Hostname: page-component-f554764f5-nwwvg Total loading time: 0 Render date: 2025-04-13T07:08:40.611Z Has data issue: false hasContentIssue false
  • English
  • Français

Global stability of a jet in crossflow

Published online by Cambridge University Press:  10 April 2009

SHERVIN BAGHERI ,
PHILIPP SCHLATTER ,
PETER J. SCHMID  and
DAN S. HENNINGSON
SHERVIN BAGHERI
Affiliation:
Linné Flow Centre, Department of Mechanics, Royal Institute of Technology (KTH), SE-10044 Stockholm, Sweden
PHILIPP SCHLATTER
Affiliation:
Linné Flow Centre, Department of Mechanics, Royal Institute of Technology (KTH), SE-10044 Stockholm, Sweden
PETER J. SCHMID
Affiliation:
Laboratoire d'Hydrodynamique (LadHyX), CNRS-Ecole Polytechnique, 91128 Palaiseau, France
DAN S. HENNINGSON*
Affiliation:
Linné Flow Centre, Department of Mechanics, Royal Institute of Technology (KTH), SE-10044 Stockholm, Sweden
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A linear stability analysis shows that the jet in crossflow is characterized by self-sustained global oscillations for a jet-to-crossflow velocity ratio of 3. A fully three-dimensional unstable steady-state solution and its associated global eigenmodes are computed by direct numerical simulations and iterative eigenvalue routines. The steady flow, obtained by means of selective frequency damping, consists mainly of a (steady) counter-rotating vortex pair (CVP) in the far field and horseshoe-shaped vortices close to the wall. High-frequency unstable global eigenmodes associated with shear-layer instabilities on the CVP and low-frequency modes associated with shedding vortices in the wake of the jet are identified. Furthermore, different spanwise symmetries of the global modes are discussed. This work constitutes the first simulation-based global stability analysis of a fully three-dimensional base flow.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 624 , 10 April 2009 , pp. 33 - 44
Copyright
Copyright © Cambridge University Press 2009

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.)

Article purchase

Temporarily unavailable

References

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 (068102), 1–4.CrossRefGoogle Scholar
Alves, L., Kelly, R. & Karagozian, A. 2007 Local stability analysis of an inviscid transverse jet. J. Fluid Mech. 581, 401–418.CrossRefGoogle Scholar
Alves, L., Kelly, R. & Karagozian, A. 2008 Transverse-jet shear-layer instabilities. Part 2. Linear analysis for large jet-to-crossflow velocity ratio. J. Fluid Mech. 602, 383–401.CrossRefGoogle Scholar
Bagheri, S., Åkervik, E., Brandt, L. & Henningson, D. S. 2009 Matrix-free methods for the stability and control of boundary layers. AIAA J. Accepted.CrossRefGoogle Scholar
Barkley, D. 2006 Linear analysis of the cylinder wake mean flow. Europhys. Lett. 75, 750–756.CrossRefGoogle Scholar
Barkley, D., Gomes, M. G. & Henderson, R. D. 2002 Three-dimensional instability in flow over a backward-facing step. J. Fluid Mech. 473, 167–190.CrossRefGoogle Scholar
Chevalier, M., Schlatter, P., Lundbladh, A. & Henningson, D. S. 2007 SIMSON: a pseudo-spectral solver for incompressible boundary layer flows. Tech Rep. TRITA-MEK 2007:07. KTH Mechanics.Google Scholar
Chomaz, J. M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357–392.CrossRefGoogle Scholar
Coelho, S. & Hunt, J. 1989 The dynamics of the near field of strong jets in crossflows. J. Fluid Mech. 200, 95–120.CrossRefGoogle Scholar
Fric, T. F. & Roshko, A. 1994 Vortical structure in the wake of a transverse jet. J. Fluid Mech. 279, 1–47.CrossRefGoogle Scholar
Giannetti, F. & Luchini, P. 2007 Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech. 581, 167–197.CrossRefGoogle Scholar
Huerre, P. 2000 Open shear flow instabilities. (ed. Batchelor, G. K., Mofatt, H. K. and Worster, M. G.) In Perspectives in Fluid Dynamics, pp. 159–229. Cambridge University Press.Google Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Kelso, R., Lim, T. & Perry, A. 1996 An experimental study of round jets in cross-flow. J. Fluid Mech. 306, 111–144.CrossRefGoogle Scholar
Lehoucq, R., Sorensen, D. & Yang, C. 1998 ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. SIAM.CrossRefGoogle Scholar
Marquet, O., Sipp, D. & Jacquin, L. 2008 Sensitivity analysis and passive control of cylinder flow. J. Fluid Mech. 615, 221–252.CrossRefGoogle Scholar
Megerian, S., Davitian, L., Alves, L. & Karagozian, A. 2007 Transverse-jet shear-layer instabilities. Part 1. Experimental studies. J. Fluid Mech. 593, 93–129.CrossRefGoogle Scholar
Muppidi, S. & Mahesh, K. 2007 Direct numerical simulation of round turbulent jets in crossflow. J. Fluid Mech. 574, 59–84.CrossRefGoogle Scholar
Pruett, C. D., Gatski, T. B., Grosch, C. E. & Thacker, W. D. 2003 The temporally filtered Navier–Stokes equations: properties of the residual stress. Phys. Fluids 15 (8), 2127–2140.CrossRefGoogle Scholar
Schmid, P. J. 2007 Nonmodal stability theory. Annu. Rev. Fluid Mech. 39, 129–162.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
Yuan, L. L., Street, R. L. & Ferziger, J. H. 1999 Large-eddy simulation of a round jet in crossflow. J. Fluid Mech. 379, 71–104.CrossRefGoogle Scholar