Visual study of the three-dimensional flow diagram around a delta wing in a subsonic stream

Experimental methods, particularly visualization methods, permit a sufficiently detailed representation of the flow around bodies of complex shape, whose analysis meets with a considerable number of difficulties. The flow around a delta wing in the 1–90-m/sec free-stream velocity range is studied in this paper by using three-dimensional visual methods. Since stream separation and vortex-system formation play the main role in the flow formation over a wing surface, the main purpose of the experiment was to trace the physical process of dynamic development of the flow resulting in separation and vortex formation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 190–194, March–April, 1976.     

Hypersonic flow past a wing at large angles of attack with detached shock wave

The thin shock layer method [1–3] has been used to solve the problem of hypersonic flow past the windward surface of a delta wing at large angles of attack, when the shock wave is detached from the leading edge (but attached to the apex of the wing) and the velocity of the gas in the shock layer is of the same order as the speed of sound. A classification of the regimes of flow past a delta wing at large angles of attack has been made. A general solution has been obtained for the problem of three-dimensional hypersonic flow past the wing allowing for nonequilibrium physicochemical processes of thermal radiation of the gas at high temperatures.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 149–157, May–June, 1985.     

Supercritical regimes of hypersonic flow past a planar yawed delta wing

Hypersonic viscous perfect gas flow past a planar delta wing in the viscous-inviscid interaction regime is considered. The effect of the yaw angle on the parameters of the laminar boundary layer on the cold wing and the formation of subcritical and supercritical flow regions is studied.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 151–158, July–August, 1995.     

Numerical solution of the problem of the flow of a supersonic gas stream over the upper surface of a delta wing in the expansion region

A numerical method is described for the calculation of supersonic flow over the arbitrary upper surface of a delta wing in the expansion region. The shock wave must be attached everywhere to the leading edge of this wing from the side of the lower surface. The stream flowing over the wing is assumed to be nonviscous. A problem with initial conditions at some plane and with boundary conditions at the wing surface and the characteristic surface is set up for the nonlinear system of equations of gas dynamics. The difference system of equations, which approximates the original system of differential equations on a grid, has a second order of accuracy and is solved by the iteration system proposed in [1]. The initial conditions are determined by the method of establishment of self-similar flow. A number of examples are considered. Comparison is made with the solutions of other authors and with experiment.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 76–81, November–December, 1973.The author thanks A. S. II'ina who conducted the calculations and V. S. Tatarenchik for advice.     

Entropy effects in hypersonic flow over blunt delta wings

The problem of hypersonic flow over blunt delta wings is considered. It is shown that in the case of large wing lengths x -100, where x is the longitudinal coordinate measured in blunt nose radii, extremal flow regimes characterized by an essentially nonuniform distribution of the gas dynamic parameters (density, entropy, Mach number) may be realized in the shock layer near the windward surface of the wing. The location of the zones of flow convergence or divergence on the surface of a delta wing with sweep angle x=75° is established. For the same wing the ranges of Mach numbers M and angles of attack leading to extremal flow regimes are indicated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, 178–181, March–April, 1991.     

Hypersonic flow past conical V-shaped wings

Hypersonic flow past delta wings with a V-shaped cross-section has been investigated both theoretically and experimentally. Much attention is given to the examination and classification of possible conical flow patterns in the vicinity of the windward surface using the thin shock layer method. Solutions for shocks both attached to and detached from the leading edges them are obtained. It is shown that qualitatively new flow patterns can appear in the flow past V-shaped wings as compared with the case of a planar wing.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 170–178, September–October, 1996.     

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.     

Asymptotic solution to the problem of viscous flow in the neighborhood of the axis of a vortex sheet

An asymptotic solution is constructed to the problem of the flow of a viscous incompressible fluid in the neighborhood of the axis of a vortex sheet generated by flow separation from sharp edges of a delta wing of small aspect ratio at large values of the Reynolds number and small angles of attack.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 57–65, January–February, 1984.     

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.     

Boundary layer transition on the surface of a delta wing in supersonic flow

Laminar-turbulent transition on the surface of a delta wing has been experimentally investigated in a supersonic wind tunnel at Mach numbers M_t8=3–5. It is shown that when M,=3, Re_L=6.5·10⁶, and =–5.5° much of the upper surface of the wing in the neighborhood of the line of symmetry is occupied by a wedge-shaped region of turbulent flow. In this region the heat fluxes reach the same values as at the heat transfer maxima induced here by separated flows and may exceed the turbulent heat flux level on the windward surface of the wing. Changing the shape of the under surface of the wing from plane to pyramidal leads to acceleration of the boundary layer transition on the under surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 87–92, May–June, 1989.     

Wings with optimal characteristics in hypersonic flow

We present some exact results and results obtained by the local variation method [1–3] from numerical solutions of variational problems on the symmetric wing of minimum drag and the wing of maximum L/D in hypersonic flow; a modification of the method of local variations is proposed for the numerical solution of variational problems with isoperimetric constraints. The Newton method [4] was used to calculate the pressure distribution over the wing surface.The author wishes to thank M. N. Kogan and O. G. Fridlender for many helpful discussions.     

Three-dimensional hypersonic gas flow over wings

The results of the theory of three-dimensionai hypersonic flow over a wing based on the use of the thin shock layer method are reviewed.Based on paper read at the Seventh Congress on Theoretical and Applied Mechanics, Moscow, August 1991. Presented by V. Ya. Neiland.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 148–161, September–October, 1992.     

Evolution of Vortex Structures on the Leeward Side of a Delta Wing

Results of an experimental study of a supersonic flow around the leeward side of a delta wing are presented. The experiments are performed on three delta wings with leading–edge sweep angles = 68°, 73°, and 78° for Mach numbers M =2—4 and angles of attack = 0—22°. Data on the structure and position of internal shock waves are obtained; the size and location of primary and secondary vortices are found. New regimes of the flow around a delta wing are identified. The chart of flow regimes around delta wings is refined and extended.     

Hypersonic flow of gas over a slender wing of variable shape

In a formulation analogous to [1–3], a study is made of the flow of a uniform homogeneous hypersonic ideal gas over the windward side of a slender wing whose surface profile depends on the time. The problem is solved by the thin shock layer method [4]. The bow shock is assumed to be attached to the leading edge of the wing at at least one point. The corrections of the first approximation to the main Newtonian flow are found. For wings of finite aspect ratio, when the bow shock is attached along the whole of the leading edge of the wing, computational formulas are obtained for determining the parameters of the gas in the shock layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 94–101, July–August, 1979.     

Combined method of calculating supersonic ideal-gas flow over a wing with a supersonic blunt leading edge

A combined numerical method, based on the successive calculation of the flow regions near the blunt leading edge and center of a wing, is proposed on the assumption that the angle of attack and the relative thickness and bluntness radius of the leading edge are small. The flow in the neighborhood of the leading edge of the wing is assumed to be identical to that on the windward surface of a slender body coinciding in shape with the surface of the blunt nose of the wing and is numerically determined in accordance with [1]. The flow parameters near the center of the wing are calculated within the framework of the law of plane sections [2]. In both regions the equations of motion of the gas are integrated by the Godunov method. The flow fields around elliptic cones are obtained within the framework of the combined method and the method of [3], A comparative analysis of the results of the calculations makes it possible to estimate the region of applicability of the method proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 159–164, January–February, 1989.The authors wish to express their gratitude to A. A. Gladkov for discussing their work, and to G. P. Voskresenskii, O. V. Ivanov, and V. A. Stebunov for making available a program for calculating supersonic flow over a wing with a detached shock.     

Mathematical simulation of unsteady flow past a wing with jets

The various approximate approaches to the investigation of the unsteady aerodynamic characteristics of an airfoil with jet flap [1–3] are applicable only for an airfoil, low jet intensity, and low oscillation frequencies. In the present paper, the method of discrete vortices [4] is generalized to the case of unsteady flow past a wing with jets and arbitrary shape in plan. The problem is solved in the linear formulation; the conditions used are standard: no flow through the wing and jet, finite velocities at the trailing edges where there is no jet, and also a dynamical condition on the jet. The wing and jet are assumed to be thin and the medium inviscid and incompressible.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 139–144, May–June, 1982.     

Skin effect in two-phase flow over a wing

The author proposes a mathematical model of the skin effect — the flow in the thin film formed on the surface of a wing in a two-phase stream and consisting of the particle component [1–6]. The possible regimes are classified and the influence of the skin effect on the overall aerodynamic characteristics of a wing moving through heavy rain is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 49–55, January–February, 1990.The author is grateful to A. N. Kraiko for discussing the topic and for his valuable comments.     

Direct and inverse problems of flow over a wing of finite span in the linear formulation

A correspondence between the solutions of the direct and the inverse problem for wing theory is established for a wing of finite span in the framework of linear theory on the basis of solution of a wave equation in Volterra form for supersonic flow and solution of the Laplace equation in the form of Green's formula for subsonic flow. For the direct problem in the case of supersonic flow an expression is derived for finding the load on the wing with maximal allowance for the wing geometry. In the inverse problem for supersonic and subsonic flows, expressions are derived for finding the wing geometry from given values of the load on the wing and the variation of the load along the span of the wing. The solution of the inverse problem is presented in the form of integrals that converge for interior points of the wing surface in the sense of the Cauchy principal value, the wing surface being represented as a vortex surface of mutually orthogonal vortex lines. The conditions of finiteness of the velocities on the edges are discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 114–125, September–October, 1979.     

Law of transverse sections for the three-dimensional boundary layer on a thin wing in a hypersonic stream

The investigation of three-dimensional flows in boundary layers is important to determine the aerodynamic characteristics of wings such as the heat fluxes and friction drag. However, the circumstance that interaction of the boundary layer and the wake with an inviscid stream can play a governing role for the formation of the flow diagram as a whole is more important. The three-dimensional flow on a thin delta wing in a hypersonic stream is investigated in this paper. An important singularity of hypersonic flow is the low value of the gas density in the boundary layer as compared with the density on its outer boundary. It is shown that in the general case when the pressure in the wing span direction varies mainly by an order, high transverse velocities originate because of the smallness of the density within the boundary layer. This circumstance permits expansion of the solution for smallspan wings in a series in an appropriate small parameter. The equations in each approximation depend on two variables, while the third—longitudinal—variable enters as a parameter. The zero approximation can be considered as the formulation of the law of transverse plane sections for a three-dimensional boundary layer. As a comparison with the exact solutions calculated for delta wings with power-law distributions of the wing thickness has shown, the first approximation yields a very good approximation. Furthermore, flow modes with a different direction of parabolicity on the whole wing, as well as zones in which interaction with the external stream should absolutely be taken into account, are found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 75–84, March–April, 1976.     

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.