Investigation of Resonant Phenomena of Flow Passing a Vibrating Cylinder in the Subcritical Regime
Date Issued
2012
Date
2012
Author(s)
Chen, Shih-Sheng
Abstract
The resonant phenomena of the flow passing a vibrating cylinder in the subcritical regime are numerically investigated by using a two-dimensional Navier-Stokes equation-solver, and implementing the spectral element method. This study mainly contains three parts:
In the first part, the resonant phenomena of the unconfined flow passing a vibrating circular cylinder in the subcritical regime are investigated. Both velocity and pressure responses are computed for Reynolds numbers, Re, between 10 and 45, and exciting Roshko numbers, between 0.1 and 6. For small vibrating amplitudes, a simplified Stuart-Landau model with a forcing term is used to describe the resonant behavior, and a four-parameter best-fit model is proposed for the regression of the Landau’s constants. This demonstrates that the proposed model is suitable for describing the flow in the subcritical regime and the linearity of the resonant Roshko number, Ro, with the Reynolds number can be further extended to a Reynolds number as low as 10. As a consequence, the critical Reynolds number of vortex shedding for the flow around a stationary cylinder can also be determined accurately and efficiently from this linear relationship. A study of probe locations reveals that the lower the Reynolds number is, the larger the deviation of resonant frequencies at various locations. Since the effect of probe locations is significant, a novel method to determine the critical condition is proposed by finding the intersection of the linear Ro-Re relationships from any two different locations. Since pressure and velocity have almost the same Ro-Re relationship, a new device for measuring free stream velocity in the regime of a very low Reynolds number has been proposed.
In the second part, the resonant phenomena of the unconfined flow passing a vibrating elliptical cylinder in the subcritical regime are investigated. The effects of changing axis ratio of the cylinder on the resonant phenomenon are studied. The axis ratios range from Ar = 0.01 to Ar = 2.0, Reynolds numbers range from 15 to 60, and the Roshko numbers range from 0.5 to 8. The investigations of the drag coefficients and the wake streamlines indicate that the axis ratio of the cylinder has a minor effect on the resonant frequency, Ro. However, the axis ratio of the cylinder is found to have a prominent effect on the resonant amplitude; namely, the smaller the axis ratio, the stronger the occurrence of resonant amplitude. The investigation of resonant responses and the probe locations shows that the ratio of velocity and pressure responses poses a great linear relationship against the probe distance behind the vibrating cylinder. Moreover, the resonant method to predict the critical conditions is examined and verified for various elliptical cylinder flows. Based on the critical values found, a reduced Reynolds number and a reduced Roshko number are proposed to unify the various linear relationships resulting from various 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.
In the third part, the resonant phenomena of the channel flow passing a vibrating cylinder with various blockage ratios Br from 1/2 to 1/12 are investigated. Reynolds numbers range from 10 to 80, and the Roshko numbers range from 0.5 to 40. Since both velocity and pressure responses are crucial to a flow meter design, it is a given that special emphasis is made on the velocity and pressure responses. The blockage ratio of the channel is found to have a considerable effect on the resonant amplitude, the response bandwidth, and the resonant frequency. The higher blockage ratio resulted in a higher resonant frequency and wider response bandwidth, but lower resonant amplitude. Furthermore, the resonant Ro-Re relationships for the flow with various blockage ratios are investigated. The concept of the reduced numbers is applied to unify these relationships. Finally, a universal resonant relationship in the subcritical regime is presented regardless of the axis ratio of the cylinder and the blockage ratio of the channel. The result may lead to applications, such as flow meters and flow mixers in low Reynolds number flows before the onset of vortex shedding.
Subjects
Axis Ratio
Blockage Ratio
Channel Flow
Elliptical Cylinder
Resonant Phenomena
Subcritical Flow
Universal Relationship
Vortex Shedding
Type
thesis
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