A level set approach for dilute non-collisional fluid-particle flows

  • Authors:

  • Hailiang Liu;Zhongming Wang;Rodney O. Fox

  • Affiliations:

  • Mathematics Department, Iowa State University, Ames, IA 50011, United States;Department of Mathematics, UCSD, La Jolla, CA 92093-0112, United States;Department of Chemical and Biological Engineering, Iowa State University, Ames, IA 50011, United States

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2011

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Abstract

Gas-particle and other dispersed-phase flows can be described by a kinetic equation containing terms for spatial transport, acceleration, and particle processes (such as evaporation or collisions). However, computing the dispersed velocity is a challenging task due to the large number of independent variables. A level set approach for computing dilute non-collisional fluid-particle flows is presented. We will consider the sprays governed by the Williams kinetic equation subject to initial distributions away from equilibrium of the form @?"i"="1^N@r"i(x)@d(@x-u"i(x)). The dispersed velocity is described as the zero level set of a smooth function, which satisfies a transport equation. This together with the density weight recovers the particle distribution at any time. Moments of any desired order can be evaluated by a quadrature formula involving the level set function and the density weight. It is shown that the method can successfully handle highly non-equilibrium flows (e.g. impinging particle jets, jet crossing, particle rebound off walls, finite Stokes number flows).