12.—The Instability due to Acoustic Radiation striking a Vortex Sheet on a Subsonic Stream

1973 ◽  
Vol 71 (2) ◽  
pp. 141-149
Author(s):  
N. Hardisty
Keyword(s):  
Mach Number ◽  
Sound Source ◽  
Acoustic Radiation ◽  
Vortex Sheet ◽  
Instability Waves ◽  
Two Fluids ◽  
Moving Fluid

SynopsisThe propagation of sound across a vortex sheet separating two fluids in relative subsonic motion is examined for both harmonic and impulsive sources, the sound source being in the moving fluid. It is found that instability waves arise in a certain region depending on M, the Mach number.

11.—The Instability due to Acoustic Radiation striking a Vortex Sheet on a Supersonic Stream

1973 ◽  
Vol 71 (2) ◽  
pp. 121-140 ◽  
Author(s):  
D. S. Jones ◽  
J. D. Morgan
Keyword(s):  
Mach Number ◽  
Relative Motion ◽  
Sound Speed ◽  
Acoustic Radiation ◽  
Vortex Sheet ◽  
Supersonic Stream ◽  
Neutral Stability ◽  
Instability Waves ◽  
Two Fluids ◽  
Impulsive Source

SynopsisThe propagation of sound across a vortex sheet separating two fluids, with the same density and sound speed, which are in supersonic relative motion is examined for both harmonic and impulsive sources. It is found that instability waves are present when M < 2√2, M being the Mach number, and it is suggested that these may account for the phenomena observed in certain experiments. For M > 2 there are also neutral stability waves and these lie in regions in the supersonic stream which are otherwise silent when the excitation is an impulsive source.

The instability of a vortex sheet on a subsonic stream under acoustic radiation

1972 ◽  
Vol 72 (3) ◽  
pp. 465-488 ◽  
Author(s):  
D. S. Jones ◽  
J. P. Morgan
Keyword(s):  
Sound Speed ◽  
Acoustic Radiation ◽  
Vortex Sheet ◽  
Harmonic Excitation ◽  
Time Dependent ◽  
Helmholtz Instability ◽  
Initial Value ◽  
Two Fluids ◽  
Harmonic Field ◽  
Time Dependent Problem

AbstractThis paper is concerned with the linear theory of the transmission of sound through a vortex sheet separating two fluids in relative motion, but with the same density and sound speed. For harmonic excitation asolution is determined, with particular attention to transition regions where large effects might be expected, and it is found that Helmholtz instability plays no role in this solution. However, this harmonic field does not lead to a solution of the initial value problem which satisfies causality. When causality is complied with an additional field must be superimposed which gives waves growing exponentially in space in the harmonic case and a singularity, which is more severe than has been previously encountered, in the time-dependent problem. The consequent effects of this instability are discussed.

6—The Instability of Two Vortex Sheets Enclosing a Subsonic Jet due to Acoustic Radiation

1974 ◽  
Vol 72 (1) ◽  
pp. 79-91 ◽  
Author(s):  
N. Hardisty
Keyword(s):  
Acoustic Radiation ◽  
Vortex Sheets ◽  
Instability Waves ◽  
Subsonic Jet

SummaryThe propagation of sound in a subsonic jet separated by two vortex sheets from two semi-infinite still media is considered and it is found that instability waves arise at particular points on the vortex sheets and that their effect is confined to certain regions.

Relation Between Sound Sources and Vortical Structures in Isotropic Compressible Turbulence

2014 ◽  
Author(s):  
Daiki Terakado ◽  
Taku Nonomura ◽  
Makoto Sato ◽  
Kozo Fujii
Keyword(s):  
Mach Number ◽  
Sound Source ◽  
Compressible Turbulence ◽  
Fine Scale ◽  
Sound Sources ◽  
Vortical Structures ◽  
Scale Structures ◽  
Mach Numbers ◽  
High Mach ◽  
Lighthill Equation

We investigate the relation between vortical structures and sound source in isotropic compressible turbulence by direct numerical simulations with various turbulent Mach numbers. The sound source is obtained numerically from the Lighthill equation. As a first step, we study the sound source from the Reynolds stress, which is the dominant source in flows at low Mach numbers. We investigate, especially, sound source structures around the “coherent fine scale eddies” [1–4] to lead a universal conclusion of sound generation mechanism from the fine scale structures in supersonic flows. We find that the sound source structures around the coherent fine scale eddies show some distorted structures only in high Mach number flows because shocklets appear around the fine scale eddies in those flows. This change in sound source structures around the coherent fine scale eddies does not appear in low and moderate Mach number cases.

scholarly journals Diffusion and chemical reaction velocity as joint factors in determining the rate of uptake of oxygen and carbon monoxide by the red blood corpuscle

1932 ◽  
Vol 111 (769) ◽  
pp. 1-36 ◽  
Keyword(s):  
Carbon Monoxide ◽  
Cross Sections ◽  
The Other ◽  
Blood Corpuscle ◽  
Reaction Velocity ◽  
Two Fluids ◽  
Mixing Chamber ◽  
Haemoglobin Solution ◽  
Moving Fluid

In a paper on this subject published four years age, Hartridge and Roughton (1927) described some preliminary experiments upon the rate of uptake of oxygen and carbon monoxide by the red blood corpuscle, the observations being made by means of their reaction velocity technique (Hartridge and Roughton, 1922–1927). The general principles of the method were as follows. Through one lead of the apparatus a suspension of reduced corpuscles in saline was forces into the mixing chamber, whilst through the other lead was forced a solution of oxygen (or carbon monoxide) in saline. The two fluids mixed in the mixing chamber within 0·001 second or less and then travelled down the observation tube. Determination of the percentage of oxyhæmoglobin (or carboxyhæmoglobin) in the moving fluid at various cross sections of the observation tube was made by means of the reversion spectroscope, these measurements, together with a knowledge of the rate of flow of the fluid down the observation tube, giving the necessary data for plotting the rate of uptake of O 2 or CO by the corpuscles against time. The most interesting feature of the results was the much slower uptake of O 2 by hæmoglobin in the intact corpuscle as compared with the of O 2 by hæmoglobin in laked solution as previously recorded by Hartridge and Roughton (1925). In the corpuscle experiments the time scale had to be expressed in hundredths of a second instead of in thousandths of a second as in the hæmoglobin solution experiments ( vide fig. 2 of Hartridge and Roghton, 1927). Confirmatory results by somewhat different technique have been obtained lately by Dirken and Mook (1931). These will be referred to again later.

scholarly journals Models of internal jumps and the fronts of gravity currents: unifying two-layer theories and deriving new results

2018 ◽  
Vol 846 ◽  
pp. 654-685 ◽  
Author(s):  
Marius Ungarish ◽  
Andrew J. Hogg
Keyword(s):  
Velocity Field ◽  
Control Volume ◽  
Gravity Current ◽  
Vortex Sheet ◽  
Gravitational Acceleration ◽  
Two Fluids ◽  
Dissipative Effects ◽  
Wake Model ◽  
New Formulation ◽  
Vorticity Balance

The steady speeds of the front of a gravity current and of an internal jump on a two-layer stratification are often sought in terms of the heights of the relatively dense fluid both up- and downstream from the front or jump, the height of the channel within which they flow, the densities of the two fluids and gravitational acceleration. In this study a unifying framework is presented for calculating the speeds by balancing mass and momentum fluxes across a control volume spanning the front or jump and by ensuring the assumed pressure field is single-valued, which is shown to be equivalent to forming a vorticity balance over the control volume. Previous models have assumed the velocity field is piecewise constant in each layer with a vortex sheet at their interface and invoked explicit or implicit closure assumptions about the dissipative effects to derive the speed. The new formulation yields all of the previously presented expressions and demonstrates that analysing the vorticity balance within the control volume is a useful means of constraining possible closure assumptions, which is arguably more effective than consideration of the flow energetics. However the new approach also reveals that a novel class of models may be developed in which there is shear in the velocity field in the wake downstream of the front or the jump, thus spreading the vorticity over a layer of non-vanishing thickness, rather than concentrating it into a vortex sheet. Mass, momentum and vorticity balances applied over the control volume allow the thickness of the wake and the speed of the front/jump to be evaluated. Results from this vortex-wake model are consistent with published numerical simulations and with data from laboratory experiments, and improve upon predictions from previous formulae. The results may be applied readily to Boussinesq and non-Boussinesq systems and because they arise as simple algebraic expressions, can be straightforwardly incorporated as jump conditions into spatially and temporally varying descriptions of the motion.

scholarly journals Attenuation of sound in a low Mach Number nozzle flow

1979 ◽  
Vol 91 (2) ◽  
pp. 209-229 ◽  
Author(s):  
M. S. Howe
Keyword(s):  
Mach Number ◽  
Large Scale ◽  
Low Frequency ◽  
Theoretical Models ◽  
Vortex Sheet ◽  
Acoustic Energy ◽  
Nozzle Flow ◽  
Finite Width ◽  
Low Mach Number ◽  
Contraction Ratio

This paper examines the energy conversion mechanisms which govern the emission of low frequency sound from an axisymmetric jet pipe of arbitrary nozzle contraction ratio in the case of low Mach number nozzle flow. The incident acoustic energy which escapes from the nozzle is partitioned between two distinct disturbances in the exterior fluid. The first of these is the free-space radiation, whose directivity is equivalent to that produced by monopole and dipole sources. Second, essentially incompressible vortex waves are excited by the shedding of vorticity from the nozzle lip, and may be associated with the large-scale instabilities of the jet. Two linearized theoretical models are discussed. One of these is an exact linear theory in which the boundary of the jet is treated as an unstable vortex sheet. The second assumes that the finite width of the mean shear layer of the real jet cannot be neglected. The analytical results are shown to compare favourably with recent attenuation measurements.

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.

Sign in / Sign up

Export Citation Format

Share Document