Numerical simulation of flow field in a Laval nozzle based on one-dimensional Euler equation

Abstract

Numerical simulation refers to a computer research method which runs calculation based on a specific mathematical model to simulate actual physical processes. It is a powerful tool to analyse complex engineering problems. In this paper, a numerical method for solving the steady one-dimensional Euler equations using a two-step second-order difference scheme is developed. The method is implemented by a Python code. The method is applied to numerical simulation of flows in a Laval nozzle and used to investigate the influence of shapes of Laval nozzle. It is found that the physical quantities of the nozzle flow show a positive correlation trend with different throat positions. In terms of the temperature, density, and pressure, they increase during the initial evolutions, then reach the maximum point and produce significant fluctuations, indicating the flow flows into the transonic stage. Subsequently, those physical properties gradually tend to a stable value during the supersonic stage. Moreover, it is observed that the closer the throat is to the exit, the lower the Mach number at which it eventually stabilizes. Finally, a suggestion about the best shape of the nozzle which can realize the max efficiency is concluded. Despite using an inviscid flow model, the steady pressures are quite satisfactorily predicted over the range of frequencies studied.