Blade Flutter Research Articles

Mathematical Modeling of the Coaxial Quadrotor Dynamics for Its Attitude and Altitude Control

In this paper, an easily implementable coaxial quadrotor model and its validation on data from a real unmanned aerial vehicle (UAV), are presented. The proposed mathematical model consists of two parts: description of orientation and position of the UAV in the three-dimensional space. It takes into consideration the gyroscopic effect, influence of the Coriolis force, viscous friction and a several drag-like effects (blade flapping, rotor drag, translational drag and profile drag). In contrast to multirotor models available in the literature, this one is characterized by complementarity in relation to the available control techniques. Depending on selection of these techniques, the model can be narrowed (simplified) to meet the needs without the loss of behaviour adequacy to a real UAV.

Development of a fully-coupled harmonic balance method and a refined energy method for the computation of flutter-induced Limit Cycle Oscillations of bladed disks with nonlinear friction contacts

Flutter stability is a dominant design constraint of modern gas and steam turbines. To further increase the feasible design space, flutter-tolerant designs are currently explored, which may undergo Limit Cycle Oscillations (LCOs) of acceptable, yet not vanishing, level. Bounded self-excited oscillations are a priori a nonlinear phenomenon, and can thus only be explained by nonlinear interactions such as dry stick–slip friction in mechanical joints. The currently available simulation methods for blade flutter account for nonlinear interactions, at most, in only one domain, the structure or the fluid, and assume the behavior in the other domain as linear. In this work, we develop a fully-coupled nonlinear frequency domain method which is capable of resolving nonlinear flow and structural effects. We demonstrate the computational performance of this method for a state-of-the-art aeroelastic model of a shrouded turbine blade row. Besides simulating limit cycles, we predict, for the first time, the phenomenon of nonlinear instability, i.e., a situation where the equilibrium point is locally stable, but for sufficiently strong perturbation (caused e.g.by an impact), the dry frictional dissipation cannot bound the flutter vibrations. This implies that linearized theory does not necessary lead to a conservative design of turbine blades. We show that this phenomenon is due to the nonlinear contact interactions at the tip shrouds, which cause a change of the vibrational deflection shape and frequency, which in turn leads to a loss of aeroelastic stability. Finally, we extend the well-known energy method to capture these effects, and conclude that it provides a good approximation and is useful for initializing the fully-coupled solver.

Verification tests of a new blade flutter research facility

Long term strategic changes in power generation approaches will require more flexibility for large power generating turbines as an unavoidable consequence of the increasing share of power generated by alternative energy sources. Demanded flexibility for the power turbine output will augment undesired flow phenomena in the low-pressure turbine module, which will consequently enhance blade flutter problems of long slender blades in turbine last stages. In order to advance the understanding of blade flutter onset conditions, the Institute of Thermomechanics of the Czech Academy of Sciences instigated an advanced research program on blade flutter research in high-speed turbomachines. A new innovative test facility for Blade Forced Flutter research was designed and built in the High-Speed Laboratory of the Institute of Thermomechanics. The concept of the new test facility is based on extensive experience with an older Transonic Flutter Cascade facility operated at the NASA Glenn Research Center in Cleveland, Ohio. At present, the first phase of verification tests of the new facility is in progress. The ongoing steady-state tests are intended for exploration of a newly proposed quasi-stationary method to investigate instigating flow conditions leading to an onset of intense blade flutter. Results of some opening tests under steady flow conditions are presented in the paper. The blade drive mechanism for unsteady tests with oscillating blades has not yet been installed in the facility. The presented paper is a work-in-progress report on the ongoing research of complex blade flutter problems.

Flutter analysis of mistuned bladed disks (Effect of bladed disk structure on flutter characteristics)

Although bladed disks are nominally designed to be cyclically symmetric (tuned system), the vibration characteristics of all the blades on a disk are slightly different due to the manufacturing tolerance, deviations in the material properties, and wear during operation. These small variations break the cyclic symmetry and split the eigenvalue pairs. Bladed disks with small variations are referred to as a mistuned system. In the forced response of a mistuned bladed disk, the responses of all the blades become different, and the response of a certain blade may become extremely large due to splitting of the duplicated eigenvalues and distortion of the vibration modes. On the other hand, many researchers suggest that mistuning suppresses blade flutter, because the complete traveling wave mode is not formed in a disk. In the previous paper, authors studied the forced response of the mistuned bladed disk, using the reduced order model SNM (Subset of Nominal system Modes), and clarified that the effect of the bladed disk structure on the amplification factor. This work is a follow-up study on the previous paper. The stability analyses of mistuned bladed disks with the free-standing blade structure and the continuous ring-blade structure are carried out extensively, using the reduced order model SNM. Comparing the results of the stability analyses of mistuned bladed disks, the effect of the bladed disk structure on the blade flutter is clarified.

Flutter suppression of wind turbine blade based on nonlinear block backstepping control

Aiming at solving the nonlinear flutter problem of aeroelastic system of wind turbine blades, a controller combing block backstepping control and variable pitch motion was designed. Based on the typical blade-section model of the spring-mass-damper and the second-order model of the pitch actuator, nonlinear aeroelastic equation of the system under steady aerodynamic was given. Considering the multivariable, strong coupling factors and the unitary pitch control of the wind turbine blade aeroelastic system, a state space equation for a single-input/multiple-output nonlinear model was deduced. Based on the principle of block control, a nonlinear system with block control standard was obtained, which was composed of two subsystems. In order to suppress blade flutter and protect the blade, backstepping control was used to control blade pitch motion. The nonlinear block backstepping controller was designed by constructing Lyapunov function, and time response which can track the dynamic error of system was demonstrated. The simulation results showed that the designed controller can converge the divergent chattering trend to zero, and make the system globally stable.

Modeling transient vibration-sound generation processes

In this paper, a problem of sound generation of two-blade rotor sinusoidal shape during helicopter landing is solved. Near and far sound field characteristics have been calculated. A comparative analysis of obtained numerical results with results for Mach number 0.2<M<0.4 is given. In particular noticed, that for a low Mach’s number M<0.1 transitional mode can occurs, which produces a blade flutter as a result.

The dynamic response of offshore wind turbines and their sensitivity to wind field models

As the rotor diameter of offshore wind turbines increases, an improved understanding of the structure of the turbulent wind field approaching the rotor is important. Present standards for computing wind loads are resting upon assumptions of neutral atmospheric conditions and a simplistic formulation of the coherence of the turbulence. In the present work, various formulations of the wind field are applied and the dynamic responses of a bottom fixed and a floating wind turbine are computed to investigate the sensitivity to the formulation of the wind field. Focus is on wind situations with above average turbulence intensity as these are expected to have a significant contribution to fatigue damage of the structure. It is observed that choice of wind spectrum, coherence formulation as well as assumptions related to atmospheric stability conditions significantly influences the dynamic loads in tower bending moment, yaw moment and blade flap moment. The differences are significant in particular in the low frequency range. This implies that in particular floaters are sensitive to the formulation of the wind field.

Investigation of Linear Higher Harmonic Control Algorithm for Rotorcraft Vibration Reduction

Abstract A linear quadratic Gaussian (LQG) controller for active vibratory loads reduction in helicopters is proposed based on a revisited higher harmonic control (HHC) input by active trailing-edge flaps (ATEFs). Conventional individual blade control (IBC) input is redefined using N − 1/rev interblade phase lead, N/rev collective, and N + 1/rev interblade phase lag signals where 1/rev frequency modulation originates from the multiblade coordinate (MBC) transform. A Mach-scaled flap blade is designed and analyzed by the multibody dynamics analysis DYMORE. A linear time-invariant representation is identified from N/rev envelopes of the input and output responses obtained by DYMORE analysis. A matlab/simulink closed-loop control simulation is designed using the identified state-space realization. The N/rev vibratory loads are reduced up to 52% with flap deflections and the linear control results match well with the nonlinear responses obtained from DYMORE. Furthermore, the multivariable closed-loop stability estimated by the loop transfer functions using disk margin analysis reveals sufficient gain and phase margins.

Numerical simulations of flutter mechanism for high-speed wide-chord transonic fan

Flutter is a self-excited aeroelastic instability phenomenon that can cause blade failure and lead to safety accidents. This paper investigates the first bending mode flutter behavior of a high-speed wide-chord transonic fan under different operating conditions. The aim is to reveal the relationship between the flow structure and blade flutter stability at different inter-blade phase angles (IBPA). Two methods are used to model the traveling wave propagation along the circumferential direction: the influence coefficient method (ICM) and the traveling wave method (TWM). The former is used to calculate the aerodynamic damping at different IBPA with fewer computational resources, and the latter is used to analyze the relationship between the flow and flutter stability. The results suggest that the most unstable behaviors occur with two nodal diameters (ND) at three representative conditions: near stall, peak efficiency, and choke. The aerodynamic damping distribution of the blade surface is concentrated primarily at the shock wave, separation, and large vibration amplitude regions, whose effects on the blade flutter stability are greatly impacted by the IBPA. When the blade IBPA is small and positive, the shock and separation areas in the suction side reduce the blade flutter stability. This shows that the IBPA strongly affects the unsteady pressure fluctuations, including the direction and shape of the pressure wave propagation, and whether the unsteady pressure can propagate downstream (cut-on) and result in different aerodynamic damping distributions on the blade surface.

Structural damping sensitivity affecting the flutter performance of a 10-MW offshore wind turbine

Classical flutter of wind turbine blades is one of the most destructive instability phenomena of wind turbines especially for several-MW-scale turbines. In the present work, flutter performance of the DTU 10-MW offshore wind turbine is investigated using a 907-degree-of-freedom aero-hydro-servo-elastic wind turbine model. This model involves the couplings between tower, blades and drivetrain vibrations. Furthermore, the three-dimensional aerodynamic effects on wind turbine blade tip have also been considered through the blade element momentum theory with Bak’s stall delay model and Shen’s tip loss correction model. Numerical simulations have been carried out using data calibrated to the referential DTU 10-MW offshore wind turbine. Comparison of the aeroelastic responses between the onshore and offshore wind turbines is made. Effect of structural damping on the flutter speed of this 10-MW offshore wind turbine is investigated. Results show that the damping in the torsional mode has predominant impact on the flutter limits in comparison with that in the bending mode. Furthermore, for shallow water offshore wind turbines, hydrodynamic loads have small effects on its aeroelastic response.

Design improvement of flapping hydrokinetic turbines

This investigation deals with the flow control and the enhancement of the output power of a flapping foil turbine. The connected gurney flap (GF) is a small arc that oscillates with a given pitching angle. The incompressible laminar flow around a simple flat plate equipped with an oscillating gurney flap is solved using a computational method. A user-defined function and a coupled layering/sliding dynamic mesh technique available in ANSYS FLUENT.15 are used to adjust both the blade and the flap positions during the turbine flapping cycle. It was shown that an appropriate synchronization between the flap oscillation and the turbine blade rotation could modify the blade flap camber, which corrects, in turn, the pressure distribution and therefore boosts the lift force during both the up-stroke and down-stroke stages. The application of this strategy of control enhances the output power dramatically compared with a clean flapping turbine blade.

Validation Studies of Linear Oscillating Compressor Cascade and Use of Influence Coefficient Method

Abstract Advanced predictions of blade flutter have been continually pursued. It is noted however that validation cases of unsteady CFD methods against experimental cases with detailed 3D unsteady pressures are still rather lacking. The main objectives of the present work are two-folds. First, validate and understand the characteristics of blade tip clearance, as well as a bubble-type flow separation for an unsteady CFD solver against a 3D oscillating cascade experiment. And second, examine the applicability of the influence coefficient method (ICM) as widely used in an oscillating linear cascade setup. In the first part, the capability of a widely used commercial solver (CFX) for unsteady flows induced by a 3D oscillating compressor cascade is examined. The present computations have shown consistently a destabilizing effect of increasing blade tip clearance, in agreement with the experiment. More remarkably, the computational analyses reveal a distinctive interplay between the inlet endwall boundary layer and the tip clearance in relation to the aerodynamic damping. Different inlet endwall boundary layer thicknesses are shown to lead to qualitatively different aeroelastic stability characteristics in relation to tip clearance. The aero-damping variation with the tip clearance under the influence of the inlet endwall boundary layer seems to correlate closely to a balancing act between the passage vortex and the tip leakage vortex. The tip clearance aeroelastic behavior seems also in line with a simple quasi-steady analysis. On the other hand, the mid-chord laminar bubble separation on suction surface, though with a clear signature in the local aero-damping, has negligible effects on the overall stability. The second part aims to examine computationally the applicability of the influence coefficient method in a linear cascade setup. The comparison between the cascade-based ICM data and a baseline “tuned cascade” shows that the differences in the sensitivity to the far-field treatment can be significant, depending on inter-blade phase angles. On the other hand, non-linearity effects closely relevant to the basic linear assumption of the ICM are shown to only have a small influence. The present results suggest that extra caution should be exercised when comparing a CFD-based tuned cascade model with a finite cascade-based ICM model, at conditions close to acoustic resonance. The resultant discrepancies may well arise from the inherently different far-field sensitivities between the two models, rather than those typical numerical and physical modeling aspects of interest (e.g., meshing, spatial and temporal discretization errors as well as turbulence modeling).

Improved Aerodynamic Analysis for Multirotor-Type UAS Flight Simulation Using Dynamic Inflow and Rigid Blade Flapping

AbstractRecently, studies on the control and aerodynamics of multirotor unmanned aircraft system (UAS) have been performed. However, some studies depend on methods that require significant computin...

Geometric Attitude and Position Control of a Quadrotor in Wind

This paper addresses flight stability and performance in wind of a quadrotor equipped with custom flow probes that measure the wind velocity. Wind-velocity measurements are used in the attitude and position control through the use of principled models that estimate the aerodynamic forces and moments. The aerodynamic moment is caused primarily by propeller blade flapping, whereas the aerodynamic force includes the induced drag from the rotors and drag over the body. A feedback-linearization controller prescribes inputs based on the aerodynamic models and quadrotor kinematics, which are developed on the special Euclidean group. The controller also addresses the thrust saturation using a variable-gain algorithm. Simulated and experimental results highlight the benefits of flow feedback and the variable-gain algorithm for the inner- and outer-loop control of attitude and position, respectively.

The influence of design parameters on the blade flutter boundaries

Blade flutter is one of the major problems that designers of modern gas-turbine engines face. In this paper, a study of the influence of the design parameters on prediction of blade flutter in compressors of gas-turbine engines is presented. As a rule, the flutter of compressor blades is predicted using simplified criteria based on the experience of designing and refining engines. These empirical and probabilistic criteria are not applicable to evaluation of the flutter since the parameters in question are not among the decisive parameters for simplified criteria. In this work, the energy method is used. It is shown that the inter-blade tension value has a significant influence on the blade flutter prediction, while the effect of other design parameters under investigation on the blade flutter prediction is insignificant.

Estimation of Wind Conditions Utilizing RC Helicopter Dynamics

This paper investigates the applicability of a remote-controlled (RC) helicopter as a sensing platform for measuring local wind conditions. A simplified nonlinear multibody helicopter dynamics model has been proposed in this paper, which models local wind conditions in addition to capturing essential helicopter states such as fuselage dynamics, rotor inflow, blade flapping, and lead lagging. The critical aerodynamic parameters for the model were extracted using indoor calibration flights. This paper also presents the performance of particle swarm optimization in optimizing and validating the helicopter's dynamic model parameters. An in-house developed multisensor instrumentation system was used to track the helicopter dynamics and extract wind model parameters through anomalies in the helicopter dynamics estimates. A three-dimensional (3-D) map of local wind conditions was generated for a controlled turbulent wind environment created in an indoor test facility. To validate the system's performance, wind parameters estimated from the proposed system were quantitatively compared against the experimentally generated 3-D wind map.

FEATURES OF MODELING THE FLOW AROUND THE HELICOPTER MAIN ROTOR TAKING INTO ACCOUNT ARBITRARY BLADES MOTION

The article considers the problem of the flow around the helicopter main rotor taking into account blades flapping in the plane of rotation and in the plane of thrust as well as the elastic blades deformation. The rotor rotation is modeled by the method of converting Navier-Stokes equations from a fixed coordinate system associated with the incoming flow into a rotating system associated with the rotor hub. For axial flow problems, this makes it possible to formulate the problem as stationary at a constant rotational speed of rotor. For a mode of skewed flow around the rotor in the terms of incident flow in this system it is necessary to solve the non-stationary problem. To solve the problem, the method of deformable grids is used, in which the equations are copied taking into account the grid nodes motion determined in accordance with the spatial blades motion, and SST turbulence model is used for closure. The results of the test calculations of the main rotor aerodynamic characteristics with and without blade flapping are presented in this paper. The coefficients of the main rotor thrust cT and the blades hinge moments mh are compared. The calculations were carried out in the CFD software ANSYS CFX (TsAGI License No. 501024). The flow around a four-bladed main rotor of a radius of 2.5 meters is modeled in the regime of skewed flow. The speed of the incoming flow came to 85 m/s under normal atmospheric conditions. The rotor was at an angle of attack of −10˚. To calculate the rotor motion without taking into account the flapping movements, we used the nonstationary system of Navier-Stokes equations with the closure with SST turbulence model. The calculation was being carried out until the change in the maximum value of the rotor thrust during one revolution became less than 1%. For modeling flapping blade movements, the control laws and equations describing the angle of blade flapping as a function from its azimuth angle obtained from the experiment were used. The procedure for reconstructing the grid according to a given law was conducted using standard grid deformation methods presented in the ANSYS CFX software. When solving the nonstationary Navier-Stokes equations, a dual time step was used. The obtained results show that accounting of the effect of flapping movements and cyclic control of the blades has an impact on the character of changing the main rotor thrust coefficient during one revolution and significantly changes the shape of the graph of the hinge moment coefficient of each blade.

Detached-Eddy Simulation Applied to Aeroelastic Stability Analysis in a Last-Stage Steam Turbine Blade

Blade flutter in the last stage is an important design consideration for the manufacturers of steam turbines. Therefore, the accurate prediction method for blade flutter is critical. Since the majority of aerodynamic work contributing to flutter is done near the blade tip, resolving the tip leakage flow can increase the accuracy of flutter predictions. The previous research has shown that the induced vortices in the tip region can have a significant influence on the flow field near the tip. The structure of induced vortices due to the tip leakage vortex cannot be resolved by unsteady Reynolds-averaged Navier–Stokes (URANS) simulations because of the high dissipation in turbulence models. To the best of author’s knowledge, the influence of induced vortices on flutter characteristics has not been investigated. In this paper, the results of detached-eddy simulation (DES) and URANS flutter simulations of a realistic-scale last-stage steam turbine are presented, and the influence of induced vortices on the flutter stability has been investigated. Significant differences for the predicted aerodynamic work coefficient distribution on the blade surface, especially on the rear half of the blade suction side near the tip, are observed. At the least stable interblade phase angle (IBPA), the induced vortices show a destabilizing effect on the blade aeroelastic stability. The motion of induced vortices during blade oscillation is dependent on the blade amplitude, and hence, the aerodynamic damping is also dependent on the blade vibration amplitude. In conclusion, the induced vortices can influence the predicted flutter characteristics of the steam turbine test case.

Influence of the Tip Clearance on the Aeroelastic Characteristics of a Last Stage Steam Turbine

In this paper, the tip clearance effects on the aeroelastic stability of a last-stage steam turbine model are investigated. Most of the unsteady aerodynamic work contributing to flutter of the long blades of the last-stage of a steam turbine is done near the tip of the blade. The flow in this region is transonic and sensitive to geometric parameters such as the tip clearance height. The KTH Steam Turbine Flutter Test Case was chosen as the test case, which is an open geometry with similar parameters to modern free-standing last-stage steam turbines. The energy method based on 3D URANS simulation was applied to investigate the flutter characteristics of the rotor blade with five tip gap height varying from 0–5% of the chord length. The numerical results show that the global aerodynamic damping for the least stable inter-blade phase angle (IBPA) increases with the tip gap height. Three physical mechanisms are found to cause this phenomenon. The primary cause of the variation in total aerodynamic damping is the interaction between tip clearance vortex and the trailing edge shock from the adjacent blade. Another mechanism is the acceleration of the flow near the aft side of the suction surface in the tip region due to the well-developed tip leakage vortex when the tip clearance height is greater than 2.5% of chord. This causes a stabilizing effect at the least stable IBPA. The third mechanism is the oscillation of the tip leakage vortex due to the blade vibration. This has a negative influence on the aeroelastic stability.

Numerical Investigation of the Effect of Design Parameters on the Blade Flutterr Prediction

Blade flutter is one of the major problems that designers of modern gas-turbine engines face. As a rule, the flutter of compressor blades is predicted using simplified criteria devised in design organizations based on the experience of designing and refining engines. In this paper a study of the influence of the design parameters on prediction of blade flutter in compressors of gas-turbine engines is presented. Empirical and probabilistic criteria are not applicable to evaluation of the flutter since the parameters in question are not among the decisive parameters for simplified criteria. In this work, a numerical algorithm for prediction of the flutter based on the energy method is used. The algorithm is applicable if the oscillation modes in vacuum are close to the corresponding modes in a flow, a condition that is always met for compressor blades, with the exception of rarely used hollow blades and blades of composite materials. It is shown that the inter-blade tension has a significant influence on the flutter boundaries, while the effect of other design parameters under investigation on the flutter boundaries is insignificant.