Turbulent Dispersers

As this chapter is primarily concerned with single-drop performance, it seems best to omit consideration of drop sizes in highly turbulent liquid fields. The work of Shinnar and Church (S7), utilizing Kolmogo-roff s hypothesis of local isotropy, seems to bear excellent promise from a fundamental viewpoint. Correlating equations for predicting drop size in stirred tanks and mixers have been given by Treybal (T3). 

---

Chapter 2 discussed the possible influence of atmospheric dispersion on vapor cloud explosion or flash fire effects. Factors such as flammable cloud size, homogeneity, and location are largely determined by the manner of flammable material released and turbulent dispersion into the atmosphere following release. Several models for calculating release and dispersion effects have been developed. Hanna and Drivas (1987) provide clear guidance on model selection for various accident scenarios. 

Generally, at any moment of time the concentration of components within a vapor cloud is highly nonhomogeneous and fluctuates considerably. The degree of homogeneity of a fuel-air mixture largely determines whether the fuel-air mixture is able to maintain a detonative combustion process. This factor is a primary determinant of possible blast effects produced by a vapor cloud explosion upon ignition. It is, therefore, important to understand the basic mechanism of turbulent dispersion. 

Flow in the atmospheric boundary layer is turbulent. Turbulence may be described as a random motion superposed on the mean flow. Many aspects of turbulent dispersion are reasonably well-described by a simple model in which turbulence is viewed as a spectrum of eddies of an extended range of length and time scales (Lumley and Panofsky 1964). 

The mixing time can be related to power per unit volume and the geometry. Turbulent dispersion can produce unmixedness within the system, if there are gradients of mean concentration. This is not considered here. A useful discussion of these equations was given by Brodkey (1975) and Baldyga (1989). 

Moore P.A., Atema J. and Gerhardt G.A. (1992). The structure of environmental odor signals from turbulent dispersion to movement through boundary layers and mucus. In Chemical Signals in Vertebrates 6 (Doty R.L. and Muller-Schwarze D., eds). Plenum, New York, pp. 79-83. 

Logical Structures. When a synthetic organic chemical is released into an aquatic system, the entire array of transport, transfer, and transformation processes begins at once to act on the chemical. Transport from the point of entry into the bulk of the system takes place by advection and by turbulent dispersion. Transfers to sorbed forms and irreversible transformation processes proceed simultaneously with the transport of the chemical. After the elapse of sufficient time, the chemical comes to be distributed throughout the system, with relatively smooth concentration gradients resulting from dilution, speciation, and... 

An attempt has been made by Tsouris and Tavlarides[5611 to improve previous models for breakup and coalescence of droplets in turbulent dispersions based on existing frameworks and recent advances. In both the breakup and coalescence models, two-step mecha-nisms were considered. A droplet breakup function was introduced as a product of droplet-eddy collision frequency and breakup efficiency that reflect the energetics of turbulent liquid-liquid dispersions. Similarly, a coalescencefunction was defined as a product of droplet-droplet collision frequency and coalescence efficiency. The existing coalescence efficiency model was modified to account for the effects of film drainage on droplets with partially mobile interfaces. A probability density function for secondary droplets was also proposed on the basis of the energy requirements for the formation of secondary droplets. These models eliminated several inconsistencies in previous studies, and are applicable to dense dispersions. 

Effect of passive chemical reaction on turbulent dispersion. AIAA Journal 6, 1797-1798. 

The vanishing effect of molecular diffusivity on turbulent dispersion Implications for turbulent mixing and the scalar flux. Journal of Fluid Mechanics 359, 299-312. 

Pheromone propagation by wind depends on the release rate of the pheromone (or any other odor) and air movements (turbulent dispersion). In wind, the turbulent diffusivity overwhelms the diffusion properties of a volatile compound or mixture itself. Diffusion properties are now properties of wind structure and boundary surfaces, and preferably termed dispersion coefficients. Two models have dominated the discussion of insect pheromone propagation. These are the time-average model (Sutton, 1953) and the Gaussian plume model. 

Strictly speaking, equations 19-52 and 19-53 are valid only if the pollutant cloud is infinitely long. A more realistic situation is treated in Box 19.2 here a pollutant patch of finite length L along the x-axis is eroded on both edges due to diffusion processes (turbulence, dispersion, etc.). Again, the boundary is of the diffusive type since the transport characteristics on both sides of the boundary are assumed to be identical. 

Hesketh et al. (2) proposed that the general equation of Hinze (14) was valid for the turbulent dispersion of a gas using any motionless mixer or an empty pipe ... 

Wilson, J.D. (1982) Turbulent dispersion in the atmospheric surface layer. Boundary-Layer Meteorology, 22, 399-420. 

Const, (power) dissipation energy per unit vessel volume Const, impeller discharge flow energy Turbulent dispersion Gas-liquid operation Reaction requiring microscale mixing... 

Transport from the atmosphere to land and water Dry deposition of particulate and gaseous pollutants Precipitation scavenging of particulate and gaseous pollutants Adsorption of gases onto particles and subsequent diy and wet deposition Transport within the atmosphere Turbulent dispersion and convection Atmospheric transformation Diffusion to the stratosphere Photochemical degradation Oxidation by free radicals and ozone Gas-to-particle conversion... 

Sorption by sediment and suspended solids Sedimentation and resuspension of solids Aerosol formation at the air-water interface Uptake and release by biota Transport within water bodies Turbulent dispersion and convection Diffusion between upper mixed layer and bottom layer Transformation Biodegradation Photochemical degradation... 

Liquid fuel sprays are not yet fullj understood [310]. The atomization process of a liquid fuel jet [376 332 345 293 309], the turbulent dispersion of the resulting droplets [256 253 262 333 319], their interaction with walls [259 365], their evaporation and combustion [290] are phenomena occurring in LES at the subgrid scale and therefore require accurate modeling. 

Eddies If tlie flow within tlie individual flow chaimels of Uie porous medium (soil) becomes turbulent, dispersion results from eddy migration. 

If a uniform concentration of a miscible liquid is more desirable than the high intensity turbulent dispersion of these materials in the stream, then it may be well to have injection points out in a more uniform, less fluctuating environment. Thus evaluation of injection point conditions can be very critical in reactions that may take different paths, depending upon chemical concentrations and fluid mechanics variables. 

The third term of Eq. (3) contains eji, which is generally modeled in terms of turbulent dispersion in a manner analogous to the well-known gradient hypothesis of Boussinesq, as proportional to the gradient of holdup in the z direction, the constant of proportionality being referred to as the turbulent dispersion coefficient ... 

In the previous section, stability criteria were obtained for gas-hquid bubble columns, gas-solid fluidized beds, liquid-sohd fluidized beds, and three-phase fluidized beds. Before we begin the review of previous work, let us summarize the parameters that are important for the fluid mechanical description of multiphase systems. The first and foremost is the dispersion coefficient. During the derivation of equations of continuity and motion for multiphase turbulent dispersions, correlation terms such as esv appeared [Eqs. (3) and (10)]. These terms were modeled according to the Boussinesq hypothesis [Eq. (4)], and thus the dispersion coefficients for the sohd phase and hquid phase appear in the final forms of equation of continuity and motion [Eqs. (5), (6), (14), and (15)]. However, for the creeping flow regime, the dispersion term is obviously not important. 

Ham et al. (1990) used Eqs. (30) and (31) and estimated the values of the solid phase dispersion coefficient using the experimental results on transition in solid-liquid fluidized beds. However, the estimated values of deviate from the experimental values of obtained by Dorgelo et al. (1985). It may be noted that the RTD based experimental values includes gross nonidealities in addition to the turbulent dispersion. 

---