Direct Numerical Simulations of pore competition in idealized micro-spall

Cavitation and micro-spall appear when a weakly compressible (or expansible) liquid is suddenly submitted to large negative pressures resulting in volume growth. After the initial phases of uniform expansion and pore opening, a longer-lasting phase of pore growth and competition appears, which is especially difficult to investigate either experimentally or numerically [Signor, PhD, 2008]. Thus this study is among the first of its kind. We present here Direct Numerical Simulations (DNS) of this latter phase for idealized conditions relevant to micro-spall: incompressible inviscid fluid, vanishing vapor pressure in cavities, ballistic uniaxial expansion, perturbed Face-Centered-Cubic arrangement of pores. Under these assumptions, the system is characterized by a single dimensionless group, the Weber number based on the number of pores per unit volume. Volume transfer between pores occurs at low enough Weber numbers, a phenomenon designated as ""pore competition"". The pore competition effect is important as it is the main phenomenon driving the evolution in time of the statistical distribution of pore sizes. Small pores shrink and eventually disappear as their volume is transferred to large pores. Pore statistics and pressure evolution profiles can then be obtained for future modelling purposes. The simulations were performed using the volume of fluid method [Tryygvason, Scardovelli & Zaleski, Cambridge, 2011] with the mixed-Youngs-central scheme for normal vector computation and interface segment reconstruction, lagrangian explicit or ""CIAM"" advection, an original adapted first order extrapolation method in the neighborhood of the free surface, and a ghost fluid method for the pressure boundary condition on the free surface. The pressure used in the boundary condition is computed using Laplace's law, which in turn involves surface tension and curvature. Curvature is computed using the height-function method. The method was tested comparing numerical solutions to solutions of the Rayleigh-Plesset equation for oscillating bubbles. An adapted procedure is used to manage the collapsing cavities. A cavity tagging and Lagrangian tracking algorithm is used to retrieve statistics of cavity sizes