We study the spatial structure of nonstationary inhomogeneous supersonic airflows as shock wave diffraction on an obstacle occurs in a shock tube of a rectangular cross section. The Mach numbers of shock waves were 2.7–4.4 at initial air pressures of 10–30 Torr. The supersonic flow in the discharge chamber was visualized by high-speed shadowgraphy and by the registration of radiation of combined volume discharge by photo camera and by ICCD camera. In experiments, a combined volume discharge with a current duration of ~ 500 ns was initiated 40–150 μs after the initial shock wave have passed an obstacle. It has been established that the radiation of the volume phase of discharge lasts 400–700 ns, and the displacement of the flow during this time does not exceed 0.6 mm. A correlation is established between the spatial distribution of discharge radiation and the low-density local areas determined as a result of two-dimensional Navier-Stokes based numerical simulation of the flow. As visualized by the glow of the discharge, the shape of the shock wave front is in good agreement with the results of shadowgraphy at different stages of diffraction and with the numerical simulation results.

The processes accompanying the formation of a contracted (columnar) high-current nanosecond electric discharge in subcentimeter gaps filled with nitrogen are numerically investigated in this work. The space between two flat electrodes is considered in the case when a potential difference of 25 kV is instantly established between them. The voltage is applied for a time interval of 200 ns and then instantly removed. The characteristics of the nonthermal and thermal stages of electric-discharge development are studied, namely: the formation and growth of a streamer, the closure of a discharge gap by a streamer, the formation of a plasma channel, secondary ionization waves, and an increase in current density and temperature in the axial region of the channel. After switching off the electric field, the gas-dynamic processes associated with the discharge thermal effect on a neutral gas are investigated. Gas-dynamic processes are determined by the propagation of shock waves and rarefaction waves in the radial direction with respect to the axis of symmetry. The quantitative values of both the electric field (electron density and intensity) and gas-dynamic parameters (temperature, pressure, and gas velocity) are determined.

t. The article is devoted to the reflection of the Trinitarian dogma in The Life of Joseph Volotsky, in which triple repetitions are found at the lexical, syntactic and plot levels of the text. The significance of the Trinitarian dogma in the biography of Joseph Volotsky is related to the controversy that erupted at the turn of the 15th—16th centuries between the Orthodox Church and the Judaizer heresy, whose adherents questioned the dogma of the Trinitarian nature of God. Joseph Volotsky became the most active participant in antiheretical activities. The Life compiled by Bishop Savva Cherny of Krutitsky in the 1740s aligns itself with the Life of Sergius of Radonezh, in which numerous triple repetitions are present. The connection between The Life of Joseph of Volotsky and the Life of Sergius of Radonezh is evidenced by the textual connection of the introductory parts of the texts; indirect proof of the importance of the figure of Sergius of Radonezh for Joseph Volotsky is also apparent in the genetic connection between the saints, based on belonging to the same line of monastic tradition: Joseph took the tonsure from Paphnutius Borovsky, whose mentor Nikita Borovsky was a novice of Sergius. Analysis of the Life for triple repetitions at the structural and event levels of the text not only indicates that the Life of Sergius of Radonezh became a literary source for the biography of the Volotsk hegumen and that the author of The Life reflected in the monument a polemic that was relevant at the time of the saint’s life, but also complements the ideas of philological medieval studies about the biography of Joseph Volotsky. Today we have to state with regret that the Life of Joseph Volotsky, with rare exceptions, has not become an object of interest for philologists; this article intends to shed light on one of the aspects of the poetics of the monument

A distributed surface sliding discharge with a duration of 500 ns in supersonic air flows with an oblique shock wave had been experimentally studied. The Mach numbers of the flows were 1.18–1.68, the density was 0.02–0.45 kg/m 3 . The discharge was initiated in a single pulse mode. With a voltage of 25 kV, the discharge current was about 1 kA. It is shown that the discharge current, as well as the spatio-temporal characteristics of the radiation depend on the parameters of the local rarefaction zone in the boundary layer. In a stationary flow with an oblique shock wave, the discharge is generated as a single channel. Analysis of high-speed shadowgraphy of the flow after discharge showed that a single discharge channel generates a semi-cylindrical shock wave. The purpose of the work was to study the motion of the shock wave generated from the discharge under different conditions of supersonic flow. Comparison of the experimental dynamic of the shock wave with the results of numerical modelling of the flow based on the non-stationary Navier–Stokes equations showed that the value of the thermal energy released in the discharge channel is 0.15–0.36 J.

The paper considers the numerical modeling of the processes of homogeneous and heterogeneous condensation and evaporation in multiphase flows using the method of moments. Nonstationary processes of gas dynamics and phase transitions in the two-dimensional plane and axisymmetric regions are described by a general system of equations. The system of equations is expanded by adding two equations. One describes the evolution of the total mass fraction of the condensing substance; the other describes the evolution of the mass fraction of solid particles. An instant wetting model is used to model heterogeneous nucleation. The Gyarmathy model is used for the approximation of the average droplet growth rate. Heterogeneous condensation is modeled based on the distribution function of foreign impurities. An approach to calculating evaporation in the heterogeneous case is proposed. A comparison of the proposed models with a numerical experiment is given. Numerical simulation of homogeneous-heterogeneous condensation in a gas-dynamic ejector is carried out.

Action of the localized pulse energy input on the supersonic channel flow around and downstream the obstacle was studied. The pulsed volume discharge with preionization via two plasma sheets was initiated in a non-stationary gas-dynamic flow in the channel with an obstacle (ledge). Experiments were in the shock tube 24mm×48mm with a special discharge chamber. The initial plane shock wave M=2.8–3.4 with a uniform flow behind it passed over the ledge in the form of a parallelepiped of 48mm×6.2mm×2mm, placed on the lower wall of the discharge chamber. The discharge was initiated in different moments of a plane shock wave (and gas flow behind it) movement in the channel. The discharge electric current duration was 200−−500ns. High-speed shadow videos of shock waves from discharge localization zones were recorded. The comparison of shadow flow images, the discharge instant glow images and CFD flowfields were matched. The pulse volume discharge energy was redistributed in the inhomogeneous flowfield (plasma self-localization effect). Influence of the localized pulse energy input on the channel supersonic flow was analyzed: dynamics of shock (blast) waves produced by self-localized plasma in separation areas near the ledge and also discontinuities produces as a result of discontinuities breakdown at oblique shock area ionization. Initial flow configuration disturbed by the pulse volume discharge was restored in time interval up to 120μs.

This study presents an experimental and numerical investigation on a surface sliding discharge in a supersonic airflow in the presence of an oblique shock wave. In experiments, flow Mach numbers were 1.20–1.68 in the shock tube combined with the discharge chamber. A single high-voltage 25 kV pulse sustains the plasma; the discharge current has a duration of ~500 ns. A surface sliding discharge is developed as a localized channel in a zone of interaction of an oblique shock wave with a boundary layer on the upper wall of the discharge chamber. The discharge channel acts as a linear source of heat and is at the origin of the induced shock wave. The flow field in the discharge chamber is spatio-temporally surveyed using high-speed shadowgraphy imaging with a frequency of up to 525,000 frames per second. The experiments show that the perturbed flow restored the initial structure after more than 100 μs. Numerical simulation with local energy input into the supersonic flow in a flat channel is carried out on the base of unsteady two-dimensional Navier–Stokes equations. It is determined that the dynamics of an induced shock wave are dependent on the energy input regime and on the flow parameters. The thermal energy release in the discharge channel of 0.22–0.29 J was estimated from a comparison of experimental data and numerical simulations.

A high-fidelity CFD code hySol is developed based on high resolution Godunov method to simulate supersonic flows using 3D unstructured grids. It is designed for accurately simulating laminar and turbulent flows with shock waves and their interactions in non–inertial reference frame. The chapter provides the experience of developing the CFD code hySol, the main features of which are presented, including a brief description of both mathematical and numerical aspects. Verification and numerical simulations are illustrated using several examples including the Prandtl–Meyer flow, the 3D flow around a sharp wedge, and the flow around the standard ballistic model HB–2.

The device skimmer is considered, which is intended to separate inert gas clusters with the aim of further collision them with a surface to increase its smoothness order. The condensation and the evaporation processes of Argon in the device are calculated. The modified method of moments (MM) is used for modeling. The droplet nucleation and growth rate coefficients were found by the semi-empirical model. Two-dimensional viscous axisymmetric case is considered. The moment equations are supplemented by the diffusion equation of a condensing gas. To solve the equations, the finite volume method is used. The Riemann problem is solved using the AUSM+ method.

The paper presents the experience of developing the hySol software package intended for numerical simulation of high–speed flows in the presence of a complex shock–wave structure. The used finite–difference scheme and software implementation are described. Examples of calculations are given.

The chapter presents a development of condensation and evaporation in flows of two-phase gas-droplet mixture in the nozzles, jets, and external area in front of the nozzle. Condensation of pure water vapor and condensation vapor into wet stream mixture flow are considered. Two different models for modeling condensation process are used. One of them is a quasi-chemical method. Another method is Method Of Moments (MOM). Also, the task of gas mixture jump from metastable state to stationary state and the task of flow of superheated steam are reviewed.

The paper is devoted to the numerical study of the shock layer–particle interaction in a supersonic flow past bodies. The shock wave associated with a moving particle and the flow in the particle wake is taken into consideration. Distinctive features of the numerical technique are the adaptive Cartesian sliding grids of high resolution, a ghost cells immersed boundary method for the realization of conditions on curvilinear boundaries, parallelization of computations on graphics processors. The results of computational experiment obtained allows to study the characteristic shock and vortex structures formed during the passage of a particle rebounding from the surface through the bow shock wave. The oscillations observed for a flow over the fla-tended cylinder are discussed.

Numerical simulations were performed of the nanosecond high-voltage breakdown in nitrogen at a voltage of 25–35 kV in the sub-centimeter discharge gaps. The streamer configurations were studied at two constant pressures, as well as at the radially varying pressure, simulating the pressure distribution in the axial region of the vortex “columnar” gas-dynamic flow. In each case, the characteristic parameters and propagation velocities of the primary and secondary streamers were calculated. It was ascertained that the law of pressure change in the radial direction strongly affects the spatial structure of the negative streamer.

The article presents a numerical study of vapor condensation appearing in an ejector. The ejector is a part of a device developed by the authors and used to purify air emissions. The article considers condensation of pure water vapor and condensation of vapor in a mixture of vapor and carrier gas. The system of axisymmetric Navier-Stokes equations and the system of moment equations are considered as a mathematical model for describing two-dimensional non-stationary gas-dynamic processes and processes of phase transitions in the device. The general system of equations is numerically solved using the finite volume method.

We report investigations of the nanosecond surface sliding discharge in supersonic airflows with the oblique shock wave at Mach numbers of the flow 1.30-1.60 in shock tube. We show that the surface sliding discharge developed in flows as a single channel located near a zone of interaction of the oblique shock with the boundary layer on the wall of the channel. A pulse voltage of 25 kV powered the discharge; the electric current was of 1 kA. The electron concentration in the localized discharge channel was (0.7-1.4).1015 cm-3 and the electron energy was of 1.8-2.2 eV from the analysis the emission spectra. High-speed flow field shadowgraphy after the surface sliding discharge showed that the localized discharge channel generates a strong shock wave, leading to restructuring the shock-wave structure of the flow within ∼100 μs and subsequent relaxation to a stationary configuration.

An experimental study was made of the dynamics of shock waves developing from a localized channel of a nanosecond surface sliding discharge in supersonic airflows past a wedge in the shock tube with Mach numbers 1.16–1.47 at a density of 0.02 kg/m3–0.20 kg/m3. It is shown that a semi-cylindrical explosive-type shock wave is formed from the discharge channel in the low-density vortex zone behind the wedge. Numerical simulations of the resulting gas-dynamic flow are performed. The shadowgraphy images of shock waves after the discharge were compared with simulations of the flow field after an energy input near the wall in a supersonic flow. The energy input region in the simulations was set in accordance with the experimental results on the geometry of the discharge channel. Based on a comparison of experimental results and simulations, it is shown that shock waves are formed when a heat energy of 0.07 ± 0.04 J is released in the channel of localized discharge in supersonic airflows.

The characteristics of a distributed sliding surface discharge with a duration of ∼300 ns (plasma sheet) in a non-uniform supersonic airflow with a vortex zone behind a thin wedge have been studied in a shock tube channel. The spatial distribution of the discharge radiation, the spectra of the discharge radiation, and the discharge current are analyzed in the flows behind plane shock waves with Mach numbers 2.4–3.5 (the Mach numbers of flows are 1.16–1.47 and the density is 0.02–0.20 kg/m3). It is shown that in an airflow with a vortex zone, the surface discharge develops as a 1–3-mm-wide channel located in the region of low density behind the wedge. The calculated electron concentration in the discharge channel is an order of magnitude higher than the electron concentration when a discharge is initiated in a homogeneous medium.

In this chapter we introduce our recent studies on terahertz (THz) and X-ray emission generated in an Ar gas-cluster jet under irradiation with high-intense ultrashort laser pulses. We carried out a numerical simulation of cluster formation processes in a supersonic jet produced under adiabatic extension of gaseous Ar into vacuum, which shows that the concentration ratios among non-clusterized Ar monomers, small-size Ar clusters and large-size Ar clusters significantly vary along the jet. The chapter presents experimental results on THz and X-ray emission generated by irradiation of the jet with intense femtosecond laser pulses at various downstream distances measured from the nozzle outlet along the axis of symmetry of the nozzle. It is shown that THz and X-ray emission from the jet is a useful tool for the study of clustering dynamics in the course of free expansion of gas through a nozzle into vacuum.