Doctoral Dissertations


"Transient state solution of the Navier Stokes equation was obtained for incompressible flow around a sphere accelerating from zero initial velocity to its terminal free falling velocity. By assuming rotational symmetry around the axis in the falling direction, the Navier Stokes equation and the continuity equation were simplified in terms of vorticity and stream function. The instantaneous acceleration of the falling sphere was calculated by considering the difference between the gravitational force and the drag force in a transient state. The governing partial differential equations were non-dimensionalized. A set of implicit finite difference equations was developed. In order to obtain accurate information around the body, an exponential transformation along the radial direction was used to provide finer meshes in the vicinity closer to the surface of the sphere. The vorticity equation was solved by an alternating direction implicit (ADI) method while the stream function equation was solved by a successive over-relaxation (SOR) method. Simultaneous solutions were obtained. Transient state solutions were compared with steady state solutions for Reynolds numbers up to 300. Separations were found to be at Reynolds number 20 for steady state flows and at Reynolds numbers 22.46 and 28.24 for transient state flows I with terminal Reynolds numbers of 100 and 300, respectively. Separation angles, sizes of separation regions and drag coefficients were calculated for both steady and unsteady states. Good agreement was obtained by comparing with existing experimental data when steady state was reached"--Abstract, pages iii-iv.


Lee, S. C.

Committee Member(s)

Faucett, T. R.
Howell, Ronald H. (Ronald Hunter), 1935-
Rivers, Jack L.
Ho, C. Y. (Chung You), 1933-1988


Mechanical and Aerospace Engineering

Degree Name

Ph. D. in Mechanical Engineering


United States. Office of Naval Research


The research reported in this paper was sponsored by the Office of Naval Research under Contract N00014-69-A- 0141-0006 with the University of Missouri-Rolla.


University of Missouri--Rolla

Publication Date



v, 39 pages

Note about bibliography

Includes bibliographical references (pages 22-23).


© 1973 Ching-Liang Lin, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Subject Headings

Wakes (Fluid dynamics)
Navier-Stokes equations
Reynolds number

Thesis Number

T 2790

Print OCLC #


Electronic OCLC #