In-line Oscillation Research Articles

Numerical Simulation of In-Line and Cross-Flow Oscillations of a Cylinder

The flow-induced vibration of a circular cylinder is simulated numerically. The finite element method is used to solve the three-dimensional incompressible Navier-Stokes equations, and the flow field is coupled with the cylinder motion. The oscillation of the cylinder in the in-line direction is shown when the reduced velocity, Ur, is smaller than 4.0. Symmetric vortices are seen for Ur≤2.5 and alternative vortices appear for Ur≥2.9, while the cylinder motion is damped at around Ur=2.6. It is found that the cross-flow oscillation of the cylinder is dominant under the alternative vortex condition. The drag and lift coefficients increase and the vortex field become finer both in space and time by the cross-flow oscillation.

An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries

A non-boundary-conforming formulation for simulating complex turbulent flows with dynamically moving boundaries on fixed Cartesian grids is proposed. The underlying finite-difference solver for the filtered incompressible Navier–Stokes equations is based on a second-order fractional step method on a staggered grid. To satisfy the boundary conditions on an arbitrary immersed interface, the velocity field at the grid points near the interface is reconstructed using momentum forcing without smearing the sharp interface. The concept of field-extension is also introduced to treat the points emerging from a moving solid body to the fluid. Laminar flow cases and large-eddy simulations (LES) are presented to demonstrate the formal accuracy and range of applicability of the method. In particular, simulations of laminar flow induced by the harmonic in-line oscillation of a circular cylinder in quiescent fluid, and from a transversely oscillating cylinder in a free-stream are presented and compared to reference simulations and experiments. LES of turbulent flow over a traveling wavy wall and transitional flow through a bileaflet prosthetic heart valve are also shown. All results are in very good agreement with reference results in the literature.

On fatigue damage accumulation from in-line and cross-flow vortex-induced vibrations on risers

Abstract Large-scale model tests of a tensioned steel riser were performed at Hanoytangen outside Bergen, Norway in 1997. The length of the model was 90 m and the diameter was 3 cm. The information from these tests consists of measured bending strains, tension, flow speed and all relevant riser data. In this work, this information is reexamined in an attempt to improve our understanding of vortex-induced vibrations (VIV) for cases with very high order of responding modes. The aim is in particular to study the relative importance of in-line (IL) and cross-flow (CF) vibrations for fatigue damage accumulation. It is shown that fatigue damage is proportional to U 2 m + 1 (U is the flow velocity) when the modes are dominated by tension. When bending controls the modes, the fatigue damage is proportional to U m + 1 . A linear SN-curve with slope parameter m = 3 is used. The Hanoytangen riser fatigue damage goes as U7 for the lowest velocities and U4 for the highest current velocities. Based on the Hanoytangen data, it seems that the transition velocity between the tension and the bending-stiffness-dominated regions is at the current velocity that gives response at a mode number where a tensioned string and an untensioned beam have equal eigenfrequencies. IL response has a significant contribution to fatigue for cases dominated by the lowest modes. The reason is that IL oscillations will take place at double the frequency of those in CF. For a tension-controlled case, this corresponds to a mode with half the wavelength, while a bending-controlled case will tend to have a wavelength ratio of 2 . Since the curvature for a given amplitude increases with the inverse modal wavelength squared, fatigue from IL tends to dominate for cases with tension-controlled modes (low current speed), while CF will dominate for bending-controlled modes (high current speed). This tendency is clearly seen in the experimental data for both CF and IL responses. Fatigue damage is calculated directly from the measured data and compared to results found by using a computer program based on a semi-empirical method. The program is able to calculate response frequencies, response amplitudes and fatigue damage. The method is limited to account for CF vibrations only. Computed results are compared to measurements. The agreement is in general good, but some discrepancy is seen for cases with high current velocity. In these cases, the real response contains high mode orders (above 25) and tends to have a stochastic nature, while the VIV-analysis model assumes that the response takes place at a limited number of discrete frequencies. Further development of the empirical model is therefore needed.

An experimental study of the in-line oscillations of a closely spaced row of cylinders in cross-flow

An experimental study has been carried out, to examine the vibratory motion in the streamwise direction of a closely spaced row of circular cylinders. The cylinders in the flexible row under study, free to respond in-line with the flow, are placed alternately between cylinders of a fixed row in a water channel. The transverse spacing of the cylinders of the same row was 3 cylinder diameters, yielding a cylinder spacing when the two rows were aligned equal to 1.5 diameters. The experiments were carried out at low Reynolds numbers over a range from 700 to 1200. Each programme of measurements started when the flow velocity was maximum, and the flexible row was displaced at a small distance downstream of the fixed row. As the velocity was gradually decreased and the flexible row was moved to a mean position upstream of the fixed in-line oscillations occurred, whose amplitude, which was not constant at different cycles, was dependent on both the stream velocity and the initial displacement between the two rows. For each flow velocity, the time history of the oscillation of the moving row was recorded, from which the response and the frequency of oscillations were obtained and are presented diagrammatically.

Vortex-induced oscillations at low Reynolds numbers: Hysteresis and vortex-shedding modes

Results are presented for the numerical simulation of vortex-induced vibrations (VIVs) of a cylinder at low Reynolds numbers (Re). A stabilized space–time finite-element formulation is utilized to solve the incompressible flow equations in primitive variables. The cylinder, of low nondimensional mass ( m * = 10 ), is free to vibrate in, both, the transverse and in-line directions. To investigate the effect of Re and reduced natural frequency, F n , two sets of computations are carried out. In the first set of computations the Reynolds number is fixed ( = 100 ) and the reduced velocity ( U * = 1 / F n ) is varied. Hysteresis, in the response of the cylinder, is observed at the low- as well as high-end of the range of reduced velocity for synchronization/lock-in. In the second set of computations, the effect of Reynolds number ( 50 ⩽ Re ⩽ 500 ) is investigated for a fixed reduced velocity ( U * = 4.92 ). The effect of the Reynolds number is found to be very significant for VIVs. While the vortex-shedding mode at low Re is 2S (two single vortices shed per cycle), at Re ∼ 300 and larger, the P + S mode of vortex shedding (a single vortex and one pair of counter-rotating vortices are released in each cycle of shedding) is observed. This is the first time that the P + S mode has been observed for a cylinder undergoing free vibrations. This change of vortex-shedding mode is hysteretic in nature and results in a very large increase in the amplitude of in-line oscillations. Since the flow ceases to remain two-dimensional beyond Re ∼ 200 , it remains to be seen whether the P + S mode of shedding can actually be observed in reality for free vibrations.

A numerical study of flow past a cylinder with cross flow and inline oscillation

Two-dimensional fluid flow around an oscillating circular cylinder is studied numerically at different values of oscillation frequency and amplitude. A novel finite element method which uses discretization along the characteristic line is used for simulation. The solver is coupled to a mesh movement scheme using the Arbitrary Lagrangian–Eulerian (ALE) formulation to account for body motion in the flow field. Two cases of cylinder motion have been studied, cross flow and inline oscillation. In both cases, occurrence of lock on is investigated and the bounds of the lock on region are determined. A comparison of the numerical results with the experimental data indicates that 2D simulation is valid up to Re = 300. Beyond that, 3D effects appear. By using flow visualization, effect of a cylinder oscillation on the flow field and wake pattern has been studied. Also, variation of the mean drag coefficient against the oscillation parameters is discussed. The numerical results are in good agreement with the experimental data available in the literature.

Water Tunnel Experiments on the In-Line Oscillation of Circular Cylinders with Finite Length

A bluff body like a marine structure can be vibrated variously by a separation flow around it. In this study, we focused on in-line oscillation of a circular cylinder under free vibration tests in two degrees of freedom. We studied typical characteristics of in-line oscillation of circular cylinders both in a smooth flow and in a turbulent flow in water tunnel tests. The circular cylinders with finite span lengths were supported elastically in two degrees of freedom. As a result, the response amplitude in the 2nd excitation region is dampened more sensitively with increasing reduced mass-damping parameter Cn than in the 1st excitation region compared with the results of circular cylinder that can oscillate only in one degree of freedom. Also the amplitude in 2nd excitation region is dampened in a turbulent flow, and the lissajous figure of a circular cylinder changed from a figure of 8 to a complex ellipse.

Flow-Induced In-line Oscillation of a Cantilevered Tapered Circular Cylinder

The flow-induced in-line oscillation of a tapered circular cylinder which was supported by a plate spring was experimentally studied through free-oscillation tests in a water tunnel. The response displacement amplitude at a cylinder tip was measured at roduced velocity Vr from 1.0 to 4.0. The taper ratio was varied from 0% to 20% to investigate its effect on the response displacement. The tip diameter of each cylinder was 20 mm and the root diameter was varied. It was found that cylinders with taper ratios of 2.5% to 10% had two excitation regions, while cylinders with taper ratios less than 1% had one excitation region. The taper ratio, therefore, affects the amplitude of the second excitation region. The reference diameter of the tapered cylinder was defined by the diameter at 1/3 length from tip in consideration of the results of oscillation characteristics of tested cylinders. The cylinder with any taper ratio did not oscillated at Vr <1.0. The amplitude of the cylinder with any taper ratio was suppressed at less mass-damping parameter Cn than 2.5, which is the suppression criteria for in-line oscillation of 2-dimensional cylinder. The guideline JEME S 012 of the Japan Society of Mechanical Engineers is valid for tapered circular cylinders, since it is established in consideration of 2-dimensional cylinder.

1305 スパン方向に有限な長さを持つ円柱の流れ方向振動に関する数値解析(オーガナイズドセッション6-II 流れの複合現象:混相流,熱流体,流体関連振動)

1305 スパン方向に有限な長さを持つ円柱の流れ方向振動に関する数値解析(オーガナイズドセッション6-II 流れの複合現象:混相流,熱流体,流体関連振動)

The Flow around a Cantilevered Circular Cylinder with Finite Span-length under Flow-Induced In-line Oscillation (Vortex Frequency Distribution along Span Direction)

The flow-induced in-line oscillation of a centilevered circular cylinder was experimentally studied by free oscillation tests in a water tunnel. Two hot-film probes were set in the wake of a test cylinder to measure the fluctuating velocity in the near-wake. These probes were moved along the span direction at some reduced velocities Vγ. Two types of test cylinders, AR 10 with the aspect ratio of 10 and AR 21 with the aspect ratio of 21, were investigated. AR 21 with an end plate had two excitation regions against Vγ but AR 10 had one excitation region. The vortex structure of the AR 21 cylinder with the end plate was the symmetrical vortex at the first excitation region and was the alternate vortex from the end of the first excitation region to the second excitation region. So, the valley between these excitation regions is caused by the characteristics of the alternate vortex. Because the vortex structure of the AR 10 cylinder was mainly symmetrical vortex at any reduced velocity, the excitatio region of AR 10 is caused by the instability related to the symmetrical vortex. The vibration characteristic that was caused by aspect ratio was explained by the flow around the tip of cylinder, because AR 10 with end plate had two excitation regions. The aspect ratio of the cylinder influeces the vortex structures and the characteristics of vibration.

Flow-induced vibrations of a tethered circular cylinder

One of the most basic examples of fluid-structure interaction is provided by a tethered body in a fluid flow. The tendency of a tethered buoy to oscillate when excited by waves is a well-known phenomenon; however, it has only recently been found that a submerged buoy will act in a similar fashion when exposed to a uniform flow at moderate Reynolds numbers, with a transverse peak-to-peak amplitude of approximately two diameters over a wide range of velocities. This paper presents results for the related problem of two-dimensional simulations of the flow past a tethered cylinder. The coupled Navier–Stokes equations and the equations of motion of the cylinder are solved using a spectral-element method. The response of the tethered cylinder system was found to be strongly influenced by the mean layover angle as this parameter determined if the oscillations would be dominated by in-line oscillations, transverse oscillations or a combination of the two. Three branches of oscillation are noted, an in-line branch, a transition branch and a transverse branch. Within the transition branch, the cylinder oscillates at the shedding frequency and modulates the drag force such that the drag signal is dominated by the lift frequency. It is found that the mean amplitude response is greatest at high reduced velocities, i.e., when the cylinder is oscillating predominantly transverse to the fluid flow. Furthermore, the oscillation frequency is synchronized to the vortex shedding frequency of a stationary cylinder, except at very high reduced velocities. Visualizations of the pressure and vorticity in the wake reveal the mechanisms behind the motion of the cylinder.

インライン振動円柱に作用する流体力(OS3 流体工学III)

インライン振動円柱に作用する流体力(OS3 流体工学III)

722 乱流中における有限長円柱のインライン振動に関する水槽実験(後流渦励起振動のメカニズム,OS-5 流体関連振動のメカニズムと計測制御(1))

722 乱流中における有限長円柱のインライン振動に関する水槽実験(後流渦励起振動のメカニズム,OS-5 流体関連振動のメカニズムと計測制御(1))

直列2円柱の流れ方向振動(GS-10振動物体)

直列2円柱の流れ方向振動(GS-10振動物体)

Flow-induced in-line oscillation of a circular cylinder

Flow-induced in-line oscillation of a circular cylinder either spring-mounted (two-dimensional rigid cylinder) or cantilevered was experimentally studied in free-oscillation tests in a water tunnel. In the free-oscillation tests of a two-dimensional cylinder, two different types of excitations appear at approximately half of the resonance flow velocity. The response amplitudes are sensitive to the reduced mass-damping parameter for the in-line oscillation in the first excitation region with a symmetric vortex street, while the alternate vortices are locked-in with the vibration of the cylinder in the second excitation region. For a cantilevered circular cylinder with a finite span-length, it is found that cylinders with aspect ratios of 5 and 10 have a single excitation region, and cylinders with aspect ratios of 14 and 21 have two excitation regions. The mechanism of vibration was also investigated using a splitter plate in the wake to prevent alternate vortices. It is noted that the amplitude of oscillation with the splitter plate is greater than that without the splitter plate, especially at Vr=2.3 to 3.0, where a cylinder with an end plate shows the second excitation region. In other words, the alternate vortices suppress the excitation amplitude in this range. The results of this study are providing important supporting data for the recent Standard JSME S012-1998, “Guideline for Evaluation of Flow-Induced Vibration of a Cylindrical Structure in a Pipe”, by the Japan Society of Mechanical Engineers.

Numerical study of flow around an inclined elliptic cylinder oscillating in line with an incident uniform flow

Numerical calculations of the flow around an inclined elliptic cylinder oscillating in-line with the incident steady flow are reported at Reynolds number R=10 3 and a fixed major–minor axis ratio of 0.5. The flow is incompressible and two-dimensional, and the in-line oscillations are harmonic. These oscillations are superimposed on the constant translational velocity as a single-frequency perturbation to examine the effect of increase of the perturbation amplitude and angle of inclination on the near-wake structure and the hydrodynamic forces acting on the cylinder. The numerical results lead to the postulation of two regimes for vortex shedding depending on the angle of inclination, which are discussed in some detail for exemplary cases.

621 有限長円柱の流れ方向振動のメカニズム

The flow-induced in-line oscillation of a cantilevered circular cylinder was experimentally studied by free oscillation tests in a water tunnel. Two hot-film probes were set near the test cylinder to measure the fluctuating velocity in the near-wake. These probes were moved along span direction at some reduced velocities. Two types of test cylinders, aspect ratio 10 (AR10) and aspect ratio 21 with the end plate (AR21), were investigated. The vortex structure of the AR21 cylinder with the end plate varied according to the reduced velocity. But the vortex structure of the AR10 cylinder is mainly symmetrical vortex at any reduced velocity. The difference between these vortex structures is related to the characteristics of vibration, i.e. the AR21 cylinder has two excitation regions but the AR10 cylinder has one region.

1626 気泡流における円柱の流れ方向振動

Flow-induced in-line oscillation of a circular cylinder has been experimentally studied by free oscillation tests in a water tunnel. The cantilevered cylinder models were supported elastically by a plate spring so as to oscillate only in the in-line direction. An end-plate (=3d) was fitted to the free end of the cantilevered cylinder to examine the influence f end-effects on the flow. Air-injection pipes were set at 300mm (=15d) upstream before a cylinder model to examine the influence of bubbles. The response characteristics of cylinder with aspect ratio of 10 in bubble flow shows only one excitation region at Vr=1.1 to 3.2 and the oscillating amplitude is smaller than that is uniform flow at Vr=2.0 to 3.2. While a cylinder with aspect ratio of 14 in bubble flow has two excitation regions. The amplitude in the second excitation region (2.5<Vr3.0) is smaller than that in uniform flow. The response characteristics of cylinder with an end-plate in bubble flow shows two excitation regions near half of the response velocity. The amplitude in second excitation region (at Vr=2.5 to 3.3) is smaller than that in uniform flow.

Wind tunnel tests on in-line oscillation of a two-dimensional circular cylinder

Flow-induced in-line oscillation of a two-dimensional circular cylinder model was experimentally investigated in a wind tunnel by the free-oscillation method in order to understand some of the fundamental characteristics of the system. The response amplitude was measured over a wide range of the mass-damping parameter. The discussion is focused primarily on the effects of model aspect ratio and on the number of degrees of freedom of the dynamic system on the response amplitude. As a result of the tests, it was found that the response amplitude of a model with aspect ratio of 6.8 is larger than that of the model with aspect ratio of 1.8. It was also determined that in the region of reduced velocity corresponding to the 1st peak of in-line oscillation, the response amplitude of the model in one degree of freedom is larger than that of the model in two degrees of freedom.

A NUMERICAL SIMULATION OF VORTEX SHEDDING FROM AN OSCILLATING CIRCULAR CYLINDER

Vortex shedding from an oscillating circular cylinder is studied by numerical solutions of the two-dimensional unsteady Navier–Stokes equations. A physically consistent method is used for the reconstruction of velocity fluxes which arise from discrete equations for the mass and momentum balances. This method ensures a second-order accuracy. Two phenomena are investigated and, in both cases, the cylinder oscillation is forced. The first is the flow induced by the harmonic in-line oscillation of cylinder in water at rest. The Reynolds number is equal to 100 and the Keulegan–Carpenter number is equal to 5. A comparison of phase-averaged velocity vectors between measurements and predictions is presented. Applying the widely used model of Morison to the computed in-line force history, the drag and the inertia coefficients are calculated and compared for different grid levels. Using these to reproduce the force functions, deviations from those originally computed are revealed. The second problem is an investigation of a transversely oscillating cylinder in a uniform flow at fixed Reynolds number equal to 185. The cylinder oscillation frequency ranges between 0·80 and 1·20 of the natural vortex-shedding frequency, and the oscillation amplitude is 20% of the cylinder diameter. As the frequency of excitation of the cylinder increases relative to the inherent vortex formation frequency, the initially formed concentration of vorticity moves closer to the cylinder until a limiting position is reached. At this point, the vorticity concentration abruptly switches to the opposite side of the cylinder. This process induces distinct changes of the topology of the corresponding streamline patterns.