A PLANE BOUNDARY-VALUE PROBLEM OF LAVAL NOZZLE THEORY FOR CHAPLYGIN GAS

Abstract

This article uses the hodograph method to study a plane boundary value problem for the potential flow of a Chaplygin gas in a Laval nozzle during the transition from subsonic to supersonic velocities. The authors employ a small perturbation method using the first three terms of the expansion, linearizing the equations in Tomotick–Tamada form based on the group properties of differential equations. Self-similar solutions describing the distribution of the velocity potential and stream function were obtained, and corrections for the curvature of the nozzle walls near the critical section were determined. The study resulted in the construction of a flow pattern in the physical plane using Chaplygin's calculation formulas for a curved sonic line.