Three-dimensional driven-cavity flows with a vertical temperature gradient

An experimental study has been made on the interaction of a vortex ring with a plane solid boundary which is inclined to the axis of the ring. Dye visualizations of the ring during the interaction revealed (i) the formation of bi-helical vortex lines around the circumferential axis of the ring, and (ii) that these vortex lines were constantly being displaced along the circumferential axis on either side of the plane of symmetry and towards the region of the ring furthest away from the wall. Key factors which may be responsible for this phenomenon have been identified and are discussed in this paper.

An experimental study of a vortex ring interacting with an inclined wall

We numerically study a vortex ring impacting a flat wall with an angle of incidence θ ≥ 0°) in three dimensions by using the lattice Boltzmann equation. The hydrodynamic behaviour of the ring–wall interacting flow is investigated by systematically varying the angle of incidence θ in the range of 0° ≤ θ ≤ 40° and the Reynolds number in the range of 100 ≤ Re ≤ 1000, where the Reynolds number Re is based on the translational speed and initial diameter of the vortex ring. We quantify the effects of θ and Re on the evolution of the vortex structure in three dimensions and other flow fields in two dimensions. We observe three distinctive flow regions in the θ–Re parameter space. First, in the low-Reynolds-number region, the ring–wall interaction dissipates the ring without generating any secondary rings. Second, with a moderate Reynolds number Re and a small angle of incidence θ, the ring–wall interaction generates a complete secondary vortex ring, and even a tertiary ring at higher Reynolds numbers. The secondary vortex ring is convected to the centre region of the primary ring and develops azimuthal instabilities, which eventually lead to the development of hairpin-like small vortices through ring–ring interaction. And finally, with a moderate Reynolds number and a sufficiently large angle of incidence θ, only a secondary vortex ring is generated. The secondary vortex wraps around the primary ring and propagates from the near end of the primary ring, which touches the wall first, to the far end, which touches the wall last. The rings develop a helical structure. Our results from the present study confirm some existing experimental observations made in the previous studies.

Numerical study of a vortex ring impacting a flat wall

It is well documented that a trailing vortex pair approaching the ground, and a vortex ring colliding head-on with a rigid plane, experience a reversal in axial velocity which is commonly referred to as “rebound”. One explanation of this phenomenon suggests that it is essentially an inviscid process due to the effect of the finite core-size, whereas another and more widely accepted explanation attributes it to the influence of a secondary vortex which is generated at the surface by viscous effects. The aim of this paper is to assess experimentally the validity of these competing explanations. To achieve this, flow visualization studies of the collision of a vortex ring with a wall are compared with those of the head-on collision of two identical rings. The head-on collision is designed to mimic the inviscid, free-slip case of a ring/wall interaction. This paper describes the experimental findings.

A note on the cause of rebound in the head-on collision of a vortex ring with a wall

An experimental study has been conducted to examine compressible vortex ring structure and propagation, and the interaction of vortex ring with generic-body configurations. The experiments used a circular 30mm internal diameter and 38mm outer diameter shock-tube. The driver and driven gas was air. A vortex ring was generated by the impulse of the shock wave emerging from the open end of the shock-tube. High-speed schlieren photography was employed. Both side view and 45˚ oblique photographs were taken. The interactions with generic shape objects, which were a circular cone, a sphere, a cube and a plane-wall, were studied. Three different driver pressures of 12, 8, and 4 bars were tested with driven gas at 1 bar; the shock wave Mach number inside the tube was 1.63, 1.52 and 1.25 respectively.

Compressible Vortex-Ring Interaction Studies with a Number of Generic Body Configurations

Experimental studies were carried out on the flowfield produced by a vortex ring approaching a plane wall perpendicular to its axis of symmetry, using smoke visualization technique. The mechanism of rebound of a vortex ring from the wall is shown to be related to generation of a shear layer separated from the wall and its subsequent development. The effects of Reynolds numbers on the trajectory of the core center of a vortex ring were also examined. Growth of the separated shear layer and generation of the secondary vortex ring due to vorticity concentration in the separated shear layer were visualized in detail.

Flowfield Produced by a Vortex Ring Near a Plane Wall

Variation of pressure was measured by using a condenser microphone, when a vortex ring was approaching a flat wall. Considerably large negative pressure was observed even at the stagnation point on the wall. This negative pressure was found to occur when the ring “rebounded” from the wall. Before the ring rebounding, the pressure variation could be predicted approximately by the potential flow theory. After the rebounding, it showed negative values, entirely different from the theory. However, this fact can be illustrated by the potential theory applied to a simple, modified model of trajectory of the ring during the rebounding, which takes account of the viscosity effect.

Pressure Variation on a Flat Wall Induced by an Approaching Vortex Ring

Flow in a two-dimensional square cavity was investigated primarily by visualization using white starch powder or aluminium powder suspended in water; the flow was generated by sliding the cavity model itself on a stationary flat plate. Experimental flow patterns at Reynolds numbers up to 1000 were compared with those obtained by numerical calculations. It was found that the experimental location of the center of vortices agrees well with the calculated one. On the other hand the sizes of secondary vortices in the experiment were somewhat smaller than those in the numerical calculations. A velocity profile along a vertical line through the center of primary vortex was experimentally obtained by using the digital image processing technique and it showed fairly good agreement with the calculated profile.

Flow in a two-dimensional square cavity : a comparison between flow visualization experiment and numerical calculations

Flow in a two-dimentional square cuvity was investigated primarily by visualization using white starch powder or aluminum powder suspended in water ; the flow was generated by sliding the cavity model itself on a stationary flat plate. Experimental flow patterns at Reynolds number up to 1000 were compared with those obtained by numerical calculations. It was found that the experimental location of the center of vortices agrees well with the calculated one. On the other hand the sizes of secondary vortices in the experiment was somewhat smaller than those in the numerical calculations. A velocity profile through the center of primary vortex, experimentally obtained along a vertical line by using the digital image processing technique, showed fairly good agreement with that of the calculated profile.

Flow in a two-dimentional square cavity (A comparison between visualized and numerically-calculated flow patterns)

We investigated the properties of a planar jet in which a cylindrical body was set on the center line of the jet near the nozzle. The spread of the jet and some flow properties, particularly behind the cylinder in the jet, were measured for four kinds of cylindrical bodies of different shapes. The downstream as follows: (1) The spread angle of the jet changes considerably with an increase in location of a maximum angle exists there. (1) In the wake region, the generation of the tone due to interaction between the jet and the cylinder plays a crucial role on the flow properties, rather than the shapes of the cylinder.

Haruo Yamabe

Papers

Flowfield Produced by a Vortex Ring Near a Plane Wall

Pressure Variation on a Flat Wall Induced by an Approaching Vortex Ring

Flow in a two-dimensional square cavity : a comparison between flow visualization experiment and numerical calculations

Flow in a two-dimentional square cavity (A comparison between visualized and numerically-calculated flow patterns)

The effect of a cylinder in a planar jet.