Impingement of high-speed cylindrical droplets embedded with an air/vapour cavity on a rigid wall: numerical analysis

Abstract

The high-speed impingement of hollow droplets embedded with a cavity has fundamental applications in various scenarios, such as in spray coating and biomedical engineering. The impingement dynamics is modulated by the wrapping medium, different from that of denser solid droplets. With air and vapour cavities, the impingement of two kinds of hollow cylindrical droplets is simulated in the present study to investigate the morphology and physical mechanisms regarding droplet and cavity dynamics. The compressible two-phase Eulerian model is used to couple with the phase transition procedure. The results detail the evolution of droplets and collapsing dynamics of the two kinds of cavities. Processes are captured in which the impinging water-hammer shock wave interacts with the cavity, and vertical liquid jets are induced to impact the embedded cavity. For the case of the air cavity, a transmitted shock wave is formed and propagates inside the cavity. The air cavities are compressively deformed and broken into a series of small cavities. Subsequently, a range of intermittent collapsing compression wavelets are generated due to the interface collapse driven by local jets. As for the vapour cavity in the saturated state, initially, once it is impacted by the impinging shock wave, it gradually shrinks accompanied by local condensation but without generation of transmitted waves. Following the first interaction between the lower and upper surfaces of the cavity, the vapour cavity undergoes continuous condensation and collapse with repeated interface fusion. The vapour cavity finally turns into liquid water blended into the surroundings, and the strong collapsing shock waves are expanded inside the droplet. The radius ratios and initial impinging speeds are chosen to analyse the variation of the collapsing time, maximum collapsing pressure and mean pressure on the rigid wall. The pressure withstood by the wall due to the collapsing cavity increases with the initial size of the cavity and initial impinging speed. The maximum local pressures in the entire fluids and the mean pressure on the wall during the collapsing of the vapour cavities are higher than those for the air cavities.

Curved surface effect on high-speed droplet impingement

“…The numerical verification of the grid sensitivity refers to the treatment methods in the present authors’ previous work (Wu et al. 2018, 2019).…”

“…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.…”

Interaction of a planar shock wave and a water droplet embedded with a vapour cavity

“…In addition, the cavity shrinks substantially. In this process, local condensation of vapour can take place (Wu et al 2019) because the local pressure inside the cavity can be higher than the saturation pressure after repeated impacts of shock/compression waves. In addition, a ring-like structure emerges on the outside surface of the droplet.…”

“…In this investigation, the effects of the shock intensities and the gas cavity sizes on the evolution of the droplet and the cavity were analysed qualitatively and quantitatively. Later, Wu, Wang & Xiang (2019) conducted numerical simulations to study the impingement of a cylindrical water column embedded with an air/vapour cavity on a rigid wall, and the interaction of the reflected water-hammer shock with the gas cavity was considered. In addition, the phase change process was considered in the numerical work of Wu et al (2019), and the differences between the collapse of an air cavity and the collapse of a vapour cavity were analysed.…”

“…Later, Wu, Wang & Xiang (2019) conducted numerical simulations to study the impingement of a cylindrical water column embedded with an air/vapour cavity on a rigid wall, and the interaction of the reflected water-hammer shock with the gas cavity was considered. In addition, the phase change process was considered in the numerical work of Wu et al (2019), and the differences between the collapse of an air cavity and the collapse of a vapour cavity were analysed. However, the interaction of a shock wave and a droplet embedded with a gas cavity has not been experimentally investigated, due to the challenge of generating such droplets.…”