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Atomization and Sprays

Published 12 issues per year

ISSN Print: 1044-5110

ISSN Online: 1936-2684

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Indexed in

TOWARD A COMPREHENSIVE THEORY OF DENSE SPRAY FLOWS

Volume 10, Issue 3-5, 2000, pp. 335-353
DOI: 10.1615/AtomizSpr.v10.i3-5.60
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ABSTRACT

A mathematical theory of dense spray flows is described. It is based on treating the flow both inside and outside the drops via the incompressible Navier-Stokes equations and the interface as Gibbs' dividing surface. Taking into account the information necessary to describe the dynamical state of the flow, a hyperspace is constructed which describes the state of the system at any instant. This hyperspace consists of a number of field axes—one which describes the instantaneous velocity field and a number which describe the instantaneous morphology of the fluids.
Following the methods of statistical mechanics, an ensemble of macroscopically identical flows is used to define a density of system points in the hyperspace. A transport equation is then written which describes the evolution of this collection of flows for all time. A unique feature of this transport equation is that the dynamics of each fluid element are embedded in the transport equation—that is, the Navier-Stokes equations and interface jump conditions are implicit constraints on the overall transport of a system point in hyperspace.
The utility of the resulting equation (the continuum-particle, continuum-field equation) is demonstrated by showing that it can be reduced, in the limit of small dispersed-phase elements, to the point-particle, continuum-field equation which, in turn, has been shown to reduce to the ensemble-averaged Navier-Stokes and spray equations. As such, the present development is the uppermost level of a hierarchy of models for continuum treatment of spray flows—analogous to the Liouville equation of the kinetic theory of gases.

CITED BY
  1. Subramaniam Shankar, Lagrangian–Eulerian methods for multiphase flows, Progress in Energy and Combustion Science, 39, 2-3, 2013. Crossref

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