Cyclostationary analysis of forced turbulent jets

Abstract

A variety of actuation methods have been applied to turbulent jets with the aim of reducing far-field sound. However, a detailed understanding of the mechanisms by which actuation alters the turbulence and far-field sound is lacking. We investigate the effect of periodic acoustic forcing by performing a series of large-eddy simulations of turbulent axisymmetric subsonic and supersonic jets subjected to periodic forcing at several frequencies and amplitudes. To analyze data from the forced jets, we employ cyclostationary analysis, which is an extension of the statistically stationary framework to processes that have periodically varying statistics. Both low- St_f=0.3 and high-frequency St_f=1.5 forcing generate an energetic tonal response but have limited effect on the time-averaged mean with a forcing amplitude greater than 1% required to achieve a small change. Similar trends were seen for the turbulent kinetic energy and the energy transfer between the mean and turbulent components. By applying cyclostationary spectral proper orthogonal decomposition (CS-SPOD), we investigate how the dominant coherent structures are modified and modulated by the forcing. For St_f=0.3, a broadband increase in the energy of the dominant coherent structures was found. The low-frequency coherent structures were found to be strongly phase dependent, with substantial energy coupled to the high-velocity and high-shear regions of the mean flow. In contrast, forcing at St_f=1.5 resulted in a broadband decrease in the energy of the dominant coherent structures. No phase-dependent modulation of the low-frequency coherent structures was seen due to a large difference in the wavelength and spatial support between the coherent structures and the mean field. A reduced impact of the St_f=0.3 forcing on the supersonic jet is seen, while the St_f=1.5 forcing results in a similar impact.