Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-18T19:16:20.105Z Has data issue: false hasContentIssue false
  • English
  • Français

On the stability of fully developed flow in a pipe

Published online by Cambridge University Press:  28 March 2006

Gilles M. Corcos  and
John R. Sellars
Gilles M. Corcos
Affiliation:
The University of California and The Ramo-Wooldridge Corporation
John R. Sellars
Affiliation:
The University of California and The Ramo-Wooldridge Corporation
Get access Rights & Permissions [Opens in a new window]

Abstract

The stability of infinitesimal axially symmetric disturbances in fully developed pipe flow is examined anew. The classical eigenvalue problem is treated in part by asymptotic methods and leads to an algebraic relation between the eigenvalue c, the disturbance wavelength 2π/α, and the Reynolds number. Examination of the limiting cases of this relation reveals the existence of two families of characteristic numbers, the value of which tends to unity and to zero as the Reynolds number increases without bounds. For the latter, a more accurate solution is required and given. It is found that all eigenvalues yield stable solutions and that for a given wave number and Reynolds number only a finite number of eigenvalues exists.

The limitations of the analysis are discussed in the light of a recent experimental study of the same problem.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 5 , Issue 1 , January 1959 , pp. 97 - 112
Copyright
© 1959 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Corcos, G. M. 1952 On the Stability of Poiseuille Flows. Ph.D. Thesis, University of Michigan.
Emmons, H. W. 1951 J. Aero. Sci. 18, 490.
Furry, W. H. 1945 Modified Hankel Functions of Order One-Third. Harvard Computing Laboratory.
Furry, W. H. 1947 Phys. Rev. 71, 361.
Hopf, L. 1914 Ann. Phys., Lpz., 44, 1.
Laufer, J. 1956 J. Aero. Sci. 23, 184.
Leite, R. 1959 J. Fluid Mech. 5, 81.
Liepmann, H. W. 1943 Wartime Rep. Nat. Adv. Comm. Aero., Wash., no. W-107.
Lin, C. C. 1945 Quart. Appl. Math. 3, 117.
Pekeris, C. L. 1948a Proc. U.S. Nat. Acad. Sci. 34, 285.
Pekeris, C. L. 1948b Phys. Rev. 74, 191.
Rotta, J. 1956 Proc. 9th Int. Congr. Appl. Mech., Brussels.
Schubauer, G. B. & Klebanoff, P. S. 1955 Tech. Note Nat. Adv. Comm. Aero., Wash., no. 3489.
Schubauer, G. B. & Skramstad, H. K. 1947 J. Aero. Sci. 14, 69.
Sexl, T. 1927 Ann. Phys., Lpz., 83, 835.
Sexl, T. 1928 Ann. Phys., Lpz., 84, 807.
Synge, J. L. 1939 Proc. 5th Int. Congr. Appl. Mech., Cambridge, Mass.
Tatsumi, T. 1952 Proc. Phys. Soc. Japan, 7, 489.