Effect of surface temperature on the stability of the swept attachment line boundary layer

At fairly high Reynolds numbers instability may develop on the line of attachment of the potential flow to the leading edge of a swept wing and lead to a transition to boundary layer turbulence directly at the leading edge [1, 2]. Although the first results relating to the stability and transition of laminar flow at the leading edge of swept wings were obtained almost 30 years ago, the problem remains topical. The stability of the swept attachment line boundary layer was recently investigated numerically with allowance for compressibility effects [3, 4]. Below we examine the effect of surface temperature on the stability characteristics of the laminar viscous heat-conducting gas flow at the leading edge of a side slipping wing.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 78–82, November–December, 1990.     

Effect of Heat Supply on the Stability of the Supersonic Swept Atiachment-Line Boundary Layer

The stability of a boundary layer with volume heat supply on the attachment line of a swept wing is investigated within the framework of the linear theory at supersonic inviscid-free-stream Mach numbers. The results of numerical calculations of the flow stability and neutral curves are presented for the flow on the leading edge of a swept wing with a swept angle χ=60° at various free-stream Mach numbers. The effect of volume heat supply on the characteristics of boundary layer stability on the attachment line is studied at a surface temperature equal to the temperature of the external inviscid flow. It is shown that in the case of a supersonic external inviscid flow volume heat supply may result in an increase in the critical Reynolds number and stabilization of disturbances corresponding to large wave numbers. For certain energy supply parameters the situation is reversed, the unstable disturbances corresponding to the main flow-instability zone are stabilized but another zone of flow-instability with small wave numbers and a significantly lower critical Reynolds number appears.     

Occurrence of Tolman-Schlichting waves in the boundary layer under the effect of external perturbations

Under small external perturbations, the initial stage of the laminar into turbulent flow transition process in boundary layers is the development of natural oscillations, Tolman-Schlichting waves, which are described by the linear theory of hydrodynamic stability. Subsequent nonlinear processes start to appear in a sufficiently narrow band of relative values of the perturbation amplitudes (1–2% of the external flow velocity) and progress quite stormily. Hence, the initial linear stage of relatively slow development of perturbations is governing, in a known sense, in the complete transition process. In particular, the location of the transition point depends, to a large extent, on the spectrum composition and intensity of the perturbations in the boundary layer, which start to develop according to linear theory laws, resulting in the long run in destruction of the laminar flow mode. In its turn, the initial intensity and spectrum composition of the Tolman-Schlichting waves evidently depend on the corresponding characteristics of the different external perturbations generating these waves. The significant discrepancy in the data of different authors on the transition Reynolds number in the boundary layer on a flat plate [1–4] is probably explained by the difference in the composition of the small perturbing factors (which have not, unfortunately, been fully checked out by far). Moreover, it is impossible to expect that all kinds of external perturbations will be transformed identically into the natural boundary-layer oscillations. The relative role of external perturbations of different nature is apparently not identical in the Tolman-Schlichting wave generation process. However, how the boundary layer reacts to small external perturbations, under what conditions and in what way do external perturbations excite Tolman-Schlichting waves in the boundary layer have practically not been investigated. The importance of these questions in the solution of the problem of the passage to turbulence and in practical applications has been emphasized repeatedly recently [5, 6], Only the first steps towards their solution have been taken at this time [4, 7–10], Out of all the small perturbing factors under the real conditions of the majority of experiments to investigate the flow stability and transition in the case of smooth polished walls, three are apparently most essential, viz.: the turbulence of the external flow, acoustic perturbations, and model vibrations. In principle, all possible mechanisms for converting the energy of these perturbations into Tolman-Schlichting waves can be subdivided into two classes (excluding the nonlinear interactions which are not examined here): 1) distributed wave generation in the boundary layer; and 2) localized wave generation at the leading edge of the streamlined model. Among the first class is both the possibility of the direct transformation of the external flow perturbations into Tolman-Schlichting waves through the boundary-layer boundary, and wave excitation because of the active vibrations of the model wall. Among the second class are all possible mechanisms for the conversion of acoustic or vortical perturbations, as well as the vibrations of the streamlined surface, into Tolman-Schlichting waves, which occurs in the area of the model leading edge.Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 5, pp. 85–94, September–October, 1978.     

Numerical experiments on the stability of leading edge boundary layer flow: A two-dimensional linear study

A numerical study is performed in order to gain insight to the stability of the infinite swept attachment line boundary layer. The basic flow is taken to be of the Hiemenz class with an added cross-flow giving rise to a constant thickness boundary layer along the attachment line. The full Navier-Stokes equations are solved using an initial value problem approach after two-dimensional perturbations of varying amplitude are introduced into the basic flow. A second-order-accurate finite difference scheme is used in the normal-to-the-wall direction, while a pseudospectral approach is employed in the other directions; temporally, an implicit Crank-Nicolson scheme is used. Extensive use of the efficient fast Fourier transform (FFT) algorithm has been made, resulting in substantial savings in computing cost. Results for the two-dimensional linear regime of perturbations are in very good agreement with past numerical and theoretical investigations, without the need for specific assumptions used by the latter, thus establishing the generality of our method.     

Receptivity of the Swept Wing Boundary Layer to a Steady Flow Inhomogeneity

The boundary layer on a plate with an inclined blunt leading edge is investigated for a free-stream flow with a small span-periodic velocity inhomogeneity. This flow simulates the penetration of the outer turbulence into the swept wing boundary layer. It is shown that the boundary layer perturbations generated by the inhomogeneity generally have a streamwise velocity component significantly greater than the initial inhomogeneity amplitude. The dependence of the perturbations on the distance from the leading edge and the spanwise inhomogeneity period is found. It is shown that the swept wing boundary layer is less sensitive to the perturbation type in question than the straight wing boundary layer.     

Experimental transition delay using glow-discharge plasma actuators

In the present work plasma actuators were applied in a flat-plate boundary layer with an adverse pressure gradient to influence the transition of the boundary layer. The first actuator downstream of the leading edge is operated in pulsed mode to introduce perturbations into the boundary layer to promote transition. Two steady operating actuators further downstream damp the perturbations significantly, which results in transition delay.     

Influence of acoustics and the flow regime in the boundary layer on nozzle walls on the mixing layer of an immersed jet

Experimental determinations were made of the width of the mixing layer and the level of turbulent pulsations in the initial section of a subsonic circular immersed jet for different parameters of the boundary layer on the nozzle walls and in the presence of acoustic excitation. It was established that the rate of expansion of the turbulent mixing layer depends on the flow regime in the boundary layer. For laminar initial boundary layer, external acoustic excitation can lead to a decrease in the expansion velocity of the mixing layer and of the intensity of the velocity pulsations on the jet axis within the initial section. If the frequency and amplitude of acoustic excitation at which a decrease in the rate of expansion of the mixing layer and of the pulsation intensity was observed remained unchanged, the influence of the acoustics disappeared when the boundary layer became turbulent. The acoustic vibrations influenced the subsonic jets by generating vortex perturbations when they interact with the edge of the nozzle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 36–42, November–December, 1982.We are grateful to K. I. Artamonov, now deceased, for support and discussing the results, and O. I. Navoznov and S. F. Agafonov for help in organizing and performing the experiments.     

Experimental investigation of the stability of a supersonic boundary layer on a plate with blunting of the leading edge

In an aerodynamic tube, an experimental investigation of the development of small natural perturbations in a laminar boundary layer on a plate was made. The measurements were made using a thermoanemometric method with a Mach number M = 2 and a unit Reynolds number Re₁ = 3.1·10⁶ m^–1. An investigation of the effect of blunting of the leading edge of the plate on the development of the perturbations was made. It is shown that blunting decreases the range of unstable frequencies and the region of instability and increases the critical Reynolds number of the loss of stability. In the initial section of the plate there is a rise in the perturbations of all frequencies up to a maximal value, whose coordinate is inversely proportional to the frequency. The development of perturbations in this region is insensitive to the state of the boundary layer. The position of the maximum does not change with blunting of the leading edge.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 65–70, July–August, 1977.     

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.     

Asymptotic analysis of the equations of a three-dimensional boundary layer

The asymptotic solutions of the self-similar equations of two- and three-dimensional boundary layers have been investigated by many authors (see, for example, [1–3]). In [4, 5], asymptotic solutions were found for non-self-similar equations for two-dimensional flow, and the propagation of perturbations near the external edge of the boundary layer was analyzed. In the present paper, asymptotic solutions are obtained for the non-self-similar equations of a three-dimensional laminar boundary layer of an incompressible fluid. It is shown that the conclusion drawn in [5] — that the boundary conditions can be transferred from infinity to a finite distance from the wall — is also true for three-dimensional flow. The obtained solutions explain the experimentally well-known phenomenon of the conservativeness of the secondary currents. The essence of this phenomenon is that a change in the sign of the transverse (along the normal to a streamline of the external flow) pressure gradient is accompanied by a very rapid change in the direction of the secondary flow near the wall, whereas in the upper layers of the boundary layer the direction remains unchanged for a substantial time.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 155–157, September–October, 1979.     

Interaction between the boundary layer and a supersonic flow when part of the wall is rapidly heated

There have been many theoretical studies of aspects of the unsteady interaction of an exterior inviscid flow with a boundary layer [1–9]. The mathematical flow models obtained in these studies by the method of matched asymptotic expansions describe a wide range of phenomena observed experimentally. These include boundary layer separation near the hinge of a flap, the flow in the neighborhood of the trailing edge of an oscillating airfoil [1–2], and the development and propagation of perturbations in a boundary layer excited by an oscillating wall or some other way [3–5]. The present paper studies the interaction of an unsteady boundary layer with a supersonic flow when a small part of the surface of a body in the flow is rapidly heated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 66–70, January–February, 1984.     

Conical flow breakdown in non-free shock-wave/boundary-layer interaction

The non-free interaction between a shock wave and the boundary layer on a swept plate set at incidence in the undisturbed flow is studied using different experimental methods including special laser techniques for visualizing supersonic conical gas flows. It is shown that under shock-layer conditions the non-free interaction can lead to conical flow breakdown before the incident shock reaches the leading edge of the plate.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 45–58. Original Russian Text Copyright © 2004 by Zubin and Ostapenko.     

Receptivity of the Blunt-Leading-Edge Plate Boundary Layer to Unsteady Vortex Perturbations

The response of the boundary layer on a plate with a blunt leading edge to frozen-in vortex perturbations whose vorticity is normal to the plate surface is found. It is shown that these vortices generate an inhomogeneity of the streamwise velocity component in the boundary layer. This inhomogeneity is analogous to the streaky structure developing as the degree of free-stream turbulence increases. The dependence of the amplitude and shape of the boundary layer inhomogeneity on the distance from the leading edge, the streamwise and spanwise scales, and other parameters is found for periodic and local initial perturbations. It is shown that the receptivity of the boundary layer decreases with increase in the frequency and with decrease in the streamwise perturbation scale.     

Relaxation of a liquid layer under the action of capillary forces

The theory of creeping motion is used to study the relaxation of an infinite viscous fluid layer (membrane) of nonuniform thickness. The propagation of boundary perturbations in a semi-infinite layer under the action of surface-tension forces is also considered. The layer has at least one common boundary with a gas. It is found that relaxation processes of an infinite layer or the propagation of boundary perturbations inside a bounded layer are non-monotonic, and that wave-like surface perturbations always arise. Relaxation times are determined. Maximum distances are found over which separate regions of the layer can affect each other.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 1, pp. 73–77, January–February, 1970.The author wishes to thank V. G. Levich for discussions.     

Method of mean-mass parameters for a three-dimensional boundary layer in a flow with vorticity

When a gas flows with hypersonic velocity over a slender blunt body, the bow shock induces large entropy gradients and vorticity near the wall in the disturbed flow region (in the high-entropy layer) [1]. The boundary layer on the body develops in an essentially inhomogeneous inviscid flow, so that it is necessary to take into account the difference between the values of the gas parameters on the outer edge of the boundary layer and their values on the wall in the inviscid flow. This vortex interaction is usually accompanied by a growth in the frictional stress and heat flux at the wall [2, 3]. In three-dimensional flows in which the spreading of the gas on the windward sections of the body causes the high-entropy layer to become narrower, the vortex interaction can be expected to be particularly important. The first investigations in this direction [4–6] studied the attachment lines of a three-dimensional boundary layer. The method proposed in the present paper for calculating the heat transfer generalizes the approach realized in [5] for the attachment lines and makes it possible to take into account this effect on the complete surface of a blunt body for three-dimensional laminar, transition, or turbulent flow regime in the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 80–87, January–February, 1981.     

Amplitude method of prediction of laminar-turbulent transition on a swept-wing

The amplitudemethod of prediction of laminar-turbulent transition on a swept-wing initiated by the simultaneous action of free-stream turbulence and surface roughness is developed. Generation of growing intrinsic perturbations in the boundary layer is described by the mechanism of distributed generation, i.e., an external perturbation generates an instability mode with the same wavelength and frequency. Generation occurs in a small neighborhood of the neutral point at which the parameters of an external perturbation and the instability modes coincide. The development of proper perturbations in the boundary layer is described by the nonlinear method of parabolized stability equations (PSE). The criterion of laminar-turbulent transition is the combined amplitude. i.e., transition begins at a point at which the sum of amplitudes of steady and traveling modes reaches a critical value.     

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.     

Supersonic flow around the trailing edge of a thin profile

The method of mergeable asymptotic expansions has recently been used effectively in investigations devoted to the study of boundary layer interaction with an external inviscid flow at high subcritical Reynolds numbers Re. The asymptotic analysis permits obtaining a limit pattern of the flow around a solid as Re þ, and determining the similarity and quantitative regularity laws which are in good agreement with experimental results. Thus by using the method of mergeable asymptotic expansions it is shown in [1–4] that near sites with high local curvature of the body contour and flow separation and attachment points, an interaction domain appears that has a small length on the order of Re^-3/8. In this flow domain, which has a three-layer structure, the pressure distribution in a first approximation already depends on the change in boundary-layer displacement thickness, while the induced pressure gradient, in turn, influences the flow in the boundary layer. An analogous situation occurs in the neighborhood of the trailing edge of a flat plate where an interaction domain also appears [5, 6]. The flow in the neighborhood of the trailing edge of a flat plate around which a supersonic viscous gas flows was examined in [7]. Numerical results in this paper show that the friction stress on the plate surface remains positive everywhere in the interaction domain, and grows on approaching the trailing edge. The supersonic flow around the trailing edge of a flat plate at a small angle of attack was investigated in [8, 9], Supersonic flow of a viscous gas in the neighborhood of the trailing edge of a flat plate at zero angle of attack is examined in [10], but with different velocity values in the inviscid part of the flow on the upper and lower sides of the plate. The more general problem of the flow around the trailing edge of a profile with small relative thickness is investigated in this paper.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 36–42, May–June, 1981.     

Influence of aspect ratio on the flow above the free end of a surface-mounted finite cylinder

The flow above the free end of a surface-mounted finite-height cylinder was studied in a low-speed wind tunnel using particle image velocimetry (PIV). Velocity measurements were made in vertical and horizontal measurement planes above the free end of finite cylinders of aspect ratios AR = 9, 7, 5 and 3, at a Reynolds number of Re = 4.2 × 10⁴. The relative thickness of the boundary layer on the ground plane was δ/D = 1.7. Flow separating from the leading edge formed a prominent recirculation zone on the free-end surface. The legs of the mean arch vortex contained within the recirculation zone terminate on the free-end surface on either side of the centreline. Separated flow from the leading edge attaches onto the upper surface of the cylinder along a prominent attachment line. Local separation downstream of the leading edge is also induced by the reverse flow and arch vortex circulation within the recirculation zone. As the cylinder aspect ratio is lowered from AR = 9 to AR = 3, the thickness of the recirculation zone increases, the arch vortex centre moves downstream and higher above the free-end surface, the attachment position moves downstream, and the termination points of the arch vortex move upstream. A lowering of the aspect ratio therefore results in accentuated curvature of the arch vortex line. Changes in aspect ratio also influence the vorticity generation in the near-wake region and the shape of the attachment line.     

Receptivity of the Flat-Plate Boundary Layer to Free-Stream Turbulence

The linear problem of generation of perturbations of a flat-plate boundary layer by external turbulence is solved. The turbulence is represented in the form of a set of space- and time-periodic vortex modes. It is shown that the boundary layer is most receptive to low-frequency longitudinal vorticity modes. The mean-square velocity fluctuations in the boundary layer and their spectrum are found for isotropic turbulence with a spectrum satisfying the Kolmogorov-Obukhov law.