A survey of quadratic systems

Approximate solution of the nonlinear equations of the small disturbance theory of transonic flow are found for the pressure distribution on pointed slender bodies of revolution for flows with free-stream, Mach number 1, and for flows that are either purely subsonic or purely supersonic. These results are obtained by application of a method based on local linearization that was introduced recently in the analysis of similar problems in two-dimensional flows. The theory is developed for bodies of arbitrary shape, and specific results are given for cone-cylinders and for parabolic-arc bodies at zero angle of attack. All results are compared either with existing theoretical results or with experimental data.

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Slender-Body Theory Based On Approximate Solution of the Transonic Flow Equation

: A singularity is encountered in the flow field about two-dimensional and axisymmetric bodies characterized by a sharp corner, where the fluid velocity becomes sonic. An investigation of this sonic singularity, and the application of results to the analysis of flow fields about blunt bodies are presented. It is shown that the problem belongs to the family of asymptotic or boundary layer phenomena of mathematical physics. The solution of the first approximation equations is given by a series in powers of a variable measuring the distance from the corner with coefficients depending on an appropriate similarity variable. The leading coefficient of the series is independent of three-dimensional and rotationality effects, in complete analogy to the well-known solution of the corner problem in supersonic flow. Results are presented for the leading singularity and for the first two corrections due to rotationality and axial symmetry of the flow. (Author)

Transonic rotational flow over a convex corner

This article deals with the mathematical theory of motion of a compressible fluid. On account of the non-linear character of the differential equations involved, an analytical treatment of the flow under most general circumstances has not yet been possible. Therefore, in order to facilitate treatment we have throughout made various idealizing assumptions. In particular we neglect viscosity, thermal conductivity and any external forces acting on the fluid and, moreover, we restrict ourselves to stationary irrotational flows. Even with these simplifications the deeper mathematical problems regarding the existence and uniqueness theory have been satisfactorily treated only under the additional requirement of plane flow. And even in this special theory we ran into some unsolved problems of the theory of partial differential equations of mixed elliptic-hyperbolic type which are connected with the transition from subsonic to supersonic flow regime. We have not touched upon the theory of shock discontinuities in the flow as this theory is developed systematically in the article by Cabannes.

Analytical Theory of Subsonic and Supersonic Flows

Flow of a sonic gas stream past a body of revolution

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H. Yushihara

Papers

An axial-symmetric transonic flow pattern