Droplet Drag Modeling on Spray Conditions

Numerical approaches have been conducted to investigate the effect of droplet deformation and internal circulation on droplet dynamics. Although droplet drag is a classical area of study, there are still theoretical gaps in understanding the motion of large droplets. In applications such as spray combustion, droplets of various sizes are generated and move with the flow. Large droplets tend to deform in the flow, and they have complex interactions with the flow because of this deformation. To better model spray, the physical understanding of droplets needs to be improved. Under spray conditions, droplets are subjected to a high-temperature-and-pressure environment, and the coupling between liquid and gas is enhanced. Therefore the deformation and internal circulation will affect the droplet drag coefficient more significantly than they would under atmospheric conditions. To study the mechanism of how droplet shape and internal circulation influence droplet dynamics, we have used direct numerical simulation (DNS) to simulate a droplet falling at its terminal velocity in high-pressure air. An in-house code developed for interface-capturing DNS of multiphase flows is employed for the simulation. The drag coefficient is calculated, and the results are consistent with the existing literature for slightly deformed droplets. The results show that the drag coefficient is directly related to the droplet deformation and droplet internal circulation. This paper also develops an analytical theory to account for the effect of the Weber number and fluid properties on droplet deformation.