Nonlinear Blade Research Articles

A study of nonlinear aeroelastic response of a long flexible blade for the horizontal axis wind turbine

As long flexible blades in large wind turbines are prone to excessive bending deformations, there are failures in dynamic analyses under linear (small deflection) conditions. Thus, a large deflection blade model is developed here to study the dynamic response. The updated Lagrangian equation is used to derive the large deflection blade model from the Euler–Bernoulli beam. Then, the nonlinear aeroelastic dynamics equations of the blade are established using blade element momentum (BEM) theory, and time-domain simulations are performed using the nonlinear Newmark and Newton–Raphson methods. The effects of structural vibrations and aerodynamic damping are considered throughout the process. Finally, the nonlinear model is applied to the DTU 10 MW wind turbine. The results show that under steady and below-rated wind speeds, the flapwise deflection of the nonlinear blade is smaller than that of the linear blade. However, this phenomenon is the opposite for above-rated wind speeds. Under a step wind, the model responds quickly to the blade’s flexible deformation. Under turbulence, the linear results are consistent with the DNVGL Bladed 4.3 results, indicating that the nonlinear blade based on the linear Euler–Bernoulli beam is reliable. Meanwhile, the flapwise deflection for both blades fluctuates slightly when turbulent speeds are lower than the rated speed (0–5 s and 41–50 s), which is distinct from the steady-state analysis. In the aeroelastic coupling analysis, responses that consider vibration feedback are significantly smaller than those without feedback, and a nonlinear blade is significantly more affected in the flapping direction than a linear blade. Finally, the aerodynamic performance of large wind turbines is negatively affected by certain turbulent wind speeds.

Parametric study on internal resonances for a simplified nonlinear blade model

This article proposes to determine and identify the physical contributions that drive the internal resonance between the bending and torsion modes of a blade. The blade is modeled as a nonlinear beam including warping, twist and pre-bending, and a discretization scheme based on a Rayleigh–Ritz approximation is performed. The modal properties of the model are compared and validated using beam theory and finite element modeling. Several configurations of the model allowing the occurrence of an internal resonance between the first torsional and the second bending modes are considered. The frequency responses near the second bending mode are obtained through the Harmonic Balance Method coupled with a branch switching algorithm to locate and track bifurcated branches related to internal resonances. Attention is paid to the identification of the geometrical nonlinear terms that enable the appearance of an internal resonance. With the help of a multiple scale analysis, it is shown that it is essentially driven by a small set of coupling parameters involving bending and torsion displacements of the commensurate modes. It is also observed in a rotating situation thanks to the hardening of the bending mode.

Computational studies of the rotors aerodynamic characteristics of multirotor drones

The article presents the results of computational studies of aerodynamic characteristics for unmanned lift-generating multi-rotor drones of various configurations. The distinctive features of rotors flow were characterized. The rotor interaction was evaluated. The computations were based on the nonlinear rotor blade vortex theory in a non-stationary arrangement. The combinations of four, eight (four coaxial) and fourteen two-bladed rotors at velocity V = 100, 150, 200 km/h were considered. Semi-empirical methods were employed to select the rotor angles of attack, rotation speed, blade installation angles and geometric parameters at the given take-off weight for each combination of rotors and flight airspeed. The computations showed that for a four-rotor lift-generating design (quad-rotor), two rotors installed downstream, depending on the velocity due to the mutual effect, have values of the thrust coefficients ≈10...20% less than those of the rotors located upstream. For a coaxial quad-copter, the effect of the upper front rotor on the upper rear rotor is similar to the effect of the front rotors on the rear ones in a four-rotor lift-generating design. The effect of the upper front rotor on the lower rear rotor does not vary in terms of the average thrust value, and variations are only local in nature. The interaction of other rotors is identical to that of the four-rotor version. A fourteen-rotor lift-generating multi-rotor drone has a complex flow pattern, which generates deviance in the thrust coefficients variation with respect to time. Depending on the mode and rotors location, the average rotor thrust coefficient can vary approximately twice. The computations showed that with the similar geometric parameters and kinematics characteristics, rotors thrust is substantially subject to variation, which causes destabilizing moments to a significant degree without additional control input. Thrust pulsations and, respectively, vibrations grow in intensity as the flight airspeed increases. Probably, the right choice of the rotor configuration and the automatic control system can counterbalance thrust surge by so-called "phasing", i.e. selecting an initial azimuth angle for each rotor.

A novel linearization approach of chord and twist angle distribution for 10 kW horizontal axis wind turbine

In the present work, the aerodynamic design of a 10 kW horizontal axis wind turbine rotor is performed using both ideal and actual rotor theories. The obtained nonlinear blade profile is optimized in order to enhance the aerodynamic performance and to ease the fabricating complexity. A unique linearization approach is employed to linearize the chord and twist distribution by dividing the congruent line of both ideal and actual models into equal divisions. The points along the identical tangent line are considered as floating new blade roots, whereas the blade tip was kept fixed based on the primary design. The linear profile based on the new value of blade root is described using algebraic equations. The local element torque, capacity factor, and the annual energy production based on the Weibull distribution are adopted to determine and assess the optimal blade profile. Both CFD investigation and the FEA analysis are performed in order to evaluate both primary and optimized blades. The aerodynamic and aeroelastic comparison in terms of power output, thrust force, blade tip deflection, and the equivalent stress distribution of both blade profiles has been done over a wide range of incoming wind speeds. Results show an enhancement in the aerodynamic performance in terms of power coefficient up to (5.9%) compared to the primary blade design. Moreover, the optimized blade has shown less tip deflection by 27.92% than the primary blade at low wind speed.

Nonlinear effects and dynamic coupling of floating offshore wind turbines using geometrically-exact blades and momentum-based methods

Nonlinear blade effects and overall dynamic coupling of floating offshore wind turbines (FOWTs) are investigated using the latest developments in nonlinear beam theory and multibody dynamics. An aero-hydro-servo-elastic coupled model is developed combining momentum-based beam theory (MBBT) and the momentum cloud method (MCM) based on a multi-time-scale coupling scheme, in which geometrically-exact blades are coupled with a highly-compliant floating platform design that allows large angular motions. Comprehensive simulations are performed and the results are analyzed to demonstrate the importance of nonlinear effects and dynamic coupling of FOWTs. Nonlinear blade dynamics are shown to be critical in assessments of turbine performance and blade fatigue. The highly-compliant floater design is found to be feasible in realistic operating conditions. A strong one-way dynamic coupling is observed from platform motions to blade vibrations. Axi-asymmetric response of the blades is found to induce significant imbalanced aerodynamic loading onto the turbine and the platform.

A novel grey decision-DE optimized internal model controller for vibration control of nonlinear uncertain aeroelastic blade system

In this paper, a novel grey decision-differential evolution (GD-DE) optimized internal model controller is proposed for the control of nonlinear aeroelastic blade system (ABS) under time-varying uncertainties and control saturations. Two-port internal model control structure is presented for saturation compensation. The filter parameter of the controller is optimally tuned by proposed GD-DE algorithm, which is designed based on the grey decision incidence theory and differential evolution algorithm. The superiority of GD-DE optimized tuning technique is verified, compared to conventional IMC tuning method and other evolutionary algorithm based techniques. The robustness is analysed by comprehensive simulations from time-invariant uncertainties to large periodic or random time-varying uncertainties. The realistic condition with input/output disturbances is also involved. Simulation results show that the proposed controller outperforms existing adaptive IMC controller and other advanced controllers with greatly improved dynamic performance, stronger robustness and better saturation compensation on various conditions.

Nonlinear Blade Stability for a Scaled Autogyro Rotor at High Advance Ratios

Despite current research advances in aircraft dynamics and increased interest in the slowed rotor concept for high-speed compound helicopters, the stability of autogyro rotors remains partially understood, particularly at lightly loaded conditions and high advance ratios. In autorotation, the periodic behavior of a rotor blade is a complex nonlinear phenomenon, further complicated by the fact that the rotor speed is not held constant. The aim of the analysis presented in this article is to investigate the underlying mechanisms that can lead to rotation-flap blade instability at high advance ratios for a teetering autorotating rotor. The stability analysis was conducted via wind tunnel tests of a scaled autogyro model combined with numerical continuation and bifurcation analysis. The investigation assessed the effect of varying the flow speed, blade pitch angle, and rotor shaft tilt relative to the flow on the rotor performance and blade stability. The results revealed that rotor instability in autorotation is associated with the existence of fold bifurcations, which bound the control-input and design parameter space within which the rotor can autorotate. This instability occurs at a lightly loaded condition and at advance ratios close to 1 for the scaled model. Finally, it was also revealed that the rotor inability to autorotate was driven by blade stall.

Computational Research of the Main Rotor Steep Descent Modes Based on the Nonlinear Blade Vortex Model

The main rotor operation is studied of the Mi-8 single-rotor helicopter in steep descent modes at the rotor angles of attack αR = 90−30 deg. The study resulted in total and distributed aerodynamic performance, rotor wake patterns and flow patterns. The vortex ring state area is designed based on the result analysis in terms of some features. The calculation results are compared with the experimental data and calculations of other authors.

CALCULATED RESEARCH OF INFLUENCE OF HELICOPTER MAIN ROTORS GEOMETRY ON THE EFFICIENCY IN HOVER MODE BASED ON THE NONLINEAR VORTEX MODEL

The efficiency of the helicopter main rotor in the hover mode is very important, because this mode essentially determines the performance characteristics of the helicopter. A feature of the helicopter rotor aerodynamics is a significant inductive blade influence that highly defines its aerodynamic characteristics. The problem of the influence of the blade twist and spatial geometric layout of the main rotor on its aerodynamic characteristics in the hover mode for a fixed value of the rotor solidity has been considered in this article. As a criterion of efficiency of the rotor in the hover mode relative efficiency (FoM – Figure of Merit) is used. The results are obtained by numerical simulation based on the nonlinear vortex blade model of the rotor, developed at the Helicopter Design Chair of the MAI. The model allows taking into account a complicated spatial shape of the free vortex path of the rotor blades that determines their inductive interaction. As the example of a four-blade main rotor with rectangular blades in plan, the influence of the value of the blades twist on the efficiency in the hover mode is studied. For different values of the rotor thrust, the values and ranges of the blade twist angles are determined, providing the maximum positive effect of the efficiency increase in hovering. For a fixed value of the blade twist, the rotor solidity, and the same operating conditions, the effect of various schemes and configurations of rotor on its efficiency in hover mode is studied. A single rotor with a different number of blades (from 2 to 6), an X-shaped rotor, coaxial rotor and rotor with crossed blades type "synchropter" are considered. The values of the efficiency increase in hovering depending on the rotor layout in comparison with the two-blade rotor are obtained. The comparative analysis of inductive velocities and streamlines for the "synchropter" rotor scheme, coaxial rotor scheme and its equivalent single rotor scheme is presented. The obtained results can be useful at the stage of preliminary design of vertically taking-off aircraft when selecting the parameters of their main rotor system.

Computational Research of the Main Rotor Hover and Vertical Descent States Based on the Nonlinear Blade Vortex Model

The research is conducted of aerodynamic performance of the Mi-8 helicopter main rotor in the hover state and the vertical descent state, including vortex ring states (VRSs). Total and distributed aerodynamic performance, wake patterns, and main rotor flow patterns are calculated. The findings and results were compared with those provided by other researchers.

Crystal orientation effect and multi-fidelity optimization of a solid single crystal superalloy turbine blade

Single crystal (SC) turbine blade adopts directional solidification casting, traditional design approach requires the [0 0 1] crystal orientation coincide with the blade stacking axis, and the principal deviation angle is less than 10 deg, the other crystal orientation is random. This design philosophy result in random fatigue life of the formed blade even in the same service environment. Crystal orientation effect on mechanical response of a SC turbine blade is investigated using finite element calculation, then presents a multi-fidelity optimization procedure for crystal orientation optimizations of the blade. A nonlinear turbine blade FEM model with orientation dependent crystal plastic theory and coupled temperature conversion provides the high-fidelity model, the low-fidelity model involves a surrogate model technique. Through the multi-fidelity optimization of crystal orientation design, taking into account the efficiency and accuracy to reduce the maximum resolved shear stress (Rss) at the dangerous position of solid turbine blade and effectively improve the fatigue life of the blades. The results demonstrate that crystal orientation have an appreciable variation on Rss in the dangerous position of solid turbine blade. The influence of temperature and structure must be taken into consideration, especially the maximum Rss has the significant effect on evaluating the fatigue life of turbine blade. The optimization model based on the approximation theory can accurately describe the response between the design variables and optimization targets. The optimization reduces the Rss and deformation by 28% and 17%, respectively. The multi-fidelity optimization strategy can effectively optimizes the crystal orientation of the blade and improves the blade life.

Wing and propeller aerodynamic interaction through nonlinear lifting line theory and blade element momentum theory

In this paper a computational methodology of aerodynamic interaction between propeller and wing is described. Presented work is focused on development of quick and accurate tool. Lifting line theory (LLT) with nonlinear airfoil characteristic is used to solve a finite span wing aerodynamic to predict downwash and lift distribution respectively. Blade element momentum theory (BEM) is used as a computational tool for estimating total thrust, torque, axial and tangential velocity distributions. Model of slipstream development is considered. Influence of propeller model to wing is simulated as contribution of higher dynamic pressure and change of angle of attack behind the propeller.

Pre-Deformation Method for Manufactured Compressor Blade Based on Load Incremental Approach

Abstract The blade deformation caused by aerodynamic and centrifugal loads during operating makes blade configurations different from their stationary shape. Based on the load incremental approach, a novel pre-deformation method for cold blade shape is provided in order to compensate blade deformation under running. Effect of nonlinear blade stiffness is considered by updating stiffness matrix in response to the variation of blade configuration when calculating deformations. The pre-deformation procedure is iterated till a converged cold blade shape is obtained. The proposed pre-deformation method is applied to a transonic compressor rotor. Effect of load conditions on blade pre-deformation is also analyzed. The results show that the pre-deformation method is easy to implement with fast convergence speed. Neither the aerodynamic load nor centrifugal load can be neglected in blade pre-deformation.

A Taylor Series Expansion Approach for Nonlinear Blade Forced Response Prediction Considering Variable Rotational Speed

In the field of turbomachinery, great efforts are made to enhance computational tools to obtain reliable predictions of the vibrational behavior of friction-damped bladed disks. As a trade-off between computational burden and level of simplification, numerous methods were developed to reduce the nonlinear systems dimension. Using component mode synthesis methods (CMS), one is capable to describe the systems motion by interface and modal coordinates. Subsequently or alternatively, the dynamic compliance matrix can be evaluated efficiently by means of modal superposition to avoid the inversion of the dynamic stiffness matrix. Only the equations corresponding to the degrees-of-freedom (DOF) subject to localized nonlinear contact forces need to be solved simultaneously, whereas the solution of the linear DOF is obtained by exploiting the algebraic character of the set of equations. In this paper, an approach is presented to account for rotational speed-dependent stiffness in the subset of nonlinear DOF without the need to re-evaluate the associated eigenvalue problem (EVP) when rotational speed is changed. This is done by means of a Taylor series expansion of the eigenvalues and eigenvectors used for the modal superposition to reconstruct the dynamic compliance matrix. In the context of forced response predictions of friction-damped blisks, the expansion is performed up to different order for a simplified blisk model with nonlinear contact interfaces. The results are compared to the solution obtained by direct evaluation of the EVP at selected rotational speeds and the solution when dynamic compliance matrix is built up by direct inversion of the dynamic stiffness matrix. Finally, the proposed methods computational performance is analyzed.

Comparison of linear and non-linear blade model predictions in Bladed to measurement data from GE 6MW wind turbine

The length and flexibility of wind turbine blades are increasing over time. Typically, the dynamic response of the blades is analysed using linear models of blade deflection, enhanced by various ad-hoc non-linear correction models. For blades undergoing large deflections, the small deflection assumption inherent to linear models becomes less valid. It has previously been demonstrated that linear and nonlinear blade models can show significantly different blade response, particularly for blade torsional deflection, leading to load prediction differences. There is a need to evaluate how load predictions from these two approaches compare to measurement data from the field.In this paper, time domain simulations in turbulent wind are carried out using the aero-elastic code Bladed with linear and non-linear blade deflection models. The turbine blade load and deflection simulation results are compared to measurement data from an onshore prototype of the GE 6MW Haliade turbine, which features 73.5m long LM blades. Both linear and non-linear blade models show a good match to measurement turbine load and blade deflections. Only the blade loads differ significantly between the two models, with other turbine loads not strongly affected. The non-linear blade model gives a better match to the measured blade root flapwise damage equivalent load, suggesting that the flapwise dynamic behaviour is better captured by the non-linear blade model. Conversely, the linear blade model shows a better match to measurements in some areas such as blade edgewise damage equivalent load.

Effect of linear and non-linear blade modelling techniques on simulated fatigue and extreme loads using Bladed

There is a trend in the wind industry towards ever larger and more flexible turbine blades. Blade tip deflections in modern blades now commonly exceed 10% of blade length. Historically, the dynamic response of wind turbine blades has been analysed using linear models of blade deflection which include the assumption of small deflections. For modern flexible blades, this assumption is becoming less valid. In order to continue to simulate dynamic turbine performance accurately, routine use of non-linear models of blade deflection may be required. This can be achieved by representing the blade as a connected series of individual flexible linear bodies - referred to in this paper as the multi-part approach. In this paper, Bladed is used to compare load predictions using single-part and multi-part blade models for several turbines. The study examines the impact on fatigue and extreme loads and blade deflection through reduced sets of load calculations based on IEC 61400-1 ed. 3. Damage equivalent load changes of up to 16% and extreme load changes of up to 29% are observed at some turbine load locations. It is found that there is no general pattern in the loading differences observed between single-part and multi-part blade models. Rather, changes in fatigue and extreme loads with a multi-part blade model depend on the characteristics of the individual turbine and blade. Key underlying causes of damage equivalent load change are identified as differences in edgewise- torsional coupling between the multi-part and single-part models, and increased edgewise rotor mode damping in the multi-part model. Similarly, a causal link is identified between torsional blade dynamics and changes in ultimate load results.

Developing a passive load reduction blade for the DTU 10 MW reference turbine

This paper presents the development of a passive load reduction blade for the DTU 10 MW reference wind turbine, using the aero-hydro-servo-elastic analysis tool 3DFloat. Passive load reduction is achieved by introducing sweep to the path of the blade elastic axis, so that out-of-plane bending deflections result in load alleviating torsional deformations of the blade. Swept blades are designed to yield similar annual energy production as a rotor with a reference straight blade. This is achieved by modifying the aerodynamic twist distribution for swept blades based on non-linear blade deflection under steady state loads. The passive load reduction capability of a blade design is evaluated by running a selection of fatigue- and extreme load cases with the analysis tool 3DFloat and determining equivalent fatigue loads, fatigue damage and extreme loads at the blade root and tower base. The influence of sweep on the flutter speed of a blade design is also investigated. A large number of blade designs are evaluated by varying the parameters defining the sweep path of a blade's elastic axis. Results show that a moderate amount of sweep can effectively reduce equivalent fatigue damage and extreme loads, without significantly reducing the flutter speed, or compromising annual energy production.

Computational modeling of interference between helicopter main and tail rotors based on nonlinear blade vortex model

The Mi-2 helicopter was taken as an example for modeling the main and tail rotors operation with account for the interference at low speed sliding flight. Aerodynamic characteristics were calculated. The form of nonlinear vortical wake was obtained.

Sensitivity of trajectory stability estimated by Lyapunov characteristic exponents

This work discusses the use of Lyapunov characteristic exponents for stability evaluation, and the analytical estimation of their sensitivity to parameters of the problem. The parametric sensitivity of the stability is formulated to provide a methodology for robustness analysis and design of dynamical systems with a complexity level varying from linear time invariant to nonlinear, non-autonomous. Characteristic exponents estimation and the analytical formulation of their sensitivity are based on the discrete QR decomposition method. The proposed methodology is illustrated considering the flapping of a helicopter blade, and helicopter ground resonance with one damper inoperative and with nonlinear blade dampers. Some aspects of characteristic exponents and sensitivity estimation from problems with complex conjugated modes, which are typical of mechanical and aerospace systems, are discussed.

Axial flow compressor blade optimization through flexible shape tuning by means of cooperative co-evolution algorithm and adaptive surrogate model

The present study is to explore potential benefits of axial flow compressor blade optimization through a flexible tuning. Modifications of blade sectional profiles and their stacking line can control spanwise blade loading distribution, reduce shock losses, and extend operating flow range. Most previous studies focused on tuning either sectional profiles or stacking line, but little work was conducted by collaboratively varying both, which may be due to abrupt rise of optimization variables and complexity. An efficient optimization method is developed to handle highly nonlinear high-dimension blade optimization problem with simultaneous variation of both sectional profiles and stacking line. It incorporates an improved cooperative co-evolution algorithm optimizer and one-stage expected improvement based adaptive surrogate model. The former decomposes the high-dimension problem into low-dimension subproblems and they can be readily solved; the latter enables the optimizer to jump out of the local minima and conduct the aim-oriented optimal search toward global optimum. A coarse surrogate model is firstly constructed with some DOE samples but it is refined during optimization process with newly identified and evaluated samples. The model prediction accuracy is gradually improved, thus it captures the distinct features (especially global optimum) of optimization problem. Both blade sectional profiles and their spatial positions are simultaneously varied. Four sectional profiles of hub, 33% span, 67% span, and shroud are parameterized, and each is defined by a mean camber line and thickness distribution. Both of them are represented, respectively, by a third-order B-Spline curve. Spatial position of each profile varies in term of sweep and lean. Blade design optimization is conducted for Rotor67 at design flow on a single workstation of Dell 7500. Performance gains are significant: at design flow, overall efficiency and pressure ratio are increased, respectively, by 1.44 and 7.24%; off-design performances are also improved over the entire flow range.