Blade Oscillation Research Articles

Aerodynamic Analysis of Blade Stall Flutter Prediction for Transonic Compressor Using Energy Method

In this study, stall flutter onset prediction in a transonic compressor is carried out using the (uncoupled) energy method with Fourier transform. As the study is conducted computationally using computational fluid dynamics (CFD)-based simulations, the energy method was employed due to its higher computational efficiency by implementing the one-way FSI (Fluid Structure Interaction) model. The energy method is relatively uncommon for determining the aerodynamic damping and flutter prediction, specifically in blade stall conditions for the 3D blade passages. The NASA Rotor 67 was chosen for the validation of the study due to the availability of a wide range of experimental data. A flutter prediction analysis was performed computationally using CFD for the two-blade passages of the rotor in the peak efficiency and stall regions. Prior to this, the modal analysis on the prestressed blade was conducted, considering the centrifugal effects. The modal analysis provided accurate blade frequency and amplitude, which were the inputs of the flutter analysis. The first three modes of blade resonance were studied with a range of nodal diameters within near-peak efficiency and stall regions. The energy method implemented in this study for the flutter analysis was successfully able to predict the aerodynamic damping coefficients of the first three modes for a range of nodal diameters from the periodic-unsteady solution of the defined blade oscillation within the regions of interest (peak efficiency and stall point). The results of the study confirm the rotor blade’s stability within the near-peak region and, most importantly, the prediction of the flutter onset in the stall region. The study concluded that the computationally inexpensive and time-efficient energy method is capable of predicting the stall flutter onset. In the future, further validations of the energy method and investigations related to flow mechanism of stall flutter onset are planned.

Effect of Blade Material of Steam Turbine Rotor on Aeroelastic Characteristics

Elements of powerful steam turbines are subjected to significant unsteady loads, in particular the rotor blades of the last stages. These loads, in some cases, can cause self-excited oscillations, which are extremely dangerous and have a negative impact on the efficiency and service life of the blade cascade. Therefore, when designing new or modernizing existing steam turbine stages, it is recommended to study the aeroelastic characteristics of the blades. The conditions for the occurrence of self-excited oscillations are influenced by both the geometric characteristics and the alloy from which the blade is made. To determine the effect of the blade material on the aeroelastic behaviour, a numerical analysis of the aeroelastic characteristics of the last stage blades made of steel and titanium alloy was performed. For the analysis, the method of simultaneous modeling of unsteady gas flow through the blade cascades and elastic vibrations of the blades (coupled problem) was used, which allows obtaining the amplitude-frequency spectrum of the interaction of unsteady loads and blade vibrations. The paper presents the results of numerical analysis for harmonic oscillations with a given amplitude and a given inter-blade phase angle, as well as for the regime of coupled vibration of blades under the action of unsteady aerodynamic forces. The dependences of the aerodamping coefficient on the inter-blade phase angle and the distribution of the coefficient along the blade are presented. The results of modeling the coupled vibration of the blades for the first six natural forms are presented in the form of a time-evolving displacement of the blade peripheral section, as well as forces and moments acting on the peripheral section. The corresponding amplitude-frequency spectra of displacements and loads in the peripheral section are also presented. The analysis of the results showed an insignificant difference in the characteristics of the proposed blade materials. For the first natural form of blade oscillations, the possibility of self-excited oscillations was found, and for the second form, there are conditions for the appearance of stable self-oscillations.

Role of periodic oscillating flow modulators on mixed convection in a long horizontal channel

Present study explores mixed convection characteristics in a long horizontal channel subjected to multiple periodically distributed flow modulators. The flow modulators are represented by oscillating blades placed along a centerline of the channel whose lower and upper walls are kept at constant high and low temperatures respectively. In replicating the blade oscillation, moving mesh approach has been adopted within Arbitrary Lagrangian–Eulerian (ALE) framework for a representative periodical unit. The corresponding non-dimensional governing mass, momentum and energy conservation equations have been solved through Galerkin finite element solver for a wide variations of modulator's dynamic condition (oscillating frequency and maximum angular displacement) for different fluids represented by Prandtl number. Heat transfer performance of the system has been demonstrated in terms of spatially-averaged transient as well as time-averaged Nusselt number while qualitative analysis of fluid flow and thermal field has been presented as streamline and isotherm plots. Present study indicates that the time averaged Nusselt number undergoes significant variation with blade oscillating frequency and maximum angular displacement depending on both the Prandtl number and Reynolds Number. Power spectrum analysis obtained through Fast Fourier Transformation (FFT) of the imposed blade frequency and induced thermal frequency reveals different correlation depending on the blade frequency. Blade friction power requirement has been found to increase at higher blade frequency as well as maximum angular displacement. However, contrary to power consumption, increase in frequency does not result in a significant rise in heat transfer. Consequently, specific heat transfer decreases at higher blade oscillating frequency and maximum angular displacement.

Визначення власних частот та форм коливань лопатки турбіни, виготовленої зі сплаву на основі алюмініду титану

This paper investigates the possibility of manufacturing the working blade of the 2nd stage of the free turbine from an experimental alloy based on titanium aluminide of the Ti-28Al-7Nb-2Mo-0.3 (Y, Re, B) system. Alloys of this class are important structural materials with a unique set of physical and mechanical characteristics. Alloys based on aluminide are characterized by low density, high heat strength, and heat resistance and have a high potential to replace nickel-based alloys designed for operation at temperatures no higher than 850°C. However, the use of a new alloy for the manufacture of a turbine blade involves calculations of the strength and oscillations of the blades. The purpose of the calculations is to determine the possibility of using an aluminide-based alloy of the Ti-28Al-7Nb-2Mo-0.3 (Y, Re, B) system instead of the VZHL12E-VI alloy for the selected working blade. The research was carried out by performing a modal analysis, determining the stress-deformed state, and checking the strength and mass characteristics. The physical properties of the materials were used as the initial data for the calculation. The geometry and temperature distribution of the blade and its fixing remained constant for the two options. A three-dimensional model of the experimental vane was built using the Unigraphics NX system, and a finite element model was developed using the Ansys software complex. It was established that when an experimental alloy is used, the mass of one blade is reduced by almost 40%. Using the finite element method, the natural frequencies and forms of blade oscillations were calculated, and Campbell’s diagrams were constructed for the original and experimental blades for the nominal operation of the engine. When using an experimental alloy, the frequencies of the blades’ natural oscillations are further from the resonant frequency. The distribution of equivalent stresses was determined, and it was shown that the maximum stresses act in the root section of the blade feather. When using the experimental alloy based on titanium aluminide, the equivalent stresses are reduced by 35% compared with the initial values. It is shown that the safety margin of the proposed material is not less than that of the VZHL12E-VI alloy.

UHBR Open-Test Case Fan ECL5/CATANA: Non-Linear Analysis of Non-Synchronous Blade Vibration at Part-Speed Conditions

Abstract The onset of non-synchronous vibrations has been predicted for a composite open-test-case UHBR fan geometry by time-linearized simulations at part-speed conditions. In the current study, time-accurate simulations with harmonic blade oscillations have been conducted to investigate the non-linear behavior. Results for different operating conditions show the evolution of aeroelastic stability. The lock-in of convected aerodynamic disturbances with structural vibration is analyzed for different vibration amplitudes and frequencies. The simulations show the development of multiple wave numbers, mode scattering, and a non-linear dependency on vibration amplitude. The results indicate the possibility of limit-cycle prediction and the necessity of strongly coupled methods for the assessment of non-synchronous vibration.

Active Edgewise Blade Damping Control of Large Wind Turbines by Using the Pitch Controller and an Interval Observer

Large wind turbines have typically poorly damped structures. Hence, the absence of damping leads to aeroelastic oscillations, and the operational rotor speed can approach the critical rotor speed. By using damping injection, the control system can actively introduce some additional damping. In the present work, a control approach to reduce oscillations of the rotor blades in the edgewise direction is proposed. The concept is based on the damping injection mechanism, and an additional level of safety is obtained by introducing the Dynamic Safety Margin (DSM) in the control law. The feedback control scheme requires some unmeasurable variables. This aspect is covered by using an interval observer. The control approach is tested by using simulations on a high-definition model implemented in an aeroservoelastic code. Simulation results are very satisfactory and promising for future experiments using hardware-in-the-loop equipment.

Numerical analysis of the performance of a composite marine propeller blade subject to structural blade oscillations

High-fidelity Large Eddy Simulations (LES) are conducted over the oscillating marine propeller blades to investigate the effects of blade oscillation on the unsteady flow behaviour as well as to analyse the performance of the composite marine propeller blades. The accuracy of the results is first verified against the reference experimental results. A nonlinear frequency-domain solution or harmonic solution method is also applied to this study, based on a high-fidelity LES model, in addition to the traditional time-domain solution method to investigate the capabilities of the frequency-domain method in predicting the unsteady flow parameters, vortex generation, and hydrodynamic damping to determine the stability of the propeller blades. Results obtained reveal that the oscillation of the blade has a great impact on the vortex generation process which could impose implications on the performance and structural integrity of the composite marine propeller blades.

Методика оцінки залежності власних частот коливань лопаток газових турбін від анізотропії монокристалу

The subject of study of this article is one of the key tasks that arises during the development and operation of aviation gas turbine engines, namely ensuring the strength of their parts. The turbine blade is one of the most heavily loaded parts of an aircraft engine. Therefore, at the stage of designing these blades, it is necessary to be able to identify and avoid possible resonance modes that appear during the flight cycle of an aircraft gas turbine engine. Such resonant oscillations of gas turbine blades can occur due to time-varying gas-dynamic forces from the action of the gas flow and are periodic in nature, as they are determined by the frequency of rotation of the rotor. In order to regulate the frequency characteristics of the blades to prevent dangerous resonant forms of oscillations that arise under the action of various harmonics of the exciting force during variable modes of operation of the aircraft engine, it is necessary to carry out a complex of various technological or structural changes. At the current stage, turbine blades of aircraft engines are manufactured by the method of single-crystal casting. As is known, single crystals have anisotropic properties, namely they manifest themselves as materials with the characteristics of cubic symmetry. A very urgent task is to investigate the effect of the anisotropy of the elastic characteristics of monocrystalline blades on their natural frequencies and forms of oscillations. In this research, the authors developed a method for determining the elastic characteristics of a single crystal, namely Young's modulus of elasticity, Poisson's ratio and pure shear modulus, which is based on available experimental data for typical heat-resistant alloys. With the help of finite element analysis on the example of a typical model of a cooled blade of a gas turbine, its modal analysis was carried out and its resonance diagram was constructed. The trend of changing the natural frequencies and forms of blade oscillations when the elastic constants of the single crystal change due to the rotation of the crystallographic system of directions was also investigated. The three-dimensional model of the blade was built using the capabilities of the NX graphics complex, all calculations were performed in the Maple computing complex, and the capabilities of the ANSYS software complex were used for finite element analysis.

Effect of Adjacent Blade Oscillation on the Forces on A Blade of a Compressor Cascade

The current trend of aircraft engines is one towards attaining high isentropic efficiency while minimizing its weight. This leads to a state where the blades are highly loaded and consequently susceptible to vibrations. High cycle fatigue caused as a result of such self-excited flutter or forced vibration due to defects in the air stream are detrimental to the engine. An understanding of the onset of instabilities is essential to predict their occurrences to avoid a catastrophic failure during operation or costly redesign during the development phase. The critical parameters in turbomachine aeroelasticity are the reduced frequency and the interblade phase angle. The damping of the system is known to be a function of the phase difference between the blade forces and the blade motion. In the present study, a linear cascade of five blades is considered to understand the effect of harmonically varying boundary conditions. The second and fourth blades of the cascade are subjected to torsional oscillation by an external mechanism. The third blade, considered as the reference, is stationary and instrumented. The unsteady pressure along the reference blade surface is measured simultaneously with the loads acting on the blade. The unsteady pressures are measured using a multi-sensor pressure scanner by multiplexing and the loads are measured using a five-channel strain gage balance. The blade displacement is determined from the integrated accelerometer signal mounted on an oscillating blade. The experiments are conducted at a low-subsonic speed and multiple oscillation frequencies. The cascade is set at zero incidence and four stagger angles. The effect of inter-blade phase angle is included as the oscillation of the walls adjacent to the reference blade. The phase difference between the harmonic motion of the neighboring walls and the pressure and load signals on the reference blade is related to the damping characteristics of the reference blade. The variation in damping is studied for the range of blade motion phase difference angles and reduced frequencies. The effect of the phase difference between the oscillating blades is seen to strongly affect the damping characteristics of the reference airfoil.

Laser triangulation measurement of blade oscillation in a transonic compressor cascade

The paper describes a method for optical measurement of oscillation of blades in a linear cascade designed for flutter research. The method uses laser triangulation, which measures the distance between the sensor and the oscillation object. The distance can be recalculated to angular displacement of the blade. However, the relation is nonlinear due to the curvature of the blade. The nonlinear dependence between the distance and angular displacement is derived and quantified analytically. The paper further analyzes the influence of light refraction in the optical window, surface quality and sensor inclination. A procedure for the nonlinear calibration is proposed and used during wind tunnel measurements in a blade cascade with forced oscillation of the middle blade.

Aeroelastic Characteristics of Rotor Blades of Last Stage of a Powerful Steam Turbine

Blades of powerful steam turbines are subjected to significant unsteady loads, which, in some cases, can lead to the appearance of self-excited oscillations or auto-oscillations. These fluctuations are extremely dangerous and negatively affect the life time of the blading. When developing new or upgrading existing turbine stages, it is necessary to carry out research on the aeroelastic behavior of the rotor blades. As a result of the modernization of a low-pressure cylinder of a 1000 MW steam turbine, the length of the rotor blades of the last stage increased to 1650 mm. In this regard, a numerical analysis of the aeroelastic characteristics of the last-stage rotor blades in the nominal operation mode was carried out. The analysis used the method of solving the coupled problem of unsteady aerodynamics and elastic blade vibrations, which allows the prediction of the amplitude-frequency spectrum of unsteady loads and blade vibrations in a viscous gas flow. The paper presents the results of numerical analysis of aeroelastic characteristics of the last stage rotor blades both for the mode of controlled harmonic oscillations with a given amplitude and inter-blade phase shift, and for the mode of coupled oscillations of the blades under influence of unsteady aerodynamic forces. The results of the simulation of coupled oscillations of blades for the first five natural forms are presented in the form of the time distribution of displacement of the blade peripheral cross-section, as well as the time distribution of forces and moments acting on the peripheral cross-section. The corresponding amplitude-frequency spectra of displacements and loads in the peripheral section are also given. The results of the calculations showed a positive damping of oscillations, the absence of flutter and auto-oscillations for the first five natural forms of oscillations of the blades in the nominal operation mode of the steam turbine

An Increase in the Energy Efficiency of Axial Turbines by Ensuring Vibration Reliability of Blade Milling

Ensuring the vibration reliability of power equipment is one of the fundamental problems in modern power machinery. This problem has become more critical due to a permanent increase in the machining performance of high-speed milling of axial turbine blades. This article aims to identify reliable vibration parameters for high-speed milling of turbine blades to increase the energy efficiency of gas and steam turbines. For this purpose, mathematical models of free and forced oscillations of turbine blades during machining were developed. As a result of considering experimental and finite element analysis data, critical frequencies and corresponding mode shapes of free oscillations were identified using regression procedures by the best fit of analytical and empirical approaches. Additionally, after considering the forced oscillations of blades during high-speed machining, the magnitude of the specific cutting force and external damping ratio in the system ‘axial turbine blade and milling head’ were evaluated. The resulting magnitude of forced oscillations during machining was calculated. Finally, the amplitude–frequency response was also assessed, considering the machining parameters. Overall, the proposed methodology increases energy efficiency due to a decrease in the obtained machining quality of turbine blades.

Aeroelastic Behavior of Long Blades of Last Stage of a 220 MW Steam Turbine

The phenomenon of flutter in steam turbines is quite rare, but when it occurs, the risk of damaging the blades and putting the whole unit out of service increases significantly. Currently, there is a tendency to increase the length of the blades of the last stages of powerful steam turbines, as a result of which the amplitude-frequency characteristics of the blade oscillations change, which can lead to the occurrence of uncontrolled self-excited oscillations. The paper presents the results of a numerical analysis of the aeroelastic characteristics of blade row of the last stage rotor of a 200 MW steam turbine, in which, during modernization, the length of the blades increased to 1200 mm, which made it necessary to check the resistance to flutter in operating modes. The analysis used the method of solving the coupled problem of unsteady aerodynamics and elastic blade vibrations, which allows to predict the amplitude-frequency spectrum of unsteady loads and blade vibrations in a viscous gas flow. The results of the calculations showed the absence of flutter and self-oscillations on the first five natural forms of blade oscillations in the nominal mode of operation of the steam turbine.

Dynamic characteristics and generation mechanism of windscreen frameless wiper blade oscillations

Dynamic characteristics and generation mechanism of windscreen frameless wiper blade oscillations

Optimisation of a forced multi-beam piezoelectric energy harvester

A high-power multi-beam piezoelectric energy harvesting device is designed to meet the demands of the emerging technologies in Body Sensors Networks (BSNs), Wireless Sensors Networks (WSNs), the Internet of Things (IoT) and the Industrial Internet of Things (IIoTs). The proposed device utilises a plucking mechanism to excite the beams, organised in a comb-like structure. The harvester is presented in different length configurations and its performance is optimised to deliver the highest power under a given set of parameter values, constraints, and excitation characteristics. The unique feature of the device is that it can be tuned to any given frequency, although it demonstrates its superior performance in the frequency range of 2–50 Hz, delivering hundreds of mW. The device optimisation is conducted using a harmonic excitation, a harmonic excitation with random phase modulations, experimental vibration data collected using an internal combustion engine, and numerical data from simulations of out-of-plane oscillations of wind turbine blades. The paper proposes solutions to a number of challenges specific for multi-beam structures that have never been addressed before. It is demonstrated for the first time that the proposed harvester is able to meet the demands of relevant sensing applications.

Numerical analysis of dynamics and durability of rotor elements in gas turbine engines

In this work, an accurate algorithm for calculating the durability of rotor wheels in gas turbine engines undergoing detuning of parameters was developed. The finite element method, underlying the Ansys Software, was used for modelling free and forced oscillations of rotor wheels. During the experiments, the detuning was simulated by attaching additional masses to the wheel blades. The calculations of frequencies, modes of forced oscillations, as well as dynamic stresses arising due to these oscillations, were carried out using the Fourier series. The schematisation of dynamic stresses, i.e. differentiation of obtained stresses into levels having specific amplitudes, was used to calculate durability. The main research result comprises the developed algorithm for calculating the durability of rotor wheels of gas-turbine engines subjected to parameter detuning. This algorithm served as a basis for the Ocs_Rotor software for investigating the natural oscillations of blades and rotor wheels under parameter detuning. Using this software, the natural frequencies and oscillation modes of the blades were calculated. Dynamic stresses under forced oscillations, as well as durability of the rotor wheel, were calculated using the obtained results. The results of calculating the service life of an actual rotor wheel having three different positions of blades under detuning allowed the construction having the maximum service life of 1.75 * 105 hours to be selected. Comparing the results of calculations, obtained using the Ocs_Rotor software, with those of field experiments, carried out at Brandenburg Technical University (Cottbus, Germany), demonstrated high accuracy characterised by a maximum error of 4 %. This suggests that the software may be used to design structures of maximum service life. The results of durability calculations of an actual rotor wheel having different blade positions under detuning allowed practical recommendations for engineers on the positioning of the blades in the wheel to be established.

Advancing asymptotic approaches to studying the longitudinal and torsional oscillations of a moving beam

This paper analyzes the influence of kinetic and physical-mechanical parameters of systems on the characteristics of dynamic processes in moving one-dimensional nonlinear-elastic systems. Improved convenient calculation formulas have been derived that describe the laws of changing the amplitude-frequency characteristics of systems for both a non-resonant case and a resonant one. An important issue of studying the influence of the speed of movement of elements of mechanisms on the oscillations of one-dimensional nonlinear-elastic systems has not been considered in detail until now in the scientific literature. This issue relates to the vibrations of shafts in gears, pipe strings when drilling oil and gas wells, the oscillations of turbine blades and rotating turbine discs, the longitudinal vibrations of the beam as an element of structures. The main reason for this in the analytical study of dynamic processes were the shortcomings of the mathematical apparatus for solving the corresponding nonlinear differential equations that describe the laws of motion of those systems. It was found that in the case of longitudinal oscillations in the moving beam with an increase in the longitudinal speed of the medium to 10 m/s, the amplitude of the oscillation also increases by 13.5 %. However, when the longitudinal velocity of the beam is 5 m/s, the amplitude will increase by only 3 %. It is established that with the growth of the amplitude, the frequency of longitudinal oscillations decreases sharply, and if the system moves at a higher speed, for example, 20 m/s, it reduces the frequency of oscillation by about 13 %. The results reported here make it possible to assess the effect of kinetic and physical-mechanical parameters on the frequency and amplitude of oscillations. The research that involved the asymptotic method makes it possible to predict resonant phenomena and obtain engineering solutions to improve the efficiency of technological equipment.

Data-driven state estimation toward blade individual load-reduction of wind turbines1

As wind turbines tend to be build larger every year, the importance of load-reducing controls to damp the rotor blade oscillations increases. For a control algorithm to perform blade individual load-reducing strategies, online information about each rotor blade’s deflection is needed. An approach for wind turbine state estimation with special attention to the rotor blade deflections is given using a Hammerstein model driven by simulation data in a Kalman Filter (KF). The Hammerstein’s linear submodel is mainly derived as time discrete state space system via least squares, while nonlinear effects are defined in terms of their proportionality. The model noise definition required by the KF is calculated by the system model’s one-step prediction error. The simulation results show the estimate to have a standard deviation of less than 2 % in edge and 9% in flap-wise direction when using an appropriate sensor configuration. Using state-of-the-art sensors, standard deviations of less than 4% and 25% respectively are achieved. The approach is particularly attractive due to the low level of tuning required. The usage of the state estimation in a closed control loop as well as the Hammerstein model in a model-based control system offer room for promising further investigations.

Direct numerical simulations of aerodynamic performance of wind turbine aerofoil by considering the blades active vibrations

In the present study, the aerodynamic performance of the horizontal-axis wind turbine blades by considering the flap-wise oscillations are numerically investigated by using direct numerical simulations (DNS). The details of flow structure can be analysed and predicted by performing DNS over an oscillating blade by considering the realistic behaviour of the wind turbine blade structure with natural vibration frequencies. In this study, the impact of vibrations on the flow separation point, laminar separation bubble (LSB) and stall over NACA-4412 aerofoil are investigated utilising the high-fidelity spectral-hp element methodology. The Reynolds number and angle of attack were selected in the range of 50,000≤Re≤75,000 and 8°≤AoA≤16°. It is found that the blade vibrations have a noticeable impact on the aerodynamic performance and delay the stall occurrence, and the lift remains high even at higher AoAs, in comparison with the stationary blade. The size of the flow separation is reduced by the blade oscillation and the vibration also affects the separation point. Due to the harmonic oscillation of the blade, the pressure signals are periodic, and the pressure fluctuations are amplified by the oscillations, especially in the flow separation region. The time-averaged lift coefficient is increased by 255.3% by raising the angle of attack, from 0° to 12° at Re = 75,000. Compared to Re = 50,000, the peak-to-peak amplitude for the angle of attack of 0° is higher, whereas that of 8° and 12° are slightly lower at Re = 75,000.

Aerodynamic and dynamic loading in a blade cascade designed for flutter research

Flow-induced vibration of turbine and compressor blades, so called blade flutter, represents a serious problem for designers and operators of large turbomachines. The research of mechanisms leading to this dangerous aeroelastic instability, which can occur especially in modern long and slender blades, is hindered by lack of experimental data. A new experimental setup for controlled flutter testing has been designed in cooperation of the Institute of Thermomechanics of the Czech Academy of Sciences and Faculty of Mechatronics of the Technical University of Liberec. The test section consists of five planar blades placed in a transonic wind tunnel, with high-frequency torsional oscillation of the middle blade driven by an electric motor. The contribution presents the results of first measurements, namely the static pressure distribution for various inlet Mach numbers, aerodynamic moments and deformation of the middle blade due to inertial loads during high-frequency oscillation.