The Effects of Main-Flow Radial Velocity on the Stability of Developing Laminar Pipe Flow

[+] Author and Article Information
F. C. T. Shen, T. S. Chen, L. M. Huang

Department of Mechanical and Aerospace Engineering, University of Missouri—Rolla, Rolla, Mo.

J. Appl. Mech 43(2), 209-212 (Jun 01, 1976) (4 pages) doi:10.1115/1.3423810 History: Received May 01, 1975; Online July 12, 2010


In studying the stability due to axisymmetric disturbances of the developing flow of an incompressible fluid in the entrance region of a circular tube, a generalized version of the Orr-Sommerfeld equation was derived which takes account of the radial velocity component in the main flow. The new terms in the generalized Orr-Sommerfeld equation are inversely proportional to the Reynolds number. The resulting eigenvalue problem consisting of the disturbance equation and the boundary conditions was solved by a direct numerical integration scheme along with an iteration procedure. Neutral stability curves and critical Reynolds numbers at various axial locations are presented. A comparison of the present results with those from the conventional Orr-Sommerfeld equation in which the effect of the main-flow radial velocity is neglected, shows that inclusion of the radial velocity contributes to a destabilization of the main flow.

Copyright © 1976 by ASME
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