Analytic expressions for interface terms in general dispersed two–phase flow laden with arbitrary–shaped dispersed elements
Keywords:
dispersed two–phase flow, arbitrary shaped elements, probability density function, indicator functionAbstract
This paper presents the methodology of the indicator function–discrete elementsprobability density function statistical average applied to Two–phaseflow modelling. This formulation allows to consider particles of arbitrary shapeand size and it can be applied to any laminar or turbulent flow. In the case ofequal sized spherical dispersed elements, the most common case found in theliterature, the final expression for the interaction terms (contributions thatdescribe the effect of the second phase on the continuous one) are obtainedwithout great difficulties due to the high isotropy of the spherical shape. Thistask, in the general case of non–spherical non–equal particles is no longerstraightforward and the derivation of the appropriate general interaction termsis presented in §4. In the case that the dispersed elements are small enough,some simplifications can be further introduced leading to a final presentation that remembers that obtained for the simplest case of spherical particles, butwhere some of the quantities must be adequately redefined.
PACS: 47.50.Cd
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