Axial Streaming Velocity Research Articles

An unexpected balance between outer Rayleigh streaming sources

Acoustic streaming generated by a plane standing wave between two infinite plates or inside a cylindrical tube is considered, under the isentropic flow assumption. A two-dimensional analysis is performed in the linear case of slow streaming motion, based on analytical formal solutions of separate problems, each associated with a specific source term (Reynolds stress term). In order to obtain these analytical solutions, a necessary geometrical hypothesis is that $(R/L)^{2}\ll 1$, where $R$ and $L$ are the guide half-width (or radius) and length. The effect of the two source terms classically taken into account is quantified in order to derive the dependence of the maximum axial streaming velocity on the axis as a function of the ratio $R/\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}$, where $\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}$ is the acoustic boundary layer thickness. The effect of two other source terms that are usually neglected, is then analysed. It is found that one of these terms can generate a counter-rotating streaming flow. While negligible for very narrow guides, this term can become important for some values of the aspect ratio $L/R$.

Plasma instability of magnetically enhanced vacuum arc thruster

A two-fluid flowing plasma model is applied to describe the plasma rotation and resulted instability evolution in magnetically enhanced vacuum arc thruster (MEVAT). Typical experimental parameters are employed, including plasma density, equilibrium magnetic field, ion and electron temperatures, cathode materials, axial streaming velocity, and azimuthal rotation frequency. It is found that the growth rate of plasma instability increases with growing rotation frequency and field strength, and with descending electron temperature and atomic weight, for which the underlying physics are explained. The radial structure of density fluctuation is compared with that of equilibrium density gradient, and the radial locations of their peak magnitudes are very close, implying that the mode may be driven by density gradient. Temporal evolution of perturbed mass flow in the cross section of plasma column is also presented, which behaves in the form of clockwise rotation (direction of electron diamagnetic drift) at edge and anti-clockwise rotation (direction of ion diamagnetic drift) in the core, separated by a mode transition layer from n = 0 to n = 1. This work, to our best knowledge, is the first treatment of plasma instability caused by rotation and axial flow in MEVAT, and is also of great practical interest for other electric thrusters where rotating plasma is concerned for long-time stable operation and propulsion efficiency optimization.

Evolution of Rayleigh streaming flow velocity components in a resonant waveguide at high acoustic levels

The interaction between an acoustic wave and a solid wall generates a mean steady flow called Rayleigh streaming, generally assumed to be second order in a Mach number expansion. This flow is well known in the case of a stationary plane wave at low amplitude: it has a half-wavelength spatial periodicity and the maximum axial streaming velocity is a quadratic function of the acoustic velocity amplitude at the antinode. For higher acoustic levels, additional streaming cells have been observed. In the present study, results of LDV and PIV measurements are compared to direct numerical simulations. The evolution of axial and radial velocity components for both acoustic and streaming flows is studied from low to high acoustic amplitudes. Two streaming flow regimes are pointed out, the axial streaming dependency upon acoustics going from quadratic to linear. The hypothesis of the radial streaming velocity being of second order in a Mach number expansion is shown to be invalid at high amplitudes. The change of regime occurs when the radial streaming velocity amplitude becomes larger than the radial acoustic velocity amplitude, high levels being therefore characterized by nonlinear interaction of the different velocity components.

Acoustic and streaming velocity components in a resonant waveguide at high acoustic levels.

Rayleigh streaming is a steady flow generated by the interaction between an acoustic wave and a solid wall, generally assumed to be second order in a Mach number expansion. Acoustic streaming is well known in the case of a stationary plane wave at low amplitude: it has a half-wavelength spatial periodicity and the maximum axial streaming velocity is a quadratic function of the acoustic velocity amplitude at antinode. For higher acoustic levels, additional streaming cells have been observed. Results of laser Doppler velocimetry measurements are here compared to direct numerical simulations. The evolution of axial and radial velocity components for both acoustic and streaming velocities is studied from low to high acoustic amplitudes. Two streaming flow regimes are pointed out, the axial streaming dependency on acoustics going from quadratic to linear. The evolution of streaming flow is different for outer cells and for inner cells. Also, the hypothesis of radial streaming velocity being of second order in a Mach number expansion, is not valid at high amplitudes. The change of regime occurs when the radial streaming velocity amplitude becomes larger than the radial acoustic velocity amplitude, high levels being therefore characterized by nonlinear interaction of the different velocity components.

Experimental investigation of acoustic streaming in a cylindrical wave guide up to high streaming Reynolds numbers

Measurements of streaming velocity are performed by means of Laser Doppler Velocimetry and Particle Image Velociimetry in an experimental apparatus consisting of a cylindrical waveguide having one loudspeaker at each end for high intensity sound levels. The case of high nonlinear Reynolds number ReNL is particularly investigated. The variation of axial streaming velocity with respect to the axial and to the transverse coordinates are compared to available Rayleigh streaming theory. As expected, the measured streaming velocity agrees well with the Rayleigh streaming theory for small ReNL but deviates significantly from such predictions for high ReNL. When the nonlinear Reynolds number is increased, the outer centerline axial streaming velocity gets distorted towards the acoustic velocity nodes until counter-rotating additional vortices are generated near the acoustic velocity antinodes. This kind of behavior is followed by outer streaming cells only and measurements in the near wall region show that inner streaming vortices are less affected by this substantial evolution of fast streaming pattern. Measurements of the transient evolution of streaming velocity provide an additional insight into the evolution of fast streaming.

Fast acoustic streaming in standing waves: Generation of an additional outer streaming cell

Rayleigh streaming in a cylindrical acoustic standing waveguide is studied both experimentally and numerically for nonlinear Reynolds numbers from 1 to 30 [Re(NL)=(U0/c0)(2)(R/δν)(2), with U0 the acoustic velocity amplitude at the velocity antinode, c0 the speed of sound, R the tube radius, and δν the acoustic boundary layer thickness]. Streaming velocity is measured by means of laser Doppler velocimetry in a cylindrical resonator filled with air at atmospheric pressure at high intensity sound levels. The compressible Navier-Stokes equations are solved numerically with high resolution finite difference schemes. The resonator is excited by shaking it along the axis at imposed frequency. Results of measurements and of numerical calculation are compared with results given in the literature and with each other. As expected, the axial streaming velocity measured and calculated agrees reasonably well with the slow streaming theory for small ReNL but deviates significantly from such predictions for fast streaming (ReNL>1). Both experimental and numerical results show that when ReNL is increased, the center of the outer streaming cells are pushed toward the acoustic velocity nodes until counter-rotating additional vortices are generated near the acoustic velocity antinodes.

Flow analysis of acoustic streaming pattern produced by ultrasonic transducer using stereoscopic PIV

Quantitative flow fields from the acoustic streaming were measured experimentally using the stereoscopic PIV. The acoustic streaming pattern between the ultrasonic transducer and stationary plate, maximum acoustic streaming velocity, velocity variation at resonance and non-resonance, variation of flow pattern and velocity with gap variation were experimentally verified. The maximum acoustic velocity between the gap in the open channel at resonance and non-resonance was located at the ultrasonic transducer center at radial direction and at the neighborhood of the ultrasonic transducer at axial direction. In the vicinity of the ultrasonic transducer surface, larger average acoustic velocity occurred at the edge of the transducer than at the transducer center at the resonant gap. At non-resonant gap, the maximum acoustic velocity exists toward the edge of the transducer. The turbulent intensity varied with gap size and maximum value existed at the transducer center with radial direction and at surface of the stationary plate or transducer with axial direction. At resonant gaps, there was almost zero radial acoustic streaming velocity at the ultrasonic transducer center and there existed only axial streaming velocity. For axial directions, maximum acoustic streaming velocity was located at z position of − 16 mm.

Effect of an obstacle on Rayleigh acoustic streaming cells

Acoustic streaming has harmful consequences on thermoacoustic machines behaviour because of the associated heat transfers. A preliminary study was carried out in order to study the effect of an obstacle on the Rayleigh cells to help in understanding the role of such phenomena in thermoacoustic machines. An obstacle was introduced in a half‐wavelength cylindrical wave guide to study its effects on acoustic streaming. The obstacle was placed at various positions along the wave guide axis and experiments were carried out at various acoustic levels. The axial streaming velocity was measured using Laser Doppler Velocimetry (LDV). It was observed that adding an obstacle in the streaming pattern modifies the latter and that new streaming vortices appear in the vicinity of the obstacle. When the obstacle position approaches a maximum of the Rayleigh streaming velocity the number and the amplitude of acoustic streaming vortices at the ends of the obstacle increase. Similar tendencies were observed when the acousti...

Measurements of inner and outer streaming vortices in a standing waveguide using laser doppler velocimetry

Measurements of the axial streaming velocity are performed by means of laser doppler velocimetry in an experimental apparatus consisting of a waveguide having loudspeakers at each end for high intensity sound levels. Streaming is characterized by an appropriate Reynolds number Re(NL), the case Re(NL)<<1 corresponding to the so-called slow streaming and the case Re(NL)>/=1 being referred to as fast streaming. The variation of axial streaming velocity with respect to the transverse coordinate is compared to the available slow streaming theory. Streaming fluid flow is measured both in the core region and in the near wall region. Streaming velocity in the center of the guide agrees reasonably well with the slow streaming theory for small Re(NL) but deviates significantly from such predictions for Re(NL)>20 and its evolution for further increasing Re(NL) is discussed. Then streaming behavior in the near wall region is particularly studied. For Re(NL)<70, two vortices are present across the guide section as predicted by slow streaming theory. Then it appears that, when the Reynolds number is increased, two other vortices become visible in the near wall region. Different stages for the generation and evolution of these inner streaming vortices are presented.

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.]

Secondary flow in basic pulse tube refrigerators

Existence of steady large-scale streaming within basic pulse tube refrigerators was shown analytically. The steady component of the second-order axial velocity and the axial streaming velocity were obtained from the first-order solutions of continuity, momentum and energy equations, assuming that the amplitude of the piston motion is small. The axial temperature gradient of the wall was considered in the analysis. The flow direction of the streaming was consistent with previous experimental observations. The effects of the axial temperature gradient on secondary flow was shown.

Strange interface deformation pulses in the flow of layered liquids

The interface in acoustically driven layered liquids, in an enclosed geometry, was found to be unstable to the production of spatially localized, quasi-periodic pulses of deformation. The most interesting property of these pulses is that they propagate in a direction opposite to that of the axial streaming velocity of both liquids. Experimental data are presented describing aspects of the phenomenon which occur only when both the interfacial tension and the density difference are small.

Strange interfacial waves in stratified flows of immiscible fluids

The interface in acoustically driven layered liquids, in an enclosed geometry, was found to be unstable at a critical value of the axial streaming velocity. Above this critical value, which depends on the system parameters, tiny, uncorrelated ripples were generated. Then, beyond a second, larger critical velocity, large quasiperiodic pulses of deformation which propagate without change of shape in a direction opposite to that of the axial streaming velocity of both liquids, are spontaneously generated. Experimental data are presented describing aspects of this novel phenomenon, which occurs only when the fluids have small values of interfacial tension (IFT) and density difference.

Results of an Experiment on Acoustic Streaming in Gases

An ultrasonic streaming experiment based on an extension of Eckart's theory has been carried out for three gases. The source was a 3-in. diameter BaTiO3 disk radiating a 185-kc sound beam into a closed 6-in. diameter tube terminated by a glass wool absorber. An A.D.P. probe microphone moved transverse to the beam to record a graph of the actual acoustic field. Tobacco smoke and Lycopodium powder were used as tracing particles. Their motion, when observed through a calibrated telescope, gives the speed of the streams. The variation of streaming with distribution of the radially symmetric acoustic pressure was studied for the region in which streaming is proportional to intensity. Conclusions are: (1) a complete knowledge of the acoustic pressure distribution P(τ) enables one to predict the streaming profile at that same cross section with excellent experimental check; (2) the variation in axial streaming velocity near the source (the “quartz wind”) can be explained by the attenuation and divergence of the sound beam; and (3) for a gas (argon) of known (zero) bulk viscosity, the absolute value of the velocity given by the extended Eckart theory is experimentally verified within 4 percent. The variation of streaming with the constants of the medium was studied for argon, dry nitrogen, and moist air. For a known acoustic field, the axial streaming velocity may be used to evaluate the sum of all attenuative mechanisms. In this sense streaming experiments may be added to the list of various types of attenuation techniques for the determination of the constants of a fluid.