Skip to main content Accessibility help
×
Home
Hostname: page-component-8bbf57454-2p2tb Total loading time: 0.308 Render date: 2022-01-21T21:43:21.656Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

Strong wave–mean-flow coupling in baroclinic acoustic streaming

Published online by Cambridge University Press:  06 November 2018

Guillaume Michel
Affiliation:
Laboratoire de Physique Statistique, École Normale Supérieure, CNRS, Université P. et M. Curie, Université Paris Diderot, Paris 75005, France
Gregory P. Chini*
Affiliation:
Department of Mechanical Engineering and Program in Integrated Applied Mathematics, University of New Hampshire, Durham, NH 03824, USA
*
Email address for correspondence: greg.chini@unh.edu

Abstract

The interaction of an acoustic wave with a stratified fluid can drive strong streaming flows owing to the baroclinic production of fluctuating vorticity, as recently demonstrated by Chini et al. (J. Fluid Mech.744, 2014, pp. 329–351). In the present investigation, a set of wave/mean-flow interaction equations is derived that governs the coupled dynamics of a standing acoustic-wave mode of characteristic (small) amplitude $\unicode[STIX]{x1D716}$ and the streaming flow it drives in a thin channel with walls maintained at differing temperatures. Unlike classical Rayleigh streaming, the resulting mean flow arises at $O(\unicode[STIX]{x1D716})$ rather than at $O(\unicode[STIX]{x1D716}^{2})$. Consequently, fully two-way coupling between the waves and the mean flow is possible: the streaming is sufficiently strong to induce $O(1)$ rearrangements of the imposed background temperature and density fields, which modifies the spatial structure and frequency of the acoustic mode on the streaming time scale. A novel Wentzel–Kramers–Brillouin–Jeffreys analysis is developed to average over the fast wave dynamics, enabling the coupled system to be integrated strictly on the slow time scale of the streaming flow. Analytical solutions of the reduced system are derived for weak wave forcing and are shown to reproduce results from prior direct numerical simulations (DNS) of the compressible Navier–Stokes and heat equations with remarkable accuracy. Moreover, numerical simulations of the reduced system are performed in the regime of strong wave/mean-flow coupling for a fraction of the computational cost of the corresponding DNS. These simulations shed light on the potential for baroclinic acoustic streaming to be used as an effective means to enhance heat transfer.

Type
JFM Papers
Copyright
© 2018 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

Amin, N. 1988 The effect of g-jitter on heat transfer. Proc. R. Soc. Lond. A 419, 151172.CrossRefGoogle Scholar
Andrade, E. N. 1931 On the circulation caused by the vibration of air in a tube. Proc. R. Soc. Lond. A 134, 445470.CrossRefGoogle Scholar
Atkas, M. K. & Ozgumus, T. 2010 The effects of acoustic streaming on thermal convection in an enclosure with differentially heated horizontal walls. Intl J. Heat Mass Transfer 53, 52895297.Google Scholar
Beisner, E., Wiggins, N. D., Yue, K.-B., Rosales, M., Penny, J., Lockridge, J., Page, R., Smith, A. & Guerrero, L. 2015 Acoustic flame suppression mechanics in a microgravity environment. Microgravity Sci. Technol. 27, 141144.CrossRefGoogle Scholar
Bengtsson, M. & Laurell, T. 2004 Ultrasonic agitation in microchannels. Anal. Bioanal. Chem. 378, 17161721.CrossRefGoogle ScholarPubMed
Burns, K. J., Vasil, G. M., Oishi, J. S., Lecoanet, D., Brown, B. P. & Quataert, E.2018 See the Dedalus entry in the Astrophysical Source Code Library, http://ascl.net/1603.015, and the Dedalus project homepage, http://dedalus-project.org.Google Scholar
Červenka, M. & Bednarřik, M. 2017 Effect of inhomogeneous temperature fields on acoustic streaming structures in resonators. J. Acoust. Soc. Am. 141, 44184426.CrossRefGoogle Scholar
Chini, G. P., Malecha, Z. & Dreeben, T. D. 2014 Large-amplitude acoustic streaming. J. Fluid Mech. 744, 329351.CrossRefGoogle Scholar
Davidson, B. J. 1973 Heat transfer from a vibrating circular cylinder. Intl J. Heat Mass Transfer 16, 17031727.CrossRefGoogle Scholar
Dreeben, T. D. & Chini, G. P. 2011 Two-dimensional streaming flows in high-intensity dicharge lamps. Phys. Fluids 23, 056101.CrossRefGoogle Scholar
Fand, R. M. & Kaye, J. 1960 Acoustic streaming near a heated cylinder. J. Acoust. Soc. Am. 32, 579584.CrossRefGoogle Scholar
Hamilton, M. F., Ilinskii, Y. A. & Zabolotskaya, E. A. 2003 Acoustic streaming generated by standing waves in two-dimensional channels of arbitrary with. J. Acoust. Soc. Am. 113, 153160.CrossRefGoogle Scholar
Holtsmark, J., Johnsen, I., Sikkeland, T. & Skalvem, S. 1954 Boundary layer flow near a cylindrical obstacle in an oscillating, incompressible fluid. J. Acoust. Soc. Am. 26, 2639.CrossRefGoogle Scholar
Hyun, S., Lee, D.-R. & Loh, B.-G. 2005 Investigation of convective heat transfer augmentation using acoustic streaming generated by ultrasonic vibrations. Intl J. Heat Mass Transfer 48, 703718.CrossRefGoogle Scholar
Karlsen, J. T., Augustsson, P. & Bruus, H. 2016 Acoustic force density acting on inhomogeneous fluids in acoustic fields. Phys. Rev. Lett. 117, 114504.CrossRefGoogle Scholar
Karlsen, J. T., Qiu, W., Augustsson, P. & Bruus, H. 2018 Acoustic streaming and its suppression in inhomogeneous fluids. Phys. Rev. Lett. 120, 054501.CrossRefGoogle Scholar
Legay, M., Gondrexon, N., Person, S. L., Boldo, P. & Bontemps, A. 2011 Enhancement of heat transfer by ultrasound: review and recent advances. Intl J. Chem. Engng 2011, 670108.Google Scholar
Lighthill, M. J. 1978 Acoustic streaming. J. Sound Vib. 61, 391418.CrossRefGoogle Scholar
Lin, Y. & Farouk, B. 2008 Heat transfer in a rectangular chamber with differentially heated horizontal walls: effects of a vibrating sidewall. Intl J. Heat Mass Transfer 51, 31793189.CrossRefGoogle Scholar
Loh, B.-G., Hyun, S., Ro, P. I. & Kleinstreuer, C. 2002 Acoustic streaming induced by ultrasonic flexural vibrations and associated enhancement of convective heat transfer. J. Acoust. Soc. Am. 111, 875883.CrossRefGoogle ScholarPubMed
Nabavi, M., Siddiqui, K. & Dargahi, J. 2008 Influence of differentially heated horizontal walls on the streaming shape and velocity in a standing wave resonator. Intl J. Heat Mass Transfer 35, 10611064.CrossRefGoogle Scholar
Nyborg, W. L. 1958 Acoustic streaming near a boundary. J. Acoust. Soc. Am. 30, 329339.CrossRefGoogle Scholar
Plumb, R. A. 1977 The interaction of two internal waves with the mean flow: implications for the theory of the quasi-biennial oscillation. J. Atmos. Sci. 34, 18471858.2.0.CO;2>CrossRefGoogle Scholar
Prangsma, G. J., Alberga, A. H. & Beenakker, J. J. M. 1973 Ultrasonic determination of the volume viscosity of N2 , CO, CH and CD4 between 77 and 300 K. Physica 64, 278288.CrossRefGoogle Scholar
Rayleigh, Lord 1884 On the circulation of air observed in Kundts tubes, and on some allied acoustical problems. Phil. Trans. R. Soc. Lond. 175, 121.CrossRefGoogle Scholar
Richardson, P. D. 1967 Heat transfer from a circular cylinder by acoustic streaming. J. Fluid Mech. 30, 337355.CrossRefGoogle Scholar
Riley, N. 2001 Steady streaming. Annu. Rev. Fluid Mech. 33, 4365.CrossRefGoogle Scholar
Riley, N. & Trinh, E. H. 2001 Steady streaming in an oscillatory inviscid flow. Phys. Fluids 13, 19561960.CrossRefGoogle Scholar
Stuart, J. T. 1966 Double boundary layers in oscillatory viscous flow. J. Fluid Mech. 24, 673687.CrossRefGoogle Scholar
Swift, G. W. 1988 Thermoacoustic engine. J. Acoust. Soc. Am. 84, 11451180.CrossRefGoogle Scholar
Vainshtein, P., Fichman, M. & Gutfinger, C. 1995 Acoustic enhancement of heat transfer between two parallel plates. Intl J. Heat Mass Transfer 38, 18931899.CrossRefGoogle Scholar
Verhaagen, B., Boutsioukis, C., van der Sluis, L. W. M. & Versluis, M. 2014 Acoustic streaming induced by an ultrasonically oscillating endodontic file. J. Acoust. Soc. Am. 135, 17171730.CrossRefGoogle Scholar
Yaralioglu, G. G., Wygant, I. O., Marentis, T. C. & Khuri-Yakub, B. T. 2004 Ultrasonic mixing in microfluidic channels using integrated transducers. Anal. Chem. 76, 36943698.CrossRefGoogle Scholar
10
Cited by

Linked content

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Strong wave–mean-flow coupling in baroclinic acoustic streaming
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Strong wave–mean-flow coupling in baroclinic acoustic streaming
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Strong wave–mean-flow coupling in baroclinic acoustic streaming
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *