Table of contents

The flow field induced by a high speed vortex ring approaching a solid wall has been experimentally and numerically studied. The type of vortex ring treated here is generated by a shock produced in a shock tube and then emitted from the tube into the atmosphere. The flow field near the wall has been clarified from the experimental and numerical results. As the vortex ring approaches the wall, a wall boundary layer is induced; thereby a wall vortex is formed. Moreover, a shocklet is generated in the narrow region between the vortex ring and wall vortex. In addition to this shocklet, another shocklet is produced between the vortex core and the separation point of the boundary layer. Concerning the flow field other than near the wall, shock focusing produced by a triple point induced by shock/vortex ring interaction is discussed.

This paper explores the propagation and interaction mechanisms demonstrated by compressible vortex rings. With spark shadowgraph and schlieren photography, we examine the vortical flow regimes produced by the impulse of a shock wave emerging from the open end of a shock tube. For shock-wave Mach numbers ranging from M_s = 1.0 to 2.0, three distinct flow regimes were identified. From M_s = 1.0 to 1.43, conventional-looking vortex rings are produced. These vortex rings are characterized by very thin cores and thus high circumferential instability wavenumbers. From M_s = 1.43 to 1.60, the axial flow velocity in the recirculating region of the vortex ring becomes supersonic, producing a rearward-facing shock wave embedded in this region. From M_s = 1.60 to 2.0, a secondary counter-rotating vortex ring forms ahead of the main vortex-ring. Finally, preliminary results on the interaction of two compressible vortex rings are presented.

In this paper we discuss the mechanisms responsible for the formation of the acoustic wave when a shock interacts with a vortex. Experimental measurements have shown that this interaction produces a primarily quadrupolar acoustic wave with a strong compression attached to the shock front. We review earlier work which shows that this strong compression is due to the distortion of the shock. The origin of the quadrupolar component is examined by comparing two-dimensional computations of the shock-vortex interaction to those of an isolated elliptical vortex. The elliptical vortex is similar to the compressed vortex produced when a shock interacts with an initially circular vortex. We concentrate on interactions in which the shock transit time is short. The pressure field of the shock-vortex interaction is compared to that of an analogous isolated elliptical vortex for three cases: a weak shock interacting with a weak vortex, a strong shock interacting with a weak vortex, and a strong shock interacting with a strong vortex. Our results indicate that both shock distortion and vortex compression are important to the formation of the acoustic wave.

Interaction of a shock wave with a vortex ring is investigated experimentally and computationally. The experimental observation is made by the shadowgraph method, using a spark light of very short duration of about 20 ns. The shadowgraphs are transformed into digital images by an image processor, and the intensity distributions are processed digitally. Compressive (longitudinal) waves generated (scattered) by the shock-vortex interaction are observed experimentally and compared with a computer simulation. The speeds of the shock wave, vortex and scattered wave obtained from the digitized images are compared with the simulation, and agreement is obtained between them. It is found that the scattered wave is regarded as an acoustic wave whose source is identified at the position and instant of the crossing of the shock wave over the core of the vortex ring.

The two-dimensional interaction between sound waves and a vortex is studied. When the mach number defined by the ratio of the typical velocity due to the vortex to the speed of sound is small and the ratio of the size of the vortex to the wavelength is large, a differential equation for the sound waves is derived. Some classes of spiral solutions of the equation are obtained by relating their phase function to the background flow due to the vortex. Using the analogies between the Aharonov-Bohm effect in quantum mechanics, shallow water waves, and sound waves, the scattering problem of an incident dislocated wave is discussed.

The purpose of this study is to investigate the feasibility of applying a kinetic molecular model to the problem of turbulence-oriented computation of compressible flow. Consider a simple two-dimensional initial value problem of the Taylor-Green-type periodic flow in a square region. The Boltzmann equation with its collision term of the BGK model is used in its integral form along the characteristics. An approximation based on small time steps is utilized for actual computation. It takes several times more steps than the corresponding Euler computation. The results show in general that basically the same pattern for flow fields in the early stages is obtained independently by the Euler and the BGK models, with less violent motion with the BGK.

The topic of this contribution is a numerical study of three-dimensional supersonic flow over a blunt fin mounted on a flat plate. The flow pattern is characterized by complex interaction of shock waves and the boundary layer along the plate surface. In this paper the steady-state results for two free stream Mach numbers M = 3 and 7 will be discussed and compared with experiments. For the numerical investigation a time-marching integration method has been applied based on a three-stage Runge-Kutta scheme. Several convergence acceleration techniques have been adopted. Since crisp shock fronts must be resolved for a proper computation of the interaction phenomena the mesh has been adapted in those regions where strong pressure gradients are expected. In addition, a special treatment of the artificial viscosity terms which enhances stability in regions with shocks has been introduced to achieve some upwind properties of the scheme which utilizes central differences for the spatial derivatives. For the simulation of turbulent flow algebraic models have been applied, namely, a Baldwin-Lomax model and a new turbulence model which is based on RNG-theory. The comparison with the experiments shows that for the case studied here the transitional character of the boundary layer has to be taken into account.