The Hydrodynamics of Gravity-Driven Vessel Drainage of Newtonian and Non-Newtonian Liquids

Abstract

The thesis covers the theoretical investigation of unsteady drainage of non-Newtonian fluids from a circular tank through a circular pipe, which is attached from the center of the tank at the bottom. This research endeavors to acquire a better knowledge of the procedures, thus the most part of the thesis is theoretical instead of experimental. Be that as it may, the expectation, is that the preferable understanding over experimental so picked up, will give down to practical benefits, for example, enhancement of the processing method, improved control of the processing and improving the value of production. The primary objective of this work is to create mathematical models so that to calculate the velocity profile, flow rate, shear stress, average velocity, time efflux, the relationship between the time (varying with the depth of a tank) and the time required for complete drainage for isothermal flow of incompressible Newtonian and in addition of non-Newtonian fluids in a circular tank. In this thesis, cylindrical co ordinates system is used for different proposed non-Newtonian models, such as Power law, Ellis, Phan Thien Tanner (PTT), Couple Stress fluids for tank drainage flow; an exact solution is obtained for each of subsequent linear Partial Differential Equation (PDE) subject to suitable boundary conditions. The effect of magnetic field on tank drainage flow for electrically conducting Newtonian and Power-law fluids are also studied. Where ever, the exact solution seems to be impossible, analytic solutions of the resulting PDE are obtained through Adomian Decomposition Method as well as Perturbation methods for electrically conducting Newtonian fluid model, while for electrically conducting Power-law fluid model only Perturbation solution have been found as the main objectives in this study. Numerical computations were also carried out in commercial CFD software Ansys FLUENT®14 based on a finite-volume method for the effect of the slip parameter for Newtonian fluid as well as power-law fluid. The second-order-upwind technique was used to discretize convective terms spatially. Convergence criteria were set at 10-3 for mass and momentum residuals, and numerical solutions are also compared with exact solution for the proposed problem, as a result we find out that numerical found high similarity under 4-5%. From the solution of Power-law fluid model, we have point out that as the fluid becomes thicker, the velocity xxv of the fluid decrease, we have also detected that for considering shear thinning fluid it will take more time to drainage completely as compared to shear-thickening fluid and we have point out that if fluid is slip on the wall of pipe which is attached with the tank, it will take a less time to drain as compared to no-slip. In this work, we have also deducted that electrical conductivity and applied field are directly proportional to velocity field; and obviously, the tank will drain fast as the electromagnetic forces increase. The analogy of the Ellis fluids and its different cases such as Newtonian, Bingham Plastic and Power-law fluid for the velocity profile and time required to complete drainage unfold that as the higher apparent viscosity for Ellis fluid, the velocity of the fluid increases; and it is also observed that Ellis fluid drains quickly as compared to its special cases. For PTT fluid model we have noted that the PTT fluid will drain fast by the increase of parameter related to elongational behavior, Deborah and Stokes number; and its also important to note that LPTT fluid drains quickly than UCM. The draining of fluid from the storage tank is generally made by the hydrodynamic pressured system and/or drain by gravity at which the fluid is forced out through a small pipe outlet, however these are used extensively throughout the industries, such as the chemical industry, petroleum industry, biomedical and pharmaceutical industry, waste-water management, water distribution and supply. For such situational uses, these investigated models accurately represent the tank draining behavior for all type tanks with such requirements. The results of the investigated models from perspective of fluid types, their exact solution and some numerical solutions should also be taken into consideration by the researchers of the fields focusing the research of fluid mechanics, analysis of the solution and their characteristics, numerical analysis, simulations, tank storage, shapes and architectural designs, bio-fluids, chemical and pharmaceutical fluid mechanics.