The flow field induced by an oscillating sphere

doi:10.1016/0022-460X(65)90112-4

Journal of Sound and Vibration

Volume 2, Issue 3, July 1965, Pages 257-269

https://doi.org/10.1016/0022-460X(65)90112-4 Get rights and content

Abstract

The method of inner and outer expansions is applied to the case of a sphere oscillating along a diameter with high Reynolds number and high Strouhal number. The entire velocity field is determined to the second order. It is found that the induced motion has a steady part, a harmonic part, and a subharmonic part. The secondary steady motion, or acoustic streaming, has a pair of toroidal cells in the boundary layer in addition to a steady streaming motion away along the axis in the outer flow field.

References (13)

P.J. Westervelt
The theory of steady rotational flow generated by a sound field
J. acoust. Soc. Amer
(1953)
W.L. Nyborg
Acoustic streaming due to attenuated plane waves
J. acoust. Soc. Amer. 25
(1953)
H. Schlichting
Berechnung ebener periodischer Grenzschichtströmungen
Physikalische Zeit
(1932)
J.M. Andres et al.
Acoustic streaming at high Reynolds numbers
J. acoust. Soc. Amer
(1953)
J.M. Andres et al.
Acoustic streaming at low Reynolds numbers
J. acoust. Soc. Amer
(1953)
J. Holtsmark et al.
Boundary layer flow near a cylindrical obstacle in an oscillating incompressible fluid
J. acoust. Soc. Amer
(1954)

There are more references available in the full text version of this article.

Cited by (43)

Convective heat exchange characteristics of acoustic-induced flows over a sphere: The role of acoustic streaming
2021, Applied Acoustics
Citation Excerpt :
Therefore, it is of great significance to explore the mechanism of heat and mass transfer enhanced by sound waves. Theoretical studies showed that when sound waves act on an object or the object makes self-excited vibration in a static fluid, two different flow field components can be formed around the object [5,6]: 1) a time-dependent oscillatory flows with period equal to the forcing period; 2) a stable acoustic streaming component independent of time. This indicates that the effect of sound wave on the heat and mass transfer rate depends on the two different flow field characteristics.
To clarify the mechanism of the enhancement of heat transfer by sound wave. We have experimentally studied the convective heat transfer characteristics of heated copper spheres under sound waves with different frequencies and sound pressure levels. The experimental results showed that the existence of an acoustic field made strengthen the cooling process of the copper sphere to some extent, and the convective heat transfer coefficient increased nonlinearly with increasing sound pressure level. The contribution of the second-order nonlinear acoustic streaming generated by the interaction between sound waves and the heated copper sphere in the process of enhancing heat transfer was theoretically analyzed. Sound frequency determines the relative strength of acoustic streaming and oscillatory flow. When the sound frequency increases, the influence of the acoustic-induced flows on the heat transfer process of the copper sphere can be divided into four stages in turn: (1) acoustic streaming control stage, (2) acoustic streaming and oscillatory flow coordinated control stage, (3) oscillatory flow control stage, (4) stable stage. There is an optimal sound frequency to enhance heat transfer. Furthermore, the flow field characteristics of the acoustic streaming outside the sphere were numerically calculated. Calculations showed that low-frequency and high-intensity sound waves can form strong acoustic streaming motion outside the sphere. This proves that acoustic streaming in the low-frequency region is the predominant mechanism affecting heat and mass transfer.
Acoustic streaming outside spherical particles and parameter analysis of heat transfer enhancement
2021, European Journal of Mechanics, B/Fluids
Citation Excerpt :
Acoustic streaming is an important physical phenomenon in nonlinear acoustics [7]. When an oscillatory flow caused by sound waves encounters a solid or a solid that has self-excited oscillation in an otherwise at rest, two different flow field components can be formed around the solid [8,9]: (i) a harmonic component with period equal to the forcing period, or time-dependent free oscillating flows; (ii) a time-averaged second-order component with vortex characteristics, where the latter is generally referred to as the acoustic streaming. This shows that the effect of sound wave on heat and mass transfer rate depends on the above two different flow field characteristics.
Acoustic streaming effects can play an important role for promoting heat and mass transfer. Considering the viscous loss inside the viscous boundary layer on the particles surface, a numerical model for the acoustic streaming outside a two-dimensional spherical particle in a plane standing wave sound field is established, and the distribution characteristics of the acoustic streaming outside the particles are simulated by the numerical method of separation time scale. The reliability of the numerical simulation is verified by comparing the simulation results with the corresponding analytical solution. Based on this, we simulate the acoustic streaming distribution characteristics outside the particles under different Reynolds numbers and Strouhal numbers, and the acoustic parameters for heat transfer enhancement by acoustic streaming are analyzed. The numerical studies show that as the Strouhal or Reynolds numbers increase, the acoustic streaming region inside the boundary layer shrinks, but the shear force increases, and the vortex structure outside the particles increased from 4 to 8. when the particles are located in different positions of the plane standing wave sound field, the acoustic streaming has a rich flow pattern structure. The parameter analysis of the influence of acoustic streaming on convective heat transfer shows that the strong acoustic streaming motion formed by the acoustic waves with the small Strouhal number and large Reynolds number can greatly promote the heat and mass transfer process. For the small Strouhal number, the inner vortex in the viscous boundary layer is the main mechanism affecting the heat and mass transfer process. And increasing the Reynolds number is the most direct and effective means to strengthen the heat and mass transfer process The study helps to reveal the mechanism of acoustic to enhance the heat transfer of objects. In addition, the numerical method can be used to evaluate the external acoustic streaming characteristics of any physical model.
Pulsatile flow of power-law fluids over a sphere: Momentum and heat transfer characteristics
2020, Powder Technology
Citation Excerpt :
Much work has been reported on the study of transient equations of motion of a particle in a viscous fluid. Currently available results have been obtained using the boundary-layer approximations and perturbation theory [15,16], inner-outer field expansions [17], finite-difference and matched asymptotic expansions for the near and far velocity fields [18], spectral methods [19,20], series truncation method [21]. Poison [22] was the first to examine the potential sinusoidal flow past a rigid sphere.
The effect of pulsatile flow on the momentum and heat transfer characteristics for a sphere in power-law fluids is investigated numerically otherwise in the steady regime. Extensive results are presented in terms of streamlines, isotherms, pressure coefficient and local Nusselt number, drag coefficient and Nusselt number over the range of conditions as: Reynolds number (5 ≤ Re ≤ 120), Prandtl number (0.7 ≤ Pr ≤ 100), power-law index (0.3 ≤ n ≤ 1.5), frequency (π/4 ≤ ω* ≤ π) and amplitude of pulsations (0 ≤ A ≤ 0.8). The vortex grows during the deceleration phase of the pulsatile cycle and vice-versa. The pulsatile flow enhances heat transfer in shear-thinning fluids by 30% (at Re = 120, Pr = 100) over that of uniform flow conditions whereas the corresponding improvement is smaller than this value for shear-thickening fluids, i.e., n > 1. This is accompanied by a marginal increase in drag.
Gas absorption into a drop in the presence of an acoustic field
2005, International Journal of Multiphase Flow
The present work considers acoustically enhanced gas absorption into a liquid drop accompanied by a homogeneous first order chemical reaction.
The mass conservation equation was solved for the flow inside the drop induced by acoustic streaming both analytically and numerically. Two cases were considered: An analytical solution was presented for the case of high Peclet numbers, while the case of arbitrary Peclet numbers was solved numerically.
The high Peclet number case is applicable for high circulation rates and serves as an upper limit on the rate of mass transfer into the drop. It also provides a check for the numerical solution.
The results indicate that the effect of the acoustic field on mass transfer is especially beneficial for absorption processes without chemical reaction, or with reactions of moderate rates. The enhancement for these processes for Peclet numbers of 500–1000 was 3.3–3.5 as compared to absorption without an acoustic field. For processes with fast chemical reactions the benefits of using an acoustic field are limited, with enhancement factors in the range of 1.5–2.3.
Structure of the streaming flow generated by a sphere in a fluid undergoing rectilinear oscillation
2023, Journal of Fluid Mechanics
Re-entrant history force transition for stick-slip Janus swimmers: Mixed Basset and slip-induced memory effects
2020, Journal of Fluid Mechanics

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The flow field induced by an oscillating sphere

Abstract

The theory of steady rotational flow generated by a sound field

J. acoust. Soc. Amer

Acoustic streaming due to attenuated plane waves

J. acoust. Soc. Amer. 25

Berechnung ebener periodischer Grenzschichtströmungen

Physikalische Zeit

Acoustic streaming at high Reynolds numbers

J. acoust. Soc. Amer

Acoustic streaming at low Reynolds numbers

J. acoust. Soc. Amer

Boundary layer flow near a cylindrical obstacle in an oscillating incompressible fluid

J. acoust. Soc. Amer