Influence of mechanical mistuning on the forced response of a turbine cascade

An experimental investigation has been conducted in the non-rotating annular test facility of the "Laboratoire de Thermique Appliquée et de Turbomachines" (LTT), "École Polytechnique Fédérale de Lausanne" (EPFL). The influence of frequency mistuning and modeshape mistuning on the forced response of a turbine cascade is thereby determined. The 20 turbine blades of the cascade are excited by gusts generated using a strutted rotor with 13 elliptical bars providing a 13th engine order excitation pattern. The blades vibrate in their first eigenmode, corresponding to either a bending vibration or a torsion vibration. The frequency mistuning study has been carried out for the cascade with a first vibration mode in torsion. The frequency mistuning is introduced by adding or removing mass. A case with a weak (case T1) and a strong random frequency mistuning (case T2) are studied. For the modeshape mistuning study the blades used exhibit a first eigenmode in bending. The modeshape mistuning is introduced by changing the bending direction, using three different directions in the experimental setup. A datum case and two mistuned case are studied: The blades all vibrate in a direction normal to the chord for the datum case, called case B0. For the first mistuned case B1, the bending direction is varied alternately from blade to blade by plus or minus 10°. The second mistuned case B2 corresponds to a random variation of the bending direction. The motions of all blades as well as the unsteady pressure distributions on selected blade surfaces are recorded during the forced response measurements. In order to quantify the forcing function, the unsteady pressure distribution is measured in a second test setup with clamped blades, allowing the isolation of the effects of motion-induced unsteady pressures. Specific objective of this work is to study the influence of mistuning of the structural properties on the forced response of a turbine cascade. Both frequency mistuning and modeshape mistuning are investigated and an attempt is made to separate their impact on the maximum vibration amplitude of the individual blades. The measurement results show that the aerodynamic force that excites the vibration comprises five significant harmonics, the first harmonic at the strut passing frequency being dominant. The dominant first harmonic leads to an aerodynamic excitation of the 13th engine order. The measured forced response amplitude plots for the frequency mistuning study show typical effects of frequency mistuning and coupling (secondary peaks). The measured forced response phase of the blade movement exhibits inter-blade phase angles that are typical for a 13th engine order excitation. The effects of frequency mistuning and coupling can be detected on the phase plots. Besides the frequency mistuning, a significant damping mistuning is present in the cascade. The damping mistuning leads to a wide scatter of maximum response amplitude. A damping factor correction is applied to the measured maximum forced response amplitudes. The corrected amplitudes are much less scattered than the uncorrected ones. The average of the maximum response amplitudes is insignificantly higher for the heavily random mistuned case T2 than for case T1. A simplified frequency mistuning model that is capable of reproducing the effects of frequency mistuning and coupling qualitatively was established. The measured forced response for the modeshape mistuning study exhibits effects of frequency and damping mistuning. The influence of the damping mistuning is eliminated by the application of a damping factor correction method. This allows a better appreciation of the modeshape mistuning on the forced response. The differences in amplitudes between the cases B0 and B1 – for the individual blades as well as for the average values – follow a periodic pattern (with same periodicity as the mistuning pattern). This is a consequence of the periodic modeshape mistuning pattern. The average of the maximum forced response amplitudes is increased for case B1 compared to case B0. Comparing base B0 to B2, the trends in differences of maximum amplitudes are not as clear as for case B0 versus B1. This is due to the non-periodic and non-symmetric mistuning pattern. Nevertheless, some trends are detectable which correlate with the absolute change in bending direction between two adjacent blades. The modeshape mistuning does not reduce the level of the forced response amplitudes for both the alternate and random modeshape mistuning pattern. The minimum, average and maximum forced response maximum amplitudes as well as their standard deviation are nearly identical for both mistuned cases B1 and B2.

Aeroelastic effects of mistuning and coupling in turbomachinery bladings

Gerhard Kahl

A numerical method has been developed to study the effects of structural mistuning on the aeroelastic behaviour of turbomachinery cascades. The specific objectives of the work presented here were the following: A method was to be developed that can assess the major effects of structural mistuning in a cascade in sub- and transonic flow situations. The influence of mechanical and aerodynamic coupling between the blades as well as coupling between multiple modes for each blade was to be included. Accurate representations of the aerodynamic forces, taken from a modern three-dimensional unsteady aerodynamic solver were to be used. The method should be applicable for design use, meaning that it has to supply results quickly for a large number of configurations. The applicability and accuracy of the method was to be demonstrated by comparison of numerical results to available data from recent experiments. The influence of major parameters on the aeroelastic stability and on the resonant amplitude of representative test cases should be assessed. The approach used to achieve these goals is the combination of a linearised Euler method for the aerodynamic calculations with a modal reduction technique, where the structural properties of each blade are represented by only a few eigenmodes. The method is validated and applied to two test cases, comprising of a transonic compressor rotor and a high pressure turbine rotor. Both are representative of modern turbomachinery designs. The final conclusions of this work are: The newly developed method is capable to assess the dominant effects of structural mistuning in turbomachinery cascades, including the mechanical and aerodynamic coupling of adjacent blades and the aerodynamic coupling of multiple modes with arbitrarily complex modeshapes. In this method, the aerodynamic characteristics of the cascade are accurately represented using the generalised unsteady aerodynamic coefficients derived from a modern three-dimensional flow solver, applicable to and validated for both sub- and transonic configurations. The simplifications employed significantly contribute to the computational efficiency of the method, making it applicable for design purposes as well as for the assessment of large parametric variations or for statistical studies of stochastically mistuned configurations. The current method is successfully validated by a comparison of numerical to experimental data. The applicability and accuracy is demonstrated by the favourable agreement between measured and computed results. Based on these validations, the method is applied to study the influence of major parameters on the aeroelastic behaviour of the selected test cases. The results show a wide range of phenomena, dependent on the type and strength of mistuning, frequency, modeshape and interblade phase angle. The results highlight the close inter-dependence of the aeroelastic stability derived from the eigenvalue analysis and the resonant amplitudes derived from the forced response analysis.

EPFL2002

Experimental investigation of a vibrating axial turbine cascade in presence of upstream generated aerodynamic gusts

Fabrice Rottmeier

An experimental investigation has been conducted in the non-rotating annular test facility of the "Laboratoire de Thermique Appliquée et de Turbomachines" (LTT), "École Polytechnique Fédérale de Lausanne" (EPFL). During this investigation, the unsteady aerodynamic response of a turbine cascade was investigated for three different cases: (1) the clamped blades subjected to periodic, upstream generated aerodynamic gusts, (2) the cascade forced to vibrate in the travelling wave mode in a uniform flow, and (3) the cascade forced to vibrate in the presence of the upstream generated aerodynamic gusts, with a common excitation frequency and a constant gust-vibration phasing. These measurements were aimed at identifying important aspects of the unsteady aeroelastic behavior of the blades. Particular attention was focused on the relationship between the time-dependent flows of (1) and (2) and that of (3) in an effort to better understand aerodynamic forced response phenomena in turbomachinery The experimental tasks detailed above have been performed in a non-rotating annular test facility using a test rig composed of rotating wake generators and a fixed turbine cascade. There are two rotating wake generators: one possesses 13 elliptical struts and the other has 22. Each one is designed to generate wake profiles similar to a blade row. The turbine cascade consist of 20 blades attached to separate torsion suspension system, with a magnetic excitation feature, allowing the control of the cascade's vibration mode. Several blades are instrumented to measure the resulting surface steady pressures, unsteady pressures and blade vibration mode The specific objectives of this investigation were: measure the unsteady aerodynamic blade response to: (1) imposed cascade vibration modes (travelling wave mode), (2) upstream generated aerodynamic gusts, and (3) combinations of these two effects. using the above experimental results, address the local validity of the assumptions inherent in linearized treatments of the forced response problem. Specifically, can the local unsteady blade loading be considered as a linear superposition of the unsteady forces derived individually from the cascade's vibration mode and from the aerodynamic gusts? The final conclusions of this work were: the simultaneous measurements have demonstrated the important influence of the gust-vibration phase angle Φ on the blade surface time-dependent pressure distribution and has identified it as the key parameter. For a given test configuration and flow condition, the selection of the gust-vibration phase angle allows a local constructive or destructive interaction between the main harmonics of both excitation sources. Generally, this suggest that the gust-vibration phase angle has an important effect on the excitation levels and excited modes of the cascade. The practical implication of this phenomenon is that the judicious choice of a gust-vibration phase angle can diminish significantly the aerodynamic excitation levels for a given cascade vibration mode, flow condition and test configuration of a single stage. It is even possible that certain periodic variations of this phase angle produces another excitation source in turbomachinery. the simultaneous vibrating cascade and upstream generated aerodynamic gusts excitations can be accurately predicted by the linear superposition of the individual gust-induced and vibration-induced unsteady flow fields. This principle was shown to be applicable locally for various test configurations, including different engine orders, inter-blade phase angles, gust-vibration phase angles, and flow conditions. The only significant discrepancies were observed in the presence of shocks, but these were limited to a localized region reducing their importance in terms of the overall unsteady aerodynamic loading of the blade. It has been shown that these discrepancies were mainly due to the variation of the shock's mean location between gust-response only, controlled-vibration only and simultaneous measurements. The main practical advantage of this linear superposition principle is that the numerical and experimental investigation of the aerodynamic forced response problem can be separated into: (1) the identification of the local forcing-function due to upstream generated gusts only, (2) a local aerodynamic stability analysis of the cascade alone. The simultaneous measurements have shown that measurement errors vary significantly as the local pressure disturbance contributions due to the gusts and the cascade's vibration mode interact constructively or destructively. Particular attention is needed in simultaneous measurements in order to separate measurement error effects and physical phenomena.

EPFL2003

Experimental Aeroelastic Analysis of Clustered Turbine Blades Vibrating in Mixed Torsion/Bending Mode

Peter Ott, Achim Zanker

This paper presents and discusses unsteady experimental results of controlled vibration measurements of blade-cluster and single-blade test cases, all subjected to the same subsonic ow conditions. The experiments were performed in a non-rotating annular test facility with the aim to investigate the influence of cluster vibrations on the aerodynamic damping of turbine rotor blades. A frequently-used blade package type was selected: a two-blade-cluster in mixed mode, combing in a alternating manner a bending and a torsion vibration mode. In addition, single-blade test cases were investigated serving as reference for the cluster case. The actuation of the 20 turbine blades was obtained by an electro-magnetic excitation system, enabling individually the adjustment of vibration amplitude and phase for each blade at one vibration frequency. The unsteady measurements obtained include time-synchronous unsteady blade surface pressures and blade displacements resulting in local and global aerodynamic blade damping. A comparison of the cluster- and the single-blade-test cases was performed and differences were identified and analyzed.

The American Institute of Aeronautics and Astronautics2013

Experimental investigation of a vibrating axial turbine cascade in presence of upstream generated aerodynamic gusts

Fabrice Rottmeier

An experimental investigation has been conducted in the non-rotating annular test facility of the "Laboratoire de Thermique Appliquée et de Turbomachines" (LTT), "École Polytechnique Fédérale de Lausanne" (EPFL). During this investigation, the unsteady aerodynamic response of a turbine cascade was investigated for three different cases: (1) the clamped blades subjected to periodic, upstream generated aerodynamic gusts, (2) the cascade forced to vibrate in the travelling wave mode in a uniform flow, and (3) the cascade forced to vibrate in the presence of the upstream generated aerodynamic gusts, with a common excitation frequency and a constant gust-vibration phasing. These measurements were aimed at identifying important aspects of the unsteady aeroelastic behavior of the blades. Particular attention was focused on the relationship between the time-dependent flows of (1) and (2) and that of (3) in an effort to better understand aerodynamic forced response phenomena in turbomachinery The experimental tasks detailed above have been performed in a non-rotating annular test facility using a test rig composed of rotating wake generators and a fixed turbine cascade. There are two rotating wake generators: one possesses 13 elliptical struts and the other has 22. Each one is designed to generate wake profiles similar to a blade row. The turbine cascade consist of 20 blades attached to separate torsion suspension system, with a magnetic excitation feature, allowing the control of the cascade's vibration mode. Several blades are instrumented to measure the resulting surface steady pressures, unsteady pressures and blade vibration mode The specific objectives of this investigation were: measure the unsteady aerodynamic blade response to: (1) imposed cascade vibration modes (travelling wave mode), (2) upstream generated aerodynamic gusts, and (3) combinations of these two effects. using the above experimental results, address the local validity of the assumptions inherent in linearized treatments of the forced response problem. Specifically, can the local unsteady blade loading be considered as a linear superposition of the unsteady forces derived individually from the cascade's vibration mode and from the aerodynamic gusts? The final conclusions of this work were: the simultaneous measurements have demonstrated the important influence of the gust-vibration phase angle Φ on the blade surface time-dependent pressure distribution and has identified it as the key parameter. For a given test configuration and flow condition, the selection of the gust-vibration phase angle allows a local constructive or destructive interaction between the main harmonics of both excitation sources. Generally, this suggest that the gust-vibration phase angle has an important effect on the excitation levels and excited modes of the cascade. The practical implication of this phenomenon is that the judicious choice of a gust-vibration phase angle can diminish significantly the aerodynamic excitation levels for a given cascade vibration mode, flow condition and test configuration of a single stage. It is even possible that certain periodic variations of this phase angle produces another excitation source in turbomachinery. the simultaneous vibrating cascade and upstream generated aerodynamic gusts excitations can be accurately predicted by the linear superposition of the individual gust-induced and vibration-induced unsteady flow fields. This principle was shown to be applicable locally for various test configurations, including different engine orders, inter-blade phase angles, gust-vibration phase angles, and flow conditions. The only significant discrepancies were observed in the presence of shocks, but these were limited to a localized region reducing their importance in terms of the overall unsteady aerodynamic loading of the blade. It has been shown that these discrepancies were mainly due to the variation of the shock's mean location between gust-response only, controlled-vibration only and simultaneous measurements. The main practical advantage of this linear superposition principle is that the numerical and experimental investigation of the aerodynamic forced response problem can be separated into: (1) the identification of the local forcing-function due to upstream generated gusts only, (2) a local aerodynamic stability analysis of the cascade alone. The simultaneous measurements have shown that measurement errors vary significantly as the local pressure disturbance contributions due to the gusts and the cascade's vibration mode interact constructively or destructively. Particular attention is needed in simultaneous measurements in order to separate measurement error effects and physical phenomena.

EPFL2003

Aeroelastic effects of mistuning and coupling in turbomachinery bladings

Gerhard Kahl

EPFL2002