Numerical simulation of three-dimensional instability of flow past a short cylinder

A. I. Aleksyuk   ; V. P. Shkadova   ; V. Ya. Shkadov

Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2016), pp. 25-30

Résumé

The two-dimensional flow around an infinitely long circular cylinder becomes three-dimensional starting with Reynolds numbers $\operatorname{Re}\approx 190$. The corresponding instability mode is called mode A. When $\operatorname{Re}\approx260$, structures with smaller cross-scale are formed in the wake as a result of a secondary three-dimensional instability (mode B). In this work, we consider the transition to three-dimensionality for a short cylinder bounded by planes. The length of the cylinder is chosen to eliminate the unstable perturbations of mode A. There have been found two modes of instability, which are analogues of modes A and B but modified under the influence of the limiting end planes. Numerical solutions of problems of three-dimensional flow are based on the Navier–Stokes equations.

Bibliographie

[1] Hammache M., Gharib M., “An experimental study of the parallel and oblique vortex shedding from circular cylinder”, J. Fluid Mech., 232 (1991), 567–590 | DOI

[2] Miller G.D., Williamson C.H.K., “Control of three-dimensional phase dynamics in a cylinder wake”, Exp. Fluids, 18:1–2 (1994), 26–35 | DOI

[3] Norberg C., “An experimental investigation of the flow around a circular cylinder: influence of aspect ratio”, J. Fluid Mech., 258 (1994), 287–316 | DOI

[4] Williamson C.H.K., “The existence of two stages in the transition to three-dimensionality of a cylinder wake”, Phys. Fluids, 31 (1988), 3165–3168 | DOI

[5] Navrose, Meena J., Mittal S., “Three-dimensional flow past a rotating cylinder”, J. Fluid Mech., 766 (2015), 28–53 | DOI | MR

[6] Persillon H., Braza M., “Physical analysis of the transition to turbulence in the wake of a circular cylinder by three-dimensional Navier–Stokes simulation”, J. Fluid Mech., 365 (1998), 23–88 | DOI | Zbl

[7] Aleksyuk A.I., Shkadova V.P., Shkadov V.Ya., “Gidrodinamicheskaya neustoichivost otryvnogo obtekaniya krugovogo tsilindra vyazkoi zhidkostyu”, Vestn. Mosk. un-ta. Matem. Mekhan., 2010, no. 5, 51–57

[8] Aleksyuk A.I., Shkadova V.P., Shkadov V.Ya., “Vozniknovenie, razvitie i zatukhanie vikhrevoi dorozhki v slede za obtekaemym telom”, Vestn. Mosk. un-ta. Matem. Mekhan., 2012, no. 3, 24–32

[9] Aleksyuk A.I., Issledovanie otryvnykh obtekanii tel metodom chislennogo resheniya uravnenii Nave–Stoksa, Kand. dis., M., 2013

[10] Williamson C.H.K., “Vortex dynamics in the cylinder wake”, Ann. Rev. Fluid Mech., 28:1 (1996), 477–539 | DOI | MR

[11] Barkley D., Henderson R.D., “Three-dimensional Floquet stability analysis of the wake of a circular cylinder”, J. Fluid Mech., 322 (1996), 215–241 | DOI | Zbl

[12] Wen C.-Y., Lin C.-Y., “Two-dimensional vortex shedding of a circular cylinder”, Phys. Fluids, 13:3 (2001), 557–560 | DOI

[13] Hughes T.J.R., Franca L.P., Hulbert G.M., “A new finite element formulation for computational fluid dynamics. VIII. The Galerkin/least-squares method for advective-diffusive equations”, Comput. Methods Appl. Mech. Eng., 73:2 (1989), 173–189 | DOI | MR | Zbl

[14] Karypis G., Kumar V., “A fast and high quality multilevel scheme for partitioning irregular graphs”, SIAM J. Sci. Comput., 20:1 (1998), 359–392 | DOI | MR

[15] Voevodin V.V., Zhumatii S.A., Sobolev S.I., Antonov A.S., Bryzgalov P.A., Nikitenko D.A., Stefanov K.S., Voevodin V.V., “Praktika superkompyutera “Lomonosov””, Otkrytye sistemy, 7 (2012), 36–39 | MR