scholarly journals Acoustic waves in ducts with sinusoidally perturbed walls and mean flow

1975 ◽  
Vol 57 (5) ◽  
pp. 1036-1039 ◽  
Author(s):  
Ali H. Nayfeh
Keyword(s):  
Acoustic Waves ◽  
Mean Flow

scholarly journals Streaming by leaky surface acoustic waves

2010 ◽  
Vol 467 (2130) ◽  
pp. 1779-1800 ◽  
Author(s):  
J. Vanneste ◽  
O. Bühler
Keyword(s):  
Surface Waves ◽  
Acoustic Waves ◽  
Surface Acoustic Waves ◽  
Acoustic Streaming ◽  
Stokes Drift ◽  
Mean Flow ◽  
Matched Asymptotics ◽  
Flow Generation ◽  
Solid Liquid Interface ◽  
Solid Liquid

Acoustic streaming, the generation of mean flow by dissipating acoustic waves, provides a promising method for flow pumping in microfluidic devices. In recent years, several groups have been experimenting with acoustic streaming induced by leaky surface waves: (Rayleigh) surface waves excited in a piezoelectric solid interact with a small volume of fluid where they generate acoustic waves and, as result of the viscous dissipation of these waves, a mean flow. We discuss the computation of the corresponding Lagrangian mean flow, which controls the trajectories of fluid particles and hence the mixing properties of the flows generated by this method. The problem is formulated using the averaged vorticity equation which extracts the dominant balance between wave dissipation and mean-flow dissipation. Particular attention is paid to the thin boundary layer that forms at the solid/liquid interface, where the flow is best computed using matched asymptotics. This leads to an explicit expression for a slip velocity, which includes the effect of the oscillations of the boundary. The Lagrangian mean flow is naturally separated into three contributions: an interior-driven Eulerian mean flow, a boundary-driven Eulerian mean flow and the Stokes drift. A scale analysis indicates that the latter two contributions can be neglected in devices much larger than the acoustic wavelength but need to be taken into account in smaller devices. A simple two-dimensional model of mean flow generation by surface acoustic waves is discussed as an illustration.

An Acoustic Time-of-Flight Approach for Unsteady Temperature Measurements: Characterization of Entropy Waves in a Model Gas Turbine Combustor

2016 ◽  
Vol 139 (4) ◽  
Author(s):  
Dominik Wassmer ◽  
Bruno Schuermans ◽  
Christian Oliver Paschereit ◽  
Jonas P. Moeck
Keyword(s):  
Gas Turbine ◽  
Acoustic Waves ◽  
Fuel Injection ◽  
Acoustic Pulse ◽  
Time Of Flight ◽  
Phase Lag ◽  
Mean Flow ◽  
Unsteady Temperature ◽  
Arrival Times ◽  
Flow Velocities

Lean premixed combustion promotes the occurrence of thermoacoustic phenomena in gas turbine combustors. One mechanism that contributes to the flame–acoustic interaction is entropy noise. Fluctuations of the equivalence ratio in the mixing section cause the generation of hot spots in the flame. These so-called entropy waves are convectively transported to the first stage of the turbine and generate acoustic waves that travel back to the flame; a thermoacoustic loop is closed. However, due to the lack of experimental tools, a detailed investigation of entropy waves in gas turbine combustion systems has not been possible up to now. This work presents an acoustic time-of-flight based temperature measurement method which allows the measurement of temperature fluctuations in the relevant frequency range. A narrow acoustic pulse is generated with an electric spark discharge close to the combustor wall. The acoustic response is measured at the same axial location with an array of microphones circumferentially distributed around the combustion chamber. The delay in the pulse arrival times corresponds to the line-integrated inverse speed of sound. For the measurement of entropy waves in an atmospheric combustion test rig, fuel is periodically injected into the mixing tube of a premixed combustor. The subsequently generated entropy waves are measured for different forcing frequencies of the fuel injection and for different mean flow velocities in the combustor. The amplitude decay and phase lag of the entropy waves adhere well to a Strouhal number scaling for different mean flow velocities.

Resonance dynamics in compressible cavity flows using time-resolved velocity and surface pressure fields

2017 ◽  
Vol 830 ◽  
pp. 494-527 ◽  
Author(s):  
Justin L. Wagner ◽  
Steven J. Beresh ◽  
Katya M. Casper ◽  
Edward P. DeMauro ◽  
Srinivasan Arunajatesan
Keyword(s):  
Velocity Field ◽  
Shear Layer ◽  
Surface Pressure ◽  
Coherent Structures ◽  
Acoustic Waves ◽  
Mode Switching ◽  
Recirculation Region ◽  
Mean Flow ◽  
Time Resolved ◽  
Phase Velocities

The resonance modes in Mach 0.94 turbulent flow over a cavity having a length-to-depth ratio of five were explored using time-resolved particle image velocimetry (TR-PIV) and time-resolved pressure sensitive paint (TR-PSP). Mode switching was quantified in the velocity field simultaneous with the pressure field. As the mode number increased from one through three, the resonance activity moved from a region downstream within the recirculation region to areas further upstream in the shear layer, an observation consistent with linear stability analysis. The second and third modes contained organized structures associated with shear layer vortices. Coherent structures occurring in the velocity field during modes two and three exhibited a clear modulation in size with streamwise distance. The streamwise periodicity was attributable to the interference of downstream-propagating vortical disturbances with upstream-travelling acoustic waves. The coherent structure oscillations were approximately $180^{\circ }$ out of phase with the modal surface pressure fluctuations, analogous to a standing wave. Modal propagation (or phase) velocities, based on cross-correlations of bandpass-filtered velocity fields were found for each mode. The phase velocities also showed streamwise periodicity and were greatest at regions of maximum constructive interference where coherent structures were the largest. Overall, the phase velocities increased with modal frequency, which coincided with the modal activity residing at higher portions of the cavity where the local mean flow velocity was elevated. Together, the TR-PIV and TR-PSP provide unique details not only on the distribution of modal activity throughout the cavity, but also new understanding of the resonance mechanism as observed in the velocity field.

scholarly journals Damping and reflection coefficient measurements for an open pipe at low Mach and low Helmholtz numbers

1993 ◽  
Vol 256 ◽  
pp. 499-534 ◽  
Author(s):  
M. C. A. M. Peters ◽  
A. Hirschberg ◽  
A. J. Reijnen ◽  
A. P. J. Wijnands
Keyword(s):  
Experimental Data ◽  
Reflection Coefficient ◽  
Strouhal Number ◽  
Acoustic Waves ◽  
High Frequency ◽  
Nonlinear Behaviour ◽  
Mean Flow ◽  
Frequency Limit ◽  
Low Frequencies ◽  
Open Pipe

The propagation of plane acoustic waves in smooth pipes and their reflection at open pipe terminations have been studied experimentally. The accuracy of the measurements is determined by comparison of experimental data with results of linear theory for the propagation of acoustic waves in a pipe with a quiescent fluid. The damping and the reflection at an unflanged pipe termination are compared.In the presence of a fully developed turbulent mean flow the measurements of the damping confirm the results of Ronneberger & Ahrens (1977). In the high-frequency limit the quasi-laminar theory of Ronneberger (1975) predicts accurately the convective effects on the damping of acoustic waves. For low frequencies a simple theory combining the rigid-plate model of Ronneberger & Ahrens (1977) with the theoretical approach of Howe (1984) yields a fair prediction of the influence of turbulence on the shear stress. The finite response time of the turbulence near the wall to the acoustic perturbations has to be taken into account in order to explain the experimental data. The model yields a quasi-stationary limit of the damping which does not take into account the fundamental difference between the viscous and thermal dissipation observed for low frequencies.Measurements of the nonlinear behaviour of the reflection properties for unflanged pipe terminations with thin and thick walls in the absence of a mean flow confirm the theory of Disselhorst & van Wijngaarden (1980), for the low-frequency limit. It appears however that a two-dimensional theory such as proposed by Disselhorst & van Wijngaarden (1980) for the high-frequency limit underestimates the acoustical energy absorption by vortex shedding by a factor 2.5.The measured influence of wall thickness on the reflection properties of an open pipe end confirms the linear theory of Ando (1969). In the presence of a mean flow the end correction δ of an unflanged pipe end varies from the value at the high-Strouhal-number limit of δ/a = 0.61, with a the pipe radius, which is close to the value in the absence of a mean flow given by Levine & Schwinger (1948) of δ/a = 0.6133, to a value of δ/a = 0.19 in the low-Strouhal-number limit which is close to the value predicted by Rienstra (1983) of δ/a = 0.26.The pressure reflection coefficient is found to agree with the theoretical predictions by Munt (1977, 1990) and Cargill (1982b) in which a full Kutta condition is included. The accuracy of the theory is fascinating in view of the dramatic simplifications introduced in the theory. For a thick-walled pipe end and a pipe terminated by a horn the end correction behaviour is similar. It is surprising that the nonlinear behaviour at low frequencies and high acoustic amplitudes in the absence of mean flow does not influence the end correction significantly.The aero-acoustic behaviour of the pipe end is dramatially influenced by the presence of a horn. In the presence of a mean flow the horn is a source of sound for a critical range of the Strouhal number.The high accuracy of the experimental data suggests that acoustic measurements can be used for a systematic study of turbulence in unsteady flow and of unsteady flow separation.

Three Dimensional Thermoacoustic Oscillation in a Premix Combustor

2001 ◽  
Author(s):  
S. Akamatsu ◽  
A. P. Dowling
Keyword(s):  
Boundary Conditions ◽  
Acoustic Waves ◽  
Linear Equations ◽  
Three Dimensional ◽  
Total System ◽  
Mean Flow ◽  
Modal Coupling ◽  
Rate Of Heat Release ◽  
Flow Through ◽  
Combustion Processes

A theory is developed to describe high frequency three-dimensional thermoacoustic waves in a simplified geometry representing a typical premix combustor. The theory considers linear modes of frequency ω and circumferential mode number m i.e. proportional to eiωt+imθ. The radial and axial dependence is determined for a cylindrical combustor. Simple geometries are investigated systematically to analyze the effect of different inlet boundary conditions to the combustion chamber on the frequency of oscillation and on the susceptibility to instability, both near and away from the cut-off frequencies. The model includes a one-dimensional mean flow, radial mode coupling and idealized combustion processes, which are added in stages to build up an understanding of the complicated acoustics of the premix combustor geometry. It is demonstrated that the flow through the premix ducts provides a frequency-dependent boundary condition at combustor inlet and causes modal coupling. Generalized linear equations of conservation of mass, momentum and energy, together with boundary conditions, are solved to identify the eigenfrequencies, ω, of the total system. Then Real ω determines the frequency of the oscillation, while Imaginary ω indicates the growth rate of the disturbance. It is found that strong resonant peaks in the pressure waves exist close to the cut-off condition for acoustic waves and that the relationship between the unsteady rate of heat release and the flow significantly influences the instability of oscillation.

Prediction of Thermoacoustic Oscillations With a Linearised Euler Methodology

2015 ◽  
Author(s):  
C. F. Quaglia ◽  
R. S. Cant
Keyword(s):  
Acoustic Waves ◽  
High Frequency ◽  
Complex Geometry ◽  
Suitable Model ◽  
Mean Flow ◽  
Predictive Tool ◽  
Frequency Dependent ◽  
One Dimensional ◽  
Transverse Acoustic ◽  
Thermoacoustic Oscillations

Combustion instabilities in the aviation, aerospace and power generation industries have been a matter of concern for engineers since the 1950s, but with the increase in computer processing speed and the development of CFD it is now possible to attempt to predict frequencies and stability of a combustion system by numerical means, or by combining numerical, analytical and experimental approaches. Currently available analytical methods for the prediction of the frequency and stability of thermoacoustic oscillations make use of one-dimensional models where the frequency of oscillation is assumed to be low enough that only plane waves propagate in the burner, with higher order modes decaying quickly. While accurate and well-suited for longitudinal oscillations, these methods are unable to predict the frequency of instabilities where the unsteady heat release couples with the higher frequency transverse acoustic modes. Therefore a method is needed for applications where high frequency transverse oscillations are important. A method in which the linearised Euler equations are employed to calculate the propagation of acoustic waves is then suitable for solving this thermoacoustic problem. When a flame model that appropriately represents the frequency-dependent dynamics of the flame front is included, this method can predict the frequency of the oscillation resulting from the coupling between acoustics and combustion in an arbitrarily complex geometry. In this paper, a linearised Euler solver called INSTANT is introduced and validated against a well known theoretical model for the calculation of thermoacoustic oscillations in a one dimensional cylindrical duct with rigid walls and a radially uniform mean flow. The frequencies of oscillation and the modeshapes for this stable configuration match the theoretical ones well. An example calculation of transverse acoustic resonant mode is then presented. The ability of the code to predict the production of an entropy mode as a result of the interaction between an acoustic wave and a heat source region and its ability to predict frequencies of oscillation and modeshapes in a one dimensional configuration give confidence it can serve as a predictive tool for high frequency, transverse thermoacoustic oscillations in the more complex geometries of practical combustion systems once a suitable model for the frequency dependent flame response is included. The development of such a flame model is left for future work.

Aerodynamic sound generation in a pipe

1968 ◽  
Vol 32 (4) ◽  
pp. 765-778 ◽  
Author(s):  
H. G. Davies ◽  
J. E. Ffowcs Williams
Keyword(s):  
Acoustic Waves ◽  
Large Scale ◽  
Sound Field ◽  
Convective Motion ◽  
Energy Output ◽  
Small Scale ◽  
Mean Flow ◽  
Limited Region ◽  
Aerodynamic Sound ◽  
Scale Turbulence

The paper deals with the problem of estimating the sound field generated by a limited region of turbulence in an infinitely long, straight, hard-walled pipe. The field is analysed in a co-ordinate system moving with the assumed uniform mean flow, and the possibility of eddy convection relative to that reference system is considered. Large-scale turbulence is shown to induce plane acoustic waves of intensity proportional to the sixth power of flow velocity. The same is true of small-scale turbulence of low characteristic frequency. In both cases convective effects increase the acoustic output and distribute the bulk of the energy in a mode propagating upstream against the mean flow. Small-scale turbulence of higher frequency excites more modes, the sound increasing with very nearly the eighth power of velocity (U7.7) as soon as the second mode is excited. In the limit, when more than about 20 modes are excited, the energy output is unaffected by the constraint of the pipe walls, increasing with the eighth power of velocity, and being substantially amplified by convective motion.

scholarly journals A Study of the Unsteady Pressure of a Cascade Near Transonic Flow Condition

1994 ◽  
Author(s):  
H. M. Atassi ◽  
J. Fang ◽  
P. Ferrand
Keyword(s):  
Transonic Flow ◽  
Acoustic Waves ◽  
Acoustic Mode ◽  
Mean Flow ◽  
Subsonic Flows ◽  
Unsteady Pressure ◽  
Acoustic Disturbances ◽  
Upstream Direction ◽  
The Mean ◽  
Pressure Magnitude

The rise of the unsteady pressure magnitude along the surface of a cascade blade in unsteady transonic flow is examined. It is shown that a similar rise in the unsteady pressure may occur for high subsonic flows where the mean flow is near sonic condition. For a subsonic cascade this unsteady pressure bulge is found to be associated with the cut-on of a new acoustic mode in the upstream direction. The level of the pressure bulge is significantly reduced as a downstream propagating mode cuts on. It is therefore proposed that this phenomenon is the result of the blockage of upstream propagating acoustic waves by the transonic mean flow. A transonic convergent-divergent nozzle is used as a model for investigating the acoustic blockage effect. Analytical and numerical computations using unsteady nonlinear Euler equations are then carried out to analyze and quantify the upstream and dowstream propagation of acoustic disturbances in the nozzle. The results confirm the sharp rise in the pressure of the upstream propagating disturbances at the nozzle throat as a result of the acoustic blockage.

A Non-Compact Effective Impedance Model for Can-to-Can Acoustic Communication: Analysis and Optimization of Damping Mechanisms

2021 ◽  
Author(s):  
Jakob G. R. von Saldern ◽  
Alessandro Orchini ◽  
Jonas P. Moeck
Keyword(s):  
Acoustic Communication ◽  
Acoustic Waves ◽  
Rotational Symmetry ◽  
Low Frequency ◽  
Coupling Model ◽  
Density Fluctuations ◽  
Mean Flow ◽  
Communication Analysis ◽  
Dissipative Effects ◽  
Effective Impedance

Abstract Can-annular combustors can feature azimuthal instabilities even if the acoustic coupling between the individual cans is weak. Recently, various studies have focused on modeling the acoustic communication between adjacent cans in can-annular systems. In this study, a coupling model is presented that, in contrast to previous models, includes the effect of density fluctuations, mean flow, and dissipative effects at the connection gaps. By assuming plane acoustic waves inside each can and exploiting the discrete rotational symmetry of the can-annular system, the acoustic can-to-can interaction can be represented by an effective Bloch-type impedance. A single can modeled with the effective impedance at the downstream end emulates the acoustic response of the entire can-annular arrangement. We then propose the idea of installing a liner just upstream of the first turbine stage to damp azimuthal instabilities. By using the proposed can-to-can coupling model, we discuss in detail the effect that the impedance of the liner has on the effective reflection coefficient for different Bloch wavenumbers. In the low-frequency limit, we derive an analytical condition for achieving maximum damping at a specific Bloch-number. We show that the damping of azimuthal modes depends on the porosity of the liner, mean flow parameters and the Bloch-structure of the mode. These results suggest the possibility of targeting the damping of modes of certain azimuthal order by geometric variations of the liner or of the connection gap. As an exemplary application of the theory, we set up a network model of a generic industrial 12-can combustor and investigate a cluster of acoustic and thermoacoustic eigenvalues for a varying liner porosity. The findings of this study provide a deeper understanding of the mechanisms that drive the can-to-can acoustic communication, and open the path for devising passive damping strategies aimed at stabilizing specific modes in can-annular combustors.

A Non-Compact Effective Impedance Model for Can-To-Can Acoustic Communication: Analysis and Optimization of Damping Mechanisms

2021 ◽  
Author(s):  
Jakob von Saldern ◽  
Alessandro Orchini ◽  
Jonas Moeck
Keyword(s):  
Acoustic Communication ◽  
Acoustic Waves ◽  
Rotational Symmetry ◽  
Low Frequency ◽  
Coupling Model ◽  
Density Fluctuations ◽  
Mean Flow ◽  
Communication Analysis ◽  
Dissipative Effects ◽  
Effective Impedance

Abstract Recently, various studies have focused on modeling the acoustic communication between adjacent cans in can-annular systems. In this study, a coupling model is presented that, in contrast to previous models, includes the effect of density fluctuations, mean flow, and dissipative effects at the connection gaps. By assuming plane acoustic waves inside each can and exploiting the discrete rotational symmetry of the can-annular system, the acoustic can-to-can interaction can be represented by an effective Bloch-type impedance. A single can modeled with the effective impedance at the downstream end emulates the acoustic response of the entire can-annular arrangement. We then propose the idea of installing a liner just upstream of the first turbine stage to damp azimuthal instabilities and discuss in detail the effect that the impedance of the liner has on the effective reflection coefficient for different Bloch wavenumbers. In the low-frequency limit, we derive an analytical condition for achieving maximum damping at a specific Bloch-number. The damping of azimuthal modes depends on the porosity of the liner, mean flow parameters and the Bloch-structure of the mode. These results suggest the possibility of targeting the damping of modes of certain azimuthal order by geometric variations of the liner or of the connection gap. The findings of this study provide a deeper understanding of the mechanisms that drive the can-to-can acoustic communication, and open the path for devising passive damping strategies aimed at stabilizing specific modes in can-annular combustors.

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