On high-speed impingement of cylindrical droplets upon solid wall considering cavitation effects

Abstract

The high-speed impingement of droplets on a wall occurs widely in nature and industry. However, there is limited research available on the physical mechanism of the complicated flow phenomena during impact. In this study, a simplified multi-component compressible two-phase fluid model, coupled with the phase-transition procedure, is employed to solve the two-phase hydrodynamics system for high-speed cylindrical droplet impaction on a solid wall. The threshold conditions of the thermodynamic parameters of the fluid are established to numerically model the initiation of phase transition. The inception of cavitation inside the high-speed cylindrical droplets impacting on the solid wall can thus be captured. The morphology and dynamic characteristics of the high-speed droplet impingement process are analysed qualitatively and quantitatively, after the mathematical models and numerical procedures are carefully verified and validated. It was found that a confined curved shock wave is generated when the high-speed cylindrical droplet impacts the wall and this shock wave is reflected by the curved droplet surface. A series of rarefaction waves focus at a position at a distance of one third of the droplet diameter away from the top pole due to the curved surface reflection. This focusing zone is identified as the cavity because the local liquid state satisfies the condition for the inception of cavitation. Moreover, the subsequent evolution of the cavitation zone is demonstrated and the effects of the impact speed, ranging from $50$ to $200~\text{m}~\text{s}^{-1}$ , on the deformation of the cylindrical droplet and the further evolution of the cavitation were studied. The focusing position, where the cavitation core is located, is independent of the initial impaction speed. However, the cavity zone is enlarged and the stronger collapsing wave is induced as the impaction speed increases.

Curved surface effect on high-speed droplet impingement

“…Local cavitation may be generated inside the droplet due to the convergence of the proper waves, as verified by experiments (Lesser & Field 1983;Field et al 1989Field et al , 2012Obreschkow et al 2011) and subsequent numerical simulations during high-speed impingement (Sanada, Ando & Colonius 2011;Kondo & Ando 2016;Kyriazis, Koukouvinis & Gavaises 2018). The cavitation evolution mechanisms during a droplet's high-speed impingement on a flat solid surface were discussed in our previous works (Wu, Xiang & Wang 2018;Wu, Wang & Xiang 2019). Some researchers deduced that cavity collapse especially near-surface cavity collapse may also induce surface damage (Okada et al 1995;Obreschkow et al 2011;Kyriazis et al 2018).…”

“…A high-speed multi-phase flow problem including complex cavitation phenomena is studied in the present work, and the compressible multi-phase fluid model including phase transition is used (Wu et al 2018). The governing equations are…”

“…The same Courant-Friedrich-Lewis (CFL) number, 0.4, is used for all of the computations. The numerical verification of the grid sensitivity refers to the treatment methods in the present authors' previous work (Wu et al 2018(Wu et al , 2019.…”

“…In the present study, the expansion speeds of the wavelets are all assumed to be constant for simplification. In the earlier impinging stage, the envelop of the compression wavelets form the front of the water-hammer shock wave (Wu et al 2018). For droplet impingement on a concave surface (as shown in figure 4a), the initial contact region is a circular arc, and hence many compression wavelets are simultaneously emitted at the initial interaction instant.…”

“…According to the droplet's geometrical profile, the intersection angle between the interface of the droplet and the solid surface increases with the impinging process, and the expansion velocity of the periphery of the contact region between the droplet and the surface gradually decreases from an infinite value at the initial interaction instant ( Wu et al 2018). Owing to the limitation of the sound speed, the propagation velocity of the water-hammer shock wave is lower than the expansion velocity of the periphery of the contact region at the very beginning.…”