Muneshige Okude

Axial Flow in a Vortex in Karman Vortex Street.

The vortex filaments in a Karman vortex street are usually not parallel to the axis of a circular cylinder perpendicular to a uniform flow in a low speed wind tunnel, but incline to the axis of the cylinder. The axial flow to the upstream direction in a vortex was observed by means of flow visualization in each vortex of the Karman vortex street. The axial flow did not take place when the vortex filaments were parallel to the axis of the cylinder. The axial flow is caused by the pressure gradient in the direction of vortex axis, because the pressure at the center of a vortex increases with diffusion of vorticity of the vortex center and with decrease in the circulation of the vortex as the vortex goes downstream. The axial flow was roughly estimated by using the measured values of circulation and vorticity of a vortex in a Karman vortex street.

Growth and decay of vortex street in the wake of a two-dimensional body.

The correlation between the streak line patterns visualized and the results obtained by the hot-wire probe was investigated in the wakes both behind a circular cylinder and a flat plate at zero incidence in a low-speed wind tunnel. When a smoke wire is set in a section of a vortex street, the pattern of streak lines shows the vortex street, if the circulation of each vortex is strong enough. If the circulation is weak, then the streak line pattern does not show the vortex street, but shows only wavy streak lines. The patterns of streak lines for both cases of a circular cylinder and a flat plate seem to show the downstream increase in the size of vortices. However, the vorticity of a vortex in the wake of a circular cylinder diffuses into the surroundings and its circulation decreases downstream. On the contrary, the vorticity in the wake of a flat plate concentrates gradually so that vortices are formed and their circulations increase for some downstream distance. Further downstream, they begin to decrease.

Rearrangement of vortex street in the wake behind a two-dimensional body.

The vortex streets in the wake behind a two-dimensional body were studied experimentally in a wind tunnel at the lower Reynolds number than the critical value. There were the regular mode at lower Reynolds numbers than the critical value and the irregular mode at the higher Reynolds numbers of vortex shedding for three types of two-dimensional bodies. In the regular mode, the rearrangement of vortex street took place at the downstream locations in the wake. The streamwise variation of the velocity fluctuations was similar to that in the wake of a circular cylinder. The dimensionless frequency, F=fh2/v, was proportional to the Reynolds number both in the primary and the secondary vortex street. The F-Re graphs for both vortex streets were nearly parallel to each other. The rearrangement of vortex street in the wake of the two-dimensional bodies was found out to be very similar to that for a circular cylinder.

Diffusion and Concentration of Vorticity in the Wake

The correlation between the flow patterns visualized and the results obtained from the hot-wire probe was investigated with the wakes both behind a circular cylinder and a flat plate at zero incidence in a low speed wind tunnel.The flow patterns for both cases seem to show the downstream increase in the size of vortices, but not always their growth. The vorticity in each vortex diffuses and its circulation decreases downstream in the wake of a circular cylinder. On the contrary, the vorticity concentrates and the circulation increases downstream in the wake of a flat plate.

Process of formation of a vortex street in the wake behind a flat plate

The process of the formation of a vortex street in the wake behind a flat plate set parallel to a uniform flow was investigated in a low speed wind tunnel. The vorticity distributions in the wake were calculated from the measured velocities using Taylors hypothesis. Just behind the plate, the equi-vorticity lines were nearly parallel to the free stream. At locations somewhat downstream, sinusoidal contour lines appeared near the wake center. Further downstream, some closed contour lines appeared in the figures mapped. The arrangement of the closed lines suggests the existence of a vortex street. The maximum value for vorticity in a wave length of the fundamental velocity fluctuation decreased in the downstream direction; the concentration of vorticity, however, increased in a region the further downstream it was. Meanwhile, the value for circulation obtained by the surface integral of vorticity within the closed contours of a vortex increased until the vortex street was established.