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Numerical simulations of transition in oscillatory plane channel flow

Published online by Cambridge University Press:  26 April 2006

Bart A. Singer ,
Joel H. Ferziger  and
Helen L. Reed
Bart A. Singer
Affiliation:
High Technology Corp., 28 Research Drive, Hampton, VA 23666, USA
Joel H. Ferziger
Affiliation:
Stanford University, Stanford, CA 94305, USA
Helen L. Reed
Affiliation:
Arizona State University, Tempe, AZ 85287, USA
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Abstract

The effect of flow oscillation on the stability of plane channel flow is studied via numerical simulation. For weak oscillation, the ratio of the Stokes layer thickness to the distance from the wall to the critical layer in steady flow provides the best normalization for the mean-flow frequency. Maximum growth rates occur when the instantaneous velocity profile has large regions of positive curvature. The effect of oscillation is generally stabilizing. However, at low frequencies, TS wave energies may vary by 106 in a cycle and irreversible secondary instability may be produced at the peak.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 208 , November 1989 , pp. 45 - 66
Copyright
© 1989 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. 1972 Handbook of Mathematical Functions. Dover.
Gottlieb, D. & Orszag, S. A. 1981 Numerical Analysis of Spectral Methods: Theory and Applications. Society for Industrial and Applied Mathematics, Phil., PA.
Grosch, C. E. & Salwen, H. 1968 The stability of steady and time-dependent plane Poiseuille flow. J. Fluid Mech. 34, 177–205.Google Scholar
Hall, P. 1975 The stability of Poiseuille flow modulated at high frequency, Prof. R. Soc. Lond. A 344, 453–464.Google Scholar
Herbert, D. M. 1972 The energy balance in modulated plane Poiseuille flow. J. Fluid Mech. 56, 73–80.Google Scholar
Herbert, Th. 1983 Modes of secondary instability in Plane Poiseuille Flow. IUTAM Symposium on Turbulence and Chaotic Phenomena in Fluids.Google Scholar
von Kerczek, C. H. 1982 The instability of oscillatory plane Poiseuille flow. J. Fluid Mech. 116, 91–114.Google Scholar
Magen, M. & Patera, A. T. 1986 Three-dimensional linear instability of parallel shear flows Phys. Fluids, 29, 364–367.Google Scholar
Moser, R. D., Moin, P. & Leonard, A. 1983 A spectral numerical method for the Navier-Stokes equations with applications to Taylor-Couette flow. J. Comput. Phys. 52, 524–544.Google Scholar
Singer, B. A., Ferziger, J. H. & Reed, H. L. 1987a Numerical simulation studies of laminarturbulent transition in the plane channel. Department of Mechanical Engineering, Stanford Univ., Stanford, Calif., Rep. TF-31.
Singer, B., Reed, H. L. & Ferziger, J. H. 1986 Investigation of the effects of initial disturbances on plane channel transition. AIAA Paper 86–0433.Google Scholar
Singer, B., Reed, H. L. & Ferziger, J. H. 1987b Effects of streamwise vortices on transition in plane-channel flow. AIAA Paper 87–0048.Google Scholar
Singer, B. A., Spalart, P., Ferziger, J. H. & Reed, H. L. 1987c Local intermodal energy transfer of the secondary instability in a plane channel. AIAA Paper 87–1202.Google Scholar