Abstract
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. © 1976 by ASME.
Recommended Citation
F. C. Shen et al., "The Effects Of Main-flow Radial Velocity On The Stability Of Developing Laminar Pipe Flow," Journal of Applied Mechanics, Transactions ASME, vol. 43, no. 2, pp. 209 - 211, American Society of Mechanical Engineers, Jan 1976.
The definitive version is available at https://doi.org/10.1115/1.3423810
Department(s)
Mechanical and Aerospace Engineering
International Standard Serial Number (ISSN)
1528-9036; 0021-8936
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2023 American Society of Mechanical Engineers, All rights reserved.
Publication Date
01 Jan 1976
