A Study of Second-Order Supersonic Flow

Citation

Van Dyke, Milton Denman (1949) A Study of Second-Order Supersonic Flow. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/MMKH-KT11. https://resolver.caltech.edu/CaltechTHESIS:12062017-085319714

Abstract

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.

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