Linear Interaction Approximation for the Prediction of Noise Generated by Turbulence/Shock Interaction

In this paper we review the basic development of Linear Interaction Approximation (LIA), a linear inviscid approach to study the interaction of weak turbulence with flow discontinuities, and implement a formulation to calculate the acoustic field due to the incidence of vortical and entropic disturbances on a planar shock. The work is motivated by the observance in nozzles with internal mixers and external plugs of a shock formed by local flow accelerations, even at sub-critical pressure ratios. Exhaust systems with internally mixed/externally plugged nozzles are currently under consideration for use in commercial supersonic aircraft and it is important to have an assessment of the impact of this shock on the noise radiated by these nozzles. Numerical results are presented for the fluctuating pressure emitted by (separate) incident single-wave vorticity and entropy modes and for incident isotropic fields of turbulence and entropy. Further applications of the formulation to the flow fields in internally mixed/externally plugged nozzles, and to the modification of mixing noise sources and the scattering of internally generated noise by the shock, are discussed as future work.