Leishman Beddoes Research Articles

Dynamic stall modeling of wind turbine blade sections based on a data-knowledge fusion method

Dynamic stall often leads to unsteady load and performance degradation in horizontal axis wind turbines. Therefore, accurate modeling of dynamic stall is crucial. However, due to the large variations of the blade aerodynamic profiles and the complexity of dynamic stall flow, numerical simulation and wind tunnel experiment are costly. On the other hand, widely used semi-empirical models have limited accuracy. Hence, this paper proposes a data-knowledge fusion method that incorporates physical knowledge into a neural network to improve its accuracy and generalization ability. Firstly, the force components of the Leishman–Beddoes model are incorporated into the network. An efficient dynamic stall model for the S809 airfoil is thus established with a small amount of high-precision experimental data. It achieves extrapolation predictions of reduced frequency and angle of attack with only 1/5 of the samples in the database to train. Moreover, to make full use of the accumulated existing airfoil data to assist in modeling other airfoils, the obtained S809 model is fused in the network to predict the aerodynamics of S810 and S814. The average relative error of the prediction cases is nearly 10%. Comprehensively, this paper provides a new paradigm for assessing the dynamic stall of the wind turbine blade.

Active Stall Flutter Suppression for a Revised Leishman–Beddoes Model

Active Stall Flutter Suppression for a Revised Leishman–Beddoes Model

A model for predicting the unsteady hydrodynamic characteristics on the blades of a horizontal axis tidal turbine

Tidal current turbines operate in a highly turbulent environment, which results in significant fluctuations in unsteady loads and consequent fatigue and dynamic failures in the rotor. Therefore, accurate calculation of these unsteady loads is crucial. However, the existing models do not take into account the influence of varying relative blade section thickness on dynamic stall when predicting the unsteady characteristics of horizontal axis tidal turbine (HATT) blades. To forecast the unsteady characteristics of the HATT blades, this study developed a method that considers the influence of relative blade thickness on dynamic stall. The modified Leishman-Beddoes (L-B) dynamic stall model, 3D rotational augmentation model, and steady-state BEM model were combined to predict the unsteady hydrodynamic characteristics of blades by synthesizing the transient inlet velocities induced by waves, shear flow and turbulence. In this method, the static parameters required for the modified L-B dynamic stall model were calculated by XFOIL within a range of small angle of attack (AoA) and then extrapolated to cover the entire range of AoA using the Viterna extrapolation method. The required dynamic parameters were obtained by CFD numerical simulation. This method, that we call HATT-UCPM, can consider both the effects of a single element on the unsteady hydrodynamic characteristics of the blades, as well as the combined effects of shear flow, waves, and turbulence on the blades in the actual marine environment. The accuracy of the method was validate through CFD numerical simulation. The results showed that the proposed method has a high consistency with the numerical simulation results, indicating that it has a good accuracy in the prediction of unsteady characteristics of HATT blades. Finally, the study examined several cases to investigate the impacts of shear flow, waves, and turbulence on the unsteady loads of blades, both individually and in combination.

Fuzzy Neural Network PID Control Used in Individual Blade Control

In order to further reduce the vibration level of helicopters, the active vibration control technology of helicopters has been extensively studied. Among them, individual blade control (IBC) independently applies high-order harmonics to each blade with an actuator, which can improve the aerodynamic environment of the blade and effectively reduce the vibration load of the hub. The rotor structural dynamics model based on the Hamilton energy variation principle and the medium deformation beam theory were established firstly, and the aerodynamic model based on the dynamic inflow model and the Leishman–Beddoes unsteady aerodynamic model were also established. The structural finite element method and the direct numerical integration method were used to calculate the vibration response of the rotor to determine the vibration load of the hub. After these, the steepest descent-golden section combinatorial optimization algorithm was used to find the optimization parameters of IBC. Based on this, the input parameters of fuzzy neural network PID control were determined, and the rotor hub vibration load control simulation was conducted. Under the effect of IBC, the vibration loads of the hub could be reduced by about 60%. The article gives the best control laws of individual harmonic pitch control and their combinations. These results can theoretically be applied to the design of control law to reduce helicopter vibration loads.

Non-normality and transient growth in stall flutter instability.

The non-normal nature and transient growth in amplitude and energy of a pitch-plunge aeroelastic system undergoing dynamic stall are explored in this paper through numerical and supporting experimental studies. Wind tunnel experiments, carried out for a canonical pitch-plunge aeroelastic system in a subsonic wind tunnel, show that the system undergoes stall flutter instability via a sub-critical Hopf bifurcation. The aeroelastic responses indicate a transient growth in amplitude and energy-possibly triggering the sub-criticality, which is critical from the purview of structural safety. The system also shows transient energy growth followed by decaying oscillation for certain initial conditions, whereas sustained limit cycle oscillations are encountered for other initial conditions at flow speeds lower than the critical speed. The triggering behavior observed in the wind tunnel experiments is understood better by resorting to study the numerical model of the nonlinear aeroelastic system. To that end, a modified semi-empirical Leishman-Beddoes dynamic stall model is adopted to represent the nonlinear aerodynamic loads of the pitch-plunge aeroelastic system. The underlying linear operator and its pseudospectral analysis indicate that the aeroelastic system is non-normal, causing amplification in amplitude and energy for a short period.

Reducing Helicopter Vibration Loads by Individual Blade Control with Genetic Algorithm

A rotor that can realize individual blade pitch control was designed. This paper focuses on finding the trend of helicopter vibration loads after applying multiple high-order harmonic control. The Glauert inflow model was introduced to calculate the induced velocity of rotor blades in a rotor disk plane, and the Leishman Beddoes (L-B) unsteady dynamic model was employed to calculate the aerodynamic forces of each section of a rotor blade. It was found that the influence of each high-order harmonic control on individual blade vibration load reduction is similar in different advanced ratios. After these calculations, the genetic algorithm was used to calculate the best combination of amplitude and phase of the higher order harmonic under a specific flight state. Under the effect of high harmonic input, the vibration loads of the hub could be reduced by about 65%. These results can be theoretically applied to design control law to reduce helicopter vibration loads.

Stall-induced fatigue damage in nonlinear aeroelastic systems under stochastic inflow: Numerical and experimental analyses

This study focuses on characterizing the fatigue damage accumulated in nonlinear aeroelastic systems subjected to stochastic inflows through both numerical simulations and wind tunnel experiments. In the mathematical model, nonlinearities are assumed to exist either in the structure (via a cubic hardening nonlinearity in the pitch stiffness), or in the flow (via dynamic stall condition), or simultaneously in both the structural and aerodynamic counterparts. The aerodynamic loads in the attached flow and dynamic stall conditions are estimated using Wagner’s formulation and semi-empirical Leishman–Beddoes model, respectively. To augment the findings to in-field flow conditions, the oncoming wind flow is considered to be randomly time-varying in nature. The stochastic input flow fluctuations are modeled using a Karhunen–Loeve Expansion formulation. The response dynamics and the associated fatigue damage of the aeroelastic system, possessing different sources of nonlinearities, are systematically investigated under isolated cases of deterministic and stochastic input flows. Specifically, the pertinent role of stochasticity in the input flow is brought out by presenting the response dynamics and the associated fatigue damage accumulation for different values of noise intensity and time scale of the input flow fluctuation. It is demonstrated that under fluctuating flow conditions, the dynamics intermittently switch between attached flow and the dynamic stall regimes even at low mean flow speeds. The intermittent nature of the response varies as the time scale and intensity of the oncoming flow are varied. The role of torsional stresses as the predominant component dictating the fatigue damage accumulation irrespective of the source of nonlinearity is illustrated. Using the rainflow counting method and Miner’s linear damage accumulation theory, it is shown that the accumulated fatigue damage is substantially higher under stochastic flow conditions as compared to deterministic input flows. Importantly, it is observed that different time scales and intensities of the oncoming flow fluctuation play a pivotal role in dictating the fatigue damage in aeroelastic systems. Finally, fatigue damage is observed to be significantly higher for torsionally dominant oscillations in the dynamical stall regime compared to the oscillations at the attached flow regime. The numerical findings are strengthened by drawing comparisons with the preliminary results obtained from wind tunnel experiments performed on a NACA 0012 airfoil undergoing dynamic stall. To the best of our knowledge, this is the first study that systematically bridges the dichotomy between the stall-induced dynamical signatures in stochastic aeroelastic systems and maps the same to the corresponding structural damage.

Numerical Study of a Horizontal Wind Turbine under Yaw Conditions

Over recent years, considerable attention has been devoted to the optimization of energy production in wind farms, where yaw angles can play a significant role. In order to quantify and maximize such potential power, the simulation of wakes is vital. In the present study, an actuator line model code was implemented in the OpenFOAM flow solver. A tip treatment was applied to involve the tip effect induced by the pressure equalization from the suction and pressure sides. The Leishman–Beddoes dynamic stall (LB-DS) model modified by Sheng et al. was employed to consider the dynamic stall phenomenon. The developed ALM-CFD solver was validated for the NREL Phase VI wind turbine reference case. The solver was then used in simulating the yawed wind turbine, and power variation was compared with UBEM and CFD. Overall, according to the obtained data, the coupled solver compared well with CFD. There was an improvement in terms of prediction of the phase delay that is due to the dynamic stall. However, there was still negligible overestimation in deep stall conditions. Based on the obtained results, it is suggested that the reduction of power output follows a cosine to the power of X function of the yaw angle. In terms of visualizing wake, the results demonstrated that the current ALM code was satisfying enough to simulate skewed wake and vortices trajectory. The effect of advancing and retreating blade was captured. It was found that yaw led to the concentration of the induced velocity downstream, resulting in a lower velocity deficit on a broader area, which is essential for wind farm optimization.

Routes to Synchronization in a pitch–plunge aeroelastic system with coupled structural and aerodynamic nonlinearities

The present study aims to investigate the synchronization characteristics of a pitch–plunge aeroelastic system subjected to coupled structural free-play and dynamic stall-induced aerodynamic nonlinearities. The semi-empirical Leishman–Beddoes (LB) aerodynamic model is used to capture the dynamic stall phenomena at large angles-of-attack (AoA). A bifurcation analysis, considering the flow-speed as the control parameter, reveals that the free-play nonlinearity is primarily responsible for the dynamical transition in the presence of the attached flow. In this case, a pitch and plunge frequency coalescence takes place through an aperiodic to periodic signature transition. Furthermore, by tracking the flow specific variables estimated using the LB model, it is observed that the onset of the dynamic stall plays a pivotal role in the bifurcation scenario at high flow speed regimes, marking the presence of stall flutter. The framework of synchronization is used to discern the response dynamics at low speed and high speed flow regime by estimating the pitch and plunge modal frequencies and their corresponding phase components. The routes to synchronization are identified to be through phase-locking (frequency coalescence) and through suppression of the plunge mode by the dominance of pitching frequency in the regimes before and after the onset of dynamic stall, respectively. Finally, it is shown that the different synchronization routes can possibly be a useful tool to identify the presence of stall flutter oscillations in a coupled aeroelastic system.

A modified Leishman–Beddoes model for airfoil sections undergoing dynamic stall at low Reynolds numbers

A modified Leishman–Beddoes (Leishman and Beddoes, 1989) model is proposed to predict the aerodynamic load responses of airfoils undergoing dynamic stall at low Reynolds, low Mach numbers and low to very high equivalent reduced pitch rates. The modifications include using Wagner function aerodynamics for the attached flow model, defining and using a time-varying reduced pitch rate, equating the time delays applied to the normal force, the separation point location and the vortex shedding and using Sheng and Galbraith’s dynamic stall onset criteria (Sheng et al., 2006).The steady and unsteady force and pitching moment measurements of three airfoils with distinct stall mechanisms (a flat plate, a NACA0012, and a NACA0018) are used to demonstrate the validity of this new model. Dynamic tests consist of oscillating the airfoils in pitch around the quarter chord with a mean angle A0=10∘ and with different prescribed reduced frequencies from k=0.015, to k=0.16, and amplitudes from, A=5° to 20°, at Reynolds numbers of the order of Re≃1.8×104. The resulting equivalent reduced pitch rates range from r′=0.001 to 0.06. The computations of the values of the different model parameters are demonstrated and it is observed that the values of the time delay parameters change continuously and smoothly with time instead of jumping discontinuously at discrete time instances as proposed by Leishman and Beddoes (1989).It is shown that the modified Leishman–Beddoes model is in good agreement with experiments for low to moderate equivalent reduced pitch rates (r′≤0.04). It also significantly improves the dynamic load prediction in this range of pitch rates, in comparison to the original Leishman–Beddoes model. Nevertheless, as for the original model, the modified model presented here becomes inaccurate at the highest equivalent reduced pitch rates of r′>0.05.

Response analysis of a pitch–plunge airfoil with structural and aerodynamic nonlinearities subjected to randomly fluctuating flows

This study focuses on numerically investigating the response dynamics of a pitch–plunge airfoil with structural nonlinearity under dynamic stall conditions. The aeroelastic responses are investigated for both deterministic and randomly time varying flow conditions. To that end, a pitch–plunge airfoil under dynamic stall condition is considered and the nonlinear aerodynamic loads are computed using a Leishman–Beddoes formulation. It is shown that the presence of structural nonlinearities can give rise to a variety of dynamical responses in the pre-flutter regime. Next, a response analysis under the presence of a randomly fluctuating wind is carried out. It is demonstrated that the route to flutter occurs via a regime of pre-flutter oscillations called intermittency. Finally, the manifestation of these stochastic responses is characterized by invoking stochastic bifurcation concepts. The route to flutter via intermittency is presented in terms of topological changes occurring in the joint-probability density function of the state variables.

Developments of a semiempirical dynamic stall model for unsteady airfoils

A new semiempirical dynamic stall model is presented to predict the aerodynamic coefficients of an airfoil in unsteady conditions. The model is mainly based on two modifications on the airfoil angle of attack which introduce an equivalent angle of attack to implement in the proposed aerodynamic coefficients. The first modification includes unsteady wake effects of the airfoil in the proposed model which are not considered in most of the semiempirical models. Hence, an effective angle of attack is introduced based on an unsteady aerodynamic theory using the Wagner function for pitching and plunging oscillations of the airfoil. The second modification takes into account time delay effects and dynamic effects due to the flow separation on the airfoil. These effects are included in the model by developing a semiempirical relationship between static and dynamic angle of attack published in the literature. Finally, the modifications form the equivalent angle of attack to implement in a set of equations based on Kirchhoff flow theory. The proposed approach dynamically approximates trailing edge separation point on the airfoil by a completely new way and contributes its effects in the aerodynamic coefficients. Moreover, apparent mass effects and the airfoil leading edge vortex contributions are sufficiently included in the model. The presented method effectively predicts unsteady lift and pitching moment coefficients of the airfoil undergoing stall conditions. Consequently, the proposed model is verified against experimental data under various test cases where obtained numerical results are in good agreement with the test data. Furthermore, the performance of the proposed model is compared with various dynamic stall models including Leishman–Beddoes model, ONERA model and Boeing–Vertol model. The comparison shows that the proposed model minimizes the number of the semiempirical parameters determined from an experiment in dynamic stall modeling compared with Leishman–Beddoes model and ONERA model. It also demonstrates that the presented model performs as well as other well-known models using the various approaches.

Fuel savings for a general cargo ship employing retractable bow foils

Route simulations were performed on a 100 m long (between perpendiculars) general cargo ship equipped with retractable bow-mounted foils, so-called wavefoils, for resistance reduction and motion damping in waves. Two round-trip routes were simulated: Orkney Islands to Iceland and across the Bay of Biscay. Ship motions and added resistance in waves were calculated in the frequency domain. Foil thrust was calculated in the time domain, based on a frequency-domain model of the vessel motions with wavefoils, using a slightly modified version of the Leishman–Beddoes dynamic stall model [22]. For both directions of each route, 1000 journeys with and without wavefoils were simulated, with wind and wave conditions obtained from ECMWF hindcast data. In the simulations, two identical ships, one equipped with wavefoils and the other without, were assumed operating in parallel, starting their journeys at random times between January 1, 2000, and December 1, 2014. The brake power was constant for the ship without wavefoils, whereas the ship with wavefoils reduced its power to obtain the same speed as the ship without wavefoils. For the most favorable route with respect to this study, Orkney Islands to Iceland, the average fuel saving was 22% for a constant brake power without foils that corresponds to a calm-water speed of 14 knots.

Vortex Lattice Simulations of Attached and Separated Flows around Flapping Wings

Flapping flight is an increasingly popular area of research, with applications to micro-unmanned air vehicles and animal flight biomechanics. Fast, but accurate methods for predicting the aerodynamic loads acting on flapping wings are of interest for designing such aircraft and optimizing thrust production. In this work, the unsteady vortex lattice method is used in conjunction with three load estimation techniques in order to predict the aerodynamic lift and drag time histories produced by flapping rectangular wings. The load estimation approaches are the Katz, Joukowski and simplified Leishman–Beddoes techniques. The simulations’ predictions are compared to experimental measurements from wind tunnel tests of a flapping and pitching wing. Three types of kinematics are investigated, pitch-leading, pure flapping and pitch lagging. It is found that pitch-leading tests can be simulated quite accurately using either the Katz or Joukowski approaches as no measurable flow separation occurs. For the pure flapping tests, the Katz and Joukowski techniques are accurate as long as the static pitch angle is greater than zero. For zero or negative static pitch angles, these methods underestimate the amplitude of the drag. The Leishman–Beddoes approach yields better drag amplitudes, but can introduce a constant negative drag offset. Finally, for the pitch-lagging tests the Leishman–Beddoes technique is again more representative of the experimental results, as long as flow separation is not too extensive. Considering the complexity of the phenomena involved, in the vast majority of cases, the lift time history is predicted with reasonable accuracy. The drag (or thrust) time history is more challenging.

Bifurcation Analysis with Aerodynamic-Structure Uncertainties by the Nonintrusive PCE Method

An aeroelastic model for airfoil with a third-order stiffness in both pitch and plunge degree of freedom (DOF) and the modified Leishman–Beddoes (LB) model were built and validated. The nonintrusive polynomial chaos expansion (PCE) based on tensor product is applied to quantify the uncertainty of aerodynamic and structure parameters on the aerodynamic force and aeroelastic behavior. The uncertain limit cycle oscillation (LCO) and bifurcation are simulated in the time domain with the stochastic PCE method. Bifurcation diagrams with uncertainties were quantified. The Monte Carlo simulation (MCS) is also applied for comparison. From the current work, it can be concluded that the nonintrusive polynomial chaos expansion can give an acceptable accuracy and have a much higher calculation efficiency than MCS. For aerodynamic model, uncertainties of aerodynamic parameters affect the aerodynamic force significantly at the stage from separation to stall at upstroke and at the stage from stall to reattach at return. For aeroelastic model, both uncertainties of aerodynamic parameters and structure parameters impact bifurcation position. Structure uncertainty of parameters is more sensitive for bifurcation. When the nonlinear stall flutter and bifurcation are concerned, more attention should be paid to the separation process of aerodynamics and parameters about pitch DOF in structure.

An improved PSO algorithm for parameter identification of nonlinear dynamic hysteretic models

The nonlinear dynamic hysteretic models used in nonlinear dynamic analysis contain generally lots of model parameters which need to be identified accurately and effectively. The accuracy and effectiveness of identification depend generally on the complexity of model, number of model parameters and proximity of initial values of the parameters. The particle swarm optimization (PSO) algorithm has the random searching ability and has been widely applied to the parameter identification in the nonlinear dynamic hysteretic models. However, the PSO algorithm may get trapped in the local optimum and appear the premature convergence not to obtain the real optimum results. In this paper, an improved PSO algorithm for identifying parameters of nonlinear dynamic hysteretic models has been presented by defining a fitness function for hysteretic model. The improved PSO algorithm can enhance the global searching ability and avoid to appear the premature convergence of the conventional PSO algorithm, and has been applied to identify the parameters of two nonlinear dynamic hysteretic models which are the Leishman-Beddoes (LB) dynamic stall model of rotor blade and the anelastic displacement fields (ADF) model of elastomeric damper which can be used as the lead-lag damper in rotor. The accuracy and effectiveness of the improved PSO algorithm for identifying parameters of the LB model and the ADF model are validated by comparing the identified results with test results. The investigations have indicated that in order to reduce the influence of randomness caused by using the PSO algorithm on the accuracy of identified parameters, it is an effective method to increase the number of repeated identifications.

An unsteady free wake model for aerodynamic performance of cycloidal propellers

A new unsteady three-dimensional aerodynamic performance prediction approach is established to achieve fast and accurate prediction of the unsteady aerodynamics of cycloidal propellers. This model is developed by the coupling of momentum theory, lifting-line method, free wake model, and the Leishman–Beddoes semi-empirical dynamic stall model. The overall calculation process includes two parts. Firstly, to reduce the computational time and improve the computational convergence, the momentum theory is coupled with the Leishman–Beddoes semi-empirical dynamic stall model to predict a uniform inflow velocity through the cycloidal propeller disc, which is set as the initial induced velocity for iterations in the subsequent process. Then, the blade aerodynamic model, which couples the unsteady lifting-line method with the Leishman–Beddoes dynamic stall model, is used to calculate the unsteady aerodynamic response of blades. The wake of cycloidal propeller is represented by a serious of finite-length shed and trailing vortex elements, and the free wake model is utilized to model the dynamics of cycloidal propeller wake. Predictions from the present model are shown to be agreed reasonably well with the overall experimental data and the computational fluid dynamics results, both in terms of the aerodynamic performance prediction of cycloidal propeller and instantaneous blade force variations.

Model test and simulation of a ship with wavefoils

The paper describes model tests of a tanker with two fixed bow-mounted foils (wavefoils), for resistance and motion reduction in waves. Measured ship resistance, wavefoil thrust and ship motions were compared with time-domain simulations. The wavefoil forces were calculated using a slightly modified Leishman–Beddoes dynamic stall model, with a two-way coupling to the ship motions. In typical sea states in head seas, employing the wavefoils reduced ship resistance by 9–17%, according to scaled model test resistance. Heave and pitch were reduced by −11% to 32% and 11% to 25%, respectively. The foils affect the flow around the hull. This should be considered when selecting the wavefoil location in the design process.

Simulating Dynamic Stall Effects for Vertical Axis Wind Turbines Applying a Double Multiple Streamtube Model

The complex unsteady aerodynamics of vertical axis wind turbines (VAWT) poses significant challenges to the simulation tools. Dynamic stall is one of the phenomena associated with the unsteady conditions for VAWTs, and it is in the focus of the study. Two dynamic stall models are compared: the widely-used Gormont model and a Leishman–Beddoes-type model. The models are included in a double multiple streamtube model. The effects of flow curvature and flow expansion are also considered. The model results are assessed against the measured data on a Darrieus turbine with curved blades. To study the dynamic stall effects, the comparison of force coefficients between the simulations and experiments is done at low tip speed ratios. Simulations show that the Leishman–Beddoes model outperforms the Gormont model for all tested conditions.

Simulating Pitching Blade With Free Vortex Model Coupled With Dynamic Stall Model for Conditions of Straight Bladed Vertical Axis Turbines

This study is on the straight bladed vertical axis turbines (VATs), which can be utilized for both wind and marine current energy. VATs have the potential of lower installation and maintenance cost. However, complex unsteady fluid mechanics of these turbines imposes significant challenges to the simulation tools. Dynamic stall is one of the phenomena associated with the unsteady conditions, and it is in the focus of the study. The dynamic stall effects are very important for VATs, since they are usually passively controlled through the dynamic stall. A free vortex model is used to calculated unsteady attached flow, while the separated flow is handled by the dynamic stall model. This is compared to the model based solely on the Leishman–Beddoes algorithm. The results are assessed against the measured data on pitching airfoils. A comparison of force coefficients between the simulations and experiments is done at the conditions similar to the conditions of H-rotor type VATs.