Numerical study of a planar shock interacting with a cylindrical water column embedded with an air cavity

Abstract

This paper performs a numerical study on the interaction of a planar shock wave with a water column embedded with/without a cavity of different sizes at high Weber numbers. The conservative-type Euler and non-conservative scalar two-equations representing the transportation of two-phase properties consist of the diffusion interface capture models. The numerical fluxes are computed by the Godunov-type Harten-Lax–van Leer contact Riemann solver coupled with an incremental fifth-order weighted essentially non-oscillatory (WENO) scheme. A third-order total variation diminishing (TVD) Runge–Kutta scheme is used to advance the solution in time. The morphology and dynamical characteristics are analysed qualitatively and quantitatively to demonstrate the breakup mechanism of the water column and formation of transverse jets under different incident shock intensities and embedded-cavity sizes. The jet tip velocities are extracted by analysing the interface evolution. The liquid column is prone to aerodynamic breakup with the formation of micro-mist at later stages instead of liquid evaporation because of the weakly heating effects of the surrounding air. It is numerically confirmed that the liquid-phase pressure will drop below the saturated vapour pressure, and the low pressure can be sustained for a certain time because of the focusing of the expansion wave, which accounts for the cavitation inside the liquid water column. The geometrical parameters of the deformed water column are identified, showing that the centreline width decreases but the transverse height increases nonlinearly with time. The deformation rates are nonlinearly correlated under different Mach numbers. The first transverse jet is found for a water column with an embedded cavity, whereas the water hammer shock and second jet do not occur under the impact of low intensity incident shock waves. The $x$-velocity component recorded at the rear stagnation point can remain unchanged for a comparable time after a declined evolution, which indicates that the downstream wall of the shocked water ring somehow moves uniformly. It can be explained that the acceleration of the downstream wall is balanced by the trailing shedding vortex, and this effect is more evident under higher Mach numbers. The increased enstrophy, mainly generated at the interface, demonstrates the competition of the baroclinic effects of the shock wave impact over dilatation.