Conical wing of maximum lift-drag ratio in a supersonic gas flow

The calculation of supersonic flow past three-dimensional bodies and wings presents an extremely complicated problem, whose solution is made still more difficult in the case of a search for optimum aerodynamic shapes. These difficulties made it necessary to simplify the variational problems and to use the simplest dependences, such as, for example, the Newton formula [1–3]. But even in such a formulation it is only possible to obtain an analytic solution if there are stringent constraints on the thickness of the body, and this reduces the three-dimensional problem for the shape of a wing to a two-dimensional problem for the shape of a longitudinal profile. The use of more complicated flow models requires the restriction of the class of considered configurations. In particular, paper [4] shows that at hypersonic flight velocities a wing whose windward surface is concave can have the maximum lift-drag ratio. The problem of a V-shaped wing of maximum lift-drag ratio is also of interest in the supersonic velocity range, where the results of the linear theory of [5] or the approximate dependences of the type of [6] can be used.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 128–133, May–June, 1986.We note in conclusion that this analysis is valid for those flow regimes for which there are no internal shock waves in the shock layer near the windward side of the wing.     

Nonequilibrium hypersonic flow of gas past a wing of small aspect ratio

It is well known [1] that nonequilibrium physicochemical processes taking place in gases at high temperature influence the gas-dynamic parameters and aerodynamic characteristics of bodies in hypersonic flight. In the present paper, the thin shock layer method [2–4] is used to consider the problem of nonequilibrium hypersonic flow of gas past a wing of small aspect ratio at an angle of attack. It is shown that the flow component of the vorticity is conserved along the streamlines, and this property is exploited to obtain an analytic solution of the equations of the three-dimensional nonequilibrium shock layer. The influence of the disequilibrium on the thickness of the shock layer and the pressure distribution is investigated.     

On the theory of a wing with small aspect ratio in a hypersonic flow

A study is made of flow over three-dimensional wings of small aspect ratio with shape close to that of a flat delta-shaped wing. The obtained results make it possible to estimate the influence of the plan shape of the leading edge and the curvature of the wing on the pattern of the flow over its windward surface and on the corresponding gas-dynamic functions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 112–117, July–August, 1980.     

Effect of blowing on supersonic dust-laden gas flow round a blunt body

One of the main problems which arise in the design of high-speed aircraft is the protection of the streamline surfaces against the erosion effect of solid particles and drops occurring in the free stream. For this purpose it is possible to use the device of blowing cold gas. This leads to the formation of a boundary layer of high density in which the particles are decelerated [1]. The present study investigates the effectiveness of this method of erosion protection in the example of supersonic flow round a sphere.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 178–181, March–April, 1986.     

Effect of fluid boundaries on flow around a low-aspect ratio wing

Large eddy simulation is applied to investigate flow around a finite-aspect-ratio wing in motion in a stratified fluid in different positions. It is shown that the wing position relative to a pycnocline has a considerable effect on the hydrodynamic wake development and the internal wave structure.     

Effect of nose shape on hypersonic flow past slender blunt bodies at an angle of attack

We examine some characteristics of hypersonic flow past slender blunt bodies of revolution at a small angle of attack 1, where is the relative body thickness. It is shown that, within the framework of hypersonic theory, for a correct-consideration of the effect of the conditions in the transitional section between the nose and the lateral surface it is necessary, in the general case, to specify the circumferential distribution of the force effect for the nose and the mass of the gas. For small , the effect of the nose, just as in two-dimensional flows [1–4], shows up only through its drag coefficient c_x, for =0. On this basis, the similarity law [1–4] for flow past such bodies, with arbitrary form of the lateral surface and differing in the shape of the nose blunting, which is valid over the entire disturbed region, with the exception of a small vicinity of the nose, is extended to the case in question.The notation r₀ and L maximum nose radius and characteristic body length - V, M, and density, velocity, Mach number, and adiabatic exponent of the gas in the approaching stream - , V²i, and V²p density, enthalpy, and pressure - x, r, and coordinate system of the cylindrical body with its center at the transitional section between the nose and the side surface - Vu, Vv, and Vw corresponding velocity components     

Aerodynamic characteristics of a delta wing in hypersonic flow

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 2, pp. 66–69, March–April, 1994.     

Determination of the vorticity on a wing of small aspect ratio in a hypersonic stream

The theory of a thin shock layer [1–3] is used to obtain a formula for calculating the component of the vorticity in the direction of the flow on a wing of small aspect ratio in a hypersonic gas stream. It is shown that for definite shapes of the wing and flow regimes zones may occur with large local values of the vorticity, which, as is well known, have a significant influence on the structure of the flow field.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–178, September–October, 1980.     

Rarefied gas flow near the forward stagnation point of a blunt body at hypersonic speeds

With reduction of the density in a hypersonic stream the transition of the flow from continuum to free molecule takes place gradually. The transition region may be divided into several regimes, in each of which a definite physical phenomenon is most significant. For the case of the flow in the vicinity of the forward stagnation point of a blunt body these phenomena include increase of the thickness of the detached shock wave and of the boundary layer, the presence of viscous flow in the entire disturbed layer ahead of the blunt body, reduction of the number of collisions between molecules and the associated relaxation effects, the increasing role of the interaction of the stream molecules with the surface, and the phenomena of slip and temperature jump.     

Stagnation region of a blunt body in two-phase hypersonic flow

The fluid-mechanics equations of a two-velocity, two-temperature medium are used to investigate flow near the stagnation point of a blunt body washed by a hypersonic stream of gas containing solid or liquid deformed particles. The effect of particles of the gasdynamic flow parameters is analyzed. A relaxation layer was found to occur near the body, with marked changes in the gas parameters. It is shown that the presence of particles in the flow reduces the shock stand-off distance. The results of computations on the dynamics and heating of particles in the shock layer are discussed. A solution in finite form is obtained in the limiting case of fine particles by the method of asymptotic expansions. The motion of solid or liquid particles in hypersonic shock layers has been the subject of several papers [1–6], in which particle dynamics was examined, assuming that the particles have a negligible influence on the gasdynamic flow parameters. The solutions obtained are therefore limited to the case of low mass particle concentration in the incident flow. A numerical solution not subject to this limitation was obtained in [7] for supersonic two-phase flow over a wedge.     

Shock wave interference on a fenced wing at hypersonic speeds

High-pressure zones on the wing, created by the reflected shocks, are experimentally demonstrated and their influence on the aerodynamic characteristics of the wing is investigated.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 135–140, May–June, 1992.The authors are grateful to V. E. Mosharov, V. N. Tarasov, and V. I. Plyashechnik for assisting with the experiments.     

Optimization of the shape of a wing in a hypersonic nonequilibrium gas flow

A variational technique of obtaining the optimal shape of a low-aspect-ratio wing with allowance for the nonequilibrium character of the flow is developed. The technique is applied to the problem of determining optimal wing shapes under terrestrial atmosphere conditions. The real-gas effect on the optimal shapes and maximum lift-drag ratio is studied. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 160–170, March–April, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 96-01-00629).     

Calculation of the viscosity effect on the aerodynamic characteristics of slender bodies at hypersonic flow velocities

Approximating dependences of the local coefficients of friction, heat transfer, and pressure induced by a boundary layer on the generalized similarity parameters, including the inviscid flow characteristics, are obtained on the basis of the results of a numerical calculation of hypersonic flow past a number of plane and axisymmetric bodies. If the inviscid flow characteristics are known, these relations can be used to take the viscosity approximately into account under conditions of interaction between the laminar boundary layer and the hypersonic inviscid stream [1].Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 142–150, July–August, 1995.