Focusing of rarefaction wave and dynamics of cavitation zone state behind its front in two-phase cylindrical liquid layer

Abstract

The evolution of the cavitation zone behind the front of a converging cylindrical rarefaction wave (RW) in a layer of two-phase distilled water is investigated numerically within the IKvanW mathematical model. The process is initiated by the generation of a shock wave (SW) exponential profile by the coaxial piston in the vicinity of the axis symmetry (R = 0 mm) in the wide range of amplitudes (Umax = 40–200 m/s) and time constants of exponent (10–40 μs). SW propagates along the radius of layer and reflects from a free surface (R = 60 or 100 mm) forming RW. The analysis of influence of SW parameters (at given exponent 10 μs for all amplitudes Umax) on the state of the cavitation zone has shown that the cavitation process is smoothly intensified for each value Umax in the distance ranging from 100–40 mm. Then, it drastically increases approaching the axis (interval 40–20 mm) and reaches 3500 units of the concentration (for Umax = 200 m/s). The total concentration becomes more than 6%. It is of interest to note that a significant effect produced by the changes in the initial parameters of state and in exponents (at Umax = 100 m/s): (1)—at R0 = 1.5 μm, k0 = 10-5, the calculation for exponent 40 μs practically coincides with the results for 30 μs. Thus, the latter can be considered as a limit value for the accepted parameters of two-phase medium state (total concentration reaches 2%) and (2)—at R0 = 7 μm, k0 = 10-3, the concentration distributions increase separately for each exponent and total concentration reaches value close to 16%.The evolution of the cavitation zone behind the front of a converging cylindrical rarefaction wave (RW) in a layer of two-phase distilled water is investigated numerically within the IKvanW mathematical model. The process is initiated by the generation of a shock wave (SW) exponential profile by the coaxial piston in the vicinity of the axis symmetry (R = 0 mm) in the wide range of amplitudes (Umax = 40–200 m/s) and time constants of exponent (10–40 μs). SW propagates along the radius of layer and reflects from a free surface (R = 60 or 100 mm) forming RW. The analysis of influence of SW parameters (at given exponent 10 μs for all amplitudes Umax) on the state of the cavitation zone has shown that the cavitation process is smoothly intensified for each value Umax in the distance ranging from 100–40 mm. Then, it drastically increases approaching the axis (interval 40–20 mm) and reaches 3500 units of the concentration (for Umax = 200 m/s). The total concentration becomes more than 6%. It is of interest to n...