Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T13:49:47.041Z Has data issue: false hasContentIssue false
  • English
  • Français

Large-amplitude acoustic streaming

Published online by Cambridge University Press:  12 March 2014

G. P. Chini ,
Z. Malecha  and
T. D. Dreeben
G. P. Chini*
Affiliation:
Department of Mechanical Engineering, Center for Fluid Physics, and Program in Integrated Applied Mathematics, University of New Hampshire, Durham, NH 03824, USA
Z. Malecha
Affiliation:
Department of Mechanical Engineering, Center for Fluid Physics, and Program in Integrated Applied Mathematics, University of New Hampshire, Durham, NH 03824, USA Faculty of Mechanical and Power Engineering, Wrocław University of Technology, Wroclaw 50-370, Poland
T. D. Dreeben
Affiliation:
Corporate Technology, OSRAM SYLVANIA, 71 Cherry Hill Drive, Beverly, MA 01915, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A mechanism is proposed for the generation of large-amplitude acoustically-driven streaming flows in which time-mean flow speeds are comparable to the instantaneous speed of fluid particles in a high-frequency sound-wave field. Motivated by streaming observed in high-intensity discharge (HID) lamps, two-dimensional flow of a density-stratified ideal gas in a channel geometry is analysed in the asymptotic limit of high-frequency acoustic-wave forcing. Predictions of streaming flow magnitudes based on classical arguments invoking Reynolds stress divergences originating in viscous boundary layers are orders of magnitude too small to account for the observed mean flows. Moreover, classical ‘Rayleigh streaming’ theory cannot account for the direction of the cellular mean flows often observed in HID lamps. In contrast, the mechanism proposed here, which invokes fluctuating baroclinic torques away from viscous boundary layers and thus is largely independent of viscous effects, can account both for the magnitude and the orientation of the observed streaming flows.

JFM classification

Geophysical and Geological Flows: Baroclinic flows Compressible Flows: Compressible Flows Vortex Flows: Vortex Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 744 , 10 April 2014 , pp. 329 - 351
Copyright
© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abdulle, A. & E, W. 2003 Finite-difference heterogeneous multi-scale method for homogenization problems. J. Comput. Phys. 191 (1), 18–39.Google Scholar
Amin, N. 1988 The effect of g-jitter on heat transfer. Proc. R. Soc. Lond. A 419, 151–172.Google Scholar
Bajaj, K., Ahlers, G. & Pesch, W. 2002 Rayleigh–Bénard convection with rotation at small Prandtl numbers. Phys. Rev. E 65, 056309: 1–13.CrossRefGoogle ScholarPubMed
Batchelor, G. K. 1973 An Introduction to Fluid Dynamics. 1st edn. Cambridge University Press, Cambridge.Google Scholar
Chung, S. K. & Trinh, E. H. 1998 Containerless protein crystal growth in rotating levitated drops. J. Cryst. Growth 194, 384–397.Google Scholar
Davidson, B. J. 1973 Heat transfer from a vibrating cylinder. Intl J. Heat Mass Transfer 76, 1703–1727.Google Scholar
Dreeben, T. D. 2008 Modelling of fluid-mechanical arc instability in pure-mercury HID lamps. J. Phys. D 41, 144023.CrossRefGoogle Scholar
Dreeben, T. D. & Chini, G. P. 2011 Two-dimensional streaming flows in high-intensity discharge lamps. Phys. Fluids 23, 056101.CrossRefGoogle Scholar
Ferziger, J. H. & Peric, M. 1999 Computational Methods for Fluid Dynamics. Springer.Google Scholar
Gaver, D. P. & Grotberg, J. B. 1986 An experimental investigation of oscillating flow in a tapered channel. J. Fluid Mech. 172, 47–61.CrossRefGoogle Scholar
Gopinath, A. & Mills, A. F. 1993 Convective heat transfer from a sphere due to acoustic streaming. ASME J. Heat Transfer 115, 332–341.CrossRefGoogle Scholar
Grotberg, J. B. 1984 Volume-cycled oscillatory flow in a tapered channel. J. Fluid Mech. 141, 249–264.Google Scholar
Issa, R. I., Gosman, A. D. & Watkins, A. P. 1986 The computation of compressible and incompressible recirculating flows by a non-iterative implicit scheme. J. Comput. Phys. 62 (1), 66–82.Google Scholar
Lighthill, M. J. 1978 Acoustic streaming. J. Sound Vib. 61, 391–418.CrossRefGoogle Scholar
Lighthill, M. J. 1991 Biomechanics of hearing sensitivity. ASME J. Vib. Acoust. 113, 1–13.Google Scholar
Lighthill, M. J. 1992 Acoustic streaming in the ear itself. J. Fluid Mech. 239, 551–606.CrossRefGoogle Scholar
Malecha, Z., Chini, G. P. & Julien, K. 2013 A multiscale algorithm for simulating spatially-extended Langmuir circulation dynamics. J. Comput. Phys.; in press, http://dx.doi.org/10.1016/j.jcp.2013.07.003.Google Scholar
Malecha, Z., Miroslaw, L., Tomczak, T., Koza, Z., Matyka, M., Tarnawski, W. & Szczerba, D. 2011 GPU-based simulation of 3D blood flow in abdominal aorta using OpenFOAM. Arch. Mech. 63 (2), 137–161.Google Scholar
Mei, C. C. 1985 Resonant reflection of surface water waves by periodic sandbars. J. Fluid Mech. 152, 315–335.Google Scholar
Merkin, J. H. 1967 Oscillatory free convection from an infinite horizontal cylinder. J. Fluid Mech. 30, 561–575.Google Scholar
Nyborg, W. L. 1953 Acoustic streaming due to attenuated plane waves. J. Acoust. Soc. Am. 25, 68–75.Google Scholar
OpenFOAM 2009 The Open Source CFD Toolbox User Guide. Free Software Foundation.Google Scholar
Piercy, J. E. & Lamb, J. 1954 Acoustic streaming in liquids. Proc. R. Soc. Lond. A 226, 43–50.Google Scholar
Rayleigh, 1883 On the circulation of air observed in Kundt’s tubes and some allied acoustical problems. Trans. R. Soc. 75, 1–21.Google Scholar
Riley, N. 2001 Steady streaming. Annu. Rev. Fluid Mech. 33, 43–65.Google Scholar
Riley, N. & Trinh, E. H. 2001 Steady streaming in oscillatory inviscid flow. Phys. Fluids 13, 1956–1960.Google Scholar
Stockwald, A., Kaestle, H. & Weiss, H. 2008 Significant efficacy enhancement of low wattage metal halide HID lamp systems by acoustically induced convection configuration. IEEE 35th International Conference on Plasma Science, 2008 (ICOPS 2008), Karlsruhe, Germany. IEEE Press.Google Scholar
Tijani, M. E. H., Zeegers, J. C. H. & de Waele, A. T. A. M. 2002 Prandtl number and thermoacoustic refrigerators. J. Acoust. Soc. Am. 112, 134–143.CrossRefGoogle ScholarPubMed
Westervelt, P. J. 1953 The theory of steady rotational flow generated by a sound field. J. Acoust. Soc. Am. 25, 60–67.Google Scholar
Witting, H. L. 1978 Acoustic resonances in cylindrical high-pressure arc discharges. J. Appl. Phys. 49, 2680–2683.Google Scholar
Wybrow, M. F. & Riley, N. 1996 Oscillatory flow over a cylinder resting on a plane boundary. Eur. J. Appl. Maths 7, 545–558.Google Scholar