Initial/inflow conditions effects on near- and far-field free-shear flow development has been a subject of numerous experimental and computational studies. Several free-shear flow studies show that statistics in all flow stages are sensitive to the initial/inflow state, suggesting also that while a self-similar state is attained by these flows, it depends on initial/inflow conditions and may not be universal, even at high Reynolds numbers. This sensitivity offers potential avenues to control shear-flow mixing in non-premixed combustion applications, ranging from automotive, to industrial, to aerospace, for example. The first part of the talk will examine the initial-condition influence on scalar-field probability density function (p.d.f.) and variance evolution. These provide metrics to characterize mixing in forced and unforced shear layers, reaching Reynolds numbers, based on shear-layer free-stream velocity difference and mixing-zone thickness, up to 500,000. The study is based on direct-numerical simulation (DNS) and large-eddy simulation (LES) of incompressible, uniform-density, temporally evolving shear layers and DNS of weakly compressible spatially evolving jets.
LES mixing estimates are subject to numerical discretization and subgrid-scale (SGS) model errors. Discretization accuracy can be evaluated from truncation error and assessed by its dispersion and dissipation properties. Dispersion errors can cause violation of physical scalar bounds resulting in unphysical mass fractions, such as greater than 1 or smaller than 0. While numerical dissipation helps mitigate such violations, it alters energy at the small scales whose behavior is critical to mixing. The second part of the talk will discuss a flux-reconstruction approach developed to mitigate unphysical scalar overshoots/undershoots, while retaining uniform high-order accuracy and discrete conservation. Robustness of the mitigation approach and LES mixing estimates with various subgrid-scale models will be discussed, outlining issues in validating implicitly-filtered LES results against DNS solutions.