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Uniformly valid solution for acoustic propagation in weakly tapered circular waveguides: liquid jet example
Joel B Lonzaga1, David B Thiessen, Philip L Marston
1Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164-2814, USA.
The Journal of the Acoustical Society of America
|July 24, 2008
Summary
This study explores ultrasound propagation in liquid jets, finding wave amplitude is enhanced near the mode cutoff. This research aids in liquid drop production and ultrasound coupling applications.
Area of Science:
- Acoustics
- Fluid Dynamics
- Wave Propagation
Background:
- Ultrasound propagation in liquid jets has applications in drop production and energy transfer.
- Liquid jets in normal gravity taper as they accelerate, affecting acoustic wave behavior.
Purpose of the Study:
- To derive a uniformly valid solution for acoustic propagation in weakly tapered liquid jets.
- To analyze the effect of jet tapering on ultrasonic wave amplitude.
Main Methods:
- Utilized Langer's transformation and the method of multiple scales for a uniformly valid asymptotic solution.
- Employed a solvability condition to determine the leading-order correction due to waveguide taper.
- Validated the asymptotic solution with finite-element numerical calculations.
Main Results:
- Developed an asymptotic solution for acoustic propagation in a tapered liquid jet waveguide.
- The ultrasonic wave amplitude is significantly enhanced in the region near the cutoff of the excited mode.
- Neglected energy losses from air transmission and thermal viscous absorption in the model.
Conclusions:
- The derived solution accurately describes ultrasound propagation in tapered liquid jets.
- The enhancement of wave amplitude near cutoff is a key finding with practical implications.
- This work provides a theoretical framework for understanding acoustic phenomena in liquid jet systems.
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