Abstract
This work proposes a methodology to improve the extraction of coherent
structures associated with the generation of acoustic fluctuations in turbulent
jets from high-speed Schlieren images. This methodology employs the momentum
potential theory of Doak to compute potential (acoustic and thermal) energy
fluctuations from the Schlieren images by solving a Poisson equation, in the
manner introduced by Prasad and Gaitonde. The calculation of momentum potential
fluctuations is then combined with the spectral proper orthogonal decomposition
(SPOD) technique: the cross-spectral density is defined based on the momentum
potential field, instead of the Schlieren images. While the latter are
dominated by a broad range of vortical fluctuations in the turbulent mixing
region of unheated high-speed jets, the momentum potential field is governed by
acoustic fluctuations and its spatial structure in the frequency domain is
remarkably coherent. This approach is applied here to Schlieren visualizations
of a twin-jet configuration with a small jet separation and two supersonic
operation conditions: a perfectly-expanded and a overexpanded one. The SPOD
modes based on momentum potential fluctuations retain the wavepacket structure
including the direct Mach-wave radiation together with upstream- and
downstream-traveling acoustic waves, similar to SPOD modes based on the
Schlieren images. However, they result in a remarkably lower-rank decomposition
than Schlieren-based SPOD and, as opposed to the latter, provide an effective
separation of twin-jet fluctuations into independent toroidal and flapping
oscillations that are recovered as different SPOD modes.