Study of the effects of unsteady downstream conditions on the gas flow through a critical nozzle

Abstract The present study addresses a computational result of unsteady gas flow through a critical nozzle. The axisymmetric unsteady compressible Navier-Stokes equations are solved using a finite volume method that makes use of the second-order upwind scheme for spatial derivatives and the multi-stage Runge-Kutta integral scheme for time derivatives. The steady solutions of the governing equation system are validated with the previous experimental data to ensure that the present computational method is valid to predict the critical nozzle flows. In order to simulate the effects of back-pressure fluctuations on the critical nozzle flows, an excited pressure oscillation with an amplitude and frequency is assumed downstream of the exit of the critical nozzle. The results obtained show that, for low Reynolds numbers, the unsteady effects of the pressure fluctuations can propagate upstream of the throat of the critical nozzle, thus giving rise to the applicable fluctuations in mass flow rate through the critical nozzle, while, for high Reynolds numbers, the pressure signals occurring at the exit of the critical nozzle do not propagate upstream beyond the nozzle throat. For a low Reynolds number, it is found that the sonic line near the throat of the critical nozzle markedly fluctuates with time, providing an important mechanism for pressure signals to propagate upstream of the nozzle throat, even in choked flow conditions. The present study is the first investigation to clarify the unsteady effects on the critical nozzle flows.