Low Frequency Acoustic Streaming in a Hele-Shaw Cell

2014 ◽  
Author(s):  
Maxime Costalonga ◽  
Hassan Peerhossaini ◽  
Philippe Brunet
Keyword(s):  
Boundary Layer ◽  
Linear Time ◽  
Acoustic Streaming ◽  
Low Frequency ◽  
Navier Stokes ◽  
Viscous Boundary Layer ◽  
Navier Stokes Equation ◽  
Acoustic Frequency ◽  
Hele Shaw Cell ◽  
Streaming Flow

When an acoustic wave propagates in a fluid, it can generate a second order flow which characteristic time is much longer than the period of the wave. Within a range of frequency between 1 and several hundred Hz, a relatively simple and versatile way to generate streaming flow is to put a vibrating object in the fluid. The flow develops vortices in the viscous boundary layer located in the vicinity of the source of vibrations, which in turns leads to an outer irrotational streaming denoted as Rayleigh streaming. Due to that the flow originates from non-linear time-irreversible terms of the Navier-Stokes equation, this phenomenon can be used to move fluids and even to generate efficient mixing at low Reynolds number, for instances in confined geometries. Here we report an experimental study of such streaming flow in a Hele-Shaw cell of 2 millimeters span using long exposure flow visualization and PIV measurements. Our study is especially focused on the effects of acoustic frequency and amplitude on flow dynamics. It is shown that some features of this flow can be predicted by simple scaling arguments, invoking a balance between viscous dissipation in the boundary layer and inertia term, and that acoustic streaming facilitates the generation of vortices.

scholarly journals Acoustic Streaming Generated by Sharp Edges: The Coupled Influences of Liquid Viscosity and Acoustic Frequency

Micromachines ◽  
2020 ◽  
Vol 11 (6) ◽  
pp. 607 ◽  
Author(s):  
Chuanyu Zhang ◽  
Xiaofeng Guo ◽  
Laurent Royon ◽  
Philippe Brunet
Keyword(s):  
Boundary Layer ◽  
Scaling Laws ◽  
Acoustic Streaming ◽  
Maximal Velocity ◽  
Liquid Viscosity ◽  
Viscous Boundary Layer ◽  
Acoustic Frequency ◽  
Streaming Velocity ◽  
Viscous Boundary ◽  
Streaming Flow

Acoustic streaming can be generated around sharp structures, even when the acoustic wavelength is much larger than the vessel size. This sharp-edge streaming can be relatively intense, owing to the strongly focused inertial effect experienced by the acoustic flow near the tip. We conducted experiments with particle image velocimetry to quantify this streaming flow through the influence of liquid viscosity ν , from 1 mm 2 /s to 30 mm 2 /s, and acoustic frequency f from 500 Hz to 3500 Hz. Both quantities supposedly influence the thickness of the viscous boundary layer δ = ν π f 1 / 2 . For all situations, the streaming flow appears as a main central jet from the tip, generating two lateral vortices beside the tip and outside the boundary layer. As a characteristic streaming velocity, the maximal velocity is located at a distance of δ from the tip, and it increases as the square of the acoustic velocity. We then provide empirical scaling laws to quantify the influence of ν and f on the streaming velocity. Globally, the streaming velocity is dramatically weakened by a higher viscosity, whereas the flow pattern and the disturbance distance remain similar regardless of viscosity. Besides viscosity, the frequency also strongly influences the maximal streaming velocity.

Fluid Flow Around a Vibrating Beam and Associated Nonlinear Damping

2000 ◽  
Author(s):  
G. Chakraborty ◽  
C. D. Mote
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Transverse Velocity ◽  
Nonlinear Damping ◽  
Navier Stokes ◽  
Vibration Velocity ◽  
Viscous Boundary Layer ◽  
Navier Stokes Equation ◽  
Velocity Amplitude

Abstract Steady flow of a viscous fluid around a transversely oscillating, simply-supported beam is driven by forces represented in the nonlinear terms of the Navier-Stokes’ equation. This flow occurs inside and outside the viscous boundary layer. The flow-velocity amplitude is proportional to the square of the amplitude of the beam transverse velocity and thus it is essentially only observable during high velocity beam vibration. This flow, known as ‘edge streaming’, does not occur in an ideal fluid. In the flow the fluid is ‘drawn in’ at the edges of the beam near the vibrational antinodal points and ‘expelled’ at the nodal points. When a rigid plate is placed parallel to the long axis of the vibrating beam and normal to the vibration velocity, vortices of different orientation are generated depending on the separation of the plate and beam surfaces. When the separation is an order of magnitude greater than the boundary layer thickness, the vortices have the rolling characteristic discussed by Rayleigh [1]. But for small separation of the order of the boundary layer thickness, the vortical axes are perpendicular to that of the former, parallel to the vibration velocity. They have been experimentally observed [6]. Owing to the streaming motion, damping, as measured by the ratio of the dissipation of energy and the total vibration energy over a time period, has a nonlinear hard representation with respect to the vibration amplitude.

Two-dimensional global low-frequency oscillations in a separating boundary-layer flow

2008 ◽  
Vol 614 ◽  
pp. 315-327 ◽  
Author(s):  
UWE EHRENSTEIN ◽  
FRANÇOIS GALLAIRE
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Perturbation Analysis ◽  
Boundary Layer Flow ◽  
Stokes Equations ◽  
Low Frequency ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Optimal Perturbation ◽  
Layer Flow

A separated boundary-layer flow at the rear of a bump is considered. Two-dimensional equilibrium stationary states of the Navier–Stokes equations are determined using a nonlinear continuation procedure varying the bump height as well as the Reynolds number. A global instability analysis of the steady states is performed by computing two-dimensional temporal modes. The onset of instability is shown to be characterized by a family of modes with localized structures around the reattachment point becoming almost simultaneously unstable. The optimal perturbation analysis, by projecting the initial disturbance on the set of temporal eigenmodes, reveals that the non-normal modes are able to describe localized initial perturbations associated with the large transient energy growth. At larger time a global low-frequency oscillation is found, accompanied by a periodic regeneration of the flow perturbation inside the bubble, as the consequence of non-normal cancellation of modes. The initial condition provided by the optimal perturbation analysis is applied to Navier–Stokes time integration and is shown to trigger the nonlinear ‘flapping’ typical of separation bubbles. It is possible to follow the stationary equilibrium state on increasing the Reynolds number far beyond instability, ruling out for the present flow case the hypothesis of some authors that topological flow changes are responsible for the ‘flapping’.

Simulation of Acoustic Streaming in a Resonator

2004 ◽  
Author(s):  
Bakhtier Farouk ◽  
Murat K. Aktas
Keyword(s):  
Flow Field ◽  
Standing Wave ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Acoustic Streaming ◽  
Flow Patterns ◽  
Vortical Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Streaming Flow

Formation of vortical flow structures in a rectangular enclosure due to acoustic streaming is investigated numerically. The oscillatory flow field in the enclosure is created by the vibration of a vertical side wall of the enclosure. The frequency of the wall vibration is chosen such that a standing wave forms in the enclosure. The interaction of this standing wave with the horizontal solid walls leads to the production of Rayleigh type acoustic streaming flow patterns in the enclosure. All four walls of the enclosure considered are thermally insulated. The fully compressible form of the Navier-Stokes equations is considered and an explicit time-marching algorithm is used to explicitly track the acoustic waves. Numerical solutions are obtained by employing a highly accurate flux corrected transport (FCT) algorithm for the convection terms. A time-splitting technique is used to couple the viscous and diffusion terms of the full Navier-Stokes equations. Non-uniform grid structure is employed in the computations. The simulation of the primary oscillatory flow and the secondary (steady) streaming flows in the enclosure is performed. Streaming flow patterns are obtained by time averaging the primary oscillatory flow velocity distributions. The effect of the amount of wall displacement on the formation of the oscillatory flow field and the streaming structures are studied. Computations indicate that the nonlinearity of the acoustic field increases with increasing amount of the vibration amplitude. The form and the strength of the secondary flow associated with the oscillatory flow field and viscous effects are found to be strongly correlated to the maximum displacement of the vibrating wall. Total number of acoustic streaming cells per wavelength is also determined by the strength and the level of the nonlinearity of the sound field in the resonator.

Acoustic streaming about a cylinder in orthogonal beams

1992 ◽  
Vol 242 ◽  
pp. 387-394 ◽  
Author(s):  
N. Riley
Keyword(s):  
Boundary Layer ◽  
Acoustic Streaming ◽  
Sound Waves ◽  
Viscous Boundary Layer ◽  
Single Beam ◽  
Plane Sound ◽  
Orthogonal Beams ◽  
Viscous Boundary ◽  
The Waves ◽  
Potential Vortex

When orthogonal, plane sound waves of the same frequency, wavelength and amplitude, but with phase difference ½π, are incident upon a circular cylinder there is a time-independent streaming about the cylinder which is in the form of a potential vortex separated from the cylinder by a thin, viscous Stokes layer. As the amplitude of the waves in one of the beams decreases, an additional viscous boundary layer is involved until, when the amplitude is sufficiently small, this flow structure is destroyed as fluid erupts from the boundary layer. In the limit of a single beam it is known that this eruption results in opposing jets perpendicular to the wavefronts of the oncoming wave.

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