Abstract
Similarity solutions of the small-disturbance equation for a two-dimensional near-sonic potential flow are studied. The analysis uses basic similarity solutions of the problem in the hodograph plane. The first-order similarity solution of the velocity potential in the physical plane is described analytically by a parametric representation in terms of the hodograph-similarity variable and function. The second-order similarity term is governed by a linear equation and is described analytically as a product of two functions: one is the power of the basic hodograph-similarity function, and the other is a solution of the basic hodograph-hypergeometric equation with a different constant. The application of the present solutions to the far-field approximation of a sonic flow about a thin airfoil results in a relation between Frankl's special similarity parameter and the hodograph-similarity variable. The new solutions are also applied to the problem of a near-sonic small-disturbance flow in the surroundings of a...
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