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.     

Vorticity of the velocity field for flow in a porous medium with random inhomogeneities

The vorticity field of the flow velocity in a porous medium with random inhomogeneities is considered in the correlation approximation of perturbation theory. The correlation tensor of the vorticity, the correlation between the vorticity and the permeability field, and the circulation of the velocity are calculated for three- and two-dimensional flows.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 157–160, July–August, 1982.     

Dynamics of thin vortex rings in a low-viscosity fluid

In order to describe the unsteady flow of a viscous fluid induced by a toroidal vorticity distribution we use the two-scale expansion method [6], By this means we obtain a vorticity distribution in the core of the thin vortex ring that is consistent with the external potential flow. The time dependence of the flow characteristics obtained confirms the experimental results for the inertial regime. The interaction of coaxial vortex rings is investigated as an example.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 52–59, September–October, 1992.     

The temporal evolution of a pair of streamwise vortices

A detailed investigation of the velocity and vorticity fields of a pair of vortices growing over a 75°-sweep delta wing is carried out through LDV measurements of three components of velocity and vorticity. Data are obtained along one of the vortices. The wing is undergoing a ramp-like pitch-up motion. The evolution of the flow field in four planes normal to the free-stream velocity is captured at 100 time instants through the wing motion. The delta wing is pitched through angles of attack ranging from 28° to 68°. From the velocity data at each incidence, the corresponding vorticity field is calculated. Hysteresis effects on vortex development and breakdown are studied through axial velocity and vorticity contours. The topologies of streamlines and vortex lines are compared with the corresponding topologies of the steady case. It is found that vortex breakdown can be detected first by a drastic reduction of the axial velocity. This phenomenon is developing in a non-axisymmetric fashion, beginning at the inboard side of the vortex. This is followed by a reduction of the axial vorticity component and finally by a reversal of the azimuthal vorticity component.This work was supported by the Air Force Office of Scientific Research, Project No. AFOSR-91-0310 and was monitored by Major Daniel Fant.     

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.     

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.     

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.     

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.     

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.     

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.     

Flow of a viscous fluid in a closed cavity in the presence of slip effects

Slip at the wall is observed in the flow of non-Newtonian fluids [1–4] and rarefied gases [5]. The most complete information on the phenomenon is obtained in capillary viscosimetry. For small radii of the capillaries and in porous media the slip effect is manifested even for Newtonian fluids (water, kerosene, for example) [6]. Experiments [2, 4] show that the influence of the entrance section can be ignored if the length of the capillary exceeds its radius by about 100 times. For the measurement of the rheological characteristics of high-viscosity fluids the use of long capillaries is difficult, and it is necessary to calculate the two-dimensional flow at the entrance section with allowance for slip. The need for such calculations also arises, for example, when one is choosing the optimal parameters of the screw devices employed in the processing of polymers [7]. Two-dimensional flows of a viscous incompressible fluid are frequently calculated with the flow function and vorticity =– used as variables [8–14]. The expressions for the vorticity on the boundary are usually obtained from the viscous no-slip condition [8, 9]. In the present paper, expressions are obtained for the vorticity on a wall in the presence of slip. The obtained expressions are used to solve a test problem on the flow of a viscous incompressible fluid in a cavity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 10–16, January–February, 1980.     

Hypersonic viscous gas flow over a delta wing in the intermediate interaction regime with allowance for wake flow

The results of calculating the hypersonic flow over a plane delta wing of finite length with allowance for wake flow in the intermediate interaction regime are presented. A comparison is made with the data for flow over a delta wing with given pressure at the trailing edge.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 142–149, September–October, 1993.     

Diffusion of a ring vortex

The diffusion of a ring vortex is investigated in the present paper with allowance for the influence of the initial radius of the toroidal vorticity distribution on the flow structure. The statement of the problem in such a formulation makes it possible to classify and reinterpret results obtained previously. A vortex pair is studied together with a vortex ring. The toroidal vorticity and stream function distributions are obtained analytically. The self-induced lift velocity of the ring vortex is found. The influence of inertial terms is investigated numerically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 10–15, November–December, 1987.     

Acoustic,entropy, and vorticity perturbations in a channel of variable cross section

A study is made of the problem of the propagation of infinitesimally small perturbations in a gas stream moving in a channel of variable cross section when the flow cannot be regarded as isentropic and irrotational. The solution is found in the framework of the linear theory of the flow of an ideal gas and the quasi-one-dimensional hydraulic approximation for the steady regime. For irrotational and isentropic perturbations in a nozzle, this problem was considered in [1–4]. In [1], the problem is generalized to take into account entropy perturbations in the nozzle for the case of longitudinal oscillations. The present paper treats arbitrary modes in a nozzle and takes into account not only entropy but also vorticity perturbations in the moving stream. For each of the three perturbation types — acoustic, entropy, and vorticity — the solutions are expanded in series in cylindrical functions. It is shown that in the considered approximation each oscillation mode can be analyzed independently of the others. In the special case of flow in a Laval nozzle, the concept of impedance (admittance), which is widely used in acoustics, is generalized to take into account entropy and vorticity perturbations. The contribution to the flow dynamics of the acoustic, entropy, and vorticity perturbations is estimated numerically for longitudinal and transverse modes.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 91–98, January–February, 1982.     

Plane vortex flow induced by a mass source (sink) in a rotating viscous fluid

A solution of the self-similar type, describing the development with time of a plane vortex flow excited by an axisymmetric mass source (sink) in a rotating viscous fluid, is obtained. Sources of two kinds — impulsive and of constant strength — are considered. The solutions for the velocity and vorticity fields are expressed in the form of functions similar to incomplete gamma functions and are presented in the form of graphs for various flow Reynolds numbers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 172–175, July–August, 1991.     

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.     

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.     

Calculation of the flow of an ideal fluid past a wing of finite thickness

The problem of irrotational flow past a wing of finite thickness and finite span can be reduced by Green's formula to the solution of a system of Fredholm equations of the second kind on the surface of the wing [1]. The wake vortex sheet is represented by a free vortex surface. Besides panel methods (see, for example, [2]) there are also methods of approximate solution of this problem based on a preliminary discretization of the solution along the span of the wing in which the two-dimensional integral equations are reduced to a system of one-dimensional integral equations [1], for which numerical methods of solution have already been developed [3–6]. At the same time, a discretization is also realized for the wake vortex sheet along the span of the wing. In the present paper, this idea of numerical solution of the problem of irrotational flow past a wing of finite span is realized on the basis of an approximation of the unknown functions which is piecewise linear along the span. The wake vortex sheet is represented by vortex filaments [7] in the nonlinear problem. In the linear problem, the sheet is represented both by vortex filaments and by a vortex surface. Examples are given of an aerodynamic calculation for sweptback wings of finite thickness with a constriction, and the results of the calculation are also compared with experimental results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 124–131, October–December, 1981.     

Heat transfer on the spreading line of a sweptback cylinder in an inhomogeneous hypersonic flow

A method is proposed for calculating heat transfer on the spreading line of blunt edges with moderate sweepback; it takes into account the influence of absorption of the inviscid vorticity of the flow by the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 175–179, July–August, 1980.     

Magnetic fluid motion driven by a high-frequency rotating magnetic field

The problem of the circulating flow of a nonisothermal magnetic fluid in a long vertical cylinder placed in a rotating magnetic field is solved in the weak vorticity approximation.Perm'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 18–22, January–February, 1996.