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Interactions of a short-pulsed plane acoustic wave with complex rigid objects: a numerical study

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Abstract

In this paper, we numerically study interactions of a short-pulsed plane acoustic wave with complex rigid objects by solving the linearized Euler equations. For the study, our numerical approach implements an immersed boundary method to satisfy the no-penetration condition on the surface of rigid objects, together with a fully-explicit staggered-grid finite-difference time-domain method having perfectly matched layers. First, we validate our approach for acoustic wave scattering by a circular cylinder, a well-known benchmark problem. Subsequently, we extend our simulations to two representative problems, namely interactions with a circular cylinder and a plano-concave lens which are of paramount interest in terms of acoustic force and acoustic focusing, respectively. Our simulations allow us to better understand the main mechanism of propagation, reflection, and scattering of acoustic waves as a result of interaction with rigid objects. In addition, the effects of pulse width on the interactions are closely investigated.

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Abbreviations

D :

Diameter of cylinder

f = f n n :

Momentum forcing

f :

Focal distance

h :

Uniform grid size (Eulerian)

i :

Imaginary unit

n :

Outward unit vector normal to the boundary

p :

Pressure field

R :

Radius of curvature of concave lens

t :

Time

U = (U x,U y,U z):

Velocity field (Lagrangian)

u = (u x, u y, u z):

Velocity field (Eulerian)

U (d) :

Desired velocity (Lagrangian)

u (d) :

Desired velocity (Eulerian)

u* :

Intermediate velocity field

X = (X,Y,Z):

Cartesian coordinate (Lagrangian)

x = (x,y,z):

Cartesian coordinate (Eulerian)

w p :

Full width at maximum half (FWHM)

Δx, Δy :

Grid sizes

Δt :

Time step size

δ h (x):

Dirac delta function

δ p :

Finite thickness of perfectly matched layer

ɷ η :

Attenuation factor

n (superscript):

Time step

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Acknowledgments

This research has been supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2020R1I1A 3070105).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Dong-A University, Busan, 49315, Korea

    Sangmo Kang

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  1. Sangmo Kang
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Correspondence to Sangmo Kang.

Additional information

Sangmo Kang received his B.S. and M.S. degrees from Seoul National University, Seoul, Republic of Korea in 1981 and 1987, respectively, and then worked for five years in Daewoo Heavy Industries, Incheon, Republic of Korea as a field engineer. He obtained his Ph.D. in Mechanical Engineering from the University of Michigan, Ann Arbor, USA in 1996. Dr. Kang is currently a Professor in the Department of Mechanical Engineering at Dong-A University, Busan, Republic of Korea. His research interests are in the area of micro and nanofluidics, turbulent flow and photoacoustics combined with the computational fluid dynamics.

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Kang, S. Interactions of a short-pulsed plane acoustic wave with complex rigid objects: a numerical study. J Mech Sci Technol 35, 4011–4022 (2021). https://doi.org/10.1007/s12206-021-0814-7

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  • DOI: https://doi.org/10.1007/s12206-021-0814-7

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