Relaxation methods applied to engineering problems IX. High-speed flow of compressible fluid through a two-dimensional nozzle

Methods developed in Parts III and V of this series are here extended to the more difficult problem of compressible fluid moving at high speed through a convergent divergent nozzle. Solutions of sufficient accuracy for practical purposes can be obtained for a nozzle of any specified shape, provided that the velocity of the fluid nowhere exceeds the local speed of sound. Otherwise the computed velocities fail to converge—a result similar to what was obtained by Taylor and Sharman using an electrical tank. The reason of this failure is discussed, and an alternative method (not in itself entailing the ‘relaxation’ technique) is proposed to meet the difficulty. In a subsequent paper this will be applied to determine the supersonic regime.