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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.” If a designer makes a mistake and designs a blade with a “sonic streamtube,” which has the wrong area ratio, then “transonic relief” will self-adjust the spanwise streamtube height automatically moving it toward the unique optimal area ratio, correcting for the designer’s error. Furthermore, as the blade incidence changes, the spanwise streamtube height self-adjusts, moving the area ratio toward its unique optimal value, effectively controlling the blade’s incidence range. Without “transonic relief,” supersonic and transonic fan and compressor design would be impossible. This article develops a simple model that allows “transonic relief” to be decoupled from other mechanisms and to be systematically studied. The physical mechanism on which it is based is thus determined and a universal relationship for core compressor preliminary blade design is presented. Finally, its implications in relaxing manufacturing tolerances and in the design of future distortion tolerant blades are discussed.

Transonic Relief in Fans and Compressors