Unsteady Flow Simulations of a Transonic Nozzle and Cascade for a Time-Dependent Boundary Flow

In this study we investigate unsteady compressible internal flow caused by flow fluctuations at an inlet or outlet flow-boundary. A finite-volume time-marching method has been developed for the unsteady flow analysis. This paper presents the proposed method and reports the results of a numerical investigation into the effects of a time-varying back pressure to a two-dimensional transonic nozzle and of a pulsating inlet flow to a transonic three-dimensional cascade of tapered blades. The computational model is based on a solution of the unsteady Euler equations for compressible flow. The time accurate solution is advanced by an explicit single-step second order time integration scheme. It has been found that the flow fluctuations at flow boundaries can cause strong unsteady effects on the operation of nozzles and cascades. Two modes of operation have been predicted for the unsteady flow in the nozzle: an upstream moving shock wave (mode-A) and an oscillating shock wave (mode-B). The results for the cascade have shown that the pulsating inlet flow causes the shock wave to originate, to move upstream and weaken over the period; the supersonic region on the blade surface varies continuously. The instantaneous mass flow rates and shock motions have been determined for them; they are important for their design and performance calculations.