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Numerical analysis of dynamic acoustic resonance with deformed liquid surfaces: the acoustic fountain

Published online by Cambridge University Press:  22 December 2023

William Cailly ,
Jun Yin  and
Simon Kuhn Open the ORCID record for Simon Kuhn [Opens in a new window]
William Cailly
Affiliation:
KU Leuven, Department of Chemical Engineering, Celestijnenlaan 200F, 3001 Leuven, Belgium
Jun Yin
Affiliation:
KU Leuven, Department of Chemical Engineering, Celestijnenlaan 200F, 3001 Leuven, Belgium
Simon Kuhn*
Affiliation:
KU Leuven, Department of Chemical Engineering, Celestijnenlaan 200F, 3001 Leuven, Belgium
*
†Email address for correspondence: simon.kuhn@kuleuven.be
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Abstract

Applying a focused ultrasonic field on a free liquid surface results in its growth eventually leading to the so-called acoustic fountain. In this work, a numerical approach is presented to further increase the understanding of the acoustic fountain phenomenon. The developed simulation method enables the prediction of the free surface motion and the dynamic acoustic field in the moving liquid. The dynamic system is a balance between inertia, surface tension and the acoustic radiation force, and its nonlinearity is demonstrated by studying the relation between the ultrasonic excitation amplitude and corresponding liquid deformation. We show that dynamic resonance is the main mechanism causing the specific acoustic fountain shapes, and the analysis of the dynamic acoustic pressure allows us to predict Faraday-instability atomisation. We show that strong resonance peaks cause atomisation bursts and strong transient deformations corresponding to previously reported experimental observations. The quantitative prediction of the dynamic acoustic pressure enables us to assess the potential of cavitation generation in acoustic fountains. The observed local high acoustic pressures above both the cavitation and the atomisation threshold hint at the coexistence of these two phenomena in acoustic fountains.

JFM classification

Drops and Bubbles: Aerosols/atomization
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 977 , 25 December 2023 , A44
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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Supplementary material: File

Cailly et al. supplementary movie 1

Simulation of the Magnitude 1 case. Top: Shape of the moving liquid surface. The vertical velocity in the centre of the fountain is displayed and the colour scale characterizes the acoustic vibration with respect to the following thresholds: Light blue: below the Faraday threshold, Red: above the Faraday threshold and below the atomisation threshold, Orange: above the atomisation threshold. Bottom: Evolution of the maximum absolute pressure over time.
Download Cailly et al. supplementary movie 1(File)
File 3.5 MB
Supplementary material: File

Cailly et al. supplementary movie 2

Simulation of the Magnitude 2 case. Top: Shape of the moving liquid surface. The vertical velocity in the centre of the fountain is displayed and the colour scale characterizes the acoustic vibration with respect to the following thresholds: Light blue: below the Faraday threshold, Red: above the Faraday threshold and below the atomisation threshold, Orange: above the atomisation threshold. Bottom: Evolution of the maximum absolute pressure over time.
Download Cailly et al. supplementary movie 2(File)
File 3.3 MB
Supplementary material: File

Cailly et al. supplementary movie 3

Simulation of the Magnitude 3 case. Top: Shape of the moving liquid surface. The vertical velocity in the centre of the fountain is displayed and the colour scale characterizes the acoustic vibration with respect to the following thresholds: Light blue: below the Faraday threshold, Red: above the Faraday threshold and below the atomisation threshold, Orange: above the atomisation threshold. Bottom: Evolution of the maximum absolute pressure over time.
Download Cailly et al. supplementary movie 3(File)
File 3.1 MB
Supplementary material: File

Cailly et al. supplementary movie 4

Simulation of the Magnitude 4 case. Top: Shape of the moving liquid surface. The vertical velocity in the centre of the fountain is displayed and the colour scale characterizes the acoustic vibration with respect to the following thresholds: Light blue: below the Faraday threshold, Red: above the Faraday threshold and below the atomisation threshold, Orange: above the atomisation threshold. Bottom: Evolution of the maximum absolute pressure over time.
Download Cailly et al. supplementary movie 4(File)
File 3.8 MB
Supplementary material: File

Cailly et al. supplementary movie 5

Simulation of the Magnitude 5 case. Top: Shape of the moving liquid surface. The vertical velocity in the centre of the fountain is displayed and the colour scale characterizes the acoustic vibration with respect to the following thresholds: Light blue: below the Faraday threshold, Red: above the Faraday threshold and below the atomisation threshold, Orange: above the atomisation threshold. Bottom: Evolution of the maximum absolute pressure over time.
Download Cailly et al. supplementary movie 5(File)
File 3.3 MB
Supplementary material: File

Cailly et al. supplementary movie 6

Simulation of the Magnitude 6 case. Top: Shape of the moving liquid surface. The vertical velocity in the centre of the fountain is displayed and the colour scale characterizes the acoustic vibration with respect to the following thresholds: Light blue: below the Faraday threshold, Red: above the Faraday threshold and below the atomisation threshold, Orange: above the atomisation threshold. Bottom: Evolution of the maximum absolute pressure over time.
Download Cailly et al. supplementary movie 6(File)
File 3.8 MB
Supplementary material: File

Cailly et al. supplementary movie 7

Simulation of the Magnitude 7 case. Top: Shape of the moving liquid surface. The vertical velocity in the centre of the fountain is displayed and the colour scale characterizes the acoustic vibration with respect to the following thresholds: Light blue: below the Faraday threshold, Red: above the Faraday threshold and below the atomisation threshold, Orange: above the atomisation threshold. Bottom: Evolution of the maximum absolute pressure over time.
Download Cailly et al. supplementary movie 7(File)
File 3.3 MB
Supplementary material: File

Cailly et al. supplementary movie 8

Simulation of the Magnitude 8 case. Top: Shape of the moving liquid surface. The vertical velocity in the centre of the fountain is displayed and the colour scale characterizes the acoustic vibration with respect to the following thresholds: Light blue: below the Faraday threshold, Red: above the Faraday threshold and below the atomisation threshold, Orange: above the atomisation threshold. Bottom: Evolution of the maximum absolute pressure over time.
Download Cailly et al. supplementary movie 8(File)
File 6.5 MB
Supplementary material: File

Cailly et al. supplementary movie 9

Simulation of the Magnitude 9 case. Top: Shape of the moving liquid surface. The vertical velocity in the centre of the fountain is displayed and the colour scale characterizes the acoustic vibration with respect to the following thresholds: Light blue: below the Faraday threshold, Red: above the Faraday threshold and below the atomisation threshold, Orange: above the atomisation threshold. Bottom: Evolution of the maximum absolute pressure over time.
Download Cailly et al. supplementary movie 9(File)
File 5.1 MB
Supplementary material: File

Cailly et al. supplementary movie 10

Simulation of the Magnitude 10 case. Top: Shape of the moving liquid surface. The vertical velocity in the centre of the fountain is displayed and the colour scale characterizes the acoustic vibration with respect to the following thresholds: Light blue: below the Faraday threshold, Red: above the Faraday threshold and below the atomisation threshold, Orange: above the atomisation threshold. Bottom: Evolution of the maximum absolute pressure over time.
Download Cailly et al. supplementary movie 10(File)
File 2.5 MB
Supplementary material: File

Cailly et al. supplementary movie 11

Simulation of the Magnitude 11 case. Top: Shape of the moving liquid surface. The vertical velocity in the centre of the fountain is displayed and the colour scale characterizes the acoustic vibration with respect to the following thresholds: Light blue: below the Faraday threshold, Red: above the Faraday threshold and below the atomisation threshold, Orange: above the atomisation threshold. Bottom: Evolution of the maximum absolute pressure over time.
Download Cailly et al. supplementary movie 11(File)
File 7 MB
Supplementary material: File

Cailly et al. supplementary movie 12

Simulation of the Magnitude 12 case. Top: Shape of the moving liquid surface. The vertical velocity in the centre of the fountain is displayed and the colour scale characterizes the acoustic vibration with respect to the following thresholds: Light blue: below the Faraday threshold, Red: above the Faraday threshold and below the atomisation threshold, Orange: above the atomisation threshold. Bottom: Evolution of the maximum absolute pressure over time.
Download Cailly et al. supplementary movie 12(File)
File 2 MB
Supplementary material: File

Cailly et al. supplementary movie 13

Simulation of the Magnitude 13 case. Top: Shape of the moving liquid surface. The vertical velocity in the centre of the fountain is displayed and the colour scale characterizes the acoustic vibration with respect to the following thresholds: Light blue: below the Faraday threshold, Red: above the Faraday threshold and below the atomisation threshold, Orange: above the atomisation threshold. Bottom: Evolution of the maximum absolute pressure over time.
Download Cailly et al. supplementary movie 13(File)
File 3.9 MB