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Acoustic Streaming and Temperature Field in the Cavity with Isothermal and Adiabatic Boundary Conditions at the Ends

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Abstract

A cylindrical cavity filled with air is considered. The cavity carries out the vibration movement along its axis. Adiabatic boundary conditions are specified on the lateral surface of the cavity. The boundary conditions at the ends of the cavity are considered in two types—adiabatic and isothermal. The features of acoustic streaming and temperature field are described when the cavity radius increases and the boundary conditions at the cavity ends are changed from adiabatic to isothermal.

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References

  1. L. K. Zarembo, Acoustic Streaming. High-Intensity Ultrasonic Fields (Plenum, New York, 1971).

    Google Scholar 

  2. M. F. Hamilton, Y. A. Ilinskii, and E. A. Zabolotskaya, “Acoustic streaming generated by standing waves in two-dimensional channels of arbitrary width,” J. Acoust. Soc. Am. 113, 153–160 (2003).

    Article  Google Scholar 

  3. M. F. Hamilton, Y. A. Ilinskii, and E. A. Zabolotskaya, “Thermal effects on acoustic streaming in standing waves,” J. Acoust. Soc. Am. 114, 3092–3101 (2003).

    Article  Google Scholar 

  4. I. Reyt, V. Daru, H. Bailliet, S. Moreau, J.-C. Valiere, D. Baltean-Carles, and C. Weisman, “Fast acoustic streaming in standing waves: generation of an additional outer streaming cell,” J. Acoust. Soc. Am. 134, 1791–1801 (2013).

    Article  Google Scholar 

  5. I. Reyt, H. Bailliet, and J.-C. Valiere, “Experimental investigation of acoustic streaming in a cylindrical wave guide up to high streaming Reynolds number,” J. Acoust. Soc. Am. 135, 27–37 (2014).

    Article  Google Scholar 

  6. V. Daru, I. Reyt, H. Bailliet, C. Weisman, and D. Baltean-Carles, “Acoustic and streaming velocity components in a resonant waveguide at high acoustic levels,” J. Acoust. Soc. Am. 141, 563–574 (2017).

    Article  Google Scholar 

  7. M. Nabavi, K. Siddiqui, and J. Dargahi, “Analysis of regular and irregular acoustic streaming patterns in a rectangular enclosure,” Wave Motion 46, 312–322 (2009).

    Article  Google Scholar 

  8. V. Daru, D. Baltean-Carles, C. Weisman, P. Debesse, and G. Gandikota, “Two-dimensional numerical simulations of nonlinear acoustic streaming in standing waves,” Wave Motion 50, 955–963 (2013).

    Article  MathSciNet  Google Scholar 

  9. A. A. Gubaidullin and A. V. Yakovenko, “Effects of heat exchange and nonlinearity on acoustic streaming in a vibrating cylindrical cavity,” J. Acoust. Soc. Am. 137, 3281–3287 (2015).

    Article  Google Scholar 

  10. A. A. Gubaidullin and A. V. Pyatkova, “Specificities of acoustic streaming in cylindrical cavity with increasing nonlinearity of the process,” Acoust. Phys. 64, 18–26 (2018).

    Article  Google Scholar 

  11. A. A. Gubaidullin and A. V. Pyatkova, “Acoustic streaming with heat exchange,” J. Phys.: Conf. Ser. 754, 022004 (2016).

    Google Scholar 

  12. M. W Thompson, A. A. Atchley, and M. J. Maccarone, “Influences of a temperature gradient and fluid inertia on acoustic streaming in a standing wave,” J. Acoust. Soc. Am. 117, 1839–1849 (2005).

    Article  Google Scholar 

  13. Y. Lin and B. Farouk, “Heat transfer in a rectangular chamber with differentially heated horizontal walls: effects of a vibrating sidewall,” Int. J. Heat Mass Transfer 51, 3179–3189 (2008).

    Article  Google Scholar 

  14. M. K. Aktas and T. Ozgumus, “The effects of acoustic streaming on thermal convection in an enclosure with differentially heated horizontal walls,” Int. J. Heat Mass Transfer 53, 5289–5297 (2010).

    Article  Google Scholar 

  15. A. A. Gubaidullin and A. V. Pyatkova, “Acoustic streaming with allowance for heat transfer,” Acoust. Phys. 62, 300–305 (2016).

    Article  Google Scholar 

  16. A. A. Gubaidullin and A. V. Pyatkova “Acoustic streaming under thermal boundary conditions of the third kind,” Acoust. Phys. 64, 280–286 (2018).

    Article  Google Scholar 

  17. A. A. Gubaidullin and A. V. Pyatkova, “Specificities of acoustic streaming under isothermal boundary conditions in cavities of different diameters,” Vestn. Tyum GU 4 (4), 105–117 (2018).

    Google Scholar 

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Funding

The study was performed by a grant from the Russian Science Foundation (project no. 15-11-10016).

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Correspondence to A. V. Pyatkova or A. A. Gubaidullin.

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Submitted by A. V. Lapin

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Pyatkova, A.V., Gubaidullin, A.A. Acoustic Streaming and Temperature Field in the Cavity with Isothermal and Adiabatic Boundary Conditions at the Ends. Lobachevskii J Math 40, 1994–1999 (2019). https://doi.org/10.1134/S1995080219110234

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  • DOI: https://doi.org/10.1134/S1995080219110234

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