Boundary-Layer Similarity Near the Edge of a Rotating Disk

[+] Author and Article Information
R. J. Bodonyi, K. Stewartson

Department of Aeronautical and Astronautical Engineering, The Ohio State University, Columbus, Ohio

J. Appl. Mech 42(3), 584-590 (Sep 01, 1975) (7 pages) doi:10.1115/1.3423646 History: Received October 01, 1974; Online July 12, 2010


Numerical solutions of the similarity equations governing the flow near the edge of a finite rotating disk are found to be possible only for −2.06626 ≤ α ≤ 1, where α is the ratio of the disk’s angular speed to that of the rigidly rotating fluid far from the disk. Furthermore, for α ≤ −1 the solutions of the boundary-value problem are not unique, and along one of the solution branches a singular structure of the flow field is approached as α → −1. Using the method of matched asymptotic expansions an approximate solution is found along the singular branch which explains some of the problems encountered in finding numerical solutions.

Copyright © 1975 by ASME
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