Analysis of the two-dimensional polydisperse liquid sprays in a laminar boundary layer flow using the similarity transformation method

摘要

Abstract In this paper we analyze the model that describes the evaporation process of multi-size (polydisperse) of fuel droplets in a laminar boundary layer flow. The spray is described using a probability density function and is based on the well-known sectional approach. The spray is described in two dimensional boundary layer directions that consists of five equations: the continuity equation, the momentum equation, the energy equation, the equation of state and the spray equation. The governing equations are a system of nonlinear partial differential equations (PDE). In order to convert the PDE to ordinary differential equations, we applied the Lees-Dorodnitsyn similarity transformation and the corresponding similar solution based on the compressible stream function. We then solve the model numerically and compare our results to the sectional approach with an experimental data.