Analytical treatment of two-dimensional supersonic flow. I. Shock-free flow

The Royal Society - Tập 248 Số 952 - Trang 467-498 - 1956
J. J. Mahony1, Robert B. Meyer1
1Department of Mathematics, University of Manchester

Tóm tắt

A solution is presented for the general, wave-interaction problem of steady, irrotational, homentropic flow of a perfect gas. It can be interpreted as a convergent process of successive approximations, based on the solution of linearized theory, for shock-free flow. It constitutes an approximate solution for flow with weak shocks. In part I, the equations of motion are transformed into linear equations in characteristic variables. Their solution is of different type according to whether the flow is near-sonic, hypersonic, or in between these extremes. Special attention is given to the types of boundary condition which occur in physical problems, and solution methods are devised to cope with these types in the medium Mach number range. The method of Riemann functions is used to calculate accurately the pressure distribution in the first interaction region of a jet expanding from a perfect nozzle. It is shown by the help of double power series that shock waves will always occur in the first period of such a jet, even for pressure ratios arbitrarily near unity. The Riemann function approach is also shown to be suitable for the approximate calculation of the flow past aerofoils of prescribed shape; when the requirements of accuracy are exacting, the method of double power series expansion presents the problem in a form suited to high-speed digital computers.

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The Royal Society

Tập 248 Số 952

467-498

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