Energy Dissipation Rate and Conjugate Depth After Hydraulic Jump for Counterflow Underflow Energy Dissipation in Spillways

To address the energy dissipation requirements of hydraulic engineering projects with medium-low water heads and medium-high unit discharges, counterflow-type underflow energy dissipation can significantly enhance the energy dissipation efficiency through the head-on collision of flows from spillways on both sides. In this study, the spillway of the Lieshen Reservoir was used as the prototype. Since gravity dominates the flow in spillways, we established a 1:15 physical model based on the Froude similarity criterion, and conducted numerical simulations using the volume of fluid method coupled with the realizable k-ε turbulence model. Furthermore, the hydraulic characteristics of counterflow energy dissipation under different flow rates and stilling basin length conditions were analyzed. The results show that the counterflow energy dissipation rate first increases before decreasing with increasing stilling basin length, and the maximum energy dissipation rate can exceed 85%; however, the change in the stilling basin depth has a small impact on the energy dissipation rate, especially under relatively high flow rates; furthermore, an empirical formula for the conjugate depth after a hydraulic jump suitable for counterflow energy dissipation with Froude number in the range of 2.0 < Fr1 < 9.7 and stilling basin depth of 0.5–1.5 m is proposed, with the relative error between its predicted and simulated values being less than 6%. Based on the analysis of the water depth outer envelope curve at the outlet section of the stilling basin, it is suggested that the sidewall height be set to 0.6–0.8 times the conjugate depth after the hydraulic jump.