Computation of spray dynamics by moment transport equations I: Theory and development

This article presents the results of a study into tbepossibility of solving for spray statistics directly without the use of stochastic simulation or Monte Carlo integration. It is based on formulating a system of low-order moment equations from the spray equation and then closing this system by use of a maximum-entropy assumption. The work has two parts: In this article, the basic formulation is presented and issues related to closure of the moment hierarchy and implementation of appropriate models are addressed. In a companion article, the model is applied to a simple case of a quasi-one-dimensional spray flow, that is, a flow in which the statistics of the flow vary in only one spatial dimension. The work shows that while it is possible to formulate the spray problem in a way that permits a very cost-effective, direct solution of the spray statistics, substantial modeling issues exist. These issues, and others related to the basic approach, are discussed in this article.