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Home » Issues » Archive of Issues » 2021 - 3 issue » pp. 505-516

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Russia Yekaterinburg
Year
2021
Volume
31
Issue
3
Pages
505-516
<<
Section Mechanics
Title Recovery of radial-axial velocity in axisymmetric swirling flows of a viscous incompressible fluid in the Lagrangian consideration of vorticity evolution
Author(-s) Prosviryakov E.Yu.a
Affiliations Institute of Engineering Science, Ural Branch of the Russian Academy of Sciencesa
Abstract Swirling laminar axisymmetric flows of viscous incompressible fluids in a potential field of body forces are considered. The study of flows is carried out in a cylindrical coordinate system. In the flows, the regions in which the axial derivative of the circumferential velocity cannot take on zero value in some open neighborhood (essentially swirling flows) and the regions in which this derivative is equal to zero (the region with layered swirl) are considered separately. It is shown that a well-known method (the method of viscous vortex domains) developed for non-swirling flows can be used for regions with layered swirling. For substantially swirling flows, a formula is obtained for calculating the radial-axial velocity of an imaginary fluid through the circumferential vorticity component, the circumferential circulation of a real fluid, and the partial derivatives of these functions. The particles of this imaginary fluid “transfer” vortex tubes of the radial-axial vorticity component while maintaining the intensity of these tubes, and also “transfer” the circumferential circulation and the product of the circular vorticity component by some function of the distance to the axis of symmetry. A non-integral method for reconstructing the velocity field from the vorticity field is proposed. It is reduced to solving a system of linear algebraic equations in two variables. The obtained result is proposed to be used to extend the method of viscous vortex domains to swirling axisymmetric flows.
Keywords Navier-Stokes equations, swirling flow, the discrete vortex method, the Helmholtz vortex theorem, method of viscous vortex domains
UDC 532.5.032
MSC 35N10, 76D05, 76D17, 76U05
DOI 10.35634/vm210311
Received 26 May 2021
Language Russian
Citation Prosviryakov E.Yu. Recovery of radial-axial velocity in axisymmetric swirling flows of a viscous incompressible fluid in the Lagrangian consideration of vorticity evolution, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, vol. 31, issue 3, pp. 505-516.
References
  1. Rosenhead L. The formation of vortices from a surface of discontinuity, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1931, vol. 134, issue 823, pp. 170-192. https://doi.org/10.1098/rspa.1931.0189
  2. Belotserkovskii S.M., Nisht M.I. Otryvnoe i bezotryvnoe obtekanie tonkikh kryl'ev ideal'noi zhidkost'yu (Separated and unseparated ideal liquid flow around thin wings), Moscow: Nauka, 1978.
  3. Cottet G.-H., Koumoutsakos P.D. Vortex methods: theory and practice, Cambridge: Cambridge University Press, 2000. https://doi.org/10.1017/CBO9780511526442
  4. Gutnikov V.A., Lifanov I.K., Setukha A.V. On modelling the aerodynamics of buildings and structures using the closed vortex method, Izvestiya Rossiiskoi Akademii Nauk. Mekhanika Zhikosti i Gaza, 2006, no. 4, pp 78-92. https://elibrary.ru/item.asp?id=9282173
  5. Kochin N.E., Kibel' I.A., Roze N.V. Teoreticheskaya gidromehanika. Chast' 1 (Theoretical fluid mechanics. Part 1), Moscow: Fizmatgiz, 1963.
  6. Golubkin V.N., Sizykh G.B. On some general properties of plane-parallel viscous fluid flows, Izvestiya Akademii Nauk SSSR. Mekhanika Zhikosti i Gaza, 1987, no. 3, pp. 176-178. https://elibrary.ru/item.asp?id=23023464
  7. Brutyan M.A., Golubkin V.N., Krapivskii P.L. On the Bernoulli equation for axisymmetric viscous fluid flows, Uchenie zapiski Tsentral'nogo Aerogidrodinamicheskogo Instituta, 1988, vol. 19, no. 2, pp. 98-100. https://elibrary.ru/item.asp?id=15513524
  8. Ogami Y., Akamatsu T. Viscous flow simulation using the discrete vortex model - the diffusion velocity method, Computers and Fluids, 1991, vol. 19, issues 3-4, pp. 433-441. https://doi.org/10.1016/0045-7930(91)90068-S
  9. Dynnikova G.Ya. Lagrange method for Navier-Stokes equations solving, Doklady Akademii Nauk, 2004, vol. 399, no. 1, pp. 42-46. https://elibrary.ru/item.asp?id=17354344
  10. Markov V.V., Sizykh G.B. Vorticity evolution in liquids and gases, Fluid Dynamics, 2015, vol. 50, no. 2, pp. 186-192. https://doi.org/10.1134/S0015462815020027
  11. Sizykh G.B. Evolution of vorticity in swirling axisymmetric flows of a viscous incompressible fluid, TsAGI Science Journal, 2015, vol. 46, no. 3, pp. 209-217. https://doi.org/10.1615/tsagiscij.2015014086
  12. Golubkin V.N., Markov V.V., Sizykh G.B. The integral invariant of the equations of motion of a viscous gas, Journal of Applied Mathematics and Mechanics, 2015, vol. 79, no. 6, pp. 566-571. https://doi.org/10.1016/j.jappmathmech.2016.04.002
  13. Sizykh G.B. Entropy value on the surface of a non-symmetric convex bow part of a body in the supersonic flow, Fluid Dynamics, 2019, vol. 54, issue 7, pp. 907-911. https://doi.org/10.1134/S0015462819070139
  14. Golubkin V.N., Sizykh G.B. On the vorticity behind 3-D detached bow shock wave, Advances in Aerodynamics, 2019, vol. 1, issue 1. https://doi.org/10.1186/s42774-019-0016-5
  15. Sizykh G.B. Closed vortex lines in fluid and gas, Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Ser. Fiziko-Matematicheskie Nauki, 2019, vol. 23, no. 3, pp. 407-416. https://doi.org/10.14498/vsgtu1723
  16. Golubkin V.N., Sizykh G.B. Generalization of the Crocco invariant for 3D gas flows behind detached bow shock wave, Russian Mathematics, 2019, vol. 63, issue 12, pp. 45-48. https://doi.org/10.3103/S1066369X19120053
  17. Mironyuk I.Yu., Usov L.A. The invariant of stagnation streamline for a stationary vortex flow of an ideal incompressible fluid around a body, Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Ser. Fiziko-Matematicheskie Nauki, 2020, vol. 24, no. 4, pp. 780-789 (in Russian). https://doi.org/10.14498/vsgtu1815
  18. Mironyuk I.Yu., Usov L.A. Stagnation points on vortex lines in flows of an ideal gas, Trydy Moskovskogo Fiziko-Tekhnicheskogo Instituta, 2020, vol. 12, no. 4 (48), pp. 171-176 (in Russian). https://elibrary.ru/item.asp?id=44950398
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