Lattice Boltzmann Method: Theory and Applications to Transport Processes.
저자
발행사항
Ann Arbor : ProQuest Dissertations & Theses, 2020
학위수여대학
Carnegie Mellon University Chemical Engineering
수여연도
2020
작성언어
영어
주제어
학위
Ph.D.
페이지수
162 p.
지도교수/심사위원
Advisor: Jhon, Myung S.;Biegler, Lorenz T.
With advances in computational power and numerical methods, almost every aspect of chemical engineering problems can now be modeled and be predicted accurately using simulations. Depending on the system, different strategies are required to make a meaningful model: some require scientific details, some require handling of big data, and some require computational efficiency. Constructing an accurate and efficient model is not a trivial task and requires tremendous amount of input and knowledge regarding such system. The focus of this thesis is the development and application of Lattice Boltzmann method (LBM), which is a complementary transport phenomena simulation technique and has been receiving tremendous amount of interests due to its advantages over traditional computational fluid dynamics (CFD). Some of the LBM’s advantages are computational efficiency, ability to bridge microscale with macroscale, inherently transient and satisfying conservation laws with constitutive relationship through the relaxation process as well as thermodynamic consistency. Furthermore, LBM’s rule-based approach allows for flexibility, unlike any other CFD methods. As a result, over the past decades, tremendous progress has been made in the development of particle-based discrete simulation methods rose in popularity. In this thesis, we will discuss a various aspects of LBM, a mesoscale description of transport process, based on kinetic theory and applied to wide range of applications. Unlike CFD, multiphase LBM is inherently advantageous due to its rule based system and straight forward algorithm, which results in high parallel efficiency.Through process of collision and streaming process of molecule representations, LBM can capture momentum and energy transport. The molecule representations are called pseudoparticle, in that the simulated particles are just the representation and not real particles.In Chapter 2, we investigate LBM descriptive for isothermal single phase fluids. Although this system is very well studied in the past, we provide condensed review needed to make stem of LBM algorithm. This covers fundamental transport equations for discrete phase space distribution function or its moment such as density and fluid velocity complement to Navier-Stokes equation in continuum mechanics. In addition, discretization of space, boundary condition, and turbulence models including large eddy simulation (LES) and k-ε model is discussed. We also developed unique inverse approach via parameter estimation method to obtain optimal parameters in turbulence model (tested for Smagorinsky model) by capturing LBM’s rule based advantage.In Chapter 3, we examine multiphase simulation which is one of our key contributions of this thesis. We generalize pseudopotential method, first introduced by Shan and Chen and extended to high density ratio limit, which is the biggest challenge in LBM community. Previously, multiphase LBM was limited to low density ratios application and/or had numerical instability issues. We can extend our simulation to high density limit and also found the causes of the numerical instability. We construct various pseudopotential models to resolve these stumbling blocks. We first improve Shan-Chen’s idea by examining two simple functional forms for pseudopotential which include stretched exponential and stretched Lorentzian form. To make thermodynamic consistency, we also use various forms of cubic equations of state (EOS) to calculate pseudopotential. Furthermore, we introduce modified form of cubic EOS to meet the requirements of stability. Utilizing Heaviside step function, we smoothen the meta-stable region of cubic EOS and achieved, for the first time in LBM community, stable high density ratio multiphase LBM. Using our modified cubic EOS, we perform multiphase simulation reaching high density ratio without any numerical instability. Our modified EOS has been verified through several different benchmark cases: droplet agglomeration and contact angle study. Especially, we investigate temperature dependences on surface tension and contact angle and compared our findings with literature data. We constructed L-σ to correlate two different surface tension formulae. L-σ plot appears to have linear relationship. In our benchmark cases, our modified EOS shows improved numerical stability over the previously used cubic EOS. To obtain physical meaning of parameters used in LBM, we also perform molecular dynamics (MD) and found that mesoscale parameters in LBM is related to molecular interaction parameters used in MD. This implies that one can numerically link mesoscale to molecular scale and make multiscale modeling to be feasible.In Chapter 4, we extend our analyses to non-isothermal systems by coupling energy transport with momentum transport. LBM can be tuned to capture energy. Internal energy density distribution function method is the current standard in thermal LBM simulation and this method has been adopted in this chapter. In this thesis, we tackle some of the cutting-edge technology such as heat assisted magnetic recording (HAMR) and pressurized water reactors (PWR). Standard LBM is used to study thermal conduction and is modified to examine nanoscale heat transfer (i.e., Cattaneo equation) to offer insights on temperature distribution along HAMR disks. We couple this thermal LBM with momentum LBM discussed in Chapter 2. We first test our simulation to natural convection (Rayleigh-Benard cell) and extend analysis to forced convection. Integrating thermal LBM with momentum LBM, for the first time, we investigate PWR using LBM. PWR is the most widely used type of a nuclear power plant. By taking benchmark examples, we compare our LBM result to CFD like Fluent as well as other empirical correlation based codes, such as MATRA and CUPID. Our LBM perform on par with other tools, if not better in some cases. To further explore our simulation to practical situation, we study role of guide tube and also implemented Jens-Lottes correlation, which accounts for the CRUD (Chalk River unidentified deposit) effect.In Chapter 5, we conclude this thesis and summarize key contribution to the field of mesoscale LBM simulation. We also provide discussion for future work plan including LBM integration with optimization using inverse approach, extension of multiscale modeling using LBM as centerpiece, and other potential LBM use in real applications. Furthermore, we briefly examined phase change induced flow and thermocapillary flow, as these have interesting applications for emerging technology. Our findings on these are summarized.
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