Direct numerical simulation of turbulent flow over a backward-facing step

Abstract

A three-dimensional, turbulent 
\nflow in a channel with a sudden expansion
\nwas studied by direct numerical simulation of the incompressible Navier-Stokes
\nequations. The objective of this study was to provide statistical data of backwardfacing
\nstep 
\nflow for turbulence modelling. Additionally, analysis of the statistical
\nand dynamical properties of the 
\nflow is performed.
\nThe Reynolds number of the main simulation was Reh = 9000, based on the
\nstep height and mean inlet velocity, with the expansion ratio ER = 2:0. The discretisation
\nis performed using the spectral/hp element method with stiffly-stable
\nvelocity correction scheme for time integration. The inlet boundary condition is
\na fully turbulent velocity and pressure field regenerated from a plane downstream
\nof the inlet. A constant 
\nflowrate was ensured by applying Stokes 
\nflow correction
\nin the inlet regeneration area.
\nTime and spanwise averaged results revealed, apart from the primary recirculation
\nbubble, secondary and tertiary corner eddies. Streamlines show an additional
\nsmall eddy at the downstream tip of the secondary corner eddy, with the
\nsame circulation direction as the secondary vortex. The analysis of the 3D, timeonly
\naverage shows the wavy spanwise structure of both primary and secondary
\nrecirculation bubble, that results in spanwise variations of the mean reattachment
\nlocation. The visualisation of spanwise averaged pressure 
\nuctuations and
\nstreamwise velocity showed that the interaction of vortices with the recirculation
\nbubble is responsible for the 
\napping of the reattachment position. The
\ncharacteristic frequency St = 0:078 was found.
\nThe analysis of small-scale energy transfer was performed to reveal large
\nbackscatter regions in strong Reynolds stress areas in the mixing layer. High
\ncorrelation of small-scale transfer with non-linear interaction of large-scale velocity
\nand small-scale vorticity was found.
\nThe data of the 
\nflow fields was archived. It contains the averages for velocities,
\npressure and Reynolds stress tensor, as well as 3D instantaneous pressure and
\nvelocity history.