Simulating air entrainment and vortex dynamics in a hydraulic jump

Abstract

The air entrainment characteristics of three separate Froude number hydraulic jumps are investigated numerically using an unsteady RANS, realizable k-ε turbulence model, with a Volume of Fluid treatment for the free surface. Mean velocity profiles, average void fraction, and Sauter mean diameter compare favorably with experimental data reported in literature. In all simulations, time-averaged void fraction profiles show good agreement with experimental values in the turbulent shear layer and an accurate representation of interfacial aeration at the free surface. Sauter mean diameter is well represented in the shear layer, and free surface entrainment results indicate bubble size remains relatively unchanged throughout the depth of the jump. Several different grid resolutions are tested in the simulations. Significant improvements in void fraction and bubble size comparison are seen when the diameter to grid size ratio of the largest bubbles in the shear layer surpasses eight. A three-dimensional simulation is carried out for one Froude number jump, showing an improvement in the prediction of entrained air and bubble size compared with two-dimensional results at a substantial increase in computation time. An analysis of three-dimensional vorticity shows a complex interaction between spanwise and streamwise vortical structures and entrained air bubbles. The jump is similar to a turbulent mixing layer, constrained by the free surface, with vortex pairing and subsequent fluctuations in free surface elevation. Downstream fluctuations of the toe are associated with a roll up of the primary spanwise vortex, fluctuations of the free surface, and counter-rotating streamwise vortex pairs. The action of these flow structures is likely responsible for the improvement in three-dimensional results.

Numerical Simulation of Hydraulic Jumps. Part 2: Recent Results and Future Outlook

“…Witt et al [67] simulated the air entrainment characteristics of three Froude number hydraulic jumps using the realizable k − model, with VOF treatment for the free surface through 2D and 3D simulations. Velocity profiles, void fraction profiles, and Sauter mean diameter were compared to the experimental data from Murzyn et al [81], Liu et al [75], and Lin et al [84], among others.…”

IDDES Evaluation of Oscillating Hydraulic Jumps

“…Moreover, experiments probe a point or a plane, the complete three-dimensional (3D) flow field is not available for analysis. Recent improvements in computing capabilities have rendered numerical simulation as a viable tool to analyse the hydraulic jump flow field [8][9][10][11][12][13][14].…”

“…Most of the earlier simulations on hydraulic jumps have been performed using Reynolds-Reynolds-Averaged Navier-Stokes (RANS) models [8][9][10][11]. Ma et al, [12] compared the performance of RANS and Detached-Eddy simulations (DES) in simulating hydraulic jumps. He reported that the DES model was superior than RANS in resolving the free surface features of hydraulic jumps.…”

Total dissolved gas prediction and optimization in RiverWare

“…Computational fluid dynamics (CFD) models have been used to model TDG exchange, mixing, and transport (Xiao-li et al, 2010 andWeber et al, 2004). However, the computational effort necessary to resolve the smallest bubbles responsible for mass transfer is prohibitive (Witt et al, 2015), and CFD models, in addition to methodologies used in the physically based TDG prediction models, require calibration of many equation coefficients specific to each case.…”