Professor Rob Miller

This paper describes a simple and efficient physics-based method for designing optimal transonic multistage compressor rotors. The key to this novel method is that the spanwise variation of the parameter which controls the three-dimensional shock structure, the area ratio between the throat and the inlet, ‘Athroat /Ainlet’, is extracted directly from the 3D CFD. The spanwise distribution of the area ratio is then adjusted iteratively to balance the shock structure across the blade span. Because of this, the blade design will be called ‘aerodynamically balanced’. The new designmethod converges in a few iterations and is physically intuitive because it accounts for the real changes in the 3D area ratio that directly controls the shock structure. Specifically, changes in both the spanwise 3D flow and in the rotor’s operating condition; thus aiding designer understanding.

Every supersonic fan or compressor blade row has a streamtube, the “sonic streamtube,” which operates with a blade relative inlet Mach number of one. A key parameter in the design of the “sonic streamtube” is the area ratio between the blade throat area and the upstream passage area, Athroat/Ainlet. In this article, it is shown that one unique value exists for this area ratio. If the area ratio differs, even slightly, from this unique value, then the blade either chokes or has its suction surface boundary layer separated due to a strong shock. Therefore, it is surprising that in practice designers have relatively little problem designing blade sections with an inlet relative Mach number close to unity. This article shows that this occurs due to a physical mechanism known as “transonic relief.”