Yes / A two-dimensional numerical model is developed to study the propagation of a solitary wave in the presence of a steady current flow. The numerical model is based on the Reynolds-averaged Navier-Stokes (RANS) equations with a k-ε turbulence closure scheme and an internal wave-maker method. To capture the air-water interface, the volume of fluid (VOF) method is used in the numerical simulation. The current flow is initialized by imposing a steady inlet velocity on one computational domain end and a constant pressure outlet on the other end. The desired wave is generated by an internal wave-maker. The propagation of a solitary wave travelling with a following/opposing current is simulated. The effects of the current velocity on the solitary wave motion are investigated. The results show that the solitary wave has a smaller wave height, larger wave width and higher travelling speed after interacting with a following current. Contrariwise, the solitary wave becomes higher with a smaller wave width and lower travelling speed with an opposing current. The regression equations for predicting the wave height, wave width and travelling speed of the resulting solitary wave are for practical engineering applications. The impacts of current flow on the induced velocity and the turbulent kinetic energy (TKE) of a solitary wave are also investigated. / National Natural Science Foundation of China Grant #51209083, #51137002 and #41176073, the Natural Science Foundation of Jiangsu Province (China) Grant #BK2011026, the 111 Project under Grant No. B12032, the Fundamental Research Funds for the Central University, China (2013B31614), and the Carnegie Trust for Scottish Universities

The development of hydrocarbon energy resources from shale, a fine-grained, low-permeability geological formation, has altered the global energy landscape. Constricting pressure exerted on a shale formation has a significant effect on the rock's apparent permeability. Gas flow in low-permeability shales is significantly different from liquid flow due to the Klinkenberg effect caused by gas molecule slip at the nanopore wall surfaces. This has the effect of increasing apparent permeability (i.e., the measured permeability). Optimizing the conductivity of the proppant assembly is another critical component of designing subsurface hydrocarbon production using hydraulic fracturing. Significant fracture conductivity can be achieved at a much lower cost than conventional material costs, according to the optimal partial-monolayer proppant concentration (OPPC) theory. However, hydraulic fracturing performance in unconventional reservoirs is problematic due of the complex geomechanical environment, and the experimental confirmation and investigation of the OPPC theory have been rare in previous studies. In this dissertation, a novel multiphysics shale transport (MPST) model was developed to account for the coupled multiphysics processes of geomechanics, fluid dynamics, and the Klinkenberg effect in shales. Furthermore, A novel multi-physics multi-scale multi-porosity shale gas transport (M3ST) model was developed based on the MPST model research to investigate shale gas transport in both transient and steady states, and a double-exponential empirical model was also developed as a powerful substitute for the M3ST model for fitting laboratory-measured apparent permeability. Additionally, throughout the laboratory experiment of fracture conductivity with proppant, the four visible stages documented the evolution of non-monotonic conductivity and proppant concentration. The laboratory methods and empirical model were then applied to the shale plugs from Central Appalachia to investigate the formation properties there. The benefits of developing these regions wisely include a smaller surface footprint, reduced infrastructure requirements, and lower development costs. The developed MPST, M3ST, double-exponential empirical models and research findings shed light on the role of multiphysics mechanisms, such as geomechanics, fluid dynamics and transport, and the Klinkenberg effect, in shale gas transport across multiple spatial scales in both steady and transient states. The fracture conductivity experiments successfully validate the theory of OPPC and illustrate that proppant embedment is the primary mechanism that causes the competing process between fracture width and fracture permeability and consequently the non-monotonic fracture conductivity evolution as a function of increasing proppant concentration. The laboratory experimental facts and the numerical fittings in this study provided critical insights into the reservoir characterization in Central Appalachia and will benefit the reservoir development using non-aqueous fracturing techniques such as CO2 and advanced proppant technologies in the future. / Doctor of Philosophy / Production of oil and gas from the extremely tight rock has changed the global energy industry, including job growth, energy security, and environment protection. However, the oil and gas production from the tight rock is difficult because of the complex rock properties. Hydraulic fracking can resolve the issue and contribute to the high production. The higher and safer production needs us to have a better understanding of oil and gas flow under the ground. A series of laboratory experiment were conducted, and a new shale gas transport model is introduced in this dissertation to explain the oil and gas flow under the complicated scenarios. The experimental results show that many factors can impact the oil and gas flow, and the model can match the experimental results very well. A few statistical methods are also used in the data analysis. The optimization of proppant pack is another important component of hydraulic fracking. Proppant particles are usually man-made ceramic tiny balls, which will be injected into the underground to keep the fractures from closing during the production. From the previous papers, it is possible to achieve high fracture conductivity at a much lower cost than traditional proppant costs. Many groups of laboratory experiment were conducted to demonstrate this guess. Many rock samples in the experiment are from Central Appalachian area, which can help the resource development in this area. The developed model and experimental research findings in this study provided critical insights into the role of the many physics mechanisms on shale gas transport, proppant optimization, and hydraulic fracking.

A quantitative understanding of thermal field evolution is vital for quality control in additive manufacturing (AM). Because of the unknown material parameters, high computational costs, and imperfect understanding of the underlying science, physically-based approaches alone are insufficient for component-scale thermal field prediction. Here, I present a new framework that integrates physically-based and data-driven approaches with quasi in situ thermal imaging to address this problem. The framework consists of (i) thermal modeling using 3D finite element analysis (FEA), (ii) surrogate modeling using functional Gaussian process, and (iii) Bayesian calibration using the thermal imaging data. Based on heat transfer laws, I first investigate the transient thermal behavior during AM using 3D FEA. A functional Gaussian process-based surrogate model is then constructed to reduce the computational costs from the high-fidelity, physically-based model. I finally employ a Bayesian calibration method, which incorporates the surrogate model and thermal measurements, to enable layer-to-layer thermal field prediction across the whole component. A case study on fused deposition modeling is conducted for components with 7 to 16 layers. The cross-validation results show that the proposed framework allows for accurate and fast thermal field prediction for components with different process settings and geometric designs. / Master of Science / This paper aims to achieve the layer to layer temperature monitoring and consequently predict the temperature distribution for any new freeform geometry. An engineering statistical synergistic model is proposed to integrate the pure statistical methods and finite element modeling (FEM), which is physically meaningful as well as accurate for temperature prediction. Besides, this proposed synergistic model contains geometry information, which can be applied to any freeform geometry. This paper serves to enable a holistic cyber physical systems-based approach for the additive manufacturing (AM) not only restricted in fused deposition modeling (FDM) process but also can be extended to powder-based process like laser engineered net shaping (LENS) and selective laser sintering (SLS). This paper as well as the scheduled future works will make it affordable for customized AM including customized geometries and materials, which will greatly accelerate the transition from rapid prototyping to rapid manufacturing. This article demonstrates a first evaluation of engineering statistical synergistic model in AM technology, which gives a perspective on future researches about online quality monitoring and control of AM based data fusion principles.

Although spectral methods have been in use for decades, there is still room for innovation, refinement and improvement of the methods in terms of efficiency and accuracy, for generalized homogeneous turbulent flows, and especially for specialized applications like the computation of atmospheric flows and numerical weather prediction. In this thesis, two such innovations are presented. First, inspired by the adaptive mesh refinement (AMR) technique, which was developed for the computation of fluid flows in physical space, an algorithm is presented for accelerating direct numerical simulation (DNS) of isotropic homogeneous turbulence in spectral space. In the adaptive spectral resolution (ASR) technique developed here the spectral resolution in spectral space is dynamically refined based on refinement criteria suited to the special features of isotropic homogeneous turbulence in two, and three dimensions. Applying ASR to computations of two- and three-dimensional turbulence allows significant savings in the computational time with little to no compromise in the accuracy of the solutions. In the second part of this thesis the effect of explicit filtering on large eddy simulation (LES) of atmospheric flows in spectral space is studied. Apply an explicit filter in addition to the implicit filter due to the computational grid and discretization schemes in LES of turbulent flows allows for better control of the numerical error and improvement in the accuracy of the results. Explicit filtering has been extensively applied in LES of turbulent flows in physical space while few studies have been done on explicitly filtered LES of turbulent flows in spectral space because of perceived limitations of the approach, which are shown here to be incorrect. Here, explicit filtering in LES of the turbulent barotropic vorticity equation (BVE) as a first model of the Earth's atmosphere in spectral space is studied. It is shown that explicit filtering increases the accuracy of the results over implicit filtering, particularly where the location of coherent structures is concerned. / Ph. D.

Accurate physical modeling and accelerated numerical simulation of turbulent flows remain primary challenges in CFD for aerospace engineering and related fields. This dissertation tackles these challenges with a focus on Reynolds-Averaged Navier--Stokes (RANS) models, which will continue to serve as the backbone for many practical aircraft applications. Specifically, in RANS turbulence modeling, the challenges include developing more efficient ensemble filters to learn nonlinear eddy viscosity models from observation data that move beyond the classical Boussinesq hypothesis, as well as developing non-equilibrium models that break away from the weak equilibrium assumption while maintaining computational efficiency. For accelerating RANS simulations, the challenges include leveraging existing simulation data to optimize the computational workflow while maintaining the method's adaptability to various computational settings. From a fundamental and mathematical perspective, we view these challenges as problems of modeling and learning complex nonlinear and nonlocal mappings, which we categorize into three types: field-to-point, field-to-field, and ensemble-to-ensemble. To model and resolve these mappings, we build up on recent advancements in machine learning and develop novel neural operator-based methods that not only possess strong representational capabilities but also preserve critical physical and mathematical principles. With the developed tools, we have demonstrated promising preliminary results in addressing these challenges and have the potential to significantly advance the state of the art in RANS turbulence modeling and simulation acceleration. / Doctor of Philosophy / Understanding and accurately predicting turbulent flows, such as those around airplanes or ships, are among the biggest challenges in computational fluid dynamics (CFD). This research aims to improve Reynolds-Averaged Navier--Stokes (RANS) models, which are widely used in practical engineering applications. Traditional RANS turbulence models are based on simplified assumptions that are linear and local, making it difficult to capture the true complexity of turbulent flows. My work addresses this limitation by developing new models that leverage advanced machine learning techniques to better represent turbulence. Specifically, I have focused on developing methods that extend beyond conventional approaches by learning more accurate local nonlinear constitutive relations and incorporating nonlocal effects---an important step toward improving simulation accuracy. In addition, I have explored strategies to accelerate RANS simulations by making more effective use of existing data, providing better initial conditions for simulations, and ultimately reducing computational costs. Preliminary results indicate that these new methods have the potential to push the boundaries of RANS turbulence modeling, enabling more accurate and efficient simulations.

No description available.

Nous étudions la rhéologie d'un ensemble de grains sphériques et frottants, par la simulation numérique, à l'échelle des grains, d'écoulements de cisaillement sous une contrainte normale P contrôlée, en présence d'un liquide interstitiel. En faible teneur, ce liquide se présente sous forme de ménisques intergranulaires qui transmettent des forces capillaires attractives ; s'il sature l'espace intergranulaire, on s'intéresse alors à l'écoulement de Stokes de la suspension dense ainsi constituée, où dominent les forces visqueuses. Les assemblages de grains secs constituent un système de référence aux propriétés mécaniques bien connues, en particulier l'approche de l'état critique de la mécanique des sols dans la limite quasi-statique. L'effet des ménisques capillaires qui joignent les grains en présence d'un liquide en faible saturation (régime pendulaire) est étudié pour les taux de cisaillement allant du régime quasi statique au régime inertiel. La rhéologie est caractérisée par le frottement interne apparent, la compacité de l'assemblage, les différences de contraintes normales et diverses variables internes, fonctions de deux paramètres de contrôle adimensionnés : le nombre inertiel I et la pression réduite P*, qui compare les forces de confinement à l'adhésion dans les contacts. Notre étude concerne les états homogènes, ce qui exclut les états de cisaillement localisés observés à faible P*, de l'ordre de 0,1. Le coefficient de frottement interne augmente de 0.35 (cas sec) à 0.9 environ pour P*=0.4, tandis que la compacité décroît de 0.59 à 0.52. L'important effet des forces capillaires sur la rhéologie, sensible pour des P* de plusieurs unités, est relié à la texture anisotrope des contacts et des ponts liquides. Lorsque P* décroît, nombre de contacts cohésifs sont maintenus pour des intervalles de déformation de plusieurs unités, survivant aux effets de rotation et de cisaillement de l'écoulement, et forment des amas percolants dans le système entier. Les résultats sont modérément sensibles à la saturation dans le régime pendulaire, mais fortement affectés par l'hystérèse de la conformation des ménisques. En présence de forces visqueuses et non plus capillaires, une version simplifiée de la dynamique stokésienne est adoptée dans laquelle les forces de lubrification entre proches voisins, supposées dominantes, sont les seules interactions hydrodynamiques. La rhéologie est fortement influencée par les contacts intergranulaires directes, qu'autorise la coupure à courte distance de la singulérité de lubrification du fait de la rugosité de surface des particules. Le même état critique que celui des grains secs est approché dans la limite quasi-statique. Nous discutons de lois rhéologiques exprimées en fonction du nombre visqueux qui remplace alors le nombre inertiel, et de la divergence de la viscosité effective à l'approche de la compacité critique en écoulement permanent, ou de la compacité maximale des assemblages aléatoires pour les configurations isotropes désordonnées / We numerically simulate the shear flow of dense assemblies of 3D frictional spherical grains under a fixed normal stress P in steady-state, either in the presence of a small amount of an interstitial liquid, which gives rise to capillary menisci and attractive forces, or in the fully saturated state, when the mechanical properties of suspensions in Stokes flow are controlled by hydrodynamic and contact forces. Dry grain assemblies are used as a reference system for which the rheological properties - in particular the approach to the critical state – are rather well known and can be measured with good accuracy. A non-saturating wetting fluid creates capillary attractive intergranular forces, the effects of which on the rheology are investigated in the pendular state, with shear rates ranging from quasistatic to inertial regimes. The system behavior is characterized by the dependence of internal friction coefficient, solid fraction, normal stress differences and internal state parameters on two dimensionless control parameters: the inertial number, I and the reduced pressure, P*, comparing confining forces to contact tensile strength. We focus on steady homogeneous flows, excluding localized flow patterns which we observe to occur for low P* (of order 0.1). The apparent internal friction coefficient increases to 0.9 in the quasistatic limit for P*=0.4, from its dry value 0.35, while solid fraction decreases from 0.59 to 0.52. We relate the significant effect of capillary forces on the macroscopic behavior of the system, up to P* values of several unities, to fabric anisotropy parameters of contact and distant interactions. As P* decreases, many cohesive contacts are observed to survive the tumbling motion associated to the shear flow, and their average age exceeds the reciprocal shear rate. Corresponding clusters of grains with enduring capillary bonds gather a large proportion of grains and percolate through the sample. The results are shown to be moderately sensitive to saturation within the pendular range, yet rather strongly affected by the hysteretic nature of liquid bridges. In the presence of viscous forces, assuming lubrication effects to dominate the hydrodynamic interactions, we adopt a simplified version of the (overdamped) Stokesian dynamics approach, in which hydrodynamic interactions only couple close neighbours. Rheological properties are strongly influenced by direct intergranular contacts and friction, which are permitted due to a very small distance lubrication cutoff modeling surface asperities. The same critical state as in the dry case is approached in the quasistatic limit. We discuss expressions of rheological laws involving the viscous number instead of the inertial number, and the divergence of effective viscosities in steady flow and in isotropic random suspensions as either the critical state or the random close packing solid fraction are approached

Doctor of Philosophy / Department of Mechanical and Nuclear Engineering / Zhongquan Zheng / A nano-material filter is an efficient device for improving indoor environmental quality (e.g. smoke reduction, air purification in buildings). Studying the effectiveness of nano-materials used in the device by computer simulation is challenging because very different size scales are involved. Therefore, numerical methods have to be developed to accommodate varying magnitudes of scales. In the current study, the simulation has been divided into three scales: macro-, micro- and nano-scale. The numerical schemes at each scale are targeted at a particular scale; however, the relationship of the general transport phenomena, physical mechanisms and properties among different scales are uniquely linked at the same time. The objective of the macro-scale simulation was to design and study a gas filter constructed with nano-material pellets. The filter was considered a packed-bed tube filled with manufactured nano-material pellets. Commercial computational fluid dynamics (CFD) packages were used along with the embedded programming macros. In the filtration process, we focused on the flow and species transport phenomena through the porous substrate. The mathematical/numerical models were built and tested based on the physical models used in the experimental setups for different materials that were tested. The results from the numerical models were validated and compared well to experimental data obtained from the pressure drop measurements and the adsorption (breakthrough) tests. In the micro-scale simulation, a modified immersed-boundary method (IBM) with the Zwikker-Kosten (ZK) porous model and the high-order schemes was validated and applied to simulate a representative porous unit that represented a periodic array of solid/porous cylinders. In the periodic unit, the solid cylinder case was used to validate the high-order schemes by comparing it to the results obtained from the commercial CFD software. The relationship between the pressure gradient and the porosity (Blake-Kozeny equation) was determined from this level and fed back to the macro-scale simulation, which provided a link between the two scales. In the porous cylinder case, both flow field and species transport were investigated with a porous model similar to the one used in the macro-scale. The species concentration change was calculated and found to be nonlinearly related to the adsorption coefficient. In the nano-scale simulation, a molecular dynamics (MD) simulation and a coupled molecular-continuum scheme were applied to solve the momentum and the mass transport problems at the molecular level at which the traditional continuum theory is no longer applicable. Both schemes were verified from the surface slip behavior study compared to the literature. The scale and shear effects in the Coutte flow were investigated, showing that in the micro-scale and macro-scale, the slip behavior could be neglected since it was only important in much smaller scales. The same hybrid scheme was then applied to a diffusion model with nano-pores constructed in the solid substrate. The adsorptions between various gases and the carbon substrate were simulated. The mass fluxes cross the fluid/solid interfaces were counted and both self-diffusivity and transport diffusivity were estimated and compared to their respective values found in the literature. The transport properties are closely related to the species transport (Fick’s law) in the macroscopic simulations. Linear concentration profiles in the channel were obtained based on those transport properties for various gases going through different sizes of nano-pores, which, as a connection to the continuum model, were to be used as boundary conditions in the continuum simulation.

Abstract : The harsh conditions of electrolytic bath in aluminium electrolysis cell have been an obstacle against the understanding of mass transfer that is at the origin of the aluminium production process. This knowledge is of great importance due to the impact that it could have on the functional parameters of the cell like current efficiency. Numerical modelling is a way to overcome the difficulties and to shed light over the hidden aspects of the electrochemical process. The electrolyte typically used in an aluminum electrolysis cell is composed of different ions moving in the electromagnetic field generated by the high intensity current needed for this industrial application. The behaviour of these ions is under the influence of concentration gradients (diffusion) and depends also on other phenomena in the cell like bath flow (convection) and electric field (migration). In this study, the coupling between these fields is treated for 1D and 2D models of the cell. The relative importance of migration and diffusion are compared for two different categories of electroactive and electroinactive ions in a transient model. For both categories of ions, migration is the dominant form of mass transfer in the very first stages of electrochemical process. However, diffusion becomes the dominant mechanism of mass transfer for electroactive ions in developed boundary layers. In 2D model, there is a concentration gradient between interelectrode and near sidewalls region. Consequently, there is a diffusion of ions in and out of the interelectrode space to diminish the depletion or overconcentration of certain electroactive ions like Al[subscript 2]OF[subscript 6][superscript -2] and AlF[subscript 4][superscript -] at the electrodes. Furthermore, the impact of convection and bath equilibrium in addition to a more suitable mass transfer model has been studied on a parallel plate electrodes reactor. Finally, an open source library is developed and built on OpenFoam (an open source C++ CFD platform) that is capable of solving mass transfer equations for different models. The description and findings of this thesis will shed light on the mass transfer mechanisms in both bulk region and boundary layers, and can be used for further studies in this field. / Résumé : L’étude des mécanismes de transfert de masse des ions dans le bain électrolytique dans une cellule d’électrolyse d’aluminium se heurte aux conditions sévères qui y sont rencontrées : haute température, milieu corrosif, etc. Cependant, il est important de connaitre ces mécanismes de transfert en raison de leurs grands impacts sur les paramètres indicatifs du procédé d’électrolyse, par exemple l’efficacité du courant. Le calcul numérique est une façon de surmonter ces difficultés et d’éclairer les aspects moins connus du procédé de production d’aluminium. L’électrolyte utilisé pour l’électrolyse est composé par différents ions qui se déplacent dans un champ électromagnétique. Ce dernier est généré par le courant électrique intense qui passe par la couche d’aluminium et le bain. Le comportement dynamique des ions est sujet à leur gradient de concentration (la diffusion), à l’écoulement du bain (la convection) et au champ électrique (la migration). Dans le cadre de cette étude, le mouvement des ions est analysé et l’importance relative de la diffusion et de la migration est comparée en régime transitoire pour deux classes d’espèces électroactives et non-électroactives. Pour ces deux types d’espèces, on observe que la migration est le mécanisme dominant de transfert de masse dès les premières phases de l’électrolyse. Cependant, la diffusion devient graduellement le mécanisme le plus important aux électrodes pour des espèces électroactives comme Al[indice inférieur 2]OF[indice inférieur 6][indice supérieur -2] et AlF[indice inférieur 4][indice supérieur -]. Le champ électrique et le champ de concentration ont été simulés à partir d’un modèle 2-D. Les résultats montrent qu’il y a un gradient de concentration entre l’espace inter-électrodes et la région proche de la couche de gelée. Par conséquent, il y a diffusion des espèces entre ces deux régions qui vient diminuer le gradient de concentration et ainsi éviter l’épuisement des ions Al[indice inférieur 2]OF[indice inférieur 6][indice supérieur -2] ou la surconcentration des ions AlF[indice inférieur 4][indice supérieur -]. En outre, un code libre a été développé et implémenté sur OpenFOAM (une plateforme libre de librairies C++). Ce code est capable de résoudre simultanément les équations du champ électrique, du transfert de masse et de Navier-Stokes. Les principaux apports de cette thèse, tel que les modèles et résultats obtenus, peuvent éclairer les mécanismes de transfert de masse dans le bain et aux électrodes et ainsi améliorer leur compréhension.

Downslope flows and regions of enhanced cooling have important impacts on society and the environment. Parameterisation of these often subgrid-scale phenomena in numerical models requires a sound understanding of the underlying physical processes, which has been the overarching aim of this work. A numerical model has been used to characterise the development of a region of enhanced cooling in an idealised alpine valley with width and depth of order 10 and 1 km, respectively, under stable, decoupled, poorly-drained conditions. A focus of this work has been to remove the uncertainty surrounding the forcing mechanisms behind the development of regions of enhanced cooling. The average valley-atmosphere cooling has been found to be almost equally partitioned between radiative and dynamics effects. Complex interactions between the downslope flows and the region of enhanced cooling have been quantified for the first time. For example, relatively large variations in the downslope flows are generally restricted to the region of enhanced cooling and cannot solely be attributed to the analytical model of [McNider, 1982a]. These flow variations generally coincide with return flows above the downslope flows, where a thin region of unstable air occurs, as well as coinciding with elongated downslope flow structures. The impact of these interactions on the dispersion of passive pollutants has been investigated. For example, pollutants are generally trapped within the region of enhanced cooling. The concentration of pollutants within the region of enhanced cooling, emitted over the lower half of the slopes, increase as the emission source moves away from the ground-based inversion that expands from the bottom of the valley. The concentration of pollutants within the region of enhanced cooling is very similar when varying the location of the emission source over the top half of the valley slopes. This work includes a test of the effects of varying the horizontal numerical grid resolution on average valley-atmosphere temperature changes.