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A Novel Lattice Boltzmann Method for Direct Numerical Simulation of Multiphase Flows

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A Novel Lattice Boltzmann Method for Direct Numerical Simulation of Multiphase Flows A Novel Lattice Boltzmann Method for Direct Numerical Simulation of Multiphase Flows Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Zhao Yu, B.S. Graduate Program in Chemical Engineering The Ohio State University 2009 Dissertation Committee: Liang-Shih Fan, Adviser Chiu-Yen Kao L. James, Lee Kurt W. Koelling Copyright by Zhao Yu 2009 ii ABSTRACT Multiphase flows involving bubbles and droplets are ubiquitous in nature and in many industrial processes. Detailed information of such flows can be acquired from direct numerical simulations that directly resolve the flow on the bubble or droplet scale. In recent years, the lattice Boltzmann method (LBM) has emerged as a novel numerical method for multiphase flow simulation. While having many favorable features such as incorporation of physics on the more fundamental level and efficient algorithm for fast computation, the current multiphase LBM still faces challenges in issues such as numerical instability and narrow parameter window, which severely restrict its application in a broad range of real world engineering problems. This dissertation presents the development of a novel multiphase LBM which significantly expands the application of the method in various flow problems. Specifically, three techniques are developed to achieve enhanced performance in three aspects: First, new interaction potential functions are developed for multi-component LBM model to improve numerical stability at high density ratios between the liquid and gas phase. Second, an adaptive mesh refinement (AMR) scheme is developed to provide sufficient resolution of the gas-liquid interface. Third, the multi-relaxation time iii (MRT) scheme is incorporated into the interaction potential model to enhance the numerical stability at low viscosities. The above new techniques are presented in detail, and simulations are performed in both 2D and 3D to evaluate their performance. It is demonstrated that the new interaction potential model is able to raise the stable density ratio from below 50 to over 1000. The AMR can provide accurate predictions of the interface, while reduce the computation cost by about 50% in real computations. In addition, with the MRT algorithm the maximum Reynolds number in bubble simulations can be increased from 100 to about 1000. The performance of the newly developed LBM technique is further illustrated in different applications. In the study of the buoyant rise of a gas bubble in a viscous liquid, simulations are carried out to investigate the shape and rise velocity of the bubble. Particularly, both bubbles with large deformation and bubbles with high Reynolds number are studied. Good agreement is found between the model predictions and experimental results in the literature. Then the collision between a liquid droplet and a porous surface is investigated. Using the adaptive mesh approach, the flows on both the droplet scale and the pore scale are direct resolved simultaneously. The deformation of the droplet on the porous surfaces is compared to that on impermeable surfaces. Finally, the LBM simulation is performed for bubble formation in microchannels. The bubble shape and formation mechanism are discussed in different regimes and compared with experimental results. iv In summary, a systematic investigation is conducted to improve the stability and accuracy of the LBM for multiphase simulations. A novel LBM model is developed and its performance is studied in various test problems. The application of the new model in the simulation of bubble rise, droplet collision, and microchannel bubble formation further illustrates the enhanced capability of the current LBM model. v DEDICATION Dedicated to my family vi ACKNOWLEDGEMENTS I would like to express my sincere gratitude to my advisor Dr. Liang-Shih Fan for his support and encouragement which made this dissertation possible. He has helped me greatly by providing me with the freedom and confidence to explore the research topics that I am interested in. I am also grateful to Dr. James Lee, Dr. Kurt Koelling, and Dr Michael Paulaitis who served on my general exam and dissertation committees. Their helpful suggestions and comments are invaluable to the quality of this dissertation. I would also like to thank the members in my research group. Particularly, I would like to thank Fei Wang and Orin Hemminger for their assistance in the experimental work. I also benefit a lot from my senior group members Drs Yang Ge, Raymond Lau and Alissa Park, who gave me important advice on my research and beyond. The help and friendship from Fanxing Li, Ray Kim, Deepak Sridhar, Zhenchao Sun, Andrew Tong, Fu-Chen Yu and Liang Zeng have made my study in OSU a joyful experience. The support of the Ohio Supercomputer Center on the computational resource for this study is also gratefully acknowledged. Finally, I would like to thank my family for their everlasting love and support. vii VITA August 1981…………………………….….. Born - Beijing, P.R. China June 2003……………………………………B.Sc. Engineering Mechanics, Tsinghua University, Beijing, P.R. China July 2003 – June 2004………………………Research Associate, Tsinghua University, Beijing, P.R. China September 2004 – December 2009……….…Graduate Research Associate, Department of Chemical and Biomolecular Engineering, The Ohio State University PUBLICATIONS 1. Yu, Z ., Fan, L-S. 2009. An Interaction Potential Based Lattice Boltzmann Method With Adaptive Mesh Refinement (AMR) For Two-Phase Flow Simulation. Journal of Computational Physics 228 6456--6478 2. Yu, Z , Wang, F., and Fan, L-S, 2008. Experimental and Numerical Studies of Water Droplet Impact on a Porous Surface in the Film-Boiling Regime, Industrial & Engineering Chemistry Research. 47(23), 9174-9182 3. Yu, Z ., Fan, L-S. 2008. Direct Simulation of the Buoyant Rise of Bubbles In Infinite Liquid Using Level Set Method. Canadian Journal of Chemical Engineering. 86, 267-275 4. Yu, Z. , Hemminger, O., Fan, L-S. 2007. Experiment and Lattice Boltzmann Simulation of Two-phase Gas-liquid Flows in Microchannels. Chemical Engineering Science, 62(24), 7172-7183 viii 5. Yu, Z ., Ge, Y., Fan, L-S, 2007. Multi-scale Simulation of Oblique Collisions of A Droplet on A Surface in the Leidenfrost Regime. Chemical Engineering Science, 62, 3462 – 3472 6. Fan, L-S., Hemminger, O., Yu, Z. , et al., 2007. Bubbles in Nanofluids. Industrial & Engineering Chemistry Research, 46(12), 4341-4346 FIELDS OF STUDY Major Field: Chemical Engineering ix TABLE OF CONTENTS ABSTRACT.......................................................................................................................iii DEDICATION................................................................................................................... vi ACKNOWLEDGEMENTS.............................................................................................. vii VITA................................................................................................................................viii TABLE OF CONTENTS.................................................................................................... x LIST OF TABLES...........................................................................................................xiii LIST OF FIGURES ......................................................................................................... xiv NOMENCLATURE ......................................................................................................xviii CHAPTER 1 INTRODUCTION .............................................................................................................. 1 1.1. Multiphase flow .................................................................................................. 1 1.2. Numerical simulation of multiphase flow........................................................... 2 1.3. Direct numerical simulation (DNS) techniques for dynamic interfaces............. 4 1.4. Scope of current work......................................................................................... 6 CHAPTER 2 OVERVIEW OF LATTICE BOLTZMANN METHOD ................................................... 9 Abstract........................................................................................................................... 9 2.1. Kinetic theory and Boltzmann equation ............................................................. 9 2.2. Lattice Boltzmann method................................................................................ 12 2.3. Boundary conditions......................................................................................... 15 2.3.1. Periodic condition ..................................................................................... 15 2.3.2. Bounce back condition .............................................................................. 15 2.3.3. Velocity condition ..................................................................................... 16 2.3.4. Pressure condition .................................................................................... 17 2.4. Force term......................................................................................................... 18 2.5. LBM for multiphase flow ................................................................................. 20 2.6. Advantages and technical barriers .................................................................... 22 2.7. Conclusions......................................................................................................
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