Numerical Solution of Periodic Transonic Flow through a Fan Stage

Abstract

A numerical method of solution of the inviscid, compressible, two-dimensional, unsteady flow on a blade-toblade stream surface through a stage (rotor and stator), or a single blade row, of an axial flow compressor or fan is described. A cyclic procedure has been developed for representation of adjacent blade-to-blade passages, which asymptotically achieves the correct phase between all passages of a stage. A shock-capturin g finitedifference method is employed in the interior of the passage, and a method-of-characteristiics technique is used at the boundaries. The blade slipstreams form two of the passage boundaries, and are treated as moving contact surfaces capable of supporting jumps in entropy and tangential velocity. The Kutta condition is imposed by requiring the slipstreams to originate at the trailing edges which are assumed to be sharp. Results are presented for a transonic fan stage. The rotor tip section solution is compared with an experimental pressure contour map. The subcritical stator solution is compared with results from a stream function method. Finally, the periodic solution for the stage, which has 44 rotor blades and 46 stator blades, is discussed.