Numerical modeling of flow and air entrainment in hydraulic jumps for a wide range of Froude numbers

The numerical modeling of hydraulic jumps remains challenging due to complex interactions among free-surface deformation, air entrainment and detrainment, and turbulent bubble transport. Whereas accurate prediction of these flows is essential for the design of hydraulic structures, existing high-fidelity tools require prohibitive computational resources for engineering applications. This study implements a three-phase mixture model based on an unsteady Reynolds-averaged Navier–Stokes framework, to numerically simulate flow and air entrainment across 12 hydraulic jumps with Froude numbers ranging from 1.98 to 8.48, representing the first systematic analysis for such a comprehensive range of Froude numbers. The model accurately represents time-averaged velocity fields and air concentration profiles, as well as dynamic features including jump toe oscillation and free-surface deformation, showing good agreement with experimental data from seven facilities. Compared to improved delayed detached eddy simulations, the proposed approach achieves similar accuracy with approximately 400-fold fewer cells and a 300-fold reduction in computational cost. The investigation shows that the selection of turbulence closure affects the accuracy of the prediction of air entrainment. These findings establish the three-phase mixture approach as a practical engineering tool for hydraulic jump simulation, offering an effective balance of accuracy and computational cost.