Hydrodynamics and turbulence of free-surface flow over a backward-facing step

Abstract

ABSTRACTThree large-eddy simulations of open channel flow over a backward-facing step are performed to investigate the effect of submergence on the turbulence, hydrodynamics, and water surface deformation downstream of the step. The deformation of the water surface, the extent of the recirculation zone as well as the strength of the shear layer are a function of relative submergence. All flows downstream of the step exhibit elevated levels of turbulent shear stress and contain significant amounts of turbulent kinetic energy. The instantaneous flow features rollers immediately behind the step and horseshoe-shaped vortices shed from the shear layer, the latter being advected towards the water surface where they cause deformations. It is shown that these vortices can originate from any location along the dividing streamline; however, they contain more energy the closer to the mean attachment location they originate.Keywords: Backward-facing stepfree surfacelarge-eddy simulationrelative submergenceturbulence AcknowledgementsAll simulations were performed on UCL's supercomputer Kathleen.Disclosure statementNo potential conflict of interest was reported by the author(s).NotationAr=channel-width-to-step-height-ratio (–)Cf=skin-friction coefficient (–)Cp=pressure coefficient (–)Er=expansion ratio (–)Fr=Froude number (–)f=frequency (Hz)f=volume force from immersed boundary points (N m−3)g=gravitational acceleration (m s−2)h=step height (m)h1=upstream depth (m)h2=downstream depth (m)K=turbulent kinetic energy (m2 s−2)Lx=computational streamwise length (m)Ly=computational spanwise width (m)Lz=computational wall-normal height (m)p=pressure (Pa)Re=bulk Reynolds number (–)Reh=step height Reynolds number (–)Reτ=friction Reynolds number (–)Ruu=u-velocity auto-correlation (–)Rvv=v-velocity auto-correlation (–)S=submergence (–)St=Strouhal number (–)t=times (s)u=filtered resolved velocity field (m s−1)u¯=time-averaged streamwise velocity (m s−1)−u′w′¯=time-averaged Reynolds shear stress (m s−2)Umax=maximum time-averaged streamwise velocity (m s−1)Um1=upstream spatially-averaged mean velocity (m s−1)Um2=downstream spatially-averaged mean velocity (m s−1)XR=reattachment length (m)Γ=interface between gas and liquid domains (–)ϵ=turbulent kinetic energy dissipation (m2 s−3)ν=kinematic viscosity (m2 s−1)ρ=density of liquid (kg m−3)τSGS=sub-grid scale stress tensor (–)τw=wall shear stress (Pa)ϕ=level set distance function (–)ψ=normalized streamfunction (–)Ωgas=gas domain (–)Ωliquid=liquid domain (–)Additional informationFundingThe work presented in this paper is supported by the EPSRC under project number EP/R022135/1. The third author is a postdoctoral fellow sponsored by EP/R022135/1 whereas the first author has been funded by UCL's Department of Civil, Environmental and Geomatic Engineering.