Spring-mounted Cylinder Research Articles

Modulation and hysteresis in vortex-induced vibration of a spring-mounted cylinder in a slowly varying oscillatory stream

The response of a spring-mounted circular cylinder constrained to vibrate with a single degree of freedom transverse to an oscillating stream is investigated using two-dimensional flow simulations. The Keulegan–Carpenter number was set at large values with the ratio of the oscillatory flow frequency fo to the natural frequency of the cylinder fn assuming values of fo/fn=0.01, 0.02, and 0.04, so as to investigate the effect of very-slowly-varying reduced velocity on the transient response. A maximum reduced velocity of 5, corresponding to a maximum Reynolds number of 150, was employed in all cases. Under these conditions, the cylinder underwent intermittent vortex-induced vibration (VIV) with amplitude modulations at the period of the oscillatory flow. Maximum VIV amplitudes of approximately half diameter occurred near the end of the flow acceleration stage. Pronounced hysteresis was observed in the plots of the ensemble-averaged amplitude and frequency, both being greater during the deceleration stage than during the acceleration stage at the same instantaneous reduced velocity over a significant part of the flow half period. The hysteresis was found to be related to ‘transient’ operating points that, in the space of normalized amplitude and frequency, join smoothly the distinct branches of steady-VIV where operating points do not exist (for the same system with varying the reduced velocity). The main deterministic VIV features were similar at all three frequency ratios examined but the stochastic features became more pronounced as fo/fn was increased. We also found that the cylinder motion and the driving fluid force sometimes were not synchronized around the point of maximum flow velocity, although this point corresponds to well within the synchronization range in steady-VIV.

Vortex Induced Vibration Numerical Simulation of a Spring-Mounted Cylinder in Current

A 2D CFD numerical method based on loose coupling algorithms was adopted to simulate vortex induce vibration of a spring-mounted cylinder. As the accuracy and reliability were focused, the effect analysis of time-step was applied to three typical reduced velocities, which was represented initial branch, upper branch and lower branch respectively. Under the effective courant number, there exist a time-step which would lead to the highest efficiency and the best match for experiment. Because of the limit of RANS method, the predicted vibration amplitude at the upper branch would be lower than experiment value, while the phase angle is sensitive to time step.

Hydrodynamic In-Line Force Coefficients of Oscillating Bluff Cylinders (Circular and Square) at Low Reynolds Numbers

An attempt to measure indirectly the hydrodynamic drag (cD) and inertia (cM) coefficients on oscillating bluff cylinders (circular and square) in quiescent fluid at low Reynolds numbers (low Stokes number) is presented. The Keulegan–Carpenter number was below 15. The experimental approach is based on performing free-decay tests of a spring-mounted cylinder submerged in a water tank. The identification of the instantaneous modal parameters (damping and frequency), via Hilbert transform, of the decaying oscillations allows the determination of (cD) and (cM) by direct comparison with the damping and natural frequency of the system in still air (tank without water). Advantages and shortcomings of this novel experimental approach are presented along the paper.

Characteristics of the Flow-Induced Vibration and Forces With 1- and 2-DOF Vibrations and Limiting Solid-to-Fluid Density Ratios

We studied various characteristics of the flow-induced vibration (FIV) of a spring-mounted cylinder, and the fluctuating lift and drag forces exerted on the cylinder due to the periodic changes in the fluid motion and vortex structure. We compared two conditions, which represent the limiting cases for the solid-to-fluid density ratio: the cylinder density is negligible relative to the fluid density, and the fluid density is negligible relative to the cylinder density. For both conditions, we examined the changes in these characteristics over a wide range of nondimensional mass-damping for one degree of freedom (1-DOF, cross-flow) and 2-DOF (cross-flow and in-line) vibration. The four cases exhibit differences (especially at low mass-damping) but also have some similarities in the characteristics of the FIV, induced forces, and energy extraction from the flow. We examined these differences and similarities, the implied errors when the in-line DOF is neglected, and the feasibility of using a single mass-damping parameter to describe the FIV.

Forced-vibration study of the aeroelastic instability of a square-section cylinder near vortex resonance

Force measurements made on a square-section cylinder forced to oscillate in a direction normal to a stream are presented. These measurements are used to estimate the values that the combined mass-damping parameter of an equivalent spring-mounted cylinder should take if it is to perform oscillation at prescribed values of amplitude ratio and reduced velocity. The mass-damping parameter appears to be predicted well by the quasisteady theory of galloping when the reduced velocity is well above lock-in. Below resonance, the parameter is negative, contrary to the predictions of quasisteady theory, and this indicates why galloping is not usually observed. It is found from the forced-vibration measurements that at a given value of reduced velocity the combined mass-damping parameter may have the same value for more than one amplitude of oscillation, and this observation explains why a spring-mounted cylinder can vibrate at more than one amplitude. An attempt is made to fit the measurements of force and phase angle around vortex resonance with predictions of the nonlinear lift oscillator model proposed by Hartlen and Currie [5]. It is found that the phase angle between the lift and the cylinder displacement is not predicted well by the theory.

Lower Mode Response of Circular Cylinders in Cross-Flow

Transverse amplitude responses of a circular cylinder in cross-flow were determined as a function of reduced velocities for a variety of spring constants and damping coefficients. Maxima were found at reduced velocities of 5 and 16, and were of comparable amplitude. The first resonance, designated the “fundamental mode,” was due to normal vortex street excitation of the spring-mass system. The second resonance, designated the “lower mode,” occurred when the natural frequency was approximately one-third of the normal vortex shedding frequency. By assuming that the driving force was sinusoidal, it was possible to evaluate the lift coefficients at resonance. Lift coefficients for the lower mode behaved similarly with amplitude ratio but were an order of magnitude lower than lift coefficients for the fundamental mode. A mechanism was used to oscillate the cylinder transversely at prescribed frequencies and amplitudes. Dominant wake frequencies were determined from a frequency analysis of the hot-wire signal for a range of velocities and a fixed frequency of oscillation. It was found that synchronization of the shedding frequency to the forcing frequency did not take place for the lower mode. The familiar “lock-in” region, or frequency synchronization over finite bandwidth, was observed for the fundamental mode only. Since the frequency associated with normal vortex shedding was not suppressed when oscillations took place in the lower mode, it would seem that a low frequency vortex street had not replaced the normal one. It is likely, then, that the spring-mounted cylinder responded subharmonically to the exciting force resulting from vortex shedding. In this regard, however, it was curious that subharmonic response was not found at a frequency ratio of 0.5 as it was at 0.33. A conceptual model, which incorporated features of both the low frequency vortex street and subharmonic response, was developed which accounted for lower mode response at a frequency ratio of 0.33 as well as the lack of response at 0.5.