Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-28T12:53:50.413Z Has data issue: false hasContentIssue false
  • English
  • Français

Towards the detection of moving separation in unsteady flows

Published online by Cambridge University Press:  25 August 2015

Philippe Miron  and
Jérôme Vétel
Philippe Miron*
Affiliation:
Department of Mechanical Engineering, LADYF, Polytechnique Montréal, Montréal, QC, H3C 3A7, Canada
Jérôme Vétel
Affiliation:
Department of Mechanical Engineering, LADYF, Polytechnique Montréal, Montréal, QC, H3C 3A7, Canada
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In many engineering systems operating with a working fluid, the best efficiency is reached close to a condition of flow separation, which makes the prediction of this condition very important in industry. Provided that wall-based quantities can be measured, we know today how to obtain good predictions for two- and three-dimensional steady and periodic flows. In these flows, the separation is defined on a fixed line attached to a material surface. The last case to elucidate is the one where this line is no longer attached to the wall but on the contrary is contained within the flow. This moving separation is probably, however, the most common case of separation in natural flows and industrial applications. Since this case has received less attention during the past few years, we propose in this study to examine some properties of moving separation in two-dimensional, unsteady flows where the separation does not leave a signature on the wall. Since in this framework separation can be extracted by using a Lagrangian frame where the separation profile can be viewed as a hyperbolic unstable manifold, we propose a method to extract the separation point defined by the Lagrangian saddle point that belongs to this unstable manifold. In practice, the separation point and profile are initially extracted by detecting the most attracting Lagrangian coherent structure near the wall, and they can then be advected in time for subsequent instants. It is found that saddle points, which initially act as separation points in the viscous wall flow region, remarkably preserve their hyperbolicity even if they are ejected from the wall towards the inviscid region. Two test cases are studied: the creeping flow of a rotating and translating cylinder close to a wall, and the unsteady separation in the boundary layer generated by a planar jet impinging onto a plane wall.

JFM classification

Boundary Layers: Boundary layer separation Wakes/Jets: Separated flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 779 , 25 September 2015 , pp. 819 - 841
Check for updates
Copyright
© 2015 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.)

References

Cassel, K. W. & Conlisk, A. T. 2014 Unsteady separation in vortex-induced boundary layers. Phil. Trans. R. Soc. Lond. A 372, 20130348.Google Scholar
Dairay, T., Fortuné, V., Lamballais, E. & Brizzi, L.-E. 2015 Direct numerical simulation of a turbulent jet impinging on a heated wall. J. Fluid Mech. 764, 362–394.Google Scholar
Didden, N. & Ho, C.-M. 1985 Unsteady separation in a boundary layer produced by an impinging jet. J. Fluid Mech. 160, 235–256.Google Scholar
Doligalski, T. L., Smith, C. R. & Walker, J. D. A. 1994 Vortex interactions with walls. Annu. Rev. Fluid Mech. 26, 573–616.Google 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.Google Scholar
El Hassan, M., Assoum, H. H., Sobolík, V., Vétel, J., Abed-Meraim, K., Garon, A. & Sakout, A. 2012 Experimental investigation of the wall shear stress and the vortex dynamics in a circular impinging jet. Exp. Fluids 52, 1475–1489.Google Scholar
Farazmand, M. & Haller, G. 2012 Computing lagrangian coherent structures from their variational theory. Chaos 22, 013128.Google Scholar
Ghosh, S., Leonard, A. & Wiggins, S. 1998 Diffusion of a passive scalar from a no-slip boundary into a two-dimensional chaotic advection field. J. Fluid Mech. 372, 119–163.Google Scholar
Green, M. A., Rowley, C. W. & Haller, G. 2007 Detection of Lagrangian coherent structures in three-dimensional turbulence. J. Fluid Mech. 572, 111–120.Google Scholar
Hackborn, W. W., Ulucakli, M. E. & Yuster, T. 1997 A theoretical and experimental study of hyperbolic and degenerate mixing regions in a chaotic Stokes flow. J. Fluid Mech. 346, 23–48.Google Scholar
Haller, G. 2000 Finding finite-time invariant manifolds in two-dimensional velocity fields. Chaos 10, 99–108.Google Scholar
Haller, G. 2002 Lagrangian coherent structures from approximate velocity data. Phys. Fluids 14, 1851–1861.Google Scholar
Haller, G. 2004 Exact theory of unsteady separation for two-dimensional flows. J. Fluid Mech. 512, 257–311.Google Scholar
Haller, G. 2011 A variational theory of hyperbolic lagrangian coherent structures. Physica D 240 (7), 574–598.Google Scholar
Haller, G. 2015 Lagrangian coherent structures. Annu. Rev. Fluid Mech. 47, 137–162.Google Scholar
Haller, G. & Beron-Vera, F. J. 2012 Geodesic theory of transport barriers in two-dimensional flows. Physica D 241, 1680–1702.Google Scholar
Haller, G. & Iacono, R. 2003 Stretching, alignment, and shear in slowly varying velocity fields. Phys. Rev. E 68, 056304.Google Scholar
Kilic, M. S., Haller, G. & Neishtadt, A. 2005 Unsteady fluid flow separation by the method of averaging. Phys. Fluids 17, 67104.Google 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 Mechanica 146, 115–126.Google Scholar
Koromilas, C. A. & Telionis, D. P. 1980 Unsteady laminar separation: an experimental study. J. Fluid Mech. 97, 347–384.Google Scholar
Lekien, F. & Haller, G. 2008 Unsteady flow separation on slip boundaries. Phys. Fluids 20, 097101.Google Scholar
Mathur, M., Haller, G., Peacock, T., Ruppert-Felsot, J. E. & Swinney, H. L. 2007 Uncovering the lagrangian skeleton of turbulence. Phys. Rev. Lett. 98, 144502.Google 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.Google Scholar
Moore, F. K. 1958 On the separation of unsteady boundary layer. In Boundary-layer Research (ed. Görtler, H.), pp. 296–311. Springer.Google Scholar
Olascoaga, M. J. & Haller, G. 2012 Forecasting sudden changes in environmental pollution patterns. Proc. Natl Acad. Sci. USA 109, 4738–4743.Google Scholar
Perry, A. E. & Chong, M. S. 1986 A series-expansion study of the Navier–Stokes equations with applications to three-dimensional separation patterns. J. Fluid Mech. 173, 207–223.Google Scholar
Perry, A. E. & Chong, M. S. 1987 A description of eddying motions and flow patterns using critical-point concepts. Annu. Rev. Fluid Mech. 19, 125–155.Google Scholar
Rott, N. 1956 Unsteady viscous flows in the vicinity of a separation point. Q. Appl. Maths 13, 444–451.Google Scholar
Ruban, A., Araki, D., Yapalparvi, R. & Gajjar, J. 2011 On unsteady boundary-layer separation in supersonic flow. Part 1. upstream moving separation point. J. Fluid Mech. 678, 124–155.Google Scholar
Sears, W. R. 1956 Some recent developments in airfoil theory. J. Aero. Sci. 23, 490–499.Google Scholar
Sears, W. R. & Telionis, D. P. 1975 Boundary-layer separation in unsteady flow. SIAM J. Appl. Maths 28, 215–235.Google Scholar
Surana, A., Grunberg, O. & Haller, G. 2006 Exact theory of three-dimensional flow separation. Part 1. steady separation. J. Fluid Mech. 564, 57–103.Google Scholar
Surana, A. & Haller, G. 2008 Ghost manifolds in slow-fast systems, with applications to unsteady fluid flow separation. Physica D 237, 1507–1529.Google 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, 107101.Google Scholar
Surana, A., Jacobs, G. B. & Haller, G. 2007 Extraction of separation and attachment surfaces from three-dimensional steady shear flows. AIAA J. 45, 1290–1302.Google Scholar
Van Dommelen, L. L. & Cowley, S. J. 1990 On the lagrangian description of unsteady boundary-layer separation. Part 1. general theory. J. Fluid Mech. 210, 593–626.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, 1–11.Google Scholar