DYNAMICS OF SPRAY COMBUSTION IN DIESEL ENGINE-LIKE CONDITIONS

The practical importance of the application of the geometric theory of differential equations to the analysis of spray heating, evaporation, and ignition/combustion is demonstrated. It is shown that the system of equations describing these processes for a mono-sized fuel droplet spray can contain non-Lipschitzian nonlinearities. The approaches to the analysis of the systems of ordinary differential equations with these nonlinearities are described. These use the concept of positively invariant manifolds. Some previously reported results of the analysis of these processes, taking and not taking into account the effects of non-Lipschitzian nonlinearities, are reviewed. Particular attention is paid to the analysis of ignition and combustion of fuel vapour/oxidiser in lean, rich and stoichiometric mixtures. It is shown that the relation between fuel vapour and oxidiser concentrations inferred from the asymptotic analysis coincides with that inferred from the rigorous solution to the system of ordinary differential equations describing these processes.