Development of Eulerian Droplets Impingement Model Using HLLC Riemann Solver and POD-based Reduced Order Method

Abstract

A finite volume method based on approximate Riemann solver is proposed as a basic building block for computing the Eulerian droplet impingement model. The HLLC approximate Riemann solver, which is originally developed for shallow water equations of the fluid depth and velocity field, is applied to the Eulerian droplet model. The positivity condition in liquid water contents is achieved through the HLLC solver. Then, a proper orthogonal decomposition method, a reduced order model that optimally captures the energy content from a large multi-dimensional data set, is utilized to efficiently predict the collection efficiency on an airfoil. It is shown that the collection efficiency reconstructed by utilizing four modes of the POD is in very close agreement with the original value.