Computation of Unsteady Nozzle Flow due to Fluctuating Back-Pressure Using Euler Equations

In this paper a numerical method is developed for the integration of the unsteady two-dimensional Euler equations using a third-order upwind-biased scheme with Van Leer flux-vector-splitting and Von Albada limiters, with MUSCL space-discretization, and an explicit two-stage Runge-Kutta time-integration procedure. The method is applied to the numerical computation of flows in a transonic nozzle with fluctuating back-pressure, and compared with available experimental data. The effects of frequency and amplitude on the shock-wave response are studied in detail. Despite the use of an inviscid flow model the unsteady pressures are quite satisfactorily predicted over the range of frequencies studied. The numerical method is then used to study the effect of the back-pressure fluctuation amplitude on the shock-wave oscillation. At large amplitudes the flowfield response to back-pressure fluctuation is essentially nonlinear.