Resonant phenomenon of elliptical cylinder flows in a subcritical regime

The resonant phenomena in the wake behind a transversely vibrating elliptical cylinder with different axis ratios from Ar=0.01 to Ar=2.0 in the subcritical regime is numerically investigated. Navier-Stokes equations are solved by a spectral element code with a triangular mesh. Reynolds numbers range from 15 to 60 and the Roshko numbers range from 0.5 to 8 for different elliptical cylinders. Both the velocity and pressure responses in the wake are measured and analyzed. The investigations of the drag coefficients and the wake streamlines indicate that the cylinder's axis ratio has a minor effect on the resonant frequency, Ro(n). However, the cylinder's axis ratio is found to have a prominent effect on the resonant amplitude; namely, the smaller the cylinder's axis ratio, the stronger the occurrence of resonant amplitude. The investigations of resonant responses of both the velocity and pressure and the probe locations may provide information for designing a flow meter based on pressure responses in the subcritical regime. It shows that the ratio of velocity and pressure responses poses a great linear relationship against the probe distance behind the vibrating cylinder. Moreover, a resonant method based on the different resonant frequencies at different probed locations in the subcritical regime to predict the critical conditions is examined and verified for different elliptical cylinders. Finally, based on the critical values found, a reduced Reynolds number and a reduced Roshko number are proposed to unify the different linear relationships resulting from different elliptical cylinder flows. The result indicates that the effect of axis ratio can be stripped off in the reduced plane, which may be applied to a more generalized cylinder shape. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3662003]