Izvestiya of Saratov University.

Physics

ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)

For citation:

Vorotnikov G. V., Zinovyev E. A., Nekrasova S. O. Gas oscillations in an annular channel induced by a longitudinal temperature gradient. Izvestiya of Saratov University. Physics , 2022, vol. 22, iss. 2, pp. 111-122. DOI: 10.18500/1817-3020-2022-22-2-111-122, EDN: SYWGFS

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
30.06.2022
Full text:
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Language: 
Russian
Heading: 
Theoretical and mathematical physics
Article type: 
Article
UDC: 
534-13
DOI: 
10.18500/1817-3020-2022-22-2-111-122
EDN: 
SYWGFS

Gas oscillations in an annular channel induced by a longitudinal temperature gradient

Autors: 
Vorotnikov Gennady Viktorovich, Samara National Research University named after Academician S. P. Korolev
Zinovyev Evgeniy Aleksandrovich, Samara National Research University named after Academician S. P. Korolev
Nekrasova Svetlana Olegovna, Samara National Research University named after Academician S. P. Korolev
Abstract: 

Background and Objectives: When selecting the design and layout scheme of the thermoacoustic converter, special requirements include the placement of heat exchangers in the areas of heat input and output. The most promising in this regard are coaxial schemes with coaxial location (tube in tube) of the acoustic pathway channels. Such design features pose their own optimization problems. To solve them, it is necessary to reveal the peculiarities of changing the dynamical parameters of oscillating gas under acoustic wave conditions. Materials and Methods: In this paper we derive a second-order linear differential equation for pressure oscillations in the annular section channel in the presence of a constant longitudinal temperature gradient based on linearized equations of compressible medium mechanics, which does not depend on other dynamical parameters. The solutions are expressed in terms of two dimensionless parameters h/δµ ; h and δµ represent, respectively, half the distance between two concentric channels and a characteristic length using the dynamical viscosity of the gas and the angular frequency of acoustic oscillations. Results: The solution of the equation makes it possible to present expressions for the dynamical parameters of gas oscillations, such as velocity, density, temperature, as functions of the dynamical pressure. Conclusion: It has been shown that the derived equation is a more general case of the Rott equation obtained for a circular section channel under the same conditions. The dynamical parameter equations derived in this paper are applied to measurements of the acoustic power distribution in a thermoacoustic transducer and make it possible to simulate linear acoustic processes in coaxial channels of thermoacoustic devices.

Key words: 
wave equation
annular channel
temperature gradient
axial velocity
acoustic gas displacement
Acknowledgments: 
The results of the work were obtained using the equipment of the Center of collective use “Intercafedral Scientific and Research Center of CAM-TECHNOLOGIES” with the financial support of the Ministry of Science and Higher Education of the Russian Federation (Project No. FSSS-2020-0019).
Reference: 
  1. Perozziello C., Grosu L., Vaglieco B. M. Free-Piston Stirling Engine Technologies and Models : A Review. Energies, 2021, vol. 14, article no. 7009. https://doi.org/10.3390/en14217009
  2. De Boer P. C. T. Basic limitations on the performance of Stirling engines. Journal of Engineering for Gas Turbines and Power, 2007, vol. 129, pp. 104–113. https://doi.org/10.1115/1.2204629
  3. Ceperley P. H. A pistonless Stirling engine – the traveling wave heat engine. J. Acoust. Soc. Am., 1979, vol. 66, pp. 1508–1513. https://doi.org/10.1121/1.383505
  4. Macdonald M., Badescu V. The International Handbook of Space Technology. Berlin, Heidelberg, Springer-Verlag, 2014. 731 p. https://doi.org/10.1007/978-3-642-41101-4
  5. Backhaus S., Tward E., Petach M. Thermoacoustic power systems for space applications. AIP Conf. Proc., 2002, vol. 608, pp. 939–945. https://doi.org/608.10.1063/1.1449822
  6. Swift G. W. Thermoacoustic engines. J. of the Acoust. Soc. of Am., 1988, vol. 84, no. 4, pp. 1145–1180. https://doi.org/10.1121/1.396617
  7. Tijani M. E. H., Spoelstra S. Study of a coaxial thermoacoustic-Stirling cooler. Cryogenics, 2008, vol. 48, pp. 77–82. https://doi.org/10.1016/j.cryogenics.2008.01.001
  8. Poignand G., Podkovskiy A., Penelet G., Lotton P., Bruneau M. Analysis of a coaxial, compact thermoacoustic heat-pump. Acta Acustica united with Acustica, 2013, vol. 99, no. 6, pp. 898–904. https://doi.org/10.3813/AAA.918669
  9. Backhaus S., Swift G. W. A thermoacoustic Stirling heat engine : Detailed study. J. of the Acoust. Soc. of Am., 2000, vol. 107, no. 6, pp. 3148–3166. https://doi.org/10.1121/1.429343
  10. Yazaki T., Iwata A., Maekawa T., Tominaga A. Travelling wave thermoacoustic engine in a looped tube. Phys. Rev. Lett., 1998, vol. 81, no. 15, pp. 3128–3131.
  11. Swift G. W. Thermoacoustic engines and refrigerators. Phys. Today, 1995, vol. 48, no. 7, pp. 22–28. https://doi.org/10.1063/1.4704199
  12. Telesz M. P. Design and testing of a thermoacoustic power converter : Masters of science thesis. Georgia Institute of Technology, 2006. 139 p.
  13. Blok K., Owczarek P., Francois M. Bi-directional turbines for converting acoustic wave power into electricity. 9th PAMIR Int. Conf. on Fund. and Appl. MHD, 2014, pp. 433–438.
  14. Elhawary M. A., Abdelmaged H., Ibrahima A., Sabry S., Abdel-Rahman E. Experimental study of a small scale bidirectional axial impulse turbine for acoustic-to-mechanical power conversion. Renewable En., 2020, vol. 159, pp. 414–426. https://doi.org/10.1016/j.renene.2020.05.162
  15. Mohammad H. R., Abolghasemi A., Stone R., Dadd M., Bailey P. Numerical modelling of a coaxial Stirling pulse tube cryocooler with an active displacer for space applications. Cryogenics, 2020, vol. 106, article no. 103048. https://doi.org/10.1016/j.cryogenics.2020.103048
  16. Zhao Y., Yu G., Tan J., Mao X., Li J., Zhab R., Li N., Dang H. CFD modeling and experimental verification of oscillating flow and heat transfer processes in the micro coaxial Stirling-type pulse tube cryocooler operating at 90–170 Hz. Cryogenics, 2018, vol. 90, pp. 30–40. https://doi.org/10.1016/j.cryogenics.2018.01.003
  17. Swift G. W., Garret S. L. Thermoacoustics : A unifying perspective for some engines and refrigerators. J. of the Acoust. Soc. of Am., 2002, vol. 113, pp. 2379–2381. https://doi.org/10.1121/1.1561492
  18. Tijdeman H. On the propagation of sound waves in cylindrical tubes. J. of Sound and Vib., 1975, vol. 39, iss. 1, pp. 1–33. https://doi.org/10.1016/S0022-460X(75)80206-9
  19. Stinson M. R. The propagation of plane sound waves in narrow and wide circular tubes, and generalization to uniform tubes of arbitrary cross‐sectional shape. J. of the Acoust. Soc. of Am., 1991, vol. 89, no. 2, pp. 550–558. https://doi.org/10.1121/1.400379
  20. Stinson M. R., Champoux Y. Propagation of sound and the assignment of shape factors in model porous materials having simple pore geometries. J. of the Acoust. Soc. of Am., 1992, vol. 91, iss. 2, pp. 685–695. https://doi.org/10.1121/1.402530
  21. Yazaki T., Tashiro Y., Biwa T. Measurements of sound propagation in narrow tubes. Proc. of the Royal Society of Math. Phys. and Eng. Sciences. 2007, vol. 463, iss. 2087, pp. 2855–2862. https://doi.org/10.1098/rspa.2007.1897
  22. Rott N. Damped and thermally driven acoustic oscillations in wide and narrow tubes. J. of Appl. Math. and Phys., 1969, vol. 20, pp. 230–243. https://doi.org/10.1007/BF01595562
  23. Rott N., Zouzoulas G. Thermally driven acoustic oscillations. Part IV : Tubes with variable cross-section. J. of Appl. Math. and Phys., 1976, vol. 27, pp. 197–224.
  24. Swift G. W. Analysis and performance of a large thermoacoustic engine. J. of the Acoust. Soc. of Am., 1992, vol. 92, iss. 3, pp. 1551–1563. https://doi.org/10.1121/1.403896
  25. Vereshchagina T. N., Mikheev A. S., Kudryaeva Yu. V. Thermoacoustic effect and its application. Voprosy atomnoj nauki i tekhniki. Ser. Yaderno-reaktornye konstanty [Problems of Atomic Science and Technology. Series : Nuclear and Reactor Constants], 2021, iss. 2, pp. 127– 138 (in Russian). https://doi.org/10.55176/2414-1038-2021-2-127-138
  26. Morii J., Biwa T., Yazaki T. Measurements of acoustic particle velocity in a coaxial duct and its application to a traveling-wave thermoacoustic heat engine. Rev. of Scientific Inst., 2014, vol. 85, iss. 9, article no. 094902. https://doi.org/10.1063/1.4893639
Received: 
21.02.2022
Accepted: 
23.04.2022
Published: 
30.06.2022
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