Optimum form of lifting bodies at hypersonic speeds

The variational problem of the form of bodies with minimum drag for given lift force, volume, and other constraints in general leads to a second-order partial differential equation even for the simplest methods of drag calculation (Newton law and averaged friction coefficient). The solution of this equation is not justified; in its place an approximate solution is suggested which consists of: a) selection of a scheme characterized by certain parameters which are determined from the solution of the extremal problem, b) determination of the optimal surface form for the selected scheme with the aid of the system of ordinary Euler equations. This paper presents a comparison of the body schemes with minimum drag and maximum L/D and presents the solution of several variational problems.At the present time we have quite complete information on the form of minimum-drag bodies for zero lift (nonlifting bodies), and both approximate and quite rigorous methods are known for solving the corresponding variational problems. This cannot be said at all of the form of lifting bodies, for which the requirements are numerous, differing essentially for vehicles of different application, and are generally not limited to a single flight regime. Account for all the mandatory requirements in solving the variational problems is not possible; therefore in the majority of cases these solutions do not yield answers which are directly suitable in practice; rather they yield limiting estimates.The natural tendency to utilize for lifting bodies the axisymmetric form which is customary for nonlifting bodies leads to the study of axisymmetric bodies at angle of attack, axisymmetric bodies with skewed base, sections of axisymmetric bodies cut by planes, etc. In order to obtain a broader view of the optimum forms of lifting bodies we must, obviously, drop the limitation to axisymmetric bodies and bodies with similar cross sections. However, in the case of an arbitrary extremal surface the Euler equation is a second-order partial differential equation, and its simple solution is difficult. In practice it seems wise to solve those variational problems whose Euler equation may be reduced to a system of ordinary differential equations. Therefore, we propose the following method for selecting the optimum forms: a) we select a scheme, a form, which is formed by a set of planes and cylindrical, conical, spherical surfaces and which is defined by parameters that are found from the solution of the extremal problem; b) for the selected scheme the generators of the scheme surface are found from the solution of the variational problem.For the calculation of the air pressure on the body surface we use the empirical Newton law, which yields in the majority of cases results which are very close to the results of the more rigorous methods.It is assumed that the pressure may vanish only at the trailing edge of the body. The frictional drag coefficient, averaged over the body surface, is assumed to be independent of the body shape. In the case of a body of simple form the hottest portion is the frontal portion and account for the thermal protection requirements reduces to the selection of suitable dimensions of this portion of the body. In the general case the problem is stated as follows: find the form of the minimum-drag body for a given lift force, volume, length, and other conditions. To the particular case of the body with maximum L/D corresponds the value of the Lagrange multiplier =–1/k.All the results of calculations presented in the paper are intended only to illustrate the method. After the present paper was submitted for publication, another study [3] appeared which also proposes a method for determining the optimal parameters.     

Supersonic flow past a cylindrical body with transverse jets at large angles of attack

Supersonic flow past a cylindrical body with a system of transverse jets ejected from its surface at angles of attack α=60–120^o is characterized by a complicated gasdynamic flow pattern [1]. The body surface is affected by both the oncoming flow and the ejected jets which shield a portion of the surface from the external flow. This results in considerable transverse and longitudinal pressure gradients appearing on the body surface. The experimental pressure distributions over a cylindrical model with four transverse jets at a Mach number M=4 and α=60°, 90°, and 120° make it possible to study the specific features of the flowfield and derive correlations for the "jet obstacle" dimensions. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 179–183, January–February, 1998.     

Optimum shape of lifting bodies for hypersonic velocities

An attempt is made at solving the variational problem as to the shape of the body possessing a maximum aerodynamic quality, without using some of the simplifying assumptions proposed earlier [1–4]; an attempt is also made to discover the effect of blunted leading edges on the parameters of the optimum bodies.Kazan'. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 82–86, January–February, 1972.     

平板大攻角绕流升力和阻力系数的计算

二维平板或二维对称薄翼型大攻角绕流升力和阻力系数与攻角之间存在的函数关系一般用数据表格的形式给出。本文根据垂直平板绕流阻力实验数据和对称薄翼型全攻角绕流实验数据,分析得到了平板大攻角绕流总压力及其升力分量和阻力分量系数的近似计算公式。结果表明：平板总压力系数约等于攻角正弦值的2倍;总压力的阻力分量系数约等于攻角正弦值平方的2倍;升力分量系数约为攻角2倍的正弦值。计算结果与两组试验数据具有较好的一致性。     

Supersonic flow past circular cones at large angles of attack

Flow past sharp-nosed circular cones is investigated for a broad range of freestream Mach numbers M>1 and cone half-angles _c at angles of attack from zero to the value at which conical flow breaks down. Several new results are obtained with regard to the position of the Ferri point, the shape of the local supersonic zones and internal shock wave, and the nonmonotonicity of the windward shock slope as a function of the angle of attack. The existence of flow regimes in which the radial velocity on the windward side is directed toward the apex of the cone is demonstrated. The investigation is carried out numerically with relaxation of the solution in a fictitious time coordinate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 6, pp. 79–84, November–December, 1973.     

Numerical analysis of heat transfer on the surface of a delta wing in a hypersonic air flow at large angles of attack

The heat transfer on a delta wing with blunt edges and various catalytic surface properties in a hypersonic air flow at 40 ° and 60 ° angles of attack has been investigated by a numerical flow model for a viscous reacting gas in the shock layer near the windward side of blunt elongated bodies.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 196–199, September–October, 1984.     

Heat transfer to blunt-edged swept wings at angle of attack in hypersonic flow

An approximate analytic solution is obtained for the relative heat fluxes on the lateral surface of swept wings of infinite span in a hypersonic viscous gas flow at angles of attack and yaw. The accuracy of the relations obtained is estimated on the basis of a comparison with numerical solutions. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 170–179, July–August, 1994.     

Hypersonic flow over a narrow delta plate at large angles of attack

The problem of hypersonic flow over a flat delta plate with a high sweepback anglex at angles of attack close to /2 is solved using a numerical algorithm based on transition to the conical solution. The existence of conical flow at /2 with the velocity vector directed towards the apex of the plate is established. Values ofC _p/sin² and the thickness of the shock layer in the plane of symmetry of the plate are given as functions of the hypersonic similarity parameterk=tan tanx. A comparison of the calculated and experimental data shows that they are in good agreement.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 183–185, September–October, 1992.     

Asymmetric vortices flow over slender body and its active control at high angle of attack

The studies of asymmetric vortices flow over slender body and its active control at high angles of attack have significant importance for both academic field and engineering area. This paper attempts to provide an update state of art to the investigations on the fields of forebody asymmetric vortices. This review emphasizes the correlation between micro-perturbation on the model nose and its response and evolution behaviors of the asymmetric vortices. The critical issues are discussed, which include the formation and evolution mechanism of asymmetric multi-vortices; main behaviors of asymmetric vortices flow including its deterministic feature and vortices flow structure; the evolution and development of asymmetric vortices under the perturbation on the model nose; forebody vortex active control especially discussed micro-perturbation active control concept and technique in more detail. However present understanding in this area is still very limited and this paper tries to identify the key unknown problems in the concluding remarks. The project supported by the National Natural Science Foundation of China (10172017), Aeronautical Science Foundation of China (02A51048) and Foundation of National Key Laboratory of Aerodynamic Design and Research (51462020504HK0101)     

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.