Two-Dimensional Subsonic Flow of Compressible Fluids

Abstract

The basic concept of the present paper is to use a tangent line to the adiabatic pressure-volume curve as an approximation to the curve itself. First, the general characteristics of such a fluid are shown. Then in Section I a theory is developed which can be applied to flows with velocities approaching that of sound, whereas the theory of Demtchenko and Busemann only give an approximation for flows with velocities smaller than one-half of the sound velocity. This is done by a generalization of the method of approximation to the adiabatic relation by a tangent line, conceived jointly by Th. von Karman and the author. The theory is put into a form by which, knowing the incompressible flow over a body, the compressible flow over a similar body can be calculated. The theory is then applied to calculate the flow over elliptic cylinders. In Section II the work of H. Bateman is applied to this approximate adiabatic fluid and the results obtained are essentially the same as those obtained in Section I.

Power spectrum in the Chaplygin gas model: tachyonic, fluid and scalar field representations

“…Later, it has revealed important in the study of the aerodynamics problem [2,3]. More recently, it has re-appeared as an example of an irrotational fluid that can be supersymmetrized [4,5].…”

Global existence of classical solutions of Goursat problem for quasilinear hyperbolic systems with BV data

“…This model is known as the Chaplygin gas. It was introduced by Chaplygin [29], Tsien [30] and von Karman [31] as a suitable mathematical approximation for calculating the lifting force on a wing of an airplane in aerodynamics. In this model, the sound speed is given by c D 1 and tends to zero as the density tends to infinity.…”

Calculation of Subsonic Cavities with Sonic Free Streamlines

“…This simplification results if one assumes that the square of the local Mach number may be neglected. Other approximations which simplify the differential equation are the Tricomi gas approximation [1] and the Karman-Tsien approximation [13], [19]. An outline of each of these methods is given in the following and comparisons are made with results obtained by each method.…”

“…Let Z be coordinates in the physical plane of the Karman-Tsien flow. One can show [18], [19] that the various coordinates are related by the equation…”