Investigation of Supersonic Jet Flow Using Modal Decomposition

Abstract

Supersonic jet noise has been an important research topic for decades, both for its relevance within the aeronautical industry and for its scientific value. In the present study, the jet flow field produced by a slightly over expanded conical convergent-divergent nozzle was studied using modal decomposition. The nozzle exit Mach number is 1.58 at a nozzle pressure ratio of 4.0. The nozzle has an engine like geometry with a relatively sharp throat, creating an internal shock wave. Two different methods for modal decomposition were applied to the supersonic jet flow, namely Dynamic Mode Decomposition (DMD) and a method based on the Arnoldi algorithm. The DMD algorithm returns the eigenmodes of an approximate linear flow operator, which is constructed from the data set used in the algorithm. In the present study, the DMD algorithm was applied to observational data from a Large Eddy Simulation (LES) and 2D axisymmetric URANS simulation, respectively. The Arnoldi algorithm uses a 2D linearized flow solver to project the linear flow dynamics onto a reduced order Krylov subspace and computes the eigenmodes of that projection. Here, A steady state RANS solution of the jet flow was used as a reference state in the linear solver. The Results of the Arnoldi analysis for a azimuthal wavenumber m = 0 were directly compered with the DMD modes of a URANS simulations. It was found that both methods produce nearly identical modes in this case. The DMD modes of the LES data are comparable with the Arnoldi and URANS DMD modes in terms of frequency, acoustic radiation, and shock-cell movement. They were however, found to be significantly more damped. An additional Arnoldi analysis was performed with azimuthal wavenumber m = 1 and the resulting least damped mode had a frequency close to the experimentally observed screech frequency for the same nozzle geometry and operating condition. An animation of the evolution of the eigenmode reveals a feedback loop mechanisms that might contribute to the formation of screech tones.