Eulerian-based Moment Methods for the Modelling of Polydisperse Liquid Sprays

A polykinetic, polydisperse spray model has been developed based upon the anisotropic Gaussian moment closure in velocity space. The Gaussian moment closure presents many desirable properties such as hyperbolicity and realizability, and can be used to describe disperse phase sprays of moderate Stokes number. Spray droplets of different sizes can be described by taking velocity moments to be functions of a size variable. By transporting additional moments in velocity and size, the parameters describing these functions are obtained. A novel kinetic flux function that uses distributions on bounded domain has been proposed and verified against an existing kinetic flux function as well as the HLLE approximate Riemann solver. A fully kinetic, realizability preserving source term scheme is also developed to handle Stokes' law drag and the d^2-law of evaporation. Numerical results for various zero-, one- and quasi-two dimensional problems demonstrate the ability of the model to capture polydisperse phenomena.M.A.S