Numerical solution of the Saint Venant equation for Non-Newtonian fluid

Abstract

Non-Newtonian fluid flow through a Venturi channel is studied using the Saint Venant equation. The nonlinear hyperbolic equation is numerically tricky to solve, therefore in this study, we consider the finite volume method with staggered grids which we find suitable for control applications. Both steady state and dynamic solutions of the fluids with different rheological properties are simulated and analyzed. The purpose of this study is to develop a numerical algorithm for estimation of flow rate of a non-Newtonian fluid in an open channel. Because a non-Newtonian fluid flow is often associated with supercritical flow upstream, the standard subcritical flume may not be suitable for estimating the flow rate. This study reveals that when a sufficient contraction is introduced in a channel, the supercritical flow jumps to subcritical flow level and then passes through the critical depth at the throat while accelerating towards the channel end. With this flow transition, the study shows that in steady states a unique relationship can be established between the flow rate and the free surface level at the gauging point. The dynamic solution also shows that the system responds positively for a step change in the flow rate, reaching the steady state solution within the simulation run time.