Rigid Circular Cylinder Research Articles

Reduced-order model for laminar vortex-induced vibration of a rigid circular cylinder with an internal nonlinear absorber

The nonlinear interaction of a laminar flow and a sprung rigid circular cylinder results in vortex-induced vibration (VIV) of the cylinder. Passive suppression of the VIV by attaching an internal nonlinear vibration absorber that acts, in essence, as a nonlinear energy sink (NES) to the cylinder has been observed in finite-element computations involving thousands of degrees of freedom (DOF). A single-DOF self-excited oscillator is developed to approximate the limit-cycle oscillation (LCO) of the cylinder undergoing VIV. This self-excited oscillator models the interaction of the flow and the cylinder. Then, a two-DOF reduced-order model for the system with the internal NES is constructed by coupling the single-DOF NES to the single-DOF self-excited oscillator. Hence, the complicated high-dimensional system of flow-cylinder-NES involving thousands of DOF is reduced to a two-DOF model. The two targeted energy transfer mechanisms responsible for passive VIV suppression that are observed in the finite-element computations are fully reproduced using the two-DOF reduced-order model. This reduction of the dynamics to an easily tractable low-dimensional reduced-order model facilitates the approximate analysis of the underlying dynamics. Moreover, the underlying assumptions of the order reduction, and the parameter ranges of validity of the reduced-order model are formulated and systematically studied.

Coupling of parabolic equation method with the scattering of sound

The problem of sound scattering by an infinitely long penetrable and impenetrable cylinder suspended over a realistic impedance ground is investigated. The analytical approach using the image source method in the scattering of sound involves expressing the total sound field at any receiver point (over a locally reacting ground) as the sum total of the direct field, the ground reflection from the source, scattered field by the actual cylinder and finally by its image. The exact solutions can then be expressed as an infinite series, containing Bessel and Hankel functions of increasing order. The coefficients of the scattered field are determined by matching the desired boundary condition (for a rigid circular cylinder, for example, the normal component of velocity is zero on the boundary). Although the preceding approach is commonly used in theoretical treatments of sound scattering, to the best of our knowledge this is the first time it has been attempted numerically with coupling to the Parabolic Equation (PE) method. Presented is a Two-dimensional case of sound scattering of PE generated acoustic field by an impenetrable (soft or rigid) and penetrable cylindrical obstacle over a finite impedance ground in a non-refractive atmosphere.

Phenomena and modeling of piezoelectric energy harvesting from freely oscillating cylinders

We investigate energy harvesting from vortex-induced vibrations of a freely moving rigid circular cylinder with a piezoelectric transducer attached to its transverse degree of freedom. The power levels that can be generated from these vibrations and variations of these levels with the freestream velocity are determined. A mathematical model that accounts for the coupled lift force, cylinder motion, and harvested voltage is presented. Linear analysis is performed to determine the effect of the electrical load resistance of the transducer on the natural frequency of the cylinder and the onset of synchronization (the shedding frequency is equal to the cylinder oscillating frequency) region. The impact of the nonlinearities on the cylinder response and harvested energy is investigated. The results show that the load resistance shifts the onset of synchronization to higher freestream velocities. For two different system parameters, the results show that the nonlinearities result in a hardening behavior for some values of the load resistance.

Selective Roughness in the Boundary Layer to Suppress Flow-Induced Motions of Circular Cylinder at 30,000<Re<120,000

A passive control means to suppress flow-induced motions (FIM) of a rigid circular cylinder in the TrSL3, high-lift, flow regime is formulated and tested experimentally. The developed method uses passive turbulence control (PTC) consisting of selectively located roughness on the cylinder surface with thickness about equal to the boundary layer thickness. The map of “PTC-to-FIM,” developed in previous work, revealed robust zones of weak suppression, strong suppression, hard galloping, and soft galloping. PTC has been used successfully to enhance FIM for hydrokinetic energy harnessing using the VIVACE Converter. PTC also revealed the potential to suppress FIM to various levels. The map is flow-direction dependent. In this paper, the “PTC-to-FIM” map is used to guide development of FIM suppression devices that are flow-direction independent and hardly affect cylinder geometry. Experiments are conducted in the Low Turbulence Free Surface Water Channel of the University of Michigan on a rigid, horizontal, circular cylinder, suspended on springs. Amplitude and frequency measurements and broad field-of-view visualization reveal complex flow structures and their relation to suppression. Several PTC designs are tested to understand the effect of PTC roughness, location, coverage, and configuration. Gradual modification of PTC parameters, leads to improved suppression and evolution of a design reducing the VIV synchronization range. Over a wide range of high reduced velocities, VIV is fully suppressed. The maximum amplitude occurring near the system’s natural frequency is reduced by about 63% compared to the maximum amplitude of the smooth cylinder.

Open rotor tone scattering

This paper describes a method for calculating the scattering of open rotor tones by an adjacent surface such as the aircraft fuselage or wing. This is of practical importance because shielding by these structures could be used to significantly reduce community noise levels. In the first part of this paper the propeller is modelled as a rotating point source and the effect of propeller translation is neglected. The scattering of sound from this rotating point source by either a rigid circular cylinder or a rigid half-plane is calculated and the reflection/shielding effect is clearly demonstrated. In the second part of this paper, the point source/stationary medium model is extended to include the effect of distributed sources and a moving medium. The extended model is then applied to calculate the effect of scattering of rotor-alone tones by a wing (which is modelled as an infinite half-plane). The effect of wing sweep and the application of the Kutta-condition at the trailing edge is investigated. An approximate method for quickly calculating open rotor tone scattering is also developed and validated.

付加物が渦励振に与える影響の実験

In Ocean development, many cylindrical shape structures are in use. These structures are subjected to many external forces, such as water current, waves and reaction force from the upper structure. Especially, the lift force induced by the shedding vortices cause the vibration of the structures. This phenomenon is called Vortex Induced Vibration, VIV. It is assumed that VIV causes fatigue damages on the structure because it contains high frequency component of vibration and it increases in drag force on the structure. One of the solutions to decrease VIV, the appendage such as splitter plates or fairings is used to be attached on the structures. However, it may happen that such appendages increase the amplitude of VIV in some situations. Meanwhile, for actual use, it must be considered not only the decreasing performance but also the ease of handling. If Computational Fluid Dynamics is used, it is easy to modify the shape of the appendage and simulate its performance in different circumstances. Before that, it is needed to reveal the influence of the motion and flow field around the structure with the appendages. In this study, a rigid circular cylinder with or without appendage was supported by coil springs in the circular tank. The motion and rotation of the cylinder were measured by tracking the markers attached on its cross section. In the same manner, those of the appendage were also measured. The flow field around the cylinder was visualized by PIV. Experimental results show that the appendage, such as splitter plate or fairing, sometimes can not decrease the amplitude of VIV. They also show that the appendage which can shorten the distance between the shedding vortices near the cylinder can decrease VIV.

117 摩擦を考慮した剛体円柱と弾性平板の接触解析(材料力学IV)

117 摩擦を考慮した剛体円柱と弾性平板の接触解析(材料力学IV)

Numerical Simulation of Vortex-Induced Vibrations of Inclined Cables under Different Wind Profiles

AbstractVortex-induced vibration of an inclined cable under wind with varying velocity profiles was investigated through computational fluid dynamics numerical simulation. As a complicated fluid-structure interaction issue, the flow field around the freely oscillating cable was simulated by Ansys CFX 11.0, and the cable oscillation as calculated using the Galerkin approach (realized by the additional subroutine, which is embedded into Ansys CFX 11.0). The shear stress transport k-ω turbulent model based on the Reynolds-averaged Navier-Stokes method was employed to simulate the behavior of turbulent flow in the CFD numerical simulation. The above computational method and turbulent model were validated through comparison of the computational results with the wind tunnel test results of a rigid circular cylinder. And then, two inclination angles, 30° and 90°, were chosen for the inclined cable; wind with a uniform velocity profile (velocity profile U) and four types of velocity profiles were used as the inle...

On the study of vortex-induced vibration of a cylinder with helical strakes

While the effect of helical strakes on suppression of Vortex-Induced Vibrations (VIV) has been studied extensively, the mechanism of VIV mitigation using helical strakes is much less well documented in the literature. In the present study, a rigid circular cylinder of diameter d=80 mm attached with three-strand helical strakes of dimensions of 10 d in pitch and 0.12 d in height was tested in a wind tunnel. It was found that the helical strakes can reduce VIV by about 98%. Unlike the bare cylinder, which experiences lock-in over the reduced velocity in the range of 5–8.5, the straked cylinder does not show any lock-in region. In exploring the mechanism of VIV reduction by helical strakes, measurements in stationary bare and straked cylinder wakes using both a single X-probe at four different Reynolds numbers, i.e. Re=10 240, 20 430, 30 610 and 40 800, and two X-probes with variable separations in the spanwise direction at Re=20 430 were conducted. It was found that vortices shed from the straked cylinder are weakened significantly. The dominate frequency varies by about 30% over the range of x/ d=10–40 in the streamwise direction while that differs by about 37.2% of the averaged peak frequency over a length of 3.125 d in the spanwise direction. The latter is supported by the phase difference between the velocity signals measured at two locations separated in the spanwise direction. The correlation length of the vortex structures in the bare cylinder wake is much larger than that obtained in the straked cylinder wake. As a result, the straked cylinder wake agrees more closely with isotropy than the bare cylinder wake. Flow visualization on the plane perpendicular to the cylinder axis at Reynolds number of about 300 reveals small-scale vortices in the shear layers of the straked cylinder wake. However, these vortices do not roll up and interact with each other to form the well-organized Karman-type vortices. Flow visualization on the plane parallel to the cylinder axis shows vortex dislocation and swirling flow, which should be responsible for the variations of the peak frequency in the streamwise as well as spanwise directions.

Experimental Investigations of the Efficiency of Round-Sectioned Helical Strakes in Suppressing Vortex Induced Vibrations

Vortex induced vibrations (VIVs) may cause a large amount of damage to deep water risers. Helical strakes are used as a mitigating measure to suppress these vibrations. The purpose of this paper is to verify the efficiency of round-sectioned helical strakes in suppressing VIV. It is believed that round-sectioned helical strakes can be more readily mounted on risers for intervention and maintenance compared with sharp-edged strakes that may have to be welded onto the risers. Systematic experimental investigations including 28 configurations of round-sectioned helical strakes were tested in an attempt to find the most suitable strake configuration. The experiments were performed in a steady flow flume with an elastically mounted rigid circular cylinder of 500 mm in length and 50 mm in outer diameter. The test cylinder was spring-supported in both the inline and cross-flow directions. The measurements were limited to mapping the displacement of the cylinder. First, the cylinder was tested without strakes as a reference case. The best configuration among the tested round-sectioned helical strake configurations was found to reduce the amplitude of oscillation relative to the bare cylinder case by 96% in the cross-flow direction and by 97% in the inline direction. The main features of this configuration are the number of starts (3), the pitch (5D), and the diameter of the strake (0.15D), where D is the outer diameter of the test cylinder. Additionally, this paper investigates the effects of varying pitch, the effects of surface roughness, and the effects of the ratio between the cross-flow and inline natural frequencies of the test rig on the efficiency of the suggested configuration of round-sectioned helical strakes.

Experimental investigation of Reynolds number effect on vortex induced vibration of rigid circular cylinder on elastic supports

Vortex induced vibration (VIV) of circular cylinders is widely accepted as depending weakly on Reynolds number (Re) and strongly on reduced velocity, mass ratio, and damping. Experiments are conducted in the regime right before transition from laminar to turbulent flow (high-Reynolds 2×l0 4−4×l0 4<Re<3.5×l0 5−6×l0 6) in the Low Turbulence Channel at the University of Michigan. Limited experimental data are available in that regime. This research was initiated in 2004 studying high-damping VIV to convert hydrokinetic energy from ocean/river currents to electricity using the VIVACE Converter. The following experimental observations are made: low and high Reynolds VIV significantly differ. The range of synchronization of the upper branch increases with increase in Reynolds number. Amplitude ratio ( A/ D) increases with Reynolds number within the upper branch. For high-Reynolds, A/ D=1.9 is achieved routinely in spite of high damping. The lower branch disappears, overtaken by extended upper branch. High-Reynolds VIV enters into the 2P domain in the Williamson–Roshko (W–R) map beginning with the initial branch. Hysteresis is not observed in these experiments possibly because parameters remain in the 2P-domain. High Reynolds numbers have a stronger influence than mass ratio on A/ D. High-damping high-Reynolds VIV amplitudes are double of those predicted by the modified Griffin plot by extrapolation.

Numerical simulation of an elementary Vortex-Induced-Vibration problem by using fully-coupled fluid solid system computation

Numerical simulation of Vortex-Induced-Vibrations (VIV) of a rigid circular elastically-mounted cylinder submitted to a fluid cross-flow has been extensively studied over the past decades, both experimentally and numerically, because of its theoretical and practical interest for understanding Flow-Induced-Vibrations (FIV) problems. In this context, the present article aims to expose a numerical study based on fully-coupled fluid-solid computations compared to previously published work [34], [36]. The computational procedure relies on a partitioned method ensuring the coupling between fluid and structure solvers. The fluid solver involves a moving mesh formulation for simulation of the fluid structure interface motion. Energy exchanges between fluid and solid models are ensured through convenient numerical schemes. The present study is devoted to a low Reynolds number configuration. Cylinder motion magnitude, hydrodynamic forces, oscillation frequency and fluid vortex shedding modes are investigated and the “lock-in” phenomenon is reproduced numerically. These numerical results are proposed for code validation purposes before investigating larger industrial applications such as configurations involving tube arrays under cross-flows [4].

Fluid-structure interaction of two bodies in an inviscid fluid

The interaction of two arbitrary bodies immersed in a two-dimensional inviscid fluid is investigated. Given the linear and angular velocities of the bodies, the solution of the potential flow problem with zero circulation around both bodies is reduced to the determination of a suitable Laurent series in a conformally mapped domain that satisfies the boundary conditions. The potential flow solution is then used to determine the force and moment acting on each body by using generalized Blasius formulas. The current formulation is applied to two examples. First, the case of two rigid circular cylinders interacting in an unbounded domain is investigated. The forces on two cylinders with prescribed motion (forced-forced) is determined and compared to previous results for validation purposes. We then study the response of a single “free” cylinder due to the prescribed motion of the other cylinder (forced-free). This forced-free situation is used to justify the hydrodynamic benefits of drafting in aquatic locomotion. In the case of two neutrally buoyant circular cylinders, the aft cylinder is capable of attaining a substantial propulsive force that is the same order of magnitude of its inertial forces. Additionally, the coupled interaction of two cylinders given an arbitrary initial condition (free-free) is studied to show the differences of perfect collisions with and without the presence of an inviscid fluid. For a certain range of collision parameters, the fluid acts to deflect the cylinder paths just enough before the collision to drastically affect the long time trajectories of the bodies. In the second example, the flapping of two plates is explored. It is seen that the interactions between each plate can cause a net force and torque at certain instants in time, but for idealized sinusoidal motions in irrotational potential flow, there is no net force and torque acting at the system center.

A new wake oscillator model for predicting vortex induced vibration of a circular cylinder

This article proposes a new wake oscillator model for vortex induced vibrations of an elastically supported rigid circular cylinder in a uniform current. The near wake dynamics related with the fluctuating nature of vortex shedding is modeled based on the classical van der Pol equation, combined with the equation for the oscillatory motion of the body. An appropriate approach is developed to estimate the empirical parameters in the wake oscillator model. The present predicted results are compared to the experimental data and previous wake oscillator model results. Good agreement with experimental results is found.

Indentation of a laminated composite plate with an interlayer rectangular void

We employ the Eshelby–Stroh formalism to study generalized plane strain infinitesimal deformations caused due to the indentation by a rigid circular cylinder of an elastic laminated plate with a through-the-width rectangular void between two adjoining layers. Assuming that the void does not close during the indentation process, we find the indentation modulus (i.e., the slope of the indentation load vs. the indentation depth curve) as a function of the void size, the void position, elastic moduli of the layers, and boundary conditions at the edges. The change in the indentation modulus caused by an interlayer void parallel to the major surfaces of an anisotropic plate can potentially be used to estimate the void size and location.

Three-Dimensional Numerical Simulations of Flows Past Smooth and Rough/Bare and Helically Straked Circular Cylinders Allowed to Undergo Two Degree-of-Freedom Motions

We simulate the flow past smooth and rough rigid circular cylinders that are either bare or outfitted with helical strakes. We consider operating conditions that correspond to high Reynolds numbers of 105 and 106, and allow for two degree-of-freedom motions such that the structure is allowed to respond to flow-induced cross-flow and in-line forces. The computations are performed using a parallelized Navier–Stokes in-house solver using overset grids. For smooth surface simulations at a Reynolds number of 105, we use a Smagorinsky large eddy simulation turbulence model and for the Reynolds number cases of 106 we make use of the unsteady Reynolds-averaged Navier–Stokes equations with a two-layer k-epsilon turbulence model. The rough surface modifications of the two-layer k-epsilon turbulence model due to Durbin et al. (2001, “Rough Wall Modification of Two-Layer k-Epsilon,” ASME J. Fluids Eng., 123, pp. 16–21) are implemented to account for surface roughness effects. In all our computations we aim to resolve the boundary layer directly by using adequate grid spacing in the near-wall region. The predicted global flow parameters under different surface conditions are in good agreement with experimental data, and significant vortex-induced vibration suppression is observed when using helically straked cylinders.

Quasisteady theory for the hydrodynamic forces on a circular cylinder undergoing vortex-induced vibration

Vortex-induced vibrations of a rigid circular cylinder were studied by constructing a theory based on a wake oscillator model under quasisteady approximations, thereby evaluating vortex-induced hydrodynamic forces acting on the cylinder. A lock-in limit line representing the boundary for the occurrence of frequency lock-in was also theoretically derived. Hydrodynamic forces in forced oscillation problems estimated by the theory were compared with measured ones. Although some discrepancies were found, particularly in cases with high-frequency oscillations, good agreement was achieved in most cases. Accordingly, we conclude that the present theory captures well real phenomena in the wake downstream of a cylinder subjected to a flow.

Spatial flow structure around a smooth circular cylinder in the critical Reynolds number regime under cross-flow condition

The spanwise flow structure around a rigid smooth circular cylinder model in cross-flow has been investigated based on the experimental data obtained from a series of wind tunnel tests. Surface pressures were collected at five spanwise locations along the cylinder over a Reynolds number range of <TEX>$1.14{\times}15^5$</TEX> to <TEX>$5.85{\times}10^5$</TEX>, which covered sub-critical, single-bubble and two-bubble regimes in the critical range. Separation angles were deduced from curve fitted to the surface pressure data. In addition, spanwise correlations and power spectra analyses were employed to study the spatial structure of flow. Results at different spanwise locations show that the transition into single-bubble and two-bubble regimes could occur at marginally different Reynolds numbers which expresses the presence of overlap regions in between the single-bubble regime and its former and later regimes. This indicates the existence of three-dimensional flow around the circular cylinder in cross-flow, which is also supported by the observed cell-like surface pressure patterns. Relatively strong spanwise correlation of the flow characteristics is observed before each transition within the critical regime, or formation of first and second separation-bubbles. It is also noted that these organized flow structures might lead to greater overall aerodynamic forces on a circular cylinder in cross-flow within the critical Reynolds number regime.

Transient Fluid Forces on a Rigid Circular Cylinder Subjected to Small Amplitude Motions

The present paper treats the transient fluid forces experienced by a rigid circular cylinder moving along a radial line in a fluid initially at rest. The body is subjected to a rapid displacement of relatively small amplitude in relation to its radius. Both infinite and cylindrically confined fluid domains are considered. Furthermore, non-negligible amplitude motions of the inner cylinder, and viscous and compressible fluid effects are addressed, successively. Different analytical methods and models are used to tackle each of these issues. For motions of non-negligible amplitude of the inner cylinder, a potential flow is assumed and the model, formulated as a two-dimensional boundary perturbation problem, is solved using a regular expansion up to second order. Subsequently, viscous and compressible effects are handled by assuming infinitesimal amplitude motions. The viscous fluid forces are formulated by solving a singular perturbation problem of the first order. Compressible fluid forces are then determined from the wave equation. A nonlinear formulation is obtained for the non-negligible amplitude motion. The viscous and compressible fluid forces, formulated in terms of convolution products, are linked to fluid history effects induced by wave propagation phenomena in the fluid domain. These models are expressed with dimensionless parameters and illustrated for a specific motion imposed on the inner cylinder. The different analytical models permit coverage of a broad range of motions. Hence, for a given geometry and imposed displacement, the appropriate fluid model can be identified and the resulting fluid forces rapidly estimated. The limits of these formulations are also discussed.

Locally enriched finite elements for the Helmholtz equation in two dimensions

This paper presents a finite element method for the solution of Helmholtz problems at high wave numbers that offers the potential of capturing many wavelengths per nodal spacing. This is done by constructing oscillatory shape functions as the product of polynomial shape functions and either Bessel functions or planar waves. The resulting elementary matrices obtained from the Galerkin-Bubnov formulation contain oscillatory terms and are evaluated using high order Gauss-Legendre integration. The problem of interest deals with the diffraction of an incident plane wave by a rigid circular cylinder. Numerical experiments are carried out on a square computational domain for which the analytical solution of the problem is imposed on its boundary. The obtained results using the proposed finite element models are compared for different locations of the computational domain, with respect to the diffracting object, and for increasing wave number. It is shown that in the near field, the plane wave basis finite element model provides more accurate results. However, far from the scattering object, the Bessel function approximating model provides better accuracy.