Unsteady Aerodynamic Loads Research Articles

Aerodynamic and structural characteristics of helicopter rotor in circling flight

To investigate the distinct properties of the helicopter rotors during circling flight, the aerodynamic and dynamic models for the main rotor are established considering the trim conditions and the flight parameters of helicopters. The free wake method is introduced to compute the unsteady aerodynamic loads of the rotor characterized by distortions of rotor wakes, and the modal superposition method is used to predict the overall structural loads of the rotor. The effectiveness of the aerodynamic and the structural methods is verified by comparison with the experimental results, whereby the influences of circling direction, radius, and velocity are evaluated in both aerodynamic and dynamic aspects. The results demonstrate that the circling condition makes a great difference to the performance of rotor vortex, as well as the unsteady aerodynamic loads. With the decrease of the circling radius or the increment of the circling velocity, the thrust of the main rotor increases apparently to balance the inertial force. Meanwhile, the harmonics of aerodynamic loads in rotor disc change severely and an evident aerodynamic load shock appears at high-order components, which further causes a shift-of-peak-phase bending moment in the flap dimension. Moreover, the advancing side of blade experiences second blade/vortex interaction, whose intensity has a distinct enhancement as the circling radius decreases with the motion of vortexes.

The influence of yaw misalignment on turbine power output fluctuations and unsteady aerodynamic loads within wind farms

Systematic wind tunnel experiments were performed to quantify the power output fluctuations and unsteady aerodynamic loads of modeled wind farms with 3 rows and 3 columns across various yaw angles. Time-resolved particle image velocimetry (PIV) was applied to characterize the flow statistics, while the power output and aerodynamic loads on the turbine tower were measured by a data logger and force cell at high temporal resolution. Results showed that the growth of the yaw misalignment angle mitigates the turbine power output fluctuation. However, this can increase the power fluctuations of downstream turbines. Measurements of the aerodynamic loads on the turbine tower revealed that the growth of the yaw angle significantly increased the fatigue loading in the side-force direction across all frequency components. At the same time, such impact was less distinctive for the thrust force. The dominating unsteady aerodynamic loads are always in the direction perpendicular to the rotor surface. Flow statistics demonstrated that yaw misalignment could effectively increase mean wake velocity, and integral time scale and reduce the turbulence intensity. Finally, theoretical models based on the coupling between turbine properties and local incoming flow statistics were derived to reveal the evolution of turbine power fluctuations and unsteady aerodynamic loads in the wake flow across various yaw misalignment.

Experimental and numerical study on 2-DOF wind-induced vibration and energy harvesting of triangular prism

The two-degrees of freedom (2-DOF) wind-induced vibration (WIV) response and energy harvesting performance of an equilateral triangular prism were conducted by numerical and experimental studies under different attack angles. The piezoelectric patch is applied in this work to extract power. To enhance the output power of the prism, an omnidirectional piezoelectric system is used to harvest energy in flow and cross flow directions simultaneously. It's found that the attack angle (α0) is a key factor influencing the power extraction performance of the system. The output power of the prism almost keeps around zero when 0° ≤ α0 ≤ 30° and increases monotonously with the increase of wind velocity for 30° < α0 ≤ 60°. Especially for α0 ≥ 55°, the power output experiences a rapid increase. The highest output power of 1.30 mW can be obtained when α0 = 60°. The WIV responses show that the amplitude in the direction perpendicular to incoming flow can reach 3.00b (b is the side length of the triangular cross section for the prism) when α0 = 60°. And the lock-in region can be observed in high reduced velocity range when 30° ≤ α0 ≤ 60°. In addition, due to the transition of vortex pattern from 2S to P + S for high attack angles, the unsteady aerodynamic loading acting on the prism results in strong WIV responses with high vibration amplitude, which then leads to the improvement of energy harvesting performance from WIV.

Discrete integration for measuring aerodynamic loads on trains in crosswinds − realizable strategies of discretization and discrete integration

Discrete integration occupies an important place in train aerodynamic tests in crosswinds. Improved delayed detached eddy simulations based on shear stress transport k-ω turbulence models were carried out to calculate the side force, lift, rolling moment around the lee rail, and surface pressure on bluff and streamlined vehicles. The changepoints and piecewise linearities of the pressure coefficients were evaluated, and the maximum coefficient of determination in the elements was 0.9973. A realizable strategy of the discretization based on the Lagrange rectangular elements was suggested, including the largest lengths and numbers of the elements. From this, a strategy of the discrete integration was presented to measure the aerodynamic loads, considering the real orientation of the elements. The maximum errors of the mean aerodynamic load coefficients of the bluff and streamlined vehicles were 4.1% and 2.2% (except the mean lift coefficient of the bluff vehicle), respectively. The errors were less than those in the previous studies, especially for the streamlined vehicle, which reduced by up to 8.7%. The unsteady aerodynamic loads with no delay obtained by the strategies were near to natural ones in the frequency range that people would be concerned about in crosswinds (at the Strouhal number of less than 0.4). Some suggestions were made for using the strategies in the full-scale tests and model tests, which provided a foundation for further studies of the running safety in natural crosswinds.

Deep learning predictions of unsteady aerodynamic loads on an airfoil model pitched over the entire operating range

For the design and certification of wind turbines, it is essential to provide fast and accurate unsteady aerodynamic load prediction models for the whole operational range of angle of attack, up to 180° for vertical-axis and 90° for horizontal-axis wind turbines. This work describes a computationally efficient unsteady forces prediction model based on a deep learning approach, namely the bidirectional long short-term memory (BiLSTM) algorithm, for an airfoil pitched over the full operational range of angles of attack up to 180°. No model has been developed to capture the unsteady forces at high angles of attack. Novel features based on operating conditions and the steady polars of the airfoil are used as inputs for the BiLSTM model. Direct measurements of steady and unsteady forces on a NACA 0021 airfoil model were conducted at reduced frequencies up to 0.075 and a Reynolds number of 120 000 in an open-jet wind tunnel for model learning and testing. The unsteady forces vary significantly from the steady values at high pitching amplitudes and post-stall angles, which, if not accounted for when simulating wind turbine performance, would result in inaccurate predictions. Furthermore, measurements revealed the effect of unsteady vorticity development and shedding on aerodynamic forces under forward and reverse flow conditions. The BiLSTM model is capable of capturing the underlying physics of unsteady aerodynamic forces under extreme operating conditions.

Research on Panel Flutter Considering the Effect of Convective Active Cooling

The aeroelastic characteristics of the panel under the action of coolant are obviously different from the flutter characteristics of the traditional panel. In order to solve this problem, the dynamics model of the panel flutter was established in this paper based on von Karman’s large deformation theory and the Kirchhoff–Love hypothesis. The panel dynamics equations were discretized into constant differential equations with finite degrees of freedom by Galerkin’s method, and solved by the fourth Runge–Kutta method in the time domain. The nonlinear modified piston theory was used to predict the unsteady aerodynamic loads, and the accuracy of the flutter analysis model was verified. On this basis, the effects of the head-panel pressure of coolant, the pressure drop ratio, the coolant injection direction, and the inertial resistance and viscous resistance on panel stability and flight stability were investigated, respectively. The results showed that reducing the pressure drop ratio, and reducing or increasing the head-panel pressure (valuing away from the freestream pressure) can improve the critical dynamic pressure when bifurcation occurs. At M∞=5.0, the pressure drop ratio causes a 22.1% increment in the critical dynamic pressure. The influence of the coolant injection direction on the panel bifurcation is mainly influenced by the head-panel pressure. The inertial resistance slows down the convergence process of the panel response, increases the limit cycle amplitude, and reduces the critical dynamic pressure of the panel, while the viscous resistance plays the opposite role. Based on these conclusions, this paper finally proposes the suppression method of panel fluttering from head-panel pressure, inertial resistance, viscous resistance, etc.

Rotational effects on the blade flow of a horizontal axis wind turbine under axial and yawed inflow conditions

Unsteady aerodynamic loads and fluctuating output power of wind turbines remain challenging to predict accurately due to the incomplete understanding of blade flow mechanisms. Rotational effects can significantly impact the wind turbine aerodynamic performance. Therefore, this paper presents a careful investigation into rotational flow characteristics of the NREL Phase VI blade under axial and yawed inflow conditions based on the DDES method. Rotational effects change the flow regime from the massive 2D trailing-edge separation into the moderate 3D leading-edge separation on the NREL Phase VI blade. Flow separation is found sufficient but not necessary for the radial flow. Under the axial inflow, rotational effects can effectively suppress the flow separation and increase the nonlinear aerodynamic loads. Under the yawed inflow, rotational effects also effectively suppress the unsteady separated flow and accelerate the flow reattachment, particularly on the downwind side. Sectional lift coefficient is therefore greatly increased at the high angles of attack due to the pronounced rotational effects. Increasing the yaw angle and wind speed may also strengthen the rotational effects and widen the difference between the 2D airfoil flow and 3D sectional flow. These findings imply that flow regime and aerodynamic hysteresis on the inboard blade can be substantially changed in comparison with the 2D airfoil flow due to strong rotational effects. This study might deepen the understanding of rotational effects on the near-wall flow of wind turbine blades and also improve the aerodynamic modelling.

Structurally Nonlinear Fluttering of a Three-Degree-Freedom Wing with Random Disturbances

The differential equations of motion are established for a three-degree-freedom wing dynamic model subjected to unsteady aerodynamic loads and random perturbations. The system is dimensionally reduced by the improved average method to obtain the standard equations. Flutter problems of the deterministic wing system with high-order structural nonlinearity are studied using Hopf bifurcation theory and numerical simulation, the critical flutter speed is obtained and the effectiveness of the improved average method in the process of dimensionality reduction is verified. The stochastic P-bifurcation behaviors of the system are analyzed considering the effects of random perturbations of the longitudinal airflow by examining the qualitative variations of the probability density function curves. The results show that the deterministic wing system has a secondary bifurcation, a bistable phenomenon in which the equilibrium and the limit cycle oscillations coexist. The random disturbances significantly increases the critical flutter speed of the wing system, and the amplitude of limit cycle oscillations increases after including random perturbations for the same incoming flow speed.

Effects of the height and chordwise installation of the vane-type vortex generators on the unsteady aerodynamics of a wind turbine airfoil undergoing dynamic stall

Dynamic stall can produce nonlinear and unsteady aerodynamic loads on wind turbines. It has attracted considerable attention recently by introducing vortex generators (VGs) to suppress the dynamic stall, although the effects of decisive VG parameters have not yet been investigated adequately. This paper aims to provide insights into the impacts of vane height and chordwise installation on the dynamic stall phenomenon of an NREL S809 airfoil equipped with VGs. Unsteady flow characteristics are identified through fully resolved URANS simulations. Unsteady flow separation can be suppressed effectively via the VG-induced streamwise vortices. Consequently, the delayed onset of dynamic stall leads to greatly increased maximum lift and accelerated flow reattachment in the downstroke process. Low-profile VGs can cause an early abrupt dynamic stall and remarkable aerodynamic hysteresis, thereby losing their effectiveness. Moreover, positioning VGs too far downstream can cause significant increases in both drag and hysteresis intensity, because the streamwise vortices decay rapidly under the high adverse pressure gradient. Increasing VG size and utilizing double-row VGs simultaneously can strengthen the VG-induced streamwise vortices and hence the boundary layer momentum transfer, resulting in effectively controlled local flow structures. Furthermore, double-row VGs perform efficiently in improving unsteady aerodynamics due to low drag penalty.

Pressure Feedback Control of Aerodynamic Loads on a Delta Wing in Transverse Gusts

A feedback active flow control (AFC) scheme is studied for control of unsteady aerodynamic loads that act on a generic tailless delta wing during transverse gust encounters. The transverse gust and the roll angle of the wing create an unsteady roll moment. The trailing edge actuators generate unbalanced lift increments on the two sides of the model to control the roll moment. Spatially distributed pressure sensors measure surface pressure on the suction side of the wing, and the real-time aerodynamic loads are estimated through models that are identified by the Sparse Identification of Nonlinear Dynamics algorithm. The aerodynamic load estimation is then used as a surrogate to provide the AFC system with a feedback signal to alleviate the unsteady roll moment due to the gust effect. A physical interpretation of the model identification results is made to locate the source of the lift and roll moment fluctuations in gust encounters. Experimental results show that the AFC effect with a momentum coefficient input of 2% is equivalent to 26° elevon deflection in terms of the roll moment change, and the AFC doubles the control authority relative to elevons. The real-time control results show that the pressure feedback control system reduces the mean roll moment error and suppresses the fluctuations to less than 20% of the uncontrolled fluctuation level at a high angle of attack.

Data-Driven Unsteady Aeroelastic Modeling for Control

Aeroelastic structures, from insect wings to wind turbine blades, experience transient unsteady aerodynamic loads that are coupled to their motion. Effective real-time control of flexible structures relies on accurate and efficient predictions of both the unsteady aeroelastic forces and airfoil deformation. For rigid wings, classical unsteady aerodynamic models have recently been reformulated in state space for control and extended to include viscous effects. Here, we further extend this modeling framework to include the deformation of a flexible wing in addition to the quasi-steady, added mass, and unsteady viscous forces. We develop low-order linear models based on data from direct numerical simulations of flow past a flexible wing at a low Reynolds number. We demonstrate the effectiveness of these models to track aggressive maneuvers with model predictive control while constraining maximum wing deformation. This system identification approach provides an interpretable, accurate, and low-dimensional representation of an aeroelastic system that can aid in system and controller design for applications where transients play an important role.

Steady and unsteady aerodynamic loading of a NACA 16-616 aerofoil in a uniform flow

AbstractThis paper investigates the hydrodynamic near-field of a NACA 16-616 aerofoil over a range of angles-of-attack, encompassing the pre-stall, stall and post-stall flow regimes. In both the static pressure and the pressure fluctuation results, it is shown that each flow regime is easily distinguished, and it is further shown that each regime has different spectral behaviour and boundary layer characteristics. It is found that the NACA 16-616 aerofoil stalls by an abrupt leading-edge mechanism, characterised by a sudden change in the static pressure and unsteady surface pressure spectra between $16^\circ $ and $17^\circ $ angles-of-attack, but of more interest is that there is a secondary yet significant trailing-edge flow separation mechanism occurring upstream of the trailing-edge and moving further upstream as the angle-of-attack increases in the pre-stall regime. A comparison is made between the spectra and coherence of the unsteady surface pressure of the NACA 16-616 aerofoil and those of the classic NACA 0012 aerofoil and shows that such a secondary mechanism has a significant impact for large pre-stall angles-of-attack on the unsteady surface pressure. This will have a significant impact on the radiated far-field sound, distinguishing the NACA 16-616 aerofoil from aerofoils that do not have this secondary mechanism. The existence and extent of this secondary trailing-edge separation mechanism is further shown by the hot-wire anemometry boundary layer velocity results that indicate separation within the pre-stall regime.

A Data-Driven Model for Aerodynamic Loads on Road Vehicles Exposed to Gusty Bora-Like Winds

Strong cross-wind gusts can cause the vehicle to overturn or slide off the road. This problem is particularly experienced on bridges, as vehicles are extremely sensitive to complex wind-bridge–vehicle interactions. While quasi-steady atmospheric winds create serious difficulties for vehicles, this fact is exacerbated by gusts of wind, as is the case with bora, where gusts of wind can reach velocities five times the average wind velocity. In the present study, experiments concerning aerodynamic loads experienced by vehicles exposed to gusty, bora-like winds are carried out. It is noted that the wind gusting and vortex shedding determine unsteady wind loads on vehicles. The experimental results are used as a basis for developing a simple data-driven modeling approach capable of predicting the time history of aerodynamic loads on vehicles exposed to cross-wind gusts. The modeling results indicate that a model using more than two-state variables is needed to capture the unsteady aerodynamic loads.

The influence of cylinders in tandem arrangement on unsteady aerodynamic loads

This paper presents an experimental study on the unsteady pressure loading for two circular cylinders in tandem arrangement for the Reynolds number in the subcritical regime. Experiments were conducted on two heavily instrumented cylinders, each with multiple static and dynamic pressure sensor devices positioned at various peripheral and spanwise locations, enabling extensive dynamic surface pressure, coherence, and turbulence length-scale analysis. Results show that the root-mean-squared pressure magnitude of the pressure distribution results is much larger for the rear cylinder than for the front cylinder. In the case of small spacing ratios, the surface pressure density findings show a decreased shedding frequency on both cylinders, however the critical spacing ratio shows a quick jump in shedding frequency. The lateral coherence results also revealed that beyond the critical spacing, a prominent peak at the fundamental vortex shedding frequency exists, with weaker peaks at shedding harmonics on the front and rear cylinders, resulting in smaller correlation length values than those for smaller spacing ratios. The discovery of tonal peaks and their associated flow mechanics on cylinders in tandem were reinforced by the lift and drag power spectral density as well as the higher-order spectral analysis, such as wavelet analysis and persistence spectrum.

Parametric modelling of unsteady load for turbine cascade and its application in clocking effect optimization and load-reduction

The circumferential phase differences of adjacent stators or rotors will lead to different unsteady aerodynamic loads of turbine (i.e., the clocking effect), which makes the modelling of unsteady load and clocking effect very complex, so an accurate and efficient modelling method for its optimization becomes essential. In this paper, a new modelling method for the unsteady aerodynamic load of turbine cascades is proposed based on the reduced-order model (ROM) and parametric training and applied to optimizing the clocking effect of a 2-stage low-pressure turbine cascade. Firstly, using the sub-block method, snapshot matrices that include the unsteady aerodynamic load on stator/rotor surfaces in different clocking positions are established, and the ROM of aerodynamic load in different clocking positions is presented based on the proper orthogonal decomposition (POD) method. Secondly, the POD coefficient matrices and the basis matrices are reconstructed based on the parametric Gaussian process regression (PGPR). The PGPR surrogate models between clocking positions and aerodynamic load are obtained. Finally, based on the established model, an efficient method is proposed for the clocking effect optimization and the aerodynamic load-reduction of a 2-stage cascade. Results show that the maximum optimization ranges for the variation altitude of unsteady aerodynamic lift and torque are 44.06% and 30.51%, respectively, which verifies the efficiency and feasibility of the proposed theories and methods.

Aerodynamic interference and unsteady loads for a hovering intermeshing rotor

Synchropters are increasingly applied for precision work in placing suspended loads due to their unique flying characteristics. However, the special intermeshing rotor structural helicopter easily introduces rotor-and-rotor interference, leading to unsteady aerodynamic loads on the rotor blades in mission flight. Hence, we use the unsteady vortex lattice method to validate and analyze the aerodynamic characteristics of the intermeshing rotor in hover. In this method, a circulation suppression technique on the blade root is introduced to enhance the stability of the rotor wake in the steady-state hover. Results show that the meniscus truncated regions on the intermeshing rotor disks formed by the blade–vortex impact are nearly unchanged to collective pitches. The low-order frequency harmonic components and phase lag phenomenon universally found in dual rotor loads and additional oscillating roll moment become inherent characteristics of the intermeshing rotor in hover, especially for kΩ caused by interference of rotor downwash flow and 2 kΩ produced by the blade–vortex interaction at 10° and 190° azimuth. Finally, the left/right rotor loads exist harmonic components of 1, 2, and 3 kΩ. In contrast, the total thrust of the intermeshing rotor system eliminates the odd-order harmonic components but aggravates the even-order harmonic components.

Unsteady aerodynamic characteristics on trains exposed to strong wind and rain environment

Crosswind associated with rainfall is a common weather condition, which threatens the operational safety of trains. This paper focuses on an investigation of the effect of crosswind associated with rainfall on train aerodynamics. The methodologies for reproducing the turbulent wind speed and instantaneous rainfall intensity are first described, and the calculation method of unsteady aerodynamic forces of trains operating in a wind-rain environment is set up using the quasi-steady method and weighting function method. Then the CFD technology is used to obtain the aerodynamic load coefficients of a train exposed to a wind-rain environment, and the computational model is verified with the experimental results. Finally, the unsteady aerodynamic load time histories, as well as the corresponding statistical characteristics of the train are investigated. The results demonstrate that the aerodynamic load coefficient is a function of yaw angle, rainfall intensity and wind velocity relative to the train under wind-rain conditions. The aerodynamic loads approximately obey normal distribution both for the quasi-steady method and weighting function method. The mean values of aerodynamic loads obtained by the two methods are almost the same, whereas the standard deviations computed by the weighting function method are smaller than those computed by the quasi-steady method. The dimensionless standard deviations of aerodynamic loads increase with the rainfall intensity, and are approximately linearly related to the rainfall intensity. The wind velocity relative to the train also has an impact on the dimensionless standard deviations of aerodynamic loads, and the impact becomes more obvious when the rainfall intensity increases. The dimensionless standard deviations of the aerodynamic loads can be expressed as quadratic polynomial functions of yaw angle, rainfall intensity and wind velocity relative to the train.

Simulation and experimental investigation on vibration of a radial turbine wheel using a two-way FSI approach

When turbine blades of a radial turbocharger are subjected to an unsteady aerodynamic load excitation force, high cycle fatigue of the turbine blades will occur when the excitation force reaches a certain level. The fatigue of the radial turbine wheel is affected by both static and dynamic stresses, and high cycle fatigue occurs when the dynamic stress reaches a certain amplitude. In this study, a two-way fluid–structure interaction (FSI) analysis method was used to predict the dynamic excitation force and dynamic response of the turbine wheel, which can precisely predict the forced vibration of the turbine wheel under the condition of rotor–stator interaction. A resonance intersection point was excited by the stator (turbine housing vortex tongue) of the radial turbocharger as the operating boundary condition, and the aerodynamic excitation caused by the rotor–stator interaction and the vibration amplitude of the turbine blade was predicted and analysed. A turbine blade dynamic measurement system (tip timing) was used to measure the dynamic deformation of turbine blades for turbochargers in real time. The simulation and measurement results showed that the errors of the predicted vibration displacements and measured mistuning blades were within the acceptable range, and the two-way FSI analysis method can precisely predict the forced vibration of the model.

Finite wing effects on the energy harvesting from stall-induced oscillations

The modeling of aeroelastic harvesters usually employs methods for two-dimensional aerodynamics. Such convenient practice reflects the lack in the literature of efficient tools with low computational cost to assess unsteady and nonlinear aerodynamics loads accounting for three-dimensional wing effects. In this sense, the present work aims to fulfill this gap by developing a nonlinear unsteady lifting line to investigate finite wing effects on the power generation from stall-induced oscillations. The aerodynamic model links the Beddoes–Leishman dynamic stall method to a linear unsteady lifting line. The optimization of energy harvesters from stall-induced pitching oscillations is revisited considering the three-dimensional aerodynamic model. Results reveal that the three-dimensional harvester’s dynamic behavior may differ from the two-dimensional case, and the harvested power reduction is observed.

Nonlinear State Dependent Riccati Equation Controller for 3-DOF Airfoil with Cubic Structural Nonlinearity

In this paper, Limit Cycle Oscillations (LCOs) of a Two-Dimensional (2-D) airfoil with cubic structural nonlinearity in the plunge Degree of Freedom (DOF) are investigated. The aerodynamic loads are modelled using the unsteady Theodorsen’s theory. Wagner function and Jones’ approximation are used to transform the unsteady aerodynamic loads from frequency domain into time domain. The aeroelastic differential equations are solved using the routine ODE45 in MATLAB to get the system response. Both subcritical and supercritical LCOs are observed in the 3-DOF airfoil with structural nonlinearity in the plunge DOF. Such LCOs are undesirable phenomena and should be suppressed within the flight envelope. A nonlinear state feedback controller is designed to minimize the amplitude of LCOs presented in the considered nonlinear aeroelastic system. The State-Dependent Riccati Equation (SDRE) approach in combination with Kalman filter technique is used to design a controller for the 2-D airfoil with trailing edge control surface (flap). The forces and moments produced by this flap’s action are used to stabilize the system and suppress the existence of LCOs. The efficiency of the proposed nonlinear controller by the SDRE and Kalman filter in suppressing the existence of subcritical and supercritical LCOs are verified by the numerical simulation results.