UMIST Polymer Engineering Dept Report

S F Bush

Basic Principles of the Model

The basic principle is to use the finite cell method described in Bush and Dyer 1976 with some of the boundaries of a cell potentially defined within the computation. This approach keeps the flow part of the computations simplest, in turn enabling the model to represent the considerable chemical and phase change complexity adequately. The finite cell method consists of three elements:

1. definitions of cells as regions of solution space to which average values of intensive conserved quantities apply. A cell need not be simply connected;
2. transport of the conserved quantities from a cell is deemed to occur at the average values;
3. For calculating changes across the time and space interval (n, n+1) the conserved quantities are assigned values at (n+1): all other quantities (including transport quantities) are assigned values at n. This results in a matrix inversion for the conserved quantities.

Application to the Soot Formation Problem

The following physical and chemical processes are important:

1. liquid fuel injection, spray development and the simultaneous creation of a weapon jet;
2. droplet evaporation with potential approach to the critical temperature, and fractionation of the fuel components;
3. simultaneous cracking and oxidation of hydrocarbon molecules in fuel;
4. soot formation by polycondensationof cracked fragments and hydrogen abstraction from hydroboiling aromatic components in the fuel.