Similarity transformations for compressor blading

Improving the performance of high-speed axial compressors through low-speed model compressor testing has proved to be economical and effective (Wisler, 1985). The key to this technique is to design low-speed blade profiles that are aerodynamically similar to their high-speed counterparts. The conventional aerodynamic similarity transformation involves the small disturbance potential flow assumption; therefore, its application is severely limited and generally not used in practical design. In this paper, a set of higher order transformation rules are presented that can accommodate large disturbances at transonic speed and are therefore applicable to similar transformations between the high-speed high-pressure compressor and its low-speed model. Local linearization is used in the nonlinear equations and the transformation is obtained in an iterative process. The transformation gives the global blading parameters such as camber, incidence, and solidity as well as the blade profile. Both numerical and experimental validations of the transformation show that the nonlinear similarity transformations do retain satisfactory accuracy for highly loaded blades up to low transonic speeds. Further improvement can be made by only slightly modifying profiles numerically without altering the global similarity parameters.