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Finite Difference Study to Evaluate the Resonance Condition of the Standing Wave Acoustic Levitation System

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Abstract

Purpose

Acoustic levitation involves no physical contact with the specimen, hence widely used for the bio/chemical studies, fluid physics studies etc. Standing wave acoustic levitation system works on resonance phenomenon. So, to obtain the right air gap/distance between the driver and the reflector surfaces for the levitation system's resonance condition is significantly important. In this paper, the finite difference method is used to calculate the air gap for the resonance between the driver and reflector surfaces. Two different 2D axisymmetric geometries of the levitation system are considered for the study. Further, the air gap is also calculated using the 2D axisymmetric model with acoustic structure interaction in the COMSOL Multiphysics software. An experimental setup is also developed to validate the numerical results. The fourth resonance mode of the standing wave acoustic levitation system is considered for the comparison of the different models.

Methods

In this paper, the Finite difference method is used to determine the resonance condition of the standing wave acoustic levitation system, which has a driver at one end and the reflector at the other. The sound source/driver is considered at the bottom, and the reflector is considered at the top. The numerical model is developed for the two different axisymmetric geometries. Then, MATLAB is used to solve these numerical models. But, other free software like OCTAVE can also be used to get the economic solution. The convergence study is performed to find out the optimum element size for geometry mesh. The finite difference results are also compared with the simulation software COMSOL Multiphysics results. Further, the experiment setup is also developed to get the experimental results which are compared with the Finite difference results.

Results

The excitation frequency of the driver is taken as 40 kHz. The resonance condition corresponding to the fourth resonance mode (for both the cases) is calculated. For both the finite difference model cases, the air gap corresponding to the fourth resonance mode is computed as 19.71 mm and 19.40 mm, respectively. Using 2D axisymmetric model of COMSOL Multiphysics, the value of the air gap between the driver surface and the reflector surface is calculated as 19.29 mm. The pressure profiles of the standing wave acoustic levitation system are also obtained and plotted using Finite difference method as well as the COMSOL Multiphysics. Further, the air gap corresponding to the fourth resonance mode is also calculated experimentally as 19.28 mm. The experimental setup of the standing wave acoustic levitation system at fourth resonance mode with three small polystyrene balls levitating freely at the pressure nodes are also shown. The small polystyrene balls are of average diameter 3 mm and the average weight of 0.15 mg.

Conclusions

In this study, the resonance condition of the standing wave acoustic levitation system is studied. The finite difference method, COMSOL Multiphysics, as well as the experimental method, are used for the study. The results (the value of the air gap between the driver and the reflector surfaces) corresponding to the fourth resonance mode are calculated and compared. Two different cases (each case has a different standing wave acoustic levitation system geometry) are solved using the finite difference method. In current study, the acoustic structure interaction was not considered. In future studies, the acoustic structure interaction can be included. This will make the numerical model closer to the actual experimental setup and will give the more accurate estimation of the resonance condition of the standing wave acoustic levitation system.

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Data availability

Data sets generated during the current study are available from the corresponding author on reasonable request.

Abbreviations

\(c\) :

Speed of sound

\(k\) :

Wave number

\(p\) :

Sound pressure amplitude

\(\Delta h_{x}\) :

Step size in x direction

\(\Delta h_{z}\) :

Step size in z direction

λ:

Wavelength corresponding to the 40 kHz

\(\omega\) :

Angular frequency

i :

Discretization index in x direction

k :

Discretization index in z direction

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Authors and Affiliations

  1. Acoustic and Vibration Laboratory, School of Engineering, Indian Institute of Technology Mandi, Mandi, India

    Saurabh Yadav & Arpan Gupta

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  1. Saurabh Yadav
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  2. Arpan Gupta
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Yadav, S., Gupta, A. Finite Difference Study to Evaluate the Resonance Condition of the Standing Wave Acoustic Levitation System. J. Vib. Eng. Technol. 12, 1923–1929 (2024). https://doi.org/10.1007/s42417-023-00953-1

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