Instability in Pipe Flow

Published

January 15, 2008

Author(s)

David Cotrell, Geoffrey B. McFadden, W. E. Alley, B. J. Alder

Abstract

An axisymmetric linear stability analysis is carried out for flow driven by an axial pressure gradient in a pipe with axisymmetric and axially-periodic radius variation (i.e., axial corrugation). The steady base flow is assumed to be axisymmetric and axially-periodic with a specified radius variation wavelength and amplitude, and the azimuthal velocity component is taken to be zero. Results show that for a suffciently large Reynolds number, the onset of vortex formation is observed in the bulge, however, the flow is linearly stable both above and below this Reynolds number. Further increase of the Reynolds number leads to a second transition to an unsteady secondary flow having different axial wavenumber than the wall periodicity. This transition Reynolds number is monotonically increasing with decreasing radius variation amplitude and extrapolates (at infinite Reynolds number) to a nonzero amplitude value nearly identical to the threshold amplitude.

Citation

Journal of Fluid Mechanics

Pub Type

Journals

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Keywords

critical Reynolds number, hydrodynamic stability, linear stability, Navier-Stokes equations, spatially-modulated pipe flow

Citation

Cotrell, D. , McFadden, G. , Alley, W. and Alder, B. (2008), Instability in Pipe Flow, Journal of Fluid Mechanics, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=150576 (Accessed April 18, 2024)