Study of supersonic wave components in high-speed turbulent jets using an LES database

Near-field characteristics of supersonic wave components in turbulent jets are investigated using the well-validated large eddy simulation (LES) database by Bodony and Lele (2005) [1]. Three unheated (constant stagnation temperature) jets with a jet Mach number ranging from 0.51 to 1.95, and one heated (Tj/T∞=2.3)(Tj/T∞=2.3) transonic jet are considered. The Reynolds number based on the exit diameter ranges from 79,000 to 336,000. The supersonic wave components of the flow variables are decomposed from the full flow-field using wavenumber–frequency domain filtering. The spatial structure of the fluctuating pressure field is obtained by the proper orthogonal decomposition (POD) of the full and filtered data. POD modes of unheated subsonic jets reveal large scale-disparity between the full and supersonic components. For the supersonic jet at Mj=1.95Mj=1.95, the energetic structures of the pressure field also contribute significantly to the supersonic components, and scale disparity is absent. The variance of the subsonic pressure components from unheated jets scales as Uj4, where UjUj is the jet exit velocity (i.e.  , |p˜2|~Uj4), which is the expected scaling for turbulence-associated hydrodynamic-pressure fluctuations. In contrast, supersonic pressure variance, which peaks within the turbulent flow region, scales with Uj8, coinciding with the far field noise intensity scaling associated with Lighthill׳s analogy. In the acoustic near-field, even higher exponent of the jet velocity scaling is found for the positive phase velocity supersonic pressure component (|p˜2|~Uj10), which is consistent with the scaling of the far-field noise at shallow exit angles [2] and [3]. The filtered velocity components also show a similar pattern, i.e., supersonic velocity variances scale with a higher power of the jet velocity, but the scaling exponents in jet-region are different for different velocity components and depend on the azimuthal mode. Previous investigations have presented two distinct spectral peaks due to the hydrodynamic and acoustic pressure components in the near-acoustic field. Using filtered components, it is found that density and velocities also show such clear hydrodynamic to acoustic transition, albeit with different transition points. The strongly directive noise radiation from subsonic jets is explained using POD projection of supersonic disturbances.