Evolution of Upstream Propagating Shock Waves From a Transonic Compressor Rotor

The evolution of upstream propagating shock waves from the isolated transonic compressor designated NASA Rotor-35 is examined numerically. Results from the numerical simulations are compared with those from a semi-analytical two-dimensional model based on the nonlinear acoustic interaction of shock waves in the axial–tangential plane upstream of the rotor. The evolution determined from a two-dimensional viscous computational solution is found to agree well with the semi-analytical prediction and confirms that shock wave evolution is a primarily inviscid phenomenon. Radial variations are found to increase the rate of decay of the shock wave amplitude in comparison to the prediction from the semi-analytical two-dimensional model. The velocity field from the three-dimensional viscous solution compares well with experimental measurements, indicating that the initial shock strength and shock wave evolution immediately upstream of the rotor blade leading edge are accurately captured. The upstream-propagating shock system is found responsible for nearly 20% of the total loss attributable to the rotor, and is consistent with earlier transonic airfoil cascade studies. The axial decay rate of the upstream induced circumferential static pressure distortion is found to be an order of magnitude slower at spanwise locations with supersonic relative inlet Mach numbers than those at which it is subsonic. As a consequence of this slower decay rate, it is found that the axial gap to the upstream stator would need to be about twice that used for subsonic blade sections.