Velocity Antinode Research Articles

Perturbation analysis of flow about spherically pulsating bubble at the velocity node of a standing wave

An analysis using the singular perturbation method for a radially pulsating gas bubble at the velocity node of a standing wave was conducted with ε = U0/(aω)≪1 as a small parameter and ωa2/ν≫1 as a large parameter. Here,a, U0, ω, and ν are length scale, velocity scale, frequency, and kinematic viscosity, respectively. While the mean oscillatory flow around the gas bubble has no net time-averaged flow component, viscous steady streaming arises due to the nonlinearity of the flow dynamics. However, with bubble surface being considered shear-free, the vorticity generation in the system is quite weak as compared with what would result from a solid boundary. Not surprisingly, the steady streaming is also weak. As already known, the steady streaming would not arise with purely radial pulsations of a bubble in an otherwise quiescent liquid. For the case of a non-pulsating bubble at the velocity node, streaming is seen at O(ε2). However, as seen with the case of a radially pulsating bubble at the velocity antinode, interaction of two oscillatory fields creates streaming at lower order. The phase difference between radial and lateral oscillations was found to play a significant role in both the streaming direction and intensity.

Acoustofluidics 15: streaming with sound waves interacting with solid particles

In Part 15 of the tutorial series "Acoustofluidics-exploiting ultrasonic standing waves forces and acoustic streaming in microfluidic systems for cell and particle manipulation," we examine the interaction of acoustic fields with solid particles. The main focus here is the interaction of standing waves with spherical particles leading to streaming, together with some discussion on one non-spherical case. We begin with the classical problem of a particle at the velocity antinode of a standing wave, and then treat the problem of a sphere at the velocity node, followed by the intermediate situation of a particle between nodes. Finally, we discuss the effect of deviation from sphericity which brings about interesting fluid mechanics. The entire Focus article is devoted to the analysis of the nonlinear fluid mechanics by singular perturbation methods, and the study of the streaming phenomenon that ensues from the nonlinear interaction. With the intention of being instructive material, this tutorial cannot by any means be considered 'complete and comprehensive' owing to the complexity of the class of problems being covered herein.

Disturbance Field Characteristics of a Transversely Excited Burner

Transverse acoustic instabilities in premixed, swirl-stabilized flames are an important problem in low NOx combustors. Transverse excitation of swirling flames involves complex interactions between acoustic waves and fluid mechanic instabilities. This paper presents high-speed PIV characterization of the flow field characteristics of a swirling, annular jet under reacting and nonreacting conditions. These data show that the flame response to transverse acoustic excitation is a superposition of acoustic and vortical disturbances that fluctuate in both the longitudinal and transverse direction. In the nozzle near-field region, the disturbance field is a complex superposition of short wavelength and convecting vortical disturbances, as well as longer wavelength transverse and longitudinal acoustic disturbances. Very near the nozzle, distinct vortical structures are evident that are associated with the separating inner and outer annulus shear layers. Their relative phasing on the left and right side of the burner annulus changes by 180° under conditions where the burner centerline is nominally at a transverse acoustic velocity node and antinode. These suggest that the dominant excited instability mode of the annular jet changes from axisymmetric to helical as the structure of the acoustic mode shape changes. Farther downstream, these structures disappear rapidly and the disturbance field is dominated by the longer wavelength, transverse acoustic field.

Internal Flow of Acoustically Levitated Droplet

One of the major recent advances for experiments in containerless processing is acoustic levitation. Although there are a lot of previous studies for acoustic levitation, characteristic of external flow of an acoustically levitated droplet is not experimentally examined enough. In this study, external flow field has been observed by using high speed camera and Particle Image Velocimetry. In the case of any levitated droplet at a velocity antinode of standing wave, toroidal vortex are generated around levitated droplet. It is found that toroidal vortex around a levitated droplet is strongly affected by viscosity of levitated samples and input voltage. In terms of water droplet, as input voltage is decreased, location of toroidal vortex is moved from bottom to top of levitated samples.

Measurement of the acoustic velocity characteristics in a standing-wave tube using out of phase PIV

The velocity fields of an acoustic standing wave in a rectangular channel are investigated. A new approach is used to measure the velocity fields using PIV. In this approach, the velocity fields are sampled at different phases in a given experimental run without synchronizing the PIV system with the excitation signal. The results show that the RMS velocities measured from this approach are in excellent agreement with the theoretical values, indicating that this new and simple approach accurately measures the RMS velocities. At the velocity antinode, the difference between the RMS measured and theoretical velocities is less than 2.4%. The results also show that this approach can be used to measure velocity fields of a standing wave in different small segments at different times and to reconstruct the entire waveform. That is, the basic statistical properties of the entire standing wave can be obtained without synchronizing PIV with the acoustic signal.

Influence of acoustic pressure amplifier dimensions on the performance of a standing-wave thermoacoustic system

A standing-wave thermoacoustic engine, employing an acoustic pressure amplifier (APA), is simulated with linear thermoacoustics to study the influence of APA’s dimensions on performance of the thermoacoustic system. Variations of operating parameters, including pressure ratio, acoustic power, hot end temperature of stack etc., versus length and diameter of APA are presented and discussed based on an analysis of pressure and velocity distribution in APA. Simulation results indicate that a largest amplification effect of both pressure ratio and acoustic power output is achieved at a critical length for the occurrence of pressure node and velocity antinode in APA, close to but less than one fourth of the wavelength. The distribution characteristics of pressure and velocity in APA are similar to a standing-wave acoustic field, which is the reason for the amplification effect. From the viewpoint of energy, the amplification effect results from the changed distribution of acoustic energy and acoustic power loss in the thermoacoustic system by APA. Experiments have been carried out to validate the simulation, and experimental data are presented.

Steady streaming around a spherical drop displaced from the velocity antinode in an acoustic levitation field

The steady (acoustic) streaming associated with a spherical drop displaced from the velocity antinode of a standing wave is studied. The ratio of the particle size to the acoustic wavelength is treated as small but non-zero, and the solution is developed in the form of a two-term expansion in terms of the corresponding smallness parameter. The drop viscosity is assumed to be much higher than that of the surrounding fluid, which is the case for a drop in a gas medium. There are essentially three distinct regions where the steady streaming flow is analysed: inside the drop (internal circulation), in the Stokes shear-wave layer at the surface on the gas side, and the gas outside the Stokes layer (the outer streaming region). Solutions for the internal circulation and the outer streaming are obtained in the limit of small Reynolds number. Despite the gas-to-liquid viscosity ratio being small, the outer streaming may be dramatically affected by the fact that the sphere is liquid as opposed to solid. The parameter that measures the effect of liquidity is essentially the viscosity ratio divided by the relative (to the particle size) thickness of the Stokes layer. The case of a solid sphere is recovered by letting this parameter go to zero.

Computation of the temperature distortion in the stack of a standing-wave thermoacoustic refrigerator

The numerical computation of the flow and heat transfer in the vicinity of a stack plate in a standing wave refrigerator is performed. Temperature distortion is observed, which appears only in the stack region, even if the acoustic standing wave outside the stack is itself sinusoidal. The distortion takes place above the whole plate surface when the length of the plate is equal to or shorter than four times the particle displacement. This condition may occur at high drive ratios and is favored by plate positions close to the velocity antinode. The thermal distortion decreases the thermoacoustic heat pumping along the plate. At high drive ratios, if the length of the plate is not large enough, the thermal distortion can typically explain a difference of about 10% between the calculated heat flux and the heat flux predicted using linear theory.

Acoustic excitation of droplet combustion in microgravity and normal gravity

This experimental study focused on methanol droplet combustion characteristics during exposure to external acoustical perturbations in both normal gravity and microgravity. Emphasis was placed on examination of excitation conditions in which the droplet was situated (1) at or near a velocity antinode (pressure node), where the droplet experienced the greatest effects of velocity perturbations, or (2) at a velocity node (pressure antinode), where the droplet was exposed to minimal velocity fluctuations. Acoustic excitation had a significantly greater influence on droplet-burning rates and flame structures in microgravity than in normal gravity. In normal gravity, acoustic excitation of droplets situated near a pressure node produced only very moderate increases in burning rate (about 11–15% higher than for nonacoustically excited, burning droplets) and produced no significant change in burning rate near a pressure antinode. In microgravity, for the same range in sound pressure level, droplet burning rates increased by over 75 and 200% for droplets situated at or near pressure antinode and pressure node locations, respectively. Observed flame deformation for droplets situated near pressure nodes or antinodes were generally consistent with the notion of acoustic radiation forces arising in connection with acoustic streaming, yet both velocity and pressure perturbations were seen to affect flame behavior, even when the droplet was situated precisely at or extremely close to node or antinode locations. Displacements of the droplet with respect to node or antinode locations were observed to have a measureable effect on droplet burning rates, yet acoustic accelerations associated with such displacements, as an analogy to gravitational acceleration, did not completely explain the significant increases in burning rate resulting from the excitation.

Simultaneous measurement of acoustic and streaming velocities in a standing wave using laser Doppler anemometry

Laser Doppler anemometry (LDA) with burst spectrum analysis (BSA) is used to study the acoustic streaming generated in a cylindrical standing-wave resonator filled with air. The air column is driven sinusoidally at a frequency of approximately 310 Hz and the resultant acoustic-velocity amplitudes are less than 1.3 m/s at the velocity antinodes. The axial component of fluid velocity is measured along the resonator axis, across the diameter, and as a function of acoustic amplitude. The velocity signals are postprocessed using the Fourier averaging method [Sonnenberger et al., Exp. Fluids 28, 217-224 (2000)]. Equations are derived for determining the uncertainties in the resultant Fourier coefficients. The time-averaged velocity-signal components are seen to be contaminated by significant errors due to the LDA/BSA system. In order to avoid these errors, the Lagrangian streaming velocities are determined using the time-harmonic signal components and the arrival times of the velocity samples. The observed Lagrangian streaming velocities are consistent with Rott's theory [N. Rott, Z. Angew. Math. Phys. 25, 417-421 (1974)], indicating that the dependence of viscosity on temperature is important. The onset of streaming is observed to occur within approximately 5 s after switching on the acoustic field.

Influences of a temperature gradient and fluid inertia on acoustic streaming in a standing wave

Following the experimental method of Thompson and Atchley [J. Acoust. Soc. Am. 117, 1828-1838 (2005)] laser Doppler anemometry (LDA) is used to investigate the influences of a thermoacoustically induced axial temperature gradient and of fluid inertia on the acoustic streaming generated in a cylindrical standing-wave resonator filled with air driven sinusoidally at a frequency of 308 Hz. The axial component of Lagrangian streaming velocity is measured along the resonator axis and across the diameter at acoustic-velocity amplitudes of 2.7, 4.3, 6.1, and 8.6 m/s at the velocity antinodes. The magnitude of the axial temperature gradient along the resonator wall is varied between approximately 0 and 8 K/m by repeating measurements with the resonator either surrounded by a water jacket, suspended within an air-filled tank, or wrapped in foam insulation. A significant correlation is observed between the temperature gradient and the behavior of the streaming: as the magnitude of the temperature gradient increases, the magnitude of the streaming decreases and the shape of the streaming cell becomes increasingly distorted. The observed steady-state streaming velocities are not in agreement with any available theory.

Observation of coronal loop torsional oscillation

We suggest that the global torsional oscillation of solar coronal loop may be observed by the periodical variation of a spectral line width. The amplitude of the variation must be maximal at the velocity antinodes and minimal at the nodes of the torsional oscillation. Then the spectroscopic observation as a time series at different heights above the active region at the solar limb may allow to determine the period and wavelength of global torsional oscillation and consequently the Alfv{\'e}n speed in corona. From the analysis of early observation (Egan & Schneeberger \cite{egan}) we suggest the value of coronal Alfv{\'e}n speed as $\sim 500 {\rm km}{\cdot}{\rm s}^{-1}$.

Enhancement of gas phase heat transfer by acoustic field application

This study discusses a possibility for enhancement of heat transfer between solids and ambient gas by application of powerful acoustic fields. Experiments are carried out by using preheated Pt wires (length 0.1–0.15 m, diameter 50 and 100 μm) positioned at the velocity antinode of a standing wave (frequency range 216–1031 Hz) or in the path of a travelling wave (frequency range 6.9–17.2 kHz). A number of experiments were conducted under conditions of gas flowing across the wire surface. Effects of sound frequency, sound strength, gas flow velocity and wire preheating temperature on the Nusselt number are examined with and without sound application. The gas phase heat transfer rate is enhanced with acoustic field strength. Higher temperatures result in a vigorous radiation from the wire surface and attenuate the effect of sound. The larger the gas flow velocity, the smaller is the effect of sound wave on heat transfer enhancement.

Measurement of the time evolution of Rayleigh streaming in high-amplitude standing waves

The time evolution of the axial component of the Rayleigh streaming velocity field in a cylindrical, air-filled resonator has been measured using laser Doppler anemometry. At low acoustic amplitudes, the measured field is in agreement with classical theory. The axial component varies sinusoidally along the axial direction and quadratically along the radial direction, and the position of maximum streaming velocity on the axis is located midway between the velocity node and velocity antinode. At higher acoustic amplitudes, the streaming velocity field initially resembles the classical result, but becomes progressively distorted as time passes. The position of maximum streaming velocity on the axis shifts towards the velocity antinode, while the streaming velocity outside the boundary layer, near the resonator wall, remains unaffected. Additionally, the radial dependence of the axial streaming velocity deviates from its initially parabolic shape, becoming flatter near the velocity node and steeper near the velocity antinode. The length of time required for the streaming to reach steady state is on the order of several minutes for a fundamental frequency of 310 Hz, a resonator radius of 23 mm, and an antinodal acoustic velocity of 6.0 m/s peak. [Work supported by ONR.]

Radiation pressure of standing waves on liquid columns and small diffusion flames

The radiation pressure of standing ultrasonic waves in air is demonstrated in this investigation to influence the dynamics of liquid columns and small flames. With the appropriate choice of the acoustic amplitude and wavelength, the natural tendency of long columns to break because of surface tension was suppressed in reduced gravity [M. J. Marr-Lyon, D. B. Thiessen, and P. L. Marston, Phys. Rev. Lett. 86, 2293–2296 (2001); 87(20), 9001(E) (2001)]. Evaluation of the radiation force shows that narrow liquid columns are attracted to velocity antinodes. The response of a small vertical diffusion flame to ultrasonic radiation pressure in a horizontal standing wave was observed in normal gravity. In agreement with our predictions of the distribution of ultrasonic radiation stress on the flame, the flame is attracted to a pressure antinode and becomes slightly elliptical with the major axis in the plane of the antinode. The radiation pressure distribution and the direction of the radiation force follow from the dominance of the dipole scattering for small flames. Understanding radiation stress on flames is relevant to the control of hot fluid objects. [Work supported by NASA.]

Passive stabilization of capillary bridges in air with acoustic radiation pressure and the equilibrium shape of bridges

Long liquid cylinders ordinarily become unstable because of a capillary instability originally studied by Rayleigh and Plateau. In the present research liquid bridges in air were acoustically stabilized to 43% beyond the natural limiting length identified by Rayleigh and Plateau [Marr-Lyon, Thiessen, and Marston, Phys. Rev. Lett. (to be published)]. The stabiliza-tion was achieved by placing the bridge at the velocity antinode of a standing wave and selecting the wavelength such that the surface-averaged radiation pressure of the sound field increases with increasing bridge radius. The tests were performed on NASA’s KC-135 aircraft in weightless conditions on bridges having volumes equal to that of a circular cylinder of the same length as the bridge. In the standing wave, the bridge becomes elliptical because of the spatial distribution of the radiation pressure. Calculations of the scattering of sound by elliptical cylinders using Mathieu functions show that elliptical deformation only weakly affects the average increase in the radiation pressure with the local bulging of a liquid bridge normally associated with the Rayleigh-Plateau instability. [Work supported by NASA.]

The use of ultrasonic standing waves to enhance optical particle sizing equipment

Fluid dynamics modelling augmented with routines to simulate acoustic forces on aerosol particles has been used to investigate the potential of combining ultrasonic standing wave fields with optical particle analysis equipment. Simulations of particle dynamics in airstreams incorporating acoustic forces predict that particles in the 1–10 μm diameter range may be effectively focused to the velocity nodes of the standing wave field. Particles move to the velocity nodes within tens of milliseconds for acoustic frequencies of 10–100 kHz and at an acoustic energy density of 100 J m −3. Larger particles are predicted to move to the velocity antinodes within similar times; however, there is a crossover region at approximately 15–20 μm particle diameter where longer times are predicted due to the competing forces driving particles to the vibration node and antinode. With sufficient transverse flow velocities the models predict that disturbances due to acoustic streaming can be overcome and a useful degree of focusing achieved for the aerosol particles. Results from a model demonstrating sampling and acoustic focusing of 3–9 μm aerosol particles to a 200 μm wide analysis area are presented.

Influence of standing sound waves on droplet combustion

The influence of acoustic fields on combustion of a single fuel droplet has been investigated using microgravity. The natural convection-free conditions allow the role of sound alone to be established by avoiding the coupling of sound-induced alternating convection and natural convection. Experiments were done with n -decane single droplets of about 1.5 mm in diameter. Sounds of 66.5 to 3353 Hz with sound pressure levels up to 135 dB were applied in a duct, which achieved maximum velocity amplitudes of about 1 m/s. As a result, a significantly deformed flame and a soot ring instead of soot shell were found in cases of large velocity amplitude. Burning rates increased with increasing velocity amplitude. The other parameters such as sound pressure level or frequency had little influence. Different influences of sound were found for droplets burning at different locations relative to the velocity antinode of the applied sound. All these observed phenomena are explained by the alternating convection due to sound and a unidirectional convection, which is a form of acoustic streaming, driven by the acoustic radiation force. A simple analysis has been made of the streaming mechanism and the increased burning rate. Differences with droplet location are explained by the enhancement in heat and mass transfer due to the two kinds of convection.

Singular perturbation analysis of an acoustically levitated sphere: Flow about the velocity node

This analysis consists of the development of the fluid flow about a spherical particle placed at the velocity node of a standing wave. High-frequency acoustic fields are being used to levitate particles in Earth gravity, and to stabilize particles in low-gravity situations. While a standing wave in an infinite medium may be purely oscillatory with no net flow components, the interaction with particles or solid walls leads to nonlinear effects that create a net steady component of the flow. In the present development, the perturbation method is employed to derive the flow field for the situation when a spherical particle is positioned at the velocity node. As found in an earlier analysis [Riley, Q. J. Mech. Appl. Math 19, 461 (1966)] applicable to a solid sphere at the velocity antinode, there is a thin shear-wave region adjacent to the spherical boundary. However, this thin Stokes layer does not cover the entire sphere in the same manner as in the previous case. In the polar regions flow reversal takes place but the Stokes layer opens to the surrounding field. On an equatorial belt region there are closed streamlines.

Experimental Study of Acoustic Velocity Effects on Simulated Solid Fuel Pyrolysis

An experimental study of the effect of acoustic velocity oscillations on solid fuel pyrolysis, modeled using dry ice sublimation, was performed. Use of dry ice as a solid fuel simulant allows the fluid mechanics of the problem to be separated from the combustion process. The experimental facility was designed to model solid waste pyrolysis in an acoustically excited incinerator. Dry ice was placed in a rectangular chamber in which resonant acoustic oscillations could be driven. A mean flow of air entered from one end of the chamber, and exhaust was removed from the opposite end. Flow visualization indicated that the mass transport near the dry ice surface was greatly increased when velocity oscillations were present. When the dry ice was positioned at an acoustic velocity antinode of a 160-dB standing oscillation, the sublimation rate was nearly 60% greater than without oscillation. For the conditions studied, the effects of velocity oscillations at a constant amplitude became greater as the mean velocity was increased. Comparison of the sublimation rates measured with dry ice located at acoustic velocity and pressure antinodes shows that, at constant amplitude, acoustic velocity oscillations have a much greater effect on the sublimation rate than pressure oscillations.