Acoustic power generated by turbulent flow over a coaxial side branch (deep cavity) resonator mounted in a rectangular duct is calculated using a semiempirical approach. Instantaneous flow velocity is decomposed into an irrotational acoustic component and vorticity-bearing hydrodynamic field. The total velocity at several phases of the acoustic oscillation cycle is measured using digital particle image velocimetry. The acoustic velocity field is numerically calculated. The emphasis is on the effect of the accurate geometry representation for the acoustic field modeling on the calculated acoustic power. Despite the generally low levels of acoustic radiation from the coaxial side branches, when the main duct is incorporated into the model for calculation of the acoustic velocity, the acoustic velocity exhibits substantial horizontal (streamwise) components in the vicinity of the cavity corners. This streamwise acoustic velocity correlates with hydrodynamic horizontal velocity fluctuations, thus contributing to the calculated acoustic power. Spatial structure and strength of the acoustic source change as the distance between the side branches varies. Global quantitative imaging approach is used to characterize the transformation of the acoustic source structure in terms of patterns of instantaneous and phase-averaged flow velocity, vorticity, and streamline topology as well as time-averaged acoustic power.

1.
Chen
,
Y. N.
, and
Sturchler
,
R.
, 1977, “
Flow-Induced Vibrations and Noise in a Pipe System With Blind Branches Due to Coupling of Vortex Shedding
,”
Internoise 77
,
Zurich
.
2.
Baldwin
,
R. M.
, and
Simmons
,
H. R.
, 1986, “
Flow-Induced Vibration in Safety Relief Valves
,”
ASME J. Pressure Vessel Technol.
0094-9930,
108
(
3
), pp.
267
272
.
3.
,
S.
, and
Bühlmann
,
E. T.
, 1992, “
Self-Excited Resonances of Two Side-Branches in Close Proximity
,”
J. Fluids Struct.
0889-9746,
6
,
583
601
.
4.
Rockwell
,
D.
, and
Naudascher
,
E.
, 1978, “
Review of Self-Sustaining Oscillations of Flow Past Cavities
,”
ASME Trans. J. Fluids Eng.
0098-2202,
100
,
152
165
.
5.
Keller
,
J. J.
, and
Escudier
,
M. P.
, 1983, “
Flow-Excited Resonances in Covered Cavities
,”
J. Sound Vib.
0022-460X,
86
(
2
), pp.
199
226
.
6.
Hourigan
,
K.
,
Stokes
,
A. N.
, and
Welsh
,
M. C.
, 1986, “
Flow-Induced Acoustic Resonance for a Bluff Body in A Duct: A Numerical study
,”
Ninth Australian Fluid Mechanics Conference
,
Auckland
.
7.
Stoneman
,
S. A. T.
,
Hourigan
,
K.
,
Stokes
,
A. N.
, and
Welsh
,
M. C.
, 1988, “
Resonant Sound Caused by Flow Past Two Plates in Tandem in a Duct
,”
J. Fluid Mech.
0022-1120,
192
, pp.
455
484
.
8.
Howe
,
M. S.
, 1975, “
Contributions to the Theory of Aerodynamic Sound, With Applications to Excess Jet Noise and the Theory of the Flute
,”
J. Fluid Mech.
0022-1120,
71
, pp.
625
673
.
9.
Dequand
,
S.
,
Hulshoff
,
S. J.
, and
Hirschberg
,
A.
, 2003, “
Self-Sustained Oscillations in a Closed Side Branch System
,”
J. Sound Vib.
0022-460X,
263
, pp.
359
386
.
10.
Dequand
,
S.
,
Willems
,
J. F. H.
,
Leroux
,
M.
,
Vullings
,
R.
,
van Weert
,
M.
,
Thieulot
,
C.
, and
Hirschberg
,
A.
, 2003, “
Simplified models of Flue Instruments: Influence of Mouth Geometry on the Sound Source
,”
J. Acoust. Soc. Am.
0001-4966,
113
, pp.
1724
1735
.
11.
Amandolese
,
X.
,
Hemon
,
P.
, and
Regardin
,
C.
, 2004, “
An Experimental Study of the Acoustic Oscillations by Flows Over Cavities
,”
ASME J. Vibr. Acoust.
0739-3717,
126
, pp.
190
195
.
12.
Oshkai
,
P.
, and
Yan
,
T.
, 2006, “
Experimental Investigation of Coaxial Side Branch Resonators
,”
ASME Pressure Vessels and Piping Division Conference
, Vancouver.
13.
Arthurs
,
D.
,
,
S.
, and
Bravo
,
R.
, 2006, “
Flow Induced Acoustic Resonances of an Annular Duct with Co-Axial Side Branches
,”
ASME Pressure Vessels and Piping Division Conference
,
Vancoucer
,
.
14.
,
S.
, and
Shine
,
S.
, 1999, “
Strouhal Numbers of Fow-Excited Acoustic Resonance of Closed Sede Branches
,”
J. Fluids Struct.
0889-9746,
13
, pp.
127
142
.
15.
Kriesels
,
P. C.
,
Peters
,
M. C. A. M.
,
Hirschberg
,
A.
,
Wijnands
,
P. J.
,
Iafrati
,
A.
,
Riccardi
,
G.
,
Piva
,
R.
, and
Bruggeman
,
J. C.
, 1995, “
High-Amplitude Vortex-Induced Pulsations in a Gas Transport System
,”
J. Sound Vib.
0022-460X,
184
, pp.
343
368
.