High-energy droplet collisions in multi-interacting hollow cone sprays

TL;DR

This study investigates high-energy droplet collisions within the interacting region of three hollow-cone sprays (the combined spray, CS) using 3D Phase Doppler Interferometry and high-speed backlight imaging at elevated liquid-sheet Weber numbers $W\!e_l$. The authors provide a detailed taxonomy of collision outcomes, including reflexive/separation, fingering, splashing, and stretching with digitations, and demonstrate a collision cascade driven by axial satellite droplets that broadens the size distribution. Ligament-mediated breakup emerges as the principal fragmentation pathway, with rescaled size distributions for CS well described by a compound gamma distribution, highlighting the role of satellite droplets in downstream atomization. The work advances understanding of multi-spray interactions, offering insights for improved modeling of poly-disperse sprays in engineering applications and natural phenomena, and identifies the need for high-$W\!e$ regime maps to generalize the observed collision dynamics.

Abstract

Droplets collide in several complex spray environments ranging from sea sprays to combustion chambers, altering their size and velocity characteristics. The present work offers a systematic investigation of such collisions within the interacting region formed by three hollow-cone sprays, termed the combined spray, at two elevated liquid sheet Weber numbers (Wel). The integrated analysis employs Phase Doppler Interferometry (PDI) and microscopic high-speed backlight imaging to characterize the collision dynamics. PDI indicates a notable reduction (11-15%) in Sauter mean diameter (SMD) at the onset of the interaction region. Images reveal frequent and high-energy droplet collisions, capturing structures associated with binary collision outcomes, namely reflexive and stretching separations, splashing, fingering, and stretching with digitations, along with complex multi-droplet collisions. These collisions produce numerous smaller satellite droplets at the expense of larger parent droplets, leading to a decrease in local SMD. Increasing Wel elevates the frequency of these outcomes, particularly highlighting stretching separation as the dominant mechanism. Furthermore, joint probability density functions from PDI and image-based analysis confirm that most satellite droplets predominantly exhibit axial motion, in contrast to the initial trajectories of parent droplets. The satellite droplets continue to move downstream, colliding with others and resulting in a cascade effect that produces finer droplets. Rescaled droplet size distributions, normalized by mean droplet diameter, are broader in the combined spray due to enhanced size reduction from collisions. These distributions are well captured by the compound gamma distribution, reflecting ligament-mediated breakup dynamics.

Figures (21)

• Figure 1: (a) Schematic illustrating geometrical and kinematic parameters of binary droplet collision. Top view at the point of contact for (b) in-plane collision with eccentricity $e = 0$, and (c) off-plane collision with $e \neq 0$.
• Figure 2: (a) Exploded view of the $CAD$ model of the hollow cone pressure swirl nozzle. (b) Triangular arrangement of three nozzles in the mounting plate. (c) Schematic of the spray test facility with phase Doppler interferometer (PDI) and backlight imaging. (d) Locations of PDI measurements in $SS$ (top row) and $CS$ (bottom row) seen from the two views. The dash-dotted line represents the centroidal axis of the arrangement. (e) Schematic illustrating the apparatus used for high-speed microscopic spray visualization. The top view of the spray width diagram shows that the camera is focused on the most interacting region in the U-V plane. The arrows show the anti-clockwise swirl motion of the sprays.
• Figure 3: Stroboscopic images of $CS$ from the multi-nozzle captured from (a) front, and (b) side views at $W\!e_l$ = 2704. In the side view, the spray from the nozzle element $N3$ appears behind that from the nozzle $N1$, as can be seen in the top-view of the nozzle arrangement. The dash-dotted line is the centroidal axis.
• Figure 4: (a) SMD and (b) AMD variation at different $z/G$ along the centroidal axis for $SS$ and $CS$ at different $W\!e_l$. The expressions of SMD and AMD are mentioned in the respective graphs, here $n_i$ is the number of droplets with diameter $d_i$.
• Figure 5: Droplet-size distribution comparison between SS and CS at different z/G for $W\!e_l$ = 1896 (a-f) and $W\!e_l$ = 2704 (g-l).