaces, even for continuous supply of liquid and air to the atomizer. Dense clusters of droplets are projected into spray chamber at frequencies very similar to those of the liquid surface waves. The clusters interact with small-scale turbulent structures of the air in the core of the spray, and with large-scale structures of the air in the shear and entrainment layers of outer regions of the spray. The phenomenon of cluster formation accounts for the observation of many flame surfaces rather than a single flame in spray combustion. Each flame surrounds a cluster of droplets, and ignition and combustion appear to occur in configurations of flames surrounding droplet clusters rather than individual droplets. 

In natural systems (lakes, oceans, atmosphere) turbulent diffusion is usually anisotropic (i.e., much larger in the horizontal than vertical direction). There are two main reasons for that observation (1) the extension of natural systems in the horizontal is usually much larger than in the vertical. Thus, the turbulent structures (often called eddies) that correspond to the mean free paths of random motions often look like pancakes that is, they are flat along the vertical axis and mainly extended along the horizontal axes. (2) Often the atmosphere or the water body in a lake or ocean is density stratified (i.e., the density increases with depth). This compresses the eddies even further in the vertical. Gravitational forces keep the water parcels from moving too far away from the depth where they are neutrally buoyant, that is, where they have the same density as their environment. Thus, the anisotropic shape of the eddies results in turbulent diffusivities which differ in size along different spatial directions. 

The gradient-flux model to describe turbulent diffusion (Eq. 18-70) has the disadvantage that turbulent diffusivity, Ex, is scale dependent. As discussed in more detail in Chapter 22, in natural systems Ex increases with increasing horizontal scale of diffusion. This means that the speed with which two fluid parcels are separated by turbulence increases the further they are from each other. This is because turbulent structures (eddies) of increasing size become effective when the size of a diffusing patch becomes larger. Typical ranges of turbulent diffusivities in the environment are summarized in Table 18.4. 

In the seventies, the growing interest in global geochemical cycles and in the fate of man-made pollutants in the environment triggered numerous studies of air-water exchange in natural systems, especially between the ocean and the atmosphere. In micrometeorology the study of heat and momentum transfer at water surfaces led to the development of detailed models of the structure of turbulence and momentum transfer close to the interface. The best-known outcome of these efforts, Deacon s (1977) boundary layer model, is similar to Whitman s film model. Yet, Deacon replaced the step-like drop in diffusivity (see Fig. 19.8a) by a continuous profile as shown in Fig. 19.8 b. As a result the transfer velocity loses the simple form of Eq. 19-4. Since the turbulence structure close to the interface also depends on the viscosity of the fluid, the model becomes more complex but also more powerful (see below). 

The above expression is very general and includes both the case of stagnant waters (u = 0, e.g., Eq. 20-24) as well as situations in which the water flow-induced turbulence dominates the exchange velocity relative to the influence of the wind. Obviously, as wind speed changes, for a given river the situation may switch between current-dominated and wind-dominated regimes. Another factor which influences the shape of the empirical function / of Eq. 20-31 is the typical size of the turbulent structures (the eddies) relative to the water depth. This leads to two different models, the small-eddy and the large-eddy model, respectively (Fig. 20.8 and Box 20.3). 

While molecular diffusivity is commonly independent of direction (isotropic, to use the correct expression), turbulent diffusivity in the horizontal direction is usually much larger than vertical diffusion. One reason is the involved spatial scales. In the troposphere (the lower part of the atmosphere) and in surface waters, the vertical distances that are available for the development of turbulent structures, that is, of eddies, are generally smaller than the horizontal distances. Thus, for pure geometrical reasons the eddies are like flat pancakes. Needless to say, they are more effective in turbulent mixing along their larger axes than along their smaller vertical extension. 

As mentioned earlier, turbulent motion is usually more intensive along the horizontal than the vertical axis. Turbulent structures (eddies) can be horizontally very large. For instance, the eddies or gyres produced by the Gulf Stream are more than 100 km wide. Thus, for horizontal transport the separation between random and directed motion plays a more crucial role than for the case of vertical diffusion. 

Thus, observing the growth of a tracer patch would allow us to calculate the horizontal diffusion coefficient. The above expression would still hold if the growing effect of random motion with patch size were considered as inferred by the picture of a spectmm of turbulent structures of different size. The turbulent diffusivities, Ex and Ey, would then depend on ax or oy. 

This accounts for the substantially higher effectiveness compared to the fibers as a consequence of their microscopic dimensions, the macromolecules are able to engage in the production and growth stages of eddies considerably earlier, thus exerting a sustained damping influence on the axial and radial turbulence structure, as conformed by LDA measurements in injection experiments. 

The coefficients of transport properties considered here include the viscosity, diffusivity, and thermal conductivity of a gas. The transport coefficients vary with gas properties if the flow is laminar. When the flow is turbulent, the transport coefficients become strongly dependent on the turbulence structure. Here we only deal with the laminar transport coefficients the discussion of the turbulent transport coefficients is given in 5.2.4. 

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