Vortex sound in the presence of a low Mach number flow across a drum-like silencer

The sound generated by a vortex propagating across a two-dimensional duct section with flexible walls (membranes) in an infinitely long rigid duct conveying a flow is investigated numerically using the matched asymptotic expansion technique and the potential theory. The effects of the initial vortex position, the mechanical properties of the flexible walls, and the mean flow on the sound generation are examined in detail. Results show that the presence of a vortex inside a uniform mean flow can strengthen or attenuate the sound generation, depending on the phase of the membrane vibration when the vortex starts vigorous interaction with the membranes and the strength of the mean flow. The results tend to imply that there is a higher chance of sound amplification when a vortex stream is moving closer to the lighter membrane under a relatively strong mean flow or when the mean flow is weak. The chances of sound amplification or attenuation are equal otherwise.     

Vortex sound under the influence of a piecewise porous material on an infinite rigid plane

The vortex dynamics and the sound generation by an inviscid vortex in the presence of a finite length porous material on an otherwise rigid plane are studied numerically in the present study in an attempt to understand the sound generation near the surface of a wall lining in a lined duct. The combined effects of the effective fluid density and flow resistance inside the porous material, and the length and thickness of the porous material on the sound generation process are examined in detail. Results obtained demonstrate the sound pressure is longitudinal dipole and show how seriously the above-mentioned parameters are affecting the vortex sound pressure under the influence of the porous material.     

Acoustic-excited vortex shedding and acoustic nonlinearity at a rectangular slit with bias flow

The acoustical response of a slit with a mean bias flow is numerically studied. By means of a potential flow model based on the discrete vortex method and a spanwise-averaged three-dimensional Green?s function, both unsteady vortical flow and slit impedance are obtained in a unified theoretical framework. The numerical simulation focuses on the acoustic-excited vortex structures of the slit flow while neglecting the viscous damping effect. Three representative flow features are demonstrated, which are the destabilized jet flow, the rolling up of vortex sheets and formation of vortex pairs, and the reversal flow with alternating vortex shedding on both sides of the slit. These features are corresponding to low, moderate, and high sound amplitude, respectively. The acoustic behavior of the slit can be divided into linear, transition, and nonlinear regimes. During its evolution through the three regimes, the resistance exhibits a constant value, a slight decrease, and a significant increase with the increasing sound amplitude. Correspondingly, the reactance first remains constant and then shows a modest decrease as the sound amplitude increases. The nonlinear effect also causes the gradual decrease of the mean bias velocity in company with the marked increase of the amplitude of the fluctuating velocity in the slit. The mean bias velocity decreases to about 80 percent of its linear value at the transition point where reversal flow begins to occur, and further decreases to only 10 percent in the highly nonlinear region. The slit impedance is also presented as a function of frequency and for different aspect ratios. And the effects of frequency and slit geometry are discussed.     

Why the phase shifts for solitons on a vortex filament are so large: a theoretical explanation

The phase "jumps" for solitons interacting on a vortex filament, observed in experiments, have been unaccounted for for more than 20 years. Using explicit formulas describing the interaction of two solitons on a thin vortex filament in the localized induction approximation, we show that an appropriate choice of the parameters of the solitons leads to large phase shifts. This result does not depend on the axial flow along the filament.     

The sound field of a rotating monopole in a plug flow

A theoretical study is performed on the sound field generated by a rotating point monopole in a jet flow, the mixing layer of which is simulated by a velocity discontinuity. Its sound in the far field is compared to the sound field generated by a rotating monopole in a uniform flow in the absence of a velocity discontinuity, which makes it possible to estimate the size of the sound refraction effect.     

Vortex sound due to a flexible boundary backed by a cavity in a low mach number mean flow

Low frequency sound radiated due to the unsteady motion of an inviscid vortex in the proximity of a flexible membrane backed by an airtight cavity on an otherwise rigid plane is investigated theoretically. Results show that both monopole and dipole are created but the latter is important only when the vortex is traversing over the membrane. The monopole results from the membrane vibration and the dipole from the transverse motion of the vortex. It is also found that these sound fields tend to counteract each other. The increase in the mean flow speed in general results in a stronger acoustic power radiation, but sound attenuation may be possible if the membrane-cavity system is weak compared with the mean flow momentum.     

圆孔声学非线性效应的数值模拟

本文发展了一种离散涡模型,模拟了在高声强声波作用下圆孔处发生的涡脱落过程。进而计算了圆孔中的声质点速度,并分析了孔中速度的畸变情况、最后给出了圆孔的非线性声阻和声抗的理论值。非线性声抗的理论预测是现有的研究圆孔声学非线性效应的准稳态模型没有满意解决的问题,因而所做的有关尝试是本文工作的特点之一。     

Basic sound generation mechanisms in inviscid vortex interactions at low Mach number

The sound generation mechanisms during finite core vortex interactions at low Mach number are investigated in the present study. The theoretical deductions show clearly that the basic sound generation mechanisms are associated with the vortex core deformation and the vorticity centroid dynamics, independent of the vortex system. Such deductions are substantiated by numerical experiments with the interactions of two-dimensional vortices, vortex pairs and vortex rings. Detailed discussions on the similarities and differences between the sound generation processes of the two-dimensional and axisymmetric vortex systems are given. The relative importance of the two sound generation mechanisms in these vortex systems, their characteristics and interactions, which are hardly found in existing literature, are also examined. The present findings have also generalized and substantiated the previous results of the authors on the topic.     

Diffraction of sound from a dipole source near to a barrier or an impedance discontinuity

Pierce's formulation for the diffraction of spherical waves by a hard wedge has been extended to the case of the sound field due to a dipole source. The same approach is also used to extend a semiempirical model for sound propagation above an impedance discontinuity due to a dipole source. The resulting formulas have been validated by comparing their numerical solutions with that computed by summing the sound fields due to two closely spaced monopole sources of equal magnitude but opposite in phase. These new formulations are then used to develop a simple model for calculating the dipole sound field diffracted by a barrier above an impedance ground. Applications of these models relate to transportation noise prediction, particularly railway noise abatement, for which dipole sources are commonly used. The numerical predictions have been found to compare reasonably well with indoor measurements using piezoceramic transducers as dipole sources.     

Sound scattering by a Karman street consisting of large-scale vortices

The scattering of acoustic waves by a vortex street formed behind a cylinder in an air flow is studied both theoretically and experimentally for the case of the sound wavelength being much less than the vortex size. The theoretical calculations show that, at flow velocities well below the sound velocity, the vortex street can be considered as a moving phase screen. The spectrum of scattered sound in the far zone is shown to consist of harmonics whose frequencies differ by a multiple of the vortex rate. The computational results agree well with the experimental data obtained for the diffraction of ultrasound of the wavelength λ=3 mm by the Karman street formed behind a circular cylinder with an 8 mm diameter at a flow velocity of 7 m/s.     

The vortex flow caused by sound in a bubbly liquid

Generation of vorticity in the field of intense sound in a bubbly liquid in the free half-space is considered. The reasons for generation of vorticity are nonlinearity, diffraction, and dispersion. Acoustic streaming differs from that in a Newtonian fluid. Under some conditions, the vortex flow changes its direction. Conclusions concern streaming induced by a harmonic or an impulse Gaussian beam.     

Differential characteristic of the flow behind a shock wave

Relationships between the derivatives on both sides of a discontinuity in a nonstationary shock wave moving with acceleration in a one-dimensional vortex flow of perfect gas are deduced. The problem of interaction between the shock wave and a weak discontinuity is solved based on these relationships.     

微圆孔非线性声阻抗及声整流现象的实验研究

在高声强下测量了微圆孔处声激发射流的速度和微圆孔的非线性声阻抗。随声压级的增加声激发射流的速度增大,实验中射流速度在 ０－１９ｍ／ｓ范围内变化,这表明出现一种强烈声整流现象;与此同时微圆孔声阻明显增大,而声抗减小,声抗最小值约是其线性值的０．７倍。此外实验结果还验证了一种微园孔声学非线性效应离散涡模型的合理性。     

On the influence of the Reynolds number on the intensity of vortex sound flowing around a cylindrical profile

Regularities of the emission of vortex sound (eolian tone) during air flow around stationary and rotating cylindrical profiles have been investigated. The influence of the flow Reynolds number on the intensity of vortex sound emission has been estimated from results of measuring the pressure fluctuation distribution on the surface of stationary cylindrical rods flowed around by air, as well as in the wake behind them. It is shown that the emission intensity depends on the location of the point of flow detachment from the profile surface and the track width near the profile. The ranges of the flow Reynolds numbers where the emission intensity increases with different flow velocities have been determined by analyzing the dependence of the profile lift coefficient on the Reynolds number. An independent way of determining the profile lift coefficient by measuring the vortex sound intensity is proposed. The results explain contradictions between the results of some authors, who experimentally observed different dependences of emission intensity on the flow velocity. The influence of the profile diameter on the vortex sound emission intensity has been investigated. The boundary Reynolds number above which the profile diameter does not affect emission has been established for stationary and rotating cylindrical profiles. It is shown that deposition of rough coatings on the rod surface may reduce the vortex sound emission intensity by affecting the point of flow detachment from the surface.     

Sound generated by a vortex convected past an elastic sheet

We study the motion and sound generated when a line vortex is convected in a uniform low-Mach flow parallel to a thin elastic sheet. The linearized sheet motion is analyzed under conditions where the unforced sheet (in the absence of the line vortex) is stationary. The vortex passage above the sheet excites a resonance mode of motion, where the sheet oscillates at its least stable eigenmode. The sources of sound in the acoustic problem include the sheet velocity and fluid vorticity. It is shown that the release of trailing-edge vortices, resulting from the satisfaction of the Kutta condition, has two opposite effects on sound radiation: while trailing-edge vortices act to reduce the pressure fluctuations occurring owing to the direct interaction of the line vortex with the unperturbed sheet, they extend and amplify the acoustic signal produced by the motion of the sheet. The sheet motion radiates higher sound levels as the system approaches its critical conditions for instability, where the effect of resonance becomes more pronounced. It is argued that the present theory describes the essential mechanism by which sound is generated as a turbulent eddy is convected in a mean flow past a thin elastic airfoil.     

A study of pulsatile jet discharged from pipe end

Noise is generated from a flow field upstream of a shock wave periodically discharged from a pipe end. A vortex ring and an underexpanded jet are periodically formed and diffused downstream. To clarify the mechanism of the noise generation, the flow field was experimentally and numerically studied. The flow field was visualized mainly by the schlieren method and the sound pressure of the noise was measured. The pulsatile flow through the pipe was numerically simulated by Random-Choice Method and using these results as the boundary condition, the pulsatile jet was simulated by TVD scheme. As a result, a good qualitative agreement was found between the flow field obtained by the calculations and that by the experiments. Furthermore, a relation between the behaviour of the vortex ring and the generation of the noise was discussed.     

Numerical prediction of tip vortex cavitation behavior and noise considering nuclei size and distribution

The tip vortex cavitation behavior and sound generation were numerically analyzed. A numerical scheme combining Eulerian flow field computation and Lagrangian particle trace approach was applied to simulate tip vortex cavitation. Flow field was computed by using hybrid method which combines Reynolds-Averaged Navier-Stokes solver with Dissipation Vortex Model. The trajectory and behavior of each cavitation bubble were computed by Newton’s second law and Rayleigh-Plesset equation, respectively. According to nuclei population data, the cavitation nuclei were distributed and convected into the tip vortex flow. Calculated volume of the cavitation bubble and the trajectory were used as the input of cavitation bubble noise analysis. The relationship of cavitation inception, sound pressure level, and cavitation nuclei size was studied at several cavitation numbers. It was found that cavitation inception of smaller nuclei is more sensitive to the change of cavitation number and cavitation noise due to the cavitated smallest nuclei has the most influence on overall tip vortex cavitation noise.     

Interaction of induced sound with flow past a square leading edged plate in a duct

The interaction of resonant sounds with the flow past a thick, blunt, flat plate in a rigid walled square duct has been examined. Sound pressure levels of up to 146 dB (re 20 μPa) have been recorded. It has been established that the resonant sound can initially be excited at a harmonic of the normal vortex shedding frequency. In some cases, the sound “feeds back” on the vortex shedding process causing a step change in the shedding frequency, increasing the Strouhal number for the plate by up to twice the normal value. This excited vortex shedding and associated resonances can be suppressed by locating the plate at incidence to the air flow direction. Complex duct modes can be generated by the vortex shedding resulting in different regions of the plate shedding at different Strouhal numbers.     

Passive oscillations of two tandem flexible filaments in a flowing soap film

The passive oscillations of flexible filaments in a flowing soap film were investigated to learn the serial interaction between them. When arranged in tandem, the downstream filament flaps at the same frequency as that of the upstream one, but with a larger amplitude, whereas the upstream one is almost unaffected compared to the single filament case. The data analysis shows the downstream filament indeed extracts energy from the vortex street and receives greater force than the upstream one or a single filament in a uniform flow.     

Experimental examination of vortex-sound generation in an organ pipe: A proposal of jet vortex-layer formation model

Aero-dynamical models of sound generation in an organ pipe driven by a thin jet are investigated through an experimental examination of the vortex-sound theory. An important measurement requirement (acoustic cross-flow as an irrotational potential flow reciprocating sinusoidally) from the vortex-sound theory is carefully realized when the pipe is driven with low blowing pressures of about 60 Pa (jet velocities of about 10 m/s). Particle image velocimetry (PIV) is applied to measure the jet velocity and the acoustic cross-flow velocity over the mouth area at the same phase by quickly switching the jet drive and the loudspeaker-horn drive. The vorticity of the jet flow field and the associated acoustic generation term are evaluated from the measurement data. It is recognized that the model of the “jet vortex-layer formation” is more relevant to the sound production than the vortex-shedding model. The acoustic power is dominantly generated by the flow–acoustic interaction near the edge, where the acoustic cross-flow velocity takes larger magnitudes. The acoustic generation formula on the vortex sound cannot deny the conventional acoustical volume-flow model because of the in-phase relation satisfied between the acoustic pressure at the mouth and the acoustic volume flow into the pipe. The vortex layers formed along both sides of the jet act as the source of an accelerating force (through the “acceleration unbalance”) with periodically alternating direction to oscillate the jet flow and to reinforce the acoustic cross-flow at the pipe mouth.