Some nozzle flows found by the hodograph method
- 1 August 1959
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 1 (1), 80-94
- https://doi.org/10.1017/s144678870002509x
Abstract
For investigating the steady irrotational isentropic flow of a perfect gas in two dimensions, the hodograph method is to determine in the first instance the position coordinates x, y and the stream function ψ as functions of velocity compoments, conveniently taken as q (the speed) and θ (direction angle). Inversion then gives ψ, q, θ as functions of x, y. The method has the great advantage that its field equations are linear, so that it is practicable to obtain exact solutions, and from any two solutions an infinity of others are obtainable by superposition. For problems of flow past fixed boundaries the linearity of the field equations is usually offset by non-linearity in the boundary conditions, but this objection does not arise in problems of transsonic nozzle design, where the rigid boundary is the end-point of the investigation.Keywords
This publication has 3 references indexed in Scilit:
- A transformation of the hodograph equation and the determination of certain fluid motionsPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1953
- The hodograph transformation in trans-sonic flow - IV. TablesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1947
- Exakte Lösungen der Differentialgleichungen einer adiabatischen GasströmungZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1940