Control of instabilities in non-Newtonian free surface fluid flows
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Data
2013-10-01
Autores
Maciel, Geraldo de Freitas [UNESP]
Ferreira, Fabiana de Oliveira [UNESP]
Fiorot, Guilherme Henrique [UNESP]
Título da Revista
ISSN da Revista
Título de Volume
Editor
Abcm Brazilian Soc Mechanical Sciences & Engineering
Resumo
Free surface flows in inclined channels can develop periodic instabilities that are propagated downstream as shock waves with well-defined wavelengths and amplitudes. Such disturbances are called roll waves and are common in channels, torrential lava, landslides, and avalanches. The prediction and detection of such waves over certain types of structures and environments are useful for the prevention of natural risks. In this work, a mathematical model is established using a theoretical approach based on Cauchy's equations with the Herschel-Bulkley rheological model inserted into the viscous part of the stress tensor. This arrangement can adequately represent the behavior of muddy fluids, such as water-clay mixture. Then, taking into account the shallow water and the Rankine-Hugoniot's (shock wave) conditions, the equation of the roll wave and its properties, profile, and propagation velocity are determined. A linear stability analysis is performed with an emphasis on determining the condition that allows the generation of such instabilities, which depends on the minimum Froude number. A sensitivity analysis on the numerical parameters is performed, and numerical results including the influence of the Froude number, the index flow and dimensionless yield stress on the amplitude, the wavelength of roll waves and the propagation velocity of roll waves are shown. We show that our numerical results were in agreement with Coussot's experimental results (1994).
Descrição
Palavras-chave
Roll waves, Non-Newtonian fluids, Mudflows, Open channels
Como citar
Journal Of The Brazilian Society Of Mechanical Sciences And Engineering. Rio De Janeiro Rj: Abcm Brazilian Soc Mechanical Sciences & Engineering, v. 35, n. 3, p. 217-229, 2013.