Closure of non-integer moments arising in multiphase flow phenomena

S. Haeri, J.S. Shrimpton

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

In this paper we consider closure problem for non-integer moments of form 〈xp〉,p∈R which are encountered in the moment evolution equations of many multiphase flow systems involving polydispersed particles, heat and mass transfer, chemical reactions, agglomeration or break-up. Two different categories of methods are considered: the first method is based on the reconstruction of the underlying PDF using Laguerre polynomials and the other is based on the direct calculation of non-integer moments using the fractional derivatives of moment generating function (MGF). By applying the results of fractional calculus an explicit equation is derived to express non-integer moments as a function of any arbitrary number of integer moments. The proposed methods are tested on several highly non-Gaussian analytical PDFs in addition to experimental agglomeration data and direct numerical simulation of fluid–particle turbulent multiphase flows.
Original languageEnglish
Pages (from-to)424-434
Number of pages11
JournalChemical Engineering Science
Volume75
Early online date9 Apr 2012
DOIs
Publication statusPublished - 18 Jun 2012

Keywords

  • fractional moments
  • moment generating function
  • Laguerre polynomial
  • multiphase flow

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