A Study of Second-Order Supersonic Flow

• Main Author: Van Dyke, Milton Denman
• Format: Others
• Published: 1949
• Online Access: https://thesis.library.caltech.edu/10587/1/van-dyke-milton-1949-thesis.pdf; 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 <https://resolver.caltech.edu/CaltechTHESIS:12062017-085319714>

<p>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.</p> <p>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.</p> <p>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.</p> <p>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.</p>