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Damping and reflection coefficient measurements for an open pipe at low Mach and low Helmholtz numbers

Published online by Cambridge University Press:  26 April 2006

M. C. A. M. Peters ,
A. Hirschberg ,
A. J. Reijnen  and
A. P. J. Wijnands
M. C. A. M. Peters
Affiliation:
Faculty of Physics, W & S 1.46, Eindhoven University of Technology, Postbus 513, 5600 MB Eindhoven, The Netherlands
A. Hirschberg
Affiliation:
Faculty of Physics, W & S 1.46, Eindhoven University of Technology, Postbus 513, 5600 MB Eindhoven, The Netherlands
A. J. Reijnen
Affiliation:
Faculty of Physics, W & S 1.46, Eindhoven University of Technology, Postbus 513, 5600 MB Eindhoven, The Netherlands
A. P. J. Wijnands
Affiliation:
Faculty of Physics, W & S 1.46, Eindhoven University of Technology, Postbus 513, 5600 MB Eindhoven, The Netherlands
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Abstract

The propagation of plane acoustic waves in smooth pipes and their reflection at open pipe terminations have been studied experimentally. The accuracy of the measurements is determined by comparison of experimental data with results of linear theory for the propagation of acoustic waves in a pipe with a quiescent fluid. The damping and the reflection at an unflanged pipe termination are compared.

In the presence of a fully developed turbulent mean flow the measurements of the damping confirm the results of Ronneberger & Ahrens (1977). In the high-frequency limit the quasi-laminar theory of Ronneberger (1975) predicts accurately the convective effects on the damping of acoustic waves. For low frequencies a simple theory combining the rigid-plate model of Ronneberger & Ahrens (1977) with the theoretical approach of Howe (1984) yields a fair prediction of the influence of turbulence on the shear stress. The finite response time of the turbulence near the wall to the acoustic perturbations has to be taken into account in order to explain the experimental data. The model yields a quasi-stationary limit of the damping which does not take into account the fundamental difference between the viscous and thermal dissipation observed for low frequencies.

Measurements of the nonlinear behaviour of the reflection properties for unflanged pipe terminations with thin and thick walls in the absence of a mean flow confirm the theory of Disselhorst & van Wijngaarden (1980), for the low-frequency limit. It appears however that a two-dimensional theory such as proposed by Disselhorst & van Wijngaarden (1980) for the high-frequency limit underestimates the acoustical energy absorption by vortex shedding by a factor 2.5.

The measured influence of wall thickness on the reflection properties of an open pipe end confirms the linear theory of Ando (1969). In the presence of a mean flow the end correction δ of an unflanged pipe end varies from the value at the high-Strouhal-number limit of δ/a = 0.61, with a the pipe radius, which is close to the value in the absence of a mean flow given by Levine & Schwinger (1948) of δ/a = 0.6133, to a value of δ/a = 0.19 in the low-Strouhal-number limit which is close to the value predicted by Rienstra (1983) of δ/a = 0.26.

The pressure reflection coefficient is found to agree with the theoretical predictions by Munt (1977, 1990) and Cargill (1982b) in which a full Kutta condition is included. The accuracy of the theory is fascinating in view of the dramatic simplifications introduced in the theory. For a thick-walled pipe end and a pipe terminated by a horn the end correction behaviour is similar. It is surprising that the nonlinear behaviour at low frequencies and high acoustic amplitudes in the absence of mean flow does not influence the end correction significantly.

The aero-acoustic behaviour of the pipe end is dramatially influenced by the presence of a horn. In the presence of a mean flow the horn is a source of sound for a critical range of the Strouhal number.

The high accuracy of the experimental data suggests that acoustic measurements can be used for a systematic study of turbulence in unsteady flow and of unsteady flow separation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 256 , November 1993 , pp. 499 - 534
Copyright
© 1993 Cambridge University Press

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References

Abom, M. & Boden, H. 1988 Error analysis of two microphone measurements in ducts with flow. J. Acoust. Soc. Am. 83, 2429–2438.Google Scholar
Abrishaman, M. 1977 Effect of flow on the acoustic impedance of a duct exit. Noise and Fluid Engineering, Proc. Winter Annual Meeting AMSE, Atlanta, Georgia, pp. 171–177.
Alfredson, R. J. & Davies, P. O. A. L. 1970 The radiation of sound from an engine exhaust. J. Sound Vib. 13, 389–408.Google Scholar
Ando, Y. 1969 On the sound radiation from semi-infinite circular pipe of certain wall thickness. Acustica 22, 219–225.Google Scholar
Bechert, D. W. 1980 Sound absorption caused by vorticity shedding, demonstrated with a jet flow. J. Sound Vib. 70, 389–405.Google Scholar
Boden, H. & Abom, M. 1986 Influence of errors on the two-microphone method for measuring acoustic properties in ducts. J. Acoust. Soc. Am. 79, 541–549.Google Scholar
Cargill, A. M. 1982a Low-frequency sound radiation and generation due to the interaction of unsteady flow with a jet pipe. J. Fluid Mech. 121, 59–105.Google Scholar
Cargill, A. M. 1982b Low frequency acoustic radiation from a jet pipe – a second order theory. J. Sound Vib. 83, 339–354.Google Scholar
Cummings, A. 1984 Acoustic nonlinearities and power losses at orifices. AIAA J. 22, 786–792.Google Scholar
Cummings, A. & Eversman, W. 1983 High amplitude acoustic transmission through duct terminations: theory. J. Sound Vib. 91, 503–518.Google Scholar
Davies, P. O. A. L. 1987 Plane wave reflection at flow intakes. J. Sound Vib. 115, 560–564.Google Scholar
Davies, P. O. A. L. 1988 Practical flow duct acoustics. J. Sound Vib. 124, 91–115.Google Scholar
Davies, P. O. A. L., Bento Coelho, J. L. & Bhattacharya, M. 1980 Reflection coefficients for an unflanged pipe with flow. J. Sound Vib. 72, 543–546.Google Scholar
Disselhorst, J. H. M. & Wijngaarden, L. van 1980 Flow in the exit of open pipes during acoustic resonance. J. Fluid Mech. 99, 293–319.Google Scholar
Hirschberg, A., Bruggeman, J. C., Wijnands, A. P. J. & Morgenstern, M. 1988 The whistler nozzle and horn as aero-acoustic sound sources in pipe systems. Proc. Inst. Acoust. 10, 701–708.Google Scholar
Howe, M. S. 1979a Attenuation of sound in a low Mach number nozzle flow. J. Fluid Mech. 91, 209–229.Google Scholar
Howe, M. S. 1979b The interaction of sound with low Mach number wall turbulence, with application to sound propagation in turbulent pipe flow. J. Fluid Mech. 94, 729–744.Google Scholar
Howe, M. S. 1984 On the absorption of sound by turbulence and other hydrodynamic flows. IMA J. Appl. Maths 32, 187–209.Google Scholar
Ingard, U. & Ising, H. 1967 Acoustic nonlinearity of an orifice. J. Acoust. Soc. Am. 42, 6–17.Google Scholar
Ingard, U. & Singhal, V. K. 1974 Sound attenuation in turbulent pipe flow. J. Acoust. Soc. Am. 55, 535–538.Google Scholar
Ingard, U. & Singhal, V. K. 1975 Effect of mean flow on the acoustic resonance of an open-ended duct. J. Acoust. Soc. Am. 58, 788–793.Google Scholar
Kirchhoff, G. 1868 Uber den Einfluss der Wärmteleitung in einem Gase auf die Schallbewegung. Pogg. Ann. 134 (6), 177–193.Google Scholar
Levine, H. & Schwinger, J. 1948 On the radiation of sound from an unflanged circular pipe. Phys. Rev. 73, 383–406.Google Scholar
Louis, B. & Isabey, D. 1992 Interaction of oscillatory and constant turbulent flows in airway-like tubes during impedance measurement. J. Appl. Phys. (submitted.)Google Scholar
Mankbadi, R. R. & Liu, J. T. C. 1992 Near-wall response in turbulent shear flows subjected to imposed unsteadiness. J. Fluid Mech. 238, 55–71.Google Scholar
Mechel, F., Schilz, W. & Dietz, J. 1965 Akustische Impedanz einder luftdurchstromten offnung. Acustica 15, 199–206.Google Scholar
Morse, P. M. & Ingard, K. U. 1968 Theoretical Acoustics. McGraw-Hill.
Munt, R. M. 1977 The interaction of sound with a subsonic jet issuing from a semi-infinite cylindrical pipe. J. Fluid Mech. 83, 609–640.Google Scholar
Munt, R. M. 1990 Acoustic transmission properties of a jet pipe with subsonic jet flow: I, the cold jet reflection coefficient. J. Sound Vib. 142, 413–436.Google Scholar
Nomura, Y., Yamamura, I. & Inawashiro, S. 1960 On the acoustic radiation from a flanged circular pipe. J. Phys. Soc. Japan 15, 510–517.Google Scholar
Peters, M. C. A. M. & Hirschberg, A. 1993 Acoustically induced periodic vortex shedding at sharp edged open channel ends: simple vortex models. J. Sound Vib. 161, 281–299.Google Scholar
Peters, M. C. A. M., Hirschberg, A., Konijnenberg, J. A., Huijsmans, F. J. J., Leeuw, R. W. de, Beek, S. S. op de & Wijnands, A. P. J. 1992 Experimental study of the aeroacoustic behaviour of an open pipe termination at low Mach numbers and low Helmholtz numbers. AIAA Paper 90-02-055, Presented at 14th Aeroacoustics Conf. Aachen, Vol. 2, pp. 350–355.
Pierce, A. D. 1989 Acoustics, an Introduction to its Physical Principles and Applications. McGraw-Hill.
Powell, A. 1951 A Schlieren study of small scale air jets and some noise measurements in two-inch diameter air jets. ARC 14726 FM 1694.
Rayleigh, Lord 1896 The Theory of Sound, vol. II, 2nd edn. Macmillan. 319–326.
Rienstra, S. W. 1983 A small Strouhal number analysis for acoustic wave-jet flow-pipe interaction. J. Sound Vib. 86, 539–556.Google Scholar
Ronneberger, D. 1975 Genaue Messung der Schalldämpfung und der Phasengeschwindigkeit in durchströmten Rohren im Hinblick auf die Weckselwirkung zwischen Schall und Turbulenz. Habilitationsschrift Mathematische-Naturwissenschaftliche Fakultät der Universität Göttingen.
Ronneberger, D. 1991 Response of wall turbulence to imposed unsteadiness. Euromech Colloq. 272, Aussois, France.
Ronneberger, D. & Ahrens, C. 1977 Wall shear stress caused by small amplitude perturbations of turbulent boundary-layer flow: an experimental investigation. J. Fluid Mech. 83, 433–464.Google Scholar
Schlichting, H. 1968 Boundary Layer Theory. McGraw-Hill.
Selerowicz, W. C., Szumowski, A. P. & Meier, G. E. A. 1991 Self-excited compressible flow in a pipe-collar nozzle. J. Fluid Mech. 228, 465–485.Google Scholar
Tijdeman, H. 1975 On the propagation of sound in cylindrical tubes. J. Sound Vib. 39, 1–33; also NLR Rep. MP 74004 U.Google Scholar
Touloukian, Y. S., Saxena, S. C. & Hestermans, P. 1975 Thermophysical Properties of Matter.
Weast, R. C. 1976 Handbook of Chemistry and Physics, 57th edn. CRC Press.
Wijngaarden, L. van 1968 On the oscillations near and at resonance in open pipes. J. Engng Maths 11, 225–240.Google Scholar
Wilson, J. A., Beavers, G. S., De Coster, M. A., Holger, D. K. & Regenfuss, M. D. 1971 Experiments on the fluid mechanics of whistling. J. Acoust. Soc. Am. 50, 366–372.Google Scholar