Formation and Amplification of Shock Waves in a Bubble “Cord”

Abstract

The structure and dynamics of the wave field generated by a bubble system in the form of an axial bubble cylinder (cord) excited by a plane shock wave propagating along the axis in an axisymmetric shock tube are numerically examined. It is shown that consecutive excitation of oscillations of the bubble zone results in formation of a quasi-steady shock wave in the cord and in the ambient liquid. Results of the numerical analysis of the maximum amplitude of the resulting wave as a function of problems parameters are described.Introduction. The problem of creation of explosive hydroacoustic sources [hydroacoustic analogs of laser systems -Shock Amplification by Systems with Energy Release (SASER)] involves the study of wave processes in media capable of accepting the energy being "pumped in." Such media absorb a comparatively weak external pulsed load and re-emit the latter with a significant increase in amplitude (owing to cumulation effects) and possible concentration of energy in a given direction [1].Among various problem formulations in this field, let us note the experimental and numerical research of explosions of cord high explosive (HE) charges and non-one-dimensional flows with axial symmetry [1-6] in free bubble media. In particular, the results for a number of problems of an underwater explosion with a detailed analysis of the structure and parameters of the wave field of cord and spiral charges, specific features of transformation of shock waves in bubble media, their amplification due to collisions and focusing, and also the problems of formation of bubble detonation waves in chemically active systems are described in [1]. The special features of the evolution of bubble detonation waves in a cylindrical bubble zone located in a volume of a "pure" liquid were examined in [2]. It was shown that origination and propagation of a detonation soliton requires that the radius of the bubble zone should be greater than a certain critical value depending on the caloric content of the gas in the bubbles, the volume content of the gas, and the bubble radius. The wave structure of the reaction zone and detonation velocity in a column of a chemically active bubble medium were numerically analyzed in [3]. It was found that the bubble detonation wave in such a system can propagate with a velocity higher than that in a one-dimensional case.Among papers dealing primarily with the behavior of various chemically active or passive media capable of radiation generation, we should note the numerical study of Kedrinskii et al. [4] who considered the excitation of a spherical cloud (cluster) of bubbles by a plane shock wave and formation in the cluster of a shock wave with a curved front with a sharp pressure gradient along this front within the framework of the Iordanskii-Kogarkovan Wijngaarden (IKW) model [7][8][9]. It was shown that, by changing the volume concentration of the gas phase, one can control the coordinate of the wave focusing spot and, in particular, form this spot in the vicinity of the bubble cluster-liquid i...