Link-wise Artificial Compressibility Method

The Artificial Compressibility Method (ACM) for the incompressible Navier-Stokes equations is (link-wise) reformulated (referred to as LW-ACM) by a finite set of discrete directions (links) on a regular Cartesian mesh, in analogy with the Lattice Boltzmann Method (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 least in the present paper), 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. Importantly, with an efficient implementation, this algorithm may be one of the few which is compute-bound and not memory-bound. Two- and three-dimensional benchmarks are investigated, and an extensive comparative study between the present approach and state of the art methods from the literature is carried out. Numerical evidences suggest that LW-ACM represents an excellent alternative in terms of simplicity, stability and accuracy.Comment: 62 pages, 20 figure

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

Efficient computations for multiphase flow problems using coupled lattice Boltzmann-level set methods

Multiphase flow simulations benefit a variety of applications in science and engineering as for example in the dynamics of bubble swarms in heat exchangers and chemical reactors or in the prediction of the effects of droplet or bubble impacts in the design of turbomachinery systems. Despite all the progress in the modern computational fluid dynamics (CFD), such simulations still present formidable challenges both from numerical and computational cost point of view. Emerging as a powerful numerical technique in recent years, the lattice Boltzmann method (LBM) exhibits unique numerical and computational features in specific problems for its ability to detect small scale transport phenomena, including those of interparticle forces in multiphase and multicomponent flows, as well as its inherent advantage to deliver favourable computational efficiencies on parallel processors. In this thesis two classes of LB methods for multiphase flow simulations are developed which are coupled with the level set (LS) interface capturing technique. Both techniques are demonstrated to provide high resolution realizations of the interface at large density and viscosity differences within relatively low computational demand and regularity restrictions compared to the conventional phase-field LB models. The first model represents a sharp interface one-fluid formulation, where the LB equation is assigned to solve for a single virtual fluid and the interface is captured through convection of an initially signed distance level set function governed by the level set equation (LSE). The second scheme proposes a diffuse pressure evolution description of the LBE, solving for velocity and dynamic pressure only. In contrast to the common kineticbased solutions of the Cahn-Hilliard equations, the density is then solved via a mass conserving LS equation which benefits from a fast monolithic reinitialization. Rigorous comparisons against established numerical solutions of multiphase NS equations for rising bubble problems are carried out in two and three dimensions, which further provide an unprecedented basis to evaluate the effect of different numerical and implementation aspects of the schemes on the overall performance and accuracy. The simulations are eventually applied to other physically interesting multiphase problems, featuring the flexibility and stability of the scheme under high Re numbers and very large deformations. On the computational side, an efficient implementation of the proposed schemes is presented in particular for manycore general purpose graphical processing units (GPGPU). Various segments of the solution algorithm are then evaluated with respect to their corresponding computational workload and efficient implementation outlines are addressed

KINETICALLY CONSISTENT THERMAL LATTICE BOLTZMANN MODELS

The lattice Boltzmann (LB) method has developed into a numerically robust and efficient technique for simulating a wide variety of complex fluid flows. Unlike conventional CFD methods, the LB method is based on microscopic models and mesoscopic kinetic equations in which the collective long-term behavior of pseudo-particles is used to simulate the hydrodynamic limit of a system. Due to its kinetic basis, the LB method is particularly useful in applications involving interfacial dynamics and complex boundaries, such as multiphase or multicomponent flows. However, most of the LB models, both single and multiphase, do not satisfy the energy conservation principle, thus limiting their ability to provide quantitatively accurate predictions for cases with substantial heat transfer rates. To address this issue, this dissertation focuses on developing kinetically consistent and energy conserving LB models for single phase flows, in particular. Firstly, through a procedure similar to the Galerkin method, we present a mathematical formulation of the LB method based on the concept of projection of the distributions onto a Hermite-polynomial basis and their systematic truncation. This formulation is shown to be capable of approximating the near incompressible, weakly compressible, and fully compressible (thermal) limits of the continuous Boltzmann equation, thus obviating the previous low-Mach number assumption. Physically it means that this formulation allows a kinetically-accurate description of flows involving large heat transfer rates. The various higher-order discrete-velocity sets (lattices) that follow from this formulation are also compiled. The resulting higher-order thermal model is validated for benchmark thermal flows, such as Rayleigh-Benard convection and thermal Couette flow, in an off-lattice framework. Our tests indicate that the D2Q39-based thermal models are capable of modeling incompressible and weakly compressible thermal flows accurately. In the validation process, through a finite-difference-type boundary treatment, we also extend the applicability of higher-order la ttices to flow-domains with solid boundaries, which was previously restricted. Secondly, we present various off-lattice time-marching schemes for solving the discrete Boltzmann equation. Specifically, the various temporal schemes are analyzed with respect to their numerical stability as a function of the maximum allowable time-step . We show that the characteristics-based temporal schemes offer the best numerical stability among all other comparable schemes. Due to this enhanced numerical stability, we show that the usual restriction no longer applies, enabling larger time-steps, and thereby reducing the computational run-time. The off-lattice scheme were also successfully extended to higher-order LB models. Finally, we present the algorithm and single-core optimization techniques for a off-lattice, higher-order LB code. Using simple cache optimization techniques and a proper choice of the data-structure, we obtain a 5-7X improvement in performance compared to a naive, unoptimized code. Thereafter, the optimized code is parallelized using OpenMP. Scalability tests indicate a parallel efficiency of 80% on shared-memory systems with up to 50 cores (strong scaling). An analysis of the higher-order LB models also show that they are less memory-bound if the off-lattice temporal schemes are used, thus making them more scalable compared to the stream-collide type scheme

Computational Fluid Dynamics Simulations

Fluid flows are encountered in our daily life as well as in engineering industries. Identifying the temporal and spatial distribution of fluid dynamic properties is essential in analyzing the processes related to flows. These properties, such as velocity, turbulence, temperature, pressure, and concentration, play important roles in mass transfer, heat transfer, reaction rate, and force analysis. However, obtaining the analytical solution of these fluid property distributions is technically difficult or impossible. With the technique of finite difference methods or finite element methods, attaining numerical solutions from the partial differential equations of mass, momentum, and energy have become achievable. Therefore, computational fluid dynamics (CFD) has emerged and been widely applied in various fields. This book collects the recent studies that have applied the CFD technique in analyzing several representative processes covering mechanical engineering, chemical engineering, environmental engineering, and thermal engineering

Computation of gold-water nanofluid natural convection in a three-dimensional tilted prismatic solar enclosure with aspect ratio and volume fraction effects

Nanofluids are increasingly being deployed in numerous energy applications owing to their impressive thermal enhancement properties. Motivated by these developments in the current study we present finite volume numerical simulations of natural convection in an inclined 3-dimensional prismatic direct absorber solar collector (DASC)containing gold-water nanofluid. Steady-state, incompressible laminar Newtonian viscous flow is assumed. The enclosure has two adiabatic walls, one hot (solar receiving) and one colder wall. ANSYS FLUENT software(version 19.1) is employed. The Tiwari-Das volume fraction nanofluid model is utilized to simulate nanoscale effects and allows a systematic exploration of volume fraction effects. The effects of thermal buoyancy (Rayleighnumber), geometrical aspect ratio and enclosure tilt angle on isotherm and temperature contour distributions are presented with extensive visualizationin three dimensions. Grid-independence tests are included. Validation with published studies from the literature is also conducted. A significant modification in vortex structure and temperature distribution is computed with volume fraction, Rayleigh number, aspect ratio and tilt angle. Heat flux and average Nusselt number results are also included. Gold nano-particles even at relatively low volume fractions are observed to achieve substantial improvement in heat transfer characteristics

Evaluating the Capabilities of Lattice Boltzmann Method for Non-Newtonian and Free-Surface Flows towards Applications in Wellbore Cementing

When oil and gas wellbores are drilled, barriers must be put in place to ensure that fluids do not leak out of the wellbore. Wellbore leakage can lead to environmental damage, loss of pressure at the wellhead, and consequently, loss of production. An important yet vulnerable barrier is the cement annulus. Creating the cement annulus, a process known as primary cementing, is difficult to perform optimally. Every well has unique subsurface conditions, and so no cement slurry mix design both performs well and is economical for all wells. Although some general guidelines and analytical techniques exist for approximating the performance of a cement slurry mix, the mechanics of primary cementing are complex. Computational methods can help better understand primary cementing and aid designers in determining the optimal mix. The lattice Boltzmann method (LBM) is a promising technique for simulating primary cementing because it is well-suited for efficiently simulating non-Newtonian flows, multiphase multicomponent flows, and flows through complex geometries--namely, some of the complexities associated with the mechanics of primary cementing. Despite the advantages of LBM, there are considerations that must be made, as with all computational methods, in regards to the accuracy and numerical stability of the solution. Issues with accuracy and numerical stability are especially prevalent in non-Newtonian flows because of the nonlinear constitutive relationship. Chapter 1 is a numerical investigation of the accuracy, stability, and computational efficiency of different LBM models in simulating non-Newtonian flows

Computational Characterization of Nonwoven Fibrous Materials: Transport and Wetting Properties

Nonwoven fibrous materials represent a platform of flexible material substrates. Nonwovens are widely used in the production of napkins, paper, filters, wound covers and face masks. In addition, for many applications, nonwoven materials interact with fluids. For example, in filtration applications, nonwoven materials are used to clean fluids containing solid particles or emulsified droplets. The filtration performance is affected not only by the geometrical arrangement of fibers in non-woven materials but also wettability of fibers. Understanding the transport properties of nonwoven materials and interactions between the dispersed droplets and solid substrate is crucial for the design and optimization of filter media. The present work is focused on: (1) obtaining pore space information from 3D structure in nonwoven media and 2) predicting the liquid transport properties in fibrous materials, including permeability and tortuosity (3) investigating droplet morphology on fibers. Chapters 1-3 provide the basis of fiber-liquid interactions and introduce the lattice Boltzmann method (LBM). Chapter 4 deals with characterization of microstructures generated from 3D reconstructed plywood and random oriented fibrous media. An algorithm based on watershed segmentation is utilized to extract pore network information including: pore diameter, throat diameter and connectivity. The effect of fiber overlapping arrangements, fiber radius and porosity on the pore space morphology was explored by statistical pore-network analysis. A thorough analysis of the correlation between effective geometrical properties and mean pore size, demonstrated that randomness on microscopic level can have a significant effect on the macroscopic properties of the fibrous media. In Chapter 5, simulations on pore-scale single phase fluid flow through fibrous media using the lattice Boltzmann method were performed. From the simulated flow field, permeability and tortuosity of nonwoven fibrous materials can be evaluated over a wide range of porosity 0.1 \u3c φ \u3c 0.9. The validity of Darcy’s law which describes the flow behavior through a porous medium was confirmed in the studied porosity regime. The simulation results were used to test the accuracy of semi-empirical scaling relations, that enabled predictions in trans-plane permeability and tortuosity based on porosity and specific surface area. Chapter 6 deals with the wetting and capillarity effects of droplets deposited on a single fiber. A multicomponent pseudopotential lattice Boltzmann model was applied to study the interface dynamics of droplets and wetting/dewetting behavior. By adopting different initial droplet configurations, we studied the stability of barrel-shaped and clam-shell droplets on a single fiber for contact angles ranging from 10° to 68°. The simulated barrel drop profile was validated with experimental results. The morphology diagram established from simulations showed that both barrel and clam-shell configurations are stable in coexistence. Dr. Ulf Schiller introduced me to the LBM, and guided my research described in Chapter 3-5. These chapters are based on publications [1, 2, 3], but significantly modified to include additional materials that has never been published. Chapter 6 has been developed to explain recent experimental results obtained in Dr. Kornev’s group. The developed simulation protocol revealed new physics related to the classical problem of fiber-drop interactions and a new diagram of morphological transitions of droplets on fibers was determined. The numerical simulations and data analysis were carried out on Palmetto high-performance computing (HPC) cluster