Numerical investigation of transitional and turbulent backward-facing step flows

Abstract

Transitional and turbulent flows over a backward-facing step are physically highly complex. Apart from vastly different mean flow regimes and the rapid generation of turbulence, additional complexities arise from the presence of large coherent structures. For the present study, the mean flow, turbulence statistics and the origin of large coherent structures were investigated using Direct Numerical Simulations and turbulence modeling approaches. The latter included Large Eddy Simulations (LES) and state-of-the-art Reynolds-Averaged Navier-Stokes (RANS) computations. Wall-distance independent forms of the RANS models were developed, validated and calibrated. The ability of computing the step flows investigated and the associated computational costs were evaluated, for both LES and RANS. By employing harmonic forcing of the shear layer and a Fourier analysis in time and in the lateral direction the generation of coherent structures was linked to specific hydrodynamic instabilities. Comparison with references in the literature, resolution and domain size studies, and variations of inflow conditions established an accurate description of the mean flow and turbulence quantities and the level of sensitivity of the flow field to boundary conditions. From the controlled environment of the simulations, a simplified scenario was proposed for the creation of large coherent structures in transitional and turbulent step flows. The scenario suggests that Kelvin-Helmholtz, elliptical and centrifugal instabilities may be the relevant physical mechanisms for the observed primary, secondary and tertiary instabilities of the shear layer, respectively. The onset of the elliptical instability can also be described as a fundamental resonance of two waves. A cascade of subharmonic resonances is regarded to be responsible for vortex mergings and the generation of low frequency waves in the flow field. Furthermore, the simulations indicate that a three-dimensional global instability of the time and spanwise averaged separation bubble may be present. It was observed that the range of all unstable lateral wavelengths has a short-wave cutoff depending on Reynolds number and an upper bound on the order of the reattachment length.