The Chaotic Mixing in Eccentric Helical Annular Mixer
|Keywords||Chaotic mixing Spiral ring Mixer HYDROELASTICITY Shear thinning fluid Mixing effect Laminar mixing Eccentric cylinder Eccentricity Periodic sequence|
Mixing of fluids is common in nature and industrial applications. There exist numerous reasons to be interested in mixing. For fluids with high viscosities such as polymers, effective mixing is not achievable by turbulent flow and laminar flow is the only method for mixing of fluids with high viscosities. With the importance of mixing for polymer processing increasing, better understanding of mixing in laminar flows is needed. Recently, mixing of liquids has been associated with the chaotic behavior of dynamics system and it is to provide a new method for analyzing and understanding numerous mixing. In this dissertation, chaotic advection of Newtonian and Non-Newtonian fluid in Eccentric Helical Annular Mixer (EHAM) has been studied systematically through experimental and computational methods. The aim is want to make sure the dominating effects on chaotic mixing in EHAM and supply with guidance for the design efficient mixer in industry.Firstly, the author investigated the impact of fluid elasticity on the chaotic mixing by experiments and numerical simulations. Results from experiments with a constant-viscosity, elastic fluids (Boger fluids) and computations using the corresponding Oldroyd_B constitutive equation are presented. The high-order finite element methods are used to obtain high accurate solutions of the steady flows. Characteristics of the chaotic mixing are analyzed by numerical simulation and experiment through examining of the asymptotic coverage of a passive tracer. The photos of experiments are analyzed by Digital Image Processing to compare the mixing in different conditions. Secondly, two new quantitative methods are employed to analyze the two-dimensional chaotic mixing in EHAM. The impacts of angular displacement and the eccentricity on the two-dimensional chaotic mixing between eccentric cylinders have been discussed. Lastly, the author investigated the impact of the axial pressure gradient on three-dimensional chaotic mixing in EHAM by computing the mixing efficiency of a tracer. Then the author proposed a quantitative method to investigate three-dimensional chaotic mixing and did the comparative studies of three-dimensional chaotic mixing in EHAM among Newtonian fluids, viscoelastic fluids and shear-thinning fluids.According to the study, the author discovered both in two-dimensional and in three-dimensional flows in EHAM, the impacts of relatively low fluid elasticity on chaotic mixing is negligible, and this disagrees with Niederkorn&Ottino’s conclusion that small deviations in the velocity field due to elasticity will produce large effects on chaotically advected patterns. Through careful analyses the author is able to concludethat the primary reason leading to Niederkorn&Ottino’s incorrect conclusion is the numerical errors of velocity fields in their calculations and the errors of eccentricity in their experiments. By numerical simulations the author found the eccentricity produces very large effects on the chaotic mixing. When the eccentricity is high, there always exist very large regular zones in time-periodic flows and these regular zones can’t be removed in aperiodic flows. The optimal configuration is that the dimensionless eccentricity is 0.5. In the case of the dimensionless eccentricity 0.5, if there are larger regular zones in the time-periodic chaotic flows, the efficiency of chaotic mixing can be improved using corresponding symmetry-breaking sequences, otherwise the efficiency of time-periodical flows is better than of the corresponding symmetry-breaking aperiodic flows. Through the numerical studies, the author can conclude that the major impact on the three-dimensional chaotic mixing is the axial average-velocity and the axial velocity distribution. As a whole, efficiency of the chaotic mixing of shear-thinning fluids is worse than of Newtonian fluids, but there are different reasons in the two-dimensional and the three-dimensional chaotic mixing in EHAM.