Steady-State and Extinction Analyses of Counterflow Spray Diffusion Flames with Arbitrary Finite Evaporation Rate

We present a new analysis of the behavior of counterflow spray diffusion flames in which the droplets are permitted to evaporate at a finite rate. The effects of fuel volatility, droplet size, and liquid fuel loading on steady-state combustion and conditions for extinction are investigated. We treat instances in which (1) the flame front is located beyond the stagnation plane in the region that, in the current model, is impenetrable to fuel droplets and (2) the flame front is located in the fuel half-plane. In case (2) droplets may actually traverse the flame front, become ignited, and burn out in the heterogeneous mode. An expression is derived for the ratio of extinction conditions with droplets present to those when all the fuel is prevaporized, enabling the direct influence of the droplets to be isolated in a compact fashion.