Numerical Simulation in Steady flow of Non-Newtonian Fluids in Pipes with Circular Cross-Section

In the chemical and process industries, it is often required to pump fluids over long distances from storage to various processing units and/or from one plant site to another. There may be a substantial frictional pressure loss in both the pipe line and in the individual units themselves. It is thus often necessary to consider the problems of calculating the power requirements for pumping through a given pipe network, the selection of optimum pipe diameter, measurement and control of flow rate, etc. A knowledge of these factors also facilitates the optimal design and layout of flow networks which may represent a significant part of the total plant cost (Chhabra & Richardson, 2008). The treatment in this chapter is restricted to the laminar, steady, incompressible fully developed flow of a non-Newtonian fluid in a circular tube of constant radius. This kind of flow is dominated by shear viscosity. Then, despite the fact that the fluid may have time-dependent behavior, experience has shown that the shear rate dependence of the viscosity is the most significant factor, and the fluid can be treated as a purely viscous or time-independent fluid for which the viscosity model describing the flow curve is given by the Generalized Newtonianmodel. Time-dependent effects only begin to manifest themselves for flow in non-circular conduits in the form of secondary flows and/or in pipe fittings due to sudden changes in the cross-sectional area available for flow thereby leading to acceleration/deceleration of a fluid element. Even in these circumstances, it is often possible to develop predictive expressions purely in terms of steady-shear viscous properties (Chhabra & Richardson, 1999). The kind of flow considered in this chapter has been already studied experimentally by Hagen Poiseuille in the first half of the XIX Century for Newtonian fluids and it has analytical solution. However, even though in steady state non-Newtonian fluids can be treated as purely viscous, the shear dependence of viscosity may result in differential equations too complex to permit analytical solutions and, consequently, it is needed to use numerical techniques to obtain numerical solutions. It is in this context when Computational Rheology plays its role 1