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Modeling sprays by the method of Laplace transforms By

By S. G. Ghosal and M. Herrmann


In many applications, a moving fluid carries a suspension of droplets of a second phase which may change in size due to evaporation or condensation. If the number of such particles is very large, it may be practically impossible to explicitly compute all of the fluid and particle degrees of freedom in a numerical simulation of the system. A method for reducing the computational size under these circumstances is presented by representing the particle cloud by means of a distribution function in the particle radius and co-ordinates. This distribution function evolves according to a Fokker Planck equation. It is shown that the Laplace Transform of the distribution function satisfies an integral differential equation that may be conveniently solved numerically in conjunction with the usual LES equations. 1. The model 1.1. The equation for the distribution function It is assumed that the filter width ℓ of the LES is much larger than particle sizes or interparticle distances, so that a cube of side ℓ still contains enough particles that the state of the system may be described by the distribution function, np(r, x, t). Here np(r, x, t) dxd

Year: 2013
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