Air–Water Flows and Head Losses on Stepped Spillways with Inclined Steps

On a stepped spillway, the staircase invert profile generates some intense turbulent dissipation during the spill, associated with a significant reduction of kinetic energy, as well as strong self-aeration. The present study focused on the effects of inclined downward steps on the air–water flow properties, flow resistance, and head losses because these mostly relate to spillway design. Some physical modeling was conducted in a relatively large facility with a 45° stepped chute ($\mathrm{1}\mathrm{V}\mathrm{:}\mathrm{1}\mathrm{H}$) operating with Reynolds numbers $2.8\times {10}^3<\mathrm{Re}<1\times {10}^6$. The presence of downward steps induced some elongated asymmetrical cavity shapes, creating a less stable cavity recirculation pattern along the entire chute, leading to different interactions with the main stream. In terms of basic air–water flow properties, the distributions of void fraction and bubble count rate presented very close results for all three stepped geometries, both qualitatively and quantitatively. The interfacial velocities did not reach any uniform equilibrium (i.e., normal flow) condition, and the fastest velocities were recorded with the $\mathrm{1}\mathrm{V}\mathrm{:}\mathrm{2.33}\mathrm{H}$ inclined downward stepped chute geometry ($\delta =23.3°$ and $\lambda /k=3$), and the slowest velocities on the horizontal stepped chute ($\delta =0$ and $\lambda /k=2$). The Darcy-Weisbach friction factor $f$ and relative head loss $\mathrm{\Delta }H/H_{\max }$ were estimated in the self-aerated flow. The comparative analyses suggested that the largest total drag and head losses were observed on the stepped chute with flat horizontal steps. An inclined downward stepped design yielded lesser head losses for all investigated flow conditions, providing an important information for practical engineers designing these hydraulic structures.