Some aspects of calculating subsonic flow over wings of complex planform

The use of wings of complex planform is characteristic of the present stage of development of aviation; with discontinuities along the leading and trailing edges; with curved edges; with variable geometry (by pivoting the wing panels). This article considers some aspects of the calculation of the over-all and distributed aerodynamic characteristics of such wings for low and high subsonic velocities. The methods, based on the lifting surface scheme and the use of discrete vortical singularities, enable quite efficient and reliable digital computation of the flow about these wings at moderate angles of attack. For steady motion of the wing a further development of the method of [1] is obtained, for harmonic oscillations an extension of [2] is obtained, and for aperiodic motions of the wing and gust inputs a modification of the method of [3] is found.The author wishes to thank T. M. Muzychenko and N. G. Lavrenko for carrying out the calculations of the examples.     

Numerical modeling of supersonic flow over wings with varying aspect ratio on a broad range of angles of attack using the law of plane sections

A method and a program based on it for solving the problem of flow in the neighborhood of bodies of different shapes introduced into a high-supersonic stream at arbitrary angles of attack are proposed. The equations of the law of plane sections are integrated by Godunov's method. It is shown that the region of applicability of Sychev's theory is much broader than indicated in [1].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 113–120, March–April, 1992.     

Supersonic flow over delta wings and elements of star-shaped bodies at angles of attack and roll

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 81–87, January–February, 1989.     

Calculation of supersonic flow around v-shaped wings by the fitting method

The problem of flow around a V-shaped wing with supersonic leading edges is solved. The method employed is that of fitting with respect to a space variable in which the system of equations of motion is hyperbolic, using the computing scheme of V. V. Rusanov, A comparison between the results of these calculations and experimental data in relation to the pressure distribution along the wing span reveals excellent agreement, except for a limited region, in which the compression jump incident on the plane of the wing interacts with the boundary layer. A comparison between the results obtained by means of the oblique-jump equations and by numerical calculations indicates that the method in question is reasonably accurate.Translated from Izvestiya Akademu Nauk SSSE, Mekhanika Zhidkosti i Gaza, No. 3, pp. 180–185, May–June, 1971.The author is grateful to A. L. Gonor and V. V. Rusanov for interest in this work.     

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.     

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。     

Calculation of perfect gas flows around elliptic cones at large angles of attack

In [1] it was suggested that for large angles of attack there is formed near the lower surface of a conical body with a smooth transversesection contour a closed (quite limited) region of ellipticity of the conical flow equations. To calculate the mixed transonic gas flow in this region use was made of the method of straight lines, previously used extensively for the solution of other gasdynamic problems [2], Using this method, on some line located entirely in the region of hyperbolicity of the equations, we determined all the gasdynamic quantities which may then be used as the initial data for continuing the calculation in the transonic region. The calculation in the hyperbolic equation region was continued by the method of characteristics. About forty versions were calculated for the flow about elliptic cones, including circular, in a supersonic perfect gas stream at angles of attack from 30 to 50°.The article then discusses the method of characteristics in the form used for the calculations. (All the equations of the method of lines are given in [1].) Also presented are newly obtained formulas for the inclinations of the surfaces of the constant-velocity modulus and constant transverse-flow Mach number on the conical shock wave. Calculation results are presented and these demonstrate basically the qualitative characteristics of the flow about sharp elliptic cones at large angles of attack.     

Design of a separation-free airfoil with outer-flow suction over a certain range of angles of attack

The problem of the design of an airfoil with slot air suction from the outer flow for a prescribed velocity distribution over the airfoil contour that ensures the absence of flow separation over a given range of angles of attack is formulated and solved. The proposed combined numerical and analytical method of airfoil design within the framework of the inviscid incompressible fluid model is based on the theory of inverse problems of aerohydrodynamics. Separationless flow past the airfoil is achieved by eliminating the falling velocity intervals from the specified velocity distribution in two given flow regimes. The flow past an airfoil with outer-flow suction is determined not only by the angle of attack as for an impermeable airfoil but also by the value of the suction mass flow. The slot is modeled by an annular channel with constant velocities on the walls. To satisfy the problem solvability conditions, free parameters are introduced into the initial velocity distribution. Examples of airfoil design are given. Kazan, Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 185–191, July–August, 2000.     

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.     

Passage of a subsonic flow around V-shaped wings

In view of the problems involved in the design of hypersonic aircraft great interest has arisen in recent years as to the behavior of wings in fast supersonic flows. Two main approaches have been used: a study of hypersonic flow around traditional wings, and a search for new configurations with optimum aerodynamic properties. Aerodynamic [1, 2], heat-transfer [3], and stability investigations (for V-shaped wings in super- and hypersonic flows) belong to the latter category. Before attaining supersonic flight the aircraft has to overcome the range of subsonic velocities. In this connection it is important to study flow around V-shaped wings at M < 1. Little research has been devoted to flow around such configurations at subsonic velocities, principal attention having been directed at the study of rapid flow around aircraft configurations with V-shaped wings or tails. The results of analytical and numerical calculations allowing for the interference of transient aerodynamic forces acting on a V-shaped and mutiple-fin tail group in combination with the fuselage were presented in [4, 5]. An experimental study of V-shaped wings as regards the influence of the wing dihedral angle on the aerodynamic characteristics of a model aircraft was presented in [6, 7].Translated from Zhurnal Prikladnoi Mekhaniki i Technicheskoi Fiziki, No. 4, pp. 102–106, July–August, 1975.     

Design of a two-element airfoil in a range of angles of attack

A numerical-analytical solution of an inverse boundary-value problem of aerohydrodynamics is obtained for a two-element airfoil in the full formulation, based on the velocity distribution defined on the sought airfoil contours in a range of angles of attack. It is demonstrated that flow separation does not occur in the entire range considered for a specified non-separated velocity distribution on the upper surfaces at the maximum angle of attack and on the lower surface at the minimum angle of attack. An example of constructing a sectional airfoil is given; verification of the results obtained is performed with the use of the Fluent software package. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 107–114, November–December, 2008.     

Design of airfoils providing the absence of separation in a compressible flow in a specified range of angles of attack

A problem of modification of the classical airfoils that ensure the absence of separation in a subsonic ideal-gas flow in a specified range of angles of attack is solved by a numerical-analytical method based on the quasi-solution of inverse boundary-value problems of aerohydrodynamics and Kármán-Jiang formulas. Loitsyanskii’s criterion of the non-separated flow is used to determine the boundary-layer separation point. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 99–106, November–December, 2008.     

Design of airfoils stall-free on a given range of angles of attack

A general formulation of the inverse boundary-value problem of aerohydrodynamics for v(s) is given for two angles of attack. This formulation includes that given in [10] as a particular case. An integral representation of the solution is constructed, and the conditions of consistency of the initial data and the solvability conditions are written down. For satisfying the latter the method of quasisolutions of inverse boundary-value problems [11, 12] is employed. A criterion is obtained for the absence of boundary layer separation as the angle of attack varies over a given range. This criterion is expressed in terms of the velocity distributions for the limiting positions. A method of specifying hydrodynamically expedient velocity distributions that takes into account the nonstalling conditions obtained is proposed. Questions of lift maximization are considered. The results of numerical calculations are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 157–164, May–June, 1990.The authors are grateful to G. Yu. Stepanov and N. B. Il'inskii for their constant interest and useful comments.     

Numerical investigation of three-dimensional laminar boundary layer flow over spheroids at angles of attack

The flow in the laminar boundary layers on spheroids with axial ratios of 611 (prolate ellipsoid of revolution) and 616 (circular wing) at angles of attack of 5 and 10° is investigated numerically. The implicit finite-difference method described in [1] is employed. The results obtained are compared with the measurements reported in [2–4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 59–68, November–December, 1990.