M.Sc Thesis
M.Sc Student Kats Gershon Investigation of Different Aspects of Spray Flame Behavior Department of Aerospace Engineering Professor Emeritus Jerrold Greenberg

Abstract

Spray combustion plays an important role in various aerospace applications, e.g. in jet engines, rocket engines.

The mathematical description of laminar flames in the presence of sprays involves a system of coupled non-linear partial differential equations, which is not generally subject to analytical solution. In order to get an insight into the complicated nature of spray combustion simple mathematical models are usually applied.

Despite the simplicity of these models, they are able to describe qualitively well the main mechanisms involved in spray flames.

The thesis deals with various simplified mathemetical models through which the behavior of laminar spray flames was investigated.

The first part of the thesis focuses on the mathematical approach of "Representation of the Arrhenius exponential reaction term by a Heaviside function" which was suggested by V. Volpert in 2006. Despite the fact that Volpert's approach exists for several years, it has not yet been applied to spray problems. In the present work I have shown the necessary changes in the approach that need to be implemented in order to fit it to combustion problems in the presence of a spray.

In addition, I showed how the modified approach can be used as a non-asymptotic alternative to solving spray flame propagation problems instead of the asymptotic approach which is commonly used. The approach was verified by application to the fundamental problem of finding the propagation velocity of a 1D laminar flame through a premixture of fuel spray and air. Comparison of the results with the predictions of asymptotic theory showed good agreement.

In addition, the analysis of the propagation of a double spray flame (both the fuel and oxygen are sprays) using the new approach was described yielding a formula for the burning velocity. This analysis is completely novel since the few works on double spray flames in the literature and they only deal only with diffusion flames.

In the second part of the thesis an investigation of edge flames in the presence of fuel  spray was presented. So far, the theoretical and experimental study of edge flames only considered gas flames. In the present work an asymptotic approach to spray edge flames was developed to obtain for the first time explicit expressions for the flame progation velocity and the location of the leading edge of the edge flame. These enabled the investigation of the influence of liquid fuel on edge flames.