M. N. Davydov

Nucleation and growth of a gas bubble in magma

The dynamics of a “collective” gas bubble in the magma melt during its decompression was numerically studied on the basis of a complete mathematical models of an explosive volcanic eruption. It is shown that the bubble size distribution obtained for the nucleation process has one peak, which allows considering a “collective” bubble. The main stages of bubble growth due to gas diffusion and changes in the viscosity of the medium are determined. It is shown that the high viscosity of the melt makes possible the transition from the Rayleigh equation to a simpler relation for the radial velocity of the bubble.

Two-Phase Models of Formation of Cavitating Spalls in a Liquid

The dynamics of the structure of a liquid layer structure (with microbubbles of a free gas) behind a rarefaction wave front is studied numerically using the two-phase Iordansky–Kogarko–van Wijngaarden model and the “frozen” mass-velocity field model. An analysis of the initial stage of cavitation by the Iordansky–Kogarko–van Wijngaarden model showed that tensile stresses behind the rarefaction wave front relax quickly and the mass-velocity field in the cavitation zone turns out to be “frozen.” This effect is used to describe the late stage of the development of the cavitation zone. These models were combined to study the formation of cavitating spalls in a free-surface liquid under shock-wave loading.

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.

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.

Smooth particle hydrodynamics method for modeling cavitation-induced fracture of a fluid under shock-wave loading

It is demonstrated that the method of smoothed particle hydrodynamics can be used to study the flow structure in a cavitating medium with a high concentration of the gas phase and to describe the process of inversion of the two-phase state of this medium: transition from a cavitating fluid to a system consisting of a gas and particles. A numerical analysis of the dynamics of the state of a hemispherical droplet under shock-wave loading shows that focusing of the shock wave reflected from the free surface of the droplet leads to the formation of a dense, but rapidly expanding cavitation cluster at the droplet center. By the time t = 500 µs, the bubbles at the cluster center not only coalesce and form a foam-type structure, but also transform to a gas-particle system, thus, forming an almost free rapidly expanding zone. The mechanism of this process defined previously as an internal “cavitation explosion” of the droplet is validated by means of mathematical modeling of the problem by the smoothed particle hydrodynamics method. The deformation of the cavitating droplet is finalized by its decomposition into individual fragments and particles.