Journal of Fluid Mechanics | 2019
Turbulent shear-layer mixing: initial conditions, and direct-numerical and large-eddy simulations
Abstract
Aspects of turbulent shear-layer mixing are investigated over a range of shear-layer Reynolds numbers, $Re_{\\unicode[STIX]{x1D6FF}}=\\unicode[STIX]{x0394}U\\unicode[STIX]{x1D6FF}/\\unicode[STIX]{x1D708}$\n , based on the shear-layer free-stream velocity difference, $\\unicode[STIX]{x0394}U$\n , and mixing-zone thickness, $\\unicode[STIX]{x1D6FF}$\n , to probe the role of initial conditions in mixing stages and the evolution of the scalar-field probability density function (p.d.f.) and variance. Scalar transport is calculated for unity Schmidt numbers, approximating gas-phase diffusion. The study is based on direct-numerical simulation (DNS) and large-eddy simulation (LES), comparing different subgrid-scale (SGS) models for incompressible, uniform-density, temporally evolving forced shear-layer flows. Moderate-Reynolds-number DNS results help assess and validate LES SGS models in terms of scalar-spectrum and mixing estimates, as well as other metrics, to $Re_{\\unicode[STIX]{x1D6FF}}\\lesssim 3.3\\times 10^{4}$\n . High-Reynolds-number LES investigations to $Re_{\\unicode[STIX]{x1D6FF}}\\lesssim 5\\times 10^{5}$\n help identify flow parameters and conditions that influence the evolution of scalar variance and p.d.f., e.g.\xa0marching versus\xa0non-marching. Initial conditions that generate shear flows with different mixing behaviour elucidate flow characteristics in each flow regime and identify elements that induce p.d.f.\xa0transition and scalar-variance behaviour. P.d.f.\xa0transition is found to be largely insensitive to local flow parameters, such as $Re_{\\unicode[STIX]{x1D6FF}}$\n , or a previously proposed vortex-pairing parameter based on downstream distance, or other equivalent criteria. The present study also allows a quantitative comparison of LES SGS models in moderate- and high- $Re_{\\unicode[STIX]{x1D6FF}}$\n forced shear-layer flows.