Boundary-layer separation criteria in the presence of suction

In order to estimate whether flow is separation-free, the boundary-layer separation criteria are used extensively. In this paper, such a criterion is derived for the case of a two-dimensional boundary layer on a heat-insulated surface in the presence of gas suction through a bounded section of the surface.     

Hypersonic flow past conical bodies

In [1, 2] Gonor considered the problem of imperfect inviscid gas flow about conical bodies at high supersonic speeds. The method of expansion in terms of a small parameter was used to obtain the solution. The small parameter used was the ratio of the densities in the free stream and behind the shock wave. However, this solution does not enable one to determine the velocity field in the vicinity of the cone surface.In the present paper, this problem is solved by the method described in [3], based on the use of the Poincaré-Lighthill-Ho method. The zero approximation is obtained, which is suitable throughout the entire flow region including the vortical layer. Outside of this layer, the solution transforms to the Gonor solution [1, 2].The author wishes to thank B. M. Bulakha for discussing the paper.     

Boundary-layer transition on a cylinder with and without separation bubbles

Boundary layer transition with and without transitional separation bubbles was investigated on a cylinder in cross flow. Measurements of the pressure distribution and hot-wire measurements within the boundary layer were carried out at two free-stream velocities and with different flow disturbances. The separation bubble reacts very sensitively to changes in inlet turbulence. Tollmien-Schlichting waves were observed in the separated shear layer just before transition, and their frequencies were in good agreement with stability theory. However, correlations concerning bubble length which were fitted using airfoil data are apparently not suitable for describing separation bubbles on cylinders. Finally, measurements in periodically disturbed flow show how the bubble reacts to this type of disturbance.     

Boundary-layer separation on a cooled body and interaction with a hypersonic flow

In previous papers, e.g., [1, 2], boundary-layer separation was investigated by analyzing solutions of the boundary-layer equations with a given external pressure distribution. In general, this kind of solution cannot be continued after the separation point. Study of the asymptotic behavior of solutions of the Navier-Stokes equations [3–5] shows that, in boundarylayer separation in supersonic flow over a smooth surface, the main effect on the flow in the immediate vicinity of the separation point is a large local pressure gradient induced by interaction with the external flow. The solution can be continued beyond the separation point and linked to the solutions in the other regions, located downstream [5]. Similar results for incompressible flow were recently obtained in [6]. We can assume that in general there is always a small region near the separation point in which separation is self-induced, and where the limiting solution of the Navier-Stokes equations does not contain unattainable singular points. However, this limiting slope picture can be more complex and can contain more regions where the behavior of the functions differed from that found in [3–6]. The present paper investigates separation on a body moving at hypersonic speed, where the ratio of the stagnation temperature to the body temperature is large. It is shown that both. for hypersonic and supersonic speeds the flow near the separation point is appreciably affected by the distribution of parameters over the entire unperturbed boundary layer, and not only in a narrow layer near the body, as was true in the flows studied earlier [3–6]. Regions may appear with appreciable transverse pressure drops within the zone occupied by layers of the unperturbed boundary layer. Similarity parameters are given, the boundary problems are formulated, and the results of computer calculation are presented. The concept of subcritical and supercritical boundary layers is refined, and the dependence of pressure coefficients responsible for separation on the temperature factor is established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 99–109, November–December 1973.     

Three-dimensional supersonic turbulent flows past conical bodies

The results of the numerical simulation of supersonic three-dimensional flow past sharp-nosed cones with circular and elliptic cross-sections in the turbulent shock-layer flow regime are presented. The calculations are performed in the local conical approximation using the system of Reynolds equations and the differential one-equation turbulence model. The numerical solutions are obtained by means of an implicit constant-direction finite-difference scheme. The emphasis is placed on the investigation of the transverse flow separation and the flow features associated with the turbulent flow regime. St.Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 99–105, January–February, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 99-01-00735).     

On the center of pressure of conical bodies

The profiles of conical bodies for which the position of the center of pressure in a supersonic flow with symmetry plane does not depend on the flow parameters are considered. The theoretical investigation of the aerodynamic characteristics of circular cones [1] has shown that their center of pressure does not depend on the angle of attack when the shock wave is attached to the apex of the cone. It was established experimentally in [2, 3] for star-shaped bodies that the position of the center of pressure for such bodies hardly changes in a wide range of Mach numbers and angles of attack.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 99–104, January–February, 1980.I thank G. G. Chernyi for discussing the results.     

Investigation of unsteady supersonic flow past conical bodies

A study is made of the three-dimensional supersonic flow of ideal gas past conical bodies executing harmonic oscillations in the plane of the angle of attack about some angle β₀ in accordance with the law α = α₀ cos ωt, so that the total angle of attack is β = β₀ + α₀ cos ωt.     

Effect of a conical separation region on cold gas-dynamic spraying

Results of an experimental and numerical study of the effect of conical separation regions artificially generated ahead of the target owing to impingement of a supersonic two-phase jet on the character of motion of particles smaller than 1 µm in diameter and on the process of cold gas-dynamic spraying as a whole are presented. Calculations predict a noticeable effect of the conical separation region artificially generated ahead of the target on the character of particle motion; in particular, the maximum velocity of the particle impact onto the target is found to be greater than that during spraying without the spike. Thus, the possibility of formation of a coating from particles smaller than 1 µm in diameter is demonstrated, and recommendations for implementation of the process in practice are given.     

Lifting bodies using the flow behind axisymmetric conical shock waves

One of the methods of designing aircraft with supersonic flight speeds involves solving an inverse problem by means of the well-known flow schemes and the substitution of rigid surfaces for the flow surfaces. Lifting bodies using the flows behind axisymmetric shock waves belong to these configurations. All lifting bodies using the flow behind a conical shock wave can be divided into two types [1]. Bodies whose leading edge passes through the apex of the conical shock wave pertain to the first type and those whose leading edge lies below the apex of the conical shock wave, to the second. For small apex angles of the basic cone at hypersonic flow velocities an approximate solution of the variation problem was obtained, which showed that the lift-drag ratio of lifting bodies of the second type is higher than that of the first [2]. The present paper gives a numerical solution of the problem for flow past lifting bodies of the second type using the flow behind axisymmetric conical shock waves with half-angles of the basic cone _S=9.5 and 18° The upper surfaces of the bodies are formed by intersecting planes parallel to the velocity vector of the oncoming flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 135–138, March–April, 1986.     

Shock layers over blunt and conical bodies in hypersonic non-equilibrium flow

It is well known that the flow-field over blunt and pointed bodies is sensitive to the non-equilibrium phenomena characteristic of high enthalpy hypersonic flows. Till date, most experiments and modelling were related to flows essentially dominated by the dissociation rate. However, in practical cases of a re-entry low density flow, the aerodynamic quantities such as the shock shape and location may also be strongly influenced by vibrational relaxation coupled with dissociation and chemical reactions. Thus, the flow about various bodies such as spheres, hemisphere–cylinders and cones is recomputed using a chemical model recently proposed by the authors and by taking into account the coupling between the vibrational relaxation and the chemical kinetics. Then, the computed shock shapes in air flow are compared to recent experimental results obtained in a ballistic range for flight velocities between 2,500 and 4,000 m/s, and in a shock tunnel for enthalpies close to 5 and 10 MJ/kg. The computed density field around hemispherical bodies is also compared to the experimental one. A good agreement, within 5%, between computed and measured results is observed. A few comparisons are also proposed with the results obtained with another well-known (empirical) model. A comparison is also made between the flow quantities along the stagnation line obtained over cylindrical and spherical bodies using the present model and those coming from a quasi-one-dimensional model recently developed, showing also a satisfactory agreement.     

Aerodynamics and static stability of star-shaped conical bodies in supersonic flow

The aerodynamics of conical bodies with a star-shaped cross section have been experimentally investigated over a broad range of variation of the parameters determining their geometry at a free-stream Mach number M=6. The position of the center of pressure of star-shaped bodies with an optimum trailing edge shape is investigated in relation to similarity parameters previously obtained theoretically. A correspondence is established between the derivatives of the normal force with respect to the angle of attack for pyramidal star-shaped bodies and bodies with the optimum trailing edge.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 142–150, November–December, 1992.     

Low frequency sound generated by flow separation in a conical diffuser

The sound field in a circular pipe generated by a concentric jet flow entering the pipe is studied. In the first case the air flow enters the pipe through a convergent nozzle only. In the second case a short diffuser is attached to the nozzle. When the diffuser half angle is small enough to ensure attached flow conditions, the sound pressure level in the duct is reduced over the entire frequency range measured. When the diffuser angle is increased up to the point where flow separation occurs, an increase in the duct sound pressure level is observed. It is shown by means of cross-correlation measurements involving the unsteady wall pressures in the diffuser and the sound pressure in the duct that the increased sound levels are in fact caused by the flow separation in the diffuser.     

On coalescence of frequencies and conical points in the dispersion spectra of elastic bodies

In this paper we discuss a general procedure for determining the critical points of the dispersion spectrum at which there is a coalescence of frequencies, i.e. critical points which are roots of double multiplicity. We further show how the general behavior of the dispersion surface in the neighborhood of the critical points can be determined analytically. For the purpose of illustration, we consider (a) plane waves propagating in an infinite, elastic, isotropic plate, which corresponds to the case of a differential equation with constant coefficients, and (b) Floquet waves of the SH-type propagating in a layered, elastic medium, which corresponds to the case of a differential equation with periodic coefficients.