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ABSTRACT
Experimental research was carried out to study surface roughness effects on the characteristics of turbulent flow downstream of a backward facing step in an open channel. Particle image velocimetry measurements were conducted over sand grain roughness and a reference smooth surface downstream of the backward facing step. The experiments were conducted at a Reynolds number of 3240 based on the step height and freestream velocity of the approach flow. The vorticity thickness, streamwise mean velocity, Reynolds stresses, triple velocity correlations and two-point correlation coefficients were obtained to quantify surface roughness effects in the separated region through to the recovery region. The results demonstrated that roughness effects on the flow characteristics are evident only in the recovery region.
Acknowledgement
The authors would like to acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada, and Dr. Karen A. Flack for profiling the sand grain roughness.
Notation
| B | = | logarithmic law constant |
| Cf | = | skin friction coefficient (–) |
| Cp | = | wall pressure coefficient (–) |
| = | Froude number (–) | |
| G | = | Clauser parameter (–) |
| h | = | step height (mm) |
| H | = | shape factor (–) |
| ks | = | equivalent sand grain roughness height (mm) |
| kt | = | average of ten maximum peak-to-trough roughness heights (mm) |
| krms | = | root mean square roughness height (µm) |
| lm | = | mixing length (mm) |
| Lxuu | = | streamwise extent of Ruu (mm) |
| Lxvv | = | streamwise extent of Rvv (mm) |
| Lyuu | = | wall-normal extent of Ruu (mm) |
| Lyvv | = | wall-normal extent of Rvv (mm) |
| Puu | = | production of the streamwise and wall-normal Reynolds normal stresses (m2 s–3) |
| Pvv | = | production of wall-normal Reynolds normal stresses (m2 s–3) |
| Pk | = | the production of turbulent kinetic energy (m2 s–3) |
| Ruu | = | streamwise correlation function (–) |
| Rvv | = | wall-normal correlation function (–) |
| = | Reynolds number based on step height and approach freestream velocity (–) | |
| = | Reynolds number based on water depth and approach freestream velocity (–) | |
| = | Reynolds number based on momentum thickness and approach freestream velocity (–) | |
| sk | = | skewness of the probability density function (–) |
| u | = | streamwise fluctuating velocity (m s–1) |
| u′ | = | streamwise turbulence intensity (m s–1) |
| u′+ | = | streamwise turbulence intensity normalized with friction velocity (–) |
| = | streamwise Reynolds normal stress (m2 s–2) | |
| = | triple velocity correlations (m3 s–3) | |
| = | the Reynolds shear stress (m2 s–2) | |
| U | = | streamwise mean velocity (m s–1) |
| Ue | = | local freestream velocity (m s–1) |
| Uo | = | approach freestream velocity (m s–1) |
| U+ | = | streamwise mean velocity normalized with friction velocity |
| Uτ | = | friction velocity (m s–1) |
| v | = | wall-normal fluctuating velocity (m s–1) |
| v′ | = | wall-normal turbulence intensity (m s–1) |
| v′+ | = | wall-normal turbulence intensity normalized with friction velocity (–-) |
| = | wall-normal Reynolds normal stress (m2 s–2) | |
| V | = | wall-normal velocity (m s–1) |
| w | = | spanwise fluctuating velocity (m s–1) |
| w′ | = | spanwise turbulence intensity (m s–1) |
| = | spanwise Reynolds normal stress. | |
| x* | = | streamwise distance normalized with step height (–) |
| xr | = | reattachment length (mm) |
| y+ | = | wall-normal distance normalized with viscous length scale |
| y* | = | wall-normal distance normalized with step height (–) |
| δ | = | Boundary layer thickness (mm) |
| ΔU | = | maximum deviation of the measured mean velocity |
| δω | = | vorticity thickness (mm) |
| θ | = | momentum thickness (mm) |
| κ | = | logarithmic law constant |
| ν | = | kinematic viscosity (m s–2) |
| Π | = | Coles wake parameter |
| τw | = | wall shear stress (Pa) |
| ω | = | vorticity (s–1) |