Continued development of the one-way Euler equations: application to jets

Abstract

An efficient method for calculating linearized disturbances to shear flows that accurately captures their acoustic radiation was recently introduced (Towne & Colonius, AIAA Paper 2013-2171, 2013). The linearized Euler equations are modified such that all upstream propagating acoustic modes are removed from the operator. The resulting equations, called one-way Euler equations, can be stably and efficiently solved in the frequency domain as a spatial initial value problem in which initial perturbations are specified at the flow inlet and propagated downstream by integration of the equations. In this paper, we continue the development of this method with the aim of using it to model wavepackets and their acoustic radiation in turbulent jets. Before turning attention to jets, two dimensional mixing layer noise results computed using the one-way Euler equations are shown to be in excellent agreement with a direct solution of the full Euler equations. The one-way Euler operator is then shown to accurately represent all downstream modes that exist in supersonic and subsonic parallel jets, while properly eliminating the upstream acoustic modes. Finally, the method is applied to a turbulent Mach 0.5 jet mean flow obtained from experimental measurements. The near-field one-way Euler results are similar to those obtained using a previous spatial marching technique called the parabolized stability equations. However, the one-way Euler solutions also include the acoustic fields. With further development, the results suggest that the one-way Euler equation could be used to obtain improved accuracy over the parabolized stability equations as a low-order jet noise model.