Non-Newtonian open channel flow over inclined porous bed
Ecoulement a surface libre d'un fluide non-newtonien sur un fond poreux
Résumé
As far as it is known, gravity-driven mass movement are yet to be completely understood by science community. The knowledge of such kind of flow is clearly necessary to enhance prevention tools for Engineering when applied to modeling natural events such as mudflows, mud floods and debris flow. However, the complexity of the problem lays basically on the proper modeling of fluid response to stress, which depends on its matrix, and even the prediction of instabilities propagation, which may render the whole scenario even more difficult to predict and control. In a simplified view, those flows can be seen as non-Newtonian fluids over natural inclined. Such representation is limited for one main reason: rheology average fluid behavior. As size of particles in fluid matrix may vary from dust and clay to rock and boulders, their dynamics in fluid matrix are completely averaged into simplified shearing laws. However, most of existing models for non-Newtonian fluid flow over open inclined neglect bed porosity. Of course, until recently, there was few scientific works relating yield stress fluids and porous medium both experimental and mathematically, rendering it difficult to propose any further model. In this work, a mathematical model for velocity profile is proposed for a steady and permanent Herschel-Bulkley fluid flow over an inclined porous bed. An preliminary mathematical evaluation of bed porosity is developed and some insights are given.
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