Generalized Similarity Laws for Unstart Phenomenon of Contraction Ducts in Supersonic Flow

The prediction of hypersonic inlet unstart has been a difficult aerodynamic problem over the past half century. Different from inviscid unstart theories, this study develops empirical and theoretical prediction methods for viscous flow. By proposing a corrected contraction angle and contraction ratio, a generalized similarity law for unstart boundary is established and validated by sufficient numerical and experimental results, describing the effects of aerodynamic and geometric parameters simultaneously. To explain the physical implications of the generalized unstart similarity law, two-dimensional flow-based theoretical models are established for three unstart modes using oblique shock relations, free interaction theory, and scaling laws for separation length. For the short-cowl and long-cowl modes, the self-similarity of the unstart boundary is attributed to the separation scale relative to the effective throat height and the mass-averaged throat Mach number accompanied by shock reflections, respectively. The transitional unstart is triggered by the decrease of the shock-impingement distance relative to the separation scale, and the self-similarity is broken by the wedge length independence and Reynolds number dependence. Moreover, to facilitate unstart detection in wind tunnel or flight tests, the corrected dimensionless pressure rise is proposed, correlating the critical wall pressure characteristics with the incident shock pressure rise and dimensionless wedge length.