Secondary droplet size distribution upon breakup of a sub-milimeter droplet in high speed cross flow

• The size distributions of secondary droplets generated by breakup of a droplet in high speed cross flow is resolved. • Droplet number probability distribution curve changes from an “M” to a parabolic shape from the early to the late stage. • Log-normal and root-normal fitting captures the size probability density well. The droplet breakup behaviors under the action of shock wave are frequently observed in liquid-fueled detonation-based engines. In this work, the secondary droplet size distribution after the breakup of a sub-milimeter droplet under high velocity cross flow conditions (the gas flow velocity is 105.64 m/s) was experimentally determined on a horizontal shock tube with the developed digital in-line holography technique. During the droplet breakup process, the spatial (two-dimensional, three-dimensional) and droplet size distributions of two characteristic stages (early and late stages) were majorly concerned based on the reconstructed droplet cloud field. At the early stage, the liquid-mist field appeared as the barrel shape, and the probability distribution of the droplet number in the cross-stream direction presented as “M shape”. While the secondary droplet cloud field appeared as the conical shape, and the probability distribution presented as the parabolic shape at the late stage. Both the probability distribution of the droplet number along the flow direction increased firstly then decreased at the early and late stages with the increasing of distance. In addition, the peak position of the droplet number probability distribution also changed with time. The secondary droplets mainly distributed in the range of 0∼20 μm for the early and late stages, and its number accounted for more than 93%. Meanwhile, the corresponding volume probabilities changed from 12% to 72%, due to the consistent stripping process. In addition, the droplet size distribution could be well described by the log-normal and root-normal distribution curves at both stages. The study of the spatial and droplet size distributions is believed to be of importance for corresponding droplet breakup modeling. When the parent droplet is released (along the – x direction), it immediately breakup into secondary droplets. These secondary droplets become more dispersed along the shockwave direction( y direction) due to shockwave transport, and smaller due to further breakup