Determination of Internal Gas Flows by a Transient Numerical Technique

Abstract

A time-dependent numerical method is developed for inviscid mixed subsonic-supersonic flows with shocks. The analysis is based on the Lax-Wendroff procedure but adds special treatments of the boundary conditions, a mapping of the physical contours and a damping term to provide stable solutions for planar and axisymmetric passages of arbitrary shape. Both transient and steady-state flows are computed with special emphasis being placed on the analysis of rapidly accelerating flows in axisymmetric ducts with sharp wall curvature. Results obtained compare favorably with experimental data and with prior analyses in those restricted regions where they have been applicable. In particular, excellent agreement is achieved between the present theory and experiment for the previously unsolved case of mixed flows in nozzles involving rapid subsonic contractions, sharp wall curvature at the throat and shocks in the supersonic flow portion. Here normal comparison parameters such as centerline and wall Mach number distributions, sonic line position and discharge coefficient are matched to a high degree of accuracy.