Effect of droplet spacing on the interactions between shocks and tandem droplets

Abstract

One of the key injector design parameters in liquid fueled rotating detonation engines is the spacing between the injector holes and the associated liquid droplets generated immediately after injection. However, while significant progress has been made in understanding shock-liquid interface interactions, the influence of droplet spacing in compressible wake-driven environments remains insufficiently characterized. To address this gap, we conduct two-dimensional simulations of 4.8 mm droplets impacted by normal shocks at Mach 1.47 and 2.4. The role of inter-drop separation in deformation and wake dynamics is quantified using automated edge detection to measure normalized projected area and interface tortuosity, Fourier analysis to extract the dominant interfacial wavelength, and spectral proper orthogonal decomposition to characterize the low-frequency coherent wake structure and its streamwise energy distribution. At Mach 1.47, the greatest downstream projected-area reduction occurs at S / D = 1.5, the highest downstream tortuosity at S / D = 2.0, and the smallest dominant wavelength at S / D = 3.0, with the S / D = 2.0 wavelength close to this minimum. At Mach 2.4, coherent wake energy shifts upstream and is distributed across multiple early antinodes. The smallest dominant wavelength occurs at S / D = 1.5, while the greatest downstream projected-area reduction and tortuosity occur at S / D = 2.0. These results show that Mach-number-dependent wake topology provides a reference for the spacing region associated with enhanced downstream response, but the dominant instability wavelength and cumulative deformation measures do not necessarily attain their extrema at the same spacing.