Turbulent motion

Fluidization. Particles suspended in a gas stream behave like a Hquid. They can be mixed by turbulent motion in a duidized bed. This mixer is used for mixing and drying, or mixing and reaction. 

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. 

Macromixing The phenomenon whereby residence times of clumps are distributed about a mean value. Mixing on a scale greater than the minimum eddy size or minimum striation thickness, by laminar or turbulent motion. 

Several potential meehanisms exist for the attrition proeess with the breaking energy of partieles originating from either bulk eireulation e.g. Ottens and de Jong (1973), Nienow and Conti (1978), Conti and Nienow (1980), Kuboi etal. (1984), Laufliiitte and Mersmann (1987), PloG and Mersmann (1989) or the turbulent motion of the fluid e.g. Evans etal. (1974), Glasgow and Lueeke (1980), Jagannathan etal. (1980), or both e.g. Synowiee etal. (1993). 

Turbulence is generated by wind shear in the surface layer and in the wake of obstacles and structures present on the earth s surface. Another powerful source of turbulent motion is an unstable temperature stratification in the atmosphere. The earth s surface, heated by sunshine, may generate buoyant motion of very large scale (thermals). 

Turbulent eddies larger than the cloud size, as such, tend to move the cloud as a whole and do not influence the internal concentration distribution. The mean concentration distribution is largely determined by turbulent motion of a scale comparable to the cloud size. These eddies tend to break up the cloud into smaller and smaller parts, so as to render turbulent motion on smaller and smaller scales effective in generating fluctuations of ever smaller scales, and so on. On the small-scale side of the spectrum, concentration fluctuations are homogenized by molecular diffusion. 

Fuel from a fiilly unobstructed jet would be diluted to a level below its lower flammability limit, and the flammable portion of the cloud would be limited to the jet itself. In practice, however, jets are usually somehow obstructed by objects such as the earth s surface, surrounding structures, or equipment. In such cases, a large cloud of flammable mixture will probably develop. Generally, such a cloud will be far from stagnant but rather in recirculating (turbulent) motion driven by the momentum of the jet. 

The blast resulting from the remaining unconfined and unobstructed parts of a cloud can be modeled by assuming a low initial strength. For extended and quiescent parts, assume minimum strength of 1. For more nonquiescent parts, which are in low-intensity turbulent motion, for instance, beeause of the momentum of a fuel release, assume a strength of 3. 

Potential centers of strong blast are found in areas in a cloud which are in intensely turbulent motion when reached by the flame. Such cloud areas are described in the introduction to this section. Practical examples of potential centers of strong blast in vapor cloud explosions are... 

The jet by which the propane is released. The jet s propane-air mixture is in intensely turbulent motion and will develop an explosive combustion rate and blast effects on ignition. 

Nesterovich NI (1979) Equations of turbulent motion of heterogeneous mixtures (in Russian). Prepr of Inst of Theor and Appl Mech USSR Academ of Science, Siberian Branch 8 28... 

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. 

Region 3 (Re > 3000) corresponds to turbulent motion of the fluid and R/pu2 is a function of both Re and e/d, with rough pipes giving high values of R/pu2. For smooth pipes there is a lower limit below which R/pu2 does not fall for any particular value of Re. 

In turbulent motion, the presence of circulating or eddy currents brings about a much-increased exchange of momentum in all three directions of the stream flow, and these eddies are responsible for the random fluctuations in velocity The high rate of transfer in turbulent flow is accompanied by a much higher shear stress for a given velocity gradient. 

Hwang and Kim (2006) investigated the pressure drop in circular stainless steel smooth micro-tubes ks/d <0.1%) with inner diameters of 244 pm, 430 pm and 792 pm. The measurements showed that the onset of flow transition from laminar to turbulent motion occurs at the Reynolds number of slightly less than 2,000. It... 

Turbulent nonpremixed flames contain a wide range of lengfh scales. For a given flame geomefry, fhe largest scales of furbulence are determined by the overall width of an unconfined jef flame or by fhe dimensions of the hardware that contain the flow. Therefore, the largest scales of turbulent motion are typically independent of Reynolds number. As the Re5molds number increases. 

Stresses acting on micro-organisms in (a) to (c) are derived on the premise that the flow forces originate from the turbulent motion of the carrier medium. In almost all cases, turbulence is assumed to be locally isotropic and homogeneous which greatly simplifies the analysis and allows the application of the Kolmogoroff s theory of turbulence to the problem [81]. The Kolomogoroff micro-scale of turbulence,... 

COLBURN, A. P. (1934) Trans. Am. Inst. Chem. Eng. 30, 187. Note on the calculation of condensation when a portion of the condensate layer is in turbulent motion. 

In some practical processes, a high relative velocity may not exist and effects of turbulence on droplet breakup may become dominant. In such situations Kolmogorov, 280 and Hinze[27°l hypothesized that the turbulent fluctuations are responsible for droplet breakup, and the dynamic pressure forces of the turbulent motion determine the maximum stable droplet size. Using Clay s data, 2811 and assuming isotropic turbulence, an expression was derived for the critical Weber number 270 ... 

Brodkey, R. S. (1966). Turbulent motion and mixing in a pipe. AIChE Journal 12, 403-404. 

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. 

Dreybrodt W, Buhmann D. A mass transfer model for dissolution and precipitation of calcite from solutions in turbulent motion. Chem Geol 1991 107-122. 

In addition to phase change and pyrolysis, mixing between fuel and oxidizer by turbulent motion and molecular diffusion is required to sustain continuous combustion. Turbulence and chemistry interaction is a key issue in virtually all practical combustion processes. The modeling and computational issues involved in these aspects have been covered well in the literature [15, 20-22]. An important factor in the selection of sub-models is computational tractability, which means that the differential or other equations needed to describe a submodel should not be so computationally intensive as to preclude their practical application in three-dimensional Navier-Stokes calculations. In virtually all practical flow field calculations, engineering approximations are required to make the computation tractable. 

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. 

A model of transfer within an oscillating droplet was proposed by Handlos and Baron (H3). They assumed that transfer within the drop was entirely by turbulent motion, random radial movement, superimposed upon toroidal circulation streamlines. No allowance was made for the variation of shape or... 

It should be kept in mind that these calculated rates of diffusion and gravitational settling are only applicable to still air. In fact, in the atmosphere the air is rarely still and is usually undergoing some degree of turbulent motion. In this case, the transport of particles becomes more complex and faster due to the velocity gradients and contorted patterns of air flow however, a discussion of this is outside the scope of this book. 

The purpose of this chapter is to provide a comprehensive discussion of some simple approaches that can be employed to obtain information on the rate of heat and mass transfer for both laminar and turbulent motion. One approach is based on dimensional scaling and hence ignores the transport equations. Another, while based on the transport equations, does not solve them in the conventional way. Instead, it replaces them by some algebraic expressions, which are obtained by what could be called physical scaling. The constants involved in these expressions are determined by comparison with exact asymptotic solutions. Finally, the turbulent motion is represented as a succession of simple laminar motions. The characteristic length and velocity scales of these laminar motions are determined by dimensional scaling. It is instructive to begin the presentation with an outline of the basic ideas. 

Conventional dimensional analysis uses single length and time scales to obtain dimensionless groups. In the first section, a new kind of dimensional analysis is developed which employs two kinds of such scales, the microscopic (molecular) scale and the macroscopic scale. This provides some physical significance to the exponent of the Reynolds number in the expression of the Sherwood number, as well as some bounds of this exponent for both laminar and turbulent motion. 

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