Three-wave interactions of disturbances in a hypersonic boundary layer on a porous surface

Abstract

Interactions of disturbances in a hypersonic boundary layer on a porous surface are considered within the framework of the weakly nonlinear stability theory. Acoustic and vortex waves in resonant threewave systems are found to interact in the weak redistribution mode, which leads to weak decay of the acoustic component and weak amplification of the vortex component. Three-dimensional vortex waves are demonstrated to interact more intensively than two-dimensional waves. The feature responsible for attenuation of nonlinearity is the presence of a porous coating on the surface, which absorbs acoustic disturbances and amplifies vortex disturbances at high Mach numbers. Vanishing of the pumping wave, which corresponds to a plane acoustic wave on a solid surface, is found to assist in increasing the length of the regions of linear growth of disturbances and the laminar flow regime. In this case, the low-frequency spectrum of vortex modes can be filled owing to nonlinear processes that occur in vortex triplets.Key words: hypersonic boundary layer, three-wave resonance systems, acoustic and vortex disturbances.Introduction. It is known that the use of various wavy and porous surfaces, slotted suction, and heated and cooled surfaces substantially affects the character of disturbance development in boundary layers. Possible consequences are, on the one hand, suppression of various disturbances and longer regions of the laminar flow and, on the other hand, intensification of exchange processes and turbulization of the boundary layer (see [1,2]). Therefore, it seems reasonable to examine these factors for the purpose of solving problems of boundary-layer control in practice.Experiments [3] performed in a T-326 hypersonic wind tunnel of the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Division of the Russian Academy of Sciences should be noted, where the composition and dynamics of disturbances along the boundary layer on solid impermeable and porous surfaces at hypersonic Mach numbers were studied. The porous coating was found to affect the disturbance dynamics at the linear and nonlinear stages of disturbance evolution. At high Mach numbers, there appear spatially growing disturbances induced by excitation of acoustic oscillations in addition to natural oscillations (traveling TollmienSchlichting vortex waves, which are the first-mode disturbances). The most intensely growing mode of these acoustic oscillations in the examined flow regimes is the second mode (see [4]).Bountin et al. [3] demonstrated that the linear stage of disturbance development in the boundary layer on a solid impermeable surface is followed by the stage of nonlinear interaction in three-wave systems. There are several triplets in this case. The first triplet relates the plane wave of the second mode with the frequency parameter F II to the pair of oblique waves of the first mode at the subharmonic half-frequency (frequency parameter F II/2 ). The second triplet relates the acoustic wave with the frequency parameter F II ...

Three-wave nonlinear interactions of disturbances in supersonic boundary layer on the solid and porous surfaces

“…In the second order of , one can find from inhomogeneous equations (2) the higherorder disturbances 1 Z as well as construct the amplitude equations for resonance triads by using the solvability conditions. , exp( ), For each wave mode, the dimensionless frequency parameter F related to the frequency by the dependency = ReF was introduced for convenience, and also the reduced dimensionless wave number b = 10 3 /Re remained constant.…”

“…Such investigations carried out for the hypersonic regime М > 5 showed that the main peculiarities accompanying the initial stages of the stability loss and transition are described sufficiently completely by the mathematical apparatus developed in this section of mechanics [1,2] and correspond to the data of experiments [3]. All the above-said was the reason for conducting such a research in supersonic regimes at moderate Mach numbers, when only the vortex oscillations are selected in the flow.…”