Excitation and development of unstable disturbances in a supersonic boundary layer

The initial-boundary value problem of the development of two-dimensional inviscid disturbances excited by an external unsteady local action, turned on at time t=0, is examined. The spectrum of the problem is investigated by means of the WKB method and numerical calculations, and the asymptotic expansions of the wave packets as t are found. It is shown that, contrary to the conclusions of [4], the inviscid instability of the supersonic boundary layer is convective. The reasons for this discrepancy are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 21–29, May–June, 1990.     

Sensitivity of a supersonic boundary layer to acoustic disturbances

The results obtained by the authors in [1] are extended to the case of arbitrary angles of incidence of the external wave. This is not a trivial generalization, since the acoustic scattering undergoes a qualitative change. It is possible to distinguish two excitation channels: the first is connected with the diffraction of the acoustic wave by the spatial inhomogeneity resulting from the displacing action of the boundary layer, and the second with the presence of concentrated acoustic field sources associated with the scattering of the wave at the leading edge. The latter makes the principal contribution to the initial amplitude of the unstable modes when the angles of incidence of the sound are substantially different from zero. At low angles of incidence there is a singularity which can be revealed by introducing narrow intervals in the neighborhood of the limiting values of the wave numbers, where the two excitation channels are approximately equivalent. It is possible to obtain composite expressions for the initial amplitudes of the unstable modes uniformly valid for all angles of incidence of the acoustic wave.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 40–47, January–February, 1992.     

Growth of artificially induced disturbances in a supersonic boundary layer

This work proposes a method of inducing artificial disturbances of adjustable amplitude in a supersonic boundary layer. Using the proposed method, an experimental study is made of the development of a three-dimensional wave packet of low intensity at a frequency of 20 kHz in the boundary layer of a flat plate at Mach number M = 2.0. The Fourier components of the wave packet are determined. The data obtained are compared with the results of calculating the linear stability of the supersonic boundary layer in a plane-parallel flow approximation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 37–43, September–October, 1984.     

Interaction between a supersonic boundary layer and acoustic disturbances

The development of disturbances in a boundary layer that have been induced by an external acoustic field are investigated. The problem is considered in the linear formulation. It is shown that the oscillations inside the supersonic boundary layer can have several times the intensity of the external disturbances. The susceptibility of the boundary layer to the acoustic disturbances increases with increasing Mach number. Cooling of the surface leads to a small decrease in the intensity of the longitudinal velocity oscillations in the layer. The effect of the parameters of the acoustic wave is considered, i.e., the effect of the frequency and phase velocity on the development of the disturbances.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 51–56, November–December, 1977.     

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.     

Linear evolution of controlled disturbances in the supersonic boundary layer on a swept wing

The linear development of controlled disturbances in the three-dimensional supersonic boundary layer on a swept model wing with a sharp leading edge is experimentally investigated at the Mach number 2. The spatial-temporal and spectral-wave characteristics of the wave train of unstable disturbances are obtained. The asymmetry of these characteristics, due to the secondary flow in the three-dimensional boundary layer, is confirmed.     

Influence of boundary layer on unsteady aerodynamic characteristics of blunt cones in a supersonic flow

A study is made of the influence of the boundary layer on the unsteady aerodynamic characteristics of blunt cones oscillating in a supersonic gas stream about zero angle of attack. A solution to the problem is constructed in the framework of the linear theory of bodies of finite thickness. Such an approach has been used [1–3] in the case of the equations of motion of an ideal gas to calculate the unsteady aerodynamic characteristics of sharp and blunt bodies of various configurations. The influence on these characteristics of the viscosity effects due to the presence on the surface of the body of a laminar boundary layer has been taken into account [4–6] for bodies of the simplest shapes (wedge, cone). The present paper considers the unsteady aerodynamic characteristics of cones and investigates the influence of rounding of the tips and laminar and turbulent flow regimes in the boundary layer.     

Stability of a supersonic boundary layer with respect to three-dimensional disturbances

The stability of a supersonic boundary layer over an intensively cooled plate with respect to three-dimensional disturbances is investigated. Two neutral stability curves, the existence of which was established in [1], are contemplated. It is shown by asymptotic analysis that each of these two neutral stability curves separates into a closed and an ordinary neutral curve in a certain range of disturbance propagation angles. As the surface is cooled, the closed neutral curve contracts to a point. The results of asymptotic analysis were confirmed by numerical integration of the stability equations.     

Numerical modeling of the receptivity of a supersonic boundary layer to entropy disturbances

Numerical modeling of the receptivity of a two-dimensional flat-plate boundary layer to entropy disturbances is carried out at the freestream Mach number M_∞ = 6. Low-intensity perturbations considered are in the form of temperature spots of various shapes and with different initial positions downstream of the shock. They are shown to be able to generate unstable disturbances in the boundary layer. This receptivity mechanism is relatively weak as compared with the receptivity to acoustic waves. When the entropy perturbations are introduced upstream of the bow shock, they first pass across the shock. Downstream of the shock this interaction generates acoustic waves which, in turn, penetrate into the boundary layer thus exciting unstable disturbances of a considerably greater amplitude than the temperature spots. Thus, the bow shock can change the receptivity mechanism.     

Numerical modeling of the receptivity of a supersonic boundary layer to acoustic disturbances

The receptivity of a supersonic (M_∞ = 6) boundary layer on a flat plate to acoustic disturbances is investigated on the basis of a numerical solution of the 2D Navier-Stokes equations. Numerical results obtained for fast and slow acoustic waves impinging on the plate at zero angle agree qualitatively with asymptotic theory. Calculations carried out for other angles of incidence of the acoustic waves reveal new features of the perturbation field in the neighborhood of the leading edge of the plate. It is shown that, due to visco-inviscid interaction, the shock formed near the leading edge may significantly affect the acoustic field and the receptivity.     

Influence of a fan of rarefaction waves on the development of a disturbance in a supersonic boundary layer

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 2, pp. 52–55, March–April, 1992.     

Influence of blowing into the boundary layer on supersonic flow past an oscillating cone

The influence of blowing on the unsteady characteristics of a boundary layer is studied for the example of supersonic flow past a sharp cone oscillating about zero angle of attack. The problem of the interaction of the inviscid exterior flow with the laminar boundary layer is solved. It is shown that blowing proportional to the heat flux improves the damping of the oscillations of the cone. If the blowing anticipates the heat flux in phase this effect is strengthened.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 43–46, July–August, 1983.     

Theory of laminar boundary layer separation in supersonic flow

A method of calculation is constructed for the Navier-Stokes equations using asymptotic expansions for high Reynolds numbers and matching techniques to join solutions (for example, [1]). The equations and boundary conditions for the first approximation, the method, and the results of numerical integration for the region lying above the separation point, including the separation point as well, are presented. A comparison is made with experimental data, and corrections corresponding to the second approximation are estimated. On the basis of these results, the limits of applicability of the approximate theories that utilize the boundary layer equations are discussed.     

The rapid expansion of a turbulent boundary layer in a supersonic flow

Rapid Distortion Approximations (RDA) may be used to simplify the Reynolds stress equations in rapidly distorted flows, as suggested by Dussauge and Gaviglio (1987). These approximations neglect diffusive and dissipative terms while retaining the production and pressure terms. The retained terms are then modeled as functions of the Reynolds stress tensor and gradients of the mean flow. The models for the pressure-strain term as developed by Lumley (1978) and Shih and Lumley (1985) are evaluated by comparing the calculated results with experimental data for the case of a Mach 2.84 turbulent boundary layer in a 20° centered expansion. The agreement between computed and experimentally obtained Reynolds stresses was found to be encouraging.Dedicated to Professor J.L. Lumley on the occasion of his 60th birthday.This work was supported by the U.S. Air Force under AFOSR Contract 89-0420. Monitored by Dr. James McMichael.