Auto-ignition of a polydisperse fuel spray

In the present paper, the effect of fuel spray polydispersity on the auto-ignition process in a fuel cloud is considered. In many engineering applications it is common practice to relate to the actual polydisperse spray as being equivalent to a monodisperse spray with all droplets therein having some average diameter. In combustion systems, the Sauter mean diameter (SMD) is frequently used for this purpose; it is based on the ratio between the total droplet volume and the total droplet surface area of all the droplets in the polydisperse spray. The main purpose of the current work is to examine qualitatively the dynamics of ignition of a truly polydisperse spray in a combustible gas medium and compare it with the dynamics of an equivalent monodisperse spray based on the SMD. Since the system of governing equations represents a multi-scale problem the method of integral manifolds is applied in order to extract the dynamical behavior. Preliminary computed results suggest that the use of the usual SMD-based monodisperse spray leads to quite a significant over-estimate of the ignition time. An alternative modified definition of the SMD, in which the overall liquid fuel volume is also conserved in the averaging process, reduces the discrepancy between the ignition time for the polydisperse spray and that of the equivalent monodisperse spray. However, it seems that some other sort of average droplet size needs to be determined to minimize the aforementioned discrepancy. These results highlight the care that must be exercised before dispensing with the behavior of the actual polydisperse spray in favor of that of an equivalent monodisperse spray, even at the expense of complexity.