Numerical investigations on non-synchronous vibration and frequency lock-in of low-pressure steam turbine last stage

The flow phenomenon of rotating instability (RI) and its induced non-synchronous vibrations (NSV) in the last stage have gradually become a security problem that restricts the long-term flexible operations of modern large-scaled low-pressure steam turbines. Especially, if one structural mode of the last stage moving blade (LSMB) is excited, significant blade vibrations may potentially lead to high-cycle fatigue failure. A loosely coupled computational fluid dynamics reduced model with prescribed blade vibrations has been established to investigate NSV of the LSMB and the potential lock-in phenomenon under low-load conditions. Firstly, calculations with reduced multi-passage domain have been verified by comparing with the results of the full-annulus one, and an appropriate reduced domain is determined. Secondly, a set of calculations by controlling blade vibration parameters indicate that lock-in phenomenon between RI frequency and blade vibration frequency may occur when nodal diameters of cascade vibrations is coincident with the wave number of RI. Furthermore, dynamic modal decomposition technology has been employed to identify the unsteady pressure field around the blade surface and to reveal the interaction relationship between the flow modes of RI and vibration-induced pressure disturbance. Finally, the blade response evaluation based on harmonic analysis shows that in NSV, the global maximum dynamic response level of locked-in case is nearly 20 times than that of unlocked one.

Rotor-Blade Interaction During Blade Resonance Drive-Through

In the future energy landscape, combined cycle power plants will increasingly take the role of providing balancing power for fluctuating renewable energy sources due to their high availability and fast start-up times. This implies more frequent cycling, a larger number of speed cycles and thus new challenges for plant design and operation. One of these challenges is a potential increase of cyclic fatigue incurred by last-stage blades during start-up and coast-down. Blade vibrations might be induced by synchronous shaft vibrations when the blade resonance is excited by lateral shaft vibrations. In this paper, we report measurement results of shaft and blade vibrations observed at some Siemens Energy steam turbines. Apart from the expected increase of blade vibrations when the double rotating speed crosses the blade resonance, a distinctive dip of shaft vibrations at the low-pressure turbine bearings is observed. We argue that this phenomenon is likely related to the aforementioned interaction between blade and shaft vibrations and present a theoretical framework to describe this interaction and the observed effect.

Finite Element Analysis of Wind Turbine Blade Vibrations

The article is devoted to the practical problem of computer simulation of the dynamic behaviour of horizontal axis wind turbine composite rotor blades. This type of wind turbine is the dominant design in modern wind farms, and as such its dynamics and strength characteristics should be carefully studied. For this purpose, in this paper the mechanical model of a rotor blade with a composite skin possessing a stiffener was developed and implemented as a finite element model in ABAQUS. On the basis of this computer model, modal analysis of turbine blade vibrations was performed and benchmark cases for the dynamic response were investigated. The response of the system subjected to a uniform underneath pressure was studied, and the root reaction force and blade tip displacement time histories were obtained from the numerical calculations conducted.

Acoustic Resonance in an Axial Multistage Compressor Leading to Non-Synchronous Blade Vibration

Significant non-synchronous blade vibrations (NSV) have been observed in an experimental three-stage high-speed compressor at part-speed conditions. High amplitude acoustic modes, propagating around the circumference and originating in the highly loaded Stage-3 have been observed in coherence with the structural vibration mode. In order to understand the occurring phenomena, a detailed numerical study has been carried out to reproduce the mechanism. Unsteady full annulus RANS simulations of the whole setup have been performed using the solver elsA. The results revealed the development of propagating acoustic modes which are partially trapped in the annulus and are in resonance with an aerodynamic disturbance in Rotor-3. The aerodynamic disturbance is identified as an unsteady separation of the blade boundary layer in Rotor-3. The results indicate that the frequency and phase of the separation adapt to match those of the acoustic wave, and are therefore governed by acoustic propagation conditions. Furthermore, the simulations clearly show the modulation of the propagating wave with the rotor blades, leading to a change of circumferential wave numbers while passing the blade row. To analyze if the effect is self-induced by the blade vibration, a noncoherent structural mode has been imposed in the simulations. Even at high vibration amplitude the formerly observed acoustic mode did not change its circumferential wave number. This phenomenon is highly relevant to modern compressor designs, since the appearance of the axially propagating acoustic waves can excite blade vibrations if they coincide with a structural eigenmode, as observed in the presented experiments.

Sparse Reconstruction Method of Non-Uniform Sampling and its Application in Blade Tip Timing System

Based on the blade vibration theory of turbomachinery and the basic principle of blade timing systems, a sparse reconstruction model is derived for the tip timing signal under an arbitrary sensor circumferential placement distribution. The proposed approach uses the sparsity of the tip timing signal in the frequency domain. The application of compressive sensing in reconstructing the blade tip timing signal and monitoring multi-mode blade vibrations is explored. To improve the reconstruction effect, a number of numerical experiments are conducted to examine the effects of various factors on synchronous and non-synchronous signals. This enables the specific steps involved in the compressive sensing reconstruction of tip timing signals to be determined. The proposed method is then applied to the tip timing data of a 27-blade rotor. The results show that the method accurately identifies the multi-mode blade vibrations at different rotation speeds. The proposed method has the advantages of low dependence on prior information, insensitivity to environmental noise, and simultaneous identification of synchronous and non-synchronous signals. The experimental results validate the effectiveness of the proposed approach in engineering applications.

Aerodynamic and Structural Numerical Investigation of Full Annulus Last Stage of Steam Turbine Under Low Load Conditions

Operating at low load conditions may cause strong and non-synchronous unsteadiness and a high blade dynamic loading for the last stage blades (LSB). Full annulus models should be used to investigate the circumferential asymmetric flow unsteadiness and blade vibrations. Currently, although full annulus models have been applied to numerical aerodynamic studies, to authors’ knowledge, there is still no research including the full annulus in structural analysis due to the high computational cost. In this paper, an unsteady aerodynamic and structural coupled analysis method for an industrial steam turbine LSB using full annulus model under low load conditions is presented. To conduct finite element method (FEM) with limited computational resources, a new structural analysis procedure is proposed to calculate the dynamic stress. The aerodynamic analysis is conducted in both steady and unsteady computational fluid dynamics (CFD) calculations. The tip pressure ratio in the steady state calculations is used to predict the aerodynamic loading intensity. The unsteady results indicate typical flow characteristics under low load conditions, which show a big separation region behind the last rotor and tip vortex between last stator and rotor. Unsteady aerodynamic loading is mapped onto the blade surface as the excitation force. The structural analysis is performed to investigate the characteristics of blade vibrations and stress distributions of the full annulus LSB. Repeating the method, a reasonable characteristics curve of vibration stress against flow rates for LSB is calculated.

Non-Synchronous Aeroacoustic Interaction in an Axial Multi-Stage Compressor

Non-engine order rotor blade vibration is an aeroelastic phenomenon of major interest for compressor designers resulting from excitation of rotor blade modes through aerodynamic instabilities. Indicators for a comparable type of instability, caused by propagating acoustic modes, have been observed in an experimental multistage high-speed compressor by Safran Helicopter Engines. It is intended to understand the cause of these instabilities by combining experimental data and numerical simulations. Unsteady pressure measurements were carried out by case-mounted and stator-mounted transducers. Rotor tip-timing and magnet-coil sensor systems were installed to measure the blade vibrations. Experimental results show non-engine order signatures in the unsteady pressure signal coherent to the shifted frequency of blade vibrations. In the present paper, the waveform of these oscillations is analyzed in detail, showing a dominant propagating acoustic mode interacting with vibrations of rotor 2. The root cause for the non-synchronous oscillations is identified as an acoustic mode that is cutoff downstream of rotor 3. During the test, the mode changes its frequency and circumferential order, affecting the amplitude of associated blade vibrations.