Self-aeration in open channel flows occurs owing to free surface air entrainment. Self-aeration development and fully cross-sectional distribution of air concentration are not thoroughly understood. In the present study, an analytical solution for the averaged cross-sectional air concentration in the gradually varying region is established using a simplified mechanism of free surface air entrainment. For a fully cross-sectional distribution of air concentration affected by the channel bottom, a model of a diffusion region without wall restraint is proposed, and two situations are classified based on averaged cross-sectional air concentration. Good agreement between measured data and calculations is obtained, and the computational accuracy of the air concentration distribution near the wall is improved. The results reveal that the channel slope determines the air entrainment quantity, while water flow discharge determines the self-aeration evolution distance. The solutions for the averaged cross-sectional air concentration and the effect of the bottom wall on air diffusion promote air–water flow applications in hydraulic engineering practices.

由于自由表面空气夹带，明渠流中发生自曝气。空气浓度的自曝气发展和全截面分布尚不完全清楚。在本研究中，使用自由表面空气夹带的简化机制，建立了渐变区域平均横截面空气浓度的解析解。针对受渠道底部影响的全截面空气浓度分布，提出了无壁面约束的扩散区模型，并根据平均截面空气浓度对两种情况进行分类。实测数据与计算结果吻合良好，提高了壁面附近空气浓度分布的计算精度。结果表明，河道坡度决定引气量，水流量决定自曝气演化距离。平均横截面空气浓度和底壁对空气扩散的影响的解决方案促进了水力工程实践中的空气-水流应用。