Mean concentration Eulerian approach

Having demonstrated that exact solution for the mean concentrations (c, (x, t j) even of inert species in a turbulent fluid is not possible in general by either the Eulerian or Lagrangian approaches, we now consider what assumptions and approximations can be invoked to obtain practical descriptions of atmospheric diffusion. In Section 18.4 we shall proceed from the two basic equations for (c,), (18.4) and (18.8), to obtain the equations commonly used for atmospheric diffusion. A particularly important aspect is the delineation of the assumptions and limitations inherent in each description. 

The Eulerian approach relies on solving a transport equation for the particle concentration or number-density. The particles are not considered individually but as a continuous field akin to heat or chemical species, but furthermore characterized by inertia phenomena. The transport equation contains a convection term in which the mean velocities are known from the turbulence model, and also a dispersion term which is at the core of the problem. This dispersion term involves a dispersion tensor or, in a ID-formulation, a dispersion coefficient that we have to determine. 

Evaluating the performance of a gas-solid transport system usually requires a means of macroscopic field description of the distribution of basic flow properties such as pressure, mass fluxes, concentrations, velocities, and temperatures of phases in the system. To conduct such an evaluation, the Eulerian continuum or multifluid approach is usually the best choice among the available approaches. 

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