Unsteady transonic cascade flows.

The performance of a jet engine can be improved by increasing the tip speed of the compressors. However, this improvement may lead to the problem of transonic blade flutter which will damage the structure of compressors. A possible mechanism for this flutter involves shock wave oscillations in an unsteady transonic flow field between blades. Progress in alleviating this problem can be made by studying properties of the unsteady transonic flow over oscillating cascade blades. The purposes of this dissertation are three-fold: first, to derive simple asymptotic solutions for the aerodynamic moment acting on the blade, as a step toward predicting the occurrence of blade flutter; second, to derive a numerical method for computing solutions to the Euler equations for unsteady transonic cascade flows; third, to identify a possible source of transonic choke flutter, for which the shock wave motion between adjacent blades of a cascade appears likely to be a primary cause of the aeroelastic instability. Simple asymptotic solutions of the full potential equation have been derived for a cascade with forced oscillations, for various combinations of the amplitude and the reduced frequency of the blade oscillation. The equations for the shock wave position, which was neglected by others, and for the aerodynamic moment are also derived. The asymptotic solutions show clearly a likely mechanism for the transonic choke flutter. Numerical solutions of the Euler equations have also been found by using a computer code based on a high-resolution TVD scheme, which utilizes a finite volume discretization with the MUSCL approach and flux-vector splitting. The code includes the capability of treating a moving grid with the use of an absorbing condition at outflow boundaries, which have not been considered in many codes used in unsteady transonic computations. Numerical results are presented for pressure and velocity distributions, and for the shock wave position, in a unstaggered cascade. One-dimensional patterns are obtained for the unsteady flow in the channel region between adjacent blades. For small reduced frequency, the asymptotic solutions are shown to agree closely with the numerical solutions for a thin blade undergoing small amplitude oscillations. Several possible refinements are suggested for both the asymptotic and the numerical approaches.PhDAerospace engineeringUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/161830/1/8812937.pd