An eigendecomposition approach to turbulence production in supersonic streamwise vortex dominated flows

Streamwise vortices have been investigated as a way to enhance air/fuel mixing in supersonic flows. Recently, they have been proposed as a way to exert a control authority on the sustainment of turbulence production. This control has direct application in scramjet combustors as molecular mixing is increased by the action of turbulence. Turbulence production is a function of the mean flow strain rates. These can be imposed by selecting specific modes of vortex interaction. However, their selection is non-trivial as the mean flow strain rates are coupled with the Reynolds stresses in turbulence production. Based on a series of experimental observations of the Reynolds stresses, which exhibits recurring morphologies, the authors have previously introduced a methodology to select specific modes of vortex interactions that would sustain turbulence. This method was experimentally tested in a Mach 2.5 flow, and the measurements showed sustained turbulence production compared to previous configurations. Although successful, this approach was limited in its use due to some simplifications. In particular, it was qualitative in nature and restricted to the sole mode of vortex merging. In this work, the previous approach is revisited using the strain rates and Reynolds stresses tensors eigendecomposition, resulting in a simplified, but quantitative, expression for turbulence production which is not restricted to a single mode of vortex interaction. Experimental comparisons show that this simplified model's predictions match well with the measurements, thus providing a useful approach for the selection of supersonic streamwise vortices configurations that sustain turbulence.