This work develops a theoretical framework for acoustic cloak scattering analysis in a low speed non-stationary fluid that is simply described as a potential flow. The equivalent sound source induced by the moving fluid local to the cloak is analytically constructed and is then estimated using Born approximation. The far-field scattering can thereafter be obtained using the associated Green's function of the convected wave equation. The results demonstrate that the proposed analytical approach, which might be helpful in the design and evaluation of cloaking systems, effectively elucidates key characteristics of the relevant physics. In addition, it can be seen that, in a moving fluid, the so-called convected cloaking design achieves better cloaking performance than the classical cloaking design.
REFERENCES
1.
C. L.
Scandrett
and A. M.
Vieira
, “Fluid-structure effects of cloaking a submerged spherical shell
,” J. Acoust. Soc. Am.
134
, 1908
–1919
(2013
).2.
S.
Zhang
, C.
Xia
, and N.
Fang
, “Broadband acoustic cloak for ultrasound waves
,” Phys. Rev. Lett.
106
, 024301
(2011
).3.
S. A.
Cummer
, B.-I.
Popa
, D.
Schurig
, D. R.
Smith
, J.
Pendry
, M.
Rahm
, and A.
Starr
, “Scattering theory derivation of a 3D acoustic cloaking shell
,” Phys. Rev. Lett.
100
, 024301
(2008
).4.
M.
Farhat
, S.
Enoch
, S.
Guenneau
, and A. B.
Movchan
, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid
,” Phys. Rev. Lett.
101
, 134501
(2008
).5.
B.-I.
Popa
, L.
Zigoneanu
, and S. A.
Cummer
, “Experimental acoustic ground cloak in air
,” Phys. Rev. Lett.
106
, 253901
(2011
).6.
H.
Chen
and C. T.
Chan
, “Acoustic cloaking in three dimensions using acoustic metamaterials
,” Appl. Phys. Lett.
91
, 183518
(2007
).7.
S. A.
Cummer
and D.
Schurig
, “One path to acoustic cloaking
,” New J. Phys.
9
, 1
–8
(2007
).8.
A. N.
Norris
, “Acoustic cloaking theory
,” Proc. R. Soc. A
464
, 2411
–2434
(2008
).9.
X.
Huang
, L.
Bai
, I.
Vinogradov
, and E.
Peers
, “Adaptive beamforming for array signal processing in aeroacoustic measurements
,” J. Acoust. Soc. Am.
131
, 2152
–2161
(2012
).10.
C.
Garcia-Meca
, S.
Carloni
, C.
Barcelo
, G.
Jannes
, J.
Sanchez-Dehesa
, and A.
Martnez
, “Analogue transformations in physics and their application to acoustics
,” Sci. Rep.
3
, 1
–5
(2009
).11.
P. Y.
Chen
and A.
Alu
, “Atomically thin surface cloak using graphene monolayers
,” ACS Nano
5
, 5855
–5863
(2011
).12.
C.
Bogey
, C.
Bailly
, and D.
Juvé
, “Computation of flow noise using source terms in linearized Euler's equations
,” AIAA J.
40
, 235
–243
(2002
).13.
X.
Huang
, X. X.
Chen
, Z. K.
Ma
, and X.
Zhang
, “Efficient computation of spinning modal Radiation through an engine bypass duct
,” AIAA J.
46
, 1413
–1423
(2008
).14.
X.
Huang
and X.
Zhang
, “A Fourier pseudospectral method for some computational aeroacoustics problems
,” Int. J. Aeroacoust.
5
, 279
–294
(2006
).15.
E.
Peers
and X.
Huang
, “High-order schemes for predicting computational aeroacoustic propagation with adaptive mesh refinement
,” Acta Mech. Sin.
29
, 1
–11
(2013
).16.
M. J.
Lighthill
, “On sound generated aerodynamically, 1. general theory
,” Proc. R. Soc. London
A221
, 564
–587
(1952
).17.
M. J.
Lighthill
, “On sound generated aerodynamically, 2. turbulence as a source of sound
,” Proc. R. Soc. London
A222
, 1
–32
(1954
).18.
L.
Gizon
, S. M.
Hanasoge
, and A. C.
Birch
, “Scattering of acoustic waves by a magnetic cylinder: Accuracy of the Born approximation
,” Astrophys. J.
643
, 549
–555
(2006
).19.
S. A.
Stotts
and R. A.
Koch
, “Rough surface scattering in a Born approximation from a two-way coupled-mode formalism
,” J. Acoust. Soc. Am.
125
, EL242
–EL248
(2009
).20.
R. D.
Sandberg
, L. E.
Jones
, N. D.
Sandham
, and P. F.
Joseph
, “Direct numerical simulations of tonal noise generated by laminar flow past airfoils
,” J. Sound Vib.
320
, 838
–858
(2009
).21.
Y.
Chao
, Z. F.
Zhou
, and M.
Zhuang
, “Acoustic intensity-based method for sound radiations in a uniform flow
,” J. Acoust. Soc. Am.
126
, 2198
–2205
(2009
).22.
S. K.
Richards
, X.
Zhang
, X. X.
Chen
, and P. A.
Nelson
, “Evaluation of non-reflecting boundary conditions for duct acoustic computation
,” J. Sound Vib.
270
, 539
–557
(2004
).23.
A. D.
Pierce
, “Wave equation for sound in fluids with unsteady inhomogeneous flow
,” J. Acoust. Soc. Am.
87
, 2292
–2299
(1990
).24.
R.
Ewert
and W.
Schröder
, “Acoustic perturbation equations based on flow decomposition via source filtering
,” J. Comp. Phys.
188
, 365
–398
(2003
).25.
A.
Agarwal
, P. J.
Morris
, and R.
Mani
, “Calculation of sound propagation in nonuniform flows: Suppression of instability waves
,” AIAA J.
42
, 80
–88
(2004
).26.
F. Q.
Hu
, M. Y.
Hussaini
, and J.
Manthey
, “Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics
,” J. Comp. Phys.
124
, 177
–191
(1996
).© 2014 Acoustical Society of America.
2014
Acoustical Society of America
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