Unsteady Aerodynamic Loads Research Articles

Development and application of a dynamic stall model for rotating wind turbine blades

In unsteady conditions of wind turbines, both the dynamic stall phenomenon and the three-dimensional (3D) rotational effect affect the rotor aerodynamics. The dynamic stall mechanism for rotating wind turbine blades is first investigated. Through the comparison of the aerodynamic data between the rotating blade and the two-dimensional (2D) airfoil, the normal force slope in the attached flow and the separation point expression in the separated flow are modified in the Beddoes-Leishman (B-L) dynamic stall model for rotating NREL wind turbine blades. The modified model is validated by the comparison between the calculation results and the experimental results of the lift and drag coefficients at different radial positions. Both the hysteresis loop shapes and the calculation values are closer to the experiment than the 2D dynamic stall model. The present dynamic stall model is then coupled to a free vortex wake model. The coupled model is used to calculate the unsteady blade aerodynamic loads and the low speed shaft torque of the NREL wind turbine in a yawed condition. The accuracy is greatly improved by the corrections presented in the paper.

Time-accurate aeroelastic simulations of a wind turbine in yaw and shear using a coupled CFD-CSD method

In the present study, aeroelastic simulations of horizontal-axis wind turbine rotor blades were conducted using a coupled CFD-CSD method. The unsteady blade aerodynamic loads and the dynamic blade response due to yaw misalignment and non-uniform sheared wind were investigated. For this purpose, a CFD code solving the RANS equations on unstructured meshes and a FEM-based CSD beam solver were used. The coupling of the CFD and CSD solvers was made by exchanging the data between the two solvers in a loosely coupled manner. The present coupled CFD-CSD method was applied to the NREL 5MW reference wind turbine rotor, and the results were compared with those of CFD-alone rigid blade calculations. It was found that aeroelastic blade deformation leads to a significant reduction of blade aerodynamic loads, and alters the unsteady load behaviours, mainly due to the torsional deformation. The reduction of blade aerodynamic loads is particularly significant at the advancing rotor blade side for yawed flow conditions, and at the upper half of rotor disk where wind velocity is higher due to wind shear.

Active control of aeroelastic oscillations of a cantilever structure using piezoelectric strips

Recently, active control of aeroelastic oscillations and the use of piezoelectric materials in vibration analysis and control of structures have been the subjects of many researches in air vehicle design. The present paper deals with the use of bonded piezoelectric sensors and actuators in control of aeroelastic oscillations of a cantilever plate under the effects of unsteady subsonic aerodynamic loading. The aerodynamic loading is calculated using a numerical panel method. The structural model of the plate undergoing small transverse oscillations is modeled using finite element formulation. The aerodynamic and structural models are coupled through an interactive computer model to transfer the data simultaneously and an active feedback control is applied to suppress the oscillations. A systematic method is also presented to obtain the gains of the feedback controller. The numerical results show that the controller can effectively reduce the amplitude of the oscillations in small amount of time and with small gains, hence lower cost.

Solar Array Mounting Effects on Flutter Characteristics of Solar-Powered UAV

Solar powered UAV has the characteristics of high aspect ratio, low structural surface density, high structural flexibility and low flutter speed. Different solar array mountings will affect the flutter characteristics of the structure. The mechanical properties of solar arrays packaged and unpackaged are measured in this paper and the solar powered UAV structural finite element model based on Patran/Nastran was also established in the paper. Two solar array mounting ways are researched: embedded solar arrays and patching solar arrays. To investigate the flutter characteristics under the two solar array mounting ways, the Doublet lattice method (DLM) aerodynamic model is used to model the unsteady aerodynamic loads. Finally, flutter speed of the structure was determined by using the P-K method and the analysis result indicate that patching solar arrays is more conductive to improve the flutter characteristics of the structure.

Predictions of unsteady HAWT aerodynamics in yawing and pitching using the free vortex method

To predict the unsteady aerodynamic loads of horizontal-axis wind turbines (HAWTs) during operations under yawing and pitching conditions, an unsteady numerical simulation method is proposed. This method includes a nonlinear lifting line method to compute the aerodynamic loads on the blades and a time-accurate free-vortex method to simulate the wake. To improve the convergence property in the nonlinear lifting line method, an iterative algorithm based on the Newton–Raphson method is developed. To increase the computational efficiency and the accuracy of the calculation, a new wake vortex model consisting of the vortex core model, the vortex sheet model and the tip vortex model is used. Wind turbines with different diameters, such as NREL Phase VI, the TU Delft model turbine and the Tjæreborg wind turbine, are used to validate the method for rotors operating at given yaw and/or pitch angles and during yawing and/or pitching processes at different wind speeds. The results, including the blade loads, the rotor torque and the locations of the tip vortex cores in the wake, agree well with the measured data and the computed data. It is shown that the proposed method can be used for predictions of unsteady aerodynamic loads and rotor wakes in the operational processes of blade pitching and/or rotor yawing.

Unsteady Aerodynamic Loads on a High-Agility Aircraft due to Wake Vortex Encounter

The presented investigation focuses on the determination of unsteady aerodynamic loads for different kinds of wake vortex encounters. The wake-generating aircraft is a delta–canard configuration, whereas for the penetration, just a delta wing is considered. Based on extensive experimental and numerical investigations of the wake vortex system of a preceding aircraft, the wake-induced angle of attack on an encountering aircraft is determined. Therefore, the induced flowfield of the wake-generating aircraft is transformed into the coordinate system of the penetrating aircraft. Because the unsteadiness results on the one hand from the velocity fluctuations inside the wake, and on the other hand from the relative movement of the two aircraft, the wake problem is split into a discrete and a continuous wake problem. Both problems lead to an unsteady distribution of the angle of attack, which is variable in the chord and spanwise directions. The resulting lift and pitching moment distribution is calculated by an alternative approach to the unsteady lifting surface method. For the discrete wake problem, the resulting loads depend on the heading and bank angle of the penetrating aircraft relative to the vortex axes. In general, negative lift, rolling, and pitching moments can be observed. Their magnitude varies with the encounter maneuver. The continuous wake problem refers to the unsteady loads due to velocity fluctuations inside the wake on an aircraft following the wake-generating aircraft. Thereby, high-frequency forces and moments act upon the following aircraft.

Predicting wind turbine blade loads and aeroelastic response using a coupled CFD–CSD method

The aeroelastic response and the airloads of horizontal-axis wind turbine rotor blades were numerically investigated using a coupled CFD–CSD method. The blade aerodynamic loads were obtained from a Navier–Stokes CFD flow solver based on unstructured meshes. The blade elastic deformation was calculated using a FEM-based CSD solver which employs a nonlinear coupled flap-lag-torsion beam theory. The coupling of the CFD and CSD solvers was accomplished in a loosely coupled manner by exchanging the information between the two solvers at infrequent intervals. At first, the present coupled CFD–CSD method was applied to the NREL 5MW reference wind turbine rotor under steady axial flow conditions, and the mean rotor loads and the static blade deformation were compared with other predicted results. Then, the unsteady blade aerodynamic loads and the dynamic blade response due to rotor shaft tilt and tower interference were investigated, along with the influence of the gravitational force. It was found that due to the aeroelastic blade deformation, the blade aerodynamic loads are significantly reduced, and the unsteady dynamic load behaviors are also changed, particularly by the torsional deformation. From the observation of the tower interference, it was also found that the aerodynamic loads are abruptly reduced as the blades pass by the tower, resulting in oscillatory blade deformation and vibratory loads, particularly in the flapwise direction.

Reduced-Order Aeroelastic Models for Dynamics of Maneuvering Flexible Aircraft

This paper investigates the model reduction, using balanced realizations, of the unsteady aerodynamics of maneuvering flexible aircraft. The aeroelastic response of the vehicle, which may be subject to large wing deformations at trimmed flight, is captured by coupling a displacement-based flexible-body dynamics formulation with an aerodynamic model based on the unsteady vortex lattice method. Consistent linearization of the aeroelastic problem allows the projection of the structural degrees of freedom on a few vibration modes of the unconstrained vehicle but preserves all couplings between the rigid and elastic motions and permits the vehicle flight dynamics to have arbitrarily large angular velocities. The high-order aerodynamic system, which defines the mapping between the small number of generalized coordinates and unsteady aerodynamic loads, is then reduced using the balanced truncation method. Numerical studies on a representative high-altitude, long-endurance aircraft show a very substantial reduction in model size, by up to three orders of magnitude, that leads to model orders (and computational cost) similar to those in conventional frequency-based methods but with higher modeling fidelity to compute maneuver and gust loads. Closed-loop results for a cantilever wing finally demonstrate the application of this approach in the synthesis of a robust stability augmentation system.

Forced responses on a radial turbine with nozzle guide vanes

Radial turbines with nozzle guide vanes are widely used in various size turbochargers. However, due to the interferences with guide vanes, the blades of impellers are exposed to intense unsteady aerodynamic excitations, which cause blade vibrations and lead to high cycle failures (HCF). Moreover, the harmonic resonance in some frequency regions are unavoidable due to the wide operation conditions. Aiming to achieve a detail insight into vibration characteristics of radial flow turbine, a numerical method based on fluid structure interaction (FSI) is presented. Firstly, the unsteady aerodynamic loads are determined by computational fluid dynamics (CFD). And the fluctuating pressures are transformed from time domain to frequency domain by fast Fourier-transform (FFT). Then, the entire rotor model is adopted to analyze frequencies and mode shapes considering mistuning in finite element (FE) method. Meanwhile, harmonic analyses, applying the pressure fluctuation from CFD, are conducted to investigate the impeller vibration behavior and blade forced response in frequency domain. The prediction of the vibration dynamic stress shows acceptable agreement to the blade actual damage in consistent tendency.

Crosswind stability analysis of a high-speed train based on fuzzy random reliability

The conventional crosswind stability analysis of high-speed trains is based on a deterministic approach with the final output being a characteristic wind curve (CWC). The CWC only provides the dividing line between the safe state and failure state of vehicles, thus it cannot be used to evaluate the overturning probability of vehicles subjected to strong winds. To overcome this shortcoming of the conventional CWC, a fuzzy stochastic approach is proposed that can make an effective assessment of the operational safety of high-speed trains exposed to stochastic winds. According to this methodology, the uncertain parameters existing in the system such as stochastic winds and aerodynamic coefficients are modelled as basic random variables, and the failure of the structure is considered as a fuzzy random event. An algorithm for computing the unsteady aerodynamic loads of high-speed trains exposed to stochastic winds is created and then the aerodynamic loads are applied to a dynamic model of the vehicle system in order to investigate the dynamic response. Importance sampling is used to conduct an analysis of the crosswind stability of high-speed trains based on fuzzy random reliability theory. This finally leads to the substitution of the conventional CWC by probabilistic characteristic wind curves (PCWCs). The conventional CWC is shown to be over-conservative, while the PCWCs can provide more significant reference for the safe operation of high-speed trains.

Numerical Simulation of Unsteady Aerodynamic Loads over an Aircraft

The unsteady aerodynamic loads are the basic of the aeroelastic. This paper focuses on the computation of the unsteady aerodynamic loads for forced periodic motions under different Mach numbers. The flow is modeled using the Euler equations and an unsteady time-domain solver is used for the computation of aerodynamic loads for forced periodic motions. The Euler equations are discretized on curvilinear multi-block body conforming girds using a cell-centred finite volume method. The implicit dual-time method proposed by Jameson is used for time-accurate calculations. Rigid body motions were treated by moving the mesh rigidly in response to the applied sinusoidal motion. For an aircraft model, a validation of the unsteady aerodynamics loads is first considered. Furthermore, a study for understanding the influence of different Mach number was conducted. A reverse of the trend of hysteretic loops can be observed with the increasing of the Mach number.

Numerical Study of Flutter of a Two-Dimensional Aeroelastic System

Numerical Study of Flutter of a Two-Dimensional Aeroelastic System: This paper deals with the problem of the aeroelastic stability of a typical aerofoil section with two degrees of freedom induced by the unsteady aerodynamic loads. A method is presented to model the unsteady lift and pitching moment acting on a two-dimensional typical aerofoil section, operating under attached flow conditions in an incompressible flow. Starting from suitable generalisations and approximations to aerodynamic indicial functions, the unsteady loads due to an arbitrary forcing are represented in a state-space form. From the resulting equations of motion, the flutter speed is computed through stability analysis of a linear state-space system.

Dynamic characteristics of lag vibration of a wind turbine blade

Lagwise dynamic characteristics of a wind turbine blade subjected to unsteady aerodynamic loads are studied in this paper. The partial differential equations governing the coupled longitudinal-transverse vibration of the blade with large bending deflection are obtained by applying Hamilton's principle. The modal problem of the coupled vibration is handled by using the method of numerical integration of Green's function. Influences of the rotating speed, the pitch angle, the setting angle, and the aerodynamic loads on natural frequencies are discussed. Results show that: (1) Lagwise natural frequencies ascend with the increase of rotating speed; effects of the rotating speed on low-frequencies are dramatic while these effects on high-frequencies become less. (2) Influences of the pitch angle on natural frequencies are little; in the range of the normal rotating speed, the first frequency ascends with the increase of the absolute value of the pitch angle, while it is contrary to the second and third frequencies. (3) Effects of the setting angle on natural frequencies depend on the rotating speed; influences are not significant at low speed, while they are dramatic on the first frequency at high speed. (4) Effects of the aerodynamic loads on natural frequencies are very little; frequencies derived from the model considering aerodynamic loads are smaller than those from the model neglecting aerodynamic loads; relative errors of the results corresponding to two models ascend with the increase of the absolute value of the setting angle.

Superposability of unsteady aerodynamic loads on bridge deck sections

The 2-dimensional unsteady aerodynamic forces, in the context of both a thin airfoil where theory of potential flow is always applicable and a bluff bridge-deck section where separated flow is typically induced, are investigated from a point of view of whether or not they conform to the principle of linear superposition in situations of various structural motions and wind gusts. It is shown that some basic preconditions that lead to the linear superposability of the unsteady aerodynamic forces in cases of thin airfoil sections are no longer valid for a bluff section. Theoretical models of bridge aerodynamics such as the one related to flutter-buffeting analysis and those concerning aerodynamic admittance (AA) functions, however, necessitate implicitly this superposability. The contradiction revealed in this work may throw light on the perplexing problem of AA functions pertaining to the description of buffeting loads of bridge decks. Some existing theoretical AA models derived from flutter derivatives according to interrelations valid only for thin airfoil theories, which have been employed rather extensively in bridge aerodynamics, are demonstrated to be illogical. Finally, with full understanding of the preconditions of the applicability of linear superposability of the unsteady aerodynamic forces, suggestions in regard to experiment-based AA functions are presented.

Nonlinear analysis and enhancement of wing-based piezoaeroelastic energy harvesters

We investigate the level of harvested power from aeroelastic vibrations for an elastically mounted wing supported by nonlinear springs. The energy is harvested by attaching a piezoelectric transducer to the plunge degree of freedom. The considered wing has a low-aspect ratio and hence three dimensional aerodynamic effects cannot be neglected. To this end, the three dimensional unsteady vortex lattice method for the prediction of the unsteady aerodynamic loads is developed. A strong coupling scheme that is based on Hamming's fourth-order predictor–corrector method and accounts for the interaction between the aerodynamic loads and the motion of the wing is employed. The effects of the electrical load resistance, nonlinear torsional spring and eccentricity between the elastic axis and the gravity axis on the level of the harvested power, pitch and plunge amplitudes are investigated for a range of operating wind speeds. The results show that there is a specific wind speed beyond which the pitch motion does not pick any further energy from the incident flow. As such, the displacement in the plunge direction grows significantly and causes enhanced energy harvesting. The results also show that the nonlinear torsional spring plays an important role in enhancing the level of the harvested power. Furthermore, the harvested power can be increased by an order of magnitude by properly choosing the eccentricity and the load resistance. This analysis is helpful in designing piezoaeroelastic energy harvesters that can operate optimally at specific wind speeds.

Aeroelastic Control of a Wind Turbine Blade Using Microtabs Based on UA97W300-10 Airfoil

The unsteady flow over a rotating wind turbine blade is described by the Beddoes-Leishman dynamic stall model. Based on the asymmetric airfoil UA97W300-10, a wind turbine blade section with unsteady aerodynamic loads is modeled as an aeroelastic system for this vibration suppression study. Aeroelastic stability of the system is analyzed by open-loop tests to identify the flutter speed. With consideration of wind turbine operations, control strategies for flutter suppression are made separately in each operation region and implemented by a designed Adaptive Controller using microtab devices, which are positioned at the trailing edge of the airfoil with deployment at the maximum height of 5% of chord length. The control effects of the Adaptive Control and microtabs are investigated by closed-loop tests. The stability of the Adaptive Controller is proved using a new Adaptive Stability Theorem, which is also illustrated by examples.

Nonlinear Aeroelastic Formulation and Postflutter Analysis of Flexible High-Aspect-Ratio Wings

The nonlinear aeroelastic modeling and the post-flutter behavior of high-altitude long-endurance wings are discussed. A parametric structural model of wings based on an exact kinematic approach is formulated and coupled with an incompressible unsteady aerodynamic model that is obtained via an indicial formulation accounting for viscous effects, including dynamic stall and flow separation. To this end, a modified Beddoes-Leishman model is employed, and the equations of motion, together with the equations governing the aerodynamic states, are obtained via a total Lagrangian formulation. The critical and post-critical dynamic aeroelastic response is evaluated, and the limit cycles occurring in the post-flutter condition past the Hopf bifurcation are studied. Together, with comparisons from the available data of an experimental wing model with tip store, the effects of the unsteady loads and dynamic stall are evaluated and compared with predictions obtained from a model using a classical quasi-steady aerodynamic formulation. Aeroelastic simulations are concurrently performed within a finite element solution platform. Space and time integrations are conducted using a numerical scheme that directly discretizes the partial differential equations, which are associated with the equations of motion of the flexible wing, and the ordinary differential equations, which are associated with the added lag-state formulation pertinent to the unsteady aerodynamic loads, in a hybrid solution form. The aim is the study of the aeroelastic behavior of these highly nonlinear wings for an improved understanding of the nonlinear phenomena occurring particularly in the neighborhood of the flutter boundary and in the post-critical regime when the unsteady aerodynamic effects and dynamic stall contribute more significantly to the wing dynamic behavior.

Linear-Frequency-Domain Predictions of Dynamic-Response Data for Viscous Transonic Flows

Determining the flutter boundaries for full aircraft configurations by time-accurately solving the Reynolds-averaged Navier–Stokes equations is prohibitive with respect to computational expense, as the unsteady aerodynamic loading must be predicted for a wide range of flight conditions, frequencies, and structural mode shapes. Nonetheless, there is an increasing demand to accurately predict flutter boundaries in the viscous transonic regime—a demand, which, until recently, could only be satisfied by high-fidelity Reynolds-averaged Navier–Stokes methods. Brought to application readiness over the last years, time-linearized/small-disturbance methods, however, have been shown to satisfy this demand as well. They retain the Reynolds-averaged Navier–Stokes method’s fidelity to a high degree, at a substantially reduced computational expense. Such a method is presented here on the basis of the TAU–Reynolds-averaged Navier–Stokes method. Denoted as the TAU linear-frequency-domain method, it is validated for both a standard transonic airfoil and a high-aspect-ratio-wing dynamic test case using rigid pitch modes. The response data obtained from the linear frequency domain are in good agreement with the experiment for a two-dimensional case. For the three-dimensional case, there are larger differences. More important, the linear-frequency-domain method is in excellent agreement to time-accurate Reynolds-averaged Navier–Stokes simulations. Depending on the linear-frequency-domain-employed-solution scheme, reductions in computational costs well beyond an order of magnitude are obtained. In addition, the limits of the so-called frozen-eddy-viscosity approach are established.

Simulating unsteady aerodynamics of helicopter rotor with panel/viscous vortex particle method

The unsteady aerodynamics of a helicopter rotor has been a central issue in the field of rotorcraft aerodynamics. This is because the rotor generates a complex time-dependent pattern of vorticity in its wake, which has significant effects on its performance, stability, loading, and vibration. Conventional free-wake methods used in most of the current comprehensive rotorcraft analysis codes are limited by the potential flow assumption and empirical formulations, such as vortex core size. Based on a numerical solution of the unsteady fluid-dynamic equations governing transportation and diffusion of vorticity, a viscous vortex particle method is coupled with an unsteady panel method to predict the unsteady aerodynamics of helicopter rotor blades with fewer empirical formulations in viscous flow. The coupled method is implemented through the trailing-edge Kutta condition, Neumann boundary condition, and by converting shed-wake doublet panels to wake vorticity. A TreeCode method is also employed to reduce computational cost for practical analysis. Helicopter rotors including the scaled model, Caradonna–Tung, and AH-1G rotors are simulated in hover and forward flight to validate the accuracy of the present approach. The unsteady dynamics of the rotor wake, such as wake contraction, tip-vortex pairing, and vortex roll-up, are well simulated. The predicted inflow distribution is more accurate than that in the conventional free-wake method, and the predicted pressure coefficient distribution and unsteady aerodynamic loads of rotor blades agree well with measured data and computational fluid-dynamics results.

Structural and mechanism design of an active trailing-edge flap blade

A conventional rotor control system restricted at 1/rev frequency component is unable to vary the hub vibratory loads and the aeroacoustic noise, which exist in high frequency components. Various active rotor control methodologies have been examined in the literature to alleviate the problem of excessive hub vibratory loads and noise. The active control device manipulates the blade pitch angle with arbitrary higher harmonic frequencies individually. In this paper, an active trailing-edge flap blade, which is one of the active control methods, is developed to reduce vibratory loads and noise of the rotor through modification of unsteady aerodynamic loads. Piezoelectric actuators installed inside the blade manipulate the motion of the trailing edge flap. The proposed blade rotates at higher speed and additional structures are included to support the actuators and the flap. This improves the design, as the blade is able to withstand increased centrifugal force. The cross-section of the active blade is designed first. A stress/strain recovery analysis is then conducted to verify its structural integrity. A one-dimensional beam analysis is also carried out to assist with the construction of the fan diagram. To select the actuator and design the flap actuation region, the flap hinge moment is estimated via a CFD analysis. To obtain the desired flap deflection of ±4°, three actuators are required. The design of the flap actuation region is validated using a test bed with a skin hinge. However, because the skin hinge induces additional flap hinge moment, it does not provide sufficient deflection angle. Therefore, the flap hinge is replaced by a pin-type hinge, and the results are evaluated.