Start shock waves and the vortex structures arising in the formation of jets

Experimental studies were made of the state behind a shock wave arising in front of a pulse jet in formation, and the development of the vortex structure of the jet itself. A comparison was made of the experimental axial density distribution in the jet in the region between the front of the gas and the primary shock wave with the solutions to the problem of an expanding spherical piston and the nonself-similar problem of a point explosion. Moscow Translated from Izvestiya, Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 146–150, September–October, 1988.     

Unsteady and nonequilibrium airflow near a stagnation line

The propagation of shock waves in a medium with a nonuniform distribution of the parameters is the subject of recently published research [1–3]. The present paper deals with the problem of the gas flow ahead of the forward point of a blunt body moving at supersonic speed in air with variable parameters. The chemical reaction processes behind the shock front are taken into account. As a result of numerical calculations by the method of characteristics with isolation of the forward shock the time-dependent position of the shock front and the distributions of the composition and gas dynamic parameters in the shock layer are found. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 170–172, November–December, 1986.     

The quasi-stationary structure of radiating shock waves. I. The one-temperature fluid

We calculate the quasi-stationary structure of a radiating shock wave propagating through a spherically symmetric shell of cold gas by solving the time-dependent equations of radiation hydrodynamics on an implicit adaptive grid. We show that this code successfully resolves the shock wave in both the subcritical and supercritical cases and, for the first time, we have reproduced all the expected features – including the optically thin temperature spike at a supercritical shock front – without invoking analytic jump conditions at the discontinuity. We solve the full moment equations for the radiation flux and energy density, but the shock wave structure can also be reproduced if the radiation flux is assumed to be proportional to the gradient of the energy density (the diffusion approximation), as long as the radiation energy density is determined by the appropriate radiative transfer moment equation. We find that Zel'dovich and Raizer's (1967) analytic solution for the shock wave structure accurately describes a subcritical shock but it underestimates the gas temperature, pressure, and the radiation flux in the gas ahead of a supercritical shock. We argue that this discrepancy is a consequence of neglecting terms which are second order in the minimum inverse shock compression ratio [, where is the adiabatic index] and the inaccurate treatment of radiative transfer near the discontinuity. In addition, we verify that the maximum temperature of the gas immediately behind the shock is given by , where is the gas temperature far behind the shock. Received 21 September 1998/ Accepted 2 February 1999     

Cellular detonation diffraction in gas–particle mixtures

Diffraction of cellular heterogeneous detonation out of a channel into open half-space in a mixture of aluminum particles and oxygen is investigated numerically. The flow is found to be very similar to gas detonation diffraction. The detonation weakening behind the step results in combustion front deceleration and decoupling from the leading shock wave. Subsequent re-initiation takes place in a transverse wave. New transverse waves are generated along the expanding front. The computations that were performed show that the critical number of cells is several times less than that for gases. This is confirmed by theoretical estimates based upon the Mitrofanov–Soloukhin approach.     

Reflection of pressure waves of moderate intensity at a solid wall in a liquid with bubbles of a readily soluble gas

The present paper is concerned with an experimental study of the process of gas dissolution behind a shock wave in a liquid with bubbles of a readily soluble gas, the influence of gas dissolution on the wave evolution, and strengthening of the shock wave after reflection from a solid wall. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 19–24, September–October, 1998.     

Re-initiation phenomenon of gaseous detonation induced by shock reflection

The two-dimensional, time-dependent, reactive Navier–Stokes equations including the effects of viscosity, thermal conduction and molecular diffusion were solved to reveal the wave evolution and chemical dynamics involved in the re-initiation process. The computation was performed for hydrogen–oxygen–argon mixtures at the low initial pressure (8.00 kPa), using detailed chemical reaction model. The results show that, the decoupled leading shock reflects on the right wall of the vertical branch. High temperature and pressure behind the reflected shock induce the generation of hot spots and local explosion. Therefore, the re-initiation of gaseous detonation occurs. In the re-initiation area, there exist very high OH concentration and no H ₂ concentration. However, in front of reflected shock, there exist relatively high H ₂ concentration and no OH radicals. Additionally, the shock–flame interaction induces RM instability. This results in the fast mixing between hot reacted gas mixture and the relatively cold unreacted gas mixture and accelerates the chemical reactions. However, the shock–flame interaction contributes much less to the re-initiation, in contrast with shock reflection. The transition of leading shock from regular reflection to Mach reflection happens during the re-initiation. The computed evolution of wave structures involved in the re-initiation is qualitatively agreeable with that from the experimental schlieren images.      

Propagation of shock waves in a porous medium saturated by a liquid with bubbles of a soluble gas

The process of evolution and reflection of shock waves of moderate amplitude from a rigid boundary in a porous medium saturated by a liquid with bubbles of a soluble gas is studied experimentally. Experimental values of the amplitude and velocity of the reflected wave are compared with the calculated results obtained using mathematical models. The process of dissolution of gas bubbles in the liquid behind the shock wave is studied. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 91–102, September–October, 2000.     

Detonation initiation developing from the Richtmyer–Meshkov instability

Detonation initiation resulting from the Richtmyer–Meshkov instability is investigated numerically in the configuration of the shock/spark-induced-deflagration interaction in a combustive gas mixture. Two-dimensional multi-species Navier–Stokes equations implemented with the detailed chemical reaction model are solved with the dispersion-controlled dissipative scheme. Numerical results show that the spark can create a blast wave and ignite deflagrations. Then, the deflagration waves are enhanced due to the Richtmyer–Meshkov instability, which provides detonation initiations with local environment conditions. By examining the deflagration fronts, two kinds of the initiation mechanisms are identified. One is referred to as the deflagration front acceleration with the help of the weak shock wave, occurring on the convex surfaces, and the other is the hot spot explosion deriving from the deflagration front focusing, occurring on the concave surfaces. The project supported by the National Natural Science Foundation of China (90205027 and 10632090).     

Enhancement of shock waves

The flow field developed behind a shock wave propagating inside a constant cross-section conduit is solved numerically for two different cases. First, when the density of the ambient gas into which the shock propagates has a logarithmic change with distance. In the second, and the more practical case, the ambient gas is composed of pairs of air–helium layers having a continually decreasing width. It is shown that in both cases meaningful pressure amplification can be reached behind the transmitted shock wave. It is especially so in the second case. By proper choice of the number of air–helium layers and their width reduction ratio, pressure amplification as high as 7.5 can be obtained.      

Radiative cooling of plasma behind a reflected shock front

Calculation of gas flow in a shock tube on the basis of ideal theory [1] leads to results that differ from the real picture. In particular, the calculated velocity of the reflected shock wave exceeds the experimentally measured velocity [2] by about 20%. The calculated parameters of shock-heated gas agree well with the experimental results only directly behind the shock front [3]. The present paper reports a theoretical and experimental investigation of the variation of the plasma parameters behind the front of a reflected shock wave in argon. A picture of the gas-dynamic processes taking place after reflection of the incident shock wave by the end of the shock tube is determined. A method is developed for approximate analytic calculation, this making it possible to determine not only the parameters of the gas directly behind the front of the reflected shock wave for different positions of the wave relative to the end of the shock tube but also the variation of these parameters in other regions behind the reflected shock wave. The calculation takes into account the influence of the boundary layer and radiative cooling in the approximation of a low degree of ionization of the plasma and persistence of equilibrium conditions in the entire region behind the reflected shock wave. The experimental and theoretical profiles of the radiation behind the reflected shock wave are compared.     

Equation of a shock wave front

Second-order differential equations of the hyperbolic type are derived for describing the local law of shock wave propagation. The shock waves are assumed to be two-dimensional unsteady in a stationary gas flow and three-dimensional steady in a supersonic flow. The behavior of the characteristics of these equations is investigated as a function of the governing flow parameters and their relative position with respect to the typical bicharacteristics of the characteristic cone behind the shock is analyzed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 159–165, May–June, 2000.     

Differential characteristics of the flow field in a plane overexpanded jet in the vicinity of the nozzle lip

A method of theoretical investigation of the flow field in a two-dimensional (plane-parallel or axisymmetric) overexpanded jet of an ideal perfect gas in the vicinity of the nozzle lip is described. The changes in curvature of the shock wave emanating from the lip, as well as the shock-wave intensity and flow parameters behind the shock are analyzed as functions of the Mach number, pressure ratio in the plane jet, and ratio of specific heats of the gas. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 72–83, May–June, 2006.     

Shock and detonation wave diffraction at a sudden expansion in gas–particle mixtures

Numerical modeling of the propagation of shock and detonation waves is carried out in a duct with an abrupt expansion for a heterogeneous mixture of fine particles of aluminum and oxygen. A considerable difference from corresponding flows in pure gas is found. The influence of the size and mass loading of particles on the flow and shock wave structure behind the backward-facing step is determined. As in gaseous detonations, three types of scenarios of detonation development are obtained. Specific features of the flow structure are revealed such as deformation of the combustion front due to interaction between the relaxation zone and the vortex structure. The influence of particle size and channel width on detonation propagation is analyzed. This paper is based on work that was presented at the 21th International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.     

Processes of hydrate formation and dissolution behind a shock wave in a liquid containing gas bubbles (mixture of nitrogen and carbon dioxide)

The processes of dissolution and hydrate formation behind a moderate-amplitude shock wave in water containing gas bubbles (mixture of nitrogen and carbon dioxide) are studied in experiments with different initial static pressures in the medium and concentrations of carbon dioxide in bubbles. An increase in static pressure in the gas-liquid medium is demonstrated to enhance the influence of the non-reacting gas (nitrogen) on the processes of dissolution and hydrate formation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 178–187, March–April, 2009.     

Regular reflection of a shock wave from a solid wall in a stream of fuel mixture

The two-dimensional stationary problem of regular reflection of a shock wave from a plane solid wall in a fuel gas mixture is examined in the case when the mixture is ignited at the intersection of the incident wave with the wall and a flame front is formed behind the reflected shock wave. The shock waves and the flame front are considered plane surfaces of discontinuity. The fuel mixture and the reaction products are considered perfect, inviscid, and non-heat-conducting gases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 161–163, July–August, 1978.     

Experimental investigation of CO vibrational deactivation in a supersonic cooling gas flow

Abstract. The vibrational relaxation time of CO molecules at collisions with H atoms was measured in shock tube experiments by means of the CARS-spectroscopy method. The measurements of the CO vibrational temperature at gas temperatures of 1800–3000 K were performed in a supersonic cooling gas flow. The gas was heated behind the incident and reflected shock wave and then flowed out of a wedge-shaped nozzle. H atoms were generated in the reflected shock wave because of dissociation of H and HO admixtures. The extremely high efficiency of H atoms in CO vibrational deactivation was confirmed. Received 1 February 2000 / Accepted 20 February 2000     

Detonation wave initiated by explosive condensation of supersaturated carbon vapor

An experimental study of the influence of condensation of supersaturated carbon vapor formed behind reflected shock waves on the process of propagation of a shock wave and formation of a detonation wave of condensation is carried out. Highly supersaturated carbon vapor was formed from thermal decay of unstable carbon suboxide C₃O₂ → C + 2CO behind a shock wave in mixtures containing 10–30% C₃O₂ in Ar. This reaction was followed by fast growth of condensed carbon particles, accompanied by heat release. Experiments have shown a considerable temperature and pressure increase in the narrow zone behind the wave front, resulting in shock wave amplification and transition to a detonation-like regime. An analysis of the kinetics and heat release in the given conditions and calculations based upon one-dimensional detonation theory have shown that in a mixture of 10% C₃O₂ + Ar, insufficient heat release resulted in a regime of “overdriven detonation”. In a mixture of 20% C₃O₂ + Ar a very good coincidence of measured values of pressure and wave velocity with calculated Chapman–Jouguet parameters is observed. In a 30% C₃O₂ + Ar mixture, an excess heat release caused a slow down of the effective condensation rate and a regime of “underdriven detonation” is observed.     

Behavior of the vorticity vector in supersonic axisymmetric swirl flows behind a detonation wave

The behavior of the vorticity vector on a discontinuity surface arising in a supersonic nonuniform combustible gas flow with the formation of a shock or detonation wave is studied. In the general case, it is a vortex flow with prescribed distributions of parameters. It is demonstrated that the ratio of the tangential component of vorticity to density remains continuous in passing through the discontinuity surface, while the quantities proper become discontinuous. Results calculated for flow vorticity behind a steady-state detonation wave in an axisymmetric supersonic flow of a combustible mixture of gases are presented. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 15–21, November–December, 2007     

Initial stage of the collision of blast waves

The collision of two blast waves is analyzed for the case of variable parameters of the gas behind the wave front and wave reflection at a plane, a cylindrical, and a spherical obstacle. The reflection of a blast wave from a nonmoving obstacle is investigated in detail. The problem of the collision of two shock waves with constant parameters behind the front is solved both in the symmetrical case (reflection from a nonmoving wall) and in the case of waves of different amplitudes by a system of algebraic relations for the compression shocks. The reflection of a strong point-source spherical shock wave from a wall has been treated in [1, 2]. The present article examines the initial stage of wave collision for an arbitrary distribution of the parameters behind the front.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 41–48, September–October, 1971.The authors are grateful to V. P. Korobeinikov for a discussion of the results and to V. P. Kolgan for furnishing the numerical solutions.     

Near-wall imaging using toluene-based planar laser-induced fluorescence in shock tube flow

A quantitative thermometry technique, based on planar laser-induced fluorescence (PLIF), was applied to image temperature fields immediately next to walls in shock tube flows. Two types of near-wall flows were considered: the side wall thermal boundary layer behind an incident shock wave, and the end wall thermal layer behind a reflected shock wave. These thin layers are imaged with high spatial resolution (15μm/pixel) in conjunction with fused silica walls and near-UV bandpass filters to accurately measure fluorescence signal levels with minimal interferences from scatter and reflection at the wall surface. Nitrogen, hydrogen or argon gas were premixed with 1–12% toluene, the LIF tracer, and tested under various shock flow conditions. The measured pressures and temperatures ranged between 0.01 and 0.8 bar and 293 and 600 K, respectively. Temperature field measurements were found to be in good agreement with theoretical values calculated using 2-D laminar boundary layer and 1-D heat diffusion equations, respectively. In addition, PLIF images were taken at various time delays behind incident and reflected shock waves to observe the development of the side wall and end wall layers, respectively. The demonstrated diagnostic strategy can be used to accurately measure temperature to about 60 μm from the wall.