Numerical Simulation Studies of Mass Transfer under Steady and Unsteady Fluid Flow in Two- and Three-Dimensional Spacer-Filled Channels A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy by Gustavo Adolfo Fimbres Weihs School of Chemical Sciences and Engineering UNESCO Centre for Membrane Science and Technology The University of New South Wales Sydney, Australia July, 2008 Abstract Hollow fibre and spiral wound membrane (SWM) modules are the most common commercially available membrane modules. The latter dominate especially for RO, NF and UF and are the focus of this study. The main difficulty these types of modules face is concentration polarisation. In SWM modules, the spacer meshes that keep the membrane leaves apart also help reduce the effects of concentration polarisation. The spacer filaments act as flow obstructions, and thus encourage flow destabilisation and increase mass transfer enhancement. One of the detrimental aspects of the use of spacers is an increase of pressure losses in SWM modules. This study analyses the mechanisms that give rise to mass transfer enhancement in narrow spacer-filled channels, and investigates the relationship between flow destabilisation, energy losses and mass transfer. It shows that the regions of high mass transfer on the membrane surface correlate mainly with those regions where the fluid flow is towards the membrane. Based on the insights gained from this analysis, a series of multi-layer spacer designs are proposed and evaluated. In this thesis, a Computational Fluid Dynamics (CFD) model was used to simulate steady and unsteady flows with mass transfer in two- and three-dimensional narrow channels containing spacers. A solute with a Schmidt number of 600 dissolving from the wall and channel Reynolds numbers up to 1683 were considered. A fully-developed concentration profile boundary condition was utilised in order to reduce the computational costs of the simulations. Time averaging and Fourier analysis were performed to gain insight into the dynamics of the different flow regimes encountered, ranging from steady flow to vortex shedding behind the spacer filaments. The relationships between 3D flow effects, vortical flow, pressure drop and mass transfer enhancement were explored. Greater mass transfer enhancement was found for the 3D geometries modelled, when compared with 2D geometries, due to wall shear perpendicular to the bulk flow and streamwise vortices. Form drag was identified as the main component of energy loss for the flow conditions analysed. Implications for the design of improved spacer meshes, such as extra layers of spacer filaments to direct the bulk flow towards the membrane walls, and filament profiles to reduce form drag are discussed. i Acknowledgements This thesis would have been impossible to produce without the direct and indirect help and support of many people. Firstly, I would like to express my most sincere gratitude to my supervisor, Professor Dianne Wiley, who provided me with much needed encouragement and advice from day one. I am deeply grateful for her support and the belief she has shown in me and in this project, which was invaluable in keeping me motivated to see this thesis through. I would like to thank Adjunct A/Professor David Fletcher from the University of Sydney for his collaboration in chapters 3 and 4 and appendix A of this thesis, and for his helpful advice and support with the CFX software. Thanks are also extended to Dr. Alessio Alexiadis for his insightful discussions of transient phenomena. The computational aspects of this thesis would not have been possible without the help and support of many University staff. I would like to particularly thank Craig Howie, Ee Meen Iliffe and Wendi O’Shea-Ryan for their IT support, and Dr. Deyan Guang for his help with the acquisition and maintenance of the computer equipment used for this study. I would like to acknowledge the Australian Research Council for funding this project through a Discovery grant. I would also like to thank the University of New South Wales and the Faculty of Engineering for scholarship funding through the “University International Postgraduate Award” and the “Supplementary Engineering Postgraduate Award”. I could not go on without mentioning my fellow students, co-workers and friends at the UNESCO centre, some of whom have come and gone, and some who are still there. Thanks to Minh, Regina, Eisham, Pierre, Paul, Alessio, Olga, Yulita, Vera, Kevin, Javeed, Ebrahim, John, Dong, Ilio and Alex, for welcoming me into the group, and making it a fun and friendly place to work in. I would like to thank my parents. Although they are far away, they have provided me with encouragement and support as if they were not on the other side of the world. Finally, I would like to especially thank my wife, Kate, whose patience has been endless, and her support everlasting, and my son, Javier, for being a source of everyday motivation for all of my efforts put into this thesis. ii Publications emanating from this thesis include the following: Journal Papers: Fimbres-Weihs, G.A.; Wiley, D.E.; Fletcher, D.F. Unsteady Flows with Mass Transfer in Narrow Zigzag Spacer-Filled Channels: A Numerical Study. Ind. Eng. Chem. Res. 2006, 45, 6594-6603. Fimbres-Weihs, G.A.; Wiley, D.E. Numerical Study of Mass Transfer in Three- Dimensional Spacer-Filled Narrow Channels with Steady Flow. J. Membr. Sci. 2007, 306, 228-243. Conference Poster: Fimbres-Weihs, G.A.; Wiley, D.E. Unsteady Flows with Mass Transfer in Narrow Spacer-Filled Channels: A Numerical Study, International Congress on Membranes and Membrane Processes (ICOM) 2005, Seoul, Korea, August 21-26, 2005. Conference Presentation: Fimbres-Weihs, G.A.; Wiley, D.E. Three-Dimensional Spacer-Filled Narrow Channels with Steady Flow, 6th International Membrane Science and Technology Conference (IMSTEC) 2007, Sydney, Australia, November 5-9, 2007 iii Table of Contents Abstract i Acknowledgements ii Table of Contents iv Nomenclature viii List of Symbols viii Greek Symbols xiii Subscripts xiv Chapter 1 1. Introduction 1 Chapter 2 2. Literature Review 5 2.1. Basic Concepts 6 2.1.1. Diffusion in Systems with Multiple Ionic Components 6 2.1.2. Mass Transfer Coefficient 9 2.1.3. Energy losses and the Friction Factor 12 2.2. Concentration Polarisation 14 2.3. Turbulence promoters and Spacer Studies 22 2.3.1. Heat transfer enhancement 22 2.3.2. Mass transfer enhancement 25 2.3.2.1. Flow regimes 27 2.3.2.2. Mechanisms for mass transfer enhancement 29 2.3.2.3. Energy loss trade-off 31 2.3.2.4. Variation of geometric characteristics 35 2.3.2.5. Effect of turbulence promoters on fouling 36 2.3.2.6. Other mass transfer enhancement techniques 38 2.4. Computational Fluid Dynamics in Membrane studies 39 2.4.1. Two-dimensional studies 39 2.4.2. Three-dimensional studies 46 2.5. Conclusion 51 iv Chapter 3 3. Methodology 54 3.1. CFD Theory 54 3.1.1. Transport Equations 54 3.1.2. Mass Transport 56 3.1.3. The Finite Volume Method 57 3.1.4. Discretisation schemes 59 3.2. Verification and Validation 62 Chapter 4 4. Unsteady Flows with Mass Transfer in Narrow zig-zag Spacer-Filled Channels 65 4.1. Introduction 65 4.2. Problem Description, Assumptions and Methods 65 4.3. Results and Discussion 68 4.3.1. Steady flow 68 4.3.2. Moderately unsteady flow 71 4.3.3. Highly unsteady flow 76 4.3.4. Friction Factor and Sherwood number 80 4.3.5. Comparison of velocity and concentration effects 82 4.3.6. Fourier Analysis 85 4.4. Conclusions 87 Chapter 5 5. Mass Transfer in Three-Dimensional Spacer-Filled Narrow Channels with Steady Flow 89 5.1. Introduction 89 5.2. Problem Description, Assumptions and Methods 90 5.2.1. Geometry description 93 5.2.2. Characterization of the projection of a vortex onto a plane 95 5.2.3. Vortices in 2D flow 96 5.3. Results and Discussion 97 5.3.1. Mesh Independence Study 97 5.3.2. Hydrodynamics 98 5.3.2.1. Validation 98 v 5.3.2.2. 90° Orientation 99 5.3.2.3. 45° Orientation 104 5.3.3. Mass Transfer effects 108 5.3.3.1. Validation 108 5.3.3.2. 90° Orientation 109 5.3.3.3. 45° Orientation 113 5.3.3.4. Comparisons of Mass Transfer effects between different geometries 115 5.4. Conclusions 118 Chapter 6 6. Multi-layer spacer designs for minimum drag and maximum mass transfer 120 6.1. Introduction 120 6.2. Problem Description, Assumptions and Methods 121 6.2.1. Channel Interpolation 125 6.2.2. Cost Estimation 127 6.3. Results and Discussion 131 6.3.1. Two-layer spacer geometries 131 6.3.2. Multi-layer spacer geometries 134 6.3.3. Unsteady flow 141 6.3.4. Economic analysis of spacer performance 143 6.3.4.1. Base membrane cost of $100/m2 145 6.3.4.2. Effect of changes in membrane cost 151 6.4. Conclusions 153 Chapter 7 7. Conclusions 157 References 165 Appendices 177 Appendix A A. Multiple Ionic Components 178 A.1. Introduction 178 vi A.2. Theory 178 A.2.1. Mass Transfer 178 A.2.2. Maxwell-Stefan diffusion model 182 A.2.3. Nernst-Planck diffusion model 185 A.3. Incorporation of Multiple Ionic Effects into CFD 188 A.4. Problem description 189 A.5. Results and Discussion 191 A.6. Conclusions 193 Appendix B B. Videos produced in the course of this thesis 194 B.1. Videos from Chapter 4 194 B.2. Videos from Chapter 5 195 B.3. Videos from Chapter 6 196 vii Nomenclature Symbol Description Units a , , c , db Empirical constants aE Ellipse major axis m ae Ellipse minor axis m A Area m2 A Area vector m2 2 Am Membrane area m 2 Amt Mass transfer area m 2 AT Cross-sectional area m ,,, Empirical constants a,aij Coefficient matrix kgmol