Formation of cylindrical shock wave in two-phase liquid layer with free surface

Abstract

Numerical model for formation of 1D cylindrical shock-wave (SW) in a liquid layer with a free surface is considered. The liquid states are pure water and distilled water containing free micro-bubbles (1.5 I¼m, 106 cm-3). The SW initiation is performed on the axis by giving the pulse of mass velocity as the exponent for maximal amplitudes from 60 to 20 m/s. A two-phase mathematical model is the system of equation describing average pressure, velocity and density (including the Rayleigh-type equation). For pure water, the distributions of maximal amplitudes both from the axis along the radius for SW and from free surface up to the axis of symmetry for rarefaction wave (RW) were calculated. The distribution of maximal amplitudes of positive SW and negative RW along the radius appears to be completely symmetric. It was shown, the SW amplitude decreases proportionally to r -0.45 (within 3 cm from axis) and then asymptotics (r -0.72) is registered. The increase of RW amplitude during propagation to the axis is a cumulative effect. In two-phase model of distilled water the cavitation begins behind the RW front. Beginning from free surface, the volumetric gas concentration increases in 300 initial values (maximum velocity 60 m/s).Numerical model for formation of 1D cylindrical shock-wave (SW) in a liquid layer with a free surface is considered. The liquid states are pure water and distilled water containing free micro-bubbles (1.5 I¼m, 106 cm-3). The SW initiation is performed on the axis by giving the pulse of mass velocity as the exponent for maximal amplitudes from 60 to 20 m/s. A two-phase mathematical model is the system of equation describing average pressure, velocity and density (including the Rayleigh-type equation). For pure water, the distributions of maximal amplitudes both from the axis along the radius for SW and from free surface up to the axis of symmetry for rarefaction wave (RW) were calculated. The distribution of maximal amplitudes of positive SW and negative RW along the radius appears to be completely symmetric. It was shown, the SW amplitude decreases proportionally to r -0.45 (within 3 cm from axis) and then asymptotics (r -0.72) is registered. The increase of RW amplitude during propagation to the axis is ...