Shock-induced cavitation and wavefront analysis inside a water droplet

Abstract

The objective of this study is to develop a basic understanding of the interaction of shock waves with density inhomogeneities. We consider the particular instance of a planar air shock impinging on a spherical water droplet and discuss to what extent this interaction can lead to the inception of cavitation inside the droplet. The effort centers on early phases of the interaction, which are analyzed using both ray theory and a hydrodynamic code. Within the context of ray theory, the occurrence of focusing is examined in detail, and parametric equations are derived for the transmitted wavefront and its multiple internal reflections. It is found that wave patterns predicted by ray calculations compare extremely well with the more accurate numerical solutions from simulations. In particular, it is shown that the internal wavefront assumes a complex time-dependent shape whose dominant feature is the existence of cusp singularities. These singular points are shown to trace out surfaces that are the caustics of the associated system of rays. From the singularities of the energy flux density of the refracted wave, the parametric equations of the caustic surface associated with the kth reflected wavefront are deduced. As a consequence of the focusing process, simulations show the formation of negative-pressure regions in the internal flow field. These low-pressure zones are identified as possible spots at which cavitation may occur, depending on the magnitude of pressure reached. Finally, numerical results provide quantitative information on the dependence of negative-pressure peaks upon incident-shock-wave strength.

A phenomenological analysis of droplet shock-induced cavitation using a multiphase modeling approach

“…40 This is because the density of rays tangent to the caustic, which gives a relative measure of the focusing strength over the caustic, is maximum at the intersection of the caustic and the droplet axis (y ¼ 0). 4 Consequently, previous research efforts on shock-induced cavitation within a cylindrical droplet assumed the cavitation bubble cloud to appear at the focus of the reflected wavefront ðx c ; y c Þ. 2,13 However, a close examination of the bubble cloud center as seen in the experimental observations shows discrepancies between the theoretical x c value and experimental measurements, errors of 42%610% and 23%65% for the shock-droplet interaction and the high-speed droplet impact, respectively.…”

“…The confined shock therefore experiences near total reflections, as well as focusing which results in the amplification of the shock local interaction with the liquid. 4 The reflected wave of the transmitted shock being an expansion wave, and some regions of the droplet are thus exposed to a tensile force which, under some conditions, may generate hydrodynamic cavitation (i.e., isothermal inertia-driven phase change). Liquid rupture arises when subject to tension exceeding a threshold value, which depends on the nature of the liquid and its purity.…”

“…As a first approach, past numerical studies used numerical models not accounting for phase change or phase expansion. 1,4,[12][13][14] The occurrence and intensity of the cavitation were evaluated by probing the pressure field and comparing the low-pressure region magnitude to the cavitation threshold given by the classical nucleation theory for homogeneous cavitation (134 MPa at 300 K), 15 or the Blake threshold pressure. 16 Recently, Kyriazis et al simulated the experiment of Field et al, that is, high-speed droplet impact, using a thermodynamically well-posed model incorporating phase change.…”

Analysis of wave converging phenomena inside the shocked two-dimensional cylindrical water column

“…Boyd & Jarrahbashi (2021) extended the shock-droplet interaction problem from the subcritical condition to the supercritical condition and studied the effects of temperature, pressure and shock intensity on the interaction. Based on the ray analysis method (Heymann 1969;Haller et al 2003;Wu, Xiang & Wang 2018), Biasiori-Poulanges & El-Rabii (2021) theoretically investigated the interaction of a planar shock wave with a liquid column and derived the concentration of rays with different reflection times and then verified their results by numerical simulations. Guan et al (2018) numerically and theoretically investigated the establishment of an internal flow field inside a water droplet subjected to shock wave impact.…”

“…The possibility of cavitation of a high-speed droplet impacting the wall was verified by Kondo & Ando (2016), Wu et al (2018) and Wu, Liu & Wang (2021b) via the numerical method. Xiang & Wang (2017) and Biasiori-Poulanges & El-Rabii (2021) expounded that the occurrence of cavitation inside the shocked water column is dependent on the incident shock wave intensity and the value of the cavitation threshold pressure. Moreover, Xiang & Wang (2017) performed a numerical study on the interaction of a planar shock wave with a water column embedded with air cavities of different sizes at high Weber numbers.…”