Nonequilibrium molecular radiation behind the front of a strong shock wave in the CO<Subscript>2</Subscript>-N<Subscript>2</Subscript>-O<Subscript>2</Subscript> mixture

Models of population of some radiating electron-vibrational states of CO, CN, and C₂ molecules are developed. The characteristics of radiation in a chemically nonequilibrium flow behind the front of a strong shock wave in a mixture of gases constituting the Martian atmosphere are calculated. The numerical data are compared with experimental results.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 13–22, March–April, 2005     

Nonlinear analysis of the flow initiated by the sudden motion of a wedge

Certain self-similar problems involving the sudden motion of a wedge which were treated in the linear approximation in [1–3] are studied by the method of matched asymptotic expansions. The nature of the wave boundary of the perturbed region is determined. Second-approximation solutions are constructed which describe flows behind weak shock fronts propagating in a stationary gas and behind fronts of weak discontinuity lines propagating by known uniform flows. A boundary-value problem is formulated whose solution describes, in first approximation, flows in the neighborhoods of points of interaction of the fronts. The existence of similarity rules of flows in these nieghborhoods is estimated. An approximate solution of the problems is given.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 37–47, May–June, 1976.     

Airflow behind strong shock front with account for nonequilibrium ionization and radiation

We consider the gas state behind a shock wave front in air with a velocity v10 km/sec. Nonequilibrium ionization and radiative transport are taken into account. We take into consideration the real air spectrum — the numerous lines, bands, and continuua. Account for the radiation leads to an integrodifferential system of equations for which a solution method is developed. As a result we obtain the gas parameter profiles behind the shock wave, which are affected by the relaxation processes and radiative cooling. The calculations were made for v=10–16 km/sec and a pressure p=10^–5–10^–2 atm ahead of the front.In order to obtain realistic results, we consider only the gas layer bounded by the shock and a surface parallel to it. It is assumed that the gas bounded by these planes is not irradiated from without. In this formulation still another defining parameter appears—the distancel between the planes. The calculations were made forl=1–100 cm.     

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.     

Structure of the heating layer ahead of the front of a strong intensely emitting shock wave

The problem of the structure and brightness of strong shock waves arises in the investigation of such phenomena as the motion of large meteoroids in the atmosphere, optical and electrical discharges, the development of strong explosions, and other similar processes and in the creation of powerful radiation sources based on them. This problem also has a general physics interest. As the propagation velocity of a strong shock wave increases the gas temperature behind its front and the role of emission grow. Part of the radiation emitted by the gas heated and compressed in a shock wave is absorbed ahead of the front, forming the so-called heating layer. The quasisteady structure of a strong intensely emitting shock wave was studied in [1, 2]. In this case a diffusional approximation and the assumption of a gray gas were used to describe the radiation transfer. They introduced the concept of a wave of critical amplitude, when the maximum temperature T_- in the heating layer reaches the temperature T_a determined on the basis of the conservation laws, i.e., from the usual shock adiabat; it is shown that behind a compression shock moving through an already heated gas there is a temperature peak in which the maximum temperature T₊ exceeds T_a. The problem of the quasisteady structure of an emitting shock wave in air of normal density was solved numerically in [3]. The angular distribution of the radiation was approximately taken into account — it was assigned by a simple cosinusoidal law. The spectral effects were taken into account in a multigroup approximation. They introduced 38 spectral intervals, which is insufficient to describe a radiation spectrum with allowance for the numerous lines and absorption bands.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 86–92, September–October, 1978.     

Shock wave ignition in N2O-CO(N2)-He mixtures

The behavior of the pressure behind shock waves in N₂O-CO-He mixtures is investigated. The pressure can be relatively easily measured and, at the same time, reflects the general influence of the experimental conditions on flow formation in the shock tube. Shock-wave mixture ignition effects and, moreover, hydrogen combustion in the contact zone are analyzed from the standpoint of their influence on the stagnation parameters and the optical properties of the flow in the shock tube nozzle. The correctness of modeling the conditions behind the reflected wave by means of mixtures similar in composition to the equilibrium products of the N₂O-CO reaction [1] is discussed in the same context.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 164–170, September–October, 1989.The authors wish to thank G. D. Smekhov for calculating the equilibrium compositions of the mixtures behind the shock waves and A. P. Zuev for stimulating discussions.     

Mathematical model of the dissociation of gas hydrates coexisting with ice in natural reservoirs

The dissociation of gas hydrate coexisting with ice in a low-temperature natural reservoir is investigated. A mathematical model of the process consisting of a generalization of the Stefan problem and containing two unknown moving phase transition boundaries — the hydrate dissociation and ice melting fronts — is constructed. It is shown that in high-permeability reservoirs the velocity of the dissociation surface is higher than that of the ice melting surface. As the permeability decreases, the fronts change places. The problem is solved in the self-similar approximation.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 84–92, March–April, 1993.     

Mach reflection of weak shock waves from a rigid wall

On the basis of experimental observations and theoretical analysis of flow structure in the neighborhood of the triple point, it is shown that one should reject the condition for equality of the angle of deflection of flows passing through the Mach front and the two other fronts and replace it with some supplementary condition. The system of consistency equations in the indicated region is closed by an equation which is obtained under the assumption of the extremality of the deflection angle of a flow passing through the incident and reflected fronts. Calculations of the pressure drops behind the shock fronts agree with experimental data in this case.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 26–33, September–October, 1973.The authors thank S. A. Khristianovich for consideration of the work and advice.     

Some physical aspects of radiative and convective heat transfer in the case of nonself-similar blowing on a plate

Heat shielding by blowing has been fairly fully studied in the neighborhood of the stagnation point of a body in a stream [1–3], but for other flow regions the investigation has barely begun [4]. It has been found that the influence of blowing on the radiative and convective fluxes and the influence of radiation on the convection on the side wall can be very different from what is obtained for the flow conditions at the stagnation point. The present paper is a study of the radiative and convective heat transfer on a plate in a H₂ + He stream for constant and self-similar blowing of carbon vapor in the form of C, C₂, and C₃.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 28–35, January–February, 1981.     

Population inversion behind a detonation wave propagating in a variable-density medium

The creation of an active medium by means of detonation has been investigated on a number of occasions. It was suggested that one could use the expansion of the detonation products of an acetylene-air mixture in vacuum [1] or the cooling of the detonation products of a mixture of hydrocarbons and air through a nozzle [2, 3]. In [4], the detonation of a solid high explosive was used to produce population inversion in the gas mixture CO₂-N₂-He(H₂O). Stimulated emission from HF molecules was observed in [5] behind the front of an overdriven detonation wave propagating in an F₂-H₂-Ar mixture in a shock tube. Population inversion behind a detonation wave was studied in H₂-F₂-He mixtures in [6–8] and in H₂-Cl₂-He mixtures in [9] with energy release on a plane and on a straight line in a medium with constant density. Similar problems were solved for shock waves propagating in both a homogeneous gaseous medium [7, 10] and in the supersonic part of an expanding nozzle. In the present paper, we study theoretically population inversion behind an overdriven detonation wave propagating in a mixture (fine carbon particles + acetylene + air) which flows through a hypersonic nozzle. The propagation of detonation in media with variable density and initial velocity was considered, for example, in [11, 12]. Analysis of the gas parameters behind a detonation wave propagating in a medium with constant density (for a given fuel) showed that the temperature difference across the detonation front is insufficient to produce population inversion of the vibrational levels of the CO₂ molecule.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 65–71, January–February, 1980.I am grateful to V. P. Korobeinikov for a helpful discussion of the results.     

Special case of the density distribution behind a nonstationary shock wave

The density distribution behind a nonstationary shock wave for a definite value of the Mach number M_*, which depends on = c_p/c_v, is considered. Use is made of the previously established fact [1] that for M = M_*() there exists a connection between the first and second derivatives of the density along the normal behind the wave. An investigation is made into the density profile in dimensionless variables behind plane, cylindrical, and spherical shock waves in the neighborhood of the shock front. In the first case, if the gas in front of the wave is homogeneous, only two types of density profile are possible (up to small quantities of third order in the coordinate). In the second and third cases, the form of the density distribution also depends on a parameter, the ratio of the first derivative along the normal of the density behind the wave to the radius of curvature of the wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 163–167, November–December, 1979.     

Temperature measurement of reflected shock wave by using chemical indicator

This report describes a new method for measuring the temperature of the gas behind the reflected shock wave in shock tube, corresponding to the reservoir temperature of a shock tunnel, based on the chemical reaction of small amount of CF₄ premixed in the test gas. The final product C₂F₄ is used as the temperature indicator, which is sampled and detected by a gas chromatography in the experiment. The detected concentration of C₂F₄ is correlated to the temperature of the reflected shock wave with the initial pressureP ₁ and test time τ as parameters in the temperature range 3 300 K<T<5 600 K, pressure range 5 kPa<P ₁<12 kPa and τ≅0.4 ms. The project supported by the China Aerodynamics Project for Basic Researches (J13.5.2 ZK04)     

Initiation of Combustion in a Supersonic Hydrogen-Air Mixture Flow by CO<Subscript>2</Subscript>-Laser Radiation

Features of the ignition kinetics of an H₂/air mixture in the supersonic flow behind an inclined shock front are analyzed when asymmetric vibrations of a small amount (<1%) of O₃ molecules specially introduced into the initial mixture are excited by 9.7 μm wavelength radiation. It is shown that this radiation leads to intensification of the chain reactions and makes it possible to organize combustion at small distances from the front (of the order of 1 m) of even relatively weak shocks at small values of the laser radiation energies absorbed by the gas. This method of initiating combustion in a supersonic flow is 10–100 times more efficient than the thermal method.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 157–167.Original Russian Text Copyright © 2005 by Lukhovitskii, Starik, and Titova.     

Lifting bodies using the flow behind axisymmetric conical shock waves

One of the methods of designing aircraft with supersonic flight speeds involves solving an inverse problem by means of the well-known flow schemes and the substitution of rigid surfaces for the flow surfaces. Lifting bodies using the flows behind axisymmetric shock waves belong to these configurations. All lifting bodies using the flow behind a conical shock wave can be divided into two types [1]. Bodies whose leading edge passes through the apex of the conical shock wave pertain to the first type and those whose leading edge lies below the apex of the conical shock wave, to the second. For small apex angles of the basic cone at hypersonic flow velocities an approximate solution of the variation problem was obtained, which showed that the lift-drag ratio of lifting bodies of the second type is higher than that of the first [2]. The present paper gives a numerical solution of the problem for flow past lifting bodies of the second type using the flow behind axisymmetric conical shock waves with half-angles of the basic cone _S=9.5 and 18° The upper surfaces of the bodies are formed by intersecting planes parallel to the velocity vector of the oncoming flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 135–138, March–April, 1986.     

Passive control of wake flow by two small control cylinders at Reynolds number 80

Passive control of the wake behind a circular cylinder in uniform flow is studied by numerical simulation at Re_D=80. Two small control cylinders are placed symmetrically along the separating shear layers at various stream locations. In the present study, the detailed flow mechanisms that lead to a significant reduction in the fluctuating lift but maintain the shedding vortex street are clearly revealed. When the stream locations lie within 0.8≤X_C/D≤3.0, the alternate shedding vortex street remains behind the control cylinders. In this case, the symmetric standing eddies immediately behind the main cylinder and the downstream delay of the shedding vortex street are the two primary mechanisms that lead to a 70–80% reduction of the fluctuating lift on the main cylinder. Furthermore, the total drag of all the cylinders still has a maximum 5% reduction. This benefit is primarily attributed to the significant reduction of the pressure drag on the main cylinder. Within X_C/D>3.0, the symmetry of the standing eddy breaks down and the staggered vortex street is similar to that behind a single cylinder at the same Reynolds number. In the latter case, the mean pressure drag and the fluctuating lift coefficients on the main cylinder will recover to the values of a single cylinder.     

Effect of the pressure of shock compression on the critical shear stresses in metals

The critical shear stresses _* behind the leading edges of shock waves were studied in aluminum at pressures of 300 and 650 kbar, copper at 240 and 550 kbar, and lead at 460 kbar by carrying out explosion experiments. The quantity in question was estimated by comparing the experimental data characterizing the fall in pressure at the leading edge of the shock wave (arising from load relaxation) with the results of calculations.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 107–110, November–December, 1970.     

A new transient method for analysis of solidification in the continuous casting of metals

Solidification processes involve complex heat and mass transfer phenomena, the modelling of which requires state-of-the art numerical techniques. An efficient and accurate transient numerical method is proposed for the analysis of phase change problems. This method combines both the enthalpy and the enhanced specific heat approaches in incorporating the effects of latent heat released due to phase change. The sensitivity and accuracy of the proposed method to both temporal and spatial discretization is shown together with closed-form solutions and the results from the enhanced specific heat approach. In order to explore the proposed method fully, a non-linear heat release, as is the case for binary alloys, is also examined. The number of operations required for the new transient approach is less than or equal to the enhanced heat capacity method depending on the averaging method adopted. To demonstrate the potential of this new finite-element technique, measurements obtained on operating machines for the casting of zinc, aluminum and steel are compared with the model predictions. The death/birth technique, together with the proper heat-transfer coefficients, were employed in order to model the casting process with minimal error due to the modelling itself.Nomenclature [A] conductance matrix - [B] matrix containing the derivative of the element shape functions - c, C _p specific heat (J kg^–1°C^–1) - effective specific heat (J kg^–1°C^–1) - f(T) local liquid fraction - f thermal load vector - H enthalpy (J kg^–1) - [H] capacitance matrix - h, h _r,h _c heat transfer coefficient (W m^–2°C^–1) - K thermal conductivity (W m^–1°C^–1) - L latent heat of solidification (J kg^–1) - l overall length (m) - N _i shape functions - Q rate of heat generation per unit volume (J m^–3) - q heat flux (W m^–2) - R residual temperature (°C) - T temperature (°C) - T _s solidus temperature (°C) - T _l liquidus temperature (°C) - T _pouring pouring temperature (°C) - T _top temperature at the top of the mould (°C) - T _w temperature of the water spray (°C) - approximated temperature (°C) - T surrounding temperature (°C) - cooling rate (°C/s) - t time (seconds) - x _i,x, y, z spatial variables (m) - t time step (s) - x element size (m) - diffusivity (m²s^–1) - density (kg m^–3) - time marching parameter - _n direction cosines of the unit outward normal to the boundary     

Three-dimensional diffraction of a shock wave

The diffraction of a shock wave (M₀=4.7) at an angle close to 180 has been experimentally investigated for the three-dimensional case. Interferograms of the flow and the pressure distribution on the back wall in the course of its interaction with the diffracted wave were obtained. Rotation of the flow structure behind the shock wave relative to the axis of symmetry was observed as the flow pattern develops in time and space.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 200–201 March–April, 1993.     

Shock waves and turbulence in a hypersonic inlet

A numerical investigation for an axisymmetric hypersonic turbulent inlet flow field of a perfect gas is presented for a three-shock configuration consisting of a biconic and a cowl. An upwind parabolized Navier-Stokes solver based on Roe's scheme is used to compute an oncoming flow Mach numberM =8, temperatureT =216 K, and pressureP =5.5293×10³ N/m². In order to assess the flow quantities, the interaction between shock and turbulence, and the inlet efficiency, three different flow calculations — laminar, turbulent with incompressible and compressible two-equationk- turbulence models — have been performed in this work.Computational results show that turbulence is markedly enhanced across an oblique shock with step-like increases in turbulence kinetic energy and dissipation rate. This enhancement is at the expense of the mean kinetic energy of the flow. Therefore, the velocity behind the shock is smaller in turbulent flow and hence the shock becomes stronger. The entropy increase through a shock is caused not only by the amplification of random molecular motion, but also by the enhancement of the chaotic turbulent flow motion. However, only the compressiblek- turbulence model can properly predict a decrease in turbulence length scale across a shock. Our numerical simulation reveals that the incompressiblek- turbulence model exaggerates the interaction between shock and turbulence with turbulence kinetic energy and dissipation rate remaining high and almost undissipated far beyond the shock region. It is shown that proper modeling of turbulence is essential for a realistic prediction of hypersonic inlet flowfield. The performed study shows that the viscous effect is not restricted in the boundary layer but extends into the main flow behind a shock wave. The loss of the available energy in the inlet performance therefore needs to be determined from the shock-turbulence interaction. The present study predicts that the inlet efficiency becomes relatively lower when turbulence is taken into account.     

Study of vibrational deactivation of molecules of carbon dioxide gas during cooling of stream in a supersonic nozzle

The vibrational temperature of the antisymmetrical type of vibrations (v ₃) of the CO₂ molecule at the exit of a supersonic nozzle is measured in the present work using the method of recording the infrared emission. Freezing in of thev ₃-type vibrations was observed during the flow of undiluted carbon dioxide in a nozzle. In this case the vibrational temperature T₃ considerably exceeded the translational temperature. On the basis of a comparison of the experimental results with calculation it can be concluded that vibrational deactivation of CO₂ molecules occurs three to five times faster than the excitation of the vibrations during heating in a shock wave. All the experiments were conducted under the following conditions: maximum expansion of gas in nozzle A/A* = 115, temperature range 1900–2400 °K, pressure range 1–17.5 atm.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 32–40, November–December, 1973.The authors are grateful to U. G. Pirumov and É. A. Ashratov for the calculation of the nozzle profile and the distribution of streamlines as well as for a discussion of the results.