On the Lagrangian/Eulerian modeling of dispersed droplet inertia: internal circulation transition.
This article addresses a limitation of Lagrangian methods for droplet tracking, when approaching the transition point of internal circulation within droplets. Laminar multiphase flow with dispersed droplets in a co-flowing airstream is considered. Analytical and numerical formulations of droplet motion are developed based on a Lagrangian finite difference method of droplet tracking. Cases of both high and low relative Reynolds numbers are formulated. The role of interfacial drag in cross-phase momentum exchange increases at higher relative Reynolds numbers. A new transition criterion is developed to characterize conditions leading to shear-driven non-uniformities of velocity within a droplet. This criterion entails a momentum Biot number, in analogy with the Biot number criterion for conjugate heat transfer problems involving conduction and convection. At sufficiently high momentum Biot numbers, appreciable changes of velocity within a droplet imply that Lagrangian methods become unsuitable and transition to Eulerian volume averaging is needed. Predicted results of Lagrangian modeling of droplet motion in a co-flowing airstream are presented and discussed.
Department of Mechanical and Manufacturing Engineering, University of Manitoba, 15 Gillson Street, Winnipeg, Manitoba, Canada, R3T 2N2.
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Milanez
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