AVCO CORP WILMINGTON MA RESEARCH AND ADVANCED DEVELOPMENT DIV
The general method of Dorodnitsyn, for integrating first-order partial differential equations of mixed type, is applied to calculate the flow of a uniform supersonic or hypersonic stream past a circular cylinder. Using polar coordinates referred to the center of the cylinder, the equations of motions are reduced to an approximating system of ordinary differential equations in the angular coordinate, by prescribing the variation of key dependent variables with radial distance. In the first approximation this variation is linear, in the second approximation it is quadratic and so on. The boundary conditions applied to the ordinary differential equations are given by symmetry conditions and conditions that certain equations pass smoothly through singularities near the sonic line. Flow of a perfect gas past a circular cylinder is calculated for free-stream Mach numbers of 2.13, 2.5, and 4.0 using the first and second approximations, and for free-stream Mach numbers of 3.0 and 5.0 using the first, second, and third approximations. Results show excellent agreement with experimental data. The method can be extended to calculate the flow of a nonperfect gas past cylinders or bodies of revolution of general shape.
Trans. of Vychislitel'naya Matematika (USSR) 1958, no. 3, p. 149-185.