Granular flow dilute phase approach

The available continuum models for dispersed multi-phase flows thus follow one of two asymptotic approaches. The dilute phase approach is formulated based on the continuum mechanical principles in terms of the local conservation equations for each of the phases. A macroscopic model is then obtained by averaging the local equations based on an appropriate averaging procedure. In the dense phase approach, on the other hand, a kinetic theory description is adopted for the dispersed particulate phase (granular material), whereas an averaged continuum model formulation is adopted for the interstitial phase. 

Three types of theoretical approaches can be used for modeling the gas-particles flows in the pneumatic dryers, namely Two-Fluid Theory [1], Eulerian-Granular [2] and the Discrete Element Method [3]. Traditionally the Two-Fluid Theory was used to model dilute phase flow. In this theory, the solid phase is being considering as a pseudo-fluid. It is assumed that both phases are occupying every point of the computational domain with its own volume fraction. Thus, macroscopic balance equations of mass, momentum and energy for both the gas and the solid... 

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