Comparison of the Influence Coefficient Method and Travelling Wave Mode Approach for the Calculation of Aerodynamic Damping of Centrifugal Compressors and Axial Turbines

2017 ◽  
Author(s):  
K. Vogel ◽  
A. D. Naidu ◽  
M. Fischer
Keyword(s):  
Centrifugal Compressor ◽  
Travelling Wave ◽  
Wave Mode ◽  
Forced Response ◽  
Computational Time ◽  
Influence Coefficient ◽  
Average Deviation ◽  
Aerodynamic Damping ◽  
Influence Coefficients ◽  
Periodic Boundaries

The prediction of aerodynamic damping is a key step towards high fidelity forced response calculations. Without the knowledge of absolute damping values, the resulting stresses from forced response calculations are often afflicted with large uncertainties. In addition, with the knowledge of the aerodynamic damping the aeroelastic contribution to mistuning can be considered. The first section of this paper compares two methods of one-way-coupled aerodynamic damping computations on an axial turbine. Those methods are: the aerodynamic influence coefficient, and the travelling wave mode method. Excellent agreement between the two methods is found with significant differences in required computational time. The average deviation between all methods for the transonic turbine is 4%. Additionally, the use of transient blade row methods with phase lagged periodic boundaries are investigated and the influence of periodic boundaries on the aerodynamic influence coefficients are assessed. A total of 23 out of 33 passages are needed to remove all influence from the periodic boundaries for the present configuration. The second part of the paper presents the aerodynamic damping calculations for a centrifugal compressor. Simulations are predominantly performed using the aerodynamic influence coefficient approach. The influence of the periodic boundaries and the recirculation channel is investigated. All simulations are performed on a modern turbocharger turbine and centrifugal compressor using ANSYS CFX V17.0 with an inhouse pre- and post-processing procedure at ABB Turbocharging. The comparison to experimental results concludes the paper.

On the Influence of Blade Aspect Ratio on Aerodynamic Damping

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Patrick Buchwald ◽  
Aydin Farahmand ◽  
Damian M. Vogt
Keyword(s):  
Harmonic Balance ◽  
Axial Compressor ◽  
Wave Mode ◽  
Scaling Factor ◽  
Influence Coefficient ◽  
Aerodynamic Damping ◽  
Compressor Rotor ◽  
Angle Change ◽  
Influence Coefficients ◽  
Bending Mode

AbstractIn order to change the blade count (BC) of axial rotor designs, a scaling technique can be applied where the blades are scaled in axial and circumferential directions while maintaining the solidity. This technique allows to adjust the blade count without changing the steady-state aerodynamics, but the influences on the aerodynamic damping are unknown. The present study is focused on the investigation of the change in aerodynamic damping of a subsonic axial compressor rotor, if the blade count is changed between 13 and 25 blades. The investigation is focused on the first bending mode family and the influences of the hub geometry on the modes are neglected. First, a comparison between the influence coefficient (IC) method and the traveling wave mode (TWM) method is conducted, which shows that the application of the IC method in combination with harmonic balance simulations offers a fast way to compute the aerodynamic damping without introducing significant errors compared with the TWM method simulations. Regarding the aerodynamic damping of the different rotor geometries, it can be noted that the amplitude of the work per cycle influence coefficient of the center blade scales linearly with the blade scaling factor and an increase in aerodynamic damping for an increase in blade count is observed. Furthermore, a simplified analytic theory is established, which explains the phase angle change of the blade influence coefficients due to the blade scaling. In the last part of the paper, an extrapolation method is proposed for the investigated geometry and mode family, which allows for the estimation of damping S-curves for scaled rotor geometries based on only one IC method simulation.

Intentional Response Reduction by Harmonic Mistuning of Bladed Disks With Aerodynamic Damping

2018 ◽  
Author(s):  
Sebastian Willeke ◽  
Lukas Schwerdt ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Wave Train ◽  
Wave Mode ◽  
Forced Response ◽  
Mode Shapes ◽  
Bladed Disks ◽  
Nodal Diameter ◽  
Aerodynamic Damping ◽  
Mode Pair ◽  
Localized Mode ◽  
Amplitude Level

A harmonic mistuning concept for bladed disks is analyzed in order to intentionally reduce the forced response of specific modes below their tuned amplitude level. By splitting a mode pair associated with a specific nodal diameter pattern, the lightly damped traveling wave mode of the nominally tuned blisk is superposed with its counter-rotating complement. Consequently, a standing wave is formed in which the former wave train benefits from an increase in aerodynamic damping. Unlike previous analyses of randomly perturbed configurations, the mode-specific stabilization is intentionally promoted through adjusting the harmonic content of the mistuning pattern. Through a re-orientation of the localized mode shapes in relation to the discrete blades, the response is additionally attenuated by an amount of up to 7.6 %. The achievable level of amplitude reduction is analytically predicted based on the properties of the tuned system. Furthermore, the required degree of mistuning for a sufficient separation of a mode pair is derived.

Investigation of Working Line Variation Onto Forced Response Vibrations of a Compressor Blisk

2020 ◽  
Author(s):  
Seif ElMasry ◽  
Arnold Kühhorn ◽  
Felix Figaschewsky
Keyword(s):  
Resonance Condition ◽  
Element Model ◽  
Forced Response ◽  
Mode Shapes ◽  
Aerodynamic Forces ◽  
Aerodynamic Damping ◽  
Single Passage ◽  
Influence Coefficients ◽  
Stator Vane ◽  
Operational Range

Abstract This paper aims to study the effect of varying the working line of a compressor onto the forced response vibrations of the blades of an integrally bladed disk (blisk). The investigated rotor belongs to a transonic research compressor, where various probes are placed to measure flow data at all stations and analyze blade vibrations. A single-passage CFD model of all compressor blade-rows is used for steady computations. Using a finite element model, the natural frequencies and mode shapes of the blisk across the operational range of the compressor are predicted. Thus, resonance conditions can be identified from the Campbell diagram. The variation of the compressor working line is investigated at 90% of the maximum shaft speed, where the resonance condition of the 11th blade mode family and the engine order corresponding to the aerodynamic distortion from the upstream stator vane is predicted. Using a single-passage model, time-accurate simulations of the investigated rotor are executed at various operating points, which cover the operational range of the compressor between choke and stall conditions. Aerodynamic damping ratios are calculated using the aerodynamic influence coefficients method at each point, in order to predict the resulting vibration amplitudes of the blades. Relatively high amplitudes of the modal aerodynamic forces are observed at the low working line. A detailed post-processing analysis is performed, as the change of flow incidence contributes largely in the increase of modal aerodynamic forces on the blade. The aerodynamic damping ratios increase with higher working lines, where the rotor achieves relatively higher pressure ratios. However, the damping decreases rapidly close to stall conditions. The trend of the predicted vibration amplitudes is compared to strain gauge measurements from the rig, which are registered during multiple acceleration maneuvers performed over different working lines. A strong correlation between the predicted and measured trends of the forced response vibration is witnessed.

Optimization-Aided Forced Response Analysis of a Mistuned Compressor Blisk

2014 ◽  
Author(s):  
Bernd Beirow ◽  
Arnold Kühhorn ◽  
Thomas Giersch ◽  
Jens Nipkau
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Strong Dependence ◽  
Forced Response ◽  
Response Analysis ◽  
Influence Coefficient ◽  
Aerodynamic Damping ◽  
Design Variables ◽  
Engine Order ◽  
Main Driver

The forced response of the first rotor of an E3E-type high pressure compressor blisk is analyzed with regard to varying mistuning, varying engine order excitations and the consideration of aeroelastic effects. For that purpose, SNM-based reduced order models are used in which the disk remains unchanged while the Young’s modulus of each blade is used to define experimentally adjusted as well as intentional mistuning patterns. The aerodynamic influence coefficient technique is employed to model aeroelastic interactions. Furthermore, based on optimization analyses and depending on the exciting EO and aerodynamic influences it is searched for the worst as well as the best mistuning distributions with respect to the maximum blade displacement. Genetic algorithms using blade stiffness variations as vector of design variables and the maximum blade displacement as objective function are applied. An allowed limit of the blades’ Young’s modulus standard deviation is formulated as secondary condition. In particular, the question is addressed if and how far the aeroelastic impact, mainly causing aerodynamic damping, combined with mistuning can even yield a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the inter-blade phase angle is the main driver for a possible response attenuation considering the fundamental blade mode. The results of the optimization analyses are compared to the forced response due to real, experimentally determined frequency mistuning as well as intentional mistuning.

scholarly journals Analysis of Experimental Time-Dependent Blade Surface Pressures From an Oscillating Turbine Cascade With the Influence-Coefficient Technique

1990 ◽  
Author(s):  
T. H. Fransson
Keyword(s):  
Experimental Data ◽  
Leading Edge ◽  
Travelling Wave ◽  
Time Dependent ◽  
Influence Coefficient ◽  
Blade Surface ◽  
Suction Surface ◽  
Local Flow ◽  
Unsteady Aerodynamic ◽  
Influence Coefficients

A two-dimensional section of the last stage of a steam turbine has been investigated experimentally in an annular non-rotating cascade facility as regards to its steady-state and time-dependent aerodynamic characteristics at design and off-design conditions. The unsteady experimental data obtained with the blades vibrating in the “travelling wave” mode indicate that one of the main reasons for the flutter susceptibility of the cascade lies in the high expansion and following shock wave close to the blade suction surface leading edge and the corresponding high unsteady loading. The decomposition of the experimental data into unsteady aerodynamic influence coefficients validates this conclusion and gives also that another reason for the flutter susceptibility can be found in the fact that the cascade is overlapped for a part of the blade surface where the local flow velocities are close to sonic. The unsteady aerodynamic influence coefficients show that the instability arises because of the time dependent aerodynamic coupling effects between, essentially, the reference blade and its immediate suction surface and, to a lesser extent, pressure surface neighbors.

Forced Response Reduction of a Blisk by Means of Intentional Mistuning

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Bernd Beirow ◽  
Arnold Kühhorn ◽  
Felix Figaschewsky ◽  
Alfons Bornhorn ◽  
Oleg V. Repetckii
Keyword(s):  
Optimization Problem ◽  
Negative Impact ◽  
Forced Response ◽  
Reduced Order Models ◽  
Integer Optimization ◽  
Safe Operation ◽  
Reduced Order ◽  
Aerodynamic Damping ◽  
Influence Coefficients ◽  
Engine Order

The effect of intentional mistuning has been analyzed for an axial turbocharger blisk with the objective of limiting the forced response due to low engine order excitation (LEO). The idea behind the approach was to increase the aerodynamic damping for the most critical fundamental mode in a way that a safe operation is ensured without severely losing aerodynamic performance. Apart from alternate mistuning, a more effective mistuning pattern is investigated, which has been derived by means of optimization employing genetic algorithms. In order to keep the manufacturing effort as small as possible, only two blade different geometries have been allowed, which means that an integer optimization problem has been formulated. Two blisk prototypes have been manufactured for purpose of demonstrating the benefit of the intentional mistuning pattern identified in this way: A first one with and a second one without employing intentional mistuning. The real mistuning of the prototypes has been experimentally identified. It is shown that the benefit regarding the forced response reduction is retained in spite of the negative impact of unavoidable additional mistuning due to the manufacturing process. Independently, further analyzes have been focused on the robustness of the solution by considering increasing random structural mistuning and aerodynamic mistuning as well. The latter one has been modeled by means of varying aerodynamic influence coefficients (AIC) as part of Monte Carlo simulations. Reduced order models have been employed for these purposes.

Forced Response Analysis of a Mistuned Compressor Blisk

2013 ◽  
Author(s):  
Bernd Beirow ◽  
Arnold Kühhorn ◽  
Thomas Giersch ◽  
Jens Nipkau
Keyword(s):  
Strong Dependence ◽  
Forced Response ◽  
Response Analysis ◽  
Influence Coefficient ◽  
Aerodynamic Damping ◽  
Design Variables ◽  
Engine Order ◽  
Main Driver ◽  
Displacement Based ◽  
Blade Frequency

The forced response of an E3E-type HPC-blisk front rotor is analyzed with regard to varying mistuning and the consideration of the fluid-structure interaction (FSI). For that purpose, a reduced order model is used in which the disk remains unchanged and mechanical properties of the blades namely stiffness and damping are adjusted to measured as well as intentional blade frequency mistuning distributions. The aerodynamic influence coefficient technique is employed to model the aeroelastics. Depending on the blade mode, the exciting engine order and aerodynamic influences it is sought for the worst mistuning distributions with respect to the maximum blade displacement based on optimization analyses. Genetic algorithms using blade alone frequencies as design variables are applied. The validity of the Whitehead-limit is assessed in this context. In particular, the question is addressed if and how far aeroelastic effects, mainly caused by aerodynamic damping, combined with mistuning can even cause a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the inter-blade phase angle is the main driver for a possible response attenuation considering the fundamental as well as a higher blade mode. Furthermore, the differences to the blisk vibration response without a consideration of the flow and an increase of the disk’s stiffness are discussed. Closing, the influence of pure damping mistuning is analyzed again using optimization.

Optimization-Aided Forced Response Analysis of a Mistuned Compressor Blisk

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Bernd Beirow ◽  
Thomas Giersch ◽  
Arnold Kühhorn ◽  
Jens Nipkau
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Strong Dependence ◽  
Forced Response ◽  
Response Analysis ◽  
Influence Coefficient ◽  
Aerodynamic Damping ◽  
Design Variables ◽  
Engine Order ◽  
Main Driver

The forced response of the first rotor of an engine 3E (technology program) (E3E)-type high pressure compressor (HPC) blisk is analyzed with regard to varying mistuning, varying engine order (EO) excitations and the consideration of aero-elastic effects. For that purpose, subset of nominal system modes (SNM)-based reduced order models are used in which the disk remains unchanged while the Young's modulus of each blade is used to define experimentally adjusted as well as intentional mistuning patterns. The aerodynamic influence coefficient (AIC) technique is employed to model aero-elastic interactions. Furthermore, based on optimization analyses and depending on the exciting EO and aerodynamic influences it is searched for the worst as well as the best mistuning distributions with respect to the maximum blade displacement. Genetic algorithms using blade stiffness variations as vector of design variables and the maximum blade displacement as objective function are applied. An allowed limit of the blades' Young's modulus standard deviation is formulated as secondary condition. In particular, the question is addressed if and how far the aero-elastic impact, mainly causing aerodynamic damping, combined with mistuning can even yield a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the interblade phase angle is the main driver for a possible response attenuation considering the fundamental blade mode. The results of the optimization analyses are compared to the forced response due to real, experimentally determined frequency mistuning as well as intentional mistuning.

An Inverse Approach to Identify Tuned Aerodynamic Damping, System Frequencies and Mistuning: Part 3 — Application to Engine Data

2019 ◽  
Author(s):  
Felix Figaschewsky ◽  
Arnold Kühhorn ◽  
Bernd Beirow ◽  
Thomas Giersch ◽  
Sven Schrape ◽  
...  
Keyword(s):  
Equations Of Motion ◽  
Travelling Wave ◽  
Forced Response ◽  
Aerodynamic Damping ◽  
Inverse Approach ◽  
Novel Approach ◽  
High Pressure Compressor ◽  
Blade Tip ◽  
Identification Approach ◽  
Reference Measurements

Abstract A novel approach for the identification of tuned aerodynamic damping, system frequencies, forcing and mistuning has been introduced in the first part of this paper. It is based on the forced response equations of motion for a blade dominated mode family. A least squares formulation allows to identify the system’s parameters directly from measured frequency response functions (FRFs) of all blades recorded during a sweep through a resonance. The second part has dealt with its modification and application to experimental modal analyses of blisks at rest. This 3rd part aims at presenting the application of the approach to blade tip timing (BTT) data acquired in rig tests. Therefore, blisk rotors of two different engines are studied: a single stage fan rig and a 4.5 stage high pressure compressor (HPC) rig. The rig test campaign of the fan blisk included also an intentional mistuning experiment that allows to study the performance of the identification approach for a similar rotor with two different mistuning levels. It is demonstrated that the approach can identify aerodynamic damping curves, system frequencies, mistuning pattern and forced travelling wave modes (TWMs) from state of the art BTT data monitored during rig or engine tests. All derived mistuning patterns could be verified with reference measurements at standstill. The derived aerodynamic damping curves and system frequencies show a reasonable agreement with simulations. For the HPC case a multitude of excited TWMs could be identified which also lines up with previous simulations.

Research on Aerodynamic Damping of Bladed Disk With Random Mistuning

2017 ◽  
Author(s):  
Lin Li ◽  
Xiaoping Yu ◽  
Peiyi Wang
Keyword(s):  
Travelling Waves ◽  
Elastic Stability ◽  
Travelling Wave ◽  
Wave Mode ◽  
Analysis Model ◽  
Aerodynamic Damping ◽  
Bladed Disk ◽  
Random Mistuning ◽  
Value Of It ◽  
Wave Modes

This paper presents an investigation on the aerodynamic damping of bladed disk (also called ‘blisk’) with mistuning. The study focuses mainly on the mechanism of the effect of random and intentional mistuning on the aero-elastic stability of blisk. For the purpose, aero-elastic stability equations of tuned and mistuned blisk in the frequency domain are established. NASA-Rotor37 is taken as the analysis model. In order to obtain the aerodynamic damping, the unsteady aero-elastic forces are calculated by the double channel harmonic method based on phase correction with aid of the general software CFX. Considering the stochastic characteristics of random mistuning, statistical analysis on the aerodynamic damping of mistuned blisk is performed. The effects of mistuning with different levels are compared. The mechanism of the effects of mistuning on the aero-elastic stability of blisk is found that mistuning couples the modes of different travelling waves and it concentrates the aerodynamic damping in a travelling wave-mode-family by increasing the aerodynamic damping ratios in forward travelling wave modes and decreasing the aerodynamic damping ratios in backward travelling wave modes. And the higher the mistuning level, the more obvious the trend. Furthermore, the following result is obtained: Whatever the mistuning level, in a traveling wave-mode-family, the aerodynamic damping of mistuned blisk is greater than the minimum aerodynamic damping of corresponding tuned blisk and less than the maximum value of it. Besides, the harmonic order of intentional mistuning that can be used to raise the aero-elastic stability of blisk is proposed.

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