Three-dimensional boundary layer on a plane delta wing in the intermediate hypersonic interaction regime

The results of calculating the three-dimensional boundary layer on a plane delta wing of finite length in the intermediate hypersonic interaction regime are presented. The effect of the hypersonic interaction parameter on the gas flow in the boundary layer and the aerodynamic characteristics is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 110–116, May–June, 1991.     

Propagation of perturbations upstream with interaction between a hypersonic flow and a boundary layer

It is shown that, for hypersonic flows with moderate and strong degrees of interaction, perturbations brought about, for example, by a bottom opening or by any other sort of obstacle are propagated up to the leading edge of a solid body. Local regions with very large pressure gradients cannot arise in the flow. This is connected with the possibility of the development of breakaway zones with a length on the order of magnitude of the size of the solid body, described in the first approximation by the equations of the boundary layer. From a mathematical point of view the problem comes down to establishing the nonsingular nature of the solution near the leading edge, and to finding eigensolutions which make it possible to satisfy the boundary conditions at the trailing edge of the solid body. It is shown that, with a weak interaction between the hypersonic flow and the boundary layer, there may arise short flow regions with free interaction and locally nonviscous flows with large pressure gradients, within the limits of which the perturbations may move upstream.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 40–49, July–August, 1970.In conclusion, the author thanks V. V. Sychev for his evaluation of the problem.     

Longitudinal-transverse interaction in a three-dimensional boundary layer

Three-dimensional flow is considered for an incompressible fluid in a boundary layer developing along a curved solid surface during interaction between it and a small uneven area (projection or depression) on the surface. It is shown that an important part in the formation of the flow round the uneven area may be played by the drop in the pressure across the boundary layer. Conditions are formulated under which this effect, which is connected with the action of centrifugal forces, is realized. On the assumption that the longitudinal dimension of the uneven area is of the order of Re^–3/14, its width of the order of O(Re^–3/7), and its height O(Re^–4/7), where Re is the Reynolds number, asymptotic equations are derived which describe the motion of the fluid in the neighborhood of the uneven area.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–50, May–June, 1987.     

A method of calculating a regime of strong viscous interaction on a delta wing

A method is proposed for calculating the three-dimensional boundary layer on a delta wing in a regime of strong viscous interaction with the exterior hypersonic flow. The results of numerical solution of a boundary-value problem are given.     

Generation of perturbations by a localized vibrator in the boundary layer of a nonswept wing

Origination and development of perturbations generated by a threedimensional vibrating surface in the boundary layer on an airfoil with a zero slip angle is experimentally studied. Surface vibrations were generated by a Mylar membrane. It is shown that highamplitude vibrations of a threedimensional surface lead to simultaneous formation of two types of perturbations in the boundary layer: quasistationary streamwise structures and wave packets accompanying them. The presence of regions with favorable and adverse pressure gradients does not exert a significant effect on evolution of streamwise structures but leads first to attenuation and then to amplification of wave packets.     

Excitation of controllable perturbations in the three-dimensional boundary layer using plasma actuators

Two versions of the structure of a multi-discharge plasma actuator intended to excite boundary layer perturbations in the neighborhood of the leading swept-wing edge are suggested. The actuator must prevent from appearance and development of the crossflow instability modes leading to laminarturbulent transition under the normal conditions. In the case of flow past a swept wing, excitation of controllable perturbations by the plasma actuator is simulated numerically in the steady-state approximation under the typical conditions of cruising flight of a subsonic aircraft. The local body force and thermal impact on the boundary layer flow which is periodic along the leading wing edge is considered. The calculations are carried out for the physical impact parameters realizable in the near-surface dielectric barrier discharge.     

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.     

Interaction of perturbations in a boundary layer

Surface irregularities and vibration, free-stream turbulence and other factors lead to the penetration of three-dimensional perturbations into the boundary layer. Classical research on the transitional boundary layer has been restricted to a low degree of turbulence and the introduction of a plane perturbation wave. The present study concentrates on the development of three-dimensional perturbations created in a model experiment, both mechanically and by means of plane elastic plates, for various Reynolds numbers. The results are analyzed on the basis of the measured spectral and correlation characteristics.Paper presented at the Fifth Conference on Theoretical and Applied Mechanics, Alma-Ata (1981) [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 68–74, September–October, 1985.     

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.     

Flow structure on a three-dimensional wing subjected to small amplitude perturbations

Small amplitude angular perturbations, of the order of one-half degree, can substantially modify the flow structure along a three-dimensional wing configuration, which is quantitatively characterized using a technique of high-image-density particle image velocimetry. Excitation at either the fundamental or the first subharmonic of the spanwise-averaged instability frequency of the separating shear layer from the stationary wing nearly eliminates the large-scale separation zone along the wing at high angle of attack. The physics of the flow is interpreted in terms of time-mean streamlines, vorticity and Reynolds stress, in conjunction with phase-averaged patterns of instantaneous vorticity. Distinctive vorticity patterns occur along the leading edge when the time-averaged separation zone is minimized.     

Laminarization of boundary layer flow on a vibrating wing

A new type of Tollmien-Schlichting wave excitation, experimentally detected in [6] in investigating the unsteady perturbation field downstream from roughness on the surface of a vibrating wing, is studied. It is shown that the generation mechanism consists in the nonlinear interaction between the unsteady disturbance produced by the vibrations of the smooth wall and the steady nonuniformity of the boundary layer above the roughness.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 26–34, March–April, 1993.     

Free interaction of a three-dimensional boundary layer with an exterior irrotational flow

Asymptotic equations describing the unsteady free interaction of a three-dimensional boundary layer with an exterior flow are derived. The orders of the independent variables and perturbations of the flow parameters are chosen in such a way that the pressure gradient that occurs in the equation of the wall layer is due to the displacement of streamlines situated near the surface of the body. The Fourier method is used to construct a solution to the linearized problem. A class of perturbations satisfying homogeneous boundary conditions on the surface of the body is found.     

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.     

Separation of a three-dimensional boundary layer

The line of separation of the three-dimensional boundary layer on an arbitrary curvilinear surface is a singular streamline on the body surface which separates the detachment region and which is a line of confluence for the limiting streamlines. Expressions are derived for the three-dimensional separation criteria on the basis of the condition of zero frictional force in the projection on the normal to the line of separation. The position of the line of separation is determined from the solution of an ordinary differential equation. An analysis is made of various cases of separation on the surface of a yawed cylinder and on the surface of sharp cones at an angle of attack in a supersonic stream. The position of the lines of separation is determined experimentally from the confluence of thin liquid films applied to the surface. It is shown that separation occurs on the sharp cone on the line z=π for values of the parameter K=?0.85.