Diffusivity turbulent

Macromixing is estabflshed by the mean convective flow pattern. The flow is divided into different circulation loops or zones created by the mean flow field. The material is exchanged between zones, increasing homogeneity. Micromixing, on the other hand, occurs by turbulent diffusion. Each circulation zone is further divided into a series of back-mixed or plug flow cells between which complete intermingling of molecules takes place. 

Validation and Application. VaUdated CFD examples are emerging (30) as are examples of limitations and misappHcations (31). ReaUsm depends on the adequacy of the physical and chemical representations, the scale of resolution for the appHcation, numerical accuracy of the solution algorithms, and skills appHed in execution. Data are available on performance characteristics of industrial furnaces and gas turbines systems operating with turbulent diffusion flames have been studied for simple two-dimensional geometries and selected conditions (32). Turbulent diffusion flames are produced when fuel and air are injected separately into the reactor. Second-order and infinitely fast reactions coupled with mixing have been analyzed with the k—Z model to describe the macromixing process. 

This solution describes a plume with a Gaussian distribution of poUutant concentrations, such as that in Figure 5, where (y (x) and (y (x) are the standard deviations of the mean concentration in thejy and directions. The standard deviations are the directional diffusion parameters, and are assumed to be related simply to the turbulent diffusivities, and K. In practice, Ct (A) and (y (x) are functions of x, U, and atmospheric stability (2,31—33). 

The generalized transport equation, equation 17, can be dissected into terms describing bulk flow (term 2), turbulent diffusion (term 3) and other processes, eg, sources or chemical reactions (term 4), each having an impact on the time evolution of the transported property. In many systems, such as urban smog, the processes have very different time scales and can be viewed as being relatively independent over a short time period, allowing the equation to be "spht" into separate operators. This greatly shortens solution times (74). The solution sequence is... 

Turbulent Diffusion FDmes. Laminar diffusion flames become turbulent with increasing Reynolds number (1,2). Some of the parameters that are affected by turbulence include flame speed, minimum ignition energy, flame stabilization, and rates of pollutant formation. Changes in flame stmcture are beHeved to be controlled entirely by fluid mechanics and physical transport processes (1,2,9). 

The physics and modeling of turbulent flows are affected by combustion through the production of density variations, buoyancy effects, dilation due to heat release, molecular transport, and instabiUty (1,2,3,5,8). Consequently, the conservation equations need to be modified to take these effects into account. This modification is achieved by the use of statistical quantities in the conservation equations. For example, because of the variations and fluctuations in the density that occur in turbulent combustion flows, density weighted mean values, or Favre mean values, are used for velocity components, mass fractions, enthalpy, and temperature. The turbulent diffusion flame can also be treated in terms of a probabiUty distribution function (pdf), the shape of which is assumed to be known a priori (1). 

The various studies attempting to increase our understanding of turbulent flows comprise five classes moment methods disregarding probabiUty density functions, approximation of probabiUty density functions using moments, calculation of evolution of probabiUty density functions, perturbation methods beginning with known stmctures, and methods identifying coherent stmctures. For a thorough review of turbulent diffusion flames see References 41—48. 

In turbulent flow, axial mixing is usually described in terms of turbulent diffusion or dispersion coefficients, from which cumulative residence time distribution functions can be computed. Davies (Turbulence Phenomena, Academic, New York, 1972, p. 93), gives Di = l.OlvRe for the longitudinal dispersion coefficient. Levenspiel (Chemical Reaction Engineering, 2d ed., Wiley, New York, 1972, pp. 253-278) discusses the relations among various residence time distribution functions, and the relation between dispersion coefficient and residence time distribution. 

Between V 9 and the concentration of solids gradually becomes more uniform in the vertical direction. This transition has been modeled by several authors as a concentration gradient where turbulent diffusion balances gravitational settling. See, for example, Karabelas (AJChE]., 23, 426 34 [1977]). 

With good diy scrubbing sorbents, the controlling resistance for gas cleaning is external turbulent diffusion, which also depends on energy dissipated by viscous and by inertial mechanisms. It turns out to Be possible to correlate mass-transfer rate as a fimctiou of the fric tiou Factor. 

Equihbrium concentrations which tend to develop at solid-liquid, gas-liquid, or hquid-liquid interfaces are displaced or changed by molecular and turbulent diffusion between biilk fluid and fluid adjacent to the interface. Bulk motion (Taylor diffusion) aids in this mass-transfer mechanism also. 

Peclet number independent of Reynolds number also means that turbulent diffusion or dispersion is directly proportional to the fluid velocity. In general, reactors that are simple in construction, (tubular reactors and adiabatic reactors) approach their ideal condition much better in commercial size then on laboratory scale. On small scale and corresponding low flows, they are handicapped by significant temperature and concentration gradients that are not even well defined. In contrast, recycle reactors and CSTRs come much closer to their ideal state in laboratory sizes than in large equipment. The energy requirement for recycle reaci ors grows with the square of the volume. This limits increases in size or applicable recycle ratios. 

Long, P. E., and Pepper, D. W., A comparison of six numerical schemes for calculating the advection of atmospheric pollution, in "Proceedings of the Third Symposium on Atmospheric Turbulence, Diffusion and Air Quality." American Meteorological Societv, Boston, 1976, pp. 181-186. 

Huber, A. H., and Snyder, W. H., Building wake effects on short stack effluents, pp. 235-242 in Preprints, Third Symposium on Atmospheric Turbulence, Diffusion and Air Quality. October 19-22, 1976, Raleigh, NC. American Meteorological Society, Boston, 1976. 

The Gaussian Plume Model is the most well-known and simplest scheme to estimate atmospheric dispersion. This is a mathematical model which has been formulated on the assumption that horizontal advection is balanced by vertical and transverse turbulent diffusion and terms arising from creation of depletion of species i by various internal sources or sinks. In the wind-oriented coordinate system, the conservation of species mass equation takes the following form ... 

Egan, B. A., 1975, Turbulent Diffusion in Complex Terrain, Lectures on Air Pollution and Environmental Impact Analyses, American Meteorological Society, Boston, MA, p 123. 

Note Equation (4.241) characterizes diffusion when the mixture element is in steady state with no turbulence. Diffusion in a pipe can be represented by Eq. (4.241) in convective mass transfer the flow and turbulence are important. 

Theories of hood performance with nonbuoyant pollution sources are based on the equation of turbulent diffusion. The following equation allows the engineer to determine the contaminant concentration decay in the uniform airflow upstream from the contaminant source ... 

The value of the coefficient of turbulent diffusion, D, depends upon the air change rate in the ventilated space and the method of air supply. Studies by Posokhin show that approximate D values for locations outside supply air jets is equal to 0.025 m-/s. Air disturbance caused by operator or robot movement results in an increase in the D value of at least two times. Studies by Zhivov et al. showed that the D value is affected by the velocity and direction of cross-drafts against the hood face, and the presence of an operator e.g., for a cross-draft directed along the hood face with velocity u = 0.5 m/s with D = 0.15 m-/s (with the presence of an operator), an increase to = 1.0 m/s results in D = 0.3 m-/s. 

The energy of large and medium-size eddies can be characterized by the turbulent diffusion coefficient. A, m-/s. This parameter is similar to the parameter used by Richardson to describe turbulent diffusion of clouds in the atmosphere. Turbulent diffusion affects heat and mass transfer between different zones in the room, and thus affects temperature and contaminant distribution in the room (e.g., temperature and contaminant stratification along the room height—see Chapter 8). Also, the turbulent diffusion coefficient is used in local exhaust design (Section 7.6). 

Studies by Elterman show that turbulent diffusion coefficients in ventilated rooms outside jets and plumes can be described using the relationship-... 

Another design method uses capture efficiency. There are fewer models for capture efficiency available and none that have been validated over a wide range of conditions. Conroy and Ellenbecker - developed a semi-empirical capture efficiency for flanged slot hoods and point and area sources of contaminant. The point source model uses potential flow theory to describe the flow field in front of a flanged elliptical opening and an empirical factor to describe the turbulent diffusion of contaminant around streamlines. 

If k goes to zero in region of low turbulence, the turbulent diffusion term simply goes to zero. The other terms remain, giving a nontrivial (i.e., neither zero nor infinity) value of ta Note that the production term in the w equation does not include k since... 

When gas concentrations are high, burning is characterized by the presence of a tall, turbulent-diffusion, flame plume. At points where the cloud s vapor had already mixed sufficiently with air, the vertical depth of the visible burning zone is about equal to the initial, visible depth of the cloud. 

T. Baron, "Reactions in Turbulent Free Jets-The Turbulent Diffusion Flame," Cbem. Eng. Prog., 50, 73 (1954),... 

In gridpoint models, transport processes such as speed and direction of wind and ocean currents, and turbulent diffusivities (see Section 4.8.1) normally have to be prescribed. Information on these physical quantities may come from observations or from other (dynamic) models, which calculate the flow patterns from basic hydrodynamic equations. Tracer transport models, in which the transport processes are prescribed in this way, are often referred to as off-line models. An on-line model, on the other hand, is one where the tracers have been incorporated directly into a d3mamic model such that the tracer concentrations and the motions are calculated simultaneously. A major advantage of an on-line model is that feedbacks of the tracer on the energy balance can be described... 

Fig. 4-15 Orders of magnitude of the average vertical molecular or turbulent diffusivity (whichever is largest) through the atmosphere, oceans, and uppermost layer of ocean sediments.

J. Kim and J. S. Kim, Modelling of lifted turbulent diffusion flames in a channel mixing layer by the flame hole dynamics. Combust. Theory Model. 10 21-37, 2006. 

In the so-called "wrinkled flame regime," the "turbulent flame speed" was expected to be controlled by a characteristic value of the turbulent fluctuations of velocity u rather than by chemistry and molecular diffusivities. Shchelkin [2] was the first to propose the law St/Sl= (1 + A u /Si) ), where A is a universal constant and Sl the laminar flame velocity of propagation. For the other limiting regime, called "distributed combustion," Summerfield [4] inferred that if the turbulent diffusivity simply replaces the molecular one, then the turbulent flame speed is proportional to the laminar flame speed but multiplied by the square root of the turbulence Reynolds number Re. ... 

Complex strain flame-front regime. Where the flame fronfs are still lamella-like but thickened due to enhanced turbulent diffusivity. Scalar transport is expected to be counter-gradient in this regime. 

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