Acoustic and disturbance energy analysis of a flow with heat communication

Abstract

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.