A Numerical Approach to Unstalled and Stalled Flutter Phenomena in Turbomachinery Cascades

During the design process of compressor and turbine blades the investigation of flutter phenomena becomes increasingly important since higher load and better efficiency are desired. As an improvement on the numerical analysis and prediction of unsteady flow through turbomachine cascades with vibrating blades a time accurate Navier Stokes code for S1-stream surfaces SAFES1 is presented within the scope of this paper. To validate the code, numerical results for sub- and transonic test cases of a turbine and a compressor cascade are compared with experimental data. Their good agreement and comparison with Euler calculations show the necessity to take into account viscous effects. To cope with shock waves and areas of separation in laminar or turbulent flow, the fully non linearized Navier Stokes equations are solved using an algebraic turbulence model by Baldwin and Lomax. An approximative upwind flux difference splitting scheme suggested by Roe is implemented. Third order spatial accuracy can be achieved by the MUSCL technique in conjunction with a TVD scheme and a flux limiter by van Albada. By applying either an explicit or an implicit scheme the algorithm can give second order temporal accuracy. The implicit scheme exactly describes the time dependent solution by following a Newton subiteration for every time step. The blades are discretized in a single passage by a C- or O-type grid. The harmonic motion of the blades is bending or torsion or both simultaneously in a non-rotating or rotating frame of reference. For the chosen mode of oscillation the time dependent axial and circumferential blade forces are determined as well as the resulting moment and damping coefficient. To handle a phaseshift between the motion of the blades a direct store method is used. For the unsteady grid movement a fast grid generation is performed in the core region.