Development of slow disturbances in a hypersonic boundary layer

The mechanisms of development of slow time-dependent disturbances in the wall region of a hypersonic boundary layer are established and a diagram of the disturbed flow patterns is plotted; the corresponding nonlinear boundary value problem is formulated for each of these regimes. It is shown that the main factors that form the disturbed flow are the gas enthalpy near the body surface, the local viscous-inviscid interaction level, and the type, either subsonic or supersonic, of the boundary layer as a whole. Numerical and analytical solutions are obtained in the linear approximation. It is established that enhancement of the local viscous-inviscid interaction or an increased role for the main supersonic region of the boundary layer makes the disturbed flow by and large “supersonic”: the upstream propagation of the disturbances becomes weaker, while their downstream growth is amplified. Contrariwise, local viscous-inviscid interaction attenuation or an increased role for the main subsonic region of the boundary layer has the opposite effect. Surface cooling favors an increased effect of the main region of the boundary layer while heating favors an increased wall region effect. It is also found that in the regimes considered disturbances travel from the turbulent flow region downstream of the disturbed region under consideration counter to the oncoming flow, which may be of considerable significance in constructing the nonlinear stability theory.     

Tollmien-Schlichting Waves in a Hypersonic Boundary Layer Flow in the Neighborhood of a Cooled Surface

A nonlinear time-dependent model of the development of longwave perturbations in a hypersonic boundary layer flow in the neighborhood of a cooled surface is constructed. The pressure in the flow is assumed to be induced the combined variation of the thicknesses of the near-wall and main parts of the boundary layer. Numerical and analytic solutions are obtained in the linear approximation. It is shown that if the main part of the boundary layer is subsonic as a whole, its action reduces the perturbation damping upstream and the perturbation growth downstream, while a supersonic, as a whole, main part of the boundary layer creates the opposite effects. An analysis of the solutions obtained makes it possible to conclude that the asymptotic model proposed can describe the three-dimensional instability of the Tollmien-Schlichting waves.     

Interaction between an unsteady pressure disturbance and a hypersonic boundary layer

The development of disturbances in a hypersonic boundary layer on a cooled surface is investigated in the case in which the characteristic velocity of disturbance propagation is small but greater than the flow velocity in the wall region of the three-layer disturbed zone with interaction. The nonlinear boundary value problem formulated involves a single similarity parameter that characterizes the contribution made by the main, on average either subsonic or supersonic, region of the boundary layer to the generation of the pressure disturbance. In the linear approximation, an analytical solution and an algebraic dispersion equation are derived. It is shown that only waves exponential in time and in the streamwise coordinate can propagate downstream when themain region of the undisturbed boundary layer is subsonic on average.     

Iterative method for supersonic flow laminar boundary layer interaction in the presence of separation

The classical two-dimensional compressible boundary-layer equations supplemented by a relation describing the interaction of boundary layer with external inviscid flow (see, e.g., [1]) are treated as the governing equations in one of the methods to study the viscous-inviscid interaction. It is then necessary in the case of supersonic flow to specify certain downstream boundary conditions for the closure of the governing system, i.e., it is a boundary-value problem (e.g., [2]). The shooting technique for parameters at the beginning of the computational region to obtain the solution satisfying such a condition usually requires large computer time since the integral curves are highly sensitive to small changes in upstream boundary conditions. A more effective method is the algorithm of global relaxations of pressure distribution along the entire computational region [1]. A numerical method to compute supersonic interacting boundary layer in the presence of separation is presented in this paper.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 89–93, January–February, 1984.     

Specific Features of the Flow in the Supercritical Boundary Layer Near a Break Point on a Cold Surface

The interaction between a boundary layer and a supersonic flow past a plate with a flap deflected at a small angle in the presence of strong cooling of the body surface is considered. For supercritical regimes, the entire interaction region is located behind the leading edge of the flap and the pressure distribution has a discontinuity of the derivative near the corner point. The flow in a break-point neighborhood with a characteristic length x of the order of the boundary layer thickness is studied. It is shown that in this region a substantial pressure difference arises. The pressure distribution along the surface is found. The viscous sublayer in this region develops under the action of the given pressure gradient.     

On Disturbance Propagation in Internal-Flow Boundary Layers

The unsteady interaction of plane-channel wall boundary layers with a supersonic inviscid flow is investigated. The flow regimes in which disturbances introduced by the boundary layer developing on one wall influence the boundary layer on the other wall are considered. The regime of relatively large pressure disturbance amplitudes generated near the nozzle outlet or by deforming the channel walls is studied. In these conditions, the interaction process is described by a system of Burgers equations with retarded arguments. Numerical solutions of this system are obtained for symmetric and antisymmetric perturbations of the channel walls.     

Singularities of the boundary layer equations and the structure of the flow in the vicinity of the convergence plane on conical bodies

The singularities of the boundary layer equations and the laminar viscous gas flow structure in the vicinity of the convergence plane on sharp conical bodies at incidence are analyzed. In the outer part of the boundary layer the singularities are obtained in explicit form. It is shown that in the vicinity of a singularity a boundary domain, in which the flow is governed by the shortened Navier-Stokes equations, is formed; their regular solutions are obtained. The viscous-inviscid interaction effect predominates in a region whose extent is of the order of the square root of the boundary layer thickness, in which the flow is described by a two-layer model, namely, the Euler equations in the slender-body approximation for the outer region and the three-dimensional boundary layer equations; the pressure is determined from the interaction conditions. On the basis of an analysis of the solutions for the outer part of the boundary layer it is shown that interaction leads to attenuation of the singularities and the dependence of the nature of the flow on the longitudinal coordinate, but does not make it possible to eliminate the singularities completely.     

Models of the Interaction between a Laminar Boundary Layer and a Transonic Flow

Possible regimes of viscous-inviscid interaction at transonic external flow velocities are investigated. It is shown that different flow regimes can exist depending on the relation between such parameters as the disturbance amplitude and the Mach and Reynolds numbers. Corresponding mathematical models are formulated and the solutions of some problems describing linear regimes of disturbance development are obtained. The models developed make it possible to describe all the possible interaction regimes.     

有序波状扰动对壁湍流相干结构的作用

本文在湍流边界层外层引入了正弦波状扰动;实验结果表明扰动波波幅沿流向是衰减的,衰减率与 Landahl(1967)的线性理论结果定性一致。本文发现在扰动波沿流向的演化过程中,出现以扰动波频率为基频的高次谐波。外层单一频率的扰动会减小内层的猝发平均周期,影响内层的流动结构。     

Disturbance evolution in the leading-edge region of a blunt flat plate in supersonic flow

The spatio-temporal dynamics of small disturbances in viscous supersonic flow over a blunt flat plate at freestream Mach number M_∞=2.5 is numerically simulated using a spectral approximation to the Navier–Stokes equations. The unsteady solutions are computed by imposing weak acoustic waves onto the steady base flow. In addition, the unsteady response of the flow to velocity perturbations introduced by local suction and blowing through a slot in the body surface is investigated. The results indicate distinct disturbance/shock-wave interactions in the subsonic region around the leading edge for both types of forcing. While the disturbance amplitudes on the wall retain a constant level for the acoustic perturbation, those generated by local suction and blowing experience a strong decay downstream of the slot. Furthermore, the results prove the importance of the shock in the distribution of perturbations, which have their origin in the leading-edge region. These disturbance waves may enter the boundary layer further downstream to excite instability modes.     

Controlling supersonic boundary layer stability by means of distributed mass transfer through a porous wall

The interaction between disturbances in a compressible boundary layer in the presence of distributed mass transfer (injection or suction) through a permeable porous wall is considered in the linear and nonlinear approximations (weakly nonlinear stability theory). The regimes of moderate and high supersonic velocities (Mach numbers M = 2 and 5.35) are studied. The boundary conditions for the disturbances on a permeable wall are derived with account for the gas compressibility in pores and the presence of a suction chamber. Maximum pore dimensions, at which the surface properties have no effect on the disturbance characteristics, which are stabilized upon suction and destabilized upon injection, are determined. When the surface properties are taken into account, intense growth of the first-mode vortex disturbances occurs, which can completely undo the stabilizing effect of the suction. Injection leads to the vortex and acoustic mode destabilization on the linear range and the enhancement of the nonlinear processes on the transitional range.     

Evolution of disturbances in a laminarized supersonic boundary layer on a swept wing

Experimental data on stability of a three-dimensional supersonic boundary layer on a swept wing are presented. The experiments are performed on a swept wing model with a lenticular profile with a 40° sweep angle of the leading edge at a zero angle of attack. The supersonic boundary layer on the swept wing was laminarized with the use of distributed roughness. A pioneering study of interaction of traveling and stationary disturbances is performed. Some specific features of this interaction are identified. The main reason for turbulence emergence in a supersonic boundary layer on a swept wing is demonstrated to be secondary crossflow instability. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 40–46, March–April, 2008.     

Stability and Transition on a Swept Cylinder in a Supersonic Flow

Results of experimental investigations of the evolution of natural disturbances and laminar–turbulent transition in a supersonic boundary layer on the attachment line of a circular cylinder with a sweep angle of 68° and a freestream Mach number M = 2 are presented. The experimental studies are supplemented by calculations of the mean flow and stability characteristics. Flow regimes in the boundary layer on the attachment line are determined by a hotwire technique as functions of the Reynolds number and height of twodimensional roughness elements. The results are compared with NASA (Ames) experiments.     

Flutter of infinite elastic plates in the boundary-layer flow at finite Reynolds numbers

The stability of an infinite elastic plate in supersonic gas flow is investigated taking into account the presence of the boundary layer formed on the plate surface. The effect of viscous and temperature disturbances of the boundary layer on the behavior of traveling waves is studied at large but finite Reynolds numbers. It is shown that in the case of the small boundary layer thickness viscosity can have both stabilizing and destabilizing effect depending on the phase velocity of disturbance propagation.     

Influence of Reynolds number on characteristics of turbulent wall boundary layers

Hot-wire anemometer measurements, using two types of probes, are reported for wall boundary layer flows with particular attention being given to the near-wall region and to measurements at high Reynolds numbers up to R 15,000. To obtain accurate near-wall measurements, the influence of wall proximity on hot-wire readings was eliminated by using a highly insulating wall material. Measurements were carried out with a single hot-wire boundary layer probe to obtain the longitudinal velocity informatemperature-wake sensor for the cross flow tion and a hot-wire, information.The results provided in the paper include measurements of averaged properties like mean velocity, rms-quantities of velocity fluctuations, probability density distributions etc. Conditional averages are also provided in order to yield information related to coherent flow structures present in boundary layer flows. It is shown that these structure remain present up to the highest Reynolds number investigated in the present study. The conditionally averaged data provide quantitative information on the mechanisms that are involved in the production of turbulence in boundary-layer flows.     

Three-Wave Interactions of Disturbances in a Supersonic Boundary Layer

Within the framework of the weakly nonlinear stability theory, group interaction of disturbances in a supersonic boundary layer is considered. The disturbances are represented by two spatial packets of traveling instability waves (wave trains) with multiple frequencies. The possibility of energy redistribution in such wave systems in the case of three-wave resonant interactions of packet constituents is considered. The model is used to test the dynamics of unstable waves arising due to introduction of controlled high-intensity disturbances into a supersonic boundary layer. It is found that this mechanism is not the main one for the features of streamwise dynamics of such nonlinear waves being observed.     

Investigation of a Gas Flow with Solid Particles in a Supersonic Nozzle

A two-phase flow with high Reynolds numbers in the subsonic, transonic, and supersonic parts of the nozzle is considered within the framework of the Prandtl model, i.e., the flow is divided into an inviscid core and a thin boundary layer. Mutual influence of the gas and solid particles is taken into account. The Euler equations are solved for the gas in the flow core, and the boundary-layer equations are used in the near-wall region. The particle motion in the inviscid region is described by the Lagrangian approach, and trajectories and temperatures of particle packets are tracked. The behavior of particles in the boundary layer is described by the Euler equations for volume-averaged parameters of particles. The computed particle-velocity distributions are compared with experiments in a plane nozzle. It is noted that particles inserted in the subsonic part of the nozzle are focused at the nozzle centerline, which leads to substantial flow deceleration in the supersonic part of the nozzle. The effect of various boundary conditions for the flow of particles in the inviscid region is considered. For an axisymmetric nozzle, the influence of the contour of the subsonic part of the nozzle, the loading ratio, and the particle diameter on the particle-flow parameters in the inviscid region and in the boundary layer is studied. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 65–77, November–December, 2005.     

Numerical modeling of perturbation propagation in a supersonic boundary layer

The growth of two-dimensional disturbances generated in a supersonic (M = 6) boundary layer on a flat plate by a periodic perturbation of the injection/suction type is investigated on the basis of a numerical solution of the Navier-Stokes equations. For small initial perturbation amplitudes, the second-mode growth rate obtained from the numerical modeling coincides with the growth rate calculated using linear theory with account for the non-parallelism of the main flow. Calculations performed for large initial perturbation amplitudes reveal the nonlinear dynamics of the perturbation growth downstream, with rapid growth of the higher multiple harmonics.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 33–44. Original Russian Text Copyright © 2004 by Egorov, Sudakov, Fedorov.