This study is devoted to a numerical modeling of a transient pseudo plastic fluid flow in an elastic pipe. The set partial equations for both the fluid are derived from the law conservations of mass, momentum and energy for the fluid and Hooke’s law for the wall pipe. The system governing this problem is presented and then solved numerically. The non-Newtonian character behavior of the fluid s modeled by the power law. The coupled method of characteristics, finite differences and Runge Kutta are used for spatial and temporal discretization respec-tively. Some results obtained are in good agreement with those found in the literature.
This study is devoted to a theoretical and numerical modeling of transient vaporous cavitation in a horizontal pipeline. The model approach is, essentially, based on that of the column separation model (CSM). The basic system of partial differential equations to solve is a hyperbolic type and adapts perfectly to the method of characteristics. This code, allows us, taking into account the unsteady part of the friction term, to determine at any point of the pipe, and at each instant, the average piezometric head, the average discharge and the change in volume of the vapor cavity. This study illustrates the coupled effect of the presence of air pockets resulting in cavitation and the unsteady term of friction, on the amplitude of the pressure wave. The calculation results are in good agreement with those reported in the literature.
An unstable flow of non-Newtonian fluid, with friction in a pipe is studied, describing the water hammer phenomenon. The equations of the problem are given, then solved by a numerical approach. The non-Newtonian behavior of the fluid, as well as the effect of the coefficient of friction which represents an additional mechanism of energy dissipation are investigated. The 1D and 2D problem is used simultaneously, based on the Runge-kutta method for the descritization in time, Finite differences, Characteristics for the descritization in space. The results of this article show by verifying with experience that these methods used, in addition to being simple, are also effective and give reasonable results.
In the original version of the book, the following correction has been incorporated: In Chapter 6, the second author's name has been changed from "Nawal Aachak" to "Nawal Achak". The book and the chapters have been updated with the change.
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