The flow structure near the windward side of V-shaped wings with an attached shock wave on the leading edges

The results of a numerical calculation of a symmetric flow of supersonic gas with the Mach number M=3 past the windward side of V-shaped wings with an opening angle =40° and apex angles =30, 45, and 90° are given. The possibility of the ascent of one or two Ferri points from the break point of the transverse contour of the wing is discovered and explained. It is shown that conical flow near wings of finite length need not exist in flow regimes corresponding to angles of attack at which a Ferri point ascends, while at angles of attack smaller and larger than a certain interval, conical flow will exist. The investigation is conducted by means of a numerical method of stabilization with an artificial viscosity. The longitudinal coordinate, relative to which the steady system of equations is hyperbolic, played the part of the time variable, usual for methods of stabilization. The numerical method constructed using the scheme of [1] is described in [2] and was successfully applied to the calculation of different regimes of supersonic flow past conical wings with supersonic leading edges [2–6]. In. the present investigation the calculation algorithm of [2] is modified and makes it possible to realize motion with respect to the parameter a, this being particularly important for the stabilization of the solution in the calculation of flow regimes for which regions with a total velocity Mach number close to unity arise in the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 122–131, January–February, 1986.     

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.     

Simulation of the aerodynamic drag of three-dimensional star-shaped bodies at hypersonic velocities

The domain of the parameters in which the aerodynamic drag of hypersonic pyramidal bodies, whose wave component is calculated within the framework of conical flows with the boundary layer displacement thickness taken into account, agrees satisfactorily with the experimental data is found. The calculation model is also applicable in the region of minimum aerodynamic drag of star-shaped bodies in the class of conical bodies equivalent in length and mid-sectional area.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 69–79, September–October, 1996.     

Separated flow over a strongly cambered conical wing at small angles of attack

The interference of supersonic flows on the concave surface of conical wings was experimentally investigated in [1] for various values of the camber and angles of attack. In order to establish the detailed structure of the interference flow the laminar flow past a wing model in the form of half the surface of a circular cone with vertex angle 2_k = 34° was numerically modeled within the framework of the quasiconical approximation for the three-dimensional Navier-Stokes equations [2]. Under this assumption, confirmed by analysis of the experimental data [1], it was found that the displacement of the external inviscid flow as a result of intense flow separation beyond the leading edges leads to flow patterns similar to those realized on V wing's with a break in the transverse contour [3]. At nonzero angles of attack weak secondary separation was detected beneath the flattened regions of primary separation located in the shaded parts of the concave surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 130–136, July–August, 1989.     

Aerodynamic characteristics of star-shaped bodies at Mach numbers M = 3–5

The results are given of an experimental investigation into the aerodynamic characteristics of star-shaped bodies with flat faces at Mach numbers M = 3–5 and angles of attack = 0–12 ° for different numbers of points of the star and different inner radii at the midsection. It is established that the star-shaped bodies have a much lower total drag than bodies of revolution of equivalent length and midsection area.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 88–93, July–August, 1981.     

Effect of longitudinal riblets on the aerodynamic characteristics of a straight wing

The results of balance aerodynamic tests on model straight wings with smooth and ribbed surfaces at an angle of attack =–4°–12°, Mach number M=0.15–0.63, and Reynolds number Re=2.4·10⁶–3.5·10⁶ are discussed. The nondimensional riblet spacings ⁺, which determines the effect of the riblets on the turbulent friction drag, and the effect of riblets on the upper and/or lower surface of a straight wing on its drag, lift, and moment characteristics are estimated.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 33–38, March–April, 1995.     

A three-dimensional variational problem in the gasdynamic theory of a lubricant

In [1–3] optimal forms of the gap were found for one-dimensional aerodynamic sliding bearings. The coefficient of the bearing capacity is optimized under the condition that the one-dimensional Reynolds equation of a gas lubricant is used to determine the pressure in the bearing. In the present article the three-dimensional problem of finding the optimal profile of an aerodynamic sliding bearing in the case of small compressibility numbers is considered. The problem is solved by the methods of variational calculation. A qualitative investigation is made of the form of the optimal profile, the results of which are confirmed by a numerical solution of a system of Euler-Lagrange equations. The results of the calculations are given for different elongations of the bearing. On the basis of the profiles obtained, optimal profiles with a rectangular pocket, which are more practical to fabricate, are found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 34–39, September–October, 1975.     

Computer calculation of aerodynamic characteristics of aircraft at supersonic velocities

A previous study by one of the present authors [1] listed a number of works dedicated to calculation of aerodynamic characteristics of aircraft of complex physical construction at supersonic velocities. A method for calculating the flow around a system of small-scale bearing surfaces was developed. The method reduces to determination of the velocity potential with subsequent differentiation to determine pressure. The present study will present a method of calculating stationary aerodynamic characteristics of aircraft of extensive size at supersonic velocities, in which the basic unknown function is the perturbed pressure p. Eliminating numerical differentiation from the calculation permits an increase in accuracy of the results obtained. The problem is solved for an entire airplane with consideration of the craft's thickness.Translated from Ivestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 96–102, May–June, 1978.     

Choking of ideal-gas flow in convergent nozzles and integral nozzle characteristics

The results of a numerical and theoretical investigation of the local and integral characteristics of convergent nozzles are presented. It is shown that self-similar (choked) nozzle flow, when the gas flow rate does not depend on the external pressure, may occur at subcritical values of the pressure ratio _c . If the nozzle contour consists of the contour of the conical nozzle and the convergent part corresponds to the boundary of the emerging jet, then on a certain interval of _c this nozzle will have a higher thrust coefficient than the initial conical nozzle.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 149–157, November–December, 1994.     

Flow around λ wings with a bend in the leading edge

In recent years a considerable number of studies have been published on flow around wings at high supersonic velocities. The researches have been conducted in two directions: there are studies of hypersonic flow around wings of traditional shape and a search is carried out for new types of lay-out which possess optimal aerodynamic characteristics. The second direction relates to the numerous studies of flow around wings with shaped transverse cross sections [1–7]. The calculation of the aerodynamic quality of a shaped delta wing composed of plane surfaces on the basis of the relationships on an oblique shock [1, 2], from the results of experiments on the pressure distribution and from weight tests [3, 4], showed that the shaped wing has a higher quality than the plane delta wing.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 171–175, January–February, 1985.     

Behavior of sonic lines in a shock layer behind a detached shock wave

A numerical investigation is made into the formation of local supersonic zones in the subsonic flow region between a detached shock wave and the surface of the body in the case of supersonic three-dimensional flow over conical bodies with opening angle _k = 120 ° of the cone in the range of Mach numbers M = 2.5–15.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No.4 pp. 143–145, July–August, 1979.We thank G. I. Petrov for suggesting the problem and for helpful advice and O. M. Belotserkovskii for constant interest in the work.     

Influence of temperature factor on the aerodynamic characteristics of a circular cylinder in a supersonic perfect gas flow

The flowfield and aerodynamic characteristics of a circular cylinder at Mach number M=5 and zero yaw angle are calculated using Navier-Stokes equations. Calculations were carried out at several Reynolds numbers for both thermally insulated and isothermal surfaces; in the latter case the temperature factor was varied.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 156–162, May–June, 1994.     

Asymptotic model of the axisymmetric breakdown of a vortex filament in an incompressible fluid

The axisymmetric flow of an incompressible fluid is considered. An exact solution of the Euler equations corresponding to the breakdown of a straight vortex filament of intensity ₀ into a vortex filament of lesser intensity and a conical vortex surface is obtained. It is shown that beyond the breakdown point in the region bounded by the conical vortex surface reverse flows occur. An investigation of the problem with allowance for viscous effects at large Reynolds numbers makes it possible to establish a relation between the free parameters entering into the solution of the Euler equations. The results obtained are useful for investigating the problem of the breakdown of a swirled jet, whose solution has recently been receiving much attention [1, 2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 47–52, November–December, 1989.     

Investigation of diffuser characteristics in an aerodynamic shock tube

An investigation has been made in an aerodynamic shock tube, with M=8, of the diffuser starting with variable Reynolds numbers, and its throttle characteristics have been recorded. The results obtained enable conclusions to be made regarding the possibility of investigating diffusers in such types of tubes. In [1] the possibility of, in principle, determining the throat starting of a diffuser in an aerodynamic shock tube, and the time to establish flow in the diffuser channel, which was 300 sec, was measured. This paper is devoted to the further investigation of diffuser operation with variable Reynolds numbers, and to determining the throttle characteristics, in particular, the total pressure reduction coefficient.Moscow. Translated from Izvestiya Akademii Nauk SSSR, mekhanika Zhidkosti i Gaza, No. 1, pp. 156–161, January–February, 1972.     

Pressure pulsations on the surface of a sphere in a subsonic stream

Many data are available on the drag C_x and the distribution of the static pressure over the surface of a sphere [1, 2]. However, there are virtually no data on pulsations of the pressure over the surface of a sphere. In the present paper, the results are given of an investigation of the total and spectral levels of the pressure pulsations at different points of the surface of a sphere at M 0.5–1.0 and Re (1.7–2.7)·.10⁶. It was found that the strongest pressure pulsations occur on the side in the region of the angle 90°. In this region at M 0.6–0.8 the relative total level o/q where q is the velocity head in the oncoming stream, reaches values 0.18–0.22. It was established that at M = 0.7–0.9 narrow-band maxima occur in the spectra of the pressure pulsations at frequencies Sh fD/V = 0.2–0.3. Data are also presented on the pulsations of the base pressure behind a spherical segment with short cylindrical and conical trailing edges.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 164–168, September–October, 1981.     

Stresses in a conical tube under sudden loading

The paper considers a thickwalled long conical tube from an ideal plastic material whose inner surface is suddenly subjected to timeconstant, uniformly distributed pressure or is given a velocity. An idealplastic zone propagates from the inner conical surface. It is assumed that the material of the tube is incompressible in both the elastic and plastic zones. The plastic material obeys the Houber–Mises plasticity condition.     

Numerical investigation of nonequilibrium flows of mixtures of fusible metal particles and gases in a laval nozzle

There are numerous papers [1–11] on the determination of the parameters of condensed oxide particles which are formed during combustion of metallized fuels. The ambiguity, and sometimes the contradictoriness, of the test results obtained [3–5, 9–11] indicate the difficulties in conducting correct experimental investigations. In this connection, numerical studies using mixtures of calibrated liquid-metal particles and different gases are of practical interest. Different probes can be calibrated by using calibrated two-phase flows, the two-phase flow around models and probes can be studied, as can the interaction between liquid-metal particles and the front of an aerodynamic compression shock, their intrusion in different entraining media, the interaction between fine particles (particle-projectiles) and large size particles (particle-targets), etc. In many cases, the prehistory of the flow and the parameters of the gas mixture with the particles in the area of the nozzle exit section must be known to investigate the above-mentioned phenomena. The parameters of different nonequilibrium flows of mixtures of gallium particles and gases in a Laval nozzle are investigated numerically in this paper; the maximum diameter (upper boundary of the spectrum) of the particles (d_s = 30 ) which are not destroyed in the nozzle under the effect of the aerodynamic forces and are suitable for use in a calibrated two-phase stream is determined. The computations were carried out in a one-dimensional approximation according to [12–14].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 86–91, March–April, 1976.The authors are grateful to V. K. Starkov and U. G. Pirumov for discussing the results of the research and to N. M. Alekseev for aid in constructing the graphs.     

Determination of specific thrust in unchoked regimes and design of a separationless convergent nozzle contour

The variation of the specific thrust R_Y on the angle of inclination of the wall is analyzed within the framework of the ideal gas model using the results of specific impulse and flow rate calculations for conical convergent nozzles. It is shown that in unchoked regimes nozzles with different have almost the same values of R_Y for both subcritical and supercritical pressure ratios _c. On the interval _C < 6 typical of convergent nozzles conical convergent nozzles with =30–90° have almost the same value of the specific thrust, maximal relative to the R_Y of nozzles with < 30°. In the presence of viscosity forces local boundary layer separation may occur in the neighborhood of the entrance section of the convergent nozzle. A method of constructing a separationless convergent nozzle contour with enhanced thrust is developed on the basis of a boundary layer separation criterion. The separationless contour is determined for given values of the flow rate, specific heat ratio, Reynolds number, wall temperature and initial boundary layer displacement thickness.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 158–164, January–February, 1990.     

Numerical investigation of laminar separation in the case of supersonic flow of viscous gas past spiked bodies

The complete Navier-Stokes equations for a compressible viscous perfect heat conducting gas have been used in a numerical investigation of laminar separation in the case of supersymmetric axisymmetric flow past cylinders with a conical nose and a spike at the front of finite thickness. The flow structure has been studied in its dependence on the length of the spike and the half-angle of the conical tip. For the considered free-stream parameters (2 M 6, 100 Re 500) and spike lengths, which do not exceed the diameter of the cylinder, the existence of steady flow regimes has been established and it has been shown that the spike in front of the body reduces its total drag and the heat flux to its surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 126–131, March–April, 1984.     

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.