[1] E. M. Flores, G. Cravotto, C. A. Bizzi, D. Santos, and G. D. Iop, “Ultrasound-assisted biomass valorization to industrial interesting products: state-of-the-art, perspectives and challenges,” Ultrasonics Sonochemistry, vol. 72, p. 105455, 2021.[3]Guida, P., Viciconte, G., Ceschin, A., Colleoni, E., Pérez, F. E. H., Saxena, S., ... & Roberts, W. L. (2022). Numerical model of an ultrasonically induced cavitation reactor and application to heavy oil processing. Chemical Engineering Journal Advances, 100362.[4]Z. Pan, A. Kiyama, Y. Tagawa, D. J. Daily, S. L. Thomson, R. Hurd, and T. T. Truscott, “Cavitation onset caused by acceleration,” Proceedings of the National Academy of Sciences of the United States of America, vol. 114, no. 32, pp. 8470–8474, 2017.[5]P Xu, S Liu, Z Zuo, Z Pan, “On the criteria of large cavitation bubbles in a tube during a transient process,” Journal of Fluid Mechanics, 913, 2021. [6] J. W. S. B. Rayleigh, The theory of sound. Macmillan & Company, 1896, vol. 2. [7]R. J. Urick, Principles of underwater sound, 3rd ed. New York: McGraw-Hill, 1983. [8] R. Esche, “Untersuchung der schwingungskavitation in flussigkeiten,” Acta Acustica united with Acustica, vol. 2, no. 6, pp. 208–218, 1952.[9]M. Strasberg, “Onset of ultrasonic cavitation in tap water,” The Journal of the Acoustical Society of America, vol. 31, no. 2, pp. 163–176, 1959.[10]F. G. Blake, “The onset of cavitation in liquids,” Tech. Memo., no. 12, 1949.[11]J.
Daily, J. Pendlebury, K. Langley, R. Hurd, S. Thomson, and T. Truscott, “Catastrophic cracking courtesy of quiescent cavitation,” Physics of Fluids, vol. 26, no. 9, p. 091107, 2014.[12]D. J. Daily, Fluid-structure interactions with flexible and rigid bodies. Brigham Young University, 2013.[13]T. Sauer, Numerical analysis. 2nd ed., Boston: Pearson, 2012. [14]C. E. Brennen, Cavitation and bubble dynamics. Cambridge University Press, jan 2013.z
Bi bliography
Conclusions and future developments
The present study investigates the cavitation onset induced by the propagation of acoustic waves in a liquid medium. This is crucial for the optimization of ultrasound-induced cavitation reactors widely used, nowadays, in many industrial processes [1, 3].
UNIFYING ACOUSTIC CAVITATION THROUGH THE FREQUENCY
Cavitation onset caused by acceleration, Pan et al. [4]
𝑡 = 𝑡0 𝑡 = 𝑡1
The classical velocity-based number, used to describe hydrodynamic cavitation, is not able to represent the cavitation in liquids that undergo an impulsive acceleration. For this reason, Pan et al. [4] have introduced a new cavitation number containing as a scaling factor the acceleration of the bottle. The experimental campaign conducted by the authors, varying the liquid medium and other parameters of the system, demonstrates that the cavitation number predicts with high accuracy the cavitation onset for the investigated dataset.
Cavitation does not occur
Traditionally, cavitation or vaporization of a liquid is predicted by the flow velocity and the liquid vapor pressure. Pan et al. showed that cavitation, in a liquid set into motion by an impulsive force (mallet-tube experiment), could be better predicted by the acceleration [4, 5].
The approach introduced by Pan et al. [4] was extended to the cavitation onset for an ultrasound device working at a nominal frequency of 24 kHz. An experimental setup based on the backlighting technique was adopted to capture the cavitation inception and to measure the displacement of the probe during its vibration.
A small portion of the domain, in correspondence with the axis of the probe, was framed using a high-speed camera (Photron Fastcam NOVA) and a zoom lens (10X magnification). The high-speed camera was triggered using the signal coming from a hydrophone placed in the liquid domain and passing through an oscilloscope.
Study of the cavitation induced by ultrasound waves
Tab. 1: Limit values found for the two different probes tested. The results are also visible in Fig. 9.
The acoustic pressure amplitude on the transducer surface can be estimated using the Rayleigh model [6]:
Fig. 1: Illustration of the mallet-tube experiment, performed by Pan et al. [4].
Fig. 2: Experimental observation made by Pan et al. [4].
Cavities are visible at the bottom of the acrylic tube.
Hydrodynamic Cavitation
Cavitation occurs
Cavitation onset caused by acceleration [4]
Experimental parameters:
• Nominal frequency: 24 kHz
• Medium: Deionized and purified water
• Camera frame rate: 200,000 fps
• Camera resolution: 128 x 224 pixels
• Prove diameter: 3 mm and 7mm
• Optical resolution: 1.98 μm/pixel
• Water temperature: 24 – 26 °C
• Dissolved oxygen: 58 -72 %
• Optical setup: 10X and Micro lens (105 mm)
Figure 3: Schematic illustration of the backlighting setup utilized for the visualization experiments. The dashed red line and the blue line indicate two different portions of the domain.
Fig. 4: Cavitation inception for the 3 mm probe at 70% of the nominal amplitude (transient state).
Fig. 5: Cavitation inception for the 7 mm probe at 70%
nominal amplitude (transient state).
Surface tracking procedure
𝑡0 5 μ𝑠 10 15
Fig. 8: Probe displacement as a function of time. The red line indicates the time at which cavitation happens.
The measurements have been performed during the transient regime of the probe vibration. The experiment was repeated five times for every combination of parameters (nominal amplitude of the ultrasound device and probe’s diameter). The cases related to the minimum and maximum value of the amplitude are reported in the table below.
Assumptions:
• Gravity and viscous effects are neglected.
• Non-linear (advection) term is neglected.
• No-slip boundary condition. Fig. 9: Urick [7] proposed a direct relation between the tensile strength of the liquid and the frequency. The chart is based on the experimental results obtained by several authors. Esche measured the cavitation threshold of water varying the frequency [8].
Strasberg [9], using a forcing frequency of 25 kHz, detected a tensile strength value ranging from 2.5 atm in tap water saturated with air to 6.5 atm in degassed water. For air-saturated and degassed water, Blake [10] measured values ranging from 3.5 atm to 4.6
Considerations :
atm.• The vapor pressure cannot be taken as a cavitation threshold for phenomena characterized by high frequencies.
• The ability to withstand negative pressure is a manifestation of the elasticity of the medium (metastable state) [14].
• The dependency on the frequency is influenced by the characteristic time of growth of a macroscopic bubble, starting from a nucleus.
Fig. 7: A sequence of high-speed images for a 3 mm probe. The movement of the ultrasound probe and the born of a cavity are visible.
For this ultrasound case, the cavitation number, introduced by Pan et al. [4], predicts the cavitation inception for a displacement amplitude equal to 0.31 μm.
Experimental Estimation of the acoustic pressure
Tensile stress:
Reinterpretation of the mallet-tube experiment (Pan et al. [16])
The acceleration curve over time is considered, instead of just the maximum value.
This allows us to take into account the characteristic frequencies of the phenomenon.
The mallet-tube problem can be described by assuming a similarity with the plane circular transducer (Rayleigh model [6]). The bottom of the mallet can be considered as the vibrating surface of the transducer and the no-slip condition can be enforced between the tube and the liquid medium.
Tab. 2: Data related to the experimental observations done at Utah State University and Brigham Young University (USU/BYU) [4, 11, 12].
Experimental parameters (USU/BYU experiments) [4, 11, 12]:
• Medium: Distilled water
• Tube material: acrylic
• Tube diameter: 55 mm
• Height: 12.5 – 17.5 mm
• Reference pressure: 86.9 kPa
Fig. 10: Trigonometric interpolation of the measured acceleration over time (Observation 3 in Tab.2).
1. Interpolation of the experimental data (Sauer [13]) 2. Velocity function by integration
Fig. 11: Trigonometric interpolation of the velocity function.
Since the wave equation is linear, it is possible to apply the superposition principle.
The trigonometric interpolation of the velocity can be used as a boundary condition for the solution of the acoustic pressure field (Rayleigh solution [6]).
Fig. 6: Vapor field generated by a probe having a diameter of 7 mm and a steady state amplitude of 49 μm.
New dimensionless number based on the frequency and tensile strength
A cavitation number is defined, including the frequency of the wave and the tensile strength of the medium.
Graphical interpretation of the cavitation number
• The vapor pressure of the liquid cannot be taken as a cavitation threshold in the context of propagation of acoustic wave at high frequency (metastable state).
• A new cavitation number, based on the frequency of the wave and the tensile strength, is proposed.
• The cavitation number is not dependent on the far field and on the reflection of the acoustic waves on the boundaries of the liquid domain.
• The modeling approach can represent the acoustic phenomena for a wide range of frequencies.
• The uncertainty region represented in the phase diagram has to be calibrated on a larger dataset.
• More experimental data are necessary to define the dependency of the tensile strength from the surface roughness of the probe (heterogeneous nucleation), the amount of dissolved air in the liquid, and the temperature.
• Apply the model to other liquid media in future experimental campaigns.
Unifying acoustic cavitation through the frequency byGianmaria Viciconteis licensed under a Creative Commons Attribution 4.0 International License.
To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/
This work is funded by King Abdullah University of Science and Technology through a Competitive Research Grant. This research is part of an academic and industrial project led by Professor William Roberts at the Clean Combustion Research Center of KAUST University. The experiments have been carried out at KAUST University, in the Splash Lab directed by Professor Tadd Truscott. Part of the equipment used for the experimental campaign has been provided by the High-Speed Fluids Imaging Laboratory, directed by Professor Sigurdur Thoroddsen.
The poster has been published on the KAUST repository: https://repository.kaust.edu.sa/
Fig. 13: Phase diagram for the cavitation onset. The values of the cavitation threshold related to the visualization experiment done with the ultrasound device are represented by the black markers.
The other markers are related to the application of the frequency-based cavitation number to the experiments done by USU/BYU groups and described by Pan et al. [4, 11, 12].
Acknowledgments
Fig. 12: Acoustic pressure on the axis, at the bottom of the mallet.
Ideal threshold:
Cavitation does not occur Cavitation occurs
3. Acoustic pressure field 4 . Tensile stress in the liquid medium
Gianmaria Viciconte
1, Paolo Guida
1, Tadd Truscott
2, & William L. Roberts
11
Clean Combustion Research Center, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
2
Splash Lab, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
Contacts: Gianmaria Viciconte (gianmaria.viciconte@kaust.edu.sa), https://orcid.org/0000-0002-1219-3263
Clean Combustion Research Center, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
The phase diagram [4] provides a graphical interpretation of the Cavitation number. For an engineering utilization of the cavitation number, the extension of the uncertainty region has to be established on a larger set of data.
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