An improved air entrainment model for stepped spillways

TL;DR

This paper enhances an air entrainment model for stepped spillways by reducing parameters, improving grid sensitivity, and proposing modifications, leading to better predictive accuracy in flow simulations across various conditions.

Contribution

The study introduces modifications to an existing air entrainment model, reducing its parameters and improving grid sensitivity for more accurate spillway flow simulations.

Findings

Improved model shows better agreement with experimental data.

Reduced parameter set simplifies model calibration.

Sensitivity to grid resolution remains a challenge.

Abstract

Numerical modelling of flow in stepped spillways is considered, focusing on a highly economical approach combining interface capturing with explicit modelling of air entrainment. Simulations are performed on spillways at four different Froude numbers, with flow parameters selected to match available experimental data. First, experiments using the model developed by Lopes et al. (Int. J. Nonlin. Sci. Num., 2017) are conducted. An extensive simulation campaign is used to carefully evaluate the predictive accuracy of the model, the influence of various model parameters, and sensitivity to grid resolution. Results reveal that, at least for the case of stepped spillways, the number of parameters governing the model can be reduced. A crucial identified deficiency of the model is its sensitivity to grid resolution. To improve the performance of the model in this respect, modifications are proposed for the interface detection algorithm and the transport equation for the volume fraction of entrained air. Simulations using the improved model formulation demonstrate better agreement with reference data for all considered flow conditions. A parameter-free criterion for predicting the inception point of air entrainment is also tested. Unfortunately, the accuracy of the considered conventional turbulence models proved to be insufficient for the criterion to work reliably.