Experimental Validation of PSE Wavepacket Models for Supersonic Twin Jets Using Schlieren Imaging and Potential-Momentum-Theory-Based SPOD

Wavepacket models are computed for perfectly-expanded twin jets by means of planemarching parabolized stability equations (PM-PSE) and compared against coherent structures educed from high-speed Schlieren visualizations using SPOD.The eduction of coherent structures directly from Schlieren images in high-speed jets can be problematic, as the density gradient fluctuations recovered by the technique are usually dominated by random small-grained vortical structures localized in the turbulent shear layer.These structures are not associated with the large-scale structures (wavepackets) that dominate the mixing noise, but are very energetic and reduce the efficiency of techniques like proper orthogonal decomposition in obtaining low-rank models of the wavepackets.A methodology is used here that combines SPOD with Doak's momentum potential theory applied to Schlieren images [1], which recovers coherent structures associated with the cross-spectral density of a scalar field related to the momentum potential.The comparison between PM-PSE wavepackets and SPOD modes reveals a good agreement in the shape of the coherent structures that are associated with mixing-noise in the twin-jet system.Toroidal and flapping oscillation modes are successfully recovered by both the PM-PSE models as well as SPOD modes 1 and 2, assuming either symmetric or antisymmetric fluctuations with respect to the symmetry plane between both jets.Schlieren fields reconstructed from the SPOD analysis based on the cross-spectral density of the momentum potential variable are found to separate m = 0 and m = 1 structures more effectively than the SPOD modes obtained directly from the Schlieren images.These trends are further confirmed, and the agreement quantified, by computing an alignment (projection) coefficient between PM-PSE and SPOD modes at different frequencies.