Flow-Excited Acoustic Resonance of Trapped Modes of a Ducted Rectangular Cavity

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Michael Bolduc ◽  
Samir Ziada ◽  
Philippe Lafon
Keyword(s):  
Shear Layer ◽  
Particle Velocity ◽  
Acoustic Mode ◽  
Velocity Fields ◽  
Mode Shapes ◽  
Trapped Modes ◽  
Mean Flow ◽  
Cross Sectional ◽  
Shallow Cavities ◽  
Axisymmetric Cavities

Flow over ducted cavities can lead to strong resonances of the trapped acoustic modes due to the presence of the cavity within the duct. Aly and Ziada (2010, “Flow-Excited Resonance of Trapped Modes of Ducted Shallow Cavities,” J. Fluids Struct., 26(1), pp. 92–120; 2011, “Azimuthal Behaviour of Flow-Excited Diametral Modes of Internal Shallow Cavities,” J. Sound Vib., 330(15), pp. 3666–3683; and 2012, “Effect of Mean Flow on the Trapped Modes of Internal Cavities,” J. Fluids Struct., 33, pp. 70–84) investigated the excitation mechanism of acoustic trapped modes in axisymmetric cavities. These trapped modes in axisymmetric cavities tend to spin because they do not have preferred orientation. The present paper investigates rectangular cross-sectional cavities as this cavity geometry introduces an orientation preference to the excited acoustic mode. Three cavities are investigated, one of which is square while the other two are rectangular. In each case, numerical simulations are performed to characterize the acoustic mode shapes and the associated acoustic particle velocity fields. The test results show the existence of stationary modes, being excited either consecutively or simultaneously, and a particular spinning mode for the cavity with square cross section. The computed acoustic pressure and particle velocity fields of the excited modes suggest complex oscillation patterns of the cavity shear layer because it is excited, at the upstream corner, by periodic distributions of the particle velocity along the shear layer circumference.

Resonance of Trapped Acoustic Modes of a Ducted Rectangular Cavity

2015 ◽  
Author(s):  
Michael Bolduc ◽  
Samir Ziada ◽  
Philippe Lafon
Keyword(s):  
Shear Layer ◽  
Particle Velocity ◽  
Acoustic Mode ◽  
Velocity Fields ◽  
Mode Shapes ◽  
Test Results ◽  
Trapped Modes ◽  
Cross Sectional ◽  
Acoustic Modes ◽  
Axisymmetric Cavities

Flow over ducted cavities can lead to strong resonances of the trapped acoustic modes due to the presence of the cavity within the duct. Aly & Ziada [1–3] investigated the excitation mechanism of acoustic trapped modes in axisymmetric cavities. These trapped modes in axisymmetric cavities tend to spin because they do not have preferred orientation. The present paper investigates rectangular cross-sectional cavities as this cavity geometry introduces an orientation preference to the excited acoustic mode. Three cavities are investigated, one of which is square while the other two are rectangular. In each case, numerical simulations are performed to characterize the acoustic mode shapes and the associated acoustic particle velocity fields. The test results show the existence of stationary modes, being excited either consecutively or simultaneously, and a particular spinning mode for the cavity with square cross-section. The computed acoustic pressure and particle velocity fields of the excited modes suggest complex oscillation patterns of the cavity shear layer because it is excited, at the upstream corner, by periodic distributions of the particle velocity along the shear layer circumference.

Modeling of Unstable Regimes in a Rijke Tube

2002 ◽  
Author(s):  
K. I. Matveev ◽  
F. E. C. Culick
Keyword(s):  
Heat Transfer ◽  
Limit Cycle ◽  
Nonlinear Models ◽  
Acoustic Mode ◽  
Heat Transfer Process ◽  
Dominant Mode ◽  
Mode Shapes ◽  
Mean Flow ◽  
Rijke Tube ◽  
Thermoacoustic Instabilities

In the ducts with mean flows and heat sources, excitation of acoustic eigen modes is possible when unsteady heat release is coupled with pressure perturbations. The simplest device for studying the fundamental principles of thermoacoustic instabilities in the presence of a mean flow is a Rijke tube. In this work a series of experiments was carried out to determine the conditions for the transition to instability and the non-linear characteristics of a Rijke tube, such as limit-cycle amplitudes and frequencies of the dominant mode. Sound, excited in the tube, affects the heat transfer process; that leads to modifications of the acoustic mode shapes and steady state properties. It was observed in the experiment that the thermoacoustic system possesses hysteresis. A mathematical model incorporating heat transfer, acoustics, and thermoacoustic interactions is developed for determining the transition to instability. The dominant nonlinear factor in the system, defining the limit-cycle characteristics, is the nonlinearity of the heater transfer function. Two approximate and generally applicable nonlinear models are considered, and results of the modeling are compared with the experimental data for one position of the heater. The influence of noise on the transitions between stable and unstable regimes is discussed.

Review of Flow-Excited Resonance of Acoustic Trapped Modes in Ducted Shallow Cavities

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Kareem Aly ◽  
Samir Ziada
Keyword(s):  
Interaction Mechanism ◽  
Acoustic Resonance ◽  
Feedback Mechanism ◽  
Mode Shapes ◽  
Trapped Modes ◽  
Resonance Amplitude ◽  
Sound Fields ◽  
Trapped Mode ◽  
Shallow Cavities ◽  
Cavity Flow Oscillations

Flow-excited resonances of acoustic trapped modes in ducted shallow cavities are reviewed in this paper. The main components of the feedback mechanism which sustains the acoustic resonance are discussed with particular emphasis on the complexity of the trapped mode shapes and the strong three-dimensionality of the cavity flow oscillations during the resonance. Due to these complexities of the flow and sound fields, it is still difficult to theoretically or numerically model the interaction mechanism which sustains the acoustic resonance. Strouhal number and resonance amplitude charts are therefore included to help designers avoid the occurrence of resonance in new installations, and effective countermeasures are provided which can be implemented to suppress trapped mode resonances in operating plants.

Numerical Simulation of Internal Cavities Acoustic Trapped Modes With Mean Flow

2010 ◽  
Author(s):  
Kareem Aly ◽  
Samir Ziada
Keyword(s):  
Mach Number ◽  
Acoustic Field ◽  
Particle Velocity ◽  
Perturbation Equation ◽  
Duct System ◽  
Trapped Modes ◽  
Mean Flow ◽  
Phase Gradient ◽  
The Mean ◽  
Mach Numbers

Flow-excited acoustic resonance of trapped modes in ducts has been reported in different engineering applications. The excitation mechanism of these modes results from the interaction between the hydrodynamic flow field and the acoustic particle velocity, and is therefore dependent on the mode shape of the resonant acoustic field, including the amplitude and phase distributions of the acoustic particle velocity. For a cavity-duct system, the aerodynamic excitation of the trapped modes can generate strong pressure pulsations at moderate Mach numbers (M>0.1). This paper investigates numerically the effect of mean flow on the characteristics of the acoustic trapped modes for a cavity-duct system. Numerical simulations are performed for a two-dimensional planar configuration and different flow Mach numbers up to 0.3. A two-step numerical scheme is adopted in the investigation. A linearized acoustic perturbation equation is used to predict the acoustic field. The results show that as the Mach number is increased, the acoustic pressure distribution develops an axial phase gradient, but the shape of the amplitude distribution remains the same. Moreover, the amplitude and phase distributions of the acoustic particle velocity are found to change significantly near the cavity shear layer with the increase of the mean flow Mach number. These results demonstrate the importance of considering the effects of the mean flow on the flow-sound interaction mechanism.

Flow-Acoustic Coupling in T-Junctions: Effect of T-Junction Geometry

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
S. Ziada ◽  
K. W. McLaren ◽  
Y. Li
Keyword(s):  
Shear Layer ◽  
Flow Velocity ◽  
Acoustic Resonance ◽  
Acoustic Mode ◽  
Coupling Mechanism ◽  
Cross Sectional ◽  
Acoustic Coupling ◽  
Pipe Expansion ◽  
Junction Geometry ◽  
Acoustic Resonances

The flow-acoustic coupling mechanism in a T-junction, which combines flows from two branches, forming the “cross-bar” of the T-junction, into one pipe, forming the “stem” of the T-junction, is investigated experimentally. The T-junction has a step pipe expansion at its inlets. The shear layer separating from this step expansion is found to excite intense acoustic resonances over multiple ranges of flow velocity. The excited acoustic mode is confined to the branch pipes and has an acoustic pressure node at the centerline of the T-junction. The length of the expansion section of the T-junction is found to control the frequency of the shear layer oscillation and therefore determines the ranges of flow velocity over which acoustic resonances are excited. Introducing asymmetry in the T-junction expansion length has shown little influence on the excitation of acoustic resonance. An additional T-junction arrangement made of rectangular cross-sectional ducts is also investigated to facilitate a flow visualization study of unsteady flow structures in the T-junction during acoustic resonance, and thereby improve understanding of the acoustic resonance mechanism and the nature of the aero-acoustic sources in the T-junction.

Passive Control of Trapped Mode Resonance of Ducted Cavities

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
M. Bolduc ◽  
M. Elsayed ◽  
S. Ziada
Keyword(s):  
Gas Flow ◽  
Passive Control ◽  
Effective Means ◽  
Acoustic Resonance ◽  
Trapped Modes ◽  
Mean Flow ◽  
Acoustic Modes ◽  
Trapped Mode ◽  
Shallow Cavities ◽  
Set Up

Gas flow over ducted cavities can excite strong acoustic resonances within the confined volumes housing the cavities. When the wavelength of the resonant acoustic modes is comparable with, or smaller than, the cavity dimensions, these modes are referred to as trapped acoustic modes. The flow excitation mechanism causing the resonance of these trapped modes in axisymmetric shallow cavities has been investigated experimentally in a series of papers by Aly and Ziada (2010, “Flow-Excited Resonance of Trapped Modes of Ducted Shallow Cavities,” J. Fluids Struct., 26, pp. 92–120; 2011, “Azimuthal Behaviour of Flow-Excited Diametral Modes of Internal Shallow Cavities,” J. Sound Vib., 330, pp. 3666–3683; 2012, “Effect of Mean Flow on the Trapped Modes of Internal Cavities,” J. Fluids Struct., 33, pp. 70–84). In this paper, the same experimental set-up is used to investigate the effect of the upstream edge geometry on the acoustic resonance of trapped modes. The investigated geometries include sharp and rounded cavity corners, chamfering the upstream edge, and spoilers of different types and sizes. Rounding-off the cavity edges is found to increase the pulsation amplitude substantially, but the resonance lock-on range is delayed, i.e., it is shifted to higher flow velocities. Similarly, chamfering the upstream corner delays the onset of resonance, but maintains its intensity in comparison with that of sharp edges. Spoilers, or vortex generators, added at the upstream edge have been found to be the most effective means to suppress the resonance. However, the minimum spoiler size which is needed to suppress the resonance increases as the cavity size becomes larger.

PIV Measurements of Turbulent Flows Over Single and Dual Rectangular Cavities

2015 ◽  
Author(s):  
Khaled J. Hammad ◽  
Kyle W. Saucier ◽  
Nicholas C. Koblick
Keyword(s):  
Shear Layer ◽  
Turbulent Flows ◽  
Velocity Fields ◽  
Free Shear Layer ◽  
Mean Flow ◽  
Cavity Depth ◽  
Piv Measurements ◽  
Reynolds Decomposition ◽  
Cavity Configuration ◽  
Layer Region

Particle Image Velocimetry (PIV) was used to measure the turbulent flow fields over single and dual rectangular cavities. Four sets of PIV measurements were acquired, corresponding to two Reynolds numbers per each cavity configuration. The cavity depth based Reynolds number was varied between 21,000 and 42,000, while the cavity length-to-depth ratio was fixed at four. Galilean decomposition is used to present instantaneous velocity fields. Turbulent velocity fields are presented using Reynolds decomposition into mean and fluctuating components. Characteristics of the instantaneous and time-averaged velocity fields corresponding to a single cavity configuration are in agreement with the observations from previous studies. All mean flow field results display a large vortical structure spanning the entire length and height of each cavity. In the case of a dual cavity configuration, the free shear layer and trailing edge regions of the second cavity were found to always display higher streamwise and crosswise flow fluctuations in comparison with the first cavity. Furthermore, a wider free shear layer region is observed in the second cavity, in comparison with the first cavity.

scholarly journals A frictional Cosserat model for the slow shearing of granular materials

2002 ◽  
Vol 457 ◽  
pp. 377-409 ◽  
Author(s):  
L. SRINIVASA MOHAN ◽  
K. KESAVA RAO ◽  
PRABHU R. NOTT
Keyword(s):  
Angular Velocity ◽  
Granular Material ◽  
Shear Layer ◽  
Granular Materials ◽  
Layer Thickness ◽  
Couette Flow ◽  
Velocity Fields ◽  
Cosserat Continuum ◽  
Cosserat Model ◽  
Cylindrical Couette Flow

A rigid-plastic Cosserat model for slow frictional flow of granular materials, proposed by us in an earlier paper, has been used to analyse plane and cylindrical Couette flow. In this model, the hydrodynamic fields of a classical continuum are supplemented by the couple stress and the intrinsic angular velocity fields. The balance of angular momentum, which is satisfied implicitly in a classical continuum, must be enforced in a Cosserat continuum. As a result, the stress tensor could be asymmetric, and the angular velocity of a material point may differ from half the local vorticity. An important consequence of treating the granular medium as a Cosserat continuum is that it incorporates a material length scale in the model, which is absent in frictional models based on a classical continuum. Further, the Cosserat model allows determination of the velocity fields uniquely in viscometric flows, in contrast to classical frictional models. Experiments on viscometric flows of dense, slowly deforming granular materials indicate that shear is confined to a narrow region, usually a few grain diameters thick, while the remaining material is largely undeformed. This feature is captured by the present model, and the velocity profile predicted for cylindrical Couette flow is in good agreement with reported data. When the walls of the Couette cell are smoother than the granular material, the model predicts that the shear layer thickness is independent of the Couette gap H when the latter is large compared to the grain diameter dp. When the walls are of the same roughness as the granular material, the model predicts that the shear layer thickness varies as (H/dp)1/3 (in the limit H/dp [Gt ] 1) for plane shear under gravity and cylindrical Couette flow.

scholarly journals Detailed Analysis of the Acoustic Mode Shapes of an Annular Combustion Chamber

1999 ◽  
Author(s):  
Günther Walz ◽  
Werner Krebs ◽  
Stefan Hoffmann ◽  
Hans Judith
Keyword(s):  
Boundary Conditions ◽  
Acoustic Mode ◽  
Mode Shapes ◽  
Maximum Deviation ◽  
Minor Importance ◽  
Velocity Of Sound ◽  
Fe Method ◽  
Shift Frequency ◽  
Space Dependence ◽  
Eigenfrequency Spectrum

To get a better understanding of the formation of thermoacoustic oscillations in an annular gasturbine combustor, an analysis of the acoustic eigenmodes has been conducted using the Finite Element (FE) method. The influence of different boundary conditions and a space dependent velocity of sound has been investigated. The boundary conditions actually define the eigenfrequency spectrum. Hence, it is crucial to know e.g. the burner impedance. In case of the combustion system without significant mixing air addition considered in this paper, the space dependence of the velocity of sound is of minor importance for the eigenfrequency spectrum leading to a maximum deviation of only 5% in the eigenvalues. It is demonstrated that the efficiency of the numerical eigenvalue analysis can be improved by making use of symmetry, by splitting the problem into several steps with alternate boundaries conditions, and by choosing the shift frequency ωs in the range of frequencies one is interested in.

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