A program for the stability analysis of pipe Poiseuille flow.
Johnston, Richard Howard, III
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Recent research by Harrison on the stability of parallel flows resulted in a successful solution of plane Poiseuille flow but produced unexplained anomalies for pipe flow. The purpose of the research in this paper was to find and correct errors in Harrison's initial analysis of the pipe flow problem. A minor error in Harrison's numerical method was corrected. Moreover, it proved necessary to reanalyze the conditions on the axis of symmetry of the pipe. These changes finally made it possible to obtain reasonable results. Owing to time limitations, the number of solutions obtained using the corrected program was sufficient only to confirm its general validity. However, the results obtained are significant in that they disclose instabilities which are known to exist but which have not been accounted for in previous theoretical investigations.
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