Numerical modeling and empirical formulation for re-aeration in nappe flow without hydraulic jump in stepped chutes

Modelagem numérica e formulação empírica para a re-aeração de escoamentos em quedas sucessivas sem ressalto hidráulico em canais em degraus

ABSTRACT

Flows in stepped chutes have been widely studied in recent decades due to the numerous dams built with roller-compacted concrete and stepped spillways. Besides this application, there is practical interest in using stepped chutes for re-aeration and desorption of volatile compounds. This work aimed to numerically model the nappe flow without a hydraulic jump, including the advection-diffusion equation for studying re-aeration. The homogeneous multiphase model was used with the advection-diffusion equation, rewritten in terms of average fields and including the turbulent Schmidt number and the k-ε turbulence model. The two-film resistance model was applied at the interface using the global mass transfer coefficient. Numerical results were compared to literature data, allowing model adjustment to experimental observations using the Schmidt number and mass transfer coefficient. Solutions show increasing dissolved oxygen concentrations along the stepped chute, with re-aeration efficiencies up to 77%. An empirical equation fitting the experimental data with a high correlation coefficient was then proposed.

Keywords:  Air-water interfaces; Computational fluid dynamics; Mass transfer; Stepped spillways