Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-06-15T02:35:48.377Z Has data issue: false hasContentIssue false

Material spike formation in highly unsteady separated flows

Published online by Cambridge University Press:  26 November 2019

Mattia Serra*
School of Engineering and Applied Sciences, Harvard University, Cambridge, MA02138, USA
Seán Crouzat
Department of Mechanical Engineering, LADYF, Polytechnique Montréal, Montréal, QC,H3C 3A7, Canada
Gaël Simon
Department of Mechanical Engineering, LADYF, Polytechnique Montréal, Montréal, QC,H3C 3A7, Canada
Jérôme Vétel
Department of Mechanical Engineering, LADYF, Polytechnique Montréal, Montréal, QC,H3C 3A7, Canada
George Haller
Institute for Mechanical Systems, ETH Zürich, Leonhardstrasse 21, 8092Zürich, Switzerland
Email address for correspondence:


We apply the recent frame-invariant theory of separation spike formation to complex unsteady flows, including a turbulent separation bubble, an impinging jet, and flows around a freely moving cylinder and a freely rotating ellipse. We show how the theory captures the onset of material spike formation, without any assumption on the flow type (steady, periodic, unsteady) or separation type (on- or off-wall, fixed or moving boundaries). We uncover new phenomena, such as the transition from on-wall to off-wall separation, the merger of initially distinct spikes, and the presence of severe material spikes that remain hidden to previous approaches. Remarkably, even in steady flows around curved boundaries, we detect material spikes in the absence of flow reversal, the main ingredient to existing separation criteria. Together, our results unveil how an involved network of spikes arises, interacts and merges dynamically, leading to the final ejection of particles from the wall in highly transient flow separation processes.

JFM Papers
© 2019 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


Azad, R. S. 1996 Turbulent flow in a conical diffuser: a review. Exp. Therm. Fluid Sci. 13 (4), 318337.CrossRefGoogle Scholar
Cassel, K. W. & Conlisk, A. T. 2014 Unsteady separation in vortex-induced boundary layers. Phil. Trans. R. Soc. Lond. A 372, 20130348.Google ScholarPubMed
Cermak, J. E. 1976 Aerodynamics of buildings. Annu. Rev. Fluid Mech. 8, 75106.CrossRefGoogle Scholar
Cloos, F.-J., Stapp, D. & Pelz, P. F. 2017 Swirl boundary layer and flow separation at the inlet of a rotating pipe. J. Fluid Mech. 811, 350371.CrossRefGoogle Scholar
Corke, T. C. & Thomas, F. O. 2015 Dynamic stall in pitching airfoils: aerodynamic damping and compressibility effects. Annu. Rev. Fluid Mech. 47, 479505.CrossRefGoogle Scholar
Dandois, J., Mary, I. & Brion, V. 2018 Large-eddy simulation of laminar transonic buffet. J. Fluid Mech. 850, 156178.CrossRefGoogle Scholar
Didden, N. & Ho, C.-M. 1985 Unsteady separation in a boundary layer produced by an impinging jet. J. Fluid Mech. 160, 235256.CrossRefGoogle Scholar
van Dommelen, L. L. & Shen, S. F. 1982 The genesis of separation. In Numerical and Physical Aspects of Aerodynamic Flows (ed. Cebeci, T.), pp. 293311. Springer.CrossRefGoogle Scholar
Duquesne, P., Maciel, Y. & Deschênes, C. 2015 Unsteady flow separation in a turbine diffuser. Exp. Fluids 56, 156.CrossRefGoogle Scholar
Elliott, J. W., Smith, F. T. & Cowley, S. J. 1983 Breakdown of boundary layers: (i) on moving surfaces; (ii) in semi-similar unsteady flow; (iii) in fully unsteady flow. Geophys. Astrophys. Fluid Dyn. 25, 77138.CrossRefGoogle Scholar
Fang, X. & Tachie, M. F. 2019 On the unsteady characteristics of turbulent separations over a forward–backward-facing step. J. Fluid Mech. 863, 9941030.CrossRefGoogle Scholar
Farazmand, M. & Haller, G. 2012 Computing Lagrangian coherent structures from their variational theory. Chaos 22, 013128.CrossRefGoogle ScholarPubMed
Gresh, T. 2018 Compressor Performance: Aerodynamics for the User, 3rd edn. Butterworth-Heinemann.Google Scholar
Gsell, S., Bourguet, R. & Braza, M. 2016 Two-degree-of-freedom vortex-induced vibrations of a circular cylinder at Re = 3900. J. Fluids Struct. 67, 156172.CrossRefGoogle Scholar
Haller, G. 2004 Exact theory of unsteady separation for two-dimensional flows. J. Fluid Mech. 512, 257311.CrossRefGoogle Scholar
Haller, G. 2011 A variational theory of hyperbolic Lagrangian coherent structures. Physica D 240 (7), 574598.Google Scholar
Hecht, F. 2012 New development in FreeFem++. J. Numer. Math. 20 (3–4), 251265.CrossRefGoogle Scholar
Kilic, M. S., Haller, G. & Neishtadt, A. 2005 Unsteady fluid flow separation by the method of averaging. Phys. Fluids 17 (6), 067104.CrossRefGoogle Scholar
Klonowska-Prosnak, M. E. & Prosnak, W. J. 2001 An exact solution to the problem of creeping flow around circular cylinder rotating in presence of translating plane boundary. Acta Mech. 146, 115126.CrossRefGoogle Scholar
Klose, B. F., Serra, M. & Jacobs, G. B.2019 The kinematics of Lagrangian flow separation in external aerodynamics. AIAA J. (submitted) arXiv:1909.04129.Google Scholar
Laizet, S. & Lamballais, E. 2009 High-order compact schemes for incompressible flows: a simple and efficient method with quasi-spectral accuracy. J. Comput. Phys. 228 (16), 59896015.CrossRefGoogle Scholar
Laizet, S. & Li, N. 2011 Incompact3d: a powerful tool to tackle turbulence problems with up to O (105) computational cores. Intl J. Numer. Meth. Fluids 67, 17351757.CrossRefGoogle Scholar
Lamarche-Gagnon, M.-É. & Vétel, J. 2018 Experimental investigation of unsteady separation in the rotor-oscillator flow. J. Fluid Mech. 844, 546566.CrossRefGoogle Scholar
Liu, C. S. & Wan, Y.-H. 1985 A simple exact solution of the Prandtl boundary layer equations containing a point of separation. Arch. Rat. Mech. Anal. 89 (2), 177185.CrossRefGoogle Scholar
Miron, P. & Vétel, J. 2015 Towards the detection of moving separation in unsteady flows. J. Fluid Mech. 779, 819841.CrossRefGoogle Scholar
Miron, P., Vétel, J. & Garon, A. 2015 On the flow separation in the wake of a fixed and a rotating cylinder. Chaos 25 (8), 087402.CrossRefGoogle Scholar
Mohammed-Taifour, A. & Weiss, J.2016 Unsteadiness in a large turbulent separation bubble 799 383–412.CrossRefGoogle Scholar
Moore, F. K. 1958 On the separation of unsteady boundary layer. In Boundary-layer Research (ed. Görtler, H.), pp. 296311. Springer.Google Scholar
Na, Y. & Moin, P. 1998 Direct numerical simulation of a separated turbulent boundary layer. J. Fluid Mech. 374, 379405.CrossRefGoogle Scholar
Prandtl, L. 1904 Über Flüssigkeitsbewegung bei sehr kleiner Reibung. Verh. III, Intern. Math. Kongr. Heidelberg 2, 484491.Google Scholar
Rott, N. 1956 Unsteady viscous flows in the vicinity of a separation point. Q. Appl. Maths 13, 444451.CrossRefGoogle Scholar
Ruban, A. I., Araki, D., Yapalparvi, R. & Gajjar, J. S. B. 2011 On unsteady boundary-layer separation in supersonic flow. Part 1. Upstream moving separation point. J. Fluid Mech. 678, 124155.CrossRefGoogle Scholar
Sears, W. R. 1956 Some recent developments in airfoil theory. J. Aero. Sci. 23, 490499.CrossRefGoogle Scholar
Sears, W. R. & Telionis, D. P. 1975 Boundary-layer separation in unsteady flow. SIAM J. Appl. Maths 28, 215235.CrossRefGoogle Scholar
Serra, M., Vétel, J. & Haller, G. 2018 Exact theory of material spike formation in flow separation. J. Fluid Mech. 845, 5192.CrossRefGoogle Scholar
Shah, R. K. & Sekulić, D. P. 2003 Fundamentals of Heat Exchanger Design. John Wiley & Sons.CrossRefGoogle Scholar
Shariff, K., Pulliam, T. H. & Ottino, J. M. 1991 A dynamical systems analysis of kinematics in the time-periodic wake of a circular cylinder. Lect. Appl. Math. 28, 613646.Google Scholar
Sun, M., Liu, Y. & Hu, Z. 2019 Turbulence decay in a supersonic boundary layer subjected to a transverse sonic jet. J. Fluid Mech. 867, 216249.CrossRefGoogle Scholar
Surana, A., Grunberg, O. & Haller, G. 2006 Exact theory of three-dimensional flow separation. Part 1. Steady separation. J. Fluid Mech. 564, 57103.CrossRefGoogle Scholar
Surana, A., Jacobs, G. B., Grunberg, O. & Haller, G. 2008 An exact theory of three-dimensional fixed separation in unsteady flows. Phys. Fluids 20 (10), 107101.CrossRefGoogle Scholar
Tianyun, G., Jianhan, L. & Mingbo, S. 2017 Symmetric/asymmetric separation transition in a supersonic combustor with single-side expansion. Phys. Fluids 29 (12), 126102.Google Scholar
Weldon, M., Peacock, T., Jacobs, G. B., Helu, M. & Haller, G. 2008 Experimental and numerical investigation of the kinematic theory of unsteady separation. J. Fluid Mech. 611, 111.CrossRefGoogle Scholar
Weymouth, G. D. 2014 Chaotic rotation of a towed elliptical cylinder. J. Fluid Mech. 743, 385398.CrossRefGoogle Scholar
Williams, J. C. 1977 Incompressible boundary-layer separation. Annu. Rev. Fluid Mech. 9 (1), 113144.CrossRefGoogle Scholar
Wu, W. & Piomelli, U. 2018 Effects of surface roughness on a separating turbulent boundary layer. J. Fluid Mech. 841, 552580.CrossRefGoogle Scholar
Yapalparvi, R. & van Dommelen, L. L. 2012 Numerical solution of unsteady boundary-layer separation in supersonic flow: upstream moving wall. J. Fluid Mech. 706, 413430.CrossRefGoogle Scholar
Yuster, T. & Hackborn, W. W. 1997 On invariant manifolds attached to oscillating boundaries in Stokes flows. Chaos 7 (4), 769776.CrossRefGoogle ScholarPubMed

Serra et al. supplementary movie 1

Movie Figure 9

Download Serra et al. supplementary movie 1(Video)
Video 6 MB

Serra et al. supplementary movie 2

Movie Figure 13

Download Serra et al. supplementary movie 2(Video)
Video 836.5 KB