MATHEMATICAL MODEL AND EXPERIMENTAL PROCEEDINGS TO DETERMINE ROLL WAVES IN OPEN CHANNELS

Abstract

The goal of this paper is consolidate a representative model previously developed by RMVP team (Rheological Studies on Viscous and Viscousplastic Materials) from UNESP - Ilha Solteira, for a typical phenomenonthat occurs on spillways, river's bed, landslides, mudflows, blood flows, for Newtonian and non-Newtonian fluids, known as roll waves. Another goal of this paper is present an experimental project designed for capturing measurements (amplitude and wavelength) of these instabilities. From a mathematical perspective, a first-order analytical model is showed, based on Cauchy's equations system, once developed by the team (Ferreira, 2007), which provides a generation condition for roll waves through temporal linear stability analysis. This model follows the remarkable work of Dressler (1949) and it is able to generate roll waves for many rheological configurations, from Newtonian to Herschel & Bulkley models, representing clean water up to muddy mixtures, respectively. A numerical routine developed in Matlab/Simulink is used to show some results that illustrate roll waves pattern. Due to the lack of roll waves data (amplitude and wavelength), the team started to focus on the experimental approach of the phenomenon, aiming to design an apparatus that would be capable to reproduce roll waves in special conditions of flow, isolated from external perturbations. This project is here presented along with a proposal of a photometric system to ascertain measures of the flow height through light absorption technique, based on experiments found in the literature. The final execution of this experiment and the correct obtaining of amplitude and wavelength will contribute for the validation of the model here presented.