Analytical and numerical studies on a single-droplet evaporation and combustion under forced convection

Existing droplet evaporation/combustion models in computational fluid dynamics (CFD) simulation of spray combustion are based on simplified 1-D models. Both these models and recently developed 3-D models of single-droplet combustion do not give the conditions for the different existing droplet combustion modes. In this paper, droplet evaporation and combustion are studied both analytically and numerically. In the analytical solution, a 2-D axisymmetric flow surrounding an evaporating and combusting droplet was considered. The governing equations were solved using an integral method, similar to the Karman–Pohlhausen method for solving boundary-layer flows with pressure gradient. The results give a local evaporation rate and flame radius in agreement with experimental results. In numerical simulation, 3-D combusting gas flows surrounding an ethanol droplet were studied. The prediction results show three modes of droplet combustion under different relative velocities, explaining the change in the evaporation constant with an increase in relative velocity observed in experiments. This implies that different droplet combustion models should be developed in simulating spray combustion. The predicted local evaporation rate and flame radius by numerical simulation are in agreement with the analytical solution in the range of azimuthal angles \(0^{\circ }<\theta <90^{\circ }\). The numerical results indicate that the drag force of an evaporating and combusting droplet is much smaller than that of a cold solid particle, and thus the currently used drag models should be modified.