Analysis of Mistuned Blisk Vibrations Using a Surrogate Lumped Mass Model with Aerodynamic Influences

Transcription

1 Analysis of Mistuned Blisk Vibrations Using a Surrogate Lumped Mass Model with Aerodynamic Influences Von der Fakultät für Maschinenbau, Elektrotechnik und Wirtschaftsingenieurwesen der Brandenburgischen Technischen Universität Cottbus zur Erlangung des akademischen Grades eines Doktor-Ingenieurs genehmigte Dissertation vorgelegt von Diplom-Ingenieur Jens Nipkau geboren am in Herzberg/Elster Vorsitzender: Gutachter: Gutachter: Prof. Dr.-Ing. habil. Dieter Bestle Prof. Dr.-Ing. Arnold Kühhorn Prof. Dr.-Ing. Christoph Egbers Tag der mündlichen Prüfung:

2 If we knew what it was we were doing, it would not be called research, would it? Albert Einstein ( )

3 Berichte aus der Luft- und Raumfahrttechnik Jens Nipkau Analysis of Mistuned Blisk Vibrations Using a Surrogate Lumped Mass Model with Aerodynamic Influences Shaker Verlag Aachen 2011

4 Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at Zugl.: Cottbus, BTU, Diss., 2011 Copyright Shaker Verlag 2011 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publishers. Printed in Germany. ISBN ISSN Shaker Verlag GmbH P.O. BOX D Aachen Phone: 0049/2407/ Telefax: 0049/2407/ Internet: info@shaker.de

5 Acknowledgements The present work contains the results of my activities as post-graduate in the International Graduate School (IGS) in the class of "Compressor Technology & Materials" at the BTU Cottbus. Special thanks go to Prof. Dr.-Ing. Arnold Kühhorn for giving me the chance to work at his chair, for his constant support of myself and my work and for reviewing the work. Moreover, I thank Prof. Dr.-Ing. Christoph Egbers for showing interest in my work, all the valuable advices and for his expertise as well as Prof. Dr.-Ing. habil. Dieter Bestle for being the chairman of the examination committee. Many thanks go to PD Dr.-Ing. habil. Bernd Beirow for his persistent support of my work with the EBM and his numerous comments on this thesis. Furthermore I m very grateful to Dr.-Ing. Bernhard Mück from Rolls-Royce Deutschland for the inspiring discussions about aeroelastic finesses and the precious hints that helped completing the thesis. Gratitude goes also to Dipl.-Ing. Sven Schrape for his comments to my work and the stimulating discussions. Special thanks go also to Dipl.-Ing. Ulrik Strehlau for providing me with the experimental data I needed and Dipl.-Ing. Thomas Giersch for his effort in adapting the aeroelastic methods for the use in Au3D. I also must not forget Dipl.-Ing. Mark Golze for his technical support and all colleagues from the Chair of Structural Mechanics and Vehicle Vibration Technology for the relaxed atmosphere and the friendly collaboration. Last but not least warm thanks go to my family for their patience and steady support. Cottbus, March 2011 Jens Nipkau

6 Summary The present work presents the aeroelastic analyses of mistuned blisk forced response employing a surrogate lumped mass model with aerodynamic influence coefficients. Prior to these, the state of the art in mistuning analysis is summarised and the theoretical background of the structural as well as the aerodynamical model employed in this work is illustrated. Consequently, the validation of the aeroelastic methods is presented at the example of the compressor like Standard Configuration 10, a standardised test case of an aerofoil vibrating in a cascade, and the aerodynamical model is validated against bidirectionally coupled fluid structure interaction simulations of a 2D compressor rotor model. Finally, the aeroelastic behaviour of a mistuned blisk is analysed featuring measured mistuning patterns and extensive probabilistic analyses of mistuned blisk forced response. Zusammenfassung Die vorliegende Arbeit beschäftigt sich mit der Analyse erzwungener Schwingungen von verstimmten Verdichterlaufrädern unter Verwendung eines diskreten Ersatzmodells und aerodynamischen Einflusskoeffizienten. Zunächst werden der Stand der Technik bezogen auf die Untersuchung verstimmter Systeme zusammengefasst und die theoretischen Hintergründe des verwendeten Struktur- sowie aerodynamischen Modells dargestellt. Im Anschluss daran werden die aeroelastischen Methoden anhand der Standard Konfiguration 10, einem standardisierten Testfall schwingender Schaufeln in einer Kaskade, überprüft und das aerodynamische Modell mit Hilfe bidirektional gekoppelter Fluid-Struktur-Interaktions- Simulationen eines 2D Modells eines Verdichterrotors validiert. Schließlich wird das aeroelastische Verhalten einer verstimmten Verdichter-Blisk untersucht, wobei neben der Analyse experimentell ermittelter Verstimmungsverteilungen auch ausführliche, probabilistische Simulationen durchgeführt wurden.

7 Contents 1 Introduction Motivation State of the Art Results of Mistuning Research Scope of the Work Blisk Vibration Behaviour Rotor Vibrations Mistuning Aeroelasticity in Compressors Blade Flutter Forced Response Aeroelastic Methods Dynamic Model of Blade Vibrations Aerodynamic Model for Aerodynamically Coupled Blade Vibrations Kinematic Formulation for Tuned Systems Determination of Force and Moment Coefficients Coefficients for Rigid Blade Motion Coefficients for General Motion Determination of Aeroelastic Eigenvalues Equivalent Blisk Model Overview about Lumped Mass Models I

8 4.2 EBM Fundamentals Structural Parameter Identification Equivalent Aerodynamic Elements Aerodynamic Influence Coefficients Time Marching for Flutter and Forced Response Analysis Forced Response in the Frequency Domain Standard Configuration Model Parameters and Flow Conditions Reference Results Details about the Numerical Simulations DModel Inviscid Steady State Simulations Inviscid Unsteady Simulations Viscous Steady State Simulations Viscous Unsteady Simulations DModel Steady State Simulations Unsteady Simulations E3E - Rotor The E3E High Pressure Compressor D Linear Cascade of Rotor Tuned Cascade Results Mistuned Cascade Results E3E - Rotor Steady State Numerical Flow Solution Modal Analysis II

9 7.2.1 Tuned System Mistuned System Identification of Aeroelastic Parameters Rotor 1 EBM Model Identification of EBM Parameters Eigenvalues of Tuned EBM Eigenvalues of Mistuned EBM Forced Response of Tuned and Mistuned EBM Summary 137 A Richardson Extrapolation 141 B Mistuning Patterns of Rotor C Eigenvalues of Mistuned Rotor 1 EBM Model 145 C.1 Mode1-1stflap C.2 Mode2-2ndflap C.3 Mode 3-1st torsion C.4 Mode 6 - tram line D Forced Response of Measured Patterns 151 E Probability Density of Positive Nodal Diameters - Mode III

10 Nomenclature Latin Symbols symbol unit meaning A m 2 area c m chord length c L lift coefficient c M moment coefficient Ĉ N/(mkg) travelling wave mode coefficient e unity vector f Hz frequency h m blade height DFT max maximum Fourier coefficient E N/m 2 Young s Modulus E kin J kinetic energy Ê complex transformation matrix f N/ kg mass normalised modal force F N force j imaginary unit I identity matrix J kgm 2 mass moment of inertia k N/m stiffness K N/m stiffness matrix ˆL N/(mkg) influence coefficient m kg mass M kg mass matrix Ma mach number n surface normal vector N number of blades IV

11 symbol unit meaning nd number of nodal diameters NH 1/s rotational speed p Pa static pressure p t Pa total pressure q m kg modal displacement r m direction vector r g grid refinement ratio Re Reynolds number s blade surface line segment t s time u m/s flow velocity u ax m/s axial velocity u τ m/s shear velocity W J work x m displacement y m DOF of heaving motion y+ dimensionless wall distance Greek Symbols symbol unit meaning α angle β flow angle δ 1/s decay rate ζ - damping ratio θ angular position κ heat capacity ratio λ 1/s eigenvalue Λ logarithmic decrement μ blade mass ratio ν amplification factor ν visc m 2 /s kinematic viscosity Ξ aerodynamic damping parameter π Ludolph s number Π pressure ratio ρ kg/m 3 density V

12 symbol unit meaning σ interblade phase angle σ STD % standard deviation τ N/m 2 wall shear stress φ angular displacement Φ mode shape vector χ displacement ratio ψ localisation parameter Ψ 1/ kg mass normalised mode shape vector ω rad/s angular frequency ω reduced frequency Ω rad/s angular excitation frequency Subscripts abbreviation meaning 1 conditions at the inlet a aerodynamic values b blade values cos value belonging to the cosine part CSM values of a particular cyclic symmetry mode d disk values eff effective f forcing Im imaginary part is isentropic i, k, n counting variables max maximum min minimum mistuned mistuned values Re real part rel relative frame of reference sec sector variables of EBM sin value belonging to the sine part tan tangential tuned tuned values VI

13 Symbols symbol ˆx x x ˆx ẋ ẍ meaning amplitude average complex number complex amplitude first time derivative second time derivative VII

14 Acronyms Abbreviation ACARE AIC AMM Au3D BTW CFD CMS CSM DOF E3E EBM EO FE FEM FMM FRF FSI FTW HCF IBPA IGV LDV LEO LPT MCSM MpCCI MTO NACA NRBC Meaning Advisory Council for Aeronautics Research in Europe Aerodynamic Influence Coefficients Asymptotic Mistuning Model Rolls-Royce Aeroelasticity Code Backward Travelling Wave Computational Fluid Dynamics Component Mode Based Synthesis Cyclic Symmetry Mode Degree Of Freedom Engine 3E Equivalent Blisk Model Engine Order Finite Element Finite Element Method Fundamental Mistuning Model Frequency Response Function Fluid Structure Interaction Forward Travelling Wave High Cycle Fatigue Interblade Phase Angle Inlet Guide Vane Laser Doppler Vibrometry Low Engine Order Low Pressure Turbine Modified Cyclic Symmetry Mode Mesh based Parallel Code Coupling Interface Maximum Take-Off National Advisory Committee for Aeronautics Non-Reflecting Boundary Conditions VIII

15 Abbreviation Meaning ODS Operating Deflection Shape PMAC Partial Modal Assurance Criterion RMS Root Mean Square ROM Reduced Order Model SC10 Standard Configuration 10 SDOF Single Degree of Freedom SMF Chair of Structural Mechanics and Vehicle Vibration Technology SNM Subset of Nominal Modes UDF User Defined Function VSV Variable Stator Vanes IX