A Study of Second-Order Supersonic Flow
<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 simpl...
| Summary: | <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> |
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