Modelling cavitation during drop impact on solid surfaces

Abstract

The impact of liquid droplets on solid surfaces at conditions inducing cavitation inside their volume has rarely been addressed in the literature. A review is conducted on relevant studies, aiming to highlight the differences from non-cavitating impact cases. Focus is placed on the numerical models suitable for the simulation of droplet impact at such conditions. Further insight is given from the development of a purpose-built compressible two-phase flow solver that incorporates a phase-change model suitable for cavitation formation and collapse; thermodynamic closure is based on a barotropic Equation of State (EoS) representing the density and speed of sound of the co-existing liquid, gas and vapour phases as well as liquid-vapour mixture. To overcome the known problem of spurious oscillations occurring at the phase boundaries due to the rapid change in the acoustic impedance, a new hybrid numerical flux discretization scheme is proposed, based on approximate Riemann solvers; this is found to offer numerical stability and has allowed for simulations of cavitation formation during drop impact to be presented for the first time. Following a thorough justification of the validity of the model assumptions adopted for the cases of interest, numerical simulations are firstly compared against the Riemann problem, for which the exact solution has been derived for two materials with the same velocity and pressure fields. The model is validated against the single experimental data set available in the literature for a 2-D planar drop impact case. The results are found in good agreement against these data that depict the evolution of both the shock wave generated upon impact and the rarefaction waves, which are also captured reasonably well. Moreover, the location of cavitation formation inside the drop and the areas of possible erosion sites that may develop on the solid surface, are also well captured by the model. Following model validation, numerical experiments have examined the effect of impact conditions on the process, utilizing both planar and 2-D axisymmetric simulations. It is found that the absence of air between the drop and the wall at the initial configuration can generate cavitation regimes closer to the wall surface, which significantly increase the pressures induced on the solid wall surface, even for much lower impact velocities. A summary highlighting the open questions still remaining on the subject is given at the end.

Curved surface effect on high-speed droplet impingement

“…Furthermore, unsteady complicated wave structures with different properties are generated inside the droplet as the confined shock wave continuously propagates and reflects from the droplet interface and the solid surface (Field, Dear & Ogren 1989;Chizhov & Schmidt 2000;Kondo & Ando 2016;Niu & Wang 2016). 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).…”

Cavitation Induction by Projectile Impacting on a Water Jet

“…The IB forcing term is introduced in the compressible Navier-Stokes equations that are solved using a density based, two-phase, explicit solver, developed by Kyriazis et al [6]. This solver is based on the homogeneous mixture approach to account for liquid, liquid-vapour and gaseous phases, that are in mechanical and thermodynamic equilibrium.…”

“…The solver is making use of a special hybrid flux calculation, to tackle issues arising when density based solvers are used for three phase cases with great variations of speed of sound. The hybrid flux is based on Primitive Variable Riemann Solver and Mach consistent flux [6]. The reader is referred to [6] where Kyriazis et al present the solver in detail.…”

“…The hybrid flux is based on Primitive Variable Riemann Solver and Mach consistent flux [6]. The reader is referred to [6] where Kyriazis et al present the solver in detail.…”

“…The IB methods, first introduced by Peskin [11] model internal boundaries by either changing the computational stencil near the solid or adding source terms in the equations. The later approach is used in this study, where forcing source terms are added in the momentum equations of an explicit density based in-house solver, developed by Kyriazis [6] on OpenFOAM platform. This solver is able to simulate cavitating flows, where the local Mach number has a wide range, in addition to the advection of immiscible compressible gas.…”