Unsteady shallow meandering flows in rectangular reservoirs: A modal analysis of URANS modelling

TL;DR

This study compares 3D URANS simulations with experimental data for shallow reservoir flows, revealing the advantages of 3D modeling and analyzing flow modes and vortices using POD and Q-criterion.

Contribution

It demonstrates the effectiveness of 3D URANS models with different turbulence closures in capturing complex meandering flow modes and vortex dynamics in shallow reservoirs.

Findings

3D models accurately predict mode frequencies.

RNG k-ε turbulence model performs best at high Reynolds numbers.

3D flow features differ from 2D and depth-averaged models.

Abstract

Shallow flows are common in natural and human-made environments. Even for simple rectangular shallow reservoirs, recent laboratory experiments show that the developing flow fields are particularly complex, involving large-scale turbulent structures. For specific combinations of reservoir size and hydraulic conditions, a meandering jet can be observed. While some aspects of this pseudo-2D flow pattern can be reproduced using a 2D numerical model, new 3D simulations, based on the unsteady Reynolds-Averaged Navier-Stokes equations, show consistent advantages as presented herein. A Proper Orthogonal Decomposition was used to characterize the four most energetic modes of the meandering jet at the free surface level, allowing comparison against experimental data and 2D (depth-averaged) numerical results. Three different isotropic eddy viscosity models (RNG k-${\epsilon}$, k-${\epsilon}$, k-${\omega}$) were tested. The 3D models accurately predicted the frequency of the modes, whereas the amplitudes of the modes and associated energy were damped for the friction-dominant cases and augmented for non-frictional ones. The performance of the three turbulence models remained essentially similar, with slightly better predictions by RNG k-${\epsilon}$ model in the case with the highest Reynolds number. Finally, the Q-criterion was used to identify vortices and study their dynamics, assisting on the identification of the differences between: i) the three-dimensional phenomenon (here reproduced), ii) its two-dimensional footprint in the free surface (experimental observations) and iii) the depth-averaged case (represented by 2D models).