Unsteady Aerodynamic Loads Research Articles

Comparison of unsteady aerodynamics on wind turbine blades using methods of ranging fidelity

In this paper the unsteady aerodynamic loads for aeroelastic bend-twist coupling predicted by methods of various fidelity are compared. These are: a fast and simplistic strip theory model based on the analytical theories by Greenberg and Loewy, an Euler and a RANS unsteady CFD simulation. The test object is the DTU 10MW reference wind turbine. The comparison uses transfer functions with bending deflections and blade torsion as an input, aerodynamic thrust and pitching moment as an output. A structural feedback is not considered. The RANS simulation has the highest fidelity and is taken as a baseline for all other methods. The temporal discretization and simulation time of the CFD have to be chosen carefully as they influence the transfer behavior. As long as the flow separation is small, the Euler simulation is very accurate. The frequency response by the strip theory has a good agreement over a broad range of flow conditions in attached flow when a distributed torsion or a flap-wise deflection is applied. Severe deviations are found for an edge-wise deformation and in-plane forces.

Modified Harmonic Balance Method for Nonlinear Aeroelastic Analysis of Two Degree-of-Freedom Airfoils in Supersonic Flow

In this paper, a new modified harmonic balance method is presented for the nonlinear aeroelastic analysis of two degree-of-freedom airfoils. Using this method, the nonlinear problem is first translated into a minimization problem, and the Particle Swarm Optimization which has high calculation efficiency is adopted to solve the problem. The proposed method is used to solve the nonlinear aeroelastic behavior of supersonic airfoil, with the unsteady aerodynamic load evaluated by the piston theory. Three examples of nonlinear aeroelasticity with significantly different coefficients are prepared, in which the frequencies and amplitudes of the limit cycles are obtained. The results show that the present current method is computationally more efficient.

Numerical Simulation of Plunging Wing Section at High Angles of Attack

In the near-stall regime, the shedding of coherent structures can result in large unsteady aerodynamic loads. Under such conditions, high-aspect-ratio wings will experience some degree of structural motion. Simulations and experiments for a chord-based Reynolds number of are carried out for a wing section with an X-56A airfoil to investigate the effect of a harmonic heaving/plunging motion on the unsteady aerodynamics. The reduced frequency of the structural motion is , and the amplitude is 3.2–9.6% based on chord length. For a plunging motion at a 10 deg mean angle of attack, the unsteady lift is in good agreement with the Theodorsen theory. As the mean angle of attack is increased up to 14 deg, the flow begins to separate intermittently from the suction side of the wing. The onset of flow separation and the shedding of the resultant stall vortex depend on the frequency and amplitude of the structural motion. Steady spanwise disturbances that are introduced at the leading edge are found to strengthen the stall vortex. For a 16 deg angle of attack, the wing section is fully stalled. However, when subjected to a low-amplitude plunging motion, the flow intermittently reattaches and the mean lift is increased.

Nonlinear aeroelastic analysis of high-aspect-ratio wings using indicial aerodynamics

A new approach for calculating the unsteady aerodynamic loads based upon the indicial functions concept in combination with a fully third-order nonlinear structural model has been developed to analyze the aeroelastic behavior of high-aspect-ratio wings over the entire range of subsonic flow. The resulting aeroelastic equations including all structural geometric nonlinearities associated with large deformations and mass distributions, along with nonlinear terms due to mass imbalance at wing’s cross section, are then rewritten in the state-space form, introducing an efficient and appropriate approach to use in both eigenvalue and time response analysis. To validate the developed aeroelastic equations, the linear and nonlinear aeroelastic behaviors of a specified wing are compared with those presented for an incompressible aerodynamic case. Quantitative and qualitative agreement between the present results and available ones confirms the unsteady indicial aerodynamics, nonlinear structural modeling, and, consequently, the developed nonlinear aeroelastic model. By changing the wing model and applying the unsteady compressible aerodynamic loads, the nonlinear aeroelastic behavior of Goland wing is then investigated, including the flutter boundary, limit cycle oscillations, pre-flutter, flutter, and post-flutter time responses, phase plane diagrams, and also the effect of flight conditions such as altitude and air speed on the aeroelastic behavior. The results represent the necessity of applying appropriate Mach-dependent aerodynamic loads to provide reasonable description of the aeroelastic analysis in the compressible flight speed regime.

Numerical studies on two turbulence models and a laminar model for aerodynamics of a vertical-axis wind turbine

The purpose of this study is the analysis of flow around a one-bladed Darrieus-type wind turbine using computational fluid dynamics (CFD). The rotor geometry consists of a NACA 0015 airfoil with chord length of 0.15 m. Numerical simulations are performed using ANSYS Fluent, employing laminar model and two turbulence models: SST k-ω and RNG k-e. The obtained numerical results of unsteady aerodynamic blade loads are compared with available experimental results from literature. Computed aerodynamic characteristics of normal and tangential forces comply with the experiment results. The RNG k-e turbulence model has a good accuracy in determining aerodynamic blade loads for the upwind and downwind parts of the rotor. The laminar model and the SST k-ω turbulence model slightly overestimate the tangential aerodynamic blade loads at the downwind part of the rotor. An averaged wind turbine velocity profile computed at one rotor radius downstream of the rotor has a Gaussian shape. The steady-state airfoil characteristics are computed for the Reynolds number comparable to the Reynolds number of a moving blade employing the SST k-ω and RNG k-e turbulence models and using the same computational grid as for unsteady simulations of the rotor.

Assessing the IEC simplified fatigue load equations for small wind turbine blades: How simple is too simple?

Abstract It is well known that wind turbine blades are fatigue critical, with much literature and methodologies available for assessing fatigue loading of large wind turbine blades. Little research effort has been directed at assessing the fatigue life of small wind turbines which operate at higher rotational speeds and are subject to highly unsteady aerodynamic loading. In this paper the simplified load model proposed in IEC 61400.2 is used to determine the fatigue life of a small 5 kW wind turbine blade. This estimated life is compared to that determined from both measured operational data and aeroelastic simulations. Fatigue life was estimated by the standard at 0.09 years, compared to 9.18 years from field measurements and 3.26 years found via aeroelastic simulations. All methods fell below the 20 year design life, with the standard over-conservative by a factor of 102 and 36 for measurements and simulations respectively. To the best of the authors' knowledge these three fatigue methods specified in the standard have not been quantitatively compared and assessed for small wind turbines. Results are of importance to small wind turbine developers as they seek best practice for determining blade fatigue life. Shortcomings of the IEC methodology are detailed and discussed.

The unsteady aerodynamics of floating wind turbine under platform pitch motion

The aerodynamic performance of floating platform wind turbines is much more complex than fixed-base wind turbines because of the flexibility of the floating platform. Due to the extra six degrees-of-freedom of the floating platform, the inflow of the wind turbine rotors is highly influenced by the motions of the floating platform. It is therefore of interest to study the unsteady aerodynamics of the wind turbine rotors involved with the interaction of the floating platform induced motions. In the present work, a lifting surface method with a free wake model is developed for analysis of the unsteady aerodynamics of wind turbines. The aerodynamic performance of the NREL 5 MW floating wind turbine under the prescribed floating platform pitch motion is studied. The unsteady aerodynamic loads, the transient of wind turbine states, and the instability of the wind turbine wakes are discussed in detail.

Unsteady loads for coaxial rotors in forward flight computed using a vortex particle method

ABSTRACTRecent advances in coaxial rotor design have shown benefits of this configuration. Nevertheless, issues related to rotor-head drag, aerodynamic performance, wake interference, and vibration should also be considered. Simulating the unsteady aerodynamic loads for a coaxial rotor, including the aerodynamic interactions between rotors and rotor blades, is an essential part of analysing their vibration characteristics. In this article, an unsteady aerodynamic analysis based on a vortex particle method is presented. In this method, a reversed-flow model for the retreating side of the coaxial rotor is proposed based on an unsteady panel technique. To account for reversed flow, shedding a vortex from the leading edge is used rather than from the trailing edge. Moreover, vortex-blade aerodynamic interactions are accounted for. The model considers the unsteady pressure term induced on a blade by tip vortices of other blades, and thus accounts for the aerodynamic interaction between the rotors and its contribution to the unsteady airloads. Coupling the reversed-flow model and the vortex-blade aerodynamic interaction model with the viscous vortex-particle method is used to simulate the complex wake of the coaxial rotor. The unsteady aerodynamic loads on the X2 coaxial rotor are simulated in forward flight, and compared with the results of PRASADUM (Parallelized Rotorcraft Analysis for Simulation And Design, developed at the University of Maryland) and CFD/CSD computations with the OVERFLOW and the CREATE-AV Helios tools. The results of the present method agree with the results of the CFD/CSD method, and compare to it better than the PRASADUM solutions. Furthermore, the influence of the aerodynamic interaction between the coaxial rotors on the unsteady airloads, frequency, wake structure, induced flow, and force distributions are analysed. Additionally, the results are also compared against computations for a single-rotor case, simulated at similar conditions as the coaxial rotor. It is shown that the effect of tip vortex interaction plays a significant role in unsteady airloads of coaxial rotors at low speeds, while the rotor blade passing effect is obviously strengthened at high-speed.

Three-dimensional aero-thermo-elasticity analysis of functionally graded cylindrical shell panels

In the present paper, the aero-thermo-elastic behavior of a finite (three-dimensional) cylindrical curved panel geometry made from functionally graded material under high supersonic airflow is investigated. A generalized differential quadrature formulation is adopted while a steady-state through-the-thickness thermal field is also assumed. The geometry curvature and structural nonlinearity effects are included based on von Karman–Donnell strain–displacement relations. The nonlinear piston theory of third order is utilized in order to predict the unsteady aerodynamics loads induced from surrounding supersonic air stream. The functionally graded material is considered with temperature-dependent properties distributed in the thickness according to a power law function. Derived from the equilibrium equations, the aero-thermo-elastic governing equations are reduced to number of ordinary differential equations through using of the generalized differential quadrature method where the structure response is derived using fourth-order Runge–Kutta technique. The contribution of some parameters including flow Mach number, flow dynamic pressure, thickness temperature gradient, and functionally graded material volume fraction index on the flutter response as well as route-to-chaos behavior are reviewed. The calculated results are compared with those available in the literature wherever available and the accuracy and quality of the adopted generalized differential quadrature formulation in analyzing the aero-thermo-elastic behavior of three-dimensional functionally graded curved panels is shown. It reveals that using a three-dimensional approach, if any of Mach number and panel’s upper surface temperature is increased, the route-to-chaos behavior is reached through quasi-periodic motions.

Dynamic assessment of nonlinear typical section aeroviscoelastic systems using fractional derivative-based viscoelastic model

Nonlinear aeroelastic systems are prone to the appearance of limit cycle oscillations, bifurcations, and chaos. Such problems are of increasing concern in aircraft design since there is the need to control nonlinear instabilities and improve safety margins, at the same time as aircraft are subjected to increasingly critical operational conditions. On the other hand, in spite of the fact that viscoelastic materials have already been successfully used for the attenuation of undesired vibrations in several types of mechanical systems, a small number of research works have addressed the feasibility of exploring the viscoelastic effect to improve the behavior of nonlinear aeroelastic systems. In this context, the objective of this work is to assess the influence of viscoelastic materials on the aeroelastic features of a three-degrees-of-freedom typical section with hardening structural nonlinearities. The equations of motion are derived accounting for the presence of viscoelastic materials introduced in the resilient elements associated to each degree-of-freedom. A constitutive law based on fractional derivatives is adopted, which allows the modeling of temperature-dependent viscoelastic behavior in time and frequency domains. The unsteady aerodynamic loading is calculated based on the classical linear potential theory for arbitrary airfoil motion. The aeroelastic behavior is investigated through time domain simulations, and subsequent frequency transformations, from which bifurcations are identified from diagrams of limit cycle oscillations amplitudes versus airspeed. The influence of the viscoelastic effect on the aeroelastic behavior, for different values of temperature, is also investigated. The numerical simulations show that viscoelastic damping can increase the flutter speed and reduce the amplitudes of limit cycle oscillations. These results prove the potential that viscoelastic materials have to increase aircraft components safety margins regarding aeroelastic stability.

Alleviating Unsteady Aerodynamic Loads with Closed-Loop Flow Control

The practical benefits and issues related to controlling unsteady loads in gusting flows with active flow control actuators are discussed. Recent methods used to model the response of flight and road vehicles to unsteady flow disturbances, as well as modeling approaches for the dynamic effects of active flow control, are presented in the framework of a feedforward/feedback control architecture. Limitations of the achievable control performance are discussed. For instance, the lift reversal and the delay time required for the lift increment to reach its maximum value are responsible for limiting the bandwidth that can be achieved with active flow control of separated flows. An estimate of the practical gust bandwidth that can be controlled with aircraft is made.

Determination of the Subsonic Flutter Stability Boundary of Blade Rows at Large Angles of Attack

This paper presents an experimental-and-numerical method for determination of the subsonic flutter stability boundary of blade rows at large angles of incident flow. The aerodynamic test rig for determining the unsteady aerodynamic loads is described. The test results are presented for a straight cascade of airfoils in a wide range of variation in the angle of attack and reduced vibration frequency, based on which the regularities in the effect of the angle of attack on the subsonic flutter stability boundary of blading are established.

Effects of Externally Mounted Store on the Nonlinear Response of Slender Wings

The nonlinear characteristics of slender wings have been studied for many years, and the influences of the geometric structural nonlinearity on the postflutter responses of the wing have been received significant attention. In this paper, the effects of the external store on the nonlinear responses of the slender wing will be discussed. Based on the Hodges–Dowell beam model, the dynamical equations of the wing which include the geometric structural nonlinearity and store effects are constructed. The unsteady aerodynamic loading of the wing will be calculated by employing Wagner function and strip theory. The slender body theory is adopted to get the aerodynamic forces of the store. The Galerkin method is used to obtain the state equations of the system and the appropriate mode combination is obtained for the cases studied in this paper. Numerical simulations are given to show that the store spanwise position and the distance between the store mass center and the elastic center of the wing are two important factors which will affect the nonlinear characteristics of the wing. These two parameters will induce the occurrence of quasi-periodic motion and branch structure in bifurcation diagrams to the system. The peak of postflutter response is also related to these parameters and the lower response peak can be obtained when the store mass center is in front of the elastic center. The models and results are helpful to the design procedure of the slender wing with store in the preliminary stage.

Unsteady Pylon Loading Caused by Propeller-Slipstream Impingement for Tip-Mounted Propellers

An experimental analysis was performed of the unsteady aerodynamic loading caused by the impingement of a propeller slipstream on a downstream lifting surface. When installed on an aircraft, this unsteady loading results in vibrations that are transmitted to the fuselage and are perceived inside the cabin as structure-borne noise. A pylon-mounted tractor–propeller configuration was installed in a low-speed wind tunnel at Delft University of Technology. Surface-microphone and particle-image-velocimetry measurements were taken to quantify the pressure fluctuations on the pylon and visualize the impingement phenomena. It was confirmed that the propeller tip vortex is the dominant source of pressure fluctuations on the pylon. Along the path of the tip vortex on the pylon, a periodic pressure response occurs with strong harmonics. The amplitude of the pressure fluctuations increases with increasing thrust setting, whereas the unsteady lift coefficient displays a nonmonotonic dependency on the propeller thrust. The lowest integral unsteady loads were obtained for cases with approximately integer ratios between the pylon chord and the wavelength of the perturbation associated with the propeller tip vortices. This implies that structure-borne-noise reductions might be obtained by matching the pylon chord with an integer multiple of the axial separation between the propeller tip vortices.

Boundary Control of a Nonhomogeneous Flexible Wing with Bounded Input Disturbances

This note deals with the boundary control problem of a nonhomogeneous flexible wing evolving under unsteady aerodynamic loads. The wing is actuated at its tip by flaps and is modeled by a distributed parameter system consisting of two coupled partial differential equations. Based on the proposed boundary control law, the well-posedness of the underlying Cauchy problem is first investigated by resorting to the semigroup theory. Then, a Lyapunov-based approach is employed to assess the stability of the closed-loop system in the presence of bounded input disturbances.

МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ДОЗВУКОВОГО ТУРБУЛЕНТНОГО ОБТІКАННЯ ПРОФІЛЮ NACA 0015, ЩО КОЛИВАЄТЬСЯ

Представлено результати розрахунків профілю NACA 0015, що коливається, для трьох режимів течії: слабкий відрив потоку, що відповідає середньому куту атаки 4°; розвинений відрив – 11° (докритичне обтікання профілю); масивний відрив – 15° (закритичне обтікання профілю). Для чисельного моделювання обтікання профілю, що коливається, застосовуються осереднені за Рейнольдсом нестаціонарні рівняння Нав'є-Стокса нестисливої рідини, замкнуті однопараметричною моделлю турбулентної в'язкості. Розроблений неявний скінчено-об'ємний чисельний алгоритм базується на методі штучної стисливості, що модифікований для розрахунку нестаціонарних задач. Аналізуються отримані поля завихренности, миттєві лінії течії, гістерезисні криві нестаціонарних аеродинамічних навантажень профілю для трьох характерних режимів обтікання. Розроблена методика дозволяє відтворювати структуру нестаціонарного відривного обтікання профілю, що коливається. Відмінності в аеродинамічних характеристиках стаціонарного профілю і профілю, що коливається, при одних і тих же кутах атаки добре узгоджуються з експериментальними даними. Порівняння результатів розрахунків обтікання профілю, що коливається з експериментальними даними і відомими розрахунками інших авторів показало перевагу моделі турбулентності SALSA в порівнянні з іншими моделями, що тестувались особливо при наявності масивного відриву потоку.

Feedback tracking control for dynamic morphing of piezocomposite actuated flexible wings

Aerodynamic properties of flexible wings can be improved via shape morphing using piezocomposite materials. Dynamic shape control of flexible wings is investigated in this study by considering the interactions between structural dynamics, unsteady aerodynamics and piezo-actuations. A novel antisymmetric angle-ply bimorph configuration of piezocomposite actuators is presented to realize coupled bending-torsional shape control. The active aeroelastic model is derived using finite element method and Theodorsen unsteady aerodynamic loads. A time-varying linear quadratic Gaussian (LQG) tracking control system is designed to enhance aerodynamic lift with pre-defined trajectories. Proof-of-concept simulations of static and dynamic shape control are presented for a scaled high-aspect-ratio wing model. Vibrations of the wing and fluctuations in aerodynamic forces are caused by using the static voltages directly in dynamic shape control. The lift response has tracked the trajectories well with favorable dynamic morphing performance via feedback tracking control.

Strain response analysis of adhesively bonded extended composite wind turbine blade suffering unsteady aerodynamic loads

Abstract Extending blades of wind turbine in service is the most effective method for increasing energy production. Adhesively bonding technology increases less mass and has simpler operation process, which is more suitable for extending blades in service. But unsteady aerodynamic loads on the blades due to stochastic turbulent inflow may lead to fatigue damage and even failure. This paper presented a study on strain response and fatigue life of adhesively bonded extended composite wind turbine blade suffering unsteady aerodynamic loads. Firstly, a loading method that applies periodic distributed aerodynamic loads on the blade was proposed to accurately simulate the unsteady distributed loads on the real extended blades in service. Secondly, strain response behaviors to unsteady aerodynamic loads and strain distribution behaviors in the adhesively bonded area were revealed. Finally, fatigue damage was predicted with unsteady aerodynamic load spectrums, rainflow cycle-counting algorithm, Goodman diagram and Miner's linear superposition principle. Based on the findings obtained from this study, the feasibility of adhesively bonding technology for extending blade was affirmed and a few potential future directions of study were addressed to reduce the risk of adhesively bonded structures.

A fast stochastic solution method for the Blade Element Momentum equations for long‐term load assessment

AbstractUnsteady power output and long‐term loads (extreme and fatigue) drive wind turbine design. However, these loads are difficult to include in optimization loops and are typically only assessed in a post‐optimization load analysis or via reduced‐order methods. Both alternatives yield suboptimal results. The reason for this difficulty lays in the deterministic approaches to long‐term loads assessment. To model the statistics of lifetime loads they require the analysis of many unsteady load cases, generated from many different random seeds—a computationally expensive procedure. In this paper, we present an alternative: a stochastic solution for the unsteady aerodynamic loads based on a projection of the unsteady Blade Element Momentum (BEM) equations onto a stochastic space spanned by chaos exponentials. This approach is similar to the increasingly popular polynomial chaos expansion, but with 2 major differences. First, the BEM equations constitute a random process, varying in time, while previous polynomial chaos expansion methods were concerned with random parameters (ie, random but constant in time or initial values). Second, a new, more efficient basis (the exponential chaos) is used. This new stochastic method enables us to obtain unsteady long‐term loads much faster, enabling unsteady loads to become accessible inside wind turbine optimization loops. In this paper we derive the stochastic BEM solution and present the most relevant results showing the accuracy of the new method.

A CFD study of coupled aerodynamic‐hydrodynamic loads on a semisubmersible floating offshore wind turbine

AbstractThe prediction of dynamic characteristics for a floating offshore wind turbine (FOWT) is challenging because of the complex load coupling of aerodynamics, hydrodynamics, and structural dynamics. These loads should be accurately calculated to yield reliable analysis results in the design phase of a FOWT. In this study, a high‐fidelity fluid‐structure interaction simulation that simultaneously considers the influence of aero‐hydrodynamic coupling due to the dynamic motion of a FOWT has been conducted using computational fluid dynamics based on an overset grid technique. The DeepCwind semisubmersible floating platform with the NREL 5‐MW baseline wind turbine model is considered for objective numerical verification with the NREL FAST code. A state‐of‐the‐art computational model based on the coupled computational fluid dynamics and dynamic structure analysis is constructed and analyzed to solve multiphase flow, 6 degrees of freedom motions of OC4 semisubmersible FOWT. A quasi‐static mooring solver is also applied to resolve the constraint motion of floater because of a 3‐line mooring system. The influence of tower shadow on the unsteady aerodynamic performance and loads is also demonstrated. Finally, complex unsteady flow fields considering blade and tower interference effects among blade‐tip vortices, shedding vortices, and turbulent wakes are numerically visualized and investigated in detail.