EVOLUTION OF A 2-D DISTURBANCE IN A SUPERSONIC BOUNDARY LAYER AND THE GENERATION OF SHOCKLETS

Through direct numerical simulation,the evolution of a 2-D disturbance in a supersonic boundary layer has been investigated.At a chosen location,a small amplitude T-S wave was fed into the boundary layer to investigate its evolution. Characteristics of non-linear evolution have been found. Two methods were applied for the detection of shocklets,and it was found that when the amplitude of the disturbance reached a certain value, shocklets would be generated, which should be taken into consideration when nonlinear theory of hydrodynamic stability for compressible flows is to be established.

Theoretical investigation on shocklets in compressible boundary layers

By the shock relationships, the wavy characteristics and the forming condi-tions of a shock wave are analyzed. The wavy characteristics of an Euler system are stud-ied theoretically. The present research focuses on the wavy characteristics of Tollmien-Schlichting （T-S） waves, the excitation conditions of shocklets in compressible boundary layers, and the viscous effect on shock. The possibility of existence of shocklets in the compressible boundary layer and the physical mechanism of formation are theoretically interpreted.

Shocklets in compressible flows

The mechanism of shocklets is studied theoretically and numerically for the stationary fluid, uniform compressible flow, and boundary layer flow. The conditions that trigger shock waves for sound wave, weak discontinuity, and Tollmien-Schlichting （T-S） wave in compressible flows are investigated. The relations between the three types of waves and shocklets are further analyzed and discussed. Different stages of the shocklet formation process are simulated. The results show that the three waves in compressible flows will transfer to shocklets only when the initial disturbance amplitudes are greater than the certain threshold values. In compressible boundary layers, the shocklets evolved from T-S wave exist only in a finite region near the surface instead of the whole wavefront.

A numerical investigation of the evolution of 2-D disturbances in hypersonic boundary layers and the effect on the flow structure due to the existence of shocklets

The evolution of 2-D disturbances in hypersonic boundary layer with Mach number 6,8, and 10 was investigated numerically by three different numerical schemes. At the entrance, second mode T-S waves with different amplitudes were introduced, and the relation between the Mach number and the amplitude of the disturbance when shocklets started to appear was investigated. By comparing the disturbance velocity profiles with those provided by linear stability theory, the effects of shocklets on flow structures were also investigated.

Existence of shocklets in a two-dimensional supersonic mixing layer and its influence on the flow structure

The spatial evolution of a T-S wave and its subharmonic wave, introduced at the inlet in a 2-D supersonic mixing layer, was investigated by using DNS. The relationship between the amplitude of the disturbance wave and the strength of the shocklet caused by the disturbance was investigated. We analyzed the shape of the disturbance velocity profile on both sides of the shocklet, and found that the existence of shocklet affected appreciably the disturbance velocity. The effects on the high speed side and low speed side of the mixing layer were found to be different.

NUMERICAL INVESTIGATION OF EVOLUTION OF DISTURBANCES IN SUPERSONIC SHARP CONE BOUNDARY LAYERS

The spatial evolution of 2-D disturbances in supersonic sharp cone boundary layers was investigated by direct numerical simulation （DNS） in high order compact difference scheme. The results suggested that, although the normal velocity in the sharp cone boundary layer was not small, the evolution of amplitude and phase for small amplitude disturbances would be well in accordance with the results obtained by the linear stability theory （LST） which supposes the flow was parallel. The evolution of some finite amplitude disturbances was also investigated, and the characteristic of the evolution was shown. Shocklets were also found when the amplitude of disturbances increased over some value.

A NUMERICAL STUDY FOR SMALL AMPLITUDE T_S WAVES IN A SUPERSONIC BOUNDARY LAYER

The propagation of the disturbance waves in a boundary layer at Mach number = 4.5 is studied by direct numerical simulation (DNS), using NND scheme, and different amplitudes A = 0.01, 0.001, 0.000 1 of the disturbance have been assumed. The numerical result shows that there might be shocklets induced in the boundary layer, even when the amplitude of disturbance wave is still small.

Imaging of the Space-time Structure of a Vortex Generator in Supersonic Flow

The fine space-time structure of a vortex generator （VG） in supersonic flow is studied with the nanoparticle-based planar laser scattering （NPLS） method in a quiet supersonic wind tunnel. The fine coherent structure at the symmetrical plane of the flow field around the VG is imaged with NPLS. The spatial structure and temporal evolution characteristics of the vortical structure are analyzed, which demonstrate periodic evolution and similar geometry, and the characteristics of rapid movement and slow change. Because the NPLS system yields the flow images at high temporal and spatial resolutions, from these images the position of a large scale structure can be extracted precisely. The position and velocity of the large scale structures can be evaluated with edge detection and correlation algorithms. The shocklet structures induced by vortices are imaged, from which the generation and development of shocklets are discussed in this paper.