Measuring the velocity of a gas wake in a shock tube from the induced electromotive force

It is shown that the velocity of the gas wake in a shock tube can be measured from the induced electromotive force for argon and xenon at initial pressures greater than 1 mm Hg and conductivities above 1 mho/cm. In a strongly ionized gas ( > 0. 01) the flow velocities measured directly behind the shock front are close to the flow velocities corresponding to steady-state ionization equilibrium. It is noted that the expenditure of energy to dissociate an admixture of air causes a noticeable increase in the velocity of the flow along the entire plug of hot gas. A 3–6% acceleration of the flow along the plug. in the equilibrium ionization zone is observed; this is probably caused by the action of the boundary layer formed on the walls of the shock tube on the free flow.     

Measurement of parameters of a gas suspension behind a shock wave in foam

A study has been made of the propagation of a shock wave in dry polyhedral foam with cell diameter 1 cm. The experiments were made in a shock tube in the range of Mach numbers M < 1.4 of the shock wave. The interaction of the shock wave with the foam was photographed. This established that the destruction of the foam by the shock wave leads to the formation of a gas-droplet flow behind the shock front. To determine the parameters of the suspension, the flow was probed by He-Ne lasers with different radiation wavelengths. The spectral-transparency method was used to find the modal diameter of the droplets of the gas suspension and the volume concentration of the droplets in the flow. The modal diameter of the droplets was 2m, and the volume concentration of the droplets decreased downstream.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 134–141, May–June, 1993.     

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.     

Propagation of shock waves in free space

The problem of the exit of a shock wave from an axisymmetric channel and its propagation in a free space occupied by an ideal gas is examined. This problem has been studied earlier in [1], in which the shock wave front was considered planar, as well as in [2], in which the wave front was regarded as a surface of an ellipsoid of revolution. The solutions obtained in these studies assumed the presence of two regions in the wave-front surface: the region of the original shock wave and a region stemming from the decomposition of an infinitesimally thin annular discontinuity of the gas parameters, with the wave intensity over the front surface in each region being considered constant, i.e., the wave character of the process over the front was not considered. In this study a solution will be achieved by the method of characteristics [3–5] of the equations of motion of the shock-wave front, as obtained in [6, 7]. Flow fields are determined for the region immediately adjacent to the shock-wave front for a wide range of shock-wave Mach numbers M _a =1.6–20.0 for = 1.4. On the basis of the data obtained, by introduction of variables connected with the length of the undisturbed zone, as calculated from the channel cross-section along the x axis, together with the pressure transition at the wave front, relationships are proposed which approach self-similarity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 163–166, September–October, 1971.In conclusion, the author thanks S. S. Semenov for his valuable advice on this study.     

Role of the absorption of radiation ahead of a shock wave with hypersonic flow around a blunt body

A study was made of conditions at the front of a strong shock wave taking account of the absorption of leading radiation. Emphasis is laid on the role of the dimensionless parameters which arise under these circumstances, and an evaluation is made of the values of these parameters for a number of practically important cases involving the entry of blunt bodies into dense layers of the Earth's atmosphere. Calculations are carried out to determine the composition and the parameters of the flow of molecular nitrogen entering into the shock wave, and conclusions are drawn with respect to the general problem of hypersonic flow around a blunt body, taking radiation into account. In an investigation of the flow of a hypersonic stream of air around a blunt body, taking account of radiation, it is necessary to have some idea of how the radiation leaving the zone of the shock wave reacts with the oncoming flow of cold air. The importance of taking this reaction into account is indicated by the results of observation of the reentry of spacecraft into dense layers of the atmosphere [1], and by existing experimental data on strong shock waves [2]. This reaction is bound up with the fact that the absorption of intense short-wave radiation from the shock wave in cold air leads to photodissociation and photoionization of the molecules of air, i.e., to an actual increase in the enthalpy of the air. Some of the general questions of the structure of a very strong direct shock wave, taking account of the absorption of radiation leading the wave front, have been investigated in [3],Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 40–47, November–December, 1970.     

Particle-in-a-box study of the evolution of an ion-acoustic shock wave

In an analysis of a one-dimensional numerical model of a nonisothermal plasma it is shown that an ion-acoustic shock wave of subcritical amplitude separates a soliton from the shock front after the reversing stage. This process is accompanied by turbulent flow behind the front and by trapping of ions in potential wells. The numerical particle-in-a-box method is being used widely to study plasma phenomena. One field in which this method has been found fruitful is in the study of a nonisothermal plasma, characterized by an ion-acoustic wave branch.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 3–5, May–June, 1971.The authors thank R. Z. Sagdeev for support and interest in this study.     

Hypersonic flow structure in a large-scale multi-diaphragm shock tube

The results of an experimental and theoretical study of the structure of the shock wave and the gas flow behind it are presented, together with data on the duration of the high-temperature working flows, the contact zones and the regions of uniform cold-flow parameters in the large (channel diameter 0.5 m, length 200 m, gas tank diameter 3 m, length 23 m) interchangeable-nozzle shock tube of the Central Scientific Research Institute of Mechanical Engineering.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 158–165, September–October, 1993.     

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.     

Interaction of the vortex structures formed in parallel pulsed jets

The experimental investigation of the lateral interaction of the heads of pulsed jets and primary shock waves at various nozzle spacings and pressure ratio numbers is described. The various stages of formation of a composite pulsed jet issuing from a multinozzle block are classified and the flow development mechanisms are explored. It is shown for both a block and a single nozzle the shock wave travels with almost the same velocity, whereas the jet front formed at the exit from a single nozzle moves much more slowly than the jet front formed beyond a nozzle block. Long-lived lateral bursts of gas, whose dimensions are an order greater than those of the jet bursts, are detected. Their long period of existence considerably increases the stabilization time of the steady-state structure and parameters as compared with a single pulsed jet with the same flow rate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 153–159, November–December, 1987.     

Investigation of a “hanging” shock wave near a generating point

The hodograph method is used to plot a hanging shock wave in the plane nonequilibrium supersonic flow of an ideal gas. This paper considers the general case of an analytical solution in the plane of the hodograph at the point of generation of the shock wave. A type of limiting line is established which makes it possible to plot a shock wave (it is found that the shock wave may not extend over the whole flow, with a convolution in the physical plane).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 30–37, November–December, 1971.     

Effect of charge separation on the structure of the front of a shock wave in a plasma

The effect of dispersion due to charge separation on the structure of the front of a shock wave in a plasma is studied. It is shown that for small values of the shock front has an oscillatory structure with a characteristic length of order .Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 134–139, May–June, 1977.The authors thank L. P. Pitaevskii for useful discussions.     

Structure of a shock wave in which multiple ionization of the atoms is taking place

Ionization relaxation in a shock wave of very large amplitude is considered, the atoms behind the front of the shock wave being multiply ionized. In calculating the structure of the shock wave and the kinetics of ionization, allowance is made for the electron component of the thermal conductivity which plays an important role in this. A simplified method of calculating the kinetics of multiple ionization is proposed, and an application of this method is presented. The results of the structure calculation show that, as a result of heating by thermal conduction, the gas is considerably ionized even in front of the jump in compression, while the electron component of the thermal conductivity passes through a maximum.Translated from Zhurnal Prikladnoi Mekhnika i Tekhnicheskoi Fiziki, No. 5, pp. 11–21, September–October, 1970.     

Supersonic flow of combustible gas mixture past sphere with account for ignition delay time

Assume an axisymmetric blunt body or a symmetric profile is located in a uniform supersonic combustible gas mixture stream with the parameters M₁, p₁, and T₁. A detached shock is formed ahead of the body and the mixture passing through the, shock is subjected to compression and heating. Various flow regimes behind the shock wave may be realized, depending on the freestream conditions. For low velocities, temperatures, or pressures in the free stream, the mixture heating may not be sufficient for its ignition, and the usual adiabatic flow about the body will take place. In the other limiting case the temperature behind the adiabatic shock and the degree of gas compression in the shock are so great that the mixture ignites instantaneously and burns directly behind the shock wave in an infinitesimally thin zone, i. e., a detonation wave is formed. The intermediate case corresponds to the regime in which the width of the reaction zone is comparable with the characteristic linear dimension of the problem, for example, the radius of curvature of the body at the stagnation point.The problem of supersonic flow of a combustible mixture past a body with the formation of a detonation front has been solved in [1, 2]. The initial mixture and the combustion products were considered perfect gases with various values of the adiabatic exponent .These studies investigated the effect of the magnitude of the reaction thermal effect and flow velocity on the flow pattern and the distribution of the gasdynamic functions behind the detonation wave.In particular, the calculations showed that the strong detonation wave which is formed ahead of the sphere gradually transforms into a Chapman-Jouguet wave at a finite distance from the axis of symmetry. For planar flow in the case of flow about a circular cylinder it is shown that the Chapman-Jouguet regime is established only asymptotically, i. e., at infinity.This result corresponds to the conclusions of [3, 4], in which a theoretical analysis is given of the asymptotic behavior of unsteady flows with planar, spherical, and cylindrical detonation waves.Available experimental data show that in many cases the detonation wave does not degenerate into a Chapman-Jouguet wave as it decays, bur rather at some distance from the body it splits into an adiabatic shock wave and a slow combustion front.The position of the bifurcation point cannot be determined within the framework of the zero thickness detonation front theory [1], and for the determination of the location of this point we must consider the structure of the combustion zone in the detonation wave. Such a study was made with very simple assumptions in [5].The present paper presents a numerical solution of the problem of combustible mixture flow about a sphere with a very simple model for the structure of the combustion zone, in which the entire flow behind the bow shock wave consists of two regions of adiabatic flow-an induction region and a region of equilibrium flow of products of combustion separated by the combustion front in which the mixture burns instantaneously. The solution is presented only for subsonic and transonic flow regions.     

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.     

Effect of Transitional Nonequilibrium on the Molecular–Dissociation Rate in a Hypersonic Shock Wave

The problem of the influence of a nonequilibrium (non–Maxwellian( distribution of translational energy over the degrees of freedom of molecules on the rate of their dissociation in a hypersonic shock wave is considered. An approximate beam—continuous medium model, which was previously applied to describe a hypersonic flow of a perfect gas, was used to study translational nonequilibrium. The degree of dissociation of diatomic molecules inside the shock–wave front, which is caused by the nonequilibrium distribution over the translational degrees of freedom, is evaluated. It is shown that the efficiency of the first inelastic collisions is determined by the dissociation rate exponentially depending on the difference in the kinetic energy of beam molecules and dissociation barrier.     

Flow of a supersonic ideal gas over a planar cascade in the case of a subsonic normal component in regimes with attached shocks

The supersonic flow of an inviscid gas that does not conduct heat over a cascade of planar pointed profiles is considered in the case when the component of the velocity vector of the undisturbed flow normal to the cascade front is subsonic. The investigation is restricted to regimes without separation and shock waves attached to the leading edges of the profiles and fairly dense cascades, for which the characteristics or shock waves leaving the trailing edges do not enter the region in front of the cascade. In such cases, the conditions behind the cascade do not influence the flow in front of it. In this sense, the flow in the cascade, as in a Laval nozzle in the case of supercritical gradients is trapped, In the hodograph plane, trapped regimes of flow over the cascade correspond to velocity vectors of the undisturbed flow that lie on a certain line (see, for example, [1–3]), which is constructed in the process of solution of the problem. This property has been called the directing influence of the cascade on the oncoming flow. Regimes with detached shocks can also be trapped if the separation of the shocks is due to the profiles being blunt. A method is proposed that for regimes with attached shocks makes it possible to calculate the entire flow field, including the wave structure at large distances from the cascade front; some results obtained by the method are also given. The study of regimes with attached shocks, for which the analysis is simplest, is, first, of interest in its own right and, second, is a stage in the creation of methods of calculation and subsequent investigation of cascades with arbitrary regimes.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 108–113, July–August, 1979.We are grateful to M. Ya. Ivanov for assistance in updating the supersonic flow calculation program of [7], to G. Yu. Stepanov for helpful comments, and to E. V. Buganov and V. A. Vostretsov for assistance in preparing the paper.     

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.     

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.     

Hypersonic flow-past of plane blunt bodies by a nonviscous radiating gas

An analytic solution is obtained in the work in a Newtonian approximation [1] for the flow-past problem for a plane blunt body by a steady-state uniform hypersonic inviscous space-radiating gas flow. The hypersonic flow-past problem for axisymmetrical blunt bodies by a nonviscous space-radiating gas has been previously considered [2–4]. In this case a satisfactory solution of the problem was obtained even in a zero-th approximation by decomposing the unknown values in terms of a parameter equal to the ratio of gas densities before and after passage of the shock wave. The solution of the problem in a zero-th approximation with respect to in the case of flow-past of plane blunt bodies does not turn out to be satisfactory, since the departure of the shock and the radiant flux to the body as gas flows into the shock layer turns out to be strongly overstated under nearly adiabatic conditions. Freeman [5] demonstrated that results may be significantly improved for flow-past of a plane blunt body by a nonradiating gas if a more precise expression is used for the tangential velocity component expressed in a new approximation with respect to the parameter . This refinement is applied in this work for solving the flow-past problem for a plane blunt body by a space-radiating gas. The distribution of the gasdynamic parameters in the shock layer, the departure of the shock wave, and the radiant heat flux to the surface of the body are found. The solution obtained is analyzed in detail for the example of flow-past regarding a circular cylinder.Translated from Zhurnal Prikladnoi Mekhanikii Tekhnicheskoi Fiziki, No. 3, 68–73, May–June, 1975.     

Transonic flows around an airfoil in wind tunnels with porous walls

A study is made of two-dimensional transonic flows of gas around an airfoil in the working part of a wind tunnel with porous walls. The values of the flow parameters are determined by the numerical solution of a boundary-value problem for the equation of the velocity potential; this problem simulates the gas flow around the profile in the tunnel with porous walls. The obtained results are then used to construct an asymptotic theory of the influence of the wind-tunnel height and the Mach number M of the flow in it on the characteristics of the flow around the airfoil.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 99–107, September–October, 1980.