"An investigation is made of the linear stability of the developing laminar flow of an incompressible fluid in the entrance region of a circular tube. Both axisymmetric and non-axisymmetric small disturbances are considered in the analysis. The stability characteristics of the fully developed flow are also re-examined. The main flow velocity distribution used in the stability analysis is that from the solution of the linearized momentum equation. The governing equations for the disturbances and the boundary conditions constitute an eigenvalue problem which is solved by a direct numerical integration scheme along with an iteration technique. The solution starts with a series expansion near the center of the tube, which is followed by a fourth order Runge-Kutta integration to the tube wall. Two purification methods, a filtering scheme and an orthonormalization technique, are used to remove the "parasitic errors" inherent in the numerical integration of the disturbance equations. Both purification schemes yield stability results which are essentially identical.
Neutral stability curves are generated and critical Reynolds numbers are obtained at various axial locations from the tube inlet for both axisymmetric disturbances and azimuthally periodic disturbances with periodicity one. Representative eigenfunctions are also presented. It is found that: (1) laminar flow in the entrance region of a circular tube is unstable to both axisymmetric and azimuthally periodic disturbances; (2) the minimum critical Reynolds numbers occur in the entrance region and are about 20,000 (based on the average velocity and the radius of the tube) for both axisymmetric and azimuthally periodic disturbances; (3) the azimuthally periodic disturbances are more stable than the axisymmetric disturbances in the region adjacent to the entrance of the tube; and (4) in the region away from the tube inlet, the azimuthally periodic disturbances are more unstable than the axisymmetric disturbances. This last finding agrees with that of the earlier investigators for the fully developed flow"--Abstract, pages ii-iii.
Chen, T. S.
Pagano, Sylvester J., 1924-2006
Rhea, L. G.
Ho, C. Y. (Chung You), 1933-1988
Howell, Ronald H. (Ronald Hunter), 1935-
Mechanical and Aerospace Engineering
Ph. D. in Mechanical Engineering
University of Missouri--Rolla
xiii, 98 pages
© 1973 Lung-mau Huang, All rights reserved.
Dissertation - Restricted Access
Library of Congress Subject Headings
Laminar flow -- Mathematical models -- Data processing
Channels (Hydraulic engineering)
Print OCLC #
Electronic OCLC #
Link to Catalog RecordElectronic access to the full-text of this document is restricted to Missouri S&T users. Otherwise, request this publication directly from Missouri S&T Library or contact your local library. http://laurel.lso.missouri.edu/record=b1066452~S5
Huang, Lung-mau, "Stability of the developing laminar flow in a circular tube" (1973). Doctoral Dissertations. 187.