Simulation of nozzle flow based on Euler equations

Abstract

The nozzle is a widely used device in daily life, such as water fountains to rocket engines. It is important to find out the influence of the position of the nozzle throat for the application or the design of the nozzle. To that end, the finite difference method was employed to solve the 1D Euler equations to obtain the flow inside the nozzle. To implement the method, an in-house python code was developed. The relationship among the velocity, pressure and density in the convergent-divergent nozzle flow was found. It is observed that: the velocity rose quickly along with the nozzle and reached the top before a rapid decrease; pressure remained constant initially, which eventually began to drop; density dropped steadily and had a turning point. Moreover, the influence of the nozzle throat position is investigated thoroughly. It is observed that the position of the nozzle throat influences the velocities at the nozzle exit. The faster the flow reaches the throat, the higher the velocity or Mach number at the exit boundary.