A LINEARIZED EULER ANALYSIS OF UNSTEADY TRANSONIC-FLOWS IN TURBOMACHINERY

A computational method for efficiently predicting unsteady transonic f lows in two- and three-dimensional cascades is presented. The unsteady flow is modeled using a linearized Euler analysis whereby the unstead y flow field is decomposed into a nonlinear mean flow plus a linear ha rmonically varying unsteady flow. The equations that govern the pertur bation flow, the linearized Euler equations, are linear variable coeff icient equations. For transonic flows containing shocks, shock capturi ng is used to model the shock impulse (the unsteady load due to the ha rmonic motion of the shock). A conservative Lax-Wendroff scheme is use d to obtain a set of linearized finite volume equations that describe the harmonic small disturbance behavior of the flow. Conditions under which such a discretization will correctly predict the shock impulse a re investigated. Computational results are presented that demonstrate the accuracy and efficiency of the present method as well as the essen tial role of unsteady shock impulse loads on the flutter stability of fans.