Thin-Flame Theory for the Combustion of a Moving Liquid Drop: Effects Due to Variable Density

The combustion of a moving liquid fuel drop has been investigated. The drop experiences a strong evaporation-induced radial velocity while undergoing slow translation. In view of the high evaporation velocity, the flow field is not in the Stokes regime. The combustion process is modelled by an indefinitely fast chemical reaction rate. While the flow and the transport in the continuous phase and the drop internal circulation are treated as quasisteady, the drop heat-up is regarded as a transient process. The transport equations of the continuous phase require analysis by a singular perturbation technique. The transient heat-up of the drop interior is solved by a series-truncation numerical method. The solution for the total problem is obtained by coupling the results for the continuous and dispersed phases. The enhancement in the mass burning rate and the deformation of the flame shape due to drop translation have been predicted. The initial temperature of the drop and the subsequent heating influence the temporal variations of the flamefront standoff ratio and the flame distance. The friction drag, the pressure drag and the drag due to interfacial momentum flux are individually predicted, and the total drag behaviour is discussed. The circulation inside the drop decreases with evaporation rate. A sufficiently large non-uniform evaporation velocity causes the circulation to reverse.