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.

Inviscid long-wave theory for the absolute instability of the rotating-disc boundary layer

2006 ◽  
Vol 462 (2069) ◽  
pp. 1467-1492 ◽  
Author(s):  
J.J Healey
Keyword(s):  
Boundary Layer ◽  
Dispersion Relation ◽  
Imaginary Axis ◽  
Reverse Flow ◽  
Saddle Points ◽  
Basic Flow ◽  
Absolute Instability ◽  
Pinch Point ◽  
Long Wave ◽  
The Absolute

This paper is concerned with the absolute instability of the boundary-layer flow produced when an infinite disc rotates in otherwise still fluid. A greater understanding of the mechanisms and properties of the absolute instability is sought through the development of an analytic theory in the inviscid long-wave limit. It is shown that the fundamental basic flow characteristic of the absolute instability is a wall-jet in the radial direction superposed with an asymptotically small cross-flow, which generates a small reverse flow outside the boundary layer in the appropriately resolved basic velocity profile. The absolute instability is produced by a modal coalescence involving the interaction of eight saddle-points of the dispersion relation. An explicit expression for the growth rate has been obtained in terms of basic flow parameters. Most curiously, the pinch-point for absolute instability is shown to become asymptotically close to a branch-cut on the imaginary axis of the complex wavenumber plane, and unstable spatial branches emanating from the pinch-point cross this imaginary axis onto a Riemann sheet of the dispersion relation composed of solutions growing exponentially with distance from the disc. The existence of such modes contradicts the expectation of monotonic exponential decay of disturbances outside a boundary layer.

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.

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 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.

GENETIC CERTIFICATION OF FODDER CROPS BREEDING ACHIEVEMENTS

1970 ◽  
pp. 40-46
Author(s):  
V. M. Kosolapov ◽  
N. N. Kozlov ◽  
I. А. Klimenko ◽  
V. N. Zolotarev
Keyword(s):  
Dna Analysis ◽  
Molecular Genetic ◽  
Practical Importance ◽  
Genetic Identification ◽  
Necessary Condition ◽  
Forage Crops ◽  
Fodder Crops ◽  
Long Time ◽  
Analytical Review ◽  
Prospects Of Application

The methods of genetic identification of forage crops varieties and forms have significant scientific and practical importance in breeding and seed multiplication, in protection of author’s rights. At the current moment molecular markers on the base of DNA-polymorphism have been applied widely for these aims. This analytical review examines the possibilities and the prospects of application the different DNA-analysis methods for assessment of forage crops genetic diversity and for development the molecular-genetic passports of breeding achievements. The objective estimation of varieties structure and presence impurities is a necessary condition for improving the methodical approaches in approbation of crops and for decision the problems of timely variety-seed renovation and its systematic replacement. The system of DNA markers that registered in genetic passport will enable to keep the initial genetic structure of variety and to maintain it in production process during long time without fluctuations of agronomic important characteristics and properties. This factor is especially valuable for development the primary seed multiplication.

Psychology: Volume 5

2019 ◽  
Keyword(s):  
World View ◽  
Science Volume ◽  
Western World ◽  
Mental Life ◽  
Long Time ◽  
The Difference ◽  
New Perspective ◽  
Indian Setting ◽  
The Mind ◽  
The Relationship

This survey of research on psychology in five volumes is a part of a series undertaken by the ICSSR since 1969, which covers various disciplines under social science. Volume Five of this survey, Explorations into Psyche and Psychology: Some Emerging Perspectives, examines the future of psychology in India. For a very long time, intellectual investments in understanding mental life have led to varied formulations about mind and its functions across the word. However, a critical reflection of the state of the disciplinary affairs indicates the dominance of Euro-American theories and methods, which offer an understanding coloured by a Western world view, which fails to do justice with many non-Western cultural settings. The chapters in this volume expand the scope of psychology to encompass indigenous knowledge available in the Indian tradition and invite engaging with emancipatory concerns as well as broadening the disciplinary base. The contributors situate the difference between the Eastern and Western conceptions of the mind in the practice of psychology. They look at this discipline as shaped by and shaping between systems like yoga. They also analyse animal behaviour through the lens of psychology and bring out insights about evolution of individual and social behaviour. This volume offers critique the contemporary psychological practices in India and offers a new perspective called ‘public psychology’ to construe and analyse the relationship between psychologists and their objects of study. Finally, some paradigmatic, pedagogical, and substantive issues are highlighted to restructure the practice of psychology in the Indian setting.

Attenuation of longitudinal electro-acoustic waves in a plasma

1974 ◽  
Vol 11 (1) ◽  
pp. 37-49
Author(s):  
R. J. Papa ◽  
P. Lindstrom
Keyword(s):  
Dispersion Relation ◽  
Electric Field ◽  
Acoustic Waves ◽  
Collision Frequency ◽  
Wave Dispersion ◽  
Signal Frequency ◽  
Variable Theory ◽  
Longitudinal Waves ◽  
Confluent Hypergeometric Functions ◽  
Linearized Boltzmann Equation

There are several practical situations in partially ionized plasmas when both collisionless (Landau) damping and electron-neutral collisions contribute to the attenuation of longitudinal waves. The longitudinal-wave dispersion relation is derived from Maxwell's equations and the linearized Boltzmann equation, in which electron-neutral collisions are represented by a Bhatnagar–Gross–Krook model that conserves particles locally. (The dispersion relation predicts that, for a given signal frequency ώ), an infinite number of complex wavenumbers kn can exist. Using Fourier–Laplace transform techniques, an integral representation for the electric field of the longitudinal waves is readily derived. Then, using theorems from complex variable theory, a modal expansion of the electric field can be made in terms of an infinite sum of confluent hypergeometric functions, whose arguments are proportional to the complex wavenumbers kn. It is demonstrated numerically that the spatial integral of the square of the electric field amplitude decreases as the electron-neutral collision frequency increases. Also, the amount of energy contained in the first few (lowest) modes, and the coupling between the modes, is examined as a function of plasma frequency, signal frequency and collision frequency.

scholarly journals Computation of vortex sheet roll-up in the Trefftz plane

1987 ◽  
Vol 184 ◽  
pp. 123-155 ◽  
Author(s):  
Robert Krasny
Keyword(s):  
Mesh Size ◽  
Vortex Sheet ◽  
Smoothing Parameter ◽  
Tip Vortex ◽  
Tip Vortices ◽  
Time Calculation ◽  
Long Time ◽  
Principal Value ◽  
Different Levels ◽  
Good Agreement

Two vortex-sheet evolution problems arising in aerodynamics are studied numerically. The approach is based on desingularizing the Cauchy principal value integral which defines the sheet's velocity. Numerical evidence is presented which indicates that the approach converges with respect to refinement in the mesh-size and the smoothing parameter. For elliptic loading, the computed roll-up is in good agreement with Kaden's asymptotic spiral at early times. Some aspects of the solution's instability to short-wavelength perturbations, for a small value of the smoothing parameter, are inferred by comparing calculations performed with different levels of computer round-off error. The tip vortices’ deformation, due to their mutual interaction, is shown in a long-time calculation. Computations for a simulated fuselage-flap configuration show a complicated process of roll-up, deformation and interaction involving the tip vortex and the inboard neighbouring vortices.

Acoustic Resonance in an Axial Multistage Compressor Leading to Non-Synchronous Blade Vibration

2020 ◽  
Author(s):  
Anne-Lise Fiquet ◽  
Agathe Vercoutter ◽  
Nicolas Buffaz ◽  
Stéphane Aubert ◽  
Christoph Brandstetter
Keyword(s):  
Acoustic Waves ◽  
High Speed ◽  
Numerical Study ◽  
Acoustic Resonance ◽  
Structural Vibration ◽  
Wave Number ◽  
Blade Vibration ◽  
Acoustic Modes ◽  
Blade Vibrations ◽  
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 noncoherent 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, since the appearance of the axially propagating acoustic waves can excite blade vibrations if they coincide with a structural eigenmode, as observed in the presented experiments.

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