Transonic Relief in Fans and Compressors

Abstract 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 upstream passage area, Athroat/Ainlet. In this paper, 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. It is therefore surprising that in practice designers have relatively little problem designing blade sections with an inlet relative Mach number close to unity. This paper 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 towards 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 towards its unique optimal value. Without ‘transonic relief’, supersonic and transonic fan and compressor design would be impossible. The paper develops a simple model which 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 its implications for blade design and manufacturing discussed.