An experimental study of a plane turbulent wall jet on smooth and rough surfaces

Abstract

This study presents an experimental investigation of incomplete similarity and the effect of surface roughness on a plane turbulent wall jet on a hydraulically smooth, transitionally rough and fully rough surface based on a new set of particle image velocimetry (PIV) measurements. The focus is on examining the changes in the characteristics of the mean velocity field. Velocity measurements were taken along the centerline of the ground plane with seven fields of view (FOV) covering the entire streamwise extent, i.e. the inflow, developing and fully developed regions. In each FOV, 2,000 and 4,000 pairs of instantaneous PIV raw images were captured at a sampling frequency of 4 Hz for the smooth and rough surface cases, respectively. Four series of measurements were conducted: two series of measurements were taken on the smooth surface at two inlet flow rates corresponding to slot Reynolds numbers of 7,190 and 14,300, respectively; then the rough surface was installed and two series of measurements were taken at the same two inlet flow rates corresponding to slot Reynolds numbers of 6,660 and 13,400, which resulted in a transitionally rough and a fully rough flow condition, respectively. In-house PIV software was used to complete the cross-correlation analysis of the PIV images and the post-correlation rejection of outlier velocity vectors with a dynamic threshold neural network technique to obtain the mean and fluctuating velocity data. The results show that at the inlet boundary, the surface roughness decreases the mass flux near the wall due to the enhanced wall shear stress. In the initial developing region, which covers the first ten slot heights of streamwise distance, the enhanced wall friction associated with the rough surface shortens the potential core. The surface roughness causes the onset of the fully developed region to appear farther downstream on the rough surface than on the smooth surface. For the low flow rate (LFR) case on the rough surface, the roughness shift decreases monotonically with distance from the slot, which indicates that the effect of surface roughness on the mean velocity profile is decreasing. The profile fitting result for the fully rough case suggests that the value of von Karman’s constant κ in the logarithmic law may depend on the surface roughness. In the fully developed region, for the LFR case, the surface roughness enlarges the thicknesses of both the outer and inner layers, though this effect is much more significant for the inner layer than for the outer layer. This is also observed for the high flow rate (HFR) case, but with a much more noticeable effect of surface roughness. The surface roughness increases the spread rate of the inner layer significantly and penetrates into the outer layer, although the impact is much less for the outer layer. For the LFR case, while in general the surface roughness tends to increase the streamwise growth rate of the inner and outer half-widths, the magnitude of this effect becomes stronger as the wall-normal distance to the surface decreases. A significant increase in the skin friction coefficient due to the surface roughness, as large as 58% - 78% for the LFR case and 72% - 75% for the HFR case, is observed. Incomplete similarity of the plane turbulent wall jet in terms of the slot height H is confirmed for all the flow conditions considered in this study, i.e., the hydraulically smooth, transitionally rough and fully rough flow cases. The outer scaling is observed to extend into the inner layer with varied extent for different flow cases, which indicates that the upper region of the inner layer in a plane wall jet is essentially part of the outer layer in a canonical zero-pressure-gradient turbulent boundary layer. In general the velocity profiles tend to collapse better when the rough surface is present compared to the smooth surface, which implies that the surface roughness strengthens the coupling between the inner and outer layers.