Experimental and theoretical investigation of galloping of transversely inclined slender prisms

Galloping is characterized by large and periodical oscillations which may lead to collapse of slender structures. This study is the first attempt of a comprehensive experimental and theoretical investigation of galloping of transversely inclined prisms. A modified quasi-steady model is proposed with a constant term to estimate the galloping of a transversely inclined prism, which is later experimentally investigated by conducting a static Synchronous Multi-Pressure Sensing System (SMPSS) test and an aeroelastic test in a boundary layer wind tunnel. The galloping responses of the prisms were measured in the aeroelastic test, while the aerodynamic force coefficients were determined from the SMPSS test. These experimental results were subsequently utilized to validate the quasi-steady model. Based on the proposed model, the galloping responses of the prisms were predicted and compared with the experimental results. The experimentally measured and theoretically predicted galloping responses are discussed with respect to aerodynamic damping ratios, onset galloping wind speeds, distributed pressure coefficients, point pressure spectra and vortex shedding frequencies. Interesting findings are summarized.     

Galloping instability and control of a rigid pendulum in a flowing soap film

A pendulum suspended in a fast flowing soap film may show sustained oscillations. The conditions necessary for self-excited motion to occur are outlined: a flow velocity above a threshold value along with geometrical constraints. The role of vortex shedding is discussed, and the observed instability is shown to be well-described by the galloping instability. Experimental results are supported by numerical simulations. Furthermore, we observe that the instability may be suppressed by attaching a long enough filament to the rear of the pendulum.     

Critical Reynolds number and galloping instabilities: experiments on circular cylinders

The current paper considers large galloping-like vibrations of circular cylinders, generically inclined and yawed to the flow. The case of a round section prone to galloping is seemingly a paradox since rotational symmetry (or close to it) and classical galloping are apparently contradictory. Still there seems to be a range of wind speeds far from those for typical Kármán vortex shedding resonance where such a phenomenon does occur. Experimental results from both static and dynamic large-scale rigid cable models, presented here, show that this range coincides with the critical Reynolds number regime, where notable symmetry-breaking characteristics such as nonzero mean lift emerge. It is shown that a fundamental difference between the inclined and non-inclined cylinder aerodynamics may exist accommodating different pressure distributions and different resulting dynamic behaviours. Unsteady pressure measurements showing avalanche-like “jumps” and vortex dislocations building between cell structures in the cylinder spanwise direction are conjectured to be a key element in the unstable behaviour experienced.     

Accurate model reduction of transient and forced wakes

Some applications of a precise method to model the transient dynamics of large scale structures in the laminar flow past a bluff body are presented. The flow is described using empirical eigenfunctions obtained by “proper orthogonal decomposition” and the models are constructed projecting the Navier–Stokes equations onto such eigenfunctions. The linear terms in the expansion coefficients as well as in the control inputs are adjusted to exactly mimic some reference solutions. Applications shown are relative to the development of flow instabilities leading to vortex shedding and the dynamics of the vortex wake under external actuation.     

低雷诺数下串列三圆柱涡激振动中的弛振现象及其影响因素

对间距比为1.2和雷诺数为100的串列三圆柱涡激振动进行数值模拟, 发现在某个折合流速之后, 三圆柱的响应均呈现为随着折合流速增大而增大的弛振现象, 平衡位置偏移、低频振动以及旋涡脱落与圆柱运动之间的时机三个因素共同决定了弛振现象的出现. 进一步的研究发现, 串列三圆柱的弛振现象仅出现在质量比不大于2.0和雷诺数不大于100的工况下. 当质量比较大时, 串列三圆柱的平衡位置固定不变, 且圆柱的振动不规律, 使得旋涡脱落与圆柱运动的时机处于变化之中. 当雷诺数较高时, 最上游圆柱的平衡位置在折合流速较大时回到初始位置, 不再参与对圆柱振动的调节, 使得圆柱的振动响应不再规律, 旋涡脱落与圆柱运动的时机也一直处于变化之中.      

Limit-cycle oscillations in unsteady flows dominated by intermittent leading-edge vortex shedding

High-frequency limit-cycle oscillations of an airfoil at low Reynolds number are studied numerically. This regime is characterized by large apparent-mass effects and intermittent shedding of leading-edge vortices. Under these conditions, leading-edge vortex shedding has been shown to result in favorable consequences such as high lift and efficiencies in propulsion/power extraction, thus motivating this study. The aerodynamic model used in the aeroelastic framework is a potential-flow-based discrete-vortex method, augmented with intermittent leading-edge vortex shedding based on a leading-edge suction parameter reaching a critical value. This model has been validated extensively in the regime under consideration and is computationally cheap in comparison with Navier–Stokes solvers. The structural model used has degrees of freedom in pitch and plunge, and allows for large amplitudes and cubic stiffening. The aeroelastic framework developed in this paper is employed to undertake parametric studies which evaluate the impact of different types of nonlinearity. Structural configurations with pitch-to-plunge frequency ratios close to unity are considered, where the flutter speeds are lowest (ideal for power generation) and reduced frequencies are highest. The range of reduced frequencies studied is two to three times higher than most airfoil studies, a virtually unexplored regime. Aerodynamic nonlinearity resulting from intermittent leading-edge vortex shedding always causes a supercritical Hopf bifurcation, where limit-cycle oscillations occur at freestream velocities greater than the linear flutter speed. The variations in amplitude and frequency of limit-cycle oscillations as functions of aerodynamic and structural parameters are presented through the parametric studies. The excellent accuracy/cost balance offered by the methodology presented in this paper suggests that it could be successfully employed to investigate optimum setups for power harvesting in the low-Reynolds-number regime.     

Roughness and turbulence intensity effects on the induced flow oscillation of a single cylinder

The effects of the surface roughness and the turbulence intensity on the dynamic characteristics of the flow induced oscillations of an elastically supported single circular cylinder in a cross flow in the vortex shedding and fluid elastic regions were experimentally investigated. The results of these experiments indicate that, for the vortex shedding region, increasing the surface roughness results in a reduction of the amplitude of oscillation, while in the fluid elastic region, increasing the surface roughness tends to enhance the oscillations. A similar trend for the dynamic response of the cylinder in the vortex shedding region was also observed when the free stream turbulence intensity was varied, while in the fluid elastic region variations in the free stream turbulence intensity were observed to have no drastic effect on the dynamic response of the cylinder.     

Roughness and turbulence intensity effects on the induced flow oscillation of a single cylinder

The effects of the surface roughness and the turbulence intensity on the dynamic characteristics of the flow induced oscillations of an elastically supported single circular cylinder in a cross flow in the vortex shedding and fluid elastic regions were experimentally investigated. The results of these experiments indicate that, for the vortex shedding region, increasing the surface roughness results in a reduction of the amplitude of oscillation, while in the fluid elastic region, increasing the surface roughness tends to enhance the oscillations. A similar trend for the dynamic response of the cylinder in the vortex shedding region was also observed when the free stream turbulence intensity was varied, while in the fluid elastic region variations in the free stream turbulence intensity were observed to have no drastic effect on the dynamic response of the cylinder.     

Effect of vortex shedding in unsteady aerodynamic forces for a low Reynolds number stationary wing at low angle of attack

This study elucidates the relation between wake vortex shedding and aerodynamic force fluctuations for a low Reynolds number wing from time resolved particle image velocimetry (TR-PIV) experimental measurements. The results reveal a periodic lift and drag variation within the shedding cycle and resolve the frequencies of those fluctuations from a proper orthogonal decomposition (POD) and power spectral density (PSD) analysis. To show the effect of vortex shedding on the body force fluctuations, the evolution of instantaneous aerodynamic forces is compared to the pressure field of the fluid flow and to the vortical structures in the wake of the airfoil. A six step model describing the vortex-force relation is proposed. It shows that changes in lift such as maximum lift and minimum lift are associated with the detachment of a vortex. It also shows that the minimum or local minimum drag value is obtained at the onset formation of a vortex on the airfoil wake. Similarly, the maximum or local maximum drag is obtained at the onset formation of the saddle on the airfoil wake. The model further explains the asymmetry observed in the unsteady drag force evolution. The model can be used to optimize flow control and fluid-structure interaction applications.     

Analyzing the fluctuating pressures acting on a circular cylinder using stochastic decomposition

Fluctuating wind pressures acting on bluff bodies are influenced by approaching turbulence and signature (body-induced) turbulence. For a circular cylinder, the signature turbulence is closely related to the formation of Karman vortex shedding. In this paper, proper orthogonal decomposition (POD) and spectral proper transformation techniques (SPT) are applied to the pressure fluctuations acting on a circular cylinder. The physical relationships between the decomposed modes and vortex shedding are discussed to identify the dominant aerodynamic behavior (lift or drag) and to evaluate its contribution to overall behavior. The effect of Reynolds number (Re) is also addressed. It is found that the application of POD and SPT can separate the along-wind and across-wind effects on the cylinder model in both subcritical and supercritical regimes. In contrast to POD, the SPT mode is formulated in the frequency domain, and the dynamic coherent structures can be defined in terms of amplitude and phase angle, which allows detection of the advection features of vortex shedding. In addition, it is observed that the energy contribution of the shedding induced lift force increases with Re and gradually becomes a dominant aerodynamic force at Reynolds numbers in the supercritical regime.     

Nonlinear modeling of combined galloping and vortex-induced vibration of square sections under flow

In this paper, we propose a model for the transverse oscillation of a square-section cylinder under flow. The fluctuating transverse force due to vortex shedding is represented using a coupled nonlinear wake oscillator, while the unsteady force for galloping caused by the varying incidence angle effects is modelled using the quasi-steady approach. First, we analytically investigate the lift behavior and phase angle variation of the square cylinder under forced vibrations. Comparison with experimental data is used to determine the form of the coupling terms and its values. The present model shows advantages in predicting the phase angle, and it successfully captures the change in sign of the phase. Second, the proposed model is directly applied in predicting free oscillation cases without any tuning. The dynamical behaviors predicted by this model are compared with published experiments under different Scruton numbers, and reasonable agreement can be found. The results indicate that the model can not only be applied in simulating the “pure galloping” and “pure VIV,” but also is able to capture the interactions of VIV and galloping, including combined and separate VIV-galloping motions.

     

Reduced‐order controllers for control of flow past an airfoil

Reduced‐order controller design by means of reduced‐order model for control of a wake flow is presented. Reduced‐order model is derived by combining the Galerkin projection with proper orthogonal decomposition (POD) or with other related reduced‐order approaches such as singular value decomposition or reduced‐basis method. In the present investigation, we discuss the applicability of the reduced‐order approaches for fast computation of the optimal control for control of vortex shedding behind a thin airfoil through unsteady blowing on the airfoil surface. Accuracy of the reduced‐order model is quantified by comparing flow fields obtained from the reduced‐order models with those from the full‐order simulations under the same free‐stream conditions. A control of vortex shedding is demonstrated for Reynolds number 100. It is found that downstream directed blowing on the upper surface of the airfoil near the leading edge is more efficient in mitigating flow separation and suppressing the vortex shedding. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical study of self-sustained oscillatory flows and heat transfer in channels with a tandem of transverse vortex generators

A numerical investigation was conducted into channel flows with a tandem of transverse vortex generators in the form of rectangular cylinders. The oscillatory behavior of the flow is studied. Data for heat transfer and flow losses are presented for 100≤Re≤400 and cylinder separation distances 1≤S/H≤4. The results are obtained by numerical solution of the full Navier-Stokes equations and the energy equation. Self-sustained flow oscillations are found for Re>100. Alternate and dynamic shedding of large vortex structures from the cylinders is observed by visualization of the numerically determined flow field. A heat transfer enhancement up to a factor 1.78 compared to plane channel flow is observed. Received on 16 July 1997     

Vortex shedding and structural loading characteristics of finned cylinders

The flow development and structural loading characteristics of cylinders with equispaced circular fins were studied experimentally for a range of fin pitches with constant fin thickness and diameter. The experiments were performed for a range of Reynolds numbers, corresponding to the shear layer transition turbulent shedding regime. Time-resolved planar Particle Image Velocimetry and direct mean drag and fluctuating lift measurements are employed to relate spatio-temporal flow development to structural loading. The results show that wake development is dominated by vortex shedding for all the cases examined. However, the fin pitch ratio has a significant effect on vortex shedding characteristics. The addition of fins increases the characteristic spatial and temporal scales of the main spanwise vortices forming in the near wake. As the fin pitch is decreased to a critical value, the coalescence of boundary layers between the adjacent fins leads to a significant enlargement of the vortex formation region. A modified vortex shedding frequency scaling is proposed, based on the effective diameter, that incorporates a Reynolds number dependence associated with the lateral boundary layers developing on the fin surfaces. A detailed analysis is conducted to characterize the strength of the vortical structures forming in the near wake. The addition of the fins is shown to produce a stabilizing effect on the roll-up process, associated with a reduction in the generation of smaller scale, three-dimensional structures. The results demonstrate that the addition of fins leads to an increase in the mean drag, which is driven primarily by the associated increase in skin friction. The significant effect of the fin pitch ratio on the characteristics of the shed vortices as well as the size of the vortex formation region is shown to lead to substantial variations in the fluctuating loads.     

Transverse galloping of circular cylinders fitted with solid and slotted splitter plates

The galloping response of a circular cylinder fitted with three different splitter plates and free to oscillate transverse to a free stream has been investigated considering variations in plate length and plate porosity. Models were mounted in a low mass and damping elastic system and experiments have been carried out in a recirculating water channel in the Reynolds number range of 1500 to 16 000. Solid splitter plates of 0.5 and 1.0 diameter in length are shown to produce severe galloping responses, reaching displacements of 1.8 diameters in amplitude at a reduced velocity of around 8. Fitting a slotted plate with a porosity ratio of 30% also caused considerable vibration, but with a reduced rate of increase with flow speed. All results are compared with the typical vortex-induced vibration response of a plain cylinder. Force decomposition in relation to the body velocity and acceleration indicates that a galloping mechanism is responsible for extracting energy from the flow and driving the oscillations. Visualisation of the flow field around the devices performed with PIV reveal that the reattachment of the free shear layers on the tip of the plates is the hydrodynamic mechanism driving the excitation.     

On the quasi-steady analysis of one-degree-of-freedom galloping with combined translational and rotational effects

Galloping is the low-frequency, self-excited oscillation of an elastic structure in a wind field. Its analysis is commonly based on a quasi-steady aerodynamic analysis, in which the instantaneous wind forces are derived from force data obtained in static wind tunnel tests. For the galloping of a rigid prismatic beam the validity of the quasi-steady assumption is critically assessed for the case that rotational effects must be included in the aerodynamics. An oscillator structure with one (torsional) degree of freedom is proposed which allows a reliable modelling. Its effective motion can be considered as being composed of a translation with a coupled rotation of the cross section, and can be regarded as a natural extension of pure translational galloping. The analysis reveals that the resulting aerodynamic damping is determined by the sectional aerodynamic normal force coefficient alone. An aerodynamic damping coefficient is defined that can be expressed uniquely in terms of an aerodynamic amplitude, allowing a normalization of the galloping curve. This result can be used to analyze both purely translational and combined galloping, which are found to differ only by the way the structural amplitude (displacement) is related to the aerodynamic amplitude. An interesting result is that for large wind speeds rotational galloping displays an aerodynamic limit, in contrast to translation galloping where the limit-cycle amplitude increases linearly with wind speed. Results obtained from wind tunnel experiments confirm the major findings of the analysis.     

VORTEX SHEDDING OF BLUFF BODIES: A REVIEW

In this paper the various types of vortex generation and the related response characteristics of bluff bodies are described. The vortices are, in general, generated by a certain stimulation, leading to one- or two-shear layer instability; the related unsteady forces could excite flexible structures such as tall towers, tall buildings and long-span bridges. Karman vortex shedding is well known as the alternate shedding vortex behind bluff bodies, but the one-shear layer instability related vortices and symmetrical vortex shedding should also be taken into account as additional mechanisms for the evaluation of structural safety, because they result in structural response at comparatively low wind speeds. In this paper, the symmetrical vortex shedding, which is enhanced by the longitudinally fluctuating flow for 2-D rectangular cylinders with a 0.5 side ratio, and one-shear layer related vortices, which are generated on the side surfaces of flat 2-D rectangular cylinders and many bridge girder box sections by the stimulation of body motion or applied sound, are introduced. Furthermore, as a peculiar 3-D vortex, the “axial vortex”, which is formed in near wake of inclined cables and then over restricted velocity ranges, is also discussed.     

Autorotation dynamics of a low aspect-ratio rectangular prism

This paper presents two previously unreported aspects of the autorotation dynamics of low aspect ratio rectangular prisms, observed during an experimental study of the dynamics of helicopter underslung loads. Low-speed wind tunnel tests of a simplified container model free to rotate on a fixed axis demonstrated (a) that autorotation rate can lock-in to a structural mode and (b) that static hysteresis in autorotation rate can occur at low speeds. Autorotation lock-in behaves in a similar manner to vortex-shedding lock-in, suggesting that a similar feedback flow process between vortex wake dynamics and body motion is operating, and may provide a partial explanation for the complex changes in behaviour of rotating slung loads at high airspeeds. Static hysteresis at low speeds results in a bifurcation diagram for autorotation which is similar to that for cross-wind galloping of a square prism, including the effects of friction and inertia. The similarity in bifurcation behaviour seems likely to indicate similar dynamics rather than flow physics, suggesting that it may be possible to apply techniques developed to model the effect of non-linear damping characteristics in galloping to the modelling of autorotation.     

AERODYNAMICS AND DYNAMICS OF RECTANGULAR PRISMS WITH MOMENTUM INJECTION

A structural member with rectangular cross-section is frequently encountered in civil, mechanical and ocean engineering applications. Structural loading in terms of steady and unsteady pressure fields, susceptibility to flow-induced instabilities, etc., for tall buildings, bridges, offshore platforms, marine risers and a wide variety of other configurations have been of interest to engineers. Recent progress in engineering materials and computer-aided design has led to structures with reduced stiffness, making them prone to wind, earthquake, as well as ocean-wave and current-excited oscillations. The present research is aimed at understanding these issues at a fundamental level through a comprehensive study of moving-surface boundary-layer control (MSBC) as applied to two-dimensional rectangular prisms with reference to drag reduction and suppression of flow-induced vibrations. Extensive wind-tunnel tests, complemented by quasisteady analysis and flow visualization study, suggest that the concept of MSBC represents a versatile tool for drag reduction and suppression of both vortex resonance and galloping type of instabilities.