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.

scholarly journals Analysis of Thermoacoustic Modes in Can-Annular Combustors Using Effective Bloch-Type Boundary Conditions

2020 ◽  
Author(s):  
Jakob von Saldern ◽  
Alessandro Orchini ◽  
Jonas Moeck
Keyword(s):  
Acoustic Waves ◽  
Gas Turbines ◽  
Rotational Symmetry ◽  
Low Frequency ◽  
Periodic Wave ◽  
Mode Shapes ◽  
Coupling Condition ◽  
Annular Combustor ◽  
Close Frequency ◽  
Type Boundary

Abstract Heavy-duty gas turbines are commonly designed with can-annular combustors, in which all flames are physically separated. Acoustically, however, the cans communicate via the upstream located compressor plenum, or at the downstream gaps found at the transition to the turbine inlet. In the present study, a coupling condition that is based on a Rayleigh conductivity and acoustic flux conservation is derived. It enables acoustic communication between adjacent cans, in which one-dimensional acoustic waves propagate. In addition, because can-annular systems commonly feature a discrete rotational symmetry, the acoustic field can be expressed as a Bloch-periodic wave in the azimuthal direction. We demonstrate how the coupling conditions resulting in a combustion system with $N$ cans can be expressed as an effective impedance for a single can. By means of this Bloch-type boundary condition, the thermoacoustics of a can-annular system can be analyzed considering only one can, thus reducing the size of the problem by a factor of N. Using this method, we investigate in frequency domain the effect of the coupling strength of a generic can-annular combustor consisting of 12 identical cans, which are connected at the downstream end. We describe generic features of can-annular systems and derive results on the frequency response of the cans at various Bloch numbers in the low-frequency and high-frequency limits. Furthermore, the formation of eigenvalue clusters with eigenvalues of close frequency and growth rate, but very different mode shapes is discussed.

scholarly journals Analysis of Thermoacoustic Modes in Can-Annular Combustors Using Effective Bloch-Type Boundary Conditions

2020 ◽  
Author(s):  
Jakob G. R. von Saldern ◽  
Alessandro Orchini ◽  
Jonas P. Moeck
Keyword(s):  
Acoustic Waves ◽  
Gas Turbines ◽  
Rotational Symmetry ◽  
Low Frequency ◽  
Periodic Wave ◽  
Mode Shapes ◽  
Coupling Condition ◽  
Annular Combustor ◽  
Close Frequency ◽  
Type Boundary

Abstract Heavy-duty gas turbines are commonly designed with canannular combustors, in which all flames are physically separated. Acoustically, however, the cans communicate via the upstream located compressor plenum, or at the downstream gaps found at the transition to the turbine inlet. In the present study, a coupling condition that is based on a Rayleigh conductivity and acoustic flux conservation is derived. It enables acoustic communication between adjacent cans, in which one-dimensional acoustic waves propagate. In addition, because can-annular systems commonly feature a discrete rotational symmetry, the acoustic field can be expressed as a Bloch-periodic wave in the azimuthal direction. We demonstrate how the coupling conditions resulting in a combustion system with N cans can be expressed as an effective impedance for a single can. By means of this Bloch-type boundary condition, the thermoacoustics of a can-annular system can be analyzed considering only one can, thus reducing the size of the problem by a factor of N. Using this method, we investigate in frequency domain the effect of the coupling strength of a generic can-annular combustor consisting of 12 identical cans, which are connected at the downstream end. We describe generic features of can-annular systems that can be efficiently addressed with this framework and derive results on the frequency response of the cans at various Bloch numbers in the low-frequency and high-frequency limits. Furthermore, the formation of eigenvalue clusters with eigenvalues of close frequency and growth rate, but very different mode shapes is discussed.

Effect of non-parallel mean flow on the Green’s function for predicting the low-frequency sound from turbulent air jets

2012 ◽  
Vol 695 ◽  
pp. 199-234 ◽  
Author(s):  
M. E. Goldstein ◽  
Adrian Sescu ◽  
M. Z. Afsar
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Low Frequency ◽  
Source Location ◽  
Parallel Flow ◽  
Numerical Calculations ◽  
Mean Flow ◽  
Frequency Sound ◽  
The Mean ◽  
Radiated Sound

AbstractIt is now well-known that there is an exact formula relating the far-field jet noise spectrum to the convolution product of a propagator (that accounts for the mean flow interactions) and a generalized Reynolds stress autocovariance tensor (that accounts for the turbulence fluctuations). The propagator depends only on the mean flow and an adjoint vector Green’s function for a particular form of the linearized Euler equations. Recent numerical calculations of Karabasov, Bogey & Hynes (AIAA Paper 2011-2929) for a Mach 0.9 jet show use of the true non-parallel flow Green’s function rather than the more conventional locally parallel flow result leads to a significant increase in the predicted low-frequency sound radiation at observation angles close to the downstream jet axis. But the non-parallel flow appears to have little effect on the sound radiated at $9{0}^{\ensuremath{\circ} } $ to the downstream axis. The present paper is concerned with the effects of non-parallel mean flows on the adjoint vector Green’s function. We obtain a low-frequency asymptotic solution for that function by solving a very simple second-order hyperbolic equation for a composite dependent variable (which is directly proportional to a pressure-like component of this Green’s function and roughly corresponds to the strength of a monopole source within the jet). Our numerical calculations show that this quantity remains fairly close to the corresponding parallel flow result at low Mach numbers and that, as expected, it converges to that result when an appropriately scaled frequency parameter is increased. But the convergence occurs at progressively higher frequencies as the Mach number increases and the supersonic solution never actually converges to the parallel flow result in the vicinity of a critical- layer singularity that occurs in that solution. The dominant contribution to the propagator comes from the radial derivative of a certain component of the adjoint vector Green’s function. The non-parallel flow has a large effect on this quantity, causing it (and, therefore, the radiated sound) to increase at subsonic speeds and decrease at supersonic speeds. The effects of acoustic source location can be visualized by plotting the magnitude of this quantity, as function of position. These ‘altitude plots’ (which represent the intensity of the radiated sound as a function of source location) show that while the parallel flow solutions exhibit a single peak at subsonic speeds (when the source point is centred on the initial shear layer), the non-parallel solutions exhibit a double peak structure, with the second peak occurring about two potential core lengths downstream of the nozzle. These results are qualitatively consistent with the numerical calculations reported in Karabasov et al. (2011).

scholarly journals Simulation and Experimental Investigation of the Stay Vane Channel Flow in a Reversible Pump Turbine at Off-Design Conditions

2017 ◽  
Vol 61 (2) ◽  
pp. 94 ◽  
Author(s):  
Sandro Erne ◽  
Gernot Edinger ◽  
Anton Maly ◽  
Christian Bauer
Keyword(s):  
Transient Flow ◽  
Guide Vane ◽  
Low Frequency ◽  
Rotating Stall ◽  
Design Flow ◽  
Flow State ◽  
Mean Flow ◽  
Load Range ◽  
Pump Turbine ◽  
Stall Inception

This work presents the assessment of the mean flow field and low frequency disturbances in the stay vane channel of a model pump turbine using transient numerical simulations and LDV-based measurements. The focus is laid on transient CFD simulations of characteristic flow states in the stay vane channel when operating at off-design conditions in pump mode. Experimental and numerical investigations obtained a shifting velocity distribution between the shroud and hub of the distributor when continuously increasing the discharge in the part-load range. Simulations captured the occurrence of this changing flow state in the stay vane channel reasonably well. A further increase of the discharge showed a uniformly redistributed mean flow of both hub and shroud side. Monitoring points and integral quantities from measurements and transient simulations were used to interpret the development of transient flow patterns in the stay vane channel at the operating point of strongest asymmetrical flow. During simulation and measurement, a dominant rotating stall inception was observed near the design flow of the pump turbine. At this point where the stall becomes severe, a high level of correlation between the signals of the upper and lower stalled flow in the stay vane channel was calculated. Further simulations for different guide vane positions predicted a strong influence of the guide vane position on the structure of rotating stall.

Spatial Stability Analysis of a Flap Side Edge Vortex

2005 ◽  
Vol 4 (1-2) ◽  
pp. 37-47
Author(s):  
Jean-Philippe Brazier ◽  
Frédéric Moens ◽  
Philippe Bardoux
Keyword(s):  
Stability Analysis ◽  
Temporal Stability ◽  
Low Frequency ◽  
Aerodynamic Noise ◽  
Navier Stokes ◽  
Mean Flow ◽  
Side Edge ◽  
Amplification Rate ◽  
Edge Vortex ◽  
Flap Deflection

The flap side edge vortex is suspected to contribute to aerodynamic noise generation. Using a temporal stability analysis, Khorrami and Singer have shown that unstable modes could exist in this vortex. Due to the convective nature of this instability, a spatial analysis is more suitable. This is the subject of the present work. The mean flow past a 2D wing with a half-span flap has been computed with a steady 3D Navier-Stokes code. Then, local linear stability calculations are performed in several planes perpendicular to the vortex axis. The vortex is assumed axisymmetric and modelled with Batchelor's analytical vortex. Using Gaster's relation, the spatial amplification rate is calculated, giving by integration the relative amplitude of the fluctuations. Some low-frequency fluctuations are seen to be preferentially amplified by the vortex, but the amplifications remain small, so that this mechanism alone should not produce important noise in this particular configuration, where the flap deflection angle is moderate.

Fluctuating boundary layer on a magnetized plate

1967 ◽  
Vol 63 (2) ◽  
pp. 513-525 ◽  
Author(s):  
Sahib Singh Chawla
Keyword(s):  
Boundary Layer ◽  
Low Frequency ◽  
Surface Current ◽  
Frequency Range ◽  
Mean Flow ◽  
Wave Type ◽  
High Frequencies ◽  
Phase Lead ◽  
The Mean ◽  
The Magnetic Field

The laminar boundary layer on a magnetized plate, when the magnetic field oscillates in magnitude about a constant non-zero mean, is analysed. For low-frequency fluctuations the solution is obtained by a series expansion in terms of a frequency parameter, while for high frequencies the flow pattern is of the ‘skin-wave’ type unaffected by the mean flow. In the low-frequency range, the phase lead and the amplitude of the skin-friction oscillations increase at first and then decrease to their respective ‘skin-wave’ values. On the other hand the phase angle of the surface current decreases from 90° to 45° and its amplitude increases with frequency.

Studies on the interaction of low‐frequency acoustic signals with the ocean bottom

Geophysics ◽  
1979 ◽  
Vol 44 (12) ◽  
pp. 1922-1940 ◽  
Author(s):  
Salvatore R. Santaniello ◽  
Frederick R. DiNapoli ◽  
Robert K. Dullea ◽  
Peter D. Herstein
Keyword(s):  
Acoustic Waves ◽  
Grazing Angle ◽  
Low Frequency ◽  
Propagation Loss ◽  
Ocean Bottom ◽  
Computer Technique ◽  
Quantitative Evidence ◽  
Ocean Sediment ◽  
Wave Models ◽  
Processing Techniques

Understanding the mechanisms by which the ocean sediment redirects impinging sound back into the ocean is necessary in developing propagation models for sonar performance prediction. The Naval Underwater Systems Center (NUSC) has (1) conducted controlled, self‐calibrating acoustic measurements where the ocean bottom interacted signal is isolated in time for analysis, (2) developed deconvolution processing techniques to aid in describing the impulse response of the ocean sediment, and (3) performed modeling to study the interaction of acoustic waves at the ocean bottom. This paper presents a synopsis of studies showing the necessity of considering the refraction of sound by the ocean sediment when predicting low‐frequency propagation loss. Constructive interference between nonplanar wave sediment refracted sound and sound reflected by the ocean‐sediment interface and subbottom layering can cause negative values of bottom loss when using plane‐wave models to interpret measured data. These models cannot account for all possible acoustic arrivals at a receiver. In addition, for a given frequency and constant ocean bottom grazing angle, bottom loss can be dependent upon both processing bandwidth and source/receiver depth. Deconvolution has aided in time resolution of signals that make up the bottom‐interacted signals. Resolution of these signals aids in interpreting results. A modeling effort utilizing the Fast Field Program (a computer technique for evaluating the field integral by the fast Fourier transform) provides quantitative evidence for the necessity of accounting for the refraction of sound by subocean sediments to interpret properly low‐frequency propagation loss measurements.

Low-Frequency Fluctuations In The Flow Over Confined Cylinder In A Narrow Rectangular Duct At Re = 3 750

2017 ◽  
Vol 12 (1) ◽  
pp. 43-49
Author(s):  
Egor Palkin ◽  
Rustam Mullyadzhanov
Keyword(s):  
Stokes Equations ◽  
Low Frequency ◽  
Horseshoe Vortex ◽  
Navier Stokes ◽  
Infinite Cylinder ◽  
Rectangular Duct ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Frequency Modulations ◽  
Bounding Surfaces

Flows between two closely spaced bounding surfaces are frequently appear in engineering applications and natural flows. In current paper the flow over a cylinder in a narrow rectangular duct was investigated by numerical computations of Navier-Stokes equations using Large eddy simulations (LES) at ReD = 3 750 based on cylinder diameter and the bulk velocity at inflow boundary. The influence of the bounding walls was demonstrated by comparing mean flow streamlines with the flow over an infinite cylinder at close Reynolds numbers. A comparison between the time-averaged velocity field in front and past the cylinder with experimental from the literature data showed good agreement although the characteristic horseshoe vortex structures are highly sensitive to Reynolds number and turbulence level at inflow boundary. Most energetic modes in recirculating region were revealed by spectral analysis. These low-frequency modulations were characterized by the pair of dominating vortices which are expected to have high influence on the heat transfer in near wake of the cylinder.

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