Linear stability of three-dimensional boundary layers

Abstract

Stability of compressible three-dimensional boundary layers on a swept wing model is studied within the framework of the linear theory. The analysis based on the approximation of local self-similarity of the mean flow was performed within the Falkner-Skan-Cooke solution extended to compressible flows. The calculated characteristics of stability for a subsonic boundary layer are found to agree well with the measured results. In the case of a supersonic boundary layer, the results calculated for a Mach number M = 2 are also in good agreement with the measured spanwise scales of nonstationary vortices of the secondary flow. The calculated growth rates of disturbances, however, are substantially different from the measured values. This difference can be attributed to a high initial amplitude of disturbances generated in the experiment, which does not allow the linear stability theory to be applied. The evolution of natural disturbances with moderate amplitudes is fairly well predicted by the theory. The effect of compressibility on crossflow instability modes is demonstrated to be insignificant.

Experimental study of nonlinear processes in a swept-wing boundary layer at the mach number M=2

“…It should be noted that disturbances grow in the frequency range from 8 to 35 kHz in the region of their linear development. The ranges of the frequencies of growing disturbances predicted by the linear theory [30] and obtained in the experiments [25] at M = 2 on the wing model with the relative thickness of the airfoil equal to 7.8% and the sweep angle χ = 40 • agree well with each other and with the experimental results of this work. The presence of nonlinear processes leads to expansion of the frequency range and to amplification of high-frequency disturbances.…”

“…The linear stage of the crossflow instability was theoretically studied in [30], and the theoretical results were compared with the experimental data [25] by means of direct numerical simulation. It was demonstrated that the theoretical data agree well with the experimental results obtained for the transverse scales of unstable vortices of the secondary flow.…”

Experimental study of stability and transition of supersonic boundary layer on swept wing at mach number 2-4

“…The linear stage of the cross- §ow instability in relation to stationary and unsteady disturbances was investigated theoretically by Gaponov and Smorodsky [15]. A direct quantitative comparison of the theory with the present authors£ experiments [13] was presented.…”

Evolution of localized artificial disturbance in 2D and 3D supersonic boundary layers

“…It was indicated that the evolution of wave train is similar to the development of traveling waves for subsonic velocities. However, the calculations on linear stability 15 showed that in Kosinov et al 10 the nonlinear evolution of disturbances was observed. To avoid this and to achieve prolongation of the linear stage in the developing disturbance, new swept wing model for controlled experiments was made with a thickness of 2.6%.…”