Pulsating Flow of Non-Newtonian Fluids in Pipes

Abstract

<p>The first part of this thesis contains a theoretical formulation and solution for unsteady flows (pulsatile and start-up flows) of non-Newtonian time-independent fluids through rigid pipes. The approach was based on the use of the equation of motion for axisymmetric unsteady flow of fluids in cylindrical coordinates. In the case of pulsating now, the unsteady behaviour of the pressure gradient was considered to be described by a periodic function of time, of sinusoidal form, added to a stationary pressure gradient, while for start-up flow the fluid was assumed to start its transient motion from rest due to instantaneous and sudden imposition of a stationary pressure gradient. The constitutive equation of generalized Bingham fluids was used since it represents the majority of time-independent fluids.</p> <p>A grid was imposed on the flow field in order to obtain a system of equations in finite difference form. The use of finite difference techniques provided detailed information about the time deformation of the pulsating and start-up velocity profiles as well as valuable information about energy consumption and flowrates under different pulsating flow conditions. The results are presented in the most general form so that they are widely applicable to any case where the assumptions and the boundary conditions are all satisfied. The main conclusion which can be drawn from the theoretical results is that the hydraulic power required to transport a fluid in pulsating flow is never less than that required for the same flowrate under steady flow conditions for all fluids except those which exhibit yield stress, i.e., Bingham fluids.</p> <p>On the experimental side, an investigation of pulsating flow of solid-liquid mixtures is presented. Solid-liquid mixtures are divided into two types, homogeneous suspensions and pseudohomogeneous/heterogeneous slurries. The terms homogeneous and pseudohomogeneous are used when solids concentration gradient along pipe vertical axis is constant for homogeneous flows and almost constant for pseudohomogeneous flows; while the term heterogeneous represents the cases where appreciable solids gradient along pipe vertical axis exists.</p> <p>The experiments were carried out for two types of solid-liquid mixtures. The first was a bentonite clay-water suspension with weight concentration ranges from 2.97% to 11.2%, while the second has coal/water slurry with weight concentrations between 5.34%-53.7%.</p> <p>The main aim of the experimental rig was to create a sinusoidal pressure gradient. The experimental set-up allowed different ranges of different flow parameters to be adopted, these were:</p> <p>1. Pulsing frequency ranging between 0-1.25 Hz.</p> <p>2. Pulsing amplitude (axial deformation of rubber bellows) of 34.6, 52.1 and 76.2 mm.</p> <p>3. Average flow velocity at 1.63, 2.18, and 2.63 m/sec.</p> <p>The effect of different combinations of these parameters on the ratio of the hydraulic power in pulsating flow to that in steady flow for the same throughput was studied.</p>