Aerodynamic Admittance Functions Research Articles

The jitter frequency domain of long-span railway cable-stayed bridges considering the influence of pneumatic admittance

The long-span bridge is highly sensitive to wind loads, and their random vibration response under static wind deformation and fluctuating wind load are relatively complex. The analysis of jitter response has become a key issue in the design. Taking the Hanjiatuo Yangtze River Bridge in the chongqing-lichuan railway as the engineering background, the influence of different aerodynamic admittance functions on the main girder jitter response is studied through frequency domain analysis. The results show that aerodynamic admittance has a great influence on the jitter response. Considering that the jitter displacement response of the aerodynamic admittance function is obviously smaller than the calculated results, the influence of aerodynamic admittance should be considered in the calculation and analysis.

A strategy for modifying the effect of turbulence integral scale on fluctuating pressures of rectangular prisms

The turbulence integral scale has a significant effect on the fluctuating pressures encountered by prisms. At present, the turbulence integral scale cannot be adequately simulated, leading to errors in the fluctuating pressure. Based on the two-wavenumber aerodynamic admittance function of fluctuating pressure, this paper describes a strategy for modifying the fluctuating pressure of rectangular prisms in turbulent flows. Using the three-dimensional theory of lift, a three-dimensional model of fluctuating pressure is established, in which the two-wavenumber power spectrum of fluctuating pressure is the product of the two-wavenumber coherence and the one-wavenumber power spectrum of fluctuating pressure, and is also the product of the two-wavenumber aerodynamic admittance function and the two-wavenumber power spectrum of oncoming velocity. An empirical form of the-wavenumber coherence of fluctuating pressure is derived, allowing the two-wavenumber power spectrum of fluctuating pressure to be calculated, and the two-wavenumber aerodynamic admittance function of fluctuating pressure to be obtained. The two-wavenumber aerodynamic admittance function of fluctuating pressure on a given body is almost independent of the turbulence, indicating that only one test is needed to modify the simulated error of fluctuating pressure. Finally, the results for a prism with a 1:3 side-ratio show that the simulated error of fluctuating pressure can be ignored when the simulated turbulence integral scale is 0.5 or 1.1 times the target value, and the simulated error is reduced from 24% to around 10% when the simulated turbulence integral scale is 0.25 times the target value.

Wind tunnel investigations of crosswind loads for static road vehicles on wide bridge decks

Accurately identifying the aerodynamic loads on vehicles is the fundamental issue for assessing the driving safety of vehicles on long-span bridges subjected to strong crosswinds. Thus, the aerodynamic interference of bridges with vehicles must be considered. However, very few studies have been conducted to quantify both the steady and unsteady crosswind loads for vehicles on wide bridge decks. In this paper, the mean and peak aerodynamic coefficients and aerodynamic admittance functions for three types of high-sided vehicles (medium trucks, buses, and tractor-trailers) on two wide bridge decks (a single-box girder and a twin-box girder) were determined by means of wind tunnel tests. The effects of vehicle position, wind angle of attack, and geometric shape of the deck on these aerodynamic parameters were investigated. The results show that the aerodynamic coefficients of vehicles on both bridge decks vary significantly with their lateral position. Moreover, the effect of wind angle of attack on the aerodynamic coefficients of vehicles on the leeward side of the twin-box girder is extremely substantial, as is the geometric shape of the bridge deck. However, the vehicle position, wind angle of attack, and bridge deck geometry all have little influence on the aerodynamic admittance functions of vehicles.

Full-scale investigation of heliostat aerodynamics through wind and pressure measurements at a pentagonal heliostat

Wind loads on heliostats are often investigated through experimental wind tunnel studies or numerical simulations. However, these approaches cannot consider the full-scale conditions but require a reproduction and simulation of both the heliostat structure and the wind conditions. Complementary full-scale investigations are therefore crucial but are at the same time relatively costly, as it is cumbersome to set up large heliostats with measurement devices. This paper introduces a new pressure measurement system which is easy-to-apply to a real-scale heliostat and enables full-scale investigations with minimized effort. The results of a first field study are presented during which wind and pressure measurements were taken simultaneously over periods of 10 min at a 48.5 m2 pentagonal Stellio heliostat. The non-dimensional pressure distributions are investigated and it is shown that the mean cp-values are very consistent amongst the measurement periods and reach values between 2.2 and 2.6. These values, in turn, are found to agree well with results of a wind tunnel study. Moreover, the behavior of the load coefficients with varying angles of attack is studied and the aerodynamic admittance functions are evaluated which give in-depth insight into the generation of aerodynamic loads. The admittance functions are found to start decreasing at a non-dimensional frequency of approximately 0.2. This finding indicates that eddies which are about the size of the heliostat or larger are fully effective in generating aerodynamic loads while the effectiveness of smaller eddies is reduced.

Strategies for identifying the two-dimensional aerodynamic admittance functions of a bridge deck

Pressure measurement experiments were carried out on three streamlined box girders with three geometric ratios of 1:50, 1:75 and 1:100 in five turbulent flow fields generated by grids. The turbulence intensities only affected the root-mean-square (RMS) of the pressure coefficients in the flow separation zone, while the turbulence integral scales affected the RMS of the pressure coefficients over the entire cross-sections. The spanwise correlations of the fluctuating winds and buffeting forces mainly varied with the turbulence integral scales. New strategies are proposed to identify the two-dimensional aerodynamic admittance functions (2D AAFs) using the two-wavenumber approach. The two-wavenumber coherence functions of fluctuating winds or buffeting forces obtained through new strategies do not need to use the empirical spanwise root-coherence function models compared to the traditional strategy. A complete analysis of 2D AAFs based on different strategies was performed. The determined 2D AAF using spanwise root-coherence function models varied with the kinds of spanwise root-coherence function model and relied on spacings chosen to fit, which caused the 2D AAF to vary in size. Therefore, the strategy without any spanwise root-coherence function models is recommended, and it is confirmed to give reliable and repeatable bridge deck 2D AAFs.

Influence of turbulent incoming flow on aerodynamic behaviors of train at 90° yaw angle

Turbulent incoming flow conditions are closely matched to the crosswinds experienced by trains in windy areas. Therefore, it is important to investigate how the turbulent inflow affects the flow dynamics around a train. The aerodynamic characteristics of a 1:8-scaled high-speed train at a 90° yaw angle were studied based on the improved delayed detached eddy simulation (IDDES) turbulence model. Four incoming flow conditions were set using a synthetic eddy method (SEM) turbulent generator, including uniform, Lu = 0.5H, Lu = 1H, and Lu = 2H inflow (Lu is turbulence integral length scale and H is reference height). The aerodynamic loads, surface pressure, mean vorticity, vortex structure, velocity deficit, turbulence characteristics, Reynold stresses, turbulence production term, and anisotropy of turbulence were thoroughly analyzed. Turbulent inflow and increasing inflow Lu increased the standard deviation of the aerodynamic loads on the train. A crisis of inflow Lu appeared around 0.5H, meaning the rolling moment and overturning moment were largest under this crisis condition. Turbulent inflow caused vortices on the train's leeward side to come closer to the train, increasing the vorticity thickness and shortening the back flow region. The Reynolds stresses on the train's leeward side under turbulent inflow conditions were strengthened. The spectrum-proper orthogonal decomposition method was used to analyze the dominant mode within the train's leeward region and the corresponding energy distribution in the frequency domain. The aerodynamic admittance function was used to investigate the frequency characteristics of the aerodynamic loads on the train.

Measurements of two-dimensional aerodynamic admittances of airfoil and rectangular cylinder in turbulent flow

The two-dimensional aerodynamic admittance functions (2D-AAFs) of an airfoil and rectangular cylinders are measured in turbulent flow via a combined theoretical and experimental method. The key of the method is to separate the so-called three-dimensional effects (3D-effects) from the three-dimensional aerodynamic admittance functions (3D-AAFs, namely the traditional aerodynamic admittance). To validate the effectiveness of the method, the 2D-AAF of an airfoil with a NACA 0015 profile is firstly determined with this method. The result shows that the Sears function could not capture the measured values of airfoil 3D-AAF, while after the 3D-effects are separated, the obtained airfoil 2D-AAF could agree well with the Sears function. This confirms that discrepancies between the 3D-AAF and the Sears function are mainly caused by the 3D-effects. The 2D-AAFs of rectangular cylinders with different aspect ratios are then obtained in a turbulent flow field. Unlike the airfoil 2D-AAF, it is observed that the 2D-AAFs of rectangular cylinders are between 1 and the Sears function. When the aspect ratio changes, the 2D-AAF of the rectangular cylinder also varies correspondingly. With the increase of aspect ratio, the 2D-AAF of a rectangular cylinder gradually approaches the Sears function, contrarily, the 2D-AAF of a rectangular cylinder is closer to the quasi-steady value 1 for less aspect ratio. This might be caused by different relative lengths of a separation bubble over the rectangular cylinder with different aspect ratios. An empirical 2D-AAF model of rectangular cylinder considering the aspect ratio is consequently proposed based on the experimental data.

Experimental study on the influence of rolling angle on aerodynamic characteristics of suspended monorail trains

Compared with railway trains, crosswinds have a greater effect on the rolling angle behavior of suspended monorail trains (SMTs), which will inevitably change the aerodynamic configuration of the train-bridge system. This paper focuses on investigating the influence of rolling angle on aerodynamic characteristics of the SMT via pressure measurements in a wind tunnel. The surface pressure distribution, aerodynamic coefficient and admittance of the SMT model were analyzed over a wide range of rolling angle. The results indicate that the rolling angle has a certain influence on the surface pressure distribution of SMT, especially in the area near the corner of the windward surface. As the rolling angle increases, the absolute aerodynamic coefficients of lift force and moment will be reduced by 66% and 45%, while increasing percentage of side force coefficient is only 4.9%. Furthermore, a series of fitting formulas are proposed to estimate the aerodynamic coefficients of the train under different rolling angles based on the experimental data. The aerodynamic admittance functions of SMT show a peak value at a specific reduced frequency near 0.05, and the lift aerodynamic admittance is found to be sensitive to the rolling angle behavior of SMT in the reduced low-frequency range.

Combining active and passive wind tunnel tests to determine the aerodynamic admittances of a bridge girder

In conventional buffeting analyses for long-span bridges, the aerodynamic admittance functions (AAF) with respect to the longitudinal (u-) and vertical (w-) turbulence components are usually assumed to be equivalent. This assumption could cause unpredictable errors due to complicated turbulence-structure interactions. This study proposes an experimental method to determine the u- and w- AAFs in the framework of three-dimensional buffeting theory. First, passive wind tunnel test is conducted to measure necessary aerodynamic parameters. Next, the turbulence characterized only by u-velocity fluctuations is generated in a multi-fan active-controlled wind tunnel to reproduce the u-velocity component in the passive wind tunnel test. The aim is to identify the u-AAF separately. Finally, the w-AAF is evaluated by combining the parameters measured in the active and passive wind tunnel tests. For a streamlined bridge girder, results show significant discrepancies between the u-AAF and w-AAF. The derivation degrees depend on the frequency and the angle of attack (AoA). This indicates the inaccuracy of the conventionally invoked assumption. In detail, the w-AAF is higher than the u-AAF at low frequencies, whereas the relationship reverses at higher frequencies. The proposed method is also applicable for other bluff-body structures, it is useful for improving the accuracy of buffeting analyses.

Statistical linearisation of a nonlinear floating offshore wind turbine under random waves and winds

This paper investigates the stochastic nonlinear dynamics of a floating offshore wind turbine (FOWT) in the frequency-domain under irregular waves and turbulent winds. The main sources of nonlinearities are estimated using statistical linearisation, which are calculated based on probability density functions (PDFs) between the degrees-of-freedom and the environment. The nonlinear mooring model captures the coupling between degrees-of-freedom when the platform has a mean displacement caused by the wind thrust, changing the natural frequency especially in surge. In addition, the nonlinear viscous drag loads offer an hydrodynamic damping that lead to better estimates of the responses. The nonlinear aerodynamic loads uses the relative motion experienced by the wind turbine under turbulent wind, and the concept of aerodynamic admittance function, which has not been applied yet to FOWTs, is included to capture the spatial effects of the wind turbulence. The results are benchmarked against nonlinear time-domain simulations using OpenFAST, and good agreement is obtained in terms of power spectral densities, PDFs and standard deviations. Several environmental conditions are used to explore some of the platform characteristics and salient features from the model. The main advantage of the following approach is the low computational cost, while providing reliable estimates of the response.

Dynamic response of railway vehicle with aerodynamic admittance function: An optimized algorithm

Wind effect for railway vehicle was a common problem, and attracted an increasing concentrate, due to the rapidly development of the high-speed railways. In order to evaluate the effect of aerodynamic admittance of a train on the safety, the buffeting force expression (BFE) of vehicle needed to be optimized. In this paper, an advanced approach for the optimization of the BFE of vehicle was proposed. According this methodology, the BFE modified by the aerodynamic admittance function (AAF) took the effect of the vertical fluctuating wind speed into consideration. For the AAFs of railway vehicle obtained by wind tunnel test, a numerical model for the vehicle system, which was fitted based on the expression of frequency responses function of mass-spring-damping system, was presented and verified by the experimental data. The effects of the fitting parameters for the numerical model on the weighting function (WF) and time history of the buffeting force of vehicle were investigated. Then, the WFs of the buffeting force for the vehicle running on the different infrastructure (including flat ground, embankment and bridge) with various wind direction angles, were carried out. Finally, the influences of different flow fields on the dynamic responses of railway vehicle moving on three types of infrastructure were calculated.

Wind tunnel test on the aerodynamic admittance of a rail vehicle in crosswinds

The aerodynamic admittance of a rail vehicle was investigated by wind tunnel test. Aerodynamic force was measured in the cases of three typical railway structures, including on the flat ground, above an embankment, and on a bridge, under two turbulent flow fields. First of all, three-component aerodynamic coefficients of the vehicle on each structure were obtained under uniform flow with respect to three wind attack angles and four wind direction angles. Secondly, the aerodynamic forces on the vehicle and the corresponding wind speed were evaluated to establish an aerodynamic admittance function of the vehicle. The aerodynamic admittance of the rail vehicle approximated a constant value in the low-frequency domain, but decreased with the reduced frequency increasing. The effects of the different reduced frequencies on the drag are greater than the lift admittance of the vehicle, while moment admittance stays steady-state. Finally, in order to reflect the unsteady characteristics of the buffeting force on the vehicle, the aerodynamic admittance functions of the vehicle were fitted to the expression of the frequency response function of a mass-spring-damping system, which was then verified. Furthermore, the effects of flat terrain and mountainous terrain were investigated, revealing that the influence of turbulence intensity on aerodynamic admittance is significant.

The effect of turbulence intensity on the unsteady gust loading on a 5:1 rectangular cylinder

The present work aims to study the effects of turbulence intensity on the three-dimensional spatial distribution of unsteady gust loading on a 5:1 rectangular cylinder. Three types of grids are adopted to produce uniform turbulent flows with different turbulence intensities and constant integral scales. The experimental results show that the turbulence intensity has a noticeable influence on the gust loading. An increase in the turbulence intensity results in a stronger spanwise correlation of the fluctuating pressures on the side surfaces. To reveal the three-dimensional aerodynamic effects of turbulence, a closed-form solution of a three-dimensional aerodynamic admittance function (3D AAF) is presented based on Ribner's three-dimensional spectral tensor theory. This 3D AAF model is expressed in terms of two-dimensional aerodynamic admittance function (2D AAF) for transversely fully correlated gusts and the gust-related spanwise correlation factor. The proposed 3D AAF can explain the mechanism of the three-dimensional aerodynamic effect of turbulence, which results in a more correlated lift force. It is observed that the filtered bandwidth in the spanwise direction amplifies as the turbulence intensity decreases, suggesting that the large-scale vortices in the separated flow are contaminated by smaller eddies. Consequently, the spanwise correlation of the lift force on a 5:1 rectangular cylinder will have the opposite tendency. Notably, it is confirmed that the 2D AAF depends only on the cross-sectional shape rather than the turbulence intensity.

Aerodynamic admittance of a 6:1 rectangular cylinder: A computational study on the role of turbulence intensity and integral length scale

The evaluation of the aerodynamic admittance is a fundamental step in the calculation of the buffeting response of flexible structures immersed in turbulent flows such as long-span bridges and slender towers. As it is well-known, bluff sections immersed in turbulent flows often exhibit a complex aerodynamic behavior, which can be greatly affected by the turbulence intensity and the integral length scales of the impinging turbulence. In this paper, computational fluid dynamics is used for the evaluation of the admittance functions of a 6:1 rectangular cylinder. Firstly, the incoming turbulence is synthetically generated. Then the aerodynamic admittance functions are evaluated considering five different inflow conditions using Large Eddy Simulations. The use of synthetic inflows allows to easily separate the role played by each characteristic of the inflow turbulence, so allowing to separately study the effect of the turbulence intensity and the length scales.

Nonuniform wind characteristics and buffeting response of a composite cable-stayed bridge in a trumpet-shaped mountain pass

Due to the spatial differences in wind fields in mountainous areas, it is an urgent problem to accurately estimate the buffeting response of long-span bridges in mountainous areas. In this paper, the spanwise variations in the mean and fluctuating wind characteristics of a bridge site are obtained based on a terrain wind tunnel test of a trumpet-shaped mountain pass. Additionally, the aerodynamic admittance function of a Π-shaped composite girder under different wind attack angles is measured in the wind tunnel. The buffeting response calculation theory considering the spanwise variations in the mean wind and fluctuating wind characteristics along the main girder is established. The influence of the nonuniform wind characteristics on the buffeting response of the main girder is analyzed. The results show that the spanwise variation in wind characteristics at the bridge site is affected by the direction of inflow and can be described by a quadratic polynomial. Nonuniform wind parameters have obvious effects on the buffeting response, and a nonuniform wind attack angle is a key factor affecting the buffeting response. It may not be appropriate to predict the buffeting response by using the single-point wind field observation results in mountainous areas.

Gust effect factors for windward walls of rigid buildings with various aspect ratios

This paper examines the aerodynamic mechanisms associated with gust effect factors for windward walls of rigid buildings. The analysis utilizes two experimental databases with 58 rectangular-plan building models. Statistical characteristics of windward wall pressures, such as skewness, kurtosis, and peak factors, are examined along with parameters related to the wind spectra and the aerodynamic admittance. It was found that the statistical characteristics depend primarily on the aspect ratio defined as the ratio of height to breadth, H/B. The results also show that the area-averaged windward wall pressures present Gaussian distributions when the aspect ratio exceeds 6. Moreover, the measured aerodynamic admittance function for area-averaged windward wall pressures, referenced to the mid-height velocity spectra, matches reasonably well with Vickery’s model. The energy content of the wind-induced pressure on windward walls are influenced by horseshoe vortex of low-rise buildings with H/B ​< ​1. The pressure fluctuations at windward wall locations near the edge conjunct with side walls are also influenced by the vortex shedding over side walls for high-rise buildings. The gust effect factor model adopted in ASCE 7–16 is able to accurately assess the gust effect factors for rigid high-rise buildings, but is inaccurate for low-rise buildings, primarily because of the role of the horseshoe vortices.

An Examination of the Gust Effect Factor for Rigid High-Rise Buildings

In order to systematically investigate the gust effect factor for rigid buildings, the derivation of the gust effect factor in ASCE 7–16 is carefully reviewed and scale model pressure tests were carried out for rectangular-plan high-rise buildings with plan aspect ratios ranging from 0.11 to 9. The gust effect factor and the aerodynamic admittance function (AAF) for area-averaged pressure coefficients and base drag coefficients were obtained and discussed in detail. The results show that the AAF has direct influence on the value of the gust effect factor, depending on whether effects of non-contemporaneous gust actions or body-generated turbulence are playing a leading role. The ASCE 7–16 gust effect factor for rigid buildings underestimates the measured values for individual walls due to differences in the AAF, peak factors, and the employment of the 3 s moving average filter. However, the ASCE 7–16 gust factor for overall drag is estimated within 5% or better.

Wind tunnel testing and frequency domain buffeting analysis of a 5000 m suspension bridge

Buffeting’s importance is highlighted in the case of super-long bridges. It remains unclear how buffeting will perform and whether the traditional methods still apply when bridge’s span is approaching its upper limitation. To figure out this, a full aeroelastic model testing has been carried out with the span arrangement 2000+5000+2000 m. A comparison with the existing bridges reveals the similarities and differences. It shows vertical and torsional buffetings are important for a 5000 m bridge while lateral response is almost static. Fundamental modes contribute most kinetic energy. With the increasing of wind speed, the aerodynamic coupling effect becomes prominent while the structural coupling effect keeps limited. Afterwards, four analytical methods, namely SRSS and CQC, with and without self-induced forces, are used for the buffeting displacements. The calculation indicates the multi-mode (CQC) analysis is still applicable on a 5000 m bridge but the mode-by-mode (SRSS) method is risky since the neglection of aerodynamic coupling effect. Parameter analysis shows aerodynamic admittance function and force coherence are decisive while the cross terms are of secondary importance. Since all data is experimentally measured, the reliability of analytical results can be ensured.

Identification of complex admittance functions using 2D-URANS models: Inflow generation and validation on rectangular cylinders

The evaluation of the aerodynamic admittance functions is a key step in the calculation of bridges and towers buffeting response. For streamlined bodies, such functions can be well approximated by the closed form solution developed by Sears. For bluff bodies, the evaluation of the admittance function still represents an open problem: experimental procedures require the use of grid turbulence or active wind tunnels. In the first case, a number of interrelated factors contribute to the obtained results while, in the second case, the experimental apparatus is of considerable complexity. In this paper, the use of Computational Fluid Dynamics for the evaluation of complex admittance functions is analyzed. Firstly, a discussion regarding the characterization of the flow in active wind tunnels and its reproduction in numerical simulations is presented. Such aspect has been often overlooked in previous studies, in which experimental procedures have been mimicked, so not taking full advantage of the CFD approach. Then, rectangular cylinders with aspect ratio ranging between 4 and 16.67 are studied by means of 2D URANS. It is shown that while 2D URANS usually lead to acceptable results, they can prove inaccurate in specific cases. Additional LES simulations led to a good matching of the experimental data.

Effects of turbulence integral scales on characteristics of fluctuating wind pressures

To investigate the effects of turbulence integral scale, four rectangular models were tested in grid-generated turbulent flows, and the characteristics of fluctuating pressures on windward surfaces were obtained. The results show that all statistical parameters except the mean pressures depend on both the longitudinal integral scale (Lux) and depth (D) of the model. The root-mean-square (rms) values of the fluctuating pressure coefficients and their correlation as well as the spanwise coherence increase with the turbulence integral scale. As the integral scale decreases, the power spectra of the fluctuating pressures in the low-frequency region, which are controlled by the quasi-steady effect, remain almost unchanged, whereas those in the high-frequency region attenuate more rapidly. To seek a potential modification method for correcting the error margin caused by an imprecisely simulated turbulence integral scale, an empirical model of aerodynamic admittance function (AAF) of fluctuating pressure was proposed with consideration of Lux /D as a key variable. Finally, using the fluctuating pressure on the model with a side ratio of 1:3 as an example, the error margins of the fluctuating pressures were discussed. It was discovered that the maximum deviation of the rms value of the fluctuating pressure coefficient reached approximately 25% when the simulated turbulence integral scale was one-sixth the target value.