Torsional Flutter Research Articles

Simulasi Numerik Aeroelastik Model Seksional 2D Jembatan Bentang Panjang untuk Mengetahui Karakteristik Ketidakstabilan Flutter

Flutter is an aerodynamic instability on a long span bridge that can cause damage to the entire bridge deck structure. The interaction between wind and structure in long span bridges can be investigated by numerical simulation. In this study, an aeroelastic simulation was performed on a 2 DoFs sectional model of a long-span bridge deck with free vibration techniques to analyze flutter speed and determine the effect of deck shape on flutter instability characteristics using ANSYS software. The simulation result data was then extracted using the Modified Ibrahim Time-Domain Method (MITD) identification method to obtain the damping ratio and flutter derivatives coefficients. The damping ratio value is used to determine the critical flutter speed, whereas the coefficient flutter derivatives is used to determine the characteristics of flutter instability and the flutter mechanism that occurs in the bridge. The results showed that the rectangular shape (bluff body) is more susceptible to flutter instability than the streamlined shape, and has a lower flutter speed value than the other shapes. The flutter mechanism that occurs is torsional flutter, whereas in the streamline body is coupling flutter.

The broad study of blade cascade under controlled torsional flutter: Dynamics of the flow and stability analysis

The experimental and numerical investigation of the flow instabilities acting on rigid blades and vice versa was conducted for both compressor and turbine configuration. The blade cascade consisted of five rectangular NACA 0010 blades, with three middle blades capable of performing harmonic motion with one degree of freedom (pitching) using force excitation. The base case (all blades fixed) and excited regime were examined. The influence of various angles of attack, harmonic frequency values, amplitude values, inter-blade phase angles and Reynolds numbers (Re) were tested. The mean flow properties as well as the fluid - structure interaction (FSI) were studied using Particle Image Velocimetry (PIV), Reynolds-averaged Navier-Stokes (RANS) CFD methods and using force measurement. Additionally, two different approaches, namely traveling wave mode (TWM) and aerodynamic influence coefficient (AIC), were adopted to estimate the aeroelastic stability of the blade cascade, and the results were compared. The results show significant aeroelastic coupling between the blades in both compressor and turbine configuration. However, the aerodynamic coupling effect for torsional flutter is more prominent in turbine configuration.

Investigation of the Difference Between Ordinary and FSI Numerical Solution for Flutter of Tandem Compressor

This research aims to analyze and compare the flutter of turbine compressor blades from experimental, numerical, and fluid structure interaction (FSI) derived data. The results proved that the FSI solution results are closer to the experimental results. A reduced velocity parameter of 5 can be regarded as the flutter boundary in the bending flutter. Additionally, the incidence angle parameter equal to 1.5 can be characterized as the torsional flutter boundary. Tandem leads to strengthening the load applied on the compressor blades, reducing the number of compressor stages, and ultimately reducing the weight of the engine. Adding tandem to the rotor increases the vibration bending frequency by a factor of 2. Increasing the compressor velocity caused the FSI vibration frequency to be close to the experimental results. It was found that the vibration range of the main rotor is greater than that of the tandem. The vibration of the rotor and the tandem is damped for approximately 0.1 s to reach a constant frequency.

Laminar flow over a rectangular cylinder experiencing torsional flutter: Dynamic response, forces and coherence modes

This study investigates the flutter response of a rectangular cylinder model with an aspect ratio of 5 at the Reynolds number Re = 100 via direct numerical simulation. The effects of two key parameters, i.e., the moment of inertia and reduced flow velocity, on the aerodynamic performance and dynamic responses of the cylinder in the state of torsional flutter are investigated. To reveal the flutter mechanism, the high-order dynamic mode decomposition (HODMD) analysis is conducted to decompose the flow field. The results show that both an increase in the moment of inertia and a higher reduced flow velocity lead to a larger torsional amplitude and a corresponding decrease in torque. At the same time, the primary frequency decreases and the size of the shedding vortex gradually enlarges. The vortices shed from the leading edge and the trailing edge of the model form a 2P wake pattern. The leading-edge vortex is significantly larger than the trailing-edge vortex in terms of strength and size. The leading edge plays a dominant role and only contributes to the odd-order HODMD modes while the even-order modes are deemed inconsequential. As the moment of inertia increases, the total energy of the higher-order modes increases, which has the same results as the power spectral density of torque, reflecting increased nonlinearity and complexity of the system. Similarly, increasing the reduced flow velocity at the same moment of inertia has similar excitation effects.

Shaping Effects on Long Span Bridge Deck Aerodynamics

An aerodynamic circumstance of wind pressure surrounding the long-span bridge allocates many theoretical and experimental research to this topic. Determination of the materials and optimal cross-sectional shape of bridge decks that affected a dynamic behavior of long span bridge deck is still included in current research issues and works to be continued in this path. These include the Lack of sufficient awareness of wind forces, stemming from complex nature, and the unpredictability of the wind nature. In this study, in addition to recognizing the aerodynamic behavior of the flutter, the acting pressure forces on the bridge deck are investigated. The geometrical shape of decks, wind velocity, and flutter conditions are adopted as design variables that affected the dynamic forces exerted on bridge decks. A common type of geometric sections of the long-span bridge deck and effective aerodynamic phenomena are examined. The hollow box steel suspended deck and double cells box girder linked via upper flanges and cells linked via the top and bottom flanges are adopted for Computational Fluid Dynamic (CFD) approach. Thus, aerodynamic instability and turbulent torsional flutter flows, as well as a trail of shedding vortices around the bridge decks, are investigated. By changing some geometrical parameters of commonly used bridge sections, the optimal cross-section in terms of turbulence created above and below the deck section is examined and an optimal cross-sectional shape variable is proposed. The shape variable and section dimensions adopted for CFD-Simulations are similar to the dimensions and materials used in previous laboratory specimens of wind tunnels to be able to interpret the results and possibly verify them with the result of the current study.

Influence of tip leakage flow on the aerodynamic damping of compressor blade torsional vibration

Based on harmonic balance calculation technology with a single-passage phase-lag periodic boundary, the influence of tip gap size on the aerodynamic damping characteristics of rotor for first-order torsional vibration is analyzed with energy method. This research shows that the aerodynamic damping coefficient of the blade has a parabolic distribution law of first decreasing and then increasing with the increase of the tip clearance size. There is a most dangerous clearance value of torsional flutter characteristics in the blade, and the aerodynamic damping under this clearance is 12.67 % lower than the maximum damping value. The influence of the leakage flow on the time-averaged flow field near the blade tip leads to significant differences in the local aerodynamic work. In addition, the effect of leakage flow on the amplitude and phase of the local first-order unsteady pressure also bring about a significant influence on local aerodynamic work near blade tip.

Experimental investigation of post-flutter properties of a suspension bridge with a [formula omitted]-shaped deck section

Paralleled experimental tests of a full-bridge model and a sectional model are conducted to investigate nonlinear post-flutter properties of a suspension bridge, including structural damping, motion amplitudes, phase angle, motion frequency and coupling effects. Structural damping is found to increase nonlinearly and remarkably as the motion amplitude increases. Modal shapes are found to evolve as the motion amplitudes increase. Nonlinear structural damping properties differ significantly between the two models. Flutter instability of both models end up with limit cycle oscillations (LCOs), which increase progressively with the oncoming wind speed. LCO amplitudes of the sectional model are significantly smaller than those of the aeroelastic model. LCOs of the full-bridge model are coupled motions among 3 major structural modes, one torsional (symmetric) and two vertical (symmetric and asymmetric). Comparisons between the two models indicate that the underlying mechanism is single DOF torsional flutter. Phase angles between the vertical and torsional motions are found to be non-zero and differ significantly between the two models. Further, the amount of time evolving from a flutter onset to a LCO state decreases obviously as the wind speed increases, and the evolution time differs obviously between the aeroelastic and section models.

Multiagent Control of Airplane Wing Stability with “Feathers” under the Flexural Torsional Flutter

This paper proposes a novel method for the unbounded oscillation prevention of an aircraft wing under the flexural torsional flutter, an innovative multiagent attitude to control an aircraft wing with a surface consisting of managed rotating “feathers” (agents). Theoretical evaluation of the method demonstrates its high aptitude to avoid an aircraft wing’s flexural-torsional vibrations via expansion of the model’s ability to dampen the wing oscillations. It potentially allows increasing an aircraft’s speed without misgiving of the flutter. A new way to control an aircraft wing based on the Speed-Gradient methodology is suggested to increase the maximal possible flight speed without a flutter occurrence. Provided experiments demonstrate the theoretical advantage of the multiagent approach to the “feathers” rotation control.

Flutter analysis methods for bridges stabilized with eccentric wings

Analysis methods for computing the flutter speed of bridges stabilized against flutter by stationary wings are presented. The wings are placed outboard the bridge deck to achieve a large lateral eccentricity, which enables them to produce enough aerodynamic damping to effectively raise the flutter speed. Given the focus on flutter, other wind effects are neglected. The analysis can thus be carried out in the frequency domain. The most sophisticated method is based on a specially developed finite aeroelastic beam element, used for modelling a bridge-deck-plus-wings segment, leading to a multi-degree-of-freedom analysis. Such analysis is recommended if the wings do not extend over the full length of the bridge, a design choice that benefits cost efficiency. Second, a simplified two-degree-of-freedom flutter analysis method is described. Simplification is achieved by establishing the wind forces on the wings assuming quasi-steady, instead of unsteady, flow and taking them into account as additional damping and stiffness. Results of example calculations are compared to those of the multi-degree-of-freedom flutter analysis. Finally, it is shown how torsional flutter of a bridge equipped with such wings can be treated in a single-degree-of-freedom analysis. The method is applied to the first Tacoma Narrows Bridge.

Flutter Analysis of The Sunda Strait Suspension Bridge

Economic movements in Indonesia and the logistics and distribution systems that accompany them are highly dependent on road transportation modes. On the other hand, the islands of Sumatra and Java are the centers of concentration for the Indonesian economy where the number of people inhabiting the two islands reaches 80% of the total population of Indonesia. In order to accelerate development and increase the economic integration of Java and Sumatra, it is necessary to build the Sunda Strait Bridge. The main bridge considered incudes the long span suspension bridge. At present, the planning and construction of the long bridge including suspension bridge was greatly affected by the failure of the Taccoma Narrow Bridge on 7 November 1944. Due to the wind load, the bridge structure shook until it finally collapsed. Although the cause of the collapse was not immediately known, it is currently concluded that it was caused by a single degree of freedom torsional flutter caused by self-excited wind load. This phenomenon is classified as an aerodynamic phenomenon on long span bridges. The flutter analysis performed on the Sunda Strait Suspension Bridge using the Direct Flutter Analysis method will be presented in this paper.

Flutter performance of box girders with different wind fairings at large angles of attack

The streamlined box is a common type of girders for long-span suspension bridges. Spanning deep canyons, long-span bridges are frequently attacked by strong winds with large angles of attack. In this situation, the flow field around the streamlined box changes significantly, leading to reduction of the flutter performance. The wind fairings have different effects on the flutter performance. Therefore, this study examines the flutter performance of box girders with different wind fairings at large angles of attack. Computational fluid dynamics (CFD) simulations were carried out to extract the flutter derivatives, and the critical flutter state of a long-span bridge was determined. Further comparisons of the wind fairings were investigated by a rapid method which is related to the input energy by the aerodynamic force. The results show that a reasonable type of wind fairings could improve the flutter performance of long-span bridges at large angles of attack. For the torsional flutter instability, the wind fairings weaken the adverse effect of the vortex attaching to the girder, and a sharper one could achieve a better result. According to the input energies on the girder with different wind fairings, the symmetrical wind fairings are more beneficial to the flutter performance.

Experimental Study of the Nonlinear Torsional Flutter of a Long-Span Suspension Bridge with a Double-Deck Truss Girder

The purpose of this study is to investigate the nonlinear torsional flutter of a long-span suspension bridge with a double-deck truss girder. First, the characteristics of nonlinear flutter are studied using the section model in the wind tunnel test. Different aerodynamic measures, e.g. upper and lower stabilizers and horizontal flaps, are applied to improve the flutter performance of the double-deck truss girder. Then, the full bridge aeroelastic model is tested in the wind tunnel to further examine the flutter performance of the bridge with the optimal truss girder. Finally, three-dimensional (3D) flutter analysis is performed to study the static wind-induced effects on the nonlinear flutter of the long-span suspension bridge. The results show that single-degree-of-freedom torsional limit cycle oscillations occur at large amplitudes for the double-deck truss section at the attack angles of [Formula: see text] and [Formula: see text]. The upper and lower stabilizers installed on the upper and lower decks, respectively, and the flaps installed near the bottoms of the sidewalks can all effectively alleviate the torsional flutter responses. Meanwhile, it is found that the torsional flutter responses of the truss girder in the aeroelastic model test are much smaller than those in the section model test. The 3D flutter analysis demonstrates that the large discrepancies between the flutter responses of the two model experiments can be attributed to the additional attack angle caused by the static wind-induced displacements. This finding highlights the importance and necessity of considering the static wind-induced effects in the flutter design of long-span suspension bridges.

Background/Resonant decomposition of the stochastic torsional flutter response of an aeroelastic oscillator under buffeting loads

The complete flutter analysis of a structure requires the repeated analysis of the aeroelastic response of the structure for various wind velocities. In a spectral approach, each of these analyses is based on the integration of the power spectral density of the aeroelastic response. Traditional integration methods struggle to efficiently estimate these integrals because of the marked peakedness of the function in the neighborhood of the poles of the system. In this paper, we have derived an extension of the Background/Resonant decomposition (which is commonly applied under the quasi-steady assumption), to aeroelastic analysis, where the stiffness and damping of the coupled system changes with frequency. Both the background and resonant components take a more general form than in the well known case. They remain simple, however, and offer therefore a straightforward understanding of the response. The proposed formulation is illustrated with several examples of torsional flutter, where the critical state corresponds either to torsional galloping either to divergence. The study is limited to single degree-of-freedom systems but constitute the cornerstone of an extension to multi degree-of-freedom systems, where such an approximation becomes very interesting in terms of computational efficiency.

Recent advances, future application and challenges in nonlinear flutter theory of long span bridges

Polynomial-type mathematical models were presented to describe the nonlinear self-excited forces of nonlinear single degree of freedom (SDOF) torsional flutter of bluff bridge decks and nonlinear coupled flutter of streamline-like flat closed box bridge decks. A full bridge analysis method for nonlinear SDOF torsional flutter of long span bridges with bluff decks was then proposed based on the aeroelastic strip theory, and verified via wind tunnel test of full bridge aeroelastic model. A full bridge analysis method of nonlinear coupled flutter of long span bridges was also established based on the aeroelastic strip theory and an approximate linear complex-modal decomposition (ALCMD), and was applied then to the nonlinear coupled flutter analysis of a 688m main-span cable-stayed bridge. The analysis results show that behaviors of self-limiting and single-frequency oscillation of the nonlinear coupled flutter can be exhibited by using the proposed coupled flutter analysis approach. A new concept of performance-based graded evaluation and fortification criteria against flutter of long span bridges was then put forward for further discussions, which will possibly be an important and prosperous field of future applications of the nonlinear flutter theory. To this end, some challenging issues was discussed for further developing nonlinear flutter theory.

A semi-analytical approach for flutter analysis of a high-aspect-ratio wing

AbstractWe present a hybrid, semi-analytical approach to perform an eigenvalue-based flutter analysis of an Unmanned Aerial Vehicle (UAV) wing. The wing has a modern design that integrates metal and composite structures. The stiffness and natural frequency of the wing are calculated using a Finite Element (FE) model. The modal parameters are extracted by applying a recursive technique to the Lanczos method in the FE model. Subsequently, the modal parameters are used to evaluate the flutter boundaries in an analytical model based on the p-method. Two-degree-of-freedom bending and torsional flutter equations derived using Lagrange’s principle are transformed into an eigenvalue problem. The eigenvalue framework is used to evaluate the stability characteristics of the wing under various flight conditions. An extension of this eigenvalue framework is applied to determine the stability boundaries and corresponding critical flutter parameters at a range of altitudes. The stability characteristics and critical flutter speeds are also evaluated through computational analysis of a reduced-order model of the wing in NX Nastran using the k- and pk-methods. The results of the analytical and computational methods are found to show good agreement with each other. A parametric study is also carried out to analyse the effects of the structural member thickness on the wing flutter speeds. The results suggest that changing the spar thickness contributes most significantly to the flutter speeds, whereas increasing the rib thickness decreases the flutter speed at high thickness values.

Effects of Flexural and Mass Axes Position of Simple Rectangular Wing on Flutter Speed

The flexibility of the modern aircraft structures paves the way for the study of aero elasticity during the verification procedures of aircraft design and stability. The structures of wing will cautiously vibrate, either linearly or non-linearly due to the coupling effect between the aerodynamic, inertial and elastic forces of the wing structure, so the designing of aircraft involves two major aero elastic considerations such as wing torsional divergence and flutter. However, flutter problems are considered from the field of dynamic stability, the modal representation of flutter analysis is done by setting up the lifting surface as a linear ordinary differential equation, then changed to Eigen values and further stability analysis has been done. In order to complete the flutter analysis as an analytical tool, two important aerodynamic theories are taken into account and we identified and solved the classical flutter derivatives by using Eigen value method and also the position of flexural and mass axis of the simple rectangular wing on flutter speed has been analysed.

Experimental studies on the aerodynamic performance of two box girders with side openings

A butterfly web girder is a box-shaped girder with discretely distributed side openings along the spanwise direction. Until now, there have been few studies related to the aerodynamic performance of the butterfly web bridge. The objective of the current study was to clarify the effects of the side openings on the aerodynamic performance of the girder. Two butterfly web girders with side ratios B/D = 3.24 and 5, where B is the girder width and D is the depth, were examined through a series of wind tunnel tests. A comparison of the results for butterfly web girders and conventional box girders of the same shape confirmed that the side openings stabilized the vortex-induced vibration and galloping when B/D = 3.24, whereas the vortex-induced vibration and torsional flutter were stabilized when B/D = 5. The change in the flow field due to the side openings contributed to the stabilization against the vibration. These findings not only confirmed the good aerodynamic performance of the butterfly web bridge but also provided a new method to stabilize the box girder against aerodynamic instabilities via discretely distributed side openings.

Evaluation of aerodynamic instability for building using fluid–structure interaction analysis combined with multi-degree-of-freedom structure model and large-eddy simulation

To evaluate the aerodynamic instability for buildings considering their high-order oscillation mode and torsional oscillation mode on which it is difficult to perform the usual wind tunnel experiments, the fluid–structure interaction (FSI) analysis code combined with a multi-degree-of-freedom structure model and large-eddy simulation was developed. The calculation results obtained in this study and the results of wind tunnel tests conducted in a previous study using a building model (average breadth 0.14 ​m ​× ​length 0.28 ​m ​× ​height 1 ​m; scale: 1/600) with a multi-degree-of-freedom structure were compared. The comparison showed that the FSI analysis results were corresponded well with those of the wind tunnel tests; for each spectrum of response displacement (wind, along-wind, and torsional direction) at the top mass node, the frequency distribution and the peak frequency of the first and second oscillation modes were in good agreement with the calculation results and the wind tunnel test results. As for the amplitude of the top displacement of the building, the results for both the along- and across-wind directions showed good correspondence. For the torsional direction, the calculation results reproduced a torsional flutter oscillation with a slightly low wind level in comparison with that observed in the wind tunnel experiments.

Investigation of flutter performance of a twin-box bridge girder at large angles of attack

Twin-box bridge girders are considered to be aerodynamically favourable, and this paper presents a study on the flutter performance of this type of girders at large angles of attack by both wind tunnel tests and computational fluid dynamics (CFD) simulations. The stationary aerodynamic performance of a twin-box bridge girder at different angles of attack is studied, and different central slot widths are considered as well. Then, the flutter derivatives of the girder are extracted and the critical flutter state of the bridge is determined. The flutter mechanism is further discussed in detail based on the dynamic flow field characteristics and the work done by aerodynamic forces. Results show that the existence of central slot is in favour of the bridge flutter stability at null angle of attack. At large angles of attack, however, the flow field around the girder is quite different. Incoming flow could pass through the central slot and affect the vortex attaching to the girder. The upstream box extracts energy from the wind flow more easily than the downstream one, which may drive the bridge to torsional flutter instability at lower wind speeds.

Numerical Fluid-Structure Interaction Study on the NREL 5MW HAWT

The development of reliable Fluid-Structure Interaction (FSI) simulation tools and models for the wind turbines is a critical step in the design procedure towards achieving optimized large wind turbine structures. Such approach will mitigate the aeroelastic instabilities like: torsional flutter, stall flutter and edgewise instability that introduce extra stresses to the turbine structure leading to reduced life time and substantial failures. In this study, FSI simulations were held using the commercial package Ansys v18.2 solvers as a preliminary step towards our on-going development of a reliable Open-Source solver. These simulations were applied to the full-scale rotor blades of the NREL 5MW reference horizontal axis wind turbine. The aerodynamic loads and structural responses computations were carried out using a steady-state FSI analysis. The computations were run on the Kyushu University multi-core Linux cluster using the public domain openMPI implementation of the standard message passing interface (MPI). Finally, the results were validated against the Technical University of Denmark’s (DTU) MIRAS aeroelastic code results as well as the widely used FLEX5-Q3UIC and FAST codes in different cases showing reasonable agreement.