Journal of Applied Nonlinear Dynamics
About the Structure of the Vortex Flow Around Cylinder With Viscous Fluid
Journal of Applied Nonlinear Dynamics 3(4) (2014) 307--315 | DOI:10.5890/JAND.2014.12.002
Rustyam G. Akhmetov; Ruslan R. Kutluev
Bashkir State Pedagogical University named after M.Akmullah, 3a Oktyabrskoy revolutsii street, Ufa, 450000, Russia
Download Full Text PDF
Abstract
he problem of stationary viscous in compressible fluid flow around the cylinder has been analyze d by means of the asymptotic methods. The fluid flow equations are considered in the variables "stream function-a vortex". Asymptotic vortex in the boundary layer near the boundary of the cylinder for average and large Reynolds numbers has been investigated. The equation of the interior boundary layer for stream function has been made by means of using the method of matched asymptotic expansions. The properties solution of the given equation are investigated by means of numerical methods under the additional condition of slipping on the boundary of the cylinder.
References
-
[1]  | Loytsyansky, L.G. (2003), Mekhanika of Liquid and Gas, Drofa, Moskow. |
-
[2]  | Ladyzhenskaya, O.A. (2003), Sixth problem of the millennium: Navier tokes equations, existence and smoothness, Uspekhi Matematicheskikh Nauk, 58:2(350), 45-78. Translate from Russian to English in Russian Mathematical Surveys, 58(2), 251-286. |
-
[3]  | Babenko, K.I., Vvedenskaya, N.D., and Orlova, M.G. (1975), Calculation of a stationary flow of the circular cylinder by viscous fiuid, Zhurnal Vychislitelnoi Matematiki and Matematicheskoi Fiziki, 15(1), 183-196. Translate from Russian to English in USSR Computational Mathematics and Mathematical Physics, 15(1), 176-190. |
-
[4]  | Afendikov, A.L. and Babenko, K.I. (1989), Mathematical modelling of turbulence in the flow of viscous incompressible fluid, Mathematical Modeling: Moscow, 1(8), 45-74. |
-
[5]  | Krasnikov, Yu.G. and Solovyev, V.R. (1999), Finding of approximate analytical solutions of the equations of Navier-Stokes for a stationary flow of the cylinder incompressible liquid, News Academy of Sciences. MZhG, 4, 22-33. |
-
[6]  | Dynnikova, G.Ya. (2008), Calculation of flow around a circular cylinder on the basis of two-dimensional Navier-Stokes equations at large Reynolds numbers with high resolution in a boundary layer, Doklady Akademii Nauk, 422(6), 755-757. Translate from Russian to English in Doklady Physics, 53(10), 544-547. |
-
[7]  | Dynnikova, G.Ya. (2009), Fast technique for solving the N-body problem in flow simulation by vortexmethods, Zhurnal Vychislitelnoi Matematiki and Matematicheskoi Fiziki, 49(8), 1458-1465. Translate from Russian to English in Computational Mathematics and Mathematical Physics, 49(8), 1389-1396. |
-
[8]  | Zakharenkov, M.N. (2001), Realization of boundary conditions of partial or complete slipping in the solution of Navier - Stokes equations in stream function-vorticity variables, Zhurnal Vychislitelnoi Matematiki and Matematicheskoi Fiziki, 41(5), 796-806. Translate from Russian to English in Computational Mathematics and Mathematical Physics, 41(5), 751-761. |
-
[9]  | Zakharenkov, M.N. (2010), Formulation of boundary conditions for vorticity in viscous incompressible flow problems, Zhurnal Vychislitelnoi Matematiki and Matematicheskoi Fiziki, 50(6), 1140-1147. Translate from Russian to English in Computational Mathematics and Mathematical Physics, 50(6), 1085-1092. |
-
[10]  | Gushchin, V.A., Shchennikov, V.V. (1974), A numerical method of solving the navier-stokes equations, Zhurnal Vychislitelnoi Matematiki and Matematicheskoi Fiziki, 14(2), 512-520. Translate from Russian to English in Computational Mathematics and Mathematical Physics, 14(2), 242-250. |
-
[11]  | Belotserkovskii, O.M., Gushchin, V.A., Shchennikov, V.V. (1975), Use of the splitting method to solve problems of the dynamics of a viscous incompressible fluid, Zhurnal Vychislitelnoi Matematiki and Matematicheskoi Fiziki, 15(1), 197-207. Translate from Russian to English in Computational Mathematics and Mathematical Physics, 15(1), 190-200. |
-
[12]  | Van Dyke, M. (1964), Perturbation methods in fluid mechanics, Academic Press, New York. |
-
[13]  | Il'in, A. M. (1989), Matching of asymptotic expansions of solutions of boundary value problems, Nauka, Moscow. Translations of Mathematical monographs (1992), Providence, RI, AmericanMath. Society, Vol.102. |
-
[14]  | Chapman, S.J., Lawry, J.M.H., and Ockendon, J.R. (1999), Ray theory for high-Peclet-number convectiondiffusion, SIAM Journal on Applied Mathematics , 60(1), 121-135. |
-
[15]  | Gupalo, Yu.P., Polyanin, A.D., Ryazantzev, Yu.S. (1985), Mass and Heat Transfer Between Reactive Particles and Flow, Nauka, Moscow. |
-
[16]  | Akhmetov, R.G., Kutluev, R.R. (2013), About vortex structure at the cylinder flow viscous fluid. Fluxes and Structures in Fluids, Proceedings of International Conference, June 25-28, MAKS Press, Saint-Petersburg, 10-13. |
-
[17]  | Lamb, G. (1932), Hydrodynamics, Cambridge University Press, Cambridge. |
-
[18]  | Kochin, N.E., Kibel, I.A. Roze, N.V. (1954), Theoretical Hydromechanics, Akademie Verlag, Berlin. |
-
[19]  | Hartman, P. (1964), Ordinary Differential Equations, New York, London, Sydney. |
-
[20]  | Bateman, G., Erdelyi, A. (1953), Highest Transcendental Functions, McGraw-Hill Book Company, New York, Toronto, London. |
-
[21]  | Arnold, V.I. (1978), Additional Chapters of the Theory of the Ordinary Differential Equations, Mir, Moskow. |