Motion of a gas shock layer with a free boundary under nonadiabatic conditions

This paper is a study of the effect of heat input (removal) on the characteristics of a shock layer produced by a gas at high supersonic velocity encountering a mobile boundary, which for generality is assumed to be free. We will use the Chernyi method, which was employed previously to solve the problem of a shock layer in an adiabatic flow [1, 2]. The results obtained can be useful for analysis of the effect of radiation (absorption) and processes involving the relaxation of internal degrees of freedom of molecules, condensation, chemical reactions, etc., whose effect on the gasdynamics of the flow in a shock layer may be similar to heat input or removal [3–5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 152–154, May–June, 1976.The author thanks A. K. Rebrov for discussion of the results.     

Theoretical analysis of acoustic instability of a hypersonic shock layer on a porous wall

The possibility of controlling the laminar-turbulent transition in hypersonic shock layers by means of porous coatings is considered. The linear stability of the shock layer to acoustic disturbances is analyzed. A dispersion relation is derived in an analytical form and analyzed for different characteristic values of porosity of the wall, which allows one to study the spectrum of acoustic disturbances in the shock layer. Analytical expressions for the growth rate of instability of acoustic disturbances are presented as functions of the reflection factor. Their structure indicates that the porous coating effectively decreases acoustic instability of the shock layer.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 44–54, January–February, 2005.     

Investigation of the hypersonic viscous shock layer around blunt bodies in a nonuniform flow

Unseparated viscous gas flow past a body is numerically investigated within the framework of the theory of a thin viscous shock layer [13–15]. The equations of the hypersonic viscous shock layer with generalized Rankine-Hugoniot conditions at the shock wave are solved by a finite-difference method [16] over a broad interval of Reynolds numbers and values of the temperature factor and nonuniformity parameters. Calculation results characterizing the effect of free-stream nonuniformity on the velocity and temperature profiles across the shock layer, the friction and heat transfer coefficients and the shock wave standoff distance are presented. The unseparated flow conditions are investigated and the critical values of the nonuniformity parameter a_k [10] at which reverse-circulatory zones develop on the front of the body are obtained as a function of the Reynolds number. The calculations are compared with the asymptotic solutions [10, 12].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 154–159, May–June, 1987.     

Hypersonic flow past a wing at large angles of attack with detached shock wave

The thin shock layer method [1–3] has been used to solve the problem of hypersonic flow past the windward surface of a delta wing at large angles of attack, when the shock wave is detached from the leading edge (but attached to the apex of the wing) and the velocity of the gas in the shock layer is of the same order as the speed of sound. A classification of the regimes of flow past a delta wing at large angles of attack has been made. A general solution has been obtained for the problem of three-dimensional hypersonic flow past the wing allowing for nonequilibrium physicochemical processes of thermal radiation of the gas at high temperatures.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 149–157, May–June, 1985.     

Asymptotic structure of inviscid disturbances in a thin shock layer

The WKB method, used in [4] to analyze the short-wave instability of a supersonic mixing layer, is employed to investigate various types of inviscid three-dimensional short-wave disturbances in a thin shock layer of perfect gas with arbitrary velocity and temperature distributions across the layer. Simple analytic expressions for the dispersion relations are obtained for neutral disturbances. The results of an asymptotic analysis are compared with direct numerical calculations for a simple model of the shock layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 72–79, November–December, 1988.     

Short-wave instability in a perfect-gas shock layer

Asymptotic methods are used to investigate the regime of two interacting waveguides. As a result of an analysis of the dispersion relation short-wave instability of the acoustic type is detected. It is shown that this instability is convective. A qualitative comparison with direct numerical calculations is carried out using a simple model of the flow in the shock layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 10–14, January–February, 1989.     

Viscous shock layer near the stagnation point on a rotating body with unsteady injection and surface cooling

Unsteady supersonic flow regimes in the neighborhood of a stagnation point are investigated on the basis of a system of viscous shock layer equations [10] containing all the terms of the Euler equations and the boundary layer equations. An analytic solution of the unsteady equations valid near the surface of the body is found in the case of strong injection. The unsteady equations of the viscous shock layer are solved numerically on the basis of a divergent implicit scheme of the second order of approximation across the shock layer, using Newtonian linearization and vector sweep methods with allowance for the boundary relations on the surface of the body and at the isolated bow shock. Certain calculation results illustrating the effect of injection, surface cooling, the swirl of the external flow and the angular velocity of the body on the structure of the steady and unsteady viscous shock layer are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 114–122, September–October, 1987.     

Parameters of flow near the axis in the shock layer in the interaction of a supersonic jet with a barrier

The axisymmetric interaction between a supersonic jet with a finite expansion ratio and a barrier is accompanied by the formation of complex sub- and supersonic flow in a shock layer whose thickness depends on the parameters of the jet and the position of the barrier. The main relationships of the interaction process have been established experimentally ([1–3] and others) and individual results of numerical calculations of such flows are known [4]. An analytical investigation of the parameters in the shock layer formed ahead of a plane barrier when an underexpanded jet impinges on it is presented below. The results of [5], where the region near the axis of a shock layer of arbitrary thickness is analyzed within the framework of a model of flow with a constant density, is placed at the basis of the analysis.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 63–70, September–October, 1978.The author thanks Yu. M. Tsirkunov for useful discussions.     

Unsteady viscous shock layer near the leading edge of a wing of infinite span

The effect of unsteady injection and wall temperature variation on the parameters of the viscous shock layer near the stagnation line of a wing of infinite span at an angle of slip is investigated on the basis of the viscous shock layer model. An analytic solution of the nonstationary problem, valid near the surface of the wing for strong injection, is obtained. A numerical investigation is carried out and some results of calculating the unsteady viscous shock layer equations for various forms of the time dependence of the injection velocity and wing surface temperature are presented. The calculations are based on a finite-difference method of the second order of approximation in the space variable and the first order of approximation in time, which makes use of expression of the equations in divergence form, Newtonian linearization and vector sweeps across the shock layer. In the steady-state case the results of the calculations are in good agreement with the data of [7].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 90–95, January–February, 1988.     

Multicomponent chemically-reacting turbulent viscous shock layer on a catalytic surface

Turbulent flows past blunt bodies at high supersonic speeds are mainly investigated within the framework of the boundary layer model. However, even at large Reynolds numbers owing to the strong entropy gradient on the lateral surface it becomes necessary to take boundary layer corrections into account in the higher approximations [1]. The use of viscous shock layer theory makes it possible to obtain fairly accurate results over a broad interval of variation of the Reynolds numbers without organizing iterations with respect to vorticity and displacement thickness. The nonequilibrium nature of both homogeneous and heterogeneous catalytic reactions is taken into account. The results obtained are compared with the experimental data [2, 3]. Previously, in [4, 5] turbulent flow was investigated within the framework of viscous shock layer theory in the case of equilibrium homogeneous reactions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 144–149, March–April, 1989.     

Calculation of a nonequilibrium viscous shock layer with allowance for coupled heat transfer

An investigation is made into the characteristics of coupled heat and mass transfer using the theory of a nonequilibrium viscous shock layer in the case of an axisymmetric blunt body moving along a given trajectory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 146–153, March–April, 1984.     

Nonequilibrium viscous shock layer on blunt cones

Some results are given of the numerical investigation into the parameters of the nonequilibrium flow of air in a viscous shock layer in the case of blunt circular cones at zero angle of attack; they are also compared with experimental data obtained during re-entry of ballistic objects into the Earth's atmosphere. The calculations were made with allowance for the nonequilibrium processes of dissociation and ionization, and also vibrational relaxation. The influence of viscosity, heat conduction, and diffusion is taken into account in the complete shock layer. The conditions on the shock wave are posed with allowance for its finite thickness. The characteristic profiles of the velocity, temperature, and electron concentration in the shock layer are given. Good agreement is obtained between the calculated and experimental data on the level and the profiles of the electron concentration. The parameters of the shock layer were determined by a method that is a natural extension of the numerical method of [1] to the case of nonequilibrium flow in a viscous shock layer. Because of this, only the main differences of the method when applied to the calculation of nonequilibrium flows of a multicomponent mixture such as dissociated and ionized air are described.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 15–20, November–December, 1979.     

Sound absorption in a shock wave

It was shown in [1–4] that the reflection of a sound wave or its transmission through a shock front should be accompanied by attenuation or intensification of the wave is regarded as a discontinuity. In accordance with current representations [5, 6], a shock wave includes a viscous shock and a lengthy relaxation zone. Equilibrium is established with respect to translational and rotational degrees of freedom in the viscous shock and with respect to internal degrees of freedom in the relaxation zone. The result of the interaction of the shock and sound waves is determined by the relationship between the length of the sound wave and the width of the shock wave.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 90–94, May–June, 1986.     

Spherical shock wave reflection from a surface with a heated gas layer

The two-dimensional axisymmetric problem of the interaction between smallscale spherical shock waves initiated by a laser explosion and an absolutely rigid surface in the presence of a layer of hot gas is numerically investigated. A number of effects previously observed in physical and numerical experiments [5–8] are confirmed, in particular: the distortion of the reflected shock front and its acceleration on passage through the hot central zone of the laser explosion (lens effect), the strong deformation of this zone, and the formation of a precursor on the surface ahead of the shock wave interacting with the thermal layer. In addition, certain new anomalous effects are revealed: the formation of a pair of suspended shocks — one on the periphery of the hot central zone upon interaction with the reflected shock wave and the other behind the Mach stem in the triple point zone, etc.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 141–147, July–August, 1989.     

Interference between a blunt edge shock layer and an impinging inclined shock at low Reynolds numbers

The interference between the shock layer on a cylinder modeling the leading edge of an air intake and an impinging plane inclined shock is investigated experimentally and numerically for a Reynolds number Re₀=32. The low-pressure wind tunnel experiments made it possible to visualize the flow and determine the local heat transfer in the presence of interference. The corresponding flow regimes were calculated numerically within the framework of the system of Navier-Stokes equations by the through-calculation method. The principal properties of the distribution of the flow characteristics for a low value of the Reynolds number were obtained for various types of interference and the differences with respect to the previously investigated interference regimes for high Reynolds numbers were examined.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 166–171, January–February, 1993.     

Distortion of the shock front in a shock tube with a divergent conical transition section

The profile of the leading shock front in a gas has been experimentally investigated in shock tubes of variable cross section. It is shown that the presence of a conical transition section between the high-pressure and low-pressure chambers leads to the retention of inhomogeneities on the surface of the wave front (slopes, twists, and bends) over a length of 20–30 diameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 141–147, July–August, 1991.     

Oblique shock/bow shock interference in rarefied flow past a cylinder

Direct statistical simulation is employed to study the flow of a rarefied diatomic gas past a cylinder in the presence of an incident oblique shock. The distinctive features of the formation of a high-pressure compressed-gas jet in the case of interference between the oblique shock and the bow shock are studied for different Reynolds numbers. The variation of the pressure and the heat transfer to the surface with the shock position relative to the center of the cylinder, the Reynolds number, and the surface temperature is analyzed. The results obtained are compared with the experimental data and the results of the numerical solutions of the Euler and boundary layer equations. Free-molecular-to-continuum flow transition is demonstrated with reference to the example of interference-free flow past a cylinder.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 171–180. Original Russian Text Copyright © 2004 by Gusev and Erofeev.     

Reflection of a plane shock wave from a rigid concave wall

We present the results of an experimental study of the reflection of a plane stationary shock wave with Mach number in the range 1.21–1.35 from a rigid cylindrical concave wall. The experiments were carried out in a shock tube. In experimental shock tube technology the reflection of a shock wave from a rigid wall is often used for obtaining high temperatures [1]. This circumstance is associated with the fact that the temperature behind the reflected wave is significantly higher than that behind the incident wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 33–39, July–August, 1970.     

Investigation of the influence of blowing on the flow in a hypersonic viscous shock layer near the stagnation streamline on a blunt body

In the framework of the approximation of local similarity to the Navier-Stokes equations, an investigation is made of the axisymmetric flow of homogeneous gas in a hypersonic shock layer, this including the region of transition through the shock wave. Boundary conditions, which take into account blowing of gas, are specified on the surface of the body and in the undisturbed flow. A numerical solution to the problem is obtained in a wide range of variation of the Reynolds number and the blowing parameter. Expressions are found for the dependences on the blowing parameter usually employed in boundary layer theory of the coefficients of friction and heat transfer on the surface of the body, which are divided by their values obtained for blowing parameter equal to zero. It is shown that these dependences are universal and the same as the dependences obtained from the solution of the equations of a hypersonic viscous shock layer with modified Rankin-Hugoniot relations across the shock wave and from the solution of the boundary layer equations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 199–202, January–February, 1980.     

Blowing of a foreign gas in a hypersonic viscous shock layer

We consider the problem of a hypersonic viscous flow of a nonreactive mixture of ideal gases around smooth thick bodies in the framework of a two-layer model of a thin shock layer for moderately small Reynolds numbers. We investigate the effect of blowing of a foreign gas through a permeable surface in the bow region of a spherical blunt body. We introduce a transformation of variables that gives a number of important advantages in the numerical solution of the problem under consideration. The problem of mass blowing from the surface of a body into a boundary layer has an extensive literature. The effect of blowing for moderately small Reynolds numbers has been considerably less studied [1–5], and in the majority of papers on this question either the critical point of a blunt body or the blowing of a gas homogeneous with the gas in the incoming flow is investigated.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 110–116, July–August, 1972.