Causes of Acoustic Resonance in a High-Speed Axial Compressor

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Bernd Hellmich ◽  
Joerg R. Seume
Keyword(s):  
Mach Number ◽  
High Speed ◽  
Axial Compressor ◽  
Acoustic Resonance ◽  
Acoustic Mode ◽  
Aerodynamic Load ◽  
Mean Flow ◽  
Resonance Frequencies ◽  
Physically Based ◽  
Good Agreement

Nonharmonic acoustic resonance was detected in the static pressure and sound signals in a four-stage high-speed axial compressor when the compressor was operating close to the surge limit. Based on prior research reported in the literature and measurements of the resonance frequency, Mach number of the mean flow, and the axial and circumferential phase shifts of the pressure signal during resonance, it is shown that the acoustic resonance is an axial standing wave of a spinning acoustic mode with three periods around the circumference of the compressor. This phenomenon occurs only if the aerodynamic load in the compressor is high, because the mode needs a high circumferential Mach number for resonance conditions. Mathematics of existing analyses of acoustic resonances in turbomachinery complex and have therefore rarely resulted in published examples of good agreement with real engine data. The present paper provides suitable, physically based simplifications of the existing mathematical models which are applicable for modes with circumferential wavelengths of more than two blade pitches and resonance frequencies considerably higher than the rotor speed.

Causes of Acoustic Resonance in a High-Speed Axial Compressor

2006 ◽  
Author(s):  
Bernd Hellmich ◽  
Joerg Seume
Keyword(s):  
Mach Number ◽  
High Speed ◽  
Axial Compressor ◽  
Acoustic Resonance ◽  
Acoustic Mode ◽  
Aerodynamic Load ◽  
Mean Flow ◽  
Resonance Frequencies ◽  
Physically Based ◽  
Good Agreement

Non-harmonic acoustic resonance was detected in the static pressure and sound signals in a four-stage high-speed axial compressor when the compressor was operating close to the surge limit. Based on prior research reported in the literature and measurements of the resonance frequency, Mach number of the mean flow, and the axial and circumferential phase shift of the pressure signal during resonance it is shown that the acoustic resonance is an axial standing wave of a spinning acoustic mode with three periods around the circumference of the compressor. This phenomenon occurs only if the aerodynamic load in the compressor is high, because the mode needs a high circumferential Mach number for resonance conditions. Mathematics of existing analyses of acoustic resonances in turbomachinery are complex and have therefore rarely resulted in published examples of good agreement with real engine data. The present paper provides suitable, physically based simplifications of the existing mathematical models which are applicable for modes with circumferential wavelengths of more than two blade pitches and resonance frequencies considerably higher than the rotor speed.

scholarly journals A Time-Shifting Algorithm for Alleviating Convergence Difficulties at Interior Acoustic Resonance Frequencies

2021 ◽  
Vol 11 (6) ◽  
pp. 2701
Author(s):  
Jui Hsiang Kao
Keyword(s):  
Point Source ◽  
Time Domain ◽  
Internal Resonance ◽  
Acoustic Resonance ◽  
Time Step ◽  
Resonance Frequencies ◽  
True Frequency ◽  
The Time Domain ◽  
Acoustic Domain ◽  
Good Agreement

This paper proposes a time-shifting boundary element method in the time domain to calculate the radiating pressures of an arbitrary object pulsating at eigenfrequencies of the interior (i.e., interior resonance frequencies). In this paper, the frequency shifting is time-step-dependent and could be viewed as an iterative, or relaxation, technique for the solution of the problem. The proposed method avoids numerical problems due to the internal resonance frequency by initializing the iteration with each scaled frequency. The scaled frequency is approximately equal to the true frequency at the last iterating time step. A sphere pulsating at the eigenfrequency in an infinite acoustic domain was calculated first; the result was compared with the analytical solution, and they were in good agreement. Moreover, two arbitrary-shaped radiators were taken as study cases to predict the radiating pressures at the interior resonance frequencies, and robustly convergent results were obtained. Finally, the accuracy of the proposed method was tested using a problem with a known solution. A point source was placed inside the object to compute the surface velocities; the computed surface pressures were identical to the pressures computed using the point source.

Acoustic resonance in the potential core of subsonic jets

2017 ◽  
Vol 825 ◽  
pp. 1113-1152 ◽  
Author(s):  
Aaron Towne ◽  
André V. G. Cavalieri ◽  
Peter Jordan ◽  
Tim Colonius ◽  
Oliver Schmidt ◽  
...  
Keyword(s):  
Mach Number ◽  
Travelling Waves ◽  
Saddle Points ◽  
Turning Points ◽  
Acoustic Resonance ◽  
Vortex Sheet ◽  
Mean Flow ◽  
Potential Core ◽  
Acoustic Modes ◽  
The Waves

The purpose of this paper is to characterize and model waves that are observed within the potential core of subsonic jets and relate them to previously observed tones in the near-nozzle region. The waves are detected in data from a large-eddy simulation of a Mach 0.9 isothermal jet and modelled using parallel and weakly non-parallel linear modal analysis of the Euler equations linearized about the turbulent mean flow, as well as simplified models based on a cylindrical vortex sheet and the acoustic modes of a cylindrical soft duct. In addition to the Kelvin–Helmholtz instability waves, three types of waves with negative phase velocities are identified in the potential core: upstream- and downstream-propagating duct-like acoustic modes that experience the shear layer as a pressure-release surface and are therefore radially confined to the potential core, and upstream-propagating acoustic modes that represent a weak coupling between the jet core and the free stream. The slow streamwise contraction of the potential core imposes a frequency-dependent end condition on the waves that is modelled as the turning points of a weakly non-parallel approximation of the waves. These turning points provide a mechanism by which the upstream- and downstream-travelling waves can interact and exchange energy through reflection and transmission processes. Paired with a second end condition provided by the nozzle, this leads to the possibility of resonance in limited frequency bands that are bound by two saddle points in the complex wavenumber plane. The predicted frequencies closely match the observed tones detected outside of the jet. The vortex-sheet model is then used to systematically explore the Mach number and temperature ratio dependence of the phenomenon. For isothermal jets, the model suggests that resonance is likely to occur in a narrow range of Mach number,$0.82<M<1$.

Numerical Studies on the Intrusive Influence of a Five-Hole Pressure Probe in a High-Speed Axial Compressor

2017 ◽  
Author(s):  
Christoph Sanders ◽  
Marius Terstegen ◽  
Magnus Hölle ◽  
Peter Jeschke ◽  
Harald Schönenborn ◽  
...  
Keyword(s):  
Mach Number ◽  
Flow Field ◽  
High Speed ◽  
Axial Compressor ◽  
Forced Response ◽  
Rotor Blades ◽  
Pressure Probe ◽  
Maximum Deviation ◽  
Hole Pressure ◽  
Forcing Functions

In this investigation, CFD calculations are conducted to evaluate the differences between five-hole pressure probe-determined flow quantities and the unaffected flow quantities without the probe’s intrusive influence. The blockage effect of the probe is described and evaluated. Furthermore, the influence of this effect is used to estimate the error when using measured stator outflows as forcing functions for the following rotor blades. To compare the flow field, both with and without the probe’s influence, a five-hole pressure probe is traversed numerically at midspan behind each stator row of a 2.5-stage axial compressor. For reproducing the blockage of the probe accurately, the full annulus of the respective stator row has to be modeled. In order to minimize the calculation time, a study to reduce the number of stator passages was successfully performed. To evaluate the flow quantities using the probe, a calibration polynomial is set up numerically. CFD simulations of the probe geometry within a uniform flow field for each pitch and yaw angle, as well as Mach number combination, are performed for this purpose. Moreover, the pressure probe data for the numerical traverses are corrected to account for velocity gradients in the wake region. The comparison of Mach number, with and without the probe’s influence, shows differences both in the width and the depth of the wake. The results of the Fourier-transformed wake profile for both cases are compared and changes in the first harmonic of Mach number of up to −13% identified. Finally, the first harmonic of the flow quantities is used to perform linearized CFD calculations and to evaluate the influence of disturbed forcing functions on the aerodynamic work of the following rotor blade. The average difference in aerodynamic excitation is about −12% with a maximum deviation of more than −30%. The results presented aim to draw attention to intrusive probe influences and their consequences for validating numerical results against experiments. Special attention is given to the discrepancies of forced response calculations with varying gust boundary conditions.

Edge, cavity and aperture tones at very low Mach numbers

1997 ◽  
Vol 330 ◽  
pp. 61-84 ◽  
Author(s):  
M. S. HOWE
Keyword(s):  
Mach Number ◽  
Response Function ◽  
Impulse Response Function ◽  
Shear Layers ◽  
Acoustic Resonator ◽  
Complex Frequency ◽  
Mean Flow ◽  
The Real ◽  
Resonance Frequencies ◽  
High Reynolds

This paper discusses self-sustaining oscillations of high-Reynolds-number shear layers and jets incident on edges and corners at infinitesimal Mach number. These oscillations are frequently sources of narrow-band sound, and are usually attributed to the formation of discrete vortices whose interactions with the edge or corner produce impulsive pressures that lead to the formation of new vorticity and complete a feedback cycle of operation. Linearized analyses of these interactions are presented in which free shear layers are modelled by vortex sheets. Detailed results are given for shear flows over rectangular wall apertures and shallow cavities, and for the classical jet–edge interaction. The operating stages of self-sustained oscillations are identified with poles in the upper half of the complex frequency plane of a certain impulse response function. It is argued that the real parts of these poles determine the Strouhal numbers of the operating stages observed experimentally for the real, nonlinear system. The response function coincides with the Rayleigh conductivity of the ‘window’ spanned by the shear flow for wall apertures and jet–edge interactions, and to a frequency dependent drag coefficient for shallow wall cavities. When the interaction occurs in the neighbourhood of an acoustic resonator, exemplified by the flue organ pipe, the poles are augmented by a sequence of poles whose real parts are close to the resonance frequencies of the resonator, and the resonator can ‘speak’ at one of these frequencies (by extracting energy from the mean flow) provided the corresponding pole has positive imaginary part.The Strouhal numbers predicted by this theory for a shallow wall cavity agree well with data extrapolated to zero Mach number from measurements in air, and predictions for the jet–edge interaction are in excellent accord with data from various sources in the literature. In the latter case, the linear theory also agrees for all operating stages with an empirical, nonlinear model that takes account of the formation of discrete vortices in the jet.

Comprehensive Smith Charts for Axial Compressor Design

2019 ◽  
Author(s):  
Mark R. Anderson
Keyword(s):  
Mach Number ◽  
High Speed ◽  
Axial Compressor ◽  
Flow State ◽  
Simple Method ◽  
Axial Compressors ◽  
Wide Range ◽  
2D Flow ◽  
Mach Numbers ◽  
Smith Chart

Abstract The “Smith Chart” has been recognized as an indispensable technique when applied to the initial design of axial compressors and turbines. The Smith Chart offers a simple method to locate the region of optimum efficiency which is achievable as a function of flow and work coefficient. The result is a targeted flow state represented by the velocity triangles that result from these coefficients. The process was originally developed, and is best documented, for axial turbines1. Over the years, several publications, of similar methods for axial compressors have been put forward. The author presented one such work2 which made significant use of optimization to develop an improved Smith chart for moderate Mach number compressor designs. In the current work, these results are expanded to both low Mach number (basically incompressible) to high-speed transonic cases as well. Similar to the previous work, the effort makes extensive use of optimization to systematically explore the optimum 2D profile shapes for a wide range of target flow and work coefficients. The method uses an FNS quasi-3D CFD solver, coupled to an efficiently parameterized geometry generator, combined with an automated optimization process. The process was applied independently to dozens of flow and work coefficient points to generate comprehensive maps of performance. Results are shown for three different relative inflow Mach numbers: 0.2, 0.75, and 1.1. The maps are displayed in classic Smith chart format of islands of stage efficiency as a function of the flow and work coefficient. Specifically, the results are for axial compressor stages of 50% reaction, the theoretical ideal reaction for 2D flow. The results and the implications over varying Mach numbers are discussed. Also included is an expanded discussion of the range and accuracy of various meanline modeling methods, along with their ability to determine the optimum design condition.

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.

The flow in the mixing region of a jet

1964 ◽  
Vol 18 (4) ◽  
pp. 529-548 ◽  
Author(s):  
Marc A. Kolpin
Keyword(s):  
Mach Number ◽  
Velocity Field ◽  
Correlation Functions ◽  
High Speed ◽  
Time Correlation ◽  
Space Time ◽  
Time Correlation Functions ◽  
List Type ◽  
Mean Flow ◽  
The Mean

The object of this work was to investigate experimentally the structure of the early shear layer of high-speed jets and its relation to the mechanism of noise generation. Of special interest was the question of the existence of periodic fluctuations in the velocity field. The experimental investigation is divided in three parts.Optical observation of the jet flow by means of the shadowgraph technique.Measurement of mean Mach number and temperature profiles.Survey by means of hot-wire of the component of the fluctuating velocity field in the mean flow direction.The shadowgraphs show very interesting features of the breakdown process of free shear layers, but fail to show any propagation of strong acoustic disturbances in the near pressure-field.Mean profile measurements show that the flow field in the range 1 [les ]x/d[les ] 4 develops in a conical fashion, i.e. the mean profiles in Mach number and temperature can be expressed in terms of a single conical variable η = (2r–d)/2x. The fluctuating velocity field is described in terms of the intensity of turbulence, its spectral distribution, and two-point space-time correlation functions. Similarity laws are given for the power spectra and the space-time correlation functions. On the cylinderr= ½d, the convection speed of the turbulent field is different for the different eddy sizes, varying from the local mean speed for small eddies to ½Uexitfor the large eddies. Measurements of the angular correlation function are reported which show no correlation of the fluctuations across the jet diameter.

Modeling of Tread Block Contact Mechanics Using Linear Viscoelastic Theory3

2008 ◽  
Vol 36 (3) ◽  
pp. 211-226 ◽  
Author(s):  
F. Liu ◽  
M. P. F. Sutcliffe ◽  
W. R. Graham
Keyword(s):  
High Speed ◽  
Slip Rate ◽  
Material Model ◽  
Contact Forces ◽  
Block Modeling ◽  
Rate Dependent ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic ◽  
The Impact ◽  
Good Agreement

Abstract In an effort to understand the dynamic hub forces on road vehicles, an advanced free-rolling tire-model is being developed in which the tread blocks and tire belt are modeled separately. This paper presents the interim results for the tread block modeling. The finite element code ABAQUS/Explicit is used to predict the contact forces on the tread blocks based on a linear viscoelastic material model. Special attention is paid to investigating the forces on the tread blocks during the impact and release motions. A pressure and slip-rate-dependent frictional law is applied in the analysis. A simplified numerical model is also proposed where the tread blocks are discretized into linear viscoelastic spring elements. The results from both models are validated via experiments in a high-speed rolling test rig and found to be in good agreement.

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