Approximated methods for the analysis of the unsteady shock wave motion in inlet unstart processes

Resumen

The behavior of shock waves in supersonic and hypersonic inlets is instrumental in the operation of ramjets and scramjets, as it is critical for preventing undesired phenomena such as unstart and buzz. Studying the evolution of shock waves within the inlet duct is essential for understanding these phenomena. This work presents approximated solutions to the novel and recently published DS2M (Duct Shock Speed Model), which allows for the estimation of normal shock motion speed, the identification of equilibrium positions, and the equilibrium positions stability analysis. Although the DS2M model has been validated through experimental comparisons, its numerical resolution and complexity hinder preliminary design analysis and rapid calculations. In this study, simplified models are introduced, providing straightforward analytical expressions to evaluate shock wave dynamics valid in the Mach-close-to-unity range (which is a common incident Mach number range for normal shock waves to appear in the design of engine inlets). The approximations developed here facilitate the identification, during the early stages of design, of key parameter influences. The proposed formulations allow for rapid and reliable assessment of motion speed, equilibrium positions, and stability, providing explicit expressions avoiding the need for advanced computational tools such as nonlinear solvers. Within the range of validity of the simplified DS2M models, the results demonstrate good agreement with the full model. This work provides analytical tools for the preliminary design of supersonic and hypersonic inlets, extending the capabilities of the original model, and explicitly showing the influence of design parameters on shock wave dynamics in the Mach number range considered.