M.Sc Student M.Sc Thesis Lerman Shaul A General Asymptotic Theory of Spray Diffusion Flames Department of Aerospace Engineering PROFESSOR EMERITUS Jerrold Greenberg

Abstract

One of the common and most practical methods of combustion for energy production in the leading aerospace applications is the utilization of liquid fuel supplied by injectors, in order to produce a fuel spray.

Combustion systems of this type are two-phased flow systems, including mass, momentum and energy exchanges between the spray and the gaseous environment. The fluid also experiences diffusion of the chemical species, non-linear chemical reaction rates and large changes in its density, caused by the heat of the exothermic chemical reactions. Since the physical phenomena that occur in the system are highly complicated, a simplified model for the problem can be greatly advantageous.

One of the common methods for describing such problems is to use the Laminar Diffusion Flame model - a simplified geometry model, in which the main mechanism controlling the combustion characteristics is the diffusion of the chemical reactants into the flame area.

This work presents the development of a simplified Laminar Diffusion Flame model, based on asymptotic formulation and general enough to cover a variety of geometric arrangements. A new analytical model for the problem is presented, which includes a curvilinear coordinate system, formerly used only for gaseous laminar flames. Also presented is a new model for the description of the evaporation front for a general geometric arrangement of the problem. The model is developed systematically, starting with spray dynamics and it's interaction with the gaseous environment, through the spray evaporation process, and ending with the combustion process, including explicit treatment of the inner structure of the chemical reaction area (the flame front). By integrating the equations across the evaporation and chemical reaction fronts, mathematical conditions to describe the jump conditions for the physical variables are developed. These conditions are used as boundary conditions for the problem in the relevant regions of the solution field.

Upon completion of the model development, the model's validity is examined by using it for the formulation of a test case, taken from a previous published work - a spray diffusion flame in a counter-flow configuration. Formulating this test case using the new model shows a complete match to the original formulation, when solved for the leading order (as was done in the previous work). In addition, first order modifications are also incorporated.

Finally, additional research directions are suggested for application of the new general formulation. Future developments to the model are also suggested.