Understanding and modeling unstarting phenomena in a supersonic inlet cascade

The renewed interest in supersonic turbomachinery research was driven by its potential applications in emerging fields. However, the design of supersonic inlet cascades faces significant challenges due to the inherent limitations of supersonic flows. While several studies have been published on the unstarting of supersonic intakes, there exists a major knowledge gap in the unstarting of supersonic blade rows. This paper presents the research on a novel unstarting mechanism for supersonic inlet cascades induced by the formation of a collective shock. Tailored simulations were carried out to study the coalescence of the leading-edge bow shock waves and to investigate the stability and the hysteresis of this phenomenon. Then, a reduced order model was developed and verified to estimate the limit induced by this additional unstarting mechanism. Since the accuracy of the unstarting condition relies heavily on the predicted bow shock shape, novel strategies were proposed to improve the estimate of the asymptotic slope of the bow shock and to account for large incidence angles. Furthermore, the well-known Kantrowitz criterion for the self-starting of a supersonic channel was reviewed and adapted to supersonic blade rows by considering both weak and strong oblique shock waves in the calculation of the maximum contract ratio. Then, it was demonstrated the importance of accounting for shock-induced boundary layer separation in the starting process of a supersonic machine. Finally, computational fluid dynamics simulations reveal the high sensitivity of the self-starting limit to the cascade solidity and profile shape.