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Mechanism of vortex oscillation around a hemisphere–cylinder body

Published online by Cambridge University Press:  14 August 2024

Zhou-Yang Wang Open the ORCID record for Zhou-Yang Wang [Opens in a new window]  and
Bao-Feng Ma Open the ORCID record for Bao-Feng Ma [Opens in a new window]
Zhou-Yang Wang
Affiliation:
Ministry-of-Education Key Laboratory of Fluid Mechanics, Beihang University, Beijing 100191, PR China
Bao-Feng Ma*
Affiliation:
Ministry-of-Education Key Laboratory of Fluid Mechanics, Beihang University, Beijing 100191, PR China
*
†Email address for correspondence: bf-ma@buaa.edu.cn
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Abstract

Previous studies have shown that low-frequency vortex oscillations occur around a hemisphere–cylinder body at different angles of attack, but the underlying mechanism is still unclear. In this study, we examine the origin of the vortex oscillation using numerical simulations and global linear stability analysis. The vortex oscillation is reproduced using numerical simulations, and the oscillatory modes are computed through dynamic mode decomposition (DMD). We obtain the base flow through a selective frequency damping method, which exhibits a pair of steady leeward vortices over the body. The four unstable modes are computed using a modified Arnoldi iteration. The antisymmetric mode with a Strouhal number of 0.105 is discovered to be responsible for the alternate oscillation of the vortex pair, and the mode with a Strouhal number of 0.220 corresponds to the in-phase vortex oscillation. Their frequencies have good agreement with the modes of DMD. The other two unstable modes with higher frequencies, one antisymmetric and one symmetric, are harmonic frequencies of the above two modes. The study conclusively verifies that the vortex oscillation over a hemisphere–cylinder body originates from a global flow instability.

JFM classification

Vortex Flows: Vortex instability Wakes/Jets: Separated flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 990 , 10 July 2024 , A20
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Åkervik, E., Brandt, L., Henningson, D.S., Hœpffner, J., Marxen, O. & Schlatter, P. 2006 Steady solutions of the Navier–Stokes equations by selective frequency damping. Phys. Fluids 18 (6), 068102.CrossRefGoogle Scholar
Bagheri, S., Schlatter, P., Schmid, P.J. & Henningson, D.S. 2009 Global stability of a jet in crossflow. J. Fluid Mech. 624, 33–44.CrossRefGoogle Scholar
Barkley, D. 2006 Linear analysis of the cylinder wake mean flow. Europhys. Lett. 75 (5), 750.CrossRefGoogle Scholar
Blackburn, H.M., Barkley, D. & Sherwin, S.J. 2008 Convective instability and transient growth in flow over a backward-facing step. J. Fluid Mech. 603, 271–304.CrossRefGoogle Scholar
Bohorquez, P., Sanmiguel-Rojas, E., Sevilla, A., Jiménez-González, J.I. & Martínez-Bazán, C. 2011 Stability and dynamics of the laminar wake past a slender blunt-based axisymmetric body. J. Fluid Mech. 676, 110–144.CrossRefGoogle Scholar
Cantwell, C.D., et al. 2015 Nektar++: an open-source spectral/hp element framework. Comput. Phys. Commun. 192, 205–219.CrossRefGoogle Scholar
Chomaz, J.-M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357–392.CrossRefGoogle Scholar
Dong, S., Karniadakis, G.E. & Chryssostomidis, C. 2014 A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains. J. Comput. Phys. 261, 83–105.CrossRefGoogle Scholar
Donnadieu, C., Ortiz, S., Chomaz, J.-M. & Billant, P. 2009 Three-dimensional instabilities and transient growth of a counter-rotating vortex pair. Phys. Fluids 21 (9), 094102.CrossRefGoogle Scholar
Edstrand, A.M., Davis, T.B., Schmid, P.J., Taira, K. & Cattafesta, L.N. 2016 On the mechanism of trailing vortex wandering. J. Fluid Mech. 801, R1.CrossRefGoogle Scholar
Geuzaine, C. & Remacle, J.-F. 2009 GMSH: a 3-D finite element mesh generator with built-in pre-and post-processing facilities. Intl J. Numer. Meth. Engng 79 (11), 1309–1331.CrossRefGoogle Scholar
He, W., Gioria, R.S., Pérez, J.M. & Theofilis, V. 2017 Linear instability of low Reynolds number massively separated flow around three naca airfoils. J. Fluid Mech. 811, 701–741.CrossRefGoogle Scholar
Hoang, N.T., Rediniotis, O.K. & Telionis, D.P. 1999 The dynamic character of the hemisphere-cylinder wake. Exp. Fluids 26 (5), 415–422.CrossRefGoogle Scholar
Hsieh, T & Wang, K.C. 1996 Three-dimensional separated flow structure over a cylinder with a hemispherical cap. J. Fluid Mech. 324, 83–108.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P.A 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22 (1), 473–537.CrossRefGoogle Scholar
Ijaz, H. & Ma, B.-F. 2022 Unsteady vortex flows around a hemisphere–cylinder body with turbulent separation. Phys. Fluids 34 (7), 077105.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Jiang, H.-G. & Ma, B.-F. 2019 Experiments on self-sustained oscillations of leeward vortices over a hemisphere cylinder. Phys. Fluids 31 (9), 097109.CrossRefGoogle Scholar
Kirby, R.M. & Sherwin, S.J. 2006 Stabilisation of spectral/hp element methods through spectral vanishing viscosity: application to fluid mechanics modelling. Comput. Meth. Appl. Mech. Engng 195 (23-24), 3128–3144.CrossRefGoogle Scholar
Le Clainche, S., Li, J.I., Theofilis, V. & Soria, J. 2015 Flow around a hemisphere-cylinder at high angle of attack and low Reynolds number. Part 1. Experimental and numerical investigation. Aerosp. Sci. Technol. 44, 77–87.CrossRefGoogle Scholar
Le Clainche, S, Rodríguez, D, Theofilis, V & Soria, J 2016 Formation of three-dimensional structures in the hemisphere-cylinder. AIAA J. 54 (12), 3884–3894.CrossRefGoogle Scholar
Leweke, T., Le Dizes, S. & Williamson, C.H.K. 2016 Dynamics and instabilities of vortex pairs. Annu. Rev. Fluid Mech. 48, 507–541.CrossRefGoogle Scholar
Ma, B.-F., Wang, Z. & Gursul, I. 2017 Symmetry breaking and instabilities of conical vortex pairs over slender delta wings. J. Fluid Mech. 832, 41–72.CrossRefGoogle Scholar
Ma, B.-F. & Yin, S.-L. 2018 Vortex oscillations around a hemisphere-cylinder body with a high fineness ratio. AIAA J. 56 (4), 1402–1420.CrossRefGoogle Scholar
Mao, X., Sherwin, S.J. & Blackburn, H.M. 2012 Non-normal dynamics of time-evolving co-rotating vortex pairs. J. Fluid Mech. 701, 430–459.CrossRefGoogle Scholar
Pier, B. 2008 Local and global instabilities in the wake of a sphere. J. Fluid Mech. 603, 39–61.CrossRefGoogle Scholar
Rowley, C.W., Mezić, I., Bagheri, S., Schlatter, P. & Henningson, D.S. 2009 Spectral analysis of nonlinear flows. J. Fluid Mech. 641, 115–127.CrossRefGoogle Scholar
Schmid, P.J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28.CrossRefGoogle Scholar
Sipp, D. & Lebedev, A. 2007 Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows. J. Fluid Mech. 593, 333–358.CrossRefGoogle Scholar
Sirangu, V. & Ng, T.T. 2012 Flow control of a slender blunt-nose body at high angles of attack. J. Aircraft 49 (6), 1904–1912.CrossRefGoogle Scholar
Strandenes, H., Jiang, F., Pettersen, B. & Andersson, H.I. 2019 Low-frequency oscillations in flow past an inclined prolate spheroid. Intl J. Heat Fluid Flow 78, 108421.CrossRefGoogle Scholar
Theofilis, V. 2011 Global linear instability. Annu. Rev. Fluid Mech. 43, 319–352.CrossRefGoogle Scholar
Xu, C. & Pasquetti, R. 2004 Stabilized spectral element computations of high Reynolds number incompressible flows. J. Comput. Phys. 196 (2), 680–704.CrossRefGoogle Scholar
Yuan, Q. & Yarusevych, S. 2020 Wake topology and dynamics over a slender body at a high incidence and their relation to structural loading. Phys. Fluids 32 (5), 055111.CrossRefGoogle Scholar