Analytic expressions for interface terms in general dispersed two–phase flow laden with arbitrary–shaped dispersed elements (2008)
This article presents the application to the two-phase flow modeling of the statistical averaging methodology using the combination of the phase indicator function and the probability density function of the dispersed elements. This formulation allows to consider particles of arbitrary shape and size and can be applied to laminar or turbulent flow. In the case of spherical dispersed elements of equal size, the most frequent reported in the literature, the final expression of the interaction terms (contributions that describe the effect of the second phase on the continuous phase) is obtained without major difficulties due to the Isotropy of the spherical shape. In the general case, however, the task is more complicated, so the derivation of the general interaction terms is addressed in §4. If the dispersed elements are small enough, additional simplifications can be introduced allowing a final expression to be obtained that recalls that obtained for the simplest case of non-spherical particles, although some quantities must be properly redefined.