V. K. Kedrinskii

On the similarity of the initial stage of failure of solids and liquids under impulse loading

Cavitation is the disturbance of continuity of a liquid (the initial stage of failure) in the field of tensile stresses; it is accompanied by the growth of vapor-gas bubbles on the cavitation nuclei that are always present in liquid media as microbubbles of a free gas, or microparticles, or both [1, 2]. One of the parameters that characterize the cavitation strength of water is the cavitation threshold, which is understood as a negative pressure, the excess above which causes an intense growth of cavitation nuclei and, as a consequence, a steep change in the dynamics of the free surface of the liquid [3], in the intensity of light scattering [1, 3], etc. Depending on the measuring technique and quality of water purification, the cavitation threshold varies from units [2, 3–6] to several hundred atmospheres [4–6], and its statistical dispersion, based on standard measuring procedures, reaches 50–100% [5, 6] and is determined by the size dispersion of cavitation nuclei, fluctuations in the nucleus distribution, nonlinear dynamics of microbubbles, and by the measuring technique.

Dynamics of a “collective” bubble in a magma melt flow behind the decompression wave front

Specific features of the dynamics of the wave field structure and growth of a “collective” bubble behind the decompression wave front in the “Lagrangian” section of the formed cavitation zone are numerically analyzed. Two cases are considered: with no diffusion of the dissolved gas from the melt to cavitation nuclei and with the diffusion flux providing an increase in the gas mass in the bubbles. In the first case, it is shown that an almost smooth decompression wave front approximately 100 m wide is formed, with minor perturbations that appear when the front of saturation of the cavitation zone with nuclei is passed. In the case of the diffusion process, the melt state behind the saturation front is principally different: jumps in mass velocity and viscosity are observed in the vicinity of the free surface, and the pressure in the “collective” cavitation bubble remains unchanged for a sufficiently long time interval, despite the bubble growth and intense diffusion of the gas from the melt. It is assumed that the diffusion process (and, therefore, viscosity) actually become factors determining the dynamics of growth of cavitation bubbles beginning from this time interval. A pressure jump is demonstrated to form near the free surface.

Focusing of an oscillating shock wave emitted by a toroidal bubble cloud

An analysis of pressure-field dynamics is performed for an axially symmetric problem of interaction between a shock wave and a “free” bubble system (toroidal cluster) giving rise to a steady oscillating shock wave. The results of a numerical study of near-axis wave structure are presented for a focusing shock wave emitted by a bubble cluster. It is shown that the wave reflected from the axis has irregular structure. The Mach disk developing on the axis has a core of finite thickness with a nonuniform radial pressure distribution. The evolution of the Mach-disk core is analyzed, and the maximum pressure in the core is computed as a function of the gas volume fraction in the cluster. The effect of geometric parameters of the toroidal bubble cloud on the cumulative effect is examined.

Opening of a system of cracks—on the mechanism of the cyclic lateral eruption of the St. Helens volcano in 1980

The dynamic behavior of a magma melt filling a slot channel (crack) in a closed explosive hydrodynamic structure is considered. The explosive hydrodynamic structure includes the volcano focal point with a connected vertical channel (conduit) closed by a slug and a system of internal cracks (dikes) near the dome, as well as a crater open into the atmosphere. A two-dimensional model of a slot eruption is constructed with the use of the Iordanskii–Kogarko–van Wijngaarden mathematical model of two-phase media and the kinetics that describes the basic physical processes in a heavy magma saturated by the gas behind the decompression wave front. A numerical scheme is developed for analyzing the influence of the boundary conditions on the conduit walls and scale factors on the melt flow structure, the role of viscosity in static modes, and dynamic formulations with allowance for diffusion processes and increasing (by several orders of magnitude) viscosity. Results of the numerical analysis of the initial stage of cavitation process evolution are discussed.

On one model of cyclic ejections of magma in the process of the explosive volcanic eruption

The dynamics of the structure of a cavitating magma flow behind the decompression wave front is experimentally studied by the method of hydrodynamic shock tubes. It is demonstrated that a discrete system of intensely cavitating zones with alternation of low and high densities of the gas phase can be formed at a certain regime of shock-wave loading of the examined fluid sample. Based on the results of a numerical analysis of the formation of an anomalous zone in the cavitating magma flow with anomalously high flow characteristics exceeding the values of these characteristics outside this zone at least by an order of magnitude, a model of an instantaneous transformation of the cavitating magma in the anomalous zone to a gas-droplet system, its ejections, and formation of a free surface on the interface is proposed. A numerical analysis shows that the characteristic wave structure and the anomalous saturation zone are fairly rapidly reconstructed in the vicinity of this free surface of the flow part remaining in the conduit after the ejections, and the above-mentioned jumps of flow characteristics are again formed in the anomalous zone.

Generation of shock waves by spherical bubble clusters in a liquid

The problem on active media [1, 2] capable of absorbing and amplifying an external disturbance and then reemitting it in the form of an acoustic pulse is one of the problems of the so-called acoustic laser (acoustic analogue of laser systems). As was shown in [3] by numerical analysis of one-dimensional cases, bubble systems, both passive and containing explosive gaseous mixtures, can be treated as active media. In such media, an excitation caused by interactions with shock waves can lead to significantly amplifying the wave field and generating an intense shock pulse.

Dynamics of discontinuity formation in a cavitating liquid layer under shock wave loading

The problem of experimental modeling of discontinuity formation in a cavitating liquid layer under shock wave loading is considered. It is shown that the discontinuity takes the shape of a spherical segment and retains it up to the closure instant. The discontinuity surface becomes covered with a dynamically growing thin boundary layer consisting of bubbles, which transforms to a ring-shaped vortex bubble cluster at the instant of the discontinuity closure, generating a secondary shock wave. Specific features of the structure of the cavitating flow discontinuity arising at loading intensities lower than 0.1 and 5 kJ are discussed.

Initial Stage of Modeling of the Magma State in a Slot Volcano with a Finite Velocity of Diaphragm Opening

Results of a numerical analysis of the dynamic behavior of a compressed magma melt in a slot channel with gradual opening of the diaphragm and results of simulations of its time evolution are reported. The Iordanskii–Kogarko–van Vijngaarden mathematical model of a twophase medium and a model that describes phase changes in the gas-saturated plasma behind the front of the decompression wave being formed are used. Results of numerical simulations of the flow with allowance for specific features of the pressure dynamics in the decompression wave, mass velocity components, volume fraction of the gas phase, and its viscosity are presented.

Dynamics of the distribution of the main parameters of the magma melt in the volcano slot cross section under instantaneous decompression

The dynamic behavior of the magma melt saturated with a strongly compressed gas at a high temperature, which is located between two rigid boundaries aligned symmetrically with respect to the vertical axis, is considered. A constant pressure is maintained at the channel bottom, while the pressure in the medium is initially distributed in accordance with the hydrostatic law. The top of the channel is hermetically sealed with a plug, which is affected by a constant pressure equal to the atmospheric value. The state of the melt after instantaneous removal of the plug is studied.

A numerical model of rupture formation in a bubbly liquid under pulsed loading

In this study, a new numerical model based on the method of particles in cells, which differs in principle from the schematic of particles in Harlow cells by the fact that the particles have their own velocity and, therefore, boundaries with a vacuum are not spread, is proposed for the first time. The model makes it possible to pass the stage of the “continuous” transition to rupture development and description of the dynamics of the further state of its “banks.” Based on the Iordansky–Kogarko–van Wijngaarden mathematical model (IKW model), the formation of rupture and its further dynamics in the bubble fluid layer in the jump region of the mass velocity is numerically investigated using the proposed method. The dynamics of the state of the medium on both rupture “banks” is calculated including the structure of the rarefaction waves, fields of mass velocity and density, and cavitation development in the time range up to 2 μs when the subsequent dynamics of the layer succumbs to the prognosis.