Lattice Boltzmann methods for multiphase flow and phase-change heat transfer

Over the past few decades, tremendous progress has been made in the development of particle-based discrete simulation methods versus the conventional continuum-based methods. In particular, the lattice Boltzmann (LB) method has evolved from a theoretical novelty to a ubiquitous, versatile and powerful computational methodology for both fundamental research and engineering applications. It is a kinetic-based mesoscopic approach that bridges the microscales and macroscales, which offers distinctive advantages in simulation fidelity and computational efficiency. Applications of the LB method are now found in a wide range of disciplines including physics, chemistry, materials, biomedicine and various branches of engineering. The present work provides a comprehensive review of the LB method for thermofluids and energy applications, focusing on multiphase flows, thermal flows and thermal multiphase flows with phase change. The review first covers the theoretical framework of the LB method, revealing certain inconsistencies and defects as well as common features of multiphase and thermal LB models. Recent developments in improving the thermodynamic and hydrodynamic consistency, reducing spurious currents, enhancing the numerical stability, etc., are highlighted. These efforts have put the LB method on a firmer theoretical foundation with enhanced LB models that can achieve larger liquid-gas density ratio, higher Reynolds number and flexible surface tension. Examples of applications are provided in fuel cells and batteries, droplet collision, boiling heat transfer and evaporation, and energy storage. Finally, further developments and future prospect of the LB method are outlined for thermofluids and energy applications

Double population cascaded lattice boltzmann method

Lattice Boltzmann Methods (LBM) are powerful numerical tools to simulate heat and mass transfer problems. Instead of directly integrating the N-S equations, LBM solves the discretized form of the Boltzmann Transport Equation (BTE), keeping track of the microscopic description of the systems. Therefore, LBM can solve fluid flows with great stability and computational efficiency, especially complex geometry fluid flows. For thermal flows, double distribution function (DDF) LBM scheme is the most popular and successful approach. But it is evident from the literature that existing double distribution function (DDF) LBM approaches, which use two collision operators, involve collision schemes which violate Galilean invariance, therefore producing instabilities for flows with high Re and Ra numbers. In this thesis, a double population cascaded lattice Boltzmann method is developed to improve the DDF LBM scheme from this drawback. The proposed method reduces the degree of violation of Galilean invariance, increasing the stability and accuracy of the LBM scheme. The scheme was implemented to simulate advection-diffusion, forced convection and natural convection heat transfer problems. The proposed scheme was also successfully tested for turbulent flow regimes and 3-D fluid flow in porous media. The results obtained from this work are in strong agreement with those available in the literature obtained through other numerical methods and experiments.Os métodos de ”Lattice”Boltzmann (LBM) são potentes ferramentas numéricas para simular problemas de transferência de massa e calor. Ao invés de integrar diretamente as equações de Navier-Stokes, o método LBM resolve, de forma discretizada, a equação de transporte de Boltzmann, acompanhando a descrição microscópica dos sistemas. O método LBM pode solucionar fluxo de fluidos com grande estabilidade e eficiência computacional, especialmente fluxos em geometrias complexas. Para fluxos térmicos, o esquema LBM de dupla função de distribuição (DDF) é a abordagem mais popular e bem sucedida. Mas é evidente, a partir da literatura, que as abordagens LBM de dupla função de distribuição (DDF), as quais utilizam dois operadores de colisão, envolvem esquemas de colisão que violam a invariância de Galileu, produzindo instabilidades para fluxos com números Re e Ra altos. Nesta tese, o método de ”Lattice”Boltzmann em cascata de dupla população em cascata é desenvolvido para corrigir o esquema DDF LBM. O método proposto reduz o grau de violação da invariância de Galileu, aumentando a estabilidade e acurácia do método LBM. O método foi implementado para simular problemas de advecção, difusão, convecções natural e forçada típicos de transferências de calor. O esquema proposto foi também bem sucedido em regimes de fluxo turbulento e em escoamentos 3-D em meios porosos. Os resultados obtidos neste trabalho estão fortemente de acordo com experimentos e métodos numéricos disponíveis na literatura

TURBULENT TRANSITION SIMULATION AND PARTICULATE CAPTURE MODELING WITH AN INCOMPRESSIBLE LATTICE BOLTZMANN METHOD

Derivation of an unambiguous incompressible form of the lattice Boltzmann equation is pursued in this dissertation. Further, parallelized implementation in developing application areas is researched. In order to achieve a unique incompressible form which clarifies the algorithm implementation, appropriate ansatzes are utilized. Through the Chapman-Enskog expansion, the exact incompressible Navier-Stokes equations are recovered. In initial studies, fundamental 2D and 3D canonical simulations are used to evaluate the validity and application, and test the required boundary condition modifications. Several unique advantages over the standard equation and alternative forms found in literature are found, including faster convergence, greater stability, and higher fidelity for relevant flows. Direct numerical simulation and large eddy simulation of transitional and chaotic flows are one application area explored with the derived incompressible form. A multiple relaxation time derivation is performed and implemented in a 2D cavity (direct simulation) and a 3D cavity (large eddy simulation). The Kolmogorov length scale, a function of Reynolds number, determines grid resolution in the 2D case. Comparison is made to the extensive literature on laminar flows and the Hopf bifurcation, and final transition to chaos is predicted. Steady and statistical properties in all cases are in good agreement with literature. In the 3D case the relatively new Vreman subgrid model provides eddy viscosity modeling. By comparing the center plane to the direct numerical simulation case, both steady and unsteady flows are found to be in good agreement, with a coarse grid, including prediction of the Hopf bifurcation. Multiphysics pore scale flow is the other main application researched here. In order to provide the substrate geometry, a straightforward algorithm is developed to generate random blockages producing realistic porosities and passages. Combined with advection-diffusion equations for conjugate heat transfer and soot particle transport, critical diesel particulate filtration phenomena are simulated. To introduce additional fidelity, a model is added which accounts for deposition caused by a variety of molecular and atomic forces. Detailed conclusions are presented to lay the groundwork for future extensions and improvements. Predominantly, higher lattice velocity large eddy simulation, improved parallelization, and filter regeneration

Mesoscopic Numerical Methods for Reactive Flows: Lattice Boltzmann Method and Beyond

Reactive flows are ubiquitous in several energy systems: internal combustion engines, industrial burners, gas turbine combustors. Numerical modeling of reactive flows is a key tool for the development of such systems. However, computational combustion is a challenging task per se. It generally includes different coupled physical and chemical processes. A single model can come to deal with simultaneous processes: turbulent mixing, multi-phase fluid-dynamics, radiative heat transfer, and chemical kinetics. It is required not only of mathematically representing these processes and coupling them to each other, but also of being numerical efficient. In some applications, the numerical model needs to be able to deal with different length scales. For instance, a continuum approach to reactive flows in porous media burners is not adequate: processes occurring at the pore-scale are not taken into account properly. It is therefore fundamental to have numerical methods able to capture phenomena at the microscopic scales and incorporate the effects in the macroscopic scale. The lattice Boltzmann method (LBM), a relatively new numerical method in computational fluid-dynamics (CFD), summarizes the requirements of numerical efficiency and potential to relate micro-and macro-scale. However, despite these features and the recent developments, application of LBM to combustion problems is limited and hence further improvements are required. In this thesis, we explore the suitability of LBM for combustion problems and extend its capabilities. The first key-issue in modeling reactive flows is represented by the fact that the model has to be able to handle the significant density and temperature changes that are tipically encountered in combustion. A recently proposed LBM model for compressible thermal flows is extended to simulate reactive flows at the low Mach number regime. This thermal model is coupled with the mass conservation equations of the chemical species. Also in this case a model able to deal with compressibility effects is derived. To this purpose, we propose a new scheme for solving the reaction-diffusion equations of chemical species where compressibility is accounted for by simply modifying the equilibrium distribution function and the relaxation frequency of models already available in the literature. This extension enables one to apply LBM to a wide range of combustion phenomena, which were not properly adressed so far. The effectiveness of this approach is proved by simulating combustion of hydrogen/air mixtures in a mesoscale channel. Validation against reference numerical solution in the continuum limit are also presented. An adequate treatment of thermal radiation is important to develop a mathematical model of combustion systems. In fact, combustion incorporates also radiation process, which tends to plays a significant role if high temperatures (and solid opaque particles) are involved. In the thesis a LBM model for radiation is presented. The scheme is derived from the radiative transfer equation for a participating medium, assuming isotropic scattering and radiative equilibrium condition. The azimuthal angle is discretized according to the lattice velocities on the computational plane, whereas an additional component of the discrete velocity normal to the plane is introduced to discretize the polar angle. The radiative LBM is used to solve a two-dimensional square enclosure bechmark problem. Validation of the model is carried out by investigating the effects of the spatial and angular discretizations and extinction coefficient on the solution. To this purpose, LBM results are compared against reference solutions obtained by means of standard Finite Volume Method (FVM). Extensive error analysis and the order of convergence of the scheme are also reported in the thesis. In order to extend the capabilities of LBM and make it more efficient in the simulation of reactive flows, in this thesis a new formulation is presented, referred to as Link-wise Artificial Compressibility Method (LW-ACM). The Artificial Compressibility Method (ACM) is (link-wise) formulated by a finite set of discrete directions (links) on a regular Cartesian grid, in analogy with LBM. The main advantage is the possibility of exploiting well established technologies originally developed for LBM and classical computational fluid dynamics, with special emphasis on finite differences, at the cost of minor changes. For instance, wall boundaries not aligned with the background Cartesian mesh can be taken into account by tracing the intersections of each link with the wall (analogously to LBM technology). LW-ACM requires no high-order moments beyond hydrodynamics (often referred to as ghost moments) and no kinetic expansion. Like finite difference schemes, only standard Taylor expansion is needed for analyzing consistency. Preliminary efforts towards optimal implementations have shown that LW-ACM is capable of similar computational speed as optimized (BGK-) LBM. In addition, the memory demand is significantly smaller than (BGK-) LBM. Two- and three-dimensional benchmarks are investigated, and an extensive comparative study between solutions obtained through FVM. Numerical evidences suggest that LW-ACM represents an excellent alternative in terms of simplicity, stability and accurac

Lattice Boltzmann Methods for Turbulent Flows – Application to Coriolis Mass Flowmeter

Komplexe Strömungsphänomene machen es schwierig Ingenieursanwendungen so detailliert und genau zu simulieren, dass eine Charakterisierung und Verbesserung ihres Funktionsprinzips möglich ist. Diese Arbeit zeigt, dass die Lattice-Boltzmann-Methode (LBM) sehr gut für diesen Zweck geeignet ist. Im Vordergrund stehen hierbei die Simulation und Modellierung von turbulenten Strömungen. Diese lassen sich auf Grund der hervorragenden Parallelisierbarkeit der LBM mit Large-eddy Simulationen an Stelle von Reynolds-gemittelten Navier--Stokes Modellen, die im industriellen Umfeld üblich sind, berechnen. Somit können komplexe transiente turbulente Strömungen simulativ untersucht werden. Die daraus gewonnenen Erkenntnisse dienen insbesondere der Auslegung und Optimierung von Bauteilen und Prozessen. Alle beschriebenen LBM Simulationen werden mit der Open Source Software OpenLB durchgeführt. Dazu wird OpenLB erweitert, um eine Validierung von implementierten Turbulenzmodellen mittels kanonischer Strömungsformen zu ermöglichen. Des Weiteren wird ein Framework für die Simulation von Fluid-Struktur Interaktion (FSI) geschaffen. Anfangs werden die Kollisionsoperatoren Bhatnagar--Gross--Krook (BGK), Entropic Lattice Boltzmann (ELB), Two-Relaxation-Time (TRT), Regularized Lattice Boltzmann (RLB) und Multiple-Relaxation-Time (MRT) in der Taylor-Green Vortex Strömung, einem klassischen Beispiel für abklingende homogene isotrope Turbulenz (DHIT), untersucht. Hierbei liegt der Fokus auf Stabilität, Konsistenz und Genauigkeit der verwendeten Schemata. Die Studie beinhaltet den Vergleich der turbulenten kinetischen Energie, der Dissipationsrate der Energie und dem Energiespektrum zu einer Referenzlösung. Drei unterschiedliche Reynoldszahlen, $\mathrm{Re}=800$, $\mathrm{Re}=1600$ und $\mathrm{Re}=3000$, werden sowohl unter Verwendung einer akustischen als auch einer diffusiven Skalierung betrachtet, um den Einfluss der Lattice Machzahl zu charakterisieren. In stark unteraufgelösten Gitterkonfigurationen zeigt das BGK Schema ein instabiles Verhalten. Divergierende Simulationen unter der Verwendung des MRT Schemas sind auf eine starke Abhängigkeit von der Lattice Machzahl zurückzuführen. Obwohl ELB die Viskosität verändert, kann kein Verhalten, das einem Wirbelviskositätsmodell entspricht, gefunden werden. Bei geringen Lattice Machzahlen zeigt das RLB Schema sehr geringe Energielevel bei hohen Wellenzahlen. Der ,,magic parameter" des TRT Schemas wird bestimmt im Hinblick auf den Energieeintrag. Trotzdem wird keine erhöhte Stabilität im Vergleich zum BGK Schema festgestellt. Insgesamt sollte die Lattice Machzahl bezüglich des verwendeten Kollisonsschemas gewählt werden, um die Stabilität zu gewährleisten und die Genauigkeit zu verbessern. Für die Realisierung eines wandmodellierten Large-Eddy Simulation (NWM-LES) Ansatzes wird der BGK Kollisionsoperator ausgewählt. Das Smagorinsky Wirbelviskositätsmodell kommt hierbei zum Einsatz und wird in der turbulenten Grenzschicht mit der van Driest\u27schen Dämpfungsfunktion verwendet. Der Einfluss verschiedener Implementierungen von Geschwindigkeitsrandbedingungen und Wandfunktionen wird in einer biperiodischen, voll ausgebildeten turbulenten Kanalströmung für Schubspannungs-Reynoldszahlen von $\mathrm{Re}_\tau=1000$, $\mathrm{Re}_\tau=2000$ und $\mathrm{Re}_\tau=5200$ untersucht. Die Validierung erfolgt mittels Daten einer direkten numerischen Simulation (DNS) für Turbulenzstatistiken erster und zweiter Ordnung. Die Anwendung dieses Ansatzes auf einen Coriolis Massendurchflussmesser (CMF) zeigt, dass der Druckverlust bis zu einer Reynoldszahl $\mathrm{Re}=127800$ beschrieben werden kann. Des Weiteren wird der entwickelte NWM-LES LBM Ansatz mit OpenFOAM, einer Open Source Implementierung der finititen Volumen Methode (FVM) für komplexe turbulente Strömungen, die relevant für Verbrennungsmotoren sind, verglichen. Der zuvor entwickelte und validierte LBM Ansatz wird mit einer Geschwindigkeitsrandbedingung für gekrümmte Ränder erweitert. Die Ergebnisse beider Strömungslöser werden mit Daten eines Particle Image Velocimetry (PIV) Experiments verglichen. Die Validierung umfasst sowohl die zeitgemittelten als auch die quadratisch gemittelten (RMS) Geschwindigkeitsfelder. Zusätzlich wird sowohl die Laufzeit der Simulation als auch die Dauer der unterschiedlichen Gittergenerierungsprozesse bestimmt. Die Performanceanalyse der getesteten Konfiguration zeigt, dass OpenLB 32-mal schneller ist als OpenFOAM. Folglich ist der entwickelte NWM-LES LBM Ansatz dazu in der Lage, komplexe turbulente Strömungen in einer Ingenieursanwendung akkurat und mit einem verringerten Rechenaufwand zu beschreiben. Wirbel induzierte Vibrationen (VIV) sind ein weiterer wichtiger Anwendungsfall für Ingenieursapplikationen. Für die Untersuchung dieser werden verschiedene Fluid-Struktur Ansätze für LBM implementiert, verglichen und evaluiert. Die zwei untersuchten Klassen sind die Moving Boundary Methods (MBM) und die Partially Saturated Methods (PSM). Als erstes wird die Galiläische Invarianz von aerodynamischen Koeffizienten für die einzelnen Schemata untersucht. Dazu wird das BGK Schema verwendet, um einen exzentrisch positionierten Zylinder in einer Couette Strömung zu simulieren. Überdies werden verschiedene Volumenapproximationsmethoden für PSM und Auffüllmechanismen für MBM verglichen. Sowohl die Gitterkonvergenz als auch die Konvergenz der Galiläischen Invarianz werden betrachtet. Die Studie der VIV-Phänomene umfasst einen transvers oszillierenden Zylinder in einem Freistrom bei einer Reynoldszahl von $\mathrm{Re}=100$. Dabei werden freie und erzwungene Oszillation betrachtet, um bekannte Phänomene, wie Lock-in und Lock-out Zonen, zu untersuchen. Die Ergebnisse zeigen, dass sowohl MBM als auch PSM eine gute Übereinstimmung zu Literaturdaten aufweisen, womit die Eignung für VIV-Simulationen bestätigt werden kann. Schließlich wird ein Fluid-Struktur Interaktionsansatz unter der Verwendung eines MBM Ansatzes für die Simulation eines CMFs realisiert. Hierbei wird OpenLB mit Elmer, einer Open Source Implementierung der Finite-Elemente-Methode, gekoppelt, um auch die Strukturdynamik zu beschreiben. Ein gestaffelter Kopplungsansatz zwischen den beiden Softwarepaketen wird präsentiert. Das Finite-Elemente-Gitter wird durch das Gittergenerierungstool Gmsh erstellt, um einen kompletten Open Source Workflow zu garantieren. Zunächst werden die Eigenmoden des CMFs berechnet und mit Messdaten verglichen. Die daraus bestimmte Anregungsfrequenz wird zur Bestimmung des Phasenshifts in einer partitionierten voll gekoppelten FSI Simulation verwendet. Der berechnete Phasenshift zeigt eine gute Übereinstimmung mit den Messdaten und bestätigt, dass dieses Modell in der Lage ist, das Funktionsprinzip eines CMFs zu beschreiben. Die durchgeführten Studien zeigen das große Potential der LBM für die Simulation von Ingenieursapplikationen, insbesondere wenn turbulente Strömungen betrachtet werden