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An asymptotic solution of radiative gas-dynamic equations for stationary interaction of two hypersonic gas flows emanating from two identical spherical sources is obtained. Under the assumption that the gas in the shock layer is in local thermodynamic equilibrium and volume emission (energy loss for radiation) occurs there, analytical expressions for the distributions of gas-dynamic functions and temperature are derived. The shock wave shape and the radiant flux on the contact plane are examined as functions of problem parameters.

Aerodynamic problems arising during design and development of braking systems for re-entry vehicles are analyzed. Aerodynamic phenomena and laws valid in a supersonic flow around a pair of bodies having different shapes are studied. Results of this research can be used in solving application problems (arrangement and optimization of experiments; design and development of various braking systems for re-entry vehicles moving with supersonic speeds in the atmosphere).

An asymptotic solution of the Euler equations that describe stationary interaction of two hypersonic gas flows from two identical spherically symmetric sources and an integral equation determining the shock wave shape are obtained with the use of a modified method of expansion of the sought functions with respect to a small parameter, which is the ratio of gas densities in the incoming flow and behind the shock wave. The solution of this equation near the axis of symmetry allows the shock wave stand-off distance from the contact plane and the radius of its curvature to be found. It is shown that the solution obtained agrees well with the known numerical solutions.

This paper analyzes the results of experiments with impact of metal spherical impactors on cylindrical targets of epoxy (filled with Al2O3 microparticles and without the filler) performed in a ballistic range. Impact velocities were limited to a range of 0.6–1.1 km/sec since higher velocities led to complete destruction of the targets. Impacts at the velocities considered produced channels of an almost cylindrical shape with the impactor stuck at the end of the channel. The strength of filled epoxy is estimated using the previously established dependence of the channel depth on the impact energy, the ratio of the densities of the impactor and target materials, and the tensile strength of the target material. It is found that at a mass fraction of the filler equal to 0.4, the strength of the target increased by a factor of approximately 1.5–2.

The numerical solution of the two-criteria variational problem of the body contour with minimum radiation heat flux and wave drag is obtained in the class of axisymmetric and plane slender bodies in hypersonic flow. Solutions obtained using the Pareto, ideal point and minimax methods are compared. It is shown that in the class of axisymmetric slender bodies the optimum body gives a decrease in the radiation heat flux as compared with a cone of up to 15% for the Pareto method, up to 13% for the ideal point method, and up to 5% for the minimax method. A solution is also obtained in the subclass of power-law slender bodies and it is shown that the optimum power-law bodies are inferior, as compared with the optimum bodies from the general class of such bodies, in reducing both radiation heating and resistance.

An analysis is made of experimental results on impact (at velocities of 0.6–6.26 km/sec) of projectiles made of Caprolon and polyethylene and compound projectiles (made of Caprolon with steel or aluminum spheres) on targets made of an epoxy resin with and without a filler (Al2O3) in a ballistic range. Impact on the edge surface of cylindrical targets with a characteristic size of 0.05 m is investigated. Complete fracture of the targets was recorded at velocities above 1 km/sec. The masses and dimensions of the collected fragments are subjected to statistical analysis. Average values of the fragment sizes and specific surface fracture energy are calculated.

The aerodynamic characteristics of cone-sphere models are studied at Mach numbers M = 6, 8.4, and 12 to 13 over a wide Reynolds number range. Models of a braking device (sphere) were connected with a load (frustum of a cone) by means of shrouds. The dependences of the aerodynamic coefficients C x and C y on the angle of attack α were obtained for different relative dimensions of the load and the braking device, shroud lengths, and Mach and Reynolds numbers. The effect of the above-mentioned parameters on the aerodynamic characteristics of the models is analyzed. The C x (ReD) dependences of load-parachutemodels in a symmetric flow are determined over the wide Mach and Reynolds number ranges 6 ≤ M ≤ 13 and 3 · 103 ≤ ReD ≤ 3 · 106.

This paper reports results from measurements of the electron concentration in wakes behind aluminum spherical models flying at velocities of 2–5 km/sec in air-xenon mixtures at a total pressure in the ballistic track of 20–100 torr. The heating of the models moving in the ballistic track and aluminum ablation from their surfaces were calculated. The rate constant of electron attachment to microparticles is found, and it is shown that it depends on the fraction of xenon in the mixture. The dependence of the coefficient of electron accommodation to the microparticle surface on the xenon concentration in the mixture is obtained and explained from a physical point of view.

The flowfield and the aerodynamic drag of a model consisting of a pair of bodies (leading body a cylinder and trailing body a hollow cylinder) connected by a cylindrical bar along the axis of symmetry is experimentally investigated at Mach numbers ranging from 0.6 to 1.7. In the course of the experiments, the trailing body cavity depth and the connecting bar length were varied.

The distinctive features of the flow in the region of interaction between an oscillating shock and a flat-plate boundary layer are studied for the laminar, transitional, and turbulent flow regimes. The flow patterns and the pressure and heat transfer distributions in the interaction region are analyzed at different intensities, frequencies, and amplitudes of the oscillating shock. The results of the interaction of oscillating and steady shocks with the flat-plate boundary layer are compared.

The results of measurements of craters caused by the interaction between impactors moving at velocities of 2–6 km/s and organic-glass targets are used to find the crater depth depending on the impact velocity and on the density ratio between the impactor and target, as well as on the target strength. A differential equation is derived for determining the crater shape, whose solution fits well the measurement results. The results of calculation of the dimensionless volume of the crater, its diameter, and the slope of its generatrix by the equation for the crater shape also fit well the measured values.

Results of experimental investigations of trans‐ or supersonic flow around two bodies (cone–disk or sphere–disk) connected by a cylindrical rod along the axis of symmetry are presented. The special features of the flow are analyzed. It is found that the dependence of the drag coefficient Cx of a pair of bodies on the Mach number within the range 0.6 ≤ M ≤ 1.7 is nonmonotonic. The reasons for the hysteresis in the dependences Cx(M) for two bodies at the stages of flow acceleration and deceleration and discrete variation of the Mach number are clarified. The influence of cone angles and sizes of both bodies on the drag coefficient is estimated.

A solution of a variational problem of a slender body with a minimum total radiative heat flux, moving in a gas with a constant velocity, is constructed. It is found that there are three types of the transverse contour of the optimum body: a circumference, a star‐shaped contour, and a contour consisting of circle arcs and sectors of straight lines. The radiation parameter affects only the shape of the longitudinal contour and does not affect the optimum shape of the transverse contour. It is shown that the use of optimum spatial bodies allows a significant (more than 50%( decrease in the radiative heat flux to the body surface as compared to bodies of revolution with similar geometric characteristics.

The results are given of experimental investigations of the interaction between spherical metal impactors and a target of organic glass. The impact velocities range from 0.7 to 2.1 km/s. Singular features of the pattern of penetration of impactors into the target are revealed. The empirical dependence of the depth of penetration on the impact energy is obtained, and comparison is made with the known formulas for superdeep penetration. An expression is derived for the limiting velocity, above which no formation of channels in the target occurs, but the impactor is completely destroyed and a crater is formed.

A solution is derived for the variational problem on the shape of a three-dimensional slender body subjected to a minimal radiation heat flux during its motion in the atmosphere with a constant hypersonic velocity. The distribution of radiation flux over the surface is approximated in the form of dependence on the local surface slope. The limitations on the body shape are provided by the isoperimetric conditions for the bulk of the body, for the area of its wettable surface, for the area of its bottom cross section, and for the perimeter of the bottom cross section, as well as the limitation on the limiting value of the wave drag. It is found that the transverse contour of the optimal body may have the form of a circle, of a star-shaped transverse contour, and of a contour consisting of arcs of a circle and line segments. It is demonstrated that the use of optimal three-dimensional bodies enables one to significantly (by more than 50%) reduce the radiation heat flux to the body surface compared with bodies of revolution which have the same preassigned geometric characteristics.

Based on the analysis of experimental data obtained in the wake behind an aluminum–magnesium body, it is shown that the change in the electron concentration along the wake axis behind the model made of the AMg–6 alloy (94% Al + 6% Mg) for velocities of 2—6 km/sec is determined by a complex system of reactions with excited states of atoms, double and triple recombination of electrons, and recharging of ions. It is shown that the dominating process determining the ion–concentration distribution is the dissociative recombination O2+ + e →(kr) O +O. By solving the inverse problem by two numerical methods, the rate constants of this reaction, which are in satisfactory agreement with the data of other authors, are found.

This paper presents the results of an experimental study on the geometric parameters of craters that originated at the impact interaction of polyethylene projectiles with a massive organic-glass target. The impactor speed ranged from 2.7 to 6.28 km/s. The shapes of the resulting craters are determined. Using statistical analysis and scaling theory, we obtained the dependence of the diameter and depth of the crater on defining parameters. The critical impact energy resulting in the catastrophic breakup of the target is estimated.

An experimental investigation is performed of the distribution of heat flux and pressure over the surface of an associated body located at different distances in the supersonic wake of another body. The results are given of an analysis of the effect of the connection of a pair of bodies on the pattern of flow and distribution of the above-identified parameters under conditions of symmetric and asymmetric flow. An increase in the perforation of an associated concave body to 5.3% causes an increase in the heat flux on its inner surface for both schemes of flow between models both in the presence of a unified separation zone and in the presence of a pressure shock before the rear body. The results of this study enable one to estimate the aerothermodynamic characteristics of deceleration units using experimental or prediction data for associated bodies [1].

The results of the experimental study of the interaction of polyethylene impactors with a massive flat organic-glass target are presented. The impactor speed ranged from 3.2 to 5.84 km/s. A statistical analysis of the mass and size distributions of fragments of the impact and chop craters of the target is done. As a result, some scaling relations are established for the geometric size of the craters, the cumulative ejected mass, the mass of the largest fragment ejected from the impact crater, and for the dust mass. The mass distribution of the impact-crater fragments is shown to obey a power law and agrees well with other authors" data for some materials. The critical impact energy e k , resulting in the catastrophic disruption of the target into individual fragments, is estimated. For organic glass, the value of e k is found to be 4 × 104J/kg. The mass of the largest (central) fragment accounts for 27 to 33% of the overall mass ejected from the impact crater. The use of the parameter Π3= σ p /ρ p v20gives the best fit to the observational data for the masses released from the impact and chop craters.

Based on the results of analysis of the experimental data obtained in the wake behind a body of aluminum/magnesium, it is found that the drop in the electron concentration along the wake axis is defined by a complex system of reactions involving excited states of atoms, by double and triple recombination of electrons, and by the ionic charge exchange. The main system of reactions is formulated. It is demonstrated that the predominant process defining the electron concentration distribution is the dissociative recombination\({\text{O}}_2^ + + e \to {\text{O}} {\text{ + O}}^{k_r } \). Two methods are employed to find, from the solution of inverse problem, the value of the rate constant of this reaction, which is in adequate agreement with the data of other authors.

Changes in the wake flow characteristics behind a body made of an aluminum-magnesium alloy and flying in air with a hypersonic speed are analyzed. It is shown that, as a result of afterburning of magnesium vapor in the wake, first, MgO forms in the gas phase, and then it condense to drops, which thermoionically emit electrons. The latter leads to accumulation of a positive charge on the drops and to a noticeable increase in the electron concentration in the wake. Calculations that illustrate the time dependence of the magnesium concentration and a substantial temperature rise in the wake, caused by magnesium afterburning, are described.

The results are given of experimental investigations of the interaction between a 2.5-g polyethylene impactor and a massive target of organic glass. The impact velocity ranges from 1 to 3.2 km/s. A statistical analysis is made of masses and sizes of fragments of the impact and spallation craters of the target.

An analysis is made of the experimental results obtained in the wake behind a body of aluminum/magnesium alloy flying at a hypersonic speed. It is demonstrated that, as a result of afterburning of magnesium vapors, MgO is first formed in the gas phase in the wake, which is followed by its condensation into microdroplets from whose surface thermionic emission occurs. This leads to the formation of a positive charge on the droplets and to a marked increase of the electron concentration in the far wake. Calculation results are given, which point to the variation of the concentration of magnesium and to an appreciable increase of the temperature in the wake due to its afterburning. These data enable one to reconstruct the rate constants of some reactions in the wake behind a model made of AMG-6 alloy

Results of microwave measurements of the electron concentration and the frequency of electron-neutral particle collisions in the wakes behind models of an aluminum-magnesium alloy flying in air- xenon mixtures at Mach numbers of 10–15 are reported. For comparison, similar measurements for models without and with aluminum decomposition are presented. The burn-up of Mg particles in the wake is found to change the form of the distribution and to increase appreciably the electron concentration in the wake. The attachment coefficients for electrons in the experiment with Al entrainment and in previous studies are shown to be in good agreement.

Experimental data on the change in the electron density in the wake of a ballistic object traveling at velocities V ∞=3.4–4.9 km/s in argon at pressures p ∞=30–100 Torr are processed and analyzed. A reaction scheme is proposed which takes into account the recombination of charged particles, processes of ionic conversion, and the excited states of the atom. The solution of the equations of a nonequilibrium boundary layer for flow in the wake is used to formulate the inverse problem of determining the rate constants for dissociative recombination Ar 2 + +e→Ar+Ar and ternary recombination Ar++e+Ar→Ar+Ar. The “nearest-neighbor” approximation is used to obtain theoretically an expression for the ternary recombination coefficient as a function of temperature and pressure. Numerous solutions of inverse problems and a comparison with experiments demonstrates the validity of the expression obtained for the ternary recombination coefficient. It is shown that this expression is valid for moderate pressures and complements the Pitaevskii result for low pressures and the Langevin result for high pressures.

Investigations on determination of the rate constants for reactions in nonequilibrium processes from ballistic experiments are reviewed. We obtained and give here the constants fro dissociative recombination in air, nitrogen, argon, krypton, and xenon and also the constants for ternary recombination of Al+ and the attachment constants for aluminum oxides.

We present measurements of the electron concentration in wakes behind aluminum spherical models flying in air with velocity 3.4–5.7 km/sec at a pressure of 10–80 torr. We have calculated the heating and entrainment of aluminum from the surface of the models as they move within the flight range. We show that condensation of Al vapor may occur at distances of more than 100 diameters of the body and pressure ≳80 torr. We pose and solve the inverse problem of determining (from experimental data) the effective attachment coefficient for attachment to air molecules and the attachment rate constants for AlO+e→AlO−, AlO2+e→AlO2−.

The range of applicability of some similitude laws for heat transfer, friction and drag coefficients is discussed on the basis of numerical solutions of the complete viscous shock layer equations describing hypersonic flow past blunt bodies.

The design of shuttle-like hypersonic spacecraft [70, 77]gives rise to the problem of investigating the spatial configurations that are optimum from the point of view of thermal heating and other characteristics, which enable the weight of the required thermal protection to be reduced. The problem of optimizing the weight of thermal protection depends on many parameters and has not yet been solved in a rigorous mathematical formulation. Approximate formulations of the optimization problem have therefore been considered, the solution of which has enabled axisymmetrical optimum shapes of bodies to be obtained with the minimum convective [43, 61, 73]and radiation [35–37, 58, 60]heat fluxes. It is known from attempts to solve variational problems of a body with minimum drag [29–31, 51–53, 62], that the transition to essentially three-dimensional configurations enables a reduction in the drag to be achieved compared with axisymmetrical bodies. A similar situation should obviously also occur when optimizing the shape of a body for heat flux. In this paper we present for the first time variational problems for finding the optimum shape of three-dimensional bodies of minimum overall thermal heating when moving along an incoming trajectory. In papers by other authors [21, 29–31, 48, 51–53, 62]the problems of determining the three-dimensional optimum aerodynamic shapes from the point of view of the minimum wave or total drag were considered. A brief review is given of research which has been done to determine the convective and radiation heating of three-dimensional bodies and the fundamental formulas for the wave drag, the fraction drag, and the convective and radiation fluxes to three-dimensional bodies moving in dense layers of planetary atmospheres are presented. The formulas depend explicitly on the conditions of entry into the atmosphere of the planet and on the geometry of the body, which enables variational problems to be formulated on determining the three-dimensional shape of the body from the conditions for minimum overall heating (convective and radiation) of the surface along the trajectory of motion.

The flow of an equilibrium-reacting multicomponent three-element air-xenon mixture is numerically investigated. The effect of multicomponent diffusion on the convective heat transfer to the body surface is examined. The dependence of the convective heat transfer to the body surface and the total shock-layer spectral radiation flux Pλm on the xenon concentration is obtained. A comparison of the calculated data for Pλm and the experimental data of [2] gives good agreement. A simple approximation for the convective heat flux at the stagnation point as a function of xenon concentration is proposed.

Supersonic nonuniform gas flow over blunt bodies without surface injection has previously been investigated by both numerical [1–3] and experimental [3] methods. The processes of surface vaporization under the influence of an intense heat flux, artificial gas injection and surface combustion [4] are all worthy of study. The problem of the interaction between a nonuniform supersonic flow and a body in the presence of intense gas injection from the surface is examined and an analytical solution is constructed.

During a space vehicle's entry into a planet's atmosphere at hypersonic speed one of the important problems is the aerodynamical surface heating due to convective and radiant heat fluxes from the gas after passing through a strong shock wave. Due to the high destructive action of this heating, an important problem is the selection of the aerodynamic shape allowing the minimum heat influx to its surface. The problem of determining the shapes of an axisymmetric body from the condition of minimum total convective heat flux along the lateral face of the body was considered under various assumptions in [1–7]. There are a number of entry conditions (for example, into the earth's atmosphere with a speed of 11 km/ sec at an altitude of about 60 km [12]) during which the radiative component becomes dominant in the total heat flux toward the body. A numerical solution of the problem of hypersonic flow of a nonviscous, non-heat-conducting radiating gas around a body is obtained at this time only for a limited class of bodies and primarily for certain entry conditions (for example, [8–12]). On the basis of these calculations it is impossible to make general conclusions concerning arbitrary body shapes. Therefore, approximate methods were proposed which permit the distribution of radiant heat flux to be obtained for an arbitrary axisymmetric body in a wide range of flight conditions [13–15]. In the present work an expression is derived for the total radiant heat flux over the entire body surface and similarity criteria are found. A variational problem is formulated to determine the shape of an axisymmetric body from the condition of minimum total radiant-heat flux over the entire body surface. It is solved analytically for the class of thin bodies and in the case of a strongly radiating gas.

An investigation is made into the convective heating of a blunt-nosed body in an expanding stream of heated gas. The gas parameters at the outer edge of the boundary layer are determined on the basis of a solution obtained earlier by the authors [3]. Expressions are obtained which make it possible to convert the convective heat flux to a body in a uniform gas stream to one in a nonuniform stream. Dimensionless numbers are found and their influence on the convective heat flux to the body is investigated.

Generalized expressions are obtained for calculating the heat fluxes and frictional stresses of the laminar and turbulent flow regimes in a boundary layer in the case of uniform and nonuniform flow past bodies.

The area rule, which is well known for wave resistance [1, 2], is generalized to the heating of three-dimensional bodies by flows which depend locally on the angle of attack. Calculations are made for triaxial ellipsoids with different ratios of the semiaxes, and the limits of applicability of the rule are found. The problem of determining the ablation of a three-dimensional body that changes its shape in a heat flow is solved. It is shown that the area rule also holds for a change of mass of three-dimensional bodies, and expressions are given for calculating the ablation.

The problem of axisymmetric nonuniform gas flow past smooth blunt bodies at high Mach numbers is investigated. The approach stream is a parallel axisymmetric flow in which the velocity and temperature depend on the radial distance from the axis of symmetry and the pressure is constant. On the axis of symmetry the velocity has a minimum and the temperature a maximum. A characteristic feature of this flow is the existence of two qualitatively different flow regimes: separated [1-4], when in the shock layer on the front of the body there is a closed region of reverse-circulating flow, and unseparated [5, 6], when there is no such zone. In this study the case of unseparated flow is investigated. The equations of a thin viscous shock layer with generalized Rankine-Hugoniot conditions at the shock and boundary conditions on the body that take into account the supply of gas from the surface are solved numerically. The effect of the gas supply on the conditions of unseparated flow is analyzed in relation to the Reynolds number, and the critical values of the nonuniformity parameter a = ak [5] are obtained. It is shown that at high Reynolds numbers the supply of gas from the surface has practically no effect on ak, while at low and intermediate Reynolds numbers it reduces the region of unseparated flow. For high Reynolds numbers and an intense supply of gas from the surface an asymptotic solution of the problem is obtained for the neighborhood of the stagnation point. This is compared with the numerical solution.

In the experimental study of phenomena occurring in the flow of air round models flying along a aeroballistic range with hypersonic velocities, the question arises of the effect of water vapor along the range on the measurements of the gas parameters, for example, on the electron concentration or on the intensity of the radiation. Water vapor is usually present in atmospheric air and, in the absence of special measures to remove it, it may have an influence on the results of measurements. In [1] a theoretical study has been made of the effect of chemical reactions involving the participation of water vapor in the air on the chemiluminescent radiation in the wake alone. In particular, there was no consideration of the effect of water vapor on the electron concentration. In the present study, the results are given of calculations of the distributions of the nonequilibrium parameters in the wake, with allowance for the occurrence of chemical reactions in the air and water vapor under conditions characteristic of aeroballistic experiments [1–3].

A solution is obtained of the flow-past problem for an axisymmetrical body with steady-state hypersonic nonviscous, space-radiating gas flow in a hypersonic approximation. It is shown as illustrated by the example of flow-past of a sphere by an air flow, that the relative distribution of the radiant flux weakly depends on a calculation of surface re-radiation, while the size of the radiant flux substantially depends on body temperature TW at a critical point. The distributions of radiant flux for sphere flow-past by a CO2-N2 gas mixture (at TW = 0) are calculated using a previously developed method. It is shown that different CO2 contents in the initial mixture of the incident gas flow weakly affect this distribution. The dependence of the distribution of the radiant flux and departure of the shock wave on the boundary condition for gas enthalpy in the pressure shock, taking into account forward radiation, is investigated. Asymptotic expressions are obtained for sphere flow-past for the case of a strongly radiating gas. Distributions of the radiant flux for different assumptions for the boundary conditions in shocks are calculated.

The laws of heat transfer associated with the interaction of underexpanded supersonic gas jets and obstacles or blunt bodies have been investigated, for example, in [1–3]. Similar problems of nonuniform flow occur when bodies move in the wake behind other bodies; however, in this case the laws of heat transfer have so far received little attention [4–8]. It has been established that for a certain Reynolds number and flow nonuniformity parameters a zone of reverse-circulatory flow develops near the front of the blunt body. However, the conditions of transition to separated flow have not been determined. This paper presents a self-similar solution of the equations of the viscous shock layer near the stagnation line in supersonic flow past an axisymmetric blunt body located behind another body. On the basis of this solution a separationless flow criterion is proposed. The effect of the nonuniformity and the Reynolds number on the shock standoff distance, the convective heat flux and the friction drag of the blunt body is investigated.

The use of an open microwave resonator with plane-parallel mirrors for plasma diagnostics was first proposed in [1]. A resonator with spherical mirrors, which provides better spatial resolution in addition to high sensitivity, was used later [2, 3] to investigate the wake flow of models moving through air at hypersonic velocities. The presence of free electrons in the flow field is caused by ionization processes behind the bow shock and in the model boundary layer in this case. However, only the results of measurements of the density of electrons are presented in [2, 3], and no information is given on another important plasma parameter: the effective collision frequency of electrons with heavy particles. In the present study we use a microwave (8-mm range) resonator for an experimental study of the flow of gas in the wake of a polymer (Kaprolon) sphere traveling through air at hypersonic velocity. The flow is visualized by the schlieren technique. The electron densities and effective collision frequency of electrons with heavy particles are determined as a function of the distance behind the sphere.

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 ɛ 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 ɛ 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 ɛ. 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.

In recent years the two-stage light gas ballistic apparatus with deformable plastic pistons has become widely used in experimental aerodynamics. The existing methods of calculating such devices either completely neglect friction of the piston on the channel wall [1–3] or use a schematization of the frictional forces [4–6], which does not have a satisfactory physical basis. In a number of studies [7, 8] the friction force was considered constant, and its value was specified not from physical considerations, but to produce the best agreement between calculated and experimental values of object velocity or driving gas pressure. Since friction is such a significant factor, its proper consideration in calculating piston motion parameters requires special study. In this connection, it is useful to consider the operation of only the first stage of the ballistic apparatus, which sets the piston in motion. Below we will consider the problem of the internal ballistics of a one-stage powder-driven apparatus in the column channel of which a piston made of polymer material moves, experiencing friction. The friction model is constructed on the basis of a series of experiments on the slow forcing of polymer specimens compressed in the longitudinal direction through a steel channel. An experimental study was made of the relationship between the gunpowder gas pressure and time within a constant volume chamber, allowing establishment of the true powder-burning law, and its deviation from the geometric law of [9]. Calculated and experimental values of maximum gas pressure and muzzle velocity of a polyethylene piston are compared.

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 ak [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].