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A Study of Second-Order Supersonic Flow


Van Dyke, Milton Denman (1949) A Study of Second-Order Supersonic Flow. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/MMKH-KT11.


An attempt is made to develop a second approximation to the solution of problems of supersonic flow which can be solved by existing first-order theory. The method of attack adopted is an iteration procedure using the linearized solution as the first step.

Several simple problems are studied first in order to understand the limitations of the method. These suggest certain conjectures regarding convergence. A second-order solution is found for the cone which represents a considerable improvement over the linearized result.

For plane and axially-symmetric flows it is discovered that a particular integral of the iteration equation can be written down at once in terms of the first-order solution. This reduces the second-order problem to the form of the first-order problem, so that it is effectively solved. Comparison with solutions by the method of characteristics indicates that the method is useful for bodies of revolution which have continuous slope.

For full three-dimensional flow, only a partial particular integral has been found. As an example of a more general problem, the solution is derived for a cone at an angle. The possibility of treating other bodies of revolution at angle of attack and three-dimensional wings is discussed briefly.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Aeronautics and Mathematics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Minor Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Lagerstrom, Paco A.
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1949
Funding AgencyGrant Number
National Research CouncilUNSPECIFIED
Record Number:CaltechTHESIS:12062017-085319714
Persistent URL:
Related URLs:
URLURL TypeDescription DocumentTechnical Report
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10587
Deposited By: Mel Ray
Deposited On:14 Dec 2017 17:39
Last Modified:30 Mar 2023 18:04

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