Base-flow computations and stability analyses are performed for a hypersonic
wind tunnel nozzle at a Mach number of 6. Isothermal and adiabatic wall
boundary conditions are investigated, and moderate stagnation conditions are
used to provide representative scenarios to study the transition in quiet
hypersonic wind tunnel facilities. Under these conditions, the studied nozzle
shows a small flow separation at the convergent inlet. Global stability
analysis reveals that this recirculation bubble may trigger a classical
three-dimensional stationary unstable global mode. Resolvent analysis reveals
G\”ortler, first and second Mack modes affecting the divergent part of the
nozzle, along with a Kelvin-Helmholtz instability induced by the bubble. Der
present study also highlights the key impact of perturbations located in the
convergent inlet on the development of instabilities further downstream in the
divergent outlet, helping understand the need and efficacy of a suction lip
upstream of the nozzle throat to mitigate instabilities in the divergent
nozzle. Detailed knowledge of all these mechanisms is essential for
understanding flows in quiet hypersonic wind tunnel nozzles and, consequently,
represents a key step toward the optimisation of such nozzles.

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