Fluid elastic instability of a small circular cylinder in the shear layer of a two-dimensional jet

Abstract

Fluid elastic instability of a long, small-diameter circular cylinder in the shear layer of a two-dimensional air jet is investigated experimentally. A metal wire 0.23 mm in diameter, used as a small circular cylinder, was flexibly mounted along the span-wise direction of the two-dimensional jet, and in the shear layer region where the shear layer thickness is much larger than the wire diameter. The motion of the metal wire was monitored by a two-channel vibration measurement system, and the flow data of the jet were documented by a hot-wire anemometer. Stability of the wire was examined in the experimental ranges of Reynolds number from 8 to 120, reduced velocity from 100 to 1400, and shear parameter from 0 to 0.14. The local flow velocity at the wire location and the wire diameter were chosen as the characteristic velocity and length, respectively, for the three non-dimensional parameters. It is illustrated that in the experimental ranges the wire is unstable and induced to vibrate if initially mounted in a shear layer with sufficient high flow velocity and velocity gradient, while the wire is stable in uniform cross flow. Fluid elastic instability is identified to be responsible for the flow induced vibration. The critical condition for the onset of the instability is determined from amplitude diagrams. It is found that on the critical condition the reduced velocity R and the shear parameter K approximately satisfy the relation RK1.44=5.0 for the small circular cylinder in the airflow with a mass ratio of 5112. Past the critical condition, the amplitude of the wire vibration increases significantly to the scale of the shear layer thickness. By analyses of the vibration amplitudes, spectral data, and orbits of the wire, it is illustrated that the wire vibration in the shear layer of the two-dimensional jet is self-excited through a Hopf bifurcation to a limit cycle state.