The Influence of Neighboring Blade Rows on the Unsteady Aerodynamic Response of Cascades

1997 ◽  
Vol 119 (1) ◽  
pp. 85-93 ◽  
Author(s):  
K. C. Hall ◽  
P. D. Silkowski
Keyword(s):  
Linear Equations ◽  
Forced Response ◽  
Analytical Models ◽  
Wave Number ◽  
Computationally Efficient ◽  
Blade Vibration ◽  
Transmission Coefficients ◽  
Unsteady Aerodynamic ◽  
Blade Row ◽  
Circumferential Wave

In this paper, we present an analysis of the unsteady aerodynamic response of cascades due to incident gusts (the forced response problem) or blade vibration (the flutter problem) when the cascade is part of a multistage fan, compressor, or turbine. Most current unsteady aerodynamic models assume the cascade to be isolated in an infinitely long duct. This assumption, however, neglects the potentially important influence of neighboring blade rows. We present an elegant and computationally efficient method to model these neighboring blade row effects. In the present method, we model the unsteady aerodynamic response due to so-called spinning modes (pressure and vorticity waves), with each mode corresponding to a different circumferential wave number and frequency. Then, for each mode, we compute the reflection and transmission coefficients for each blade row. These coefficients can be obtained from any of the currently available unsteady linearized aerodynamic models of isolated cascades. A set of linear equations is then constructed that couples together the various spinning modes, and the linear equations are solved via LU decomposition. Numerical results are presented for both the gust response and blade vibration problems. To validate our model, we compare our results to other analytical models, and to a multistage vortex lattice model. We show that the effect of neighboring blade rows on the aerodynamic damping of vibrating cascades is significant, but nevertheless can be modeled with a small number of modes.

scholarly journals The Influence of Neighboring Blade Rows on the Unsteady Aerodynamic Response of Cascades

1995 ◽  
Author(s):  
Kenneth C. Hall ◽  
Peter D. Silkowski
Keyword(s):  
Linear Equations ◽  
Forced Response ◽  
Analytical Models ◽  
Wave Number ◽  
Computationally Efficient ◽  
Blade Vibration ◽  
Transmission Coefficients ◽  
Unsteady Aerodynamic ◽  
Blade Row ◽  
Circumferential Wave

In this paper, we present an analysis of the unsteady aerodynamic response of cascades due to incident gusts (the forced response problem) or blade vibration (the flutter problem) when the cascade is part of a multistage fan, compressor, or turbine. Most current unsteady aerodynamic models assume the cascade to be isolated in an infinitely long duct. This assumption, however, neglects the potentially important influence of neighboring blade rows. We present an elegant and computationally efficient method to model these neighboring blade row effects. In the present method, we model the unsteady aerodynamic response due to so-called spinning modes (pressure and vorticity waves), with each mode corresponding to a different circumferential wave number and frequency. Then, for each mode, we compute the reflection and transmission coefficients for each blade row. These coefficients can be obtained from any of the currently available unsteady linearized aerodynamic models of isolated cascades. A set of linear equations is then constructed that couples together the various spinning modes, and the linear equations are solved via LU decomposition. Numerical results are presented for both the gust response and blade vibration problems. To validate our model, we compare our results to other analytical models, and to a multistage vortex lattice model. We show that the effect of neighboring blade rows on the aerodynamic damping of vibrating cascades is significant, but nevertheless can be modeled with a small number of modes.

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

2020 ◽  
Author(s):  
Anne-Lise Fiquet ◽  
Agathe Vercoutter ◽  
Nicolas Buffaz ◽  
Stéphane Aubert ◽  
Christoph Brandstetter
Keyword(s):  
Acoustic Waves ◽  
High Speed ◽  
Numerical Study ◽  
Acoustic Resonance ◽  
Structural Vibration ◽  
Wave Number ◽  
Blade Vibration ◽  
Acoustic Modes ◽  
Blade Vibrations ◽  
Circumferential Wave

Abstract 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.

Combined-Simultaneous Gust and Oscillating Compressor Blade Unsteady Aerodynamics

1999 ◽  
Author(s):  
Kuk Kim Frey ◽  
Sanford Fleeter
Keyword(s):  
Superposition Principle ◽  
Oscillation Amplitude ◽  
Unsteady Aerodynamics ◽  
Forced Response ◽  
Influence Coefficient ◽  
Torsion Mode ◽  
Unsteady Aerodynamic ◽  
Forcing Function ◽  
Blade Row ◽  
Gust Response

Experiments are performed in a 3-stage axial flow research compressor to investigate and quantify the simultaneous-combined gust and motion induced unsteady aerodynamic response of compressor 1st stage rotor blades. The gust response unsteady aerodynamics are experimentally modeled with a 2/rev forcing function. The torsion mode unsteady aerodynamics are investigated utilizing an experimental influence coefficient technique in conjunction with a unique drive system. Combined gust and oscillating unsteady aerodynamics are obtained by superposition of the separate oscillating blade row and the gust response unsteady aerodynamics. Simultaneous gust and motion induced unsteady aerodynamic response are obtained by driving the torsion mode oscillation in the presence of the 2/Rev forcing function. The effects of steady loading are quantified, with airfoil oscillation amplitude effects also studied. The combined unsteady aerodynamics establish the applicability limitations of the superposition principle at high oscillation amplitudes and high loading. In addition, the gust-blade motion phase angle is identified as a key parameter, with the accuracy of forced response prediction and the alteration of blade row stability due to gust interaction dependent on the gust-blade motion phase.

1997 Best Paper Award—Structures and Dynamics Committee: A Coupled Mode Analysis of Unsteady Multistage Flows in Turbomachinery

1998 ◽  
Vol 120 (3) ◽  
pp. 410-421 ◽  
Author(s):  
P. D. Silkowski ◽  
K. C. Hall
Keyword(s):  
Computational Method ◽  
Reflection And Transmission Coefficients ◽  
Mode Analysis ◽  
Full Potential ◽  
Reflection And Transmission ◽  
Linear System Of Equations ◽  
Transmission Coefficients ◽  
Coupled Mode ◽  
Unsteady Aerodynamic ◽  
Blade Row

A computational method is presented for predicting the unsteady aerodynamic response of a vibrating blade row that is part of a multistage turbomachine. Most current unsteady aerodynamic theories model a single blade row isolated in an infinitely long duct. This assumption neglects the potentially important influence of neighboring blade rows. The present “coupled mode” analysis is an elegant and computationally efficient method for modeling neighboring blade row effects. Using this approach, the coupling between blade rows is modeled using a subset of the so-called spinning modes, i.e., pressure, vorticity, and entropy waves, which propagate between the blade rows. The blade rows themselves are represented by reflection and transmission coefficients. These coefficients describe how spinning modes interact with, and are scattered by, a given blade row. The coefficients can be calculated using any standard isolated blade row model; here we use a linearized full potential flow model together with rapid distortion theory to account for incident vortical gusts. The isolated blade row reflection and transmission coefficients, interrow coupling relationships, and appropriate boundary conditions are all assembled into a small sparse linear system of equations that describes the unsteady multistage flow. A number of numerical examples are presented to validate the method and to demonstrate the profound influence of neighboring blade rows on the aerodynamic damping of a cascade of vibrating airfoils.

ACOUSTIC RESONANCE IN AN AXIAL MULTISTAGE COMPRESSOR LEADING TO NON-SYNCHRONOUS BLADE VIBRATION

2021 ◽  
pp. 1-12
Author(s):  
Anne Lise Fiquet ◽  
Stephane Aubert ◽  
Christoph Brandstetter ◽  
Nicolas Buffaz ◽  
Agathe Vercoutter
Keyword(s):  
High Speed ◽  
Numerical Study ◽  
Acoustic Resonance ◽  
High Amplitude ◽  
Acoustic Mode ◽  
Structural Vibration ◽  
Wave Number ◽  
Blade Vibration ◽  
Acoustic Modes ◽  
Circumferential Wave

Abstract 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 non-coherent 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 as observed in the presented experiments.

Application of Unsteady Aerodynamics and Aeroelasticity in Heavy-Duty Gas Turbines

2005 ◽  
Author(s):  
Matthew Montgomery ◽  
Mehrzad Tartibi ◽  
Frank Eulitz ◽  
Stefan Schmitt
Keyword(s):  
Gas Turbines ◽  
Unsteady Aerodynamics ◽  
Forced Response ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Heavy Duty ◽  
Unsteady Aerodynamic ◽  
Modern Computer ◽  
Blade Row ◽  
Unsteady Effects

Modern computer simulations can predict some aspects of the unsteady aerodynamic phenomena associated with turbomachinery blade rows. This allows analysts to investigate aeroelastic phenomena, such as flutter, and blade-row interactions, such as forced response and unsteady effects on performance. This paper describes tools and design processes used to numerically investigate unsteady aerodynamic phenomena in heavy-duty gas turbines. A linearized Navier-Stokes method from the DLR has been used to predict the aerodynamic damping of both compressor and turbine airfoils under a variety of operating conditions. Some of these predictions were validated with engine experience. Other CFD codes, including TRACE from the DLR and ITSM3D from the University of Stuttgart, have been used to predict blade-row interaction. This includes the prediction of forced response due to rotor-vane interaction and unsteady effects on performance. The effects of airfoil clocking, including the effects of cooling flow injection, have also been investigated.

Blade Resonant Forced Response Excited by Combustor Acoustic Eigenmodes

2015 ◽  
Author(s):  
Arrigo Beretta-Müller ◽  
Jaroslaw Szwedowicz
Keyword(s):  
Turbine Blade ◽  
Pressure Fluctuations ◽  
Fem Analysis ◽  
Forced Response ◽  
Point Of View ◽  
Engineering Practice ◽  
Common Source ◽  
Blade Vibration ◽  
Blade Row ◽  
Axial Turbines

In accordance with common engineering practice, the main source for forced response and subsequent high cycle fatigue problems in axial turbines is classical rotor-stator interaction. This criterion determines the excitability of a blade row for its relative circumferential motion with respect to upstream and downstream blade rows that generate time dependent pressure fields due to potential and viscous flow phenomena as well as possible shock waves. This publication focuses on a less common source of blade vibration excitation induced by acoustic eigenmodes of a combustion chamber. The article gives an overview of a historical example where acoustic pulsations had the potential for exciting harmful vibration on the adjacent first rotating turbine blade row. A 3D acoustic FEM analysis is performed to predict acoustic eigenmodes of the combustion cavity that could potentially excite vibration of the first turbine stage. Acoustic modes in the range of the critical frequencies from the point of view of resonance with structural eigenfrequencies of neighbouring components are identified and compared to engine measurements. The knowledge gained of the critical frequencies allows for mitigation of the excitation sources with Helmholtz dampers. This paper delivers an additional excitability criterion of rotating blades by acoustic pressure fluctuations in the combustor. Turbine blade excitation is currently assessed only by considering the number of burners in the combustor chamber.

A Coupled Mode Analysis of Unsteady Multistage Flows in Turbomachinery

1997 ◽  
Author(s):  
Peter D. Silkowski ◽  
Kenneth C. Hall
Keyword(s):  
Computational Method ◽  
Reflection And Transmission Coefficients ◽  
Mode Analysis ◽  
Full Potential ◽  
Reflection And Transmission ◽  
Linear System Of Equations ◽  
Transmission Coefficients ◽  
Coupled Mode ◽  
Unsteady Aerodynamic ◽  
Blade Row

A computational method is presented for predicting the unsteady aerodynamic response of a vibrating blade row which is part of a multistage turbomachine. Most current unsteady aerodynamic theories model a single blade row isolated in an infinitely long duct. This assumption neglects the potentially important influence of neighboring blade rows. The present ‘coupled mode’ analysis is an elegant and computationally efficient method for modelling neighboring blade row effects. Using this approach, the coupling between blade rows is modelled using a subset of the so-called spinning modes, i.e. pressure, vorticity, and entropy waves which propagate between the blade rows. The blade rows themselves are represented by reflection and transmission coefficients. These coefficients describe how spinning modes interact with, and are scattered by, a given blade row. The coefficients can be calculated using any standard isolated blade row model; here we use a linearized full potential flow model together with rapid distortion theory to account for incident vortical gusts. The isolated blade row reflection and transmission coefficients, inter-row coupling relationships, and appropriate boundary conditions are all assembled into a small sparse linear system of equations which describes the unsteady multistage flow. A number of numerical examples are presented to validate the method and to demonstrate the profound influence of neighboring blade rows on the aerodynamic damping of a cascade of vibrating airfoils.

Aerodynamic Asymmetry Analysis of Unsteady Flows in Turbomachinery

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Kivanc Ekici ◽  
Robert E. Kielb ◽  
Kenneth C. Hall
Keyword(s):  
Harmonic Balance ◽  
Coupling Effect ◽  
Unsteady Flows ◽  
Unsteady Aerodynamic ◽  
Blade Row ◽  
Balance Technique ◽  
Turbomachinery Blades ◽  
Aerodynamic Asymmetry ◽  
Frequency Domain Approach ◽  
Harmonic Balance Technique

A nonlinear harmonic balance technique for the analysis of aerodynamic asymmetry of unsteady flows in turbomachinery is presented. The present method uses a mixed time-domain/frequency-domain approach that allows one to compute the unsteady aerodynamic response of turbomachinery blades to self-excited vibrations. Traditionally, researchers have investigated the unsteady response of a blade row with the assumption that all the blades in the row are identical. With this assumption the entire wheel can be modeled using complex periodic boundary conditions and a computational grid spanning a single blade passage. In this study, the steady/unsteady aerodynamic asymmetry is modeled using multiple passages. Specifically, the method has been applied to aerodynamically asymmetric flutter problems for a rotor with a symmetry group of 2. The effect of geometric asymmetries on the unsteady aerodynamic response of a blade row is illustrated. For the cases investigated in this paper, the change in the diagonal terms (blade on itself) dominated the change in stability. Very little mode coupling effect caused by the off-diagonal terms was found.

Extension of forward modeling phase-screen code in isotropic and anisotropic media up to critical angle

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM107-SM114 ◽  
Author(s):  
James C. White ◽  
Richard W. Hobbs
Keyword(s):  
Critical Angle ◽  
Model Space ◽  
Anisotropic Media ◽  
Forward Modeling ◽  
Phase Screen ◽  
Computationally Efficient ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Phase Corrections ◽  
Converted Phases

The computationally efficient phase-screen forward modeling technique is extended to allow investigation of nonnormal raypaths. The code is developed to accommodate all diffracted and converted phases up to critical angle, building on a geometric construction method. The new approach relies upon prescanning the model space to assess the complexity of each screen. The propagating wavefields are then divided as a function of horizontal wavenumber, and each subset is transformed to the spatial domain separately, carrying with it angular information. This allows both locally accurate 3D phase corrections and Zoeppritz reflection and transmission coefficients to be applied. The phase-screen code is further developed to handle simple anisotropic media. During phase-screen modeling, propagation is undertaken in the wavenumber domain where exact expressions for anisotropic phase velocities are available. Traveltimes and amplitude effects from a range of anisotropic shales are computed and compared with previous published results.

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