A technique for estimating an acoustic field in a resonance tube is suggested. The estimation of an acoustic field in a resonance tube is important for the development of the thermoacoustic engine, and can be conducted employing two sensors to measure pressure. While this measurement technique is known as the two-sensor method, care needs to be taken with the location of pressure sensors when conducting pressure measurements. In the present study, particle image velocimetry (PIV) is employed instead of a pressure measurement by a sensor, and two-dimensional velocity vector images are extracted as sequential data from only a one- time recording made by a video camera of PIV. The spatial velocity amplitude is obtained from those images, and a pressure distribution is calculated from velocity amplitudes at two points by extending the equations derived for the two-sensor method. By means of this method, problems relating to the locations and calibrations of multiple pressure sensors are avoided. Furthermore, to verify the accuracy of the present method, the experiments are conducted employing the conventional two-sensor method and laser Doppler velocimetry (LDV). Then, results by the proposed method are compared with those obtained with the two-sensor method and LDV.
References
1.
S. N.
Backhaus
and G. W.
Swift
, “A thermoacoustic Stirling heat engine
,” Nature
399
, 335
–338
(1999
).2.
G. R.
Kirchhoff
, “Über den Einfluss der Wärmeleitung in einem Gase auf die Schallbewegung (“On the influence of heat conduction in a gas on sound propagation”)
,” Ann. Phys.
210
(6), 177
–193
(1868
).3.
4.
C.
Zwikker
and C. W.
Kosten
, Sound Absorbing Materials
(Elsevier
, Amsterdam
, 1949
), pp. 25
–52
.5.
D. E.
Weston
, “The theory of the propagation of plane sound waves in tubes
,” Proc. Phys. Soc. London
B. 66
, 695
–709
(1953
).6.
A. S.
Iberall
, “Attenuation of oscillatory pressures in instrument lines
,” J. Res. Nat. Bur. Stand.
45
, 85
–108
(1950
).7.
N.
Rott
, “Damped and thermally driven acoustic oscillations in wide and narrow tubes
,” Z. Angew. Math. Phys. (J. Appl. Math. Phys.)
20
(2
), 230
–243
(1969
).8.
H.
Tijdeman
, “On the propagation of sound waves in cylindrical tubes
,” J. Sound Vib.
39
, 1
–33
(1975
).9.
A. M.
Fusco
, W. C.
Ward
, and G. W.
Swift
, “Two-sensor power measurements in lossy ducts
,” J. Acoust. Soc. Am.
91
(4
), 2229
–2235
(1992
).10.
T.
Biwa
, Y.
Ueda
, H.
Nomura
, U.
Mizutani
, and T.
Yazaki
, “Measurement of the Q value of an acoustic resonator
,”Phys. Rev. E
72
, 026601
(2005
).11.
M.
Miwa
, T.
Sumi
, T.
Biwa
, Y.
Ueda
, and T.
Yazaki
, “Measurement of acoustic output power in a traveling wave engine
,” Ultrasonics
44
, e1527
–e1529
(2006
).12.
T.
Biwa
, Y.
Tashiro
, H.
Nomura
, Y.
Ueda
, and T.
Yazaki
, “Acoustic intensity measurement in a narrow duct by a two-sensor method
,” Rev. Sci. Instrum.
78
, 086110
(2007
).13.
T.
Biwa
, Y.
Tashiro
, H.
Nomura
, Y.
Ueda
, and T.
Yazaki
, “Experimental verification of a two-sensor acoustic intensity measurement in lossy ducts
,” J. Acoust. Soc. Am.
124
(3
), 1584
–1590
(2008
).14.
T.
Biwa
, R.
Komatsu
, and T.
Yazaki
, “Acoustical power amplification an damping by temperature gradients
,” J. Acoust. Soc. Am.
129
(1
), 132
–137
(2011
).15.
J. C.
Valiere
, P.
Herzog
, V.
Valeau
, and G.
Tournois
, “Acoustic velocity measurements in the air by means of laser Doppler velocimetry: Dynamic and frequency range limitations and signal processing improvements
,” J. Sound Vib.
229
, 607
–626
(2000
).16.
H.
Bailliet
, P.
Lotton
, M.
Bruneau
, V.
Gusev
, J. C.
Valiere
, and B.
Gazengel
, “Acoustic power flow measurement in a thermoacoustic resonator by means of laser Doppler anemometry (L.D.A.) and microphonic measurement
,” Appl. Acoust.
60
, 1
–11
(2000
).17.
Y.
Ueda
, T.
Biwa
, and U.
Mizutani
, “Experimental studies of a thermoacoustic Stirling prime mover and its application to a cooler
,” J. Acoust. Soc. Am.
115
(3
), 1134
–1141
(2004
).18.
T.
Iwase
, T.
Biwa
, and T.
Yazaki
, “Acoustic impedance measurements of pulse tube refrigerators
,” J. App. Phys.
107
, 034903
(2010
).19.
C.
Desjouy
, G.
Penelet
, P.
Lotton
, and J.
Blondeau
, “Measurement of acoustic streaming in a closed-loop traveling wave resonator using lase Doppler velocimetry
,” J. Acoust. Soc. Am.
126
(5
), 2176
–2183
(2009
).20.
S.
Moreau
, H.
Bailliet
, and J. C.
Valiere
, “Effect of a stack on Rayleigh streaming cells investigated by laser Doppler velocimetry for application to thermoacoustic devices (L)
,” J. Acoust. Soc. Am.
125
(6
), 3514
–3517
(2009
).21.
T.
Biwa
and T.
Yazaki
, “Observation of energy cascade creating periodic shock waves in a resonator (L)
,” J. Acoust. Soc. Am.
127
(3
), 1189
–1192
(2009
).22.
X.
Mao
, Z.
Yu
, A. J.
Jaworski
, and D.
Marx
, “PIV studies of coherent structures generated at the end of a stack of parallel plates in a standing wave acoustic field
,” Exp. Fluids
45
, 833
–846
(2008
).23.
A.
Berson
, M.
Michard
, and P.
Blanc-Benon
, “Measurement of acoustic velocity in the stack of a thermoacoustic refrigerator using particle image velocimetry
,” Heat Mass Transfer
44
, 1015
–1023
(2008
).24.
A. J.
Jaworski
, X.
Mao
, and Z.
Yu
, “Entrance effects in the channels of the parallel plate stack in oscillatory flow conditions
,” Exp. Therm. Fluid Sci.
33
, 495
–502
(2009
).25.
L.
Shi
, Z.
Yu
, and A. J.
Jaworski
, “Vortex shedding flow patterns and their transitions in oscillatory flows past parallel-plate thermoacoustic stacks
,” Exp. Therm. Fluid Sci.
34
, 954
–965
(2010
).26.
L.
Shi
, Z.
Yu
, and A. J.
Jaworski
, “Application of laser-based instrumentation for measurement of time-resolved temperature and velocity fields in the thermoacoustic system
,” Int. J. Therm. Sci.
49
, 1688
–1701
(2010
).27.
L.
Shi
, X.
Mao
, and A. J.
Jaworski
, “Application of planar laser-induced fluorescence measurement techniques to study the heat transfer characteristics of parallel-plate heat exchangers in thermoacoustic devices
,” Meas. Sci. Technol.
21
, 115405
(2010
).28.
L.
Shi
, Z.
Yu
, and A. J.
Jaworski
, “Investigation into the Strouhal numbers associated with vortex shedding from parallel-plate thermoacoustic stacks in oscillatory flow conditions
,” Eur. J. Mech. B
30
, 206
–217
(2011
).29.
A. J.
Jaworski
and A.
Piccolo
, “Heat transfer processes in parallel-plate heat exchangers of thermoacoustic devices—Numerical and experimental approaches
,” Appl. Therm. Eng.
42
, 145
–153
(2012
).30.
Z.
Yu
, X.
Mao
, and A. J.
Jaworski
, “Experimental study of heat transfer in oscillatory gas flow inside a parallel-plate channel with imposed axial temperature gradient
,” Int. J. Heat Mass Transfer
77
, 1023
–1032
(2014
).31.
I.
Reyt
, Y.
Rafat
, L.
Mongeau
, R.
Taher
, and H.
Bailliet
, “PIV measurements of 3- dimensional acoustic Rayleigh streaming in a square-section standing wave resonator
,” in Proceedings of the Acoustics 2012 Nantes Conference
(2012
), pp. 1109
–1114
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