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,$0.82<M<1$.

scholarly journals Acoustic modes in jet and wake stability

2019 ◽  
Vol 867 ◽  
pp. 804-834 ◽  
Author(s):  
Eduardo Martini ◽  
André V. G. Cavalieri ◽  
Peter Jordan
Keyword(s):  
Dispersion Relation ◽  
Acoustic Waves ◽  
Reverse Flow ◽  
Saddle Points ◽  
Vortex Sheet ◽  
Necessary Condition ◽  
Absolute Instability ◽  
Acoustic Modes ◽  
Long Time ◽  
New Perspective

Motivated by recent studies that have revealed the existence of trapped acoustic waves in subsonic jets (Towne et al., J. Fluid Mech., vol. 825, 2017, pp. 1113–1152), we undertake a more general exploration of the physics associated with acoustic modes in jets and wakes, using a double vortex-sheet model. These acoustic modes are associated with eigenvalues of the vortex-sheet dispersion relation; they are discrete modes, guided by the vortex sheet; they may be either propagative or evanescent; and under certain conditions they behave in the manner of acoustic-duct modes. By analysing these modes we show how jets and wakes may both behave as waveguides under certain conditions, emulating ducts with soft or hard walls, with the vortex-sheet impedance providing effective ‘wall’ conditions. We consider, in particular, the role that upstream-travelling acoustic modes play in the dispersion-relation saddle points that underpin the onset of absolute instability. The analysis illustrates how departure from duct-like behaviour is a necessary condition for absolute instability, and this provides a new perspective on the stabilising and destabilising effects of reverse flow, temperature ratio and compressibility; it also clarifies the differing symmetries of jet (symmetric) and wake (antisymmetric) instabilities. An energy balance, based on the vortex-sheet impedance, is used to determine stability conditions for the acoustic modes: these may become unstable in supersonic flow due to an energy influx through the shear layers. Finally, we construct the impulse response of flows with zero and finite shear-layer thickness. This allows us to show how the long-time wavepacket behaviour is indeed determined by interaction between Kelvin–Helmholtz and acoustic modes.

Finite-wavelength scattering of incident vorticity and acoustic waves at a shrouded-jet exit

2008 ◽  
Vol 612 ◽  
pp. 407-438 ◽  
Author(s):  
ARNAB SAMANTA ◽  
JONATHAN B. FREUND
Keyword(s):  
Mach Number ◽  
Acoustic Waves ◽  
Vortex Sheet ◽  
Acoustic Mode ◽  
Uniform Flow ◽  
Sharp Edge ◽  
Potential Mechanism ◽  
Ambient Flow ◽  
Acoustic Modes ◽  
Cylindrical Vortex

As the vortical disturbances of a shrouded jet pass the sharp edge of the shroud exit some of the energy is scattered into acoustic waves. Scattering into upstream-propagating acoustic modes is a potential mechanism for closing the resonance loop in the ‘howling’ resonances that have been observed in various shrouded jet configurations over the years. A model is developed for this interaction at the shroud exit. The jet is represented as a uniform flow separated by a cylindrical vortex sheet from a concentric co-flow within the cylindrical shroud. A second vortex sheet separates the co-flow from an ambient flow outside the shroud, downstream of its exit. The Wiener–Hopf technique is used to compute reflectivities at the shroud exit. For some conditions it appears that the reflection of finite-wavelength hydrodynamic vorticity modes on the vortex sheet defining the jet could be sufficient to reinforce the shroud acoustic modes to facilitate resonance. The analysis also gives the reflectivities for the shroud acoustic modes, which would also be important in establishing resonance conditions. Interestingly, it is also predicted that the shroud exit can be ‘transparent’ for ranges of Mach numbers, with no reflection into any upstream-propagating acoustic mode. This is phenomenologically consistent with observations that indicate a peculiar sensitivity of resonances of this kind to, say, jet Mach number.

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.

Flow Excited Resonance of a Confined Shallow Cavity in Low Mach Number Flow and Its Control

2002 ◽  
Author(s):  
S. Ziada ◽  
H. Ng ◽  
C. Blake
Keyword(s):  
Mach Number ◽  
Shear Layer ◽  
Control Method ◽  
Acoustic Resonance ◽  
Synthetic Jet ◽  
Low Mach Number ◽  
Acoustic Modes ◽  
Shallow Cavities ◽  
Number Flow ◽  
Low Mach Number Flow

Shallow cavities exposed to unbounded, low Mach number flow are generally weak aeroacoustic sources because their acoustic modes are heavily damped. This paper focuses on a cavity mounted on the wall of a duct to investigate the effect of “confinement”, i.e. solid boundaries close to the cavity, on the aeroacoustic response of shallow cavities in low Mach number flow (M &lt; 0.3). It is found that the transverse acoustic modes of the duct-cavity combination are excited by the higher order modes of the cavity shear layer oscillations. The nature of the excitation mechanism as well as the effects of the cavity and duct dimensions are investigated by means of measurements of the amplitude and phase distributions of the acoustic pressure, complemented with flow visualization of the cavity shear layer oscillation. A method to predict the onset of resonance is also suggested. It is also shown that the acoustic resonance is effectively suppressed by a feedback control method, which generates a synthetic jet acting at the cavity upstream corner. The effect of the phase and gain of the controller transfer function is studied in some detail.

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.

scholarly journals Streamwise-travelling waves of spanwise wall velocity for turbulent drag reduction

2009 ◽  
Vol 627 ◽  
pp. 161-178 ◽  
Author(s):  
MAURIZIO QUADRIO ◽  
PIERRE RICCO ◽  
CLAUDIO VIOTTI
Keyword(s):  
Drag Reduction ◽  
Travelling Waves ◽  
Phase Speed ◽  
Travelling Wave ◽  
Wall Turbulence ◽  
Energetic Efficiency ◽  
Friction Drag ◽  
Mean Flow ◽  
The Waves ◽  
Spanwise Velocity

Waves of spanwise velocity imposed at the walls of a plane turbulent channel flow are studied by direct numerical simulations. We consider sinusoidal waves of spanwise velocity which vary in time and are modulated in space along the streamwise direction. The phase speed may be null, positive or negative, so that the waves may be either stationary or travelling forward or backward in the direction of the mean flow. Such a forcing includes as particular cases two known techniques for reducing friction drag: the oscillating wall technique (a travelling wave with infinite phase speed) and the recently proposed steady distribution of spanwise velocity (a wave with zero phase speed). The travelling waves alter the friction drag significantly. Waves which slowly travel forward produce a large reduction of drag that can relaminarize the flow at low values of the Reynolds number. Faster waves yield a totally different outcome, i.e. drag increase (DI). Even faster waves produce a drag reduction (DR) effect again. Backward-travelling waves instead lead to DR at any speed. The travelling waves, when they reduce drag, operate in similar fashion to the oscillating wall, with an improved energetic efficiency. DI is observed when the waves travel at a speed comparable with that of the convecting near-wall turbulence structures. A diagram illustrating the different flow behaviours is presented.

scholarly journals Wavepackets and trapped acoustic modes in a turbulent jet: coherent structure eduction and global stability

2017 ◽  
Vol 825 ◽  
pp. 1153-1181 ◽  
Author(s):  
Oliver T. Schmidt ◽  
Aaron Towne ◽  
Tim Colonius ◽  
André V. G. Cavalieri ◽  
Peter Jordan ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Dispersion Relation ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Acoustic Waves ◽  
Experimental Studies ◽  
Mean Flow ◽  
Potential Core ◽  
Acoustic Modes ◽  
Global Modes

Coherent features of a turbulent Mach 0.9, Reynolds number$10^{6}$jet are educed from a high-fidelity large eddy simulation. Besides the well-known Kelvin–Helmholtz instabilities of the shear layer, a new class of trapped acoustic waves is identified in the potential core. A global linear stability analysis based on the turbulent mean flow is conducted. The trapped acoustic waves form branches of discrete eigenvalues in the global spectrum, and the corresponding global modes accurately match the educed structures. Discrete trapped acoustic modes occur in a hierarchy determined by their radial and axial order. A local dispersion relation is constructed from the global modes and found to agree favourably with an empirical dispersion relation educed from the simulation data. The product between direct and adjoint modes is then used to isolate the trapped waves. Under certain conditions, resonance in the form of a beating occurs between trapped acoustic waves of positive and negative group velocities. This resonance explains why the trapped modes are prominently observed in the simulation and as tones in previous experimental studies. In the past, these tones were attributed to external factors. Here, we show that they are an intrinsic feature of high-subsonic jets that can be unambiguously identified by a global linear stability analysis.

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.

scholarly journals Jet–flap interaction tones

2018 ◽  
Vol 853 ◽  
pp. 333-358 ◽  
Author(s):  
Peter Jordan ◽  
Vincent Jaunet ◽  
Aaron Towne ◽  
André V. G. Cavalieri ◽  
Tim Colonius ◽  
...  
Keyword(s):  
Mach Number ◽  
High Frequency ◽  
Acoustic Pressure ◽  
Travelling Waves ◽  
Pressure Measurements ◽  
Sound Waves ◽  
Potential Core ◽  
Spectral Peaks ◽  
Band Limited ◽  
High Mach

Motivated by the problem of jet–flap interaction noise, we study the tonal dynamics that occurs when an isothermal turbulent jet grazes a sharp edge. We perform hydrodynamic and acoustic pressure measurements to characterise the tones as a function of Mach number and streamwise edge position. The observed distribution of spectral peaks cannot be explained using the usual edge-tone model, in which resonance is underpinned by coupling between downstream-travelling Kelvin–Helmholtz wavepackets and upstream-travelling sound waves. We show, rather, that the strongest tones are due to coupling between Kelvin–Helmholtz wavepackets and a family of trapped, upstream-travelling acoustic modes in the potential core, recently studied by Towneet al. (J. Fluid Mech.vol. 825, 2017) and Schmidtet al. (J. Fluid Mech.vol. 825, 2017). We also study the band-limited nature of the resonance, showing the high-frequency cutoff to be due to the frequency dependence of the upstream-travelling waves. Specifically, at high Mach number, these modes become evanescent above a certain frequency, whereas at low Mach number they become progressively trapped with increasing frequency, which inhibits their reflection in the nozzle plane.

scholarly journals Influence of the Monsoon Trough on Westward-Propagating Tropical Waves over the Western North Pacific. Part II: Energetics and Numerical Experiments

2015 ◽  
Vol 28 (23) ◽  
pp. 9332-9349 ◽  
Author(s):  
Liang Wu ◽  
Zhiping Wen ◽  
Renguang Wu
Keyword(s):  
North Pacific ◽  
Numerical Experiments ◽  
Western North Pacific ◽  
Monsoon Trough ◽  
Water Model ◽  
Mean Flow ◽  
Horizontal Structure ◽  
Rotational Flows ◽  
The Mean ◽  
The Waves

Abstract Part I of this study examined the modulation of the monsoon trough (MT) on tropical depression (TD)-type–mixed Rossby–gravity (MRG) and equatorial Rossby (ER) waves over the western North Pacific based on observations. This part investigates the interaction of these waves with the MT through a diagnostics of energy conversion that separates the effect of the MT on TD–MRG and ER waves. It is found that the barotropic conversion associated with the MT is the most important mechanism for the growth of eddy energy in both TD–MRG and ER waves. The large rotational flows help to maintain the rapid growth and tilted horizontal structure of the lower-tropospheric waves through a positive feedback between the wave growth and horizontal structure. The baroclinic conversion process associated with the MT contributes a smaller part for TD–MRG waves, but is of importance comparable to barotropic conversion for ER waves as it can produce the tilted vertical structure. The growth rates of the waves are much larger during strong MT years than during weak MT years. Numerical experiments are conducted for an idealized MRG or ER wave using a linear shallow-water model. The results confirm that the monsoon background flow can lead to an MRG-to-TD transition and the ER wave amplifies along the axis of the MT and is more active in the strong MT state. Those results are consistent with the findings in Part I. This indicates that the mean flow of the MT provides a favorable background condition for the development of the waves and acts as a key energy source.

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