Experimental study of strong shock propagation in a channel

The widespread use of shock tubes in laboratory practice is well known. However, despite existing information [1] about shock-wave velocities of 100 km/sec, experimental data on the size of the shock-heated region behind the shock front are confined to the Mach numbers M = 10 [2]. Theoretical data do not go beyond the limit of this range except for air where calculations were performed up to M = 20 [3, 4]. Behind strong shocks, the effects resulting from viscosity, thermal conductivity, and radiation of the medium should lead to serious deviation of the actual flow from the idealized pattern for uniform motion of a piston in a channel filled with anonviscous, thermally nonconducting, and nonradiating medium. It is therefore practical to make an experimental study of the behavior of density and of the size of the shock-heated region behind a shock front propagating down the channel of a shock tube that is capable of producing velocities up to 8 km/sec.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 23–28, July–August, 1976.     

Ionization and nonequilibrium radiation of air behind strong shock waves

It is shown that at high velocities of shock waves (V 9.5 km/sec) an important factor influencing the rate of ionization is the depletion of the number of excited states of the atoms through de-excitation. In the case of low pressures (p 1 torr) and for a bounded and optically transparent region of gas heated by the shock wave (for example, for the motion of gas in a shock tube or in a shock layer near a blunt body), the effective ionization rate k_f depends on the pressure [1], which leads to violation of the law of binary similarity which holds under these conditions without allowance for de-excitation. On leaving the relaxation zone, the gas arrives at a stationary state with constant parameters differing from those in thermodynamic equilibrium. The electron concentration and also the radiation intensity in the continuum and the lines are lower than the values for thermodynamic equilibrium. These considerations explain the results of known experiments and some new experiments on ionization and radiation of air behind a travelling shock wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 105–112, January–February, 1980.     

Experimental investigation of the emission in the unsteady flow region behind strong shock fronts in mixtures of co and CO2 with nitrogen and argon

Mixtures of CO (or CO₂) gases and N₂ behind strong shock fronts at temperatures 4000–10 000 ° K have been investigated with a view to elucidating the mechanism of the physicochemical processes in the unsteady region of the gas flow behind a shock front leading to the behavior of strongly radiating CN and C₂ molecules and C atoms and also determining the quantitative characteristics of the chemical reactions. A shock tube was used in the investigations, which made it possible to obtain the intensity distribution of the radiation of several components — CN, C₂, and C — behind shock fronts.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 120–129, March–April, 1981.We thank S. A. Losev and O. P. Shatalov for assisting in the work and for valuable discussions.     

Nonequilibrium ionizatlon of air behind a shock wave front at speeds of 5–10 km/sec

The solution of the problem of nonequilibrium ionization of dissociating air in a shock wave propagating with a speed of 5–10 km/sec has shown that the electron concentration distribution has a maximum behind the wave front for speeds below 9 km/sec.The formation of this maximum is caused by the high associative ionization rate in comparison with the nitrogen dissociation rate. In the nonequilibrium region behind the shock wave front there is formed a considerable concentration peak of the molecular ions which are formed as a result of associative ionization and charge exchange.The author wishes to thank V. P. Stulov for useful discussions.     

Nonequilibrium ionization accompanying hypersonic flow of carbon dioxide gas over blunt bodies

A study is made of the nonequilibrium ionization in the shock layer when carbon dioxide gas flows over cones with spherical noses at velocity 4–7 km/sec, the density of the oncoming flow being 10^–8-10^–5 g/cm³. The influence of admixtures of nitrogen and sodium on the electron concentration is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 183–186, January–February, 1981.     

Relaxation and none quilibrium radiation behind shock waves in air

This article discusses relaxation behind shock waves in air at velocities from 8 to 12 km/sec. Profiles are obtained for the parameters of the gas behind the front. The populations of the radiating states of the atoms and the molecules are calculated. In a number of spectral ranges the intensity of the radiation passes through a maximum exceeding the equilibrium level. A comparison is made with experimental data obtained in shock tubes. The radiant heat fluxes from the relaxation zone are calculated. The contribution of this radiation to the radiative heating of blunt bodies with flow around them at hypersonic velocities is evaluated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 4, pp. 161–174, July–August, 1970.The authors thank their co-workers in the High Temperature Institute of the Academy of Sciences of the USSR, above all, L. M. Biberman, V. S. Vorob'ev, A. N. Larar'kov, and G. É. Norman for their valuable evaluations and for their interest in the work.     

Peessure intensification on the front of a shock wave propagating in a heterogeneous system

An increase in pressure in the wave front as compared to the pulse initiating the wave has been observed experimentally in a study of shock-wave propagation in aqueous suspensions of bentonite [1]. In suspensions in which the solid phase is in the form of colloidal size particles =10^–7–10^–8 m of the mineral montmorillonite with mass content c=6%, with multishock loading an intensification of this effect from experiment to experiment was observed [2]. In order to study the principles involved in this anomalous intensification of pressure on the shock wave front, as well as to clarify the effect of the nature of the material in the dispersed phase, experiments were performed with particles of another broad class of clay-like minerals — kaolinite.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 86–92, September–October, 1986.     

Shock heating of plasma in a rapidly increasing magnetic field

The experimental excitation of intense collisionless shock waves (M 5) with subsequent plasma compression by the magnetic field of a shock coil is described. A magnetic plug > 20 kOe is produced in 100 × 10^–9 sec by a current generator, a long line with 250-kV water insulation and a characteristic impedance of l At an initial deuterium-plasma density of 2 × 10¹⁴ cm^–3, shock waves with a front width of 20c/₀₃and a velocity of 5 × 10₇ cm/sec are recorded. The ion energy after the accumulation, determined from the neutron yield, turns out to be 2 ke V. Axial shock waves excited by the plasma flow beneath the shock coil are observed.Translated from Zhurnal Prikladnoi Mekhaniki i Teknicheskoi Fiziki, Vol. 11, No. 2, pp. 28–38, March–April, 1970.The authors thank G. I. Budker and R. Z. Sagdeev for formulating the problem, R. I. Soloukhin for interest in the study, and S. P. Shalamov for construction of the apparatus.     

Shock Compression of a Plate on a Wedged–Shaped Target

Problems of compression of a plate on a wedge–shaped target by a strong shock wave and plate acceleration are studied using the equations of dissipationless hydrodynamics of compressible media. The state of an aluminum plate accelerated or compressed by an aluminum impactor with a velocity of 5—15 km/sec is studied numerically. For a compression regime in which a shaped–charge jet forms, critical values of the wedge angle are obtained beginning with which the shaped–charge jet is in the liquid or solid state and does not contain the boiling liquid. For the jetless regime of shock–wave compression, an approximate solution with an attached shock wave is constructed that takes into account the phase composition of the plate material in the rarefaction wave. The constructed solution is compared with the solution of the original problem. The temperature behind the front of the attached shock wave was found to be considerably (severalfold) higher than the temperature behind the front of the compression wave. The fundamental possibility of initiating a thermonuclear reaction is shown for jetless compression of a plate of deuterium ice by a strong shock wave.     

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.     

Base-pressure pulsations behind a cylinder and disk in a subsonic stream flow

Base-pressure fluctuations behind a long cylinder (l/d 5–10) and the disk (l/ d 0.0) is investigated experimentally in this paper. The spectral and correlation characteristics of the base-pressure fluctuations behind axisymmetric bodies at a Mach number M 1.0 are generalized on the basis of the data obtained and the results of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 181–183, January–February, 1977.     

Laminar boundary layer on blunt bodies with account for vorticity of the external flow

This paper presents the technique for and results from numerical calculations of the hypersonic laminar boundary layer on blunted cones with account for the vorticity of the external flow caused by the curved bow shock wave. It is assumed that the air in the boundary layer is in the equilibrium dissociated state, but the Prandtl number is assumed constant, =0.72. The calculations were made in the range of velocities 3–8 km/sec, cone half-angles _k=0°–20°. With account for the vortical interaction of the boundary layer with the external flow, the distribution of the thermal flux and friction will depend on the freestream Reynolds number (other conditions being the same). In the calculations the Reynolds number R, calculated from the freestream parameters and the radius of the spherical blunting, varies from 2.5·10³ to 5.10⁴. For the smaller Reynolds numbers the boundary layer thickness on the blunting becomes comparable with the shock standoff, and for R<2.5·10³ it is apparent that we must reconsider the calculation scheme. With R>5·10⁴ for cones which are not very long the vortical interaction becomes relatively unimportant. The results of the calculations are processed in accordance with the similarity criteria for hypersonic viscous gas flow past slender blunted cones [1, 2].     

On shock layer method for the hypersonic flow problems

Chernyi’s series method[1] is not proper for the case that(γ-l)/(γ+l)<<2/(γ+1)×M²sin²β (γ=c_p/c_v-adiabatic index number, M-Much number, β-shock incidence). In this paper, we only suppose that in the neighbour of the shock, there exists a shock layer in which the density of the gas is very big, but we do not remove the case that (γ-1)/(γ+1)<<2/(γ+1)M²sin²β.     

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.     

Study of radiative and convective heat transfer when a radiating mixture of carbon dioxide and nitrogen flows past the critical point of a body

The results are given of an investigation of the convective and radiative heat transfer at the leading critical point of a body in the flow of a radiating mixture of carbon dioxide and nitrogen, taking account of viscosity and thermal conductivity. The system of equations is written down under the assumption that the shock layer is thin, and its solution is obtained in the region between the body and the shock wave. It is assumed that there is local thermodynamic equilibrium throughout the compressed layer. The coefficients of absorption of the mixture are assumed to depend on the wavelength, the temperature, and the pressure. From the solution we determine the radiative and convective thermal fluxes at the wall, taking account of their interaction for temperatures behind the shock wave of 9000–12000 deg K and pressures of p=1 and 10 atm. By analyzing these results it is concluded that the effect of radiation on the convective heat transfer is insignificant, the effect being qualitatively different at large and small pressures. The fundamental contributions to the radiant thermal flux at the wall in the versions of the problem considered come from the following spectral interval: 0.128–0.33, where there is a fourth positive system of carbon monoxide bands (~43%), and 0.33–0.66, where there is an ultraviolet system of cyanogen (~40%). The contribution from the spectral interval 0.80–1.15 is ~20%. Only about 15% of the radiant energy comes from the comparatively large interval 0.45–0.80. As the pressure increases, the contribution from the ultraviolet part of the spectrum falls, and the contribution from the visible part of the spectrum increases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 39–47, March–April, 1971.     

Stabilization of plasma flow in a transverse magnetic field

Results are given of a theoretical and experimental investigation of the intensive interaction between a plasma flow and a transverse magnetic field. The calculation is made for problems formulated so as to approximate the conditions realized experimentally. The experiment is carried out in a magneto-hydrodynamic (MHD) channel with segmented electrodes (altogether, a total of 10 pairs of electrodes). The electrode length in the direction of the flow is 1 cm, and the interelectrode gap is 0.5 cm. The leading edge of the first electrode pair is at x = 0. The region of interaction (the region of flow) for 10 pairs of electrodes is of length 14.5 cm. An intense shock wave S propagates through argon with an initial temperature T_o = 293 °K and pressure p_o = 10 mm Hg. The front S moves with constant velocity in the region x < 0 and at time t = 0 is at x = 0. The flow parameters behind the incident shock wave are determined from conservation laws at its front in terms of the gas parameters preceding the wave and the wave velocity W_S. The parameters of the flow entering the interaction region are as follows: temperature T ₀ ¹ = 10,000 °K, pressure P ₀ ¹ = 1.5 atm, conduction ₀ ¹ = 3000 ^–1·m^–1, velocity of flow u ₀ ¹ = 3000 m·sec^–1, velocity of sounda ₀ ¹ = 1600 m·sec^–1, degree of ionization = 2%, 0.4. The induction of the transverse magnetic field B = [0, B_y(x), 0] is determined only by the external source. Induced magnetic fields are neglected, since the magnetic Reynolds number Re_m 0.1. It is assumed that the current j = (0, 0, jz) induced in the plasma is removed using the segmented-electrode system of resistance R_e. The internal plasma resistance is R_i = h(A)^–1 (h = 7.2 cm is the channel height; A = 7 cm² is the electrode surface area). From the investigation of the intensive interaction between the plasma flow and the transverse magnetic field in [1–6] it is possible to establish the place x* and time t* of formation of the shock discontinuity formed by the action of ponderomotive forces (the retardation wave R_T), its velocity W_T, and also the changes in its shape in the course of its formation. Two methods are used for the calculation. The characteristic method is used when there are no discontinuities in the flow. When a shock wave R_T is formed, a system of nonsteady one-dimensional equations of magnetohydrodynamics describing the interaction between the ionized gas and the magnetic field is solved numerically using an implicit homogeneous conservative difference scheme for the continuous calculation of shock waves with artificial viscosity [2].Translated from Izvestiya Akademiya Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 112–118, September–October, 1977.     

The influence of boundary layer growth on shock tube test times

Summary A theoretical and experimental investigation of the limitation on shock tube test times which is caused by the development of laminar and turbulent boundary layers behind the incident shock is presented. Two theoretical methods of predicting the test time have been developed. In the first a linearised solution of the unsteady one-dimensional conservation equations is obtained which describes the variations in the average flow properties external to the boundary layer. The boundary layer growth behind the shock is related to the actual extent of the hot flow and not, as in previous unsteady analyses, to its ideal extent. This new unsteady analysis is consequently not restricted to regions close to the diaphragm. Shock tube test times are determined from calculations of the perturbed shock and interface trajectories. In the second method a constant velocity shock is assumed and test times are determined by approximately satisfying only the condition of mass continuity between the shock and the interface. A critical comparison is made between this and previous theories which assume a constant velocity shock. Test times predicted by the constant shock speed theory are generally in agreement with those predicted by the unsteady theory, although the latter predicts a transient maximum test time in excess of the final asymptotic value. Shock tube test times have also been measured over a wide range of operating conditions and these measurements, supplemented by those reported elsewhere, are compared with the predictions of the theories; good agreement is generally obtained. Finally, a simple method of estimating shock tube test times is outlined, based on self similar solutions of the constant shock speed analysis.Nomenclature a speed of sound - A, B, C constants defined in section 5.3 - D shock tube diameter - K =/q ^m, boundary layer growth constant, see Appendices A and B - l hot flow length - m constant, =1/2 or 4/5 for laminar or turbulent boundary layers, respectively - M ₀ initial shock Mach number at the diaphragm - M _s shock Mach number at station x _s - M ₂ =(U ₀–u ₂)/a ₂, hot flow Mach number relative to the shock front - N = ₂ a ₂/ ₃ a ₃, the ratio of acoustic impedances across the interface - P pressure - P* =P _e–P ₂, perturbation pressure - q boundary layer growth coordinate defined in § 2 - Q =(W–1+S) K - r radial distance from shock tube axis - S boundary layer integral defined by equation A6 - t time - t =/ , dimensionless ratio of test times - T =l/l , Roshko's dimensionless ratio of hot flow lengths - u axial flow velocity in laboratory coordinate system, see figure 1a - u* =u _e–u₂, perturbation axial flow velocity - U shock velocity - U ₀ initial shock velocity at the diaphragm - U* =U–U ₀, perturbation shock velocity - v axial flow velocity in shock-fixed coordinate system, see figure 1b - w radial flow velocity - W =U ₀/(U ₀–u ₂), density ratio across the shock - x axial distance from shock tube diaphragm - x _s, x _s axial distance between shock wave and diaphragm - t = _I/ , dimensionless ratio of test times - X =l _I/l , Roshko's dimensionless ratio of hot flow lengths - y =(D/2)–r, radial distance from the shock tube wall - ratio of specific heats - boundary layer thickness; undefined - boundary layer displacement thickness - boundary layer thickness defined by equation A2 - characteristic direction defined by dx/dt = (u ₂–a ₂) - =(M ₀ ² +1)/(M ₀ ² –1) - viscosity - characteristic direction defined by dx/dt=(u ₂+a ₂) - density - * = _te–₂, perturbation density - Prandtl number - shock tube test time - =M ₀ ² /(M ₀ ² –1) Suffices 1 conditions in the undisturbed flow ahead of the shock - 2 conditions immediately behind an unattenuated shock - 3 conditions in the expanded driver gas - 4 conditions in the undisturbed driver gas - e conditions between the shock and the interface, averaged across the inviscid core flow - i conditions at the interface - I denotes the predictions of ideal shock tube theory - asymptotic conditions given when x _s and t - s conditions at or immediately behind the shock - w conditions at the shock tube wall - a, b, b ¹, c, d, d ¹, f, f ¹, g, g ¹, j, k, k ¹ conditions at the points indicated in figure 2     

Plasmoid structure in an electrodynamic accelerator

By means of a high-speed photorecorder it was observed that a plasmoid in an electrodynamic accelerator consists of separate sheets moving at approximately identical velocities. The following parameters of these sheets have been measured: velocity — 6 · 10⁶ cm/sec, diameter — 0. 2 cm, charged particle density in sheet — 2. 5 · 10¹⁷ cm^–3, temperature — 3.4 · 10⁴°K, and average current in sheet — 4 · 10³ a. It is shown that the sheets are pinches. The pinch plasma consists essentially of ions of oxygen O⁺ and silicon Si⁺, Si²⁺, and Si³⁺. The gas filling the tube is only slightly entrained. The existence of a limiting pinch radius is shown, and an expression agreeing closely with experiment is obtained for it.The nonuniformity of plasmoids in electrodynamic accelerators has been reported on a number of occasions. Thus, Mawardi and Naraghi [1] observed a sheet-type structure in a coaxial accelerator using magnetic probes. They proposed a mechanism of internal instability of the plasma flux with a frozen-in magnetic field. A. M. Kovalev [2] attributed the formation of new current sheets to successive breakdowns behind the moving plasmoid.In this article a more detailed experimental investigation of plasmoid sheets and the conditions under which they occur is described. Time resolution with a high-speed photorecorder (PR) was employed. From the Doppler shift of the spectral lines, data were obtained on the velocities of the different ions making up the plasmoid and the degree of entrainment of the gas filling the tube. The charged particle density in the sheets was determined from the quadratic Stark effect of the spectral lines of the oxygen ions. From the relative intensity of the lines of trivalent and univalent silicon ions, the plasma temperature in the plasmoid was measured. The experimental data obtained make it possible to propose another explanation of the origin of the sheets.The author is indebted to V. L. Granovskii for his notes and to O. A. Malkin for suggestions and assistance with the work.     

On the initial stage of a point explosion in a radiating gas

A study is made of the initial stage of a point explosion in a radiating gray gas whose absorption coefficient is approximated by the dependenceK=x()e ^–n ,where is the density and e is the internal energy of the gas. It is shown that for n > —1/3 the initial stage of the process differs significantly from the solution of the problem in not only the classical adiabatic case [1, 2] but also in the case of a medium with nonlinear thermal conductivity [2–4]. The supply of energy to the medium at a point leads to instantaneous heating of the complete medium. The form of this heating is found analytically. The method of matched asymptotic expansions is used to investigate the behavior of the solution in the neighborhood of the center. It is found that for definite conditions at the center of the perturbed region there are formed a shock wave and a region of reverse flow of the gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 75–82, May–June, 1980.I should like to thank V. P. Korobeinikov for interest in the work and a helpful discussion of it.     

Determination of gradients of flow variables behind three-dimensional stationary and pseudo stationary curved shock waves in conducting gases

Summary In this paper we have obtained the gradients of magnetic field, velocity, pressure and density behind a shock wave in three dimensional steady motion of a conducting gas. For the shock configuration, we take a continuous differentiable function of coordinates and it is assumed that the components of the magnetic field H ⁱ , velocity components u ⁱ , pressure p and density behind the shock-surface are differentiable functions. Moreover we take H ⁱ , u ⁱ , p and in front of the shock-wave as constant quantities. In § 4 we have obtained the gradients of flow and field quantities behind the pseudostationary shockwave. § 5 is devoted to the calculation of gradients of flow and field quantities in cases where the normal component of the magnetic field is zero on both sides of the shock wave. In § 6 the relation between the curvature k of the shock-surface and the curvature K of the stream line just behind the shock surface in two dimensional steady motion has been derived. § 7 deals with the determination of the ratio K/k for an attached shock in the case of a wedge.