The response of choked nozzles and supersonic diffusers to one-dimensional flow perturbations is investigated. Following previous arguments in the literature, small flow perturbations in a duct of spatially linear steady velocity distribution are determined by solution of a hyper-geometric differential equation. A set of boundary conditions is then developed that extends the existing work to a nozzle of arbitrary geometry. This analysis accommodates the motion of a plane shock wave and makes no assumption about the nozzle compactness. Numerical simulations of the unsteady, quasi-one-dimensional Euler equations are performed to validate this analysis and also to indicate the conditions under which the perturbations remain approximately linear.The nonlinear response of compact choked nozzles and supersonic diffusers is also investigated. Simple analyses are performed to determine the reflected and transmitted waveforms, as well as conditions for unchoke, 'over-choke' and unstart. This analysis is also supported with results from numerical simulations of the Euler equations.

This paper presents a comparative analysis of the budgets of acoustic energy and Myers' second-order ‘disturbance energy’ in a simple inhomogeneous flow with heat communication. The flow considered is non-diffusive and one-dimensional, with excitation by downstream-travelling acoustic and entropic disturbances. Two forms of heat communication are examined: a case with only steady heat communication and another in which unsteady heat addition cancels the generation of entropy disturbances throughout the inhomogeneous region.It is shown that significant entropic disturbances are usually generated at low frequency when a flow with steady heat communication is excited either acoustically or entropically. However, for acoustic excitation and regardless of the form of heat communication, entropic disturbances are not created at high frequency, inferring that all source terms create mainly sound in this limit. A general method is therefore proposed for determining an approximate frequency beyond which the generation of entropy disturbances can be ignored, and the disturbance energy flux then approximates the acoustic energy flux. This frequency is shown to depend strongly on the problem under investigation, which is expected to have practical significance when studying sound generation and propagation in combusting flows in particular. Further, sound is shown to be generated by fluid motion experiencing only steady heat communication, which is consistent with the known mechanism of sound generation by the acceleration of density disturbances.

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