The Effect of Fluctuations in Temperature and Oxygen Concentration on the Lifetime of a Fuel Droplet

Monte-Carlo calculations are undertaken to determine the lifetime of fuel droplets which encounter temperature and oxygen fluctuations along their path through a turbulent flame. Two kinds of ignition and extinction criteria are used: fixed values of Yυ and T for ignition and Yυ for extinction, and size-dependent values based on finite kinetics. It is assumed that ignition and extinetion are instantaneous, and that the behaviour is otherwise quasi-steady, i.e, the droplet either evaporates or burns at the corresponding quasi-steady rate. Droplet dynamics and convective effects are excluded from the model. Ambient temperature and oxygen concentrations take on random values between prescribed limits, and maintain these values for periods of random duration. Each such period is the travel time of the droplet over a random distance of the other of a scale factor times its initial diameter. Calculations are carried out for both uncorrelated and correlated temperature and oxygen concentrations. The output of the calculation is the distribution of droplet lifetimes, as a function of the parameters: initial drop size, droplet velocity, and the scale of flucutuations in the ambient fields. In all cases droplet lifetimes significantly exceed the minimum burning time. The finite kinetic ignition and extinction criteria prediet longer lifetimes than the fixed values of Yo and T. A simple parameter correlates the statistical influences in the simulation.