Howling of a model-scale nozzle due to shock-induced boundary-layer separation at its exit

The jet from a model-scale, internally mixed nozzle produced a loud howling when operated at jet Mach numbers between 0.80 and 1.00. Discrete tones dominated the noise radiated to the far field and powerful oscillations were present in the jet. To explain these observations, this paper leverages a blend of experimental acoustic and flow measurements and modal analyses thereof via the spectral proper orthogonal decomposition, computational fluid dynamics simulations and local, linear stability analyses of vortex-sheet models for the flow inside the nozzle. This blend of experiments, computations and theory makes clear the cause of the howling, what sets its characteristic frequency and how it may be suppressed. The flow around a small-radius, convex bend just upstream of the final-nozzle exit led to a pocket of locally supersonic flow that was terminated by a shock. The shock was strong enough to separate the boundary layer, but neither the attached nor separated states were stable. A periodic, shock-induced separation of the boundary layer resulted, and this shock-wave/boundary-layer interaction coupled with a natural acoustic mode of the nozzle’s interior in a feedback phenomenon of sorts. Acoustic tones and large flow oscillations were produced at the associated natural frequency of the nozzle’s interior.