Numerical Modeling of Flow and Air Entrainment in Hydraulic Jumps for a Wide Range of Froude Numbers

TL;DR

This paper presents a computationally efficient three-phase mixture model using URANS to simulate flow and air entrainment in hydraulic jumps across a wide Froude number range, matching experimental data.

Contribution

The study introduces a systematic URANS-based three-phase mixture model for hydraulic jumps, achieving high accuracy with significantly reduced computational resources.

Findings

Model accurately predicts velocity and air concentration profiles.

Good agreement with experimental data from seven facilities.

Comparable accuracy to IDDES with much lower computational cost.

Abstract

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 (URANS) framework, to numerically simulate flow and air entrainment across twelve 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 (IDDES), 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.