Aerodynamic Damping Ratios Research Articles

Flow field characteristics and vibration responses of saddle-shaped membrane structures

Elastically mounted flexible membrane roofs exposed to flows are prone to vortex-induced vibrations and even aero-instability due to the strong fluid–structure interaction (FSI). This study is to investigate the FSI mechanism in the saddle-shaped membrane structure over a range of Reynolds numbers and wind directions in laminar flows, by bridging structural vibration responses and flow dynamics. The aeroelastic characteristics of membrane structures, including statistics of displacement responses, oscillation frequency, and oscillation damping ratios, were identified from the perspective of time and frequency domains. Simultaneously, the particle image velocimetry system was employed to visualize the flow features, including velocity vector, turbulence intensity, and vortex evolution in both space and time. The flow modes were further decomposed by proper orthogonal decomposition (POD) to capture the salient aspects of the flow. Three patterns of POD modes are identified, and the first mode plays the dominant role in POD modes. It showed that as the wind Reynolds number increases, the space between the shear layer and membrane surface would be narrowed, and resultantly the vortices turn out smaller in scale and closer in space. This trend leads to an increase in the frequency of vortex shedding and a stronger FSI effect. When the frequency of vortex shedding approaches the fundamental frequency of structures, the vibration of the membrane would be shifted from turbulent buffeting to vortex-induced resonance, featured with lock-in frequency, significant amplified displacement, and negative aerodynamic damping ratio.

Flutter Suppression Effects of Movable Vertical Stabilizers on Suspension Bridges With Steel Box Girders

As the combination of springs and vertical stabilizers, the movable downward vertical central stabilizer (MDVCS) is proposed to further control the nonlinear flutter of super long‐span suspension bridges in this paper. A series of flutter suppression tests of closed‐box girders and twin‐box steel girders with various MDVCSs are conducted. Based on the coupled flutter theoretical method, the sensitivity analysis of two important parameters including the height and stiffness of MDVCS are carried out to compare their nonlinear flutter control mechanism. The results show that the flutter critical wind speed (Ucr) of the closed‐box girder continued to increase with the decrease of the height of the DVCS and the increase of spring stiffness, whereas the Ucr of the twin‐box girder increased at first and then decreased. The cubic polynomial function and quadratic Holliday function are suitable to modify the correction coefficients of Ucr for the closed‐box girder with various stiffnesses and heights of MDVCS, while the Lorentz peak‐value function and cubic polynomial function are suitable to modify the Ucr of the twin‐box girder. Furthermore, the MDVCS significantly changes the rules of two positive and negative aerodynamic damping ratios for the closed‐box girder and two negative aerodynamic damping ratios for the twin‐box girder. Besides, the peak vertical displacement amplitudes of the box girder are about half of the MDVCS, since both the height and stiffness of MDVCS alter the elliptical radius of vertical phase planes to affect the limit cycle oscillation of soft flutter, especially for the leeward MDVCS for the twin‐box girder.

Cross-Wind Aeroelastic Effects of Tall Buildings with a Hexagonal Cross-Section

This research investigates the cross-wind aeroelastic effects of tall buildings with hexagonal cross-sections by using aeroelastic models with multiple-degree-of-freedom (MDOF). Cross-wind displacement and acceleration responses at the top of each model are measured using the wind tunnel test. The aerodynamic damping ratios for the two representative wind directions are identified by analyzing the measured responses using the random decrement technique. Results show that large-amplitude vortex-induced vibrations occur for one of the representative wind directions where the vertex of the hexagonal model is against the approaching wind, while there is no significant VIV observed for the other representative wind direction where the face of the hexagonal model is perpendicular to the approaching wind. The most dangerous wind direction is then identified based on the discussion. Two expressions for the cross-wind aerodynamic damping ratio are established for the two wind representative wind directions. The two equations can be used in engineering practice to estimate the cross-wind aerodynamic damping ratio of hexagonal tall buildings.

Closed-form derivation of aerodynamic damping matrix and pitch vector of an aero-servo-elastic wind turbine system

This paper develops closed-form expressions of aerodynamic damping matrix and pitch controller of an aero-servo-elastic wind turbine (WT) system. This facilitates establishing a linearized WT model completely analytically at an arbitrary operational point, without resorting to extensive numerical linearizations or fittings. The rotor blade flexibility and pitch controller are included in the model development, thus unfolding a full understanding of the aerodynamic coupling effects. The linearized WT model is verified by good agreement with results from the original nonlinear WT model. Based on the verified linearized model, it is seen that aerodynamic coupling between tower fore–aft and side–side vibrations is solely due to the tower top rotations, and the top rotations also significantly enlarge the diagonal aerodynamic damping coefficients. Both tower top rotations and flexible blade–tower interaction play important roles in tower aerodynamic damping ratios. The developed formulas of load coefficients are also readily applicable to a FE modeling framework of the tower–foundation system.

Experimental Investigation of Unsteady Aerodynamic Forces and Vortex-Induced Aeroelastic Effects of a Slender Structure in Uniform and Turbulent Flows

Slender structures are sensitive to wind loads, and aeroelastic effects during vortex-induced resonance have considerable influences on their survivability, serviceability, and habitability. However, the vortex-induced aeroelastic effects and the effects of turbulence intensity on unsteady aerodynamic forces of an aeroelastic prism remain far from been fully understood. In this study, a series of wind tunnel tests, including the pressure measurements of a rigid model and simultaneous measurements of the pressure and response of an aeroelastic model, were conducted in three different wind flows. The characteristics of unsteady aerodynamic forces and the effects of turbulence intensity on the unsteady aerodynamic forces were systematically investigated. The mechanism of aeroelastic effects and the variations of aerodynamic damping ratios were also discussed. Wind-induced responses were predicted by the unsteady aerodynamic forces and compared with the measured values. The experimental results show that vortex-induced aeroelastic effects on the wind-induced responses and the unsteady aerodynamic forces are significant. An increase in the turbulence intensity may result in a weak correlation of the unsteady aerodynamic forces and thus suppress the vortex-induced aeroelastic effects. Moreover, the amplitudes of the positive and negative peaks of the aerodynamic damping ratios decrease with the increase of the turbulence intensity. In addition, the wind-induced responses predicted by the unsteady aerodynamic forces measured from the aeroelastic model are the closest to the measured responses.

Wind-Induced Instability Mechanism of Old Tacoma Narrows Bridge from Aerodynamic Work Perspective

Postflutter limit cycle oscillations (LCOs) are typical nonlinear aeroelastic phenomena for bridge girders. An H-shaped section with a roughly 5:1 aspect ratio, treated as a simplified section of the Old Tacoma Narrows Bridge, was chosen for wind-induced instability re-evaluation, considering its vibration amplitude-dependent aerodynamics characteristics and nonlinear structural damping effects from the energy perspective of aerodynamic work. Forced vibrations at large torsional amplitudes in a wind tunnel were realized with the help of an improved forced motion apparatus (FMA), and synchronous measurements of forces and displacements on the FMA were achieved. Self-excited forces (SEFs) were extracted, and an energy map showing quantitative relationships between vibration amplitude, reduced velocity, and aerodynamic work acting on the section were established. Furthermore, the postflutter LCOs phenomena originating from the energy balance between nonlinear aerodynamic work input and energy consumption by structural damping effects were reillustrated, and nonlinear structural damping effects of prototype bridges are therefore discussed. Moreover, the instability paths of the bridge were investigated by the energy map, considering its vibration amplitude-dependent aerodynamics and structural damping effects from an aerodynamic work perspective. The results show that LCO velocity basically increases with vibration amplitude at different structural damping ratios in torsional degree of freedom, characterizing postflutter LCOs phenomena. The structural damping ratio at the bridge’s collapse is also re-estimated as about 0.0115 with better coincidence of on-the-spot observation and theoretical analysis. In addition, both the aerodynamic damping ratio considering nonlinear characteristics of the SEFs and the structural damping ratio basically increasing with vibration amplitude contribute to postflutter LCOs phenomena of the Tacoma Bridge. The instability paths of the bridge essentially rely on the competitive relationships between structural damping ratios, structural stiffness degeneration, and oncoming wind velocities in the process of collapse.

Wind tunnel study of wind effects on 90° helical and square tall buildings: A comparative study

Wind effects on a square model and a 90° helical model are investigated by both pressure measurement and aero-elastic model tests in a boundary layer wind tunnel. Based on the pressure measurement results, local wind force coefficients, base moment coefficients, vertical correlation coefficients and power spectral densities for the two models were analyzed and discussed in detail. The aerodynamic damping ratios were calculated by the random decrement technique (RDT) on the basis of the wind-induced acceleration obtained from the aero-elastic tests. Comparisons of wind loads and wind-induced accelerations were made for the square and helical models. The results shown that the aerodynamic damping should not be ignored, especially for across-wind direction. Moreover, the helical model has been proved to yield a better behavior in aerodynamic performance than square model. This study aims to provide useful information for wind-resistant design of helical building.

Wind force of super high-rise buildings with hexagonal section

To study the wind force of super high-rise buildings with hexagonal section, a series of wind tunnel tests of synchronous pressure models were carried out. The alongwind force coefficient, as well as the power spectral density (PSD) and the RMS base moment of crosswind force were studied. Thereafter, the empirical formulae of wind force were established. Meanwhile, wind tunnel tests of multiple-degree-of-freedom (MDOF) aero-models were conducted to measure the crosswind responses. The aerodynamic damping ratios were identified by analyzing the time histories of measured responses. Finally, the aerodynamic damping ratios obtained from the aero-model test and the analytical model of wind force obtained from the synchronous pressure model were combined to calculate the crosswind dynamic response. The comparison between the wind induced response of calculation result and that of aero-model test shows that the wind force analytical model proposed in this paper is reliable. This study can provide references for the wind resistance design and standard improvement of super high-rise buildings with hexagonal section.

Vibration Analyses of an Axial Turbine Wheel With Intentional Mistuning

Abstract The last-stage bladed disk of a steam turbine is analyzed with respect to both flutter susceptibility and limitation of forced response. Due to the lack of variable stator vanes, unfavorable flow conditions may occur, which can lead to flow separation in some circumstances. Consequently, there is the risk of flutter in principle, particularly at nominal speed under part load conditions. For this reason, intentional mistuning is employed by the manufacturer with the objective to prevent any self-excited vibrations. A first step in this direction is done by choosing alternate mistuning, which keeps the manufactural efforts in limits since only two different blade designs are allowed. In this sense, two different series of blades have been made. However, it is well known that small deviations from the design intention are unavoidable due to the manufacturing procedure, which could be proved by bonk tests carried out earlier. The influence of these additional but unwanted deviations is considered in numerical simulations. Moreover, the strong dependence of blade frequencies on the speed is taken into account since centrifugal stiffening effects significantly attenuate the blade-to-blade frequency difference in this particular case. Focusing on the first flap mode, it could be shown that a mitigation of flutter susceptibility is achieved by prescribing alternate mistuning, which indeed evokes an increase of originally small aerodynamic damping ratios. Nevertheless, the occurrence of negative damping ratios could not be completely precluded at part load conditions. That is why optimization studies are conducted based on genetic algorithms with the objective function of maximizing the lowest aerodynamic damping ratios. Again, only two different blade designs are admitted. Finally, mistuning patterns could be identified causing a tremendous increase of aerodynamic damping ratios. The robustness of the solutions found could be proved by superimposing additional random mistuning.

An efficient coupled-mode flutter analysis method for turbomachinery

An efficient aeroelastic eigenvalue method based on time domain system identification has been developed to analyze coupled-mode flutter in turbomachinery. The aeroelastic stability problem is transformed into a generalized eigenvalue problem (GEP) by incorporating the aeroelastic equation and an aerodynamic modal force model. The aerodynamic modal force model correlates the generalized aerodynamic modal force with generalized motion variables by influence coefficient matrices which are calculated through a time domain system identification method. The aerodynamic damping ratios and the corresponding eigenfrequencies for all interblade phase angles (IBPA) can be obtained conveniently from a single time domain aerodynamic computation. The proposed method has been validated and demonstrated by presenting results for NASA Rotor 67 flutter cases in this paper.

Identification of nonlinear aerodynamic damping of wind-excited flexible structures by curve-fitting non-Gaussian response probability density function

This study presents a new approach for identification of nonlinear aerodynamic damping of wind-excited flexible structures from stochastic response time history that can be modeled as the output of a single-degree-of-freedom system under a white noise excitation. The amplitude-dependent aerodynamic damping ratio is described as a polynomial function of vibration displacement or velocity. Based on the equivalent nonlinear equation approach, the probability density function (PDF) of displacement can be given in terms of damping model parameters, which generally follows a hardening non-Gaussian distribution. It is proposed to identify the damping model parameters by curve-fitting displacement PDF determined from the response data using a nonlinear least-square optimization technique. Firstly, the stochastic response of a tall building with a known nonlinear aerodynamic model is simulated and the performance of the proposed approach is investigated. This method is then applied to a square-shaped tall building model and a bridge deck section using wind tunnel measured data. Finally, it is used for a traffic-signal-support structure using field measurement response data. The results are also compared with those from other existing approaches. The proposed approach permits determination of nonlinear aerodynamic damping from single stochastic response history and is very easy to use in practice.

A semi-analytical model of aerodynamic damping for horizontal axis wind turbines and its applications

A semi-analytical model of the aerodynamic damping for horizontal axis wind turbines was established. Considering the translational and rotational degrees of freedom of tower-top, aerodynamic damping forces on the rotor were calculated by the blade element momentum theory and simplified to a resultant force at the tower-top and a resultant couple. Thereafter, the semi-analytical solution of modal aerodynamic damping ratios was suggested. Subsequently, the modal aerodynamic damping ratios of the NREL 5 MW and WP 1.5 MW wind turbines were calculated by the semi-analytical solution and identified from their dynamic response to validate this solution. And, the sensitivity analysis was performed to evaluate the influence of control parameters on the modal aerodynamic damping ratios of wind turbines. Finally, the uncouple analysis method with this aerodynamic damping model was used to predict the dynamic response amplitude of wind turbines, wherein the aero-servo-elastic fully coupled analysis were set as the reference method to examine the reliability of this uncoupled method. The results indicated that the uncoupled analysis method employing this aerodynamic damping model can accurately predict the dynamic response of horizontal axis wind turbines excited by a combined wind-earthquake loading, which is significantly better than the existing uncoupled model.

Evaluation of an Uncoupled Method for Analyzing the Seismic Response of Wind Turbines Excited by Wind and Earthquake Loads

There is a significant interaction between wind and earthquakes for large-scaled wind turbines due to an aeroelastic effect. This study evaluates the accuracy of an uncoupled method extensively utilized to analyze the seismic response of wind turbines at the operational state. Initially, the oscillation of the blade for the National Renewable Energy Laboratory (NREL) 5 MW wind turbine excited by wind and wind-earthquake combination, respectively, is compared using the fully coupled method to verify the assumption in this uncoupled method. Subsequently, the influence of ground motions on the aerodynamic loadings of the rotor is discussed to evaluate the interaction between wind and earthquake loads. In addition, the accuracy of the uncoupled method is assessed by comparing the analysis results of the coupled and uncoupled methods, where different mean wind speed and equivalent aerodynamic damping ratio are considered. The results indicate that the oscillation velocity of blades and thrust on the rotor are significantly influenced by ground motions. Moreover, the amplitude of thrust variations caused by earthquakes increases monotonously with the oscillation velocity amplitude of blade-root. The errors between the two models are beyond the engineering margins for some earthquakes, such that it is difficult to optimize a consistent aerodynamic damping in the uncoupled model to accurately predict the seismic response of wind turbines.

Experimental investigation on flow-induced vibration of flexible multi cylinders in atmospheric boundary layer

Experimental investigations of the flow-induced vibration (FIV) of flexible multi cylinders in tandem, side-by-side and staggered arrangements were conducted in an atmospheric boundary layer wind tunnel over a wide spacing ratio and incidence angles. All cylinders were cantilever supported and allowed to vibrate in cross-flow and inline directions. The vibration characteristics and transition features are identified among different configurations, and the responses dependent on reduced velocity under each configuration are discussed. Four regimes of the FIV of tandem cylinders are classified, where cylinder 1 vibrates divergently similar to galloping in Regime Ⅰ (l < 1.6, α = 0°) but is suppressed in Regime Ⅱ (1.6 ≤ l < 3, α = 0°), cylinder 2 always vibrates obviously in all four regimes, and cylinder 3 has a distinct vibration in only Regimes Ⅱ, Ⅲ (3 ≤ l ≤ 5, α = 0°) and Ⅳ (l >5, α = 0°), in which l is the nondimensional center-to-center distance and α is the incidence angle. There are two regimes for side-by-side cylinders, in which a divergent vibration of cylinder 1 is observed in Regime V (l < 1.6, α = 90°) and only cylinder 3 vibrates significantly in Regime VI (1.6 ≤ l ≤ 3.2, α = 90°). The aerodynamic properties analyzed through a prediction method are used to explain the vibration mechanism, in which the negative aerodynamic damping ratio branches sustain the divergent vibration in Regime I. Based on the comprehensive study above, the FIV phenomenon of flexible multi cylinders can be understood in atmospheric environment with nonuniform inflow, high turbulence intensity and subcritical Reynolds numbers. Finally, the potential of harvesting wind energy via this technique, showing the highest efficiency 52% but limited at Ur≥30, is discussed.

Flutter analysis of a one-and-a-half-stage fan at low speed using nonlinear harmonic method

Multirow effects on flutter stability of a 1.5-stage fan at low speed are investigated using nonlinear harmonic method in a one-way coupled fashion. In the first part, the mesh-independence verification and validation of nonlinear harmonic method to simulate multirow effects are performed. In the second part, multirow effects are separated into two parts including acoustic reflection and rotor–stator interaction induced by relative motion between rotor and stators with each part investigated individually. Effect of acoustic reflection from upstream and downstream blade rows is investigated separately using a harmonic truncation method to avoid the change of time-mean flow. The results show that acoustic reflection can have a large effect on flutter stability of rotor blade. The simulation of the rotor–stator interaction effect indicates that the rotor–stator interaction does not significantly affect the flutter stability of rotor blade in this case. Lastly, the variation of aerodynamic modal damping ratio with the size of gap between inlet guide vane and rotor is investigated. Aerodynamic modal damping ratio at a nodal diameter whose fundamental mode is cut-on varies periodically with gap size. Wave splitting method is employed to further investigate the relation between the phase difference between incoming and outgoing wave and aero damping, which can be used to improve the flutter stability at the design stage.

An aerodynamic anti-galloping technique of iced 8-bundled conductors in ultra-high-voltage transmission lines

Galloping of iced conductors is a kind of self-excited aeroelastic vibration with low frequency and large amplitude causing various damages on transmission tower-line systems. A newly designed galloping simulation device is employed in the wind tunnel for developing an aerodynamic anti-galloping technique of iced 8-bundled conductors in ultra-high-voltage (UHV) transmission lines. The anti-galloping technique is based on the proposed rotary clamp spacers, which allow the connected sub-conductors to rotate around its axis. Iced 8-bundled conductor models of UHV lines with and without twistable sub-conductors have been tested in the wind tunnel under various wind attack angles and five different ratios of vertical vibration frequency over the torsional. Aerodynamic damping ratios were identified from measured response data, and were used as indicators of galloping for iced 8-bundled conductor models with and without twistable sub-conductors. Equations of motion for iced 8-bundled conductors with and without twistable sub-conductors are respectively established, and the aerodynamic instability of the system can then be predicted by solving the eigenvalue problem associated with equations of motion. In order to further validate the anti-galloping effects of the rotary clamp spacers, finite element simulation has been conducted for a real UHV transmission line with a span of 500 m located in the galloping-prone area.

Added mass and damping effects on vibrating bridge decks in still air

Due to the windless-air-induced added mass and damping effects, the mechanical frequency and damping ratio of a bridge deck model in wind tunnel test are usually under-estimated and over-estimated, respectively. In this study, the vertical and torsional added mass and damping and their effects on the mechanical frequency and damping ratio of an ideal plate and five typical bridge decks are thoroughly investigated based on single degree-of-freedom free vibration numerical simulations. The aerodynamic forces are linearly expressed as functions of vibrating accelerations, velocities, added mass coefficients, and added damping coefficients. The discrepancies between two-dimensional (2D) and three-dimensional (3D) simulations are found to be small. The numerical simulation accuracy is validated through comparison with the results from the Theodorsen expression and forced vibration simulations. It is found that the added mass coefficients are insensitive to the vibration amplitudes, while the added damping coefficients almost linearly increase with the amplitudes. Based on the added mass and damping coefficients, the vertical and torsional air-induced frequency reduction coefficients and aerodynamic damping ratios are calculated. Both the frequency reduction coefficients and aerodynamic damping ratios are closely related to deck configurations and model mass/mass moment of inertia, while independent of vibration frequencies. For the concerned six section models, the vertical and torsional frequency reduction coefficients are mainly located in the ranges of (1.0%, 2.5%) and (0.4%, 1.2%), respectively. The aerodynamic damping ratios are significantly dependent on the vibration amplitudes and may exceed the mechanical damping ratios for large amplitude cases. Based on numerical simulations, the mechanical frequency and damping ratio of a spring-suspended deck model can be identified by excluding the added mass and damping effects.

Identification method and application of aerodynamic damping characteristics of super high-rise buildings under narrow-band excitation

Aerodynamic damping is an important parameter for assessing the wind–structure interaction of super high-rise buildings. A new analysis method is proposed, which first uses the complex blind source separation technique to achieve the effective decoupling of complicated coupled signals and then the Bayesian spectral density approach (BSDA) considering the actual structural aerodynamic characteristics, namely, new Bayesian spectral density approach (NewBSDA), to conduct the parameter identification of decoupled signals effectively. The proposed method is applied to the modal parameter identification of the aeroelastic model test of an 838 m super high-rise building. Results show that the complex blind source separation technique can effectively decouple the coupled signals generated by similar sway modal frequencies in the aeroelastic model. Results of the proposed method are considerably more reasonable than those of the traditional BSDA due to the actual aerodynamic characteristics considered. Comparison shows that BSDA substantially underestimates the cross-wind aerodynamic damping of the structure near the critical wind speed. Given that along-wind aerodynamic loads are wide-band excitations, the aerodynamic damping ratios identified by BSDA and NewBSDA are close. Furthermore, the characteristics of aerodynamic forces identified by the proposed method are satisfactory, which further illustrates the rationality and validity of the method.

Improved expression for across-wind aerodynamic damping ratios of super high-rise buildings

To study across-wind aerodynamic damping ratios of super high-rise buildings, wind tunnel tests of multi-degree-of-freedom (MDOF) aero-elastic models with various aspect ratios and mass-damping parameters were carried out. The relationship between aero-damping ratio and reduced wind velocity (Vr), wind field roughness, aspect ratio, structural mass, structural damping as well as across-wind displacement was investigated systematically. It was found that the positive aerodynamic damping ratio is negatively correlated with the structural damping ratio and structural mass at Vr lower than critical reduced velocity of resonance (Vc). However, when Vr is close to or slightly bigger than Vc, the absolute value of negative aerodynamic damping ratio is positively correlated with structural damping but negatively correlated with structural mass. Therefore, the empirical function based on aerodynamic damping ratio alone cannot be reliably established, because the aerodynamic damping ratio alone is insufficient to assess aerodynamic effects. Thus, these considerations lead to a proposal of the concept of reduced damping ratio. This concept allows an improved empirical function of aerodynamic damping ratio to be established. Effects of the aspect ratio, reduced wind velocity, wind field terrain, structural damping and mass density were all considered in this empirical function.

Experimental study of aerodynamic damping of a twisted supertall building

The aerodynamic damping ratios and aeroelastic instability of a 180° helical supertall building with good aerodynamic behavior in both the along-wind and across-wind responses were investigated using an aeroelastic model test (rocking vibration model test). The aerodynamic damping ratios for the 180° helical and square models were evaluated using the random decrement technique. Furthermore, the effect of the triggering level and number of time segments on the evaluation of the aerodynamic damping ratio was also investigated. It was found that both the mean and fluctuating displacement responses of the 180° helical model in the along- and across-wind directions showed better aerodynamic behaviors than those of the square model. Aeroelastic instability of the 180° helical model was not observed at any of the reduced velocities considered in the study. In the along-wind direction, the aerodynamic damping ratios of the 180° helical model exhibit similar trends to those of the square model. However, in the across-wind direction, the aerodynamic damping ratios of the 180° helical model show significantly different trends than those of the square model. Furthermore, there was no effect of the variation in the wind direction on the aerodynamic damping ratio of the 180° helical model. We found that in the evaluation of the aerodynamic damping ratio, it is possible to adopt the triggering level at the value of the standard deviation or √2 times of the standard deviation of the displacement responses if the random decrement signature has a high number of triggering points.