Turbulent mixing model description

Based on the above examples, we can conclude that while localness is a desirable property, it is not sufficient for ensuring physically realistic predictions. Indeed, a key ingredient that is missing in all mixing models described thus far (except the FP and EMST70 models) is a description of the conditional joint scalar dissipation rates (e ) and their dependence on the chemical source term. For example, from the theory of premixed turbulent flames, we can expect that (eY F, f) will be strongly dependent on the chemical... 

As the alternative, a phenomenological description of turbulent mixing gives good results for many situations. An apparent diffusivity is defined so that a diffusion-type equation may be used, and the magnitude of this parameter is then found from experiment. The dispersion models lend themselves to relatively simple mathematical formulations, analogous to the classical methods for heat conduction and diffusion. 

Theoretical description of reagents turbulent mixing in tubular canals is based on the following main model assumptions ... 

The theoretical description of the turbulent mixing of reactants in tubular devices is based on the following model assumptions the medium is a Newtonian incompressible medium, and the flow is axis-symmetrical and nontwisted turbulent flow can be described by the standard model [16], with such parameters as specific kinetic energy of turbulence K and the velocity of its dissipation e and the coefficient of turbulent diffusion is equal to the kinematic coefficient of turbulent viscosity D, = Vj- =... 

An interpretation of these results is presented in terms of the competition between turbulent mixing and the inhomogeneities generated by the feeding of the reactor. The effects are illustrated (Pig. 1) on a realistic example, the simple kinetic model which has been used to give a near-quantitative description of the bistable region of the iodate-arsenous acid system [ 3,... 

Donaldson, C. (1975). On the modeling of the scalar correlations necessary to construct a second-order closure description of turbulent reacting flows, in Turbulent Mixing in Nonreactive and Reactive Flows, S. N. B. Murthy, ed.. Plenum Press, New York, pp. 131-162. 

Glaser and Litt (G4) have proposed, in an extension of the above study, a model for gas-liquid flow through a b d of porous particles. The bed is assumed to consist of two basic structures which influence the fluid flow patterns (1) Void channels external to the packing, with which are associated dead-ended pockets that can hold stagnant pools of liquid and (2) pore channels and pockets, i.e., continuous and dead-ended pockets in the interior of the particles. On this basis, a theoretical model of liquid-phase dispersion in mixed-phase flow is developed. The model uses three bed parameters for the description of axial dispersion (1) Dispersion due to the mixing of streams from various channels of different residence times (2) dispersion from axial diffusion in the void channels and (3) dispersion from diffusion into the pores. The model is not applicable to turbulent flow nor to such low flow rates that molecular diffusion is comparable to Taylor diffusion. The latter region is unlikely to be of practical interest. The model predicts that the reciprocal Peclet number should be directly proportional to nominal liquid velocity, a prediction that has been confirmed by a few determinations of residence-time distribution for a wax desulfurization pilot reactor of 1-in. diameter packed with 10-14 mesh particles. 

Different investigations of the possible connection between rotation and the Li dip have appeared in the literature. Most relied on highly simplified descriptions of the rotation-induced mixing processes. In the MC model of Tassoul Tassoul (1982) used by Charbonneau Michaud (1988), the feed-back effect due to angular momentum (hereafter AM) transport as well as the induced turbulence were ignored. Following Zahn (1992), Charbonnel et al. (1992, 1994) considered the interaction between MC and turbulence induced by rotation, but the transport of AM was not treated self-consistently. 

The material covered in the appendices is provided as a supplement for readers interested in more detail than could be provided in the main text. Appendix A discusses the derivation of the spectral relaxation (SR) model starting from the scalar spectral transport equation. The SR model is introduced in Chapter 4 as a non-equilibrium model for the scalar dissipation rate. The material in Appendix A is an attempt to connect the model to a more fundamental description based on two-point spectral transport. This connection can be exploited to extract model parameters from direct-numerical simulation data of homogeneous turbulent scalar mixing (Fox and Yeung 1999). 

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