Study on high-Weber-number droplet collision by a parallel, adaptive interface-tracking method

Abstract

We have established a parallel, adaptive interface-tracking framework in order to conduct, based on the framework, direct simulation of binary head-on droplet collision in the high-Weber-number regime (from 200 to 1500) that exhibits complex topological changes and substantial length scale variations. The overall algorithms include a combined Eulerian and Lagrangian solver to track moving interfaces, conservative Lagrangian mesh modification and reconstruction, cell-based unstructured adaptive mesh refinement (AMR) in the Eulerian solver, and associated Eulerian and Lagrangian domain partitions to minimize communication overhead. Based on the combined computational and experimental efforts, we have resolved for the first time the free-surface instabilities of the colliding droplets at such high Weber number. We detail the characteristics of coalescence, stretch, end pinching, fingering, free-surface movement and drop breakup. The Taylor–Culick rim is present soon after the collision. Furthermore, we observe two types of longitudinal instabilities on the rim, namely, the Rayleigh–Taylor (RT)-type instability in the initial deceleration phase of the circular sheet right after droplet coalescence, and later the Rayleigh–Plateau (RP) instabilities. As the Taylor–Culick rim disintegrates in the retraction phase, fingering effect is profound and resulting in wider droplet size distribution.

Numerical study of head-on droplet collisions at high Weber numbers

“…From the numerical side, the anisotropic grid arrangement is an unavoidable source of disturbance that may lead to the development of a stronger instability than in the experiment. Based on our simulation results, the breakup mechanism of the rim at an extremely high Weber number (We = 1520) is not as different as at relatively lower Weber numbers in terms of whether the rim is completely detached from the fluid sheet before the formation of secondary droplets, which is in disagreement with the conclusion of Kuan et al (2014).…”

“…Their results show that the instability of the rim of the water collision complex emerges at much smaller Weber numbers compared to isopropanol droplets. Recently, Kuan, Pan & Shyy (2014) conducted a numerical study of head-on collisions of water droplets at high Weber numbers, employing a parallel, adaptive interface tracking method, and compared their results with the experimental work of Pan et al (2009). Their simulations capture the unstable rim of the collision complex and show good agreement with corresponding experimental results of Pan et al (2009) up to We = 442.…”

“…In contrast, our results show that the rim is still connected to the sheet and the secondary droplets are splattered out from the rim. We presume that Kuan et al (2014) reached their conclusion because the lamella was not stabilized, which typically leads to a non-physical lamella rupture at the joint between the lamella and the sheet and therefore the separation of the rim from the sheet. 6.2.…”

“…Due to the restriction of the computational resource, the simulation is only conducted until t * = 1.05. Kuan et al (2014) concluded on the basis of their numerical observations that at this extremely high Weber number the whole toroidal rim will be separated from the sheet and will then break up into secondary droplets. In contrast, our results show that the rim is still connected to the sheet and the secondary droplets are splattered out from the rim.…”

A Numerical Investigation on the Collision Behavior of Unequal-Sized Micro-Nano Droplets

“…It was found that the small droplet spread on the large one’s surface at a high Weber number, while the small droplet penetrated into the large one at a low Weber number. Kuan et al [ 16 ] developed a parallel, adaptive Eulerian-Lagrangian interface-tracking method to investigate head-on collisions of water droplets at high Weber numbers. Their simulations found that the rim grew with bread-like structures, and the extent of the retraction and deformation on the rim becomes weaker as the Weber number increases.…”