Instability of a three-dimensional supersonic boundary layer

Abstract

532.526The instability of three-dimensional boundary layers has become an area of intensive theoretical and experimental research in the last decade [1, 2]. Such boundary layers are encountered in particular in the flow of air past swept wings on aircraft in regions of negative and positive longitudinal pressure gradients.Nearly all of the studies have been conducted for subsonic flow velocities. However, despite the large volume of research, the problem is still not fully resolved: there are qualitative differences between not only the theoretical and experimental data, but also the experimental results obtained by different groups of researchers. The complexity of the problem lies in the fact that together with known Tollmien-Schlichting (TS) waves -the formation of which leads to the transition to turbulence in two-dimensional boundary layers -additional instability waves connected with secondary flows develop in the three-dimensional case. These flows are stationary vortices whose axes are directed mainly along the streamlines of the external flow, as well as some travelling (non-TS) waves. The formation of all of these waves and their relative role in the transition depends heavily on the external conditions.Only two experiments have been conducted at supersonic velocities [3, 4]. The models in them were circular cylinders positioned at a 45 ~ angle to the incoming flow at Math numbers M = 10 and 3.5, respectively. The turbulence transition was studied on the basis of measurements of certain integral quantities -without measurement of the development of processes in the boundary layer. Stationary vortices were detected by visualization on the surfaces.The goal in this investigation is to use measurements made inside a boundary layer to establish if wave processes that are similar to the subsonic case occur in flow about a supersonic airfoil with a sharp leading edge under the "natural" conditions of operation of a wind tunnel. To determine the flow parameters (M**, Re 1, T, U,.), we measured pressure in the afterburner chamber and static pressure in the working part with balances. Stagnation temperature was measured with a thermoeouple. A description of this system was presented in [7]. Measurents of the fluctuation characteristics of the flow during the experiment were performed using instruments and programs developed to measure the transient parameters of a supersonic flow (supersonic boundary layer) [7].Pulsations were measured using a constant-resistance hot-wire anemometer [7] with sensors made of tungsten wire 6 #m in diameter. The length of the sensor wire was 1.2 mm. The sensor was mounted on a holder inserted in the guide bar of

Experimental study of evolution of disturbances in a supersonic boundary layer on a swept-wing model under controlled conditions

“…The minimum of pU(z ~) near z r ~ 4.5-6.0 mm observed in all distributions is caused by a steady streamwise perturbation. Steady vortices in a three-dimensional boundary layer were observed in experiments [9][10][11][12]. In contrast to the results of these papers, the size of a steady perturbation obtained in our experiments is several times greater than the scale of cross-flow steady vortices.…”

“…King [10] concluded that crossflow vortices are less susceptible to acoustic disturbances than the fundamental-mode disturbances or Tollmien-Schlichting waves. Some results of numerical investigation of instability of a three-dimensional boundary layer for M = 3.5 are presented in [11].The first experimental studies of instability of a three-dimensional boundary layer at supersonic velocities were conducted in [12,13]. Evolution of natural fluctuations in the boundary layer on a swept wing was studied.…”

Linear stability of three-dimensional boundary layers

“…The experiments [6] showed that the distribution of the mean and fluctuating characteristics in the boundary layer at supersonic velocities is the same as that at subsonic velocities. Natural fluctuations enhance in the downstream direction.…”

“…Experimental investigations of stability of three-dimensional supersonic boundary layers are now undertaken [6,9,10]. To analyze and interpret the experimental data, they have to be compared with the results calculated by the linear theory.…”

On the oblique breakdown mechanism in a supersonic boundary layer on a swept wing at Mach 2

“…If the issues of stability of the laminar boundary layer at subsonic speeds were studied thoroughly in both experimental and theoretical papers [1,2], for supersonic speeds these problems are less investigated [1,[3][4][5][6][7][8].…”