Scale Effects of Nappe Dispersion in Ski-Jump Energy Dissipation

The primary cause of the scale effect in scaled models for flood discharge and energy dissipation lies in the dissimilarity of the air dispersion patterns of the ski-jump nappe. To uncover the scale-effect relationship governing the air dispersion patterns of ski-jump energy dissipation nappes in high dams, a series of scaled physical model tests were conducted at the Baihetan Hydropower Station. The air dispersion patterns were systematically observed, as well as the distribution characteristics of entrained air concentration in the ski-jump nappe across various scales. Based on the experimental observations, a two-dimensional stochastic diffusion numerical model was developed, successfully replicating the dispersion process of the nappe as it gradually transformed from a crescent shape to a circular one. Furthermore, by calibrating the concentration distribution curve, a quantitative relationship was established between the random displacement parameter σ and the Weber number. The study revealed that when the Weber number (We) is below 40,000, σ increases rapidly and approximately linearly with We, indicating a high sensitivity to dispersion degree. However, once We surpasses 40,000, the growth rate significantly decelerates, approaching saturation, suggesting that the dispersion degree closely approximates the prototype condition. Consequently, it is suggested that the Weber number control threshold for the physical model of ski-jump water–air two-phase flow in high dams be set above 40,000, providing a valuable reference for selecting large-scale models.