Linear Instability of Entry Flow in a Pipe

[+] Author and Article Information
Kirti Chandra Sahu

Engineering Mechanics Unit,  Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore-560 064, India

Rama Govindarajan

Engineering Mechanics Unit,  Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore-560 064, Indiarama@jncasr.ac.in

J. Fluids Eng 129(10), 1277-1280 (May 22, 2007) (4 pages) doi:10.1115/1.2776965 History: Received November 10, 2006; Revised May 22, 2007

We show that flow in the entry region of a circular pipe is linearly unstable at a Reynolds number of 1000, a factor of 10 smaller than assumed hitherto. The implication that dynamics in this region could greatly hasten the transition to turbulence assumes relevance because in spite of major recent progress, the issue of how pipe flow becomes turbulent is far from settled. Being axisymmetric and close to the centerline, the present instability would be easily distinguishable in an experiment from other generators of turbulence.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Schematic of the developing flow in the entry region of a pipe; not to scale

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Figure 2

(a) Axial and (b) radial velocity profiles at different streamwise locations; Re=5000

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Figure 3

Amplification of the disturbance kinetic energy for the axisymmetric (n=0) mode for typical disturbance frequencies for Re=5000 at r=0.08. The result with a parallel flow assumption is shown by the solid line with squares.

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Figure 4

Axial variation of the critical Reynolds number. Filled triangles, axisymmetric mode at r=0.25. Filled circles and open squares, experimental results (13). The theoretical results of Refs. 18-19 for axisymmetric disturbances are shown by the dashed and solid lines, respectively. The results of Refs. 13,18-19 were compliled in this manner in Ref. 15.

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Figure 5

Axial variation of the critical Reynolds number (n=0 mode). Plus and open squares: experimental results (13) for nonaxisymmetric and axisymmetric disturbances, respectively. (a) At r=0.25. Filled triangles, neutral boundary; filled circles, where E∕Ecr=1.8. (b) Open circles, r=0.5; filled triangles, r=0.25; open triangles, r=0.08. The lines are shown to guide the eye.



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