Estimation of the skin friction in a turbulent wall jet flow over smooth and rough surfaces was studied experimentally. Wall jet flows can be found in many engineering applications in which knowledge of the skin friction behavior is essential for predicting the drag force as well as the heat transfer rate at the wall. Although there are many studies which consider a wall jet on a smooth surface, only a few experiments have examined wall jet flows on a rough surface. This paper reports on an experimental investigation which used a two-component laser Doppler anemometry (LDA) system to measure the mean velocity field in a plane turbulent wall jet on both smooth and transitionally rough surfaces. The Reynolds number based on the slot height and exit velocity of the jet was approximately Re = 7500. A glass plate was used for the smooth surface, while the rough surface consisted of a 36-grit sheet glued to the glass plate. The momentum-viscosity scaling originally introduced by Narasimha et al. (1973) and revisited by Wygnanski et al. (1992) can be used to construct a similarity profile for a wall jet on a smooth surface, which together with the momentum integral equation leads to a convenient expression for the friction velocity and hence skin friction coefficient Cf. This approach has been used to process the experimental results, which gives values of Cf which are consistent with the results of other methods and some existing empirical correlations. However, for rough wall flow, the friction at the wall is not only governed by viscosity, but also by surface roughness. Hogg et al. (1997) suggested that for a fully rough surface, the viscosity be replaced by the roughness parameter Uoke, where Uo and ke are the initial velocity and roughness length, respectively. Here, this approach is applied to our recent velocity measurements in a wall jet on a transitionally rough surface, where both viscous and roughness effects are present. The present results indicate that for an equivalent sand-grain roughness range of 40 < ks+ < 70, the momentum-viscosity scaling is able to capture the skin friction behavior compared to that obtained from the logarithmic and power laws. The results also show that the scalings proposed by Hogg et al. (1997) and Wygnanski et al. (1992) both result in similar values for the friction velocity. However, the values of Cf estimated by both scalings are considerably larger (approximately 47%) than those obtained from the logarithmic and power laws.
Discussion: “Complete Velocity Profile and ‘Optimum’ Skin Friction Formulas for the Plane Wall-Jet” (Hammond, G. P., 1982, ASME J. Fluids Eng., 104, pp. 59–65)
