A Wall Effects and Means of Controlling the Evolution of Swirling Flows with Vortex Breakdown

Document Type : Regular Article

Authors

1 Dynamique des Moteurs et Vibroacoustique Laboratory, M’Hamed Bougara Boumerdes University, Algeria

2 Energétique, Mécanique et Ingénieries Laboratory, M’Hamed Bougara Boumerdes University, Algeria

3 GéniePhysique des Hydrocarbures Laboratory, M’Hamed Bougara Boumerdes University, Algeria

Abstract

This paper investigates numerically the bubble-type vortex breakdown apparition in the case of closed rotating flows of a viscous, axisymmetric, and incompressible fluid. First, a truncated conical/cylindrical cavity of spherical end disks is used to simulate and analyze the vortex structure under rigid surface conditions. The geometric effects of the enclosure are also studied. Vortex breakdown is demonstrated beyond the lower disk rotation rate threshold by introducing the no-slip condition imposed on the upper wall. The objective is to explore ways of controlling the evolution of this physical event by modifying the confinement conditions upstream of the vortex rupture. Particular attention is also paid to the effective kinematic viscosity, thermal diffusivity and geometric control of recirculation zones on the axis of rotation (axial bubble type). The second geometry consists of a spherical annulus formed by two concentric hemispheres in differential rotation under plat-free surface conditions. The results show that rotation of the inner hemisphere induces a vortex bubble on the polar axis. In contrast, the outer hemisphere rotation induces a toroidal vortex on the equator.

Keywords

Main Subjects


Bhaumik, S. K., & Lakshmisha, K. N. (2007). Lattice boltzmann simulation of the lid-diven swirling flow in a confined cylindrical cavity. Computers fluids, 36(7), 1163-173. https://doi.org/10.1016/j.compfluid.2007.02.001##
Bühler, K. (2009). Pattern formation in rotating fluids. Journal of Thermal Science, 18(2), 109-118. https://doi.org/10.1007/s11630-009-0109-2##
Cabeza, C., Sarasúa, G., Marti, A. C., & Bove, I. (2005). A simple mechanism for controlling vortex breakdown in a closed flow. Arxiv Preprint Physics, 0512248. https://doi.org/10.48550/arXiv.physics/0512248##
Dash, S., & Singh, N. (2016). Effects of partial heating of top rotating lid with axial temperature gradient on vortex breakdown in case of axisymmetric stratified lid-driven swirling flow. Yildiz Technical University Press, Istanbul, Turkey J. Thermal Eng, 2, 883-896. https://eds.yildiz.edu.tr/journal-of-thermal-engineering/Articles##
Dash, S. C., & Singh, N. (2018). Stability boundaries for vortex breakdowns and boundaries between oscillatory and steady swirling flow in a cylindrical annulus with a top rotating lid. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40(7), 1-19. https://doi.org/10.1007/s40430-018-1256-8##
Escudier, M. P. (1984). Observations of the flow produced in a cylindrical container by a rotating endwall. Experiments in fluids, 2(4), 189-196. https://doi.org/10.1007/BF00571864##
Escudier, M. P., J. O’Leary, & Poole, R. J. (2007). Flow produced in a conical Container by a rotating endwall. International Journal of Heat and Fluid Flow, 28(6), 1418-1428. https://doi.org/10.1016/j.ijheatfluidflow.2007.04.018##
Herrada, M. A., & Shtern, V. (2003). Vortex breakdown control by adding near-axis swirl and temperature gradients. Physical Review E, 68(4), 041202. https://doi.org/10.1103/PhysRevE.68.041202##
Husain, H. S., Shtern, V., & Hussain, F. (2003). Control of vortex breakdown by addition of near-axis swirl. Physics of Fluids, 15(2), 271-279. https://doi.org/10.1063/1.1530161##
Imoula, M., Saci, R., Benkoussas, B., & Gatignol, R. (2016). Characterization of swirling flows in a partly open cylinder. Journal of Applied Fluid Mechanics, 9(6), 3167-3176. https://doi.org/10.29252/JAFM.09.06.26281.##
Jacono, D. L., Sørensen, J. N., Thompson, M. C., & Hourigan, K. (2008). Control of vortex breakdown in a closed cylinder with a small rotating rod. Journal of Fluids and Structures, 24(8), 1278-1283. https://doi.org/10.1016/j.jfluidstructs.2008.06.015##
Leibovich, S. (1978). The structure of vortex breakdown. Annual Review of Fluid Mechanics, 10(1), 221-246. https://doi.org/10.1146/annurev.fl.10.010178.001253##
Lopez, J. M. (1990). Axisymmetric vortex breakdown flow. Journal of Fluid Mechanics, 221, 533- 552. https://doi.org/10.1017/S0022112090003664##
Meunier, P., & Hourigan, K. (2013). Mixing in a vortex breakdown flow. Journal of Fluid Mechanics, 731, 195. https://doi.org/10.1017/jfm.2013.226##
Mununga, L., Jacono, D. L., Sorensen, J. N., Leweke, T., Thompson, M. C., & Hourigan, K. (2014). Control of confined vortex breakdown with partial rotating lids. Journal of Fluid Mechanics, 738, 5-33. https://doi.org/10.1017/jfm.2013.596##
Pereira, J. C. F., & Sousa, J. M. M. (1997). Steady and transient topologies of confined vortex breakdown generated by a rotating cone. Opti. Diag. Eng, 2, 61-70. http://www.lasef.ist.utl.pt/lasef/##
Rudolf, P. A. V. E. L. (2008). Simulation of vortex breakdown in an enclosed cylinder as a preliminary study of the draft tube vortex rope creation.  Proceedings of the WSEAS Fluid Mechanics Conference, Rhodos. http://khzs.fme.vutbr.cz/~rudolf##
Serre, E., & Bontoux, P. (2001). Eclatement tourbillonnaire dans une cavité rotor–stator cylindrique. Comptes Rendus de l'Académie des Sciences-Series IIB- Mechanics, 329(9), 671-677. https://doi.org/10.1016/S1620-7742(01)01385-X##
Sousa, J. M. M. (2008). Steady vortex breakdown in swirling flow inside a closed container: Numerical simulations, PIV and LDV measurements. The Open Mechanical Engineering Journal, 2(1).  https://doi.org/10.2174/1874155X00802010069##
Sturzenegger, J. C., Sarasúa, L. G., & Martí, A. C. (2012). Analytical solutions for the axisymmetric flow inside a cylindrical container with a rod along the axis at low Reynolds numbers. Journal of Fluids and Structures, 28, 473-479. https://doi.org/10.1016/j.jfluidstructs.2011.11.002##
Turan, O., Yigit, S., & Chakraborty, N. (2018). Effects of wall heating on laminar mixed convection in a cylindrical enclosure with a rotating end wall. International Journal of Thermal Sciences, 131, 80-93. https://doi.org/10.1016/j.ijthermalsci.2018.05.005##
Vogel, H. U. (1968). Experimetelle ergebnisse ueber die laminare stroemung in einem zylindrischen gehaeuse mit darin rotierender scheibe. Max-Planck-Instiut fur Stromung- sforschung, Gottingen Bericht, 6. https://cir.nii.ac.jp/crid/1571698599901859968##
Yalagach, A., & Salih, A. (2016). Study of vortex breakdown in a cylindrical cavity with a rotating endwall. International Journal of FluidMechanics Research, 43(3). https://www.dl.begellhouse.com/journals/71cb29ca5b40f8f8,2404c1223f03c958,3ca81cf80d27c2c7.html##
Yu, Y., Li, B. W., & Thess, A. (2013). The effect of a uniform magnetic field on vortex breakdown in a cylinder with a rotating upper lid. Computers &Fluids, 88, 510-523. https://doi.org/10.1016/j.compfluid.2013.10.006##