Investigation of a hypersonic viscous shock layer on rotating axisymmetric bodies in the presence of blowing

The hypersonic flow of a laminar stream of viscous compressible gas past blunt axisyrametric bodies rotating about the longitudinal axis is considered. It is assumed that gas blows from the surface of the body. The solution of the problem is obtained by a finite-difference method in a wide range of Reynolds numbers and blowing and rotation parameters. Some results of the calculations characterizing the effect of the rotation on the velocity and temperature profiles across the shock layer, on the friction and heat transfer coefficients, and the shock wave separation are given for the neighborhood of the stagnation point. For large Reynolds numbers and strong blowing an analytic solution of the problem is found in an approximation of two inviscid layers separated by a contact surface. The calculations are made for the flow past a sphere and a paraboloid and it is shown that in the presence of rotation the maximum of the heat flux is shifted from the stagnation point onto the side surface of the body. The dependence of the pressure distribution, the heat flux, and the friction coefficient is investigated for cases of constant and variable blowing over the contour of the body.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 106–114, January–February, 1986.     

Asymptotic solutions of the thin viscous shock layer equations near the symmetry plane of blunt bodies in hypersonic rarefied gas flow

The hypersonic rarefied gas flow over blunt bodies near the symmetry plane is investigated for the regime transitional from continuum to free-molecular. Three rarefied gas flow regimes are considered depending on the relationship between the determining parameters of the problem. For all regimes, at small Reynolds numbers, asymptotic solutions of the thin viscous shock layer equations near the symmetry plane of blunt bodies are obtained in the form of simple analytical expressions for the heat transfer, skin friction and pressure coefficients as functions of the gas-dynamic parameters of the free-stream flow and the geometric parameters and temperature of the body. With decrease in the Reynolds number these coefficients approach their values in free-molecular flow (with the accommodation coefficient equal to unity). From comparison with the data calculated using the direct simulation Monte Carlo method, the accuracy and applicability limits of the analytical solution are estimated.     

Study of the turbulent flow of a gas over long blunt bodies in a viscous shock layer

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 69–75, January–February, 1993.     

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.     

Numerical investigation of nonuniform flow around a sphere within the framework of the model of a viscous shock layer

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 62–67, September–October, 1991.     

The blunt-body problem in a nonuniform hypersonic viscous gas flow

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. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 120–125, November–December, 1986. In conclusion the authors wish to thank I. G. Eremeitsev for useful suggestions and G. A. Tirskii for discussing their work.     

Unsteady supersonic flow around blunt bodies with detached shock wave

The numerical method of calculating the supersonic three-dimensional flow about blunt bodies with detached shock wave presented in [1–3] is applied to the case of unsteady flow. The formulation of the unsteady problem is analogous to that of [4], which assumes smallness of the unsteady disturbances.The paper presents some results of a study of the unsteady flow about blunt bodies over a wide range of variation of the Mach number M=1.50– and dimensionless oscillation frequency l/V=0–1.0. A comparison is made with the results obtained from the Newton theory.     

Non-stationary effects in hypersonic nonuniform dusty-gas flow past a blunt body

In the framework of the two-fluid model, a hypersonic flow of a nonuniform dusty gas with low inertial (non-depositing) particles around a blunt body is considered. The particle mass concentration is assumed to be small, so that the effect of particles on the carrier phase is significant only inside the boundary layer where the particles accumulate. Stepshaped and harmonic nonuniformities of the particle concentration ahead of the bow shock wave are considered and the corresponding nonstationary distributions of the particle concentration in the shock layer are studied. On the basis of numerical study of nonstationary two-phase boundary layer equations derived by the matched asymptotic expansion method, the effects of free-stream particle concentration nonuniformities on the thermal flux, and the friction coefficient in the neighborhood of stagnation point are investigated, in particular, the most “dangerous” nonuniformity periods are found. The project supported by the Russian Foundation for Basic Research (project No. 96-01-00313) and the National Natural Science Foundation of China (joint RFBR-NSFC grant No. 96-01-00017c)     

Unsteady three-dimensional viscous shock layer in nonuniform gas flow in the neighborhood of a stagnation point

The combined influence of unsteady effects and free-stream nonuniformity on the variation of the flow structure near the stagnation line and the mechanical and thermal surface loads is investigated within the framework of the thin viscous shock layer model with reference to the example of the motion of blunt bodies at constant velocity through a plane temperature inhomogeneity. The dependence of the friction and heat transfer coefficients on the Reynolds number, the shape of the body and the parameters of the temperature inhomogeneity is analyzed. A number of properties of the flow are established on the basis of numerical solutions obtained over a broad range of variation of the governing parameters. By comparing the solutions obtained in the exact formulation with the calculations made in the quasisteady approximation the region of applicability of the latter is determined. In a number of cases of the motion of a body at supersonic speed in nonuniform media it is necessary to take into account the effect of the nonstationarity of the problem on the flow parameters. In particular, as the results of experiments [1] show, at Strouhal numbers of the order of unity the unsteady effects are important in the problem of the motion of a body through a temperature inhomogeneity. In a number of studies the nonstationary effect associated with supersonic motion in nonuniform media has already been investigated theoretically. In [2] the Euler equations were used, while in [3–5] the equations of a viscous shock layer were used; moreover, whereas in [3–4] the solution was limited to the neighborhood of the stagnation line, in [5] it was obtained for the entire forward surface of a sphere. The effect of free-stream nonuniformity on the structure of the viscous shock layer in steady flow past axisymmetric bodies was studied in [6, 7] and for certain particular cases of three-dimensional flow in [8–11].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 175–180, May–June, 1990.     

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.     

Hypersonic three-dimensional viscous shock layer in a nonuniform gas flow in the neighborhood of the stagnation point

Three-dimensional hypersonic viscous gas flow past smooth blunt bodies in the presence of injection or suction is considered. The effect of the nonuniformity of the approach stream on the shock-wave standoff, the flow structure and the friction and heat transfer coefficients is investigated with reference to the examples of flow from a supersonic spherical source and flow of the far wake type. It is shown that this effect depends importantly on the Reynolds number, the nature of the nonuniformity and the shape of the body.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 136–145, November–December, 1987.     

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.     

Radiation in a hypersonic shock layer generated around a projectile

Radiation emitted from the shock layer generated around a hypersonic flight model is experimentally investigated by using a ballistic range (two-stage light-gas gun). A polyethylene projectile of 1.2 cm in diameter is launched in this facility at the velocity of 5 km/sec (M=15), and the emission from the induced shock layer around the projectile is observed with a spectroscope. As a result, molecular band-spectra from NO and N₂ are detected along with those from carboncontaining molecules. Total emission power is measured with a diode-type powermeter. In addition, dimension effect of the flight model is theoretically and numerically examined, and a scaling law on thermochemical structure of the shock layer is developed. It shows that the thickness of thermal boundary-layer formed on the model surface does not follow the conventional scaling law based on the reaction distance and on the energy relaxation distance. Finally, the radiative field around the projectile is numerically computed, and the total power emitted from the shock layer is estimated. From the comparison between computed and measured results, the validity of the calculation model is discussed.     

Hypersonic viscous flow around extended bodies

The characteristic feature of flow around an extended body is the interaction of the thickened boundary layer with the external nonviscous flow. This phenomenon becomes more significant at low Reynolds numbers and high Mach numbers. Theoretical investigation of this interaction is difficult because of the presence of shock waves, which are characteristic of hypersonic velocities; the position and curvature of these shock waves depend on the state of the boundary layer developing in conditions of pronounced vorticity of the external flow. With increasing rarefaction of the flow, the problem begins to take on an elliptic character, and this necessitates the use of methods of investigation of more general form than the classical boundary-layer theory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 164–166, March–April, 1976.The authors thank V. G. Farafonov and V. N. Arkhipov for guidance and assistance in the work.     

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.