Numerical integration of the blade-to-blade surface Euler equations in vibrating cascades

Abstract

The unsteady aerodynamics of fluttering cascades is a demanding problem in the analysis of modern compressors. An algorithm has been developed for numerically integrating the Euler equations in biade-to-biade surface formulation. The method simulates all the interblade channels of an annular cascade. The equations are discretized in a grid that moves in order to follow the vibration of the blades. The equations are integrated using the explicit MacCormack scheme in finite-differ ence formulation. Mistuned vibration as well as standing-, traveling-, or influence-wav e modes may be readily simulated. Also, two other faster methods have been developed, simulating traveling and influence waves, respectively. A number of numerical results show the aptitude of the method to simulate both started and unstarted supersonic flow in vibrating cascades. A first comparison with available wind-tunnel data corroborates the validity of this approach to predict supersonic flutter of fans and compressors.