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Thesis (Ph. D.)--Oregon State University, 2009. / Printout. Includes bibliographical references (leaves 113-127). Also available on the World Wide Web.

Thesis (Ph.D.)--Mechanical Engineering, Georgia Institute of Technology, 2009. / Committee Co-Chair: Aidun, K. Cyrus; Committee Co-Chair: Ghiaasiaan, Mostafa; Committee Member: Deng, Yulin; Committee Member: Empie, Jeff; Committee Member: Patterson, Tim.

The purpose of this master thesis is to investigate the usage of the Lattice Boltzmann Method (LBM) of Computational Fluid Dynamics (CFD) for real-time prediction of indoor air flows inside a data center module. Thermal prediction is useful in data centers for evaluating the placement of heat-generating equipment and air conditioning. To perform the simulation a program called RAFSINE was used, written by Nicholas Delbosc at the University of Leeds, which implemented LBM on Graphics Processing Units (GPUs) using NVIDIA CUDA. The program used the LBM model called Bhatnagar-Gross-Krook (BGK) on a 3D lattice and had the capability of executing thermal simulations in real-time or faster than real-time. This fast rate of execution means a future application for this simulation could be as a predictive input for automated air conditioning control systems, or for fast generation of training data sets for automatic fault detection systems using machine learning. In order to use the LBM CFD program even from hardware not equipped with NVIDIA GPUs it was deployed on a remote networked server accessed through Virtual Network Computing (VNC). Since RAFSINE featured interactive OpenGL based 3D visualization of thermal evolution, accessing it through VNC required use of the VirtualGL toolkit which allowed fast streaming of visualization data over the network. A simulation model was developed describing the geometry, temperatures and air flows of an experimental data center module at RISE SICS North in Luleå, Sweden, based on measurements and equipment specifications. It was then validated by comparing it with temperatures recorded from sensors mounted in the data center. The thermal prediction was found to be accurate on a room-level within ±1° C when measured as the average temperature of the air returning to the cooling units, with a maximum error of ±2° C on an individual basis. Accuracy at the front of the server racks varied depending on the height above the floor, with the lowest points having an average accuracy of ±1° C, while the middle and topmost points had an accuracy of ±2° C and ±4° C respectively. While the model had a higher error rate than the ±0.5° C accuracy of the experimental measurements, further improvements could allow it to be used as a testing ground for air conditioning control or automatic fault detection systems.

[pt] Esta pesquisa é motivada, principalmente, por problemas da geomecânica do petróleo como produção de sólidos em poços produtores e dano mecânico de formação. Produção de sólidos é o fenômeno onde partículas sólidas são produzidas juntamente com os fluidos de um reservatório de formação geralmente pouco ou não consolidada, podendo também ocorrer em formações mais resistentes. Dano de formação é o termo usado para identificar a redução da permeabilidade por diversos processos que ocorrem nas formações geológicas, e que reduzem a produtividade e injetividade de poços de sistemas de produção de óleo e gás. Neste trabalho desenvolveu-se uma ferramenta numérica com acoplamento fluidomecânico (mono e bifásico) para ser utilizada em análises destes problemas na microescala (poro e grão). Utilizou-se o método dos elementos discretos (DEM) para a simulação do movimento e interação das partículas sólidas e o método de lattice-Boltzmann (LBM) para a simulação do fluxo nos poros do meio geológico. A principal diferença desta ferramenta numérica em relação a trabalhos anteriores que acoplam o DEM com o LBM (DEM-LBM) está na implementação da formulação do LBM incompressível sugerida por (He e Luo, 1997) permitindo a aplicação de gradientes de pressão sensivelmente maiores do que na formulação convencional, o que é importante para as simulações de produção de sólidos. A ferramenta desenvolvida pode ser vista como um laboratório virtual para testar/verificar leis constitutivas, e que aliada a dados experimentais poderá melhorar o entendimento de mecanismos básicos envolvidos nos processos de dano mecânico de formação e de produção de sólidos. O programa computacional implementado foi verificado através de comparações com soluções analíticas ou resultados publicados na literatura. Simulações relacionadas às aplicações de interesse foram realizadas. / [en] The present research was mainly motivated by petroleum geomechanics problems such as solids production and formation damage. Solids production is related to phenomena whereby solid particles are produced together with fluids from reservoir rocks having little or no consolidation although it is reported that those phenomena have already happened to more resistant materials. Formation damage is the term used in order to identify permeability reduction occurring for various processes and which reduce productivity and injectivity of wells in oil and gas production systems. In the present work, a numerical tool considering fluidmechanical coupling (one and two phase flow) was developed for analyses in the microscale (pores and grains). The DEM (Discrete Element Method) was used for the simulation of motion and interaction of solid particles and the lattice Boltzmann method (LBM) for the simulation of flow inside pores of the geological media. The main difference between the developed tool and the ones developed in previous works that couple DEM with LBM is the introduction of incompressible LBM as suggested by (He e Luo, 1997), one that allows the application of pressure gradients considerably larger than the conventional formulation which is important for the simulation of solids production. The developed tool can be viewed as a virtual laboratory for testing and verification of constitutive laws which together with experimental data may improve the understanding of basic phenomena involved in formation damage and solids production. The numerical implementation was verified through comparisons with analytical solutions and other results from the literature. Simulations related to practical applications were carried out and discussed.

Ce manuscrit est consacré au développement et à la validation d'un nouveau modèle de collision destiné à améliorer la stabilité des modèles lattice Boltzmann (LB) d'ordre élevés lors de la simulation d'écoulements : (1) isothermes et faiblement compressibles à nombre de Reynolds élevés, ou (2) compressibles et comprenant des discontinuités telles que des ondes de choc. Ce modèle de collision s'appuie sur une étape de régularisation améliorée. Cette dernière inclut désormais un calcul par récurrence des coefficients hors-équilibre du développement en polynômes d'Hermite. Ces formules de récurrence sont directement issues du développement de Chapman-Enskog, et permettent de correctement filtrer les contributions non-hydrodynamiques émergeant lors de l'utilisation de maillages sous-résolus. Cette approche est d'autant plus intéressante quelle est compatible avec un grand nombre de réseaux de vitesses discrètes. Ce modèle LB d'ordre élevé est validé tout d'abord pour des écoulements isothermes à nombre de Reynolds élevé. Un couplage avec une technique de capture de choc permet ensuite d'étendre son domaine de validité aux écoulements compressibles incluant des ondes de choc. Ce travail se conclut avec une étude de stabilité linéaire des modèles considérés, le tout dans le cas d'écoulements isothermes. Ceci permet de quantifier de manière distincte l'impact des discrétisations en vitesse et numérique, sur le comportement spéctrale du jeu d'équations associé. Cette étude permet au final de confirmer le gain en stabilité induit par le nouveau modèle de collision. / This thesis is dedicated to the derivation and the validation of a new collision model as a stabilization technique for high-order lattice Boltzmann methods (LBM). More specifically, it intends to stabilize simulations of: (1) isothermal and weakly compressible flows at high Reynolds numbers, and (2) fully compressible flows including discontinuities such as shock waves. The new collision model relies on an enhanced regularization step. The latter includes a recursive computation of nonequilibrium Hermite polynomial coefficients. These recursive formulas directly derive from the Chapman-Enskog expansion, and allow to properly filter out second- (and higher-) order nonhydrodynamic contributions in underresolved conditions. This approach is even more interesting since it is compatible with a very large number of velocity sets. This high-order LBM is first validated in the isothermal case, and for high-Reynolds number flows. The coupling with a shock-capturing technique allows to further extend its validity domain to the simulation of fully compressible flows including shockwaves. The present work ends with the linear stability analysis(LSA) of the new approach, in the isothermal case. This leads to a proper quantification of the impact induced by each discretization (velocity and numerical) on the spectral properties of the related set of equations. The LSA of the recursive regularized LBM finally confirms the drastic stability gain obtained with this new approach.

Master of Science / Mechanical and Nuclear Engineering / Hitesh Bindra / This thesis extends the application of Lattice Boltzmann Methods (LBM) to radiation transport problems in thermal sciences and nuclear engineering. LBM is used to solve the linear Boltzmann transport equation through discretization into Lattice Boltzmann Equations (LBE). The application of weighted summations for the scattering integral as set forth by Bindra and Patil are used in this work. Simplicity and localized discretization are the main advantages of using LBM with fixed lattice configurations for radiation transport problems. Coupled solutions to radiation transport and material energy transport are obtained using a single framework LBM. The resulting radiation field of a one dimensional participating and conducting media are in very good agreement with benchmark results using spherical harmonics, the P₁ method. Grid convergence studies were performed for this coupled conduction-radiation problem and results are found to be first-order accurate in space. In two dimensions, angular discretization for LBM is extended to higher resolution schemes such as D₂Q₈ and a generic formulation is adopted to derive the weights for Radiation Transport Equations (RTEs). Radiation transport in a two dimensional media is solved with LBM and the results are compared to those obtained from the commercial software COMSOL, which uses the Discrete Ordinates Method (DOM) with different angular resolution schemes. Results obtained from different lattice Boltzmann configurations such as D₂Q₄ and D₂Q₈ are compared with DOM and are found to be in good agreement. The verified LBM based radiation transport models are extended for their application into coupled multi-physics problems. A porous radiative burner is modeled as a homogeneous media with an analytical velocity field. Coupling is performed between the convection-diffusion energy transport equation with the analytical velocity field. Results show that radiative transport heats the participating media prior to its entering into the combustion chamber. The limitations of homogeneous models led to the development of a fully coupled LBM multi-physics model for a heterogeneous porous media. This multi-physics code solves three physics: fluid flow, conduction-convection and radiation transport in a single framework. The LBE models in one dimension are applied to solve one-group and two-group eigenvalue problems in bare and reflected slab geometries. The results are compared with existing criticality benchmark reports for different problems. It is found that results agree with benchmark reports for thick slabs (>4 mfp) but they tend to disagree when the critical slab dimensions are less than 3 mfp. The reason for this disagreement can be attributed to having only two angular directions in the one dimensional problems.