Turbulent eddy diffusivity

Turbulent (eddy diffusivity) mixing, which occurs due to stochastic pressure and flow fluctuations... 

The decreased overall density of the mixing layer with combustion increases the dimensions of the large vortices and reduces the rate of entrainment of fluids into the mixing layer [12]. Thus it is appropriate to modify the simple phenomenological approach that led to Eq. (31) to account for turbulent diffusion by replacing the molecular diffusivity with a turbulent eddy diffusivity e. Consequently, the turbulent form of Eq. (38) becomes... 

In Chapter 7 we define mass transfer coefficients for binary and multicomponent systems. In subsequent chapters we develop mass transfer models to determine these coefficients. Many different models have been proposed over the years. The oldest and simplest model is the film model this is the most useful model for describing multicomponent mass transfer (Chapter 8). Empirical methods are also considered. Following our discussions of film theory, we describe the so-called surface renewal or penetration models of mass transfer (Chapter 9) and go on to develop turbulent eddy diffusivity based models (Chapter 10). Simultaneous mass and energy transport is considered in Chapter 11. 

This chapter describes models of mass transfer in turbulent conditions. Beginning with a brief survey of turbulent eddy diffusivity models we develop solutions to the binary mass transport equations at length before presenting the corresponding multicomponent results. 

For computation of the fluxes themselves. Algorithms 8.1, 8.4, and 8.5 may be used more or less as written simply replace all quantities in molar units by the corresponding quantities in the turbulent eddy diffusivity model. 

ANALYSIS NIq are asked to determine the rate of production of methane. We shall use the turbulent eddy diffusivity model to represent the transport processes in the gas phase. The mass fluxes are given by Eq. 10.4.24... 

We shall, as before, use Newton s method to solve all the independent equations simultaneously. The independent variables that are to be determined by iteration are the fluxes and the interface compositions and temperature. However, the use of the turbulent eddy diffusion model for the vapor-phase mass transport means that the mass fluxes and n 2, and the molar fluxes Aj and A2, appear in the set of model equations. These fluxes are related by... 

A comparison of the interactive film models that use the Chilton-Colburn analogy to obtain the heat and mass transfer coefficients with the turbulent eddy diffusivity models. 

In considering very many condenser simulations (not just those reviewed here) we have yet to find an application where the differences between any of the multicomponent film models that account for interaction effects (Krishna-Standart, 1976 Toor-Stewart-Prober, 1964 Krishna, 1979a-d Taylor-Smith, 1982) are significant. There is also very little difference between the turbulent eddy diffusivity model and the film models that use the Chilton-Colburn analogy (Taylor et al., 1986). This result is important because it indicates that the Chilton-Colburn analogy, widely used in design calculations, is unlikely to lead to large... 

A number of investigators used the wetted-wall column data of Modine to test multicomponent mass transfer models (Krishna, 1979, 1981 Furno et al., 1986 Bandrowski and Kubaczka, 1991). Krishna (1979b, 1981a) tested the Krishna-Standart (1976) multicomponent film model and also the linearized theory of Toor (1964) and Stewart and Prober (1964). Furno et al. (1986) used the same data to evaluate the turbulent eddy diffusion model of Chapter 10 (see Example 11.5.3) as well as the explicit methods of Section 8.5. Bandrowski and Kubaczka (1991) evaluated a more complicated method based on the development in Section 8.3.5. The results shown here are from Furno et al. (1986). 

In the five chapters that make up Part II (Chapters 7-11) we consider the estimation of rates of mass and energy transport in multicomponent systems. Multicomponent mass transfer coefficients are defined in Chapter 1, Chapter 8 develops the multicomponent film model, Chapter 9 describes unsteady-state diffusion models, and Chapter 10 considers models based on turbulent eddy diffusion. Chapter 11 shows how the additional complication of simultaneous mass and energy transfer may be handled. 

Effective diffusivity of component i in multicomponent mixture [m /s] Turbulent eddy diffusivity [m /s]... 

For Sc > 1000 c = 1/2 and for Sc < 500 c = 1/3 applied. This finding could be described in terms of the multi-parameter King model (King 1976), which contained a combination of molecular diffusion and turbulent eddy diffusion. 

There are a number of criticisms to this approach. First, the model is incomplete, since once growth begins it continues without limit. Nonlinear saturation and interactions with predators would be needed to stop this. The diffusion coefficient D certainly does not originate from the Brownian motion of the organisms, since this would be irrelevant to these processes above, say, on the millimeter scale. It is rather a turbulent eddy-diffusion coefficient aimed to... 

FIGURE 18.6 Vertical turbulent eddy diffusivity Kn under unstable conditions derived by Lamb and Duran (1977). 

FIGURE 18.7 Comparison of vertical profiles of vertical turbulent eddy diffusivity Kzz. 

All existing flames are divided into two classes those without premixing of the reactants and those in prepared mixtures. The first class comprises both diffusion flames intermixed by molecular diffusion (laminar diffusion flames) and by turbulent (eddy) diffusion (turbulent diffusion flames) and highly rarefied flames for which the admission and intermixing of reactants is realized either by diffusion, of by the Knudsen molecular flow (see [230]). 

Chen et al. [1999] derived correlations for gas holdup, turbulent eddy diffusivity, and liquid recirculation velocity from measurements in a bubble column with a diameter of 0.45 m. 

Turbulent (Eddy) dififusivity model in which a turbulent (eddy) diffusivity p, is introduced according to Eq. (1.7) to replace unknown pu Uj, called Bous-sinesq postulate. The p, is obtained by Eq. (1.14) where two unknowns k and a are involved. They are represented, respectively, by Eqs. (1.11a) and (1.13a). These equations should be further modeled to suit numerical computation. This model is commonly called fe e model. Several modifications have been made to extent its application. The weakness of this model is that the p, is isotropic and results in discrepancy when applying to the case of anisotropic flow. 

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