Very large eddy simulations of spatially evolving supersonic turbulent shear layers

The objective of this research was to further the understanding of the fundamental physical mechanisms which control turbulence and entrainment at different levels of compressibility for supersonic shear flows. Very Large Eddy Simulations (VLES) were performed based on the two-dimensional unsteady Euler equations without any empirical coefficients for turbulence modeling. These equations were used to study the spatially evolving mixing characteristics of unforced, planar, confined shear layers formed by two parallel streams of supersonic air that come into contact after passing over a splitter plate. The computations were performed using the conservative Finite Element Method-Flux Corrected Transport (FEM-FCT) scheme with unstructured adaptive grids. In general, it was found that the highest simulation fidelity was obtained by using a full turbulence spectra consistent with measured turbulent kinetic energy levels and an incompressible wavelength distribution. This model is the most physically consistent and yields the best comparison with the downstream experimental data. The computational investigation noted modifications of organized coherent structures as well asymmetric entrainment, i.e. the high speed fluid is entrained and convoluted to a greater extent than that of the lower speed stream, and their subsequent importance in mixing. The round vortex shape of incompressible circular eddies was modified to an oblique flattened shape with decreased transverse height as convective Mach number (M$\sb{\rm c}$) increases. The high speed side convolutions of organized lumps of fluid are also decreased as M$\sb{\rm c}$ increases. However, the overall vortex size are only slightly modified, whereas the angular orientation is significantly modified. The merging process is very different as a function of M$\sb{\rm c}$: the rotational vortex pairing process at low M$\sb{\rm c}$ is modified to a slapping process at high M$\sb{\rm c}$. This slapping process, which results in eddy flattening and oblique angles at higher M$\sb{\rm c}$, reduces the degree of coherency. Turbulence statistics of velocity and mixture fraction also investigated for three different M$\sb{\rm c}$'s. The converged peak values of V$\sbsp{\rm rms}{\prime}$, f$\sbsp{\rm rms}{\prime}$ and Reynolds stress are reduced, while U$\sbsp{\rm rms}{\prime}$ peak values remain constant as M$\sb{\rm c}$ increases (coherency decreases). Those observations are consistent with experimental results and observations of coherency effects.U of I OnlyETDs are only available to UIUC Users without author permissio