The Favre Averaged Drag Model for Turbulent Dispersion in Eulerian Multi-Phase Flows


The Favre Averaged Drag Model for Turbulent Dispersion in Eulerian Multi-Phase Flows

Burns, A. D.; Frank, T.; Hamill, I.; Shi, J.-M.

A general framework is presented for the modeling of turbulent dispersion in Eulerian Multi-Phase Flows. The approach is based on a double averaging procedure of the local instant equations. We start with the ensemble averaged equations of Eulerian multi-phase flow. We perform a second time average of these, in order to form equations which may be used to model turbulent multi-phase flows. These are conveniently expressed in terms of Favre or Mass averaged variables. Turbulent dispersion is modeled by performing a time average of the interphase drag term in its modeled form, and expressing it in terms of Favre averaged variables. The resulting double averaged momentum equations contain additional terms which account for a turbulent dispersion force. We call the resulting model the Favre Averaged Drag (FAD) model for turbulent dispersion. It is first presented in a general form which may be used in conjunction with any Reynolds averaged turbulence model, and for an arbitrary number of phases with arbitrary morphologies. For the purposes of this study, we make two further specializations, to poly-dispersed multiphase flows, and to turbulence models which employ the eddy diffusivity hypothesis. The resulting model is compared to several other models that have appeared in the literature, We show that all are special cases of the FAD model, within certain physical and mathematical limitations. Hence the FAD model encompasses all of these models, but has a potentially wider range of universality. The FAD model has been implemented in the commercial CFD package, CFX-5, and tested against a range of dispersed multiphase flows, including bubbly flows in vertical pipes, and liquid-solid flows in mixing vessels. The FAD model is shown to yield superior predictions in all cases.

Keywords: Multi-fluid model; turbulent dispersion model; drag force; Favre average; double average

  • Contribution to proceedings
    5th International Conference on Multiphase Flow, ICMF 04, 30.05.-04.06.04, Yokohama, Japan
    ICMF2004 Proceedings CD-ROM, paper No. 392, 1-17

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Publ.-Id: 6158