Dissertations / Theses on the topic 'Multiscale flow'

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 245-254).
Granular materials are common in everyday experience, but have long-resisted a complete theoretical description. Here, we consider the regime of slow, dense granular flow, for which there is no general model, representing a considerable hurdle to industry, where grains and powders must frequently be manipulated. Much of the complexity of modeling granular materials stems from the discreteness of the constituent particles, and a key theme of this work has been the connection of the microscopic particle motion to a bulk continuum description. This led to development of the "spot model", which provides a microscopic mechanism for particle rearrangement in dense granular flow, by breaking down the motion into correlated group displacements on a mesoscopic length scale. The spot model can be used as the basis of a multiscale simulation technique which can accurately reproduce the flow in a large-scale discrete element simulation of granular drainage, at a fraction of the computational cost. In addition, the simulation can also successfully track microscopic packing signatures, making it one of the first models of a flowing random packing. To extend to situations other than drainage ultimately requires a treatment of material properties, such as stress and strain-rate, but these quantities are difficult to define in a granular packing, due to strong heterogeneities at the level of a single particle. However, they can be successfully interpreted at the mesoscopic spot scale, and this information can be used to directly test some commonly-used hypotheses in modeling granular materials, providing insight into formulating a general theory.
by Christopher Harley Rycroft.
Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2011.
Cataloged from PDF version of thesis.
Includes bibliographical references.
The design of entrained flow gasifiers and their operation has largely been an experience based enterprise. Most, if not all, industrial scale gasifiers were designed before it was practical to apply CFD models. Moreover, gasification CFD models developed over the years may have lacked accuracy or have not been tested over a wide range of operating conditions, gasifier geometries and feedstock compositions. One reason behind this shortcoming is the failure to incorporate detailed physics and chemistry of the coupled non-linear phenomena occurring during solid fuel gasification. In order to accurately predict some of the overall metrics of gasifier performance, like fuel conversion and syngas composition, we need to first gain confidence in the sub-models of the various physical and chemical processes in the gasifier. Moreover, in a multiphysics problem like gasification modeling, one needs to balance the effort expended in any one submodel with its effect on the accuracy of predicting some key output parameters. Focusing on these considerations, a multiscale CFD gasification model is constructed in this work with special emphasis on the development and validation of key submodels including turbulence, particle turbulent dispersion and char consumption models. The integrated model is validated with experimental data from various pilot-scale and laboratory-scale gasifier designs, further building confidence in the predictive capability of the model. Finally, the validated model is applied to ascertain the impact of changing the values of key operating parameters on the performance of the MHI and GE gasifiers. The model is demonstrated to provide useful quantitative estimates of the expected gain or loss in overall carbon conversion when critical operating parameters such as feedstock grinding size, gasifier mass throughput and pressure are varied.
by Mayank Kumar.
Ph.D.

The topic of this thesis is fast and accurate simulation techniques used for simulations of flow and transport in porous media, in particular petroleum reservoirs. Fast and accurate simulation techniques are becoming increasingly important for reservoir management and development, as the geological models increase in size and level of detail and require more computational resources to be utilized. The multiscale framework is a promising approach to facilitate simulation of detailed geological models. In contrast to traditional upscaling approaches, the multiscale methods have the detailed geological models present at all times. The work in this thesis includes development of a multiscale-multiphysics method for naturally fractured reservoirs and a new coarsening strategy for geological models to facilitate fast and accurate transport simulations in a multiscale framework. In addition, the work comprises an application of the multiscale framework for flow and transport simulation for rate optimization loops. The coarsening strategy generates flow-based transport grids and is based on amalgamating cells from a fine model, typically the geological model, according to an indicator function. The research indicates a great potential for flexibility and scalability suitable for multi-fidelity simulators

This thesis is about the stabilization of the numerical solution of the Euler and Navier- Stokes equations of compressible flow. When simulating numerically the flow equations, if no stabilization is added, the solution presents non-physical (but numerical) oscillations. For this reason the stabilization of partial differential equations and of the fluid dynamics equations is of great importance. In the framework of the so-called variational multiscale stabilization, we present here a stabilization method for compressible flow. The method assessment is done first of all on a batch of academical examples for different Mach numbers, for viscous and inviscid, steady and transient flow. Afterwards the method is applied to atmospheric flow simulations. To this end we solve the Euler equations for dry and moist atmospheric flow. In the presence of moisture a set of transport equations for water species should be solved as well. This domain of application is a real challenge from the stabilization point of view because the correct amount of stabilization must be added in order to preserve the physical properties of the atmospheric flow. At this point, in order to even improve our method, we turn towards local preconditioning. Local preconditiong permits to reduce the stiffness problems that present the flow equations and cause a bad and slow convergence to the solution. With this purpose in mind we combine our stabilization method with local preconditioning and present a stabilization method for the preconditioned Navier-Stokes equations of compressible flow, that we call P-VMS. This method is tested over several examples at different Mach numbers and proves a significant improvement not only in the convergence to the solution but also in the accuracy and robustness of the method. Finally, the benefits of P-VMS are theoretically assessed using Fourier stability analysis. As a result of this analysis a modification on the computation of the time step is done even improving the convergence of the method.
Aquesta tesi tracta sobre l'estabilització de la solució numèrica de les equacions d'Euler i Navier-Stokes de flux compressible. Quan es simulen numèricament les equacions que governen els fluids, si no s'afegeix cap estabilització, la solució presenta oscil·lacions no físiques sinó numèriques. Per aquest motiu l'estabilització de les equacions en derivades parcials i de les equacions de la mecànica de fluids és de gran importància. Dins del marc de l'anomenada estabilització de multiescales variacionals, presentem aquí un mètode d'estabilització per flux compressible. L'evaluació del mètode es realitza primer en varis exemples acadèmics per diferents nombres de Mach, per flux viscós, inviscid, estacionari i transitori. Després el mètode s'aplica a simulacions de flux atmosfèric. Per això, resolem les equacions d'Euler per flux atmosfèric sec i humit. En presència d'humitat, també s'ha de resoldre un grup d'equacions de transport d'espècies d'aigua. Aquest domini d'aplicació representa un desafiament des del punt de vista de l'estabilització, donat que s'ha d'afegir la quantitat adequada d'estabilització per tal de preservar les propietats físiques del flux atmosfèric. Arribat aquest punt, per tal de millorar el nostre mètode, ens interessem pels precondicionadors locals. Els precondicionadors locals permeten reduir els problemes de rigidesa que presenten les equacions dels fluids i que són causa d'una pitjor i més lenta convergència cap a la solució. Amb aquest propòsit en ment, combinem el nostre mètode d'estabilització amb els precondicionadors locals i presentem un mètode d'estabilització per les equacions de Navier-Stokes de flux compressible, anomenem aquest màtode P-VMS. Aquest mètode es evaluat per mitjà de varis exemples per diferents nombres de Mach i demostra una millora sustancial no només pel que fa la convergència cap a la solució, sinó també en la precisió i robusteza del mètode. Finalment els beneficis del P-VMS es demostren teòricament a través de l'anàlisi d'estabilitat de Fourier. Com a resultat d'aquest anàlisi, sorgeix una modificació en el càlcul del pas de temps que millora un cop més la convergència del mètode

We consider two problems encountered in simulation of fluid flow through porous media. In macroscopic models based on Darcy's law, the permeability field appears as data. The first problem is that the permeability field generally is not entirely known. We consider forward propagation of uncertainty from the permeability field to a quantity of interest. We focus on computing p-quantiles and failure probabilities of the quantity of interest. We propose and analyze improved standard and multilevel Monte Carlo methods that use computable error bounds for the quantity of interest. We show that substantial reductions in computational costs are possible by the proposed approaches. The second problem is fine scale variations of the permeability field. The permeability often varies on a scale much smaller than that of the computational domain. For standard discretization methods, these fine scale variations need to be resolved by the mesh for the methods to yield accurate solutions. We analyze and prove convergence of a multiscale method based on the Raviart–Thomas finite element. In this approach, a low-dimensional multiscale space based on a coarse mesh is constructed from a set of independent fine scale patch problems. The low-dimensional space can be used to yield accurate solutions without resolving the fine scale.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2008.
Includes bibliographical references (p. 75-78).
Multiscale phenomena are ubiquitous to flow and transport in porous media. They manifest themselves through at least the following three facets: (1) effective parameters in the governing equations are scale dependent; (2) some features of the flow (especially sharp fronts and boundary layers) cannot be resolved on practical computational grids; and (3) dominant physical processes may be different at different scales. Numerical methods should therefore reflect the multiscale character of the solution. We concentrate on the development of simulation techniques that account for the heterogeneity present in realistic reservoirs, and have the ability to solve for coupled pressure-saturation problems (on coarse grids). We present a variational multiscale mixed finite element method for the solution of Darcy flow in porous media, in which both the permeability field and the source term display a multiscale character. The formulation is based on a multiscale split of the solution into coarse and subgrid scales. This decomposition is invoked in a variational setting that leads to a rigorous definition of a (global) coarse problem and a set of (local) subgrid problems. One of the key issues for the success of the method is the proper definition of the boundary conditions for the localization of the subgrid problems. We identify a weak compatibility condition that allows for subgrid communication across element interfaces, something that turns out to be essential for obtaining high-quality solutions. We also remove the singularities due to concentrated sources from the coarse-scale problem by introducing additional multiscale basis functions, based on a decomposition of fine-scale source terms into coarse and deviatoric components.
(cont.) The method is locally conservative and employs a low-order approximation of pressure and velocity at both scales. We illustrate the performance of the method on several synthetic cases, and conclude that the method is able to capture the global and local flow patterns accurately.
by Francois-Xavier Dub.
S.M.

The human placenta is characterised by a unique circulatory arrangement, with numerous villous trees containing fetal vessels immersed in maternal blood. Placental tissue therefore manifests a multiscale structure balancing microscopic delivery of nutrients and macroscopic flow. The aims of this study are to examine the interaction between these scales and to understand the influence of placental organisation on the effectiveness of nutrient uptake, which can be compromised in pathologies like pre-eclampsia and diabetes. We first systematically analyse solute transport by a unidirectional flow past an array of microscopic sinks, taking up a dissolved nutrient or gas, for both regular and random sink distributions. We classify distinct asymptotic transport regimes, each characterised by the dominance of advective, diffusive or uptake effects at the macroscale, and analyse a set of simplified model problems to assess the accuracy of homogenization approximations as a function of governing parameters (Peclet and Damkohler numbers) and the statistical properties of the sink distribution. The difference between the leading-order homogenization approximation and the exact solute distribution is determined by large spatial gradients at the scale of individual villi (depending on transport parameter values) and substantial fluctuations that can be correlated over lcngthscales comparable to the whole domain. In addition, we consider the nonlinear advective effects of solute-carriers, such as red blood cells carrying oxygen. Homogenization of the solute-carrier-facilitated transport introduces an effective Peclet number that depends on the slowly varying leading-order concentration, so that an asymptotic transport regime can be changed within the domain. At large Peclet and Damkohler numbers (typical for oxygen transport in the human placenta), nonlinear advection due to solute-carriers leads to a more uniform solute distribution than for a linear carrier-free transport, suggesting a "homogenizing" effect of red blood cells on placental oxygen transport. We then use image analysis and homogenization concepts to extract the effective transport properties (diffusivity and hydraulic resistance) from the microscopic images of histological sections of the normal human placenta. The resulting two-dimensional tensor quantities allow us to assess the anisotropy of placental tissue for solute transport. We also show how the pattern of villous centres of mass can be characterised using an integral correlation measure, and identify the minimum spatial scale over which the distribution of villous branches appears statistically homogeneous. Finally, we propose a mathematical model for maternal blood flow in a placental functional unit (a placentone), describing flow of maternal blood via Darcy's law and steady advective transport of a dissolved nutrient. An analytical method of images and computational integration along streamlines are employed to find flow and solute concentration distributions, which are illustrated for a range of governing system parameters. Predictions of the model agree with experimental radioangiographic studies of tracer dynamics in the intervillous space. The model supports the hypothesis that basal veins are located on the periphery of the placentone in order to optimise delivery of nutrients. We also explain the importance of dilatation of maternal spiral arteries and suggest the existence of an optimal volume fraction of villous tissue, which can both be involved in the placental dysfunction. Theoretical studies of this thesis thus constitute a step towards modelling-based diagnostics and treatment of placental disorders.

The study of hemodynamic patterns in large blood vessels, such as the ascending aortic artery, brachiocephalic trunk, right carotid artery and right subclavian artery presents the challenging complexity of vessel wall compliance induced by the high levels of shear stress gradients and blood flow pulsatility. Accurate prediction of hemodynamics in such conditions requires a complete Fluid Structure Interaction (FSI) analysis that couples the fluid flow behavior throughout the cardiac cycle with the structural response of the vessel walls. This research focuses on the computational study of a Multiscale Fluid-Structure Interaction on the arterial wall by coupling Finite Volumes Method (FVM) predictions of the Fluid Dynamics within the artery with Finite Elements Method (FEM) predictions of the Elasto-Dynamics response of the arterial walls and 1-D closed loop electrical circuit system to generate the dynamic pressure pulse. To this end, a commercial FVM Computational Fluid Dynamics (CFD) code (STAR-CCM+ 7.09.012) will be coupled through an external interface with a commercial FEM Elasto-Dynamics code (ABAQUS V6.12). The coupling interface is written in such a way that the wall shear stresses and pressures predicted by the CFD analysis will be passed as boundary conditions to the FEM structural solver. The deformations predicted by the FEM structural solver will be passed to the CFD solver to update the geometry in an implicit manner before the following iteration step. The coupling between the FSI and the 1-D closed loop lump parameter circuit updated the pressure pulse and mass flow rates generated by the circuit in an explicit manner after the periodic solution in the FSI analysis had settled. The methodology resulting from this study will be incorporated in a larger collaborative research program between UCF and ORHS that entails optimization of surgical implantation of Left Ventricular Assist Devices (LVAD) cannulae and bypass grafts with the aim to minimize thrombo-embolic events. Moreover, the work proposed will also be applied to another such collaborative project focused on the computational fluid dynamics modeling of the circulation of congenitally affected cardiovascular systems of neonates, specifically the Norwood and Hybrid Norwood circulation of children affected by the hypoplastic left heart syndrome.
M.S.M.E.
Masters
Mechanical and Aerospace Engineering
Engineering and Computer Science
Mechanical Engineering; Thermo-Fluids

Most engineering systems have some degree of uncertainty in their input and operating parameters. The interaction of these parameters leads to the uncertain nature of the system performance and outputs. In order to quantify this uncertainty in a computational model, it is necessary to include the full range of uncertainty in the model. Currently, there are two major technical barriers to achieving this: (1) in many situations -particularly those involving multiscale phenomena-the stochastic nature of input parameters is not well defined, and is usually approximated by limited experimental data or heuristics; (2) incorporating the full range of uncertainty across all uncertain input and operating parameters via conventional techniques often results in an inordinate number of computational scenarios to be performed, thereby limiting uncertainty analysis to simple or approximate computational models. This first objective is addressed through combining molecular and macroscale modeling where the molecular modeling is used to quantify the stochastic distribution of parameters that are typically approximated. Specifically, an adsorption separation process is used to demonstrate this computational technique. In this demonstration, stochastic molecular modeling results are validated against a diverse range of experimental data sets. The stochastic molecular-level results are then shown to have a significant role on the macro-scale performance of adsorption systems. The second portion of this research is focused on reducing the computational burden of performing an uncertainty analysis on practical engineering systems. The state of the art for uncertainty analysis relies on the construction of a meta-model (also known as a surrogate model or reduced order model) which can then be sampled stochastically at a relatively minimal computational burden. Unfortunately these meta-models can be very computationally expensive to construct, and the complexity of construction can scale exponentially with the number of relevant uncertain input parameters. In an effort to dramatically reduce this effort, a novel methodology "QUICKER (Quantifying Uncertainty In Computational Knowledge Engineering Rapidly)" has been developed. Instead of building a meta-model, QUICKER focuses exclusively on the output distributions, which are always one-dimensional. By focusing on one-dimensional distributions instead of the multiple dimensions analyzed via meta-models, QUICKER is able to handle systems with far more uncertain inputs.
Ph. D.

This thesis focuses on two important issues in turbulence theory of wall-bounded flows. One is the recent debate on the form of the mean velocity profile (is it a log-law or a power-law with very weak power exponent?) and on its scalings with Reynolds number. In particular, this study relates the mean flow profile of the turbulent channel flow with the underlying topological structure of the fluctuating velocity field through the concept of critical points, a dynamical systems concept that is a natural way to quantify the multiscale structure of turbulence. This connection gives a new phenomenological picture of wall-bounded turbulence in terms of the topology of the flow. This theory validated against existing data, indicates that the issue on the form of the mean velocity profile at the asymptotic limit of infinite Reynolds number could be resolved by understanding the scaling of turbulent kinetic energy with Reynolds number. The other major issue addressed here is on the fundamental mechanism(s) of viscoelastic turbulence that lead to the polymer-induced turbulent drag reduction phenomenon and its dynamical aspects. A great challenge in this problem is the computation of viscoelastic turbulent flows, since the understanding of polymer physics is restricted to mechanical models. An effective numerical method to solve the governing equation for polymers modelled as nonlinear springs, without using any artificial assumptions as usual, was implemented here for the first time on a three-dimensional channel flow geometry. The superiority of this algorithm is depicted on the results, which are much closer to experimental observations. This allowed a more detailed study of the polymer-turbulence dynamical interactions, which yields a clearer picture on a mechanism that is governed by the polymer-turbulence energy transfers.

The following dissertation introduces the hazard of methane buildup in the gob zone, a caved region behind a retreating longwall face. This region serves as a reservoir for methane that can bleed into the mine workings. As this methane mixes with air delivered to the longwall panel, explosive concentrations of methane will be reached. Computational fluid dynamics (CFD) is one of the many approaches to study the gob environment. Several studies in the past have researched this topic and a general approach has been developed that addresses much of the complexity of the problem. The topic of research herein presents an improvement to the method developed by others. This dissertation details a multi-scale approach that includes the entire mine ventilation network in the computational domain. This allows one to describe these transient, difficult to describe boundaries. The gob region was represented in a conventional CFD model using techniques consistent with past efforts. The boundary conditions, however, were cross coupled with a transient network model of the balance of the ventilation airways. This allows the simulation of complex, time dependent boundary conditions for the model of the gob, including the influence of the mine ventilation system (MVS). The scenario modeled in this dissertation was a property in south western Pennsylvania, working in the Pittsburgh seam. A calibrated ventilation model was available as a result of a ventilation survey and tracer gas study conducted by NIOSH. The permeability distribution within the gob was based upon FLAC3d modeling results drawn from the literature. Using the multi-scale approach, a total of 22 kilometers of entryway were included in the computational domain, in addition to the three dimensional model of the gob. The steady state solution to the problem, modeling using this multi-scale approach, was validated against the results from the calibrated ventilation model. Close agreement between the two models was observed, with an average percent difference of less than two percent observed at points scattered throughout the MVS. Transient scenarios, including roof falls at key points in the MVS, were modeling to illustrate the impact on the gob environment.

2010 - 2011
In the last decades, the modeling of crowd motion and pedestrian .ow has attracted the attention of applied mathematicians, because of an increasing num- ber of applications, in engineering and social sciences, dealing with this or similar complex systems, for design and optimization purposes. The crowd has caused many disasters, in the stadiums during some major sporting events as the "Hillsborough disaster" occurred on 15 April 1989 at Hills- borough, a football stadium, in She¢ eld, England, resulting in the deaths of 96 people, and 766 being injured that remains the deadliest stadium-related disaster in British history and one of the worst ever international football accidents. Other example is the "Heysel Stadium disaster" occurred on 29 May 1985 when escaping, fans were pressed against a wall in the Heysel Stadium in Brussels, Belgium, as a result of rioting before the start of the 1985 European Cup Final between Liv- erpool of England and Juventus of Italy. Thirty-nine Juventus fans died and 600 were injured. It is well know the case of the London Millennium Footbridge, that was closed the very day of its opening due to macroscopic lateral oscillations of the structure developing while pedestrians crossed the bridge. This phenomenon renewed the interest toward the investigation of these issues by means of mathe- matical modeling techniques. Other examples are emergency situations in crowded areas as airports or railway stations. In some cases, as the pedestrian disaster in Jamarat Bridge located in South Arabia, mathematical modeling and numerical simulation have already been successfully employed to study the dynamics of the .ow of pilgrims, so as to highlight critical circumstances under which crowd ac- cidents tend to occur and suggest counter-measures to improve the safety of the event. In the existing literature on mathematical modeling of human crowds we can distinguish two approaches: microscopic and macroscopic models. In model at microscopic scale pedestrians are described individually in their motion by ordinary di¤erential equations and problems are usually set in two-dimensional domains delimiting the walking area under consideration, with the presence of obstacles within the domain and a target. The basic modeling framework relies on classical Newtonian laws of point. The model at the macroscopic scale consists in using partial di¤erential equations, that is in describing the evolution in time and space of pedestrians supplemented by either suitable closure relations linking the velocity of the latter to their density or analogous balance law for the momentum. Again, typical guidelines in devising this kind of models are the concepts of preferred direction of motion and discomfort at high densities. In the framework of scalar conservation laws, a macroscopic onedimensional model has been proposed by Colombo and Rosini, resorting to some common ideas to vehicular tra¢ c modeling, with the speci.c aim of describing the transition from normal to panic conditions. Piccoli and Tosin propose to adopt a di¤erent macroscopic point of view, based on a measure-theoretical framework which has recently been introduced by Canuto et al. for coordination problems (rendez-vous) of multiagent systems. This approach consists in a discrete-time Eulerian macroscopic representation of the system via a family of measures which, pushed forward by some motion mappings, provide an estimate of the space occupancy by pedestrians at successive time steps. From the modeling point of view, this setting is particularly suitable to treat nonlocal interactions among pedestrians, obstacles, and wall boundary conditions. A microscopic approach is advantageous when one wants to model di¤erences among the individuals, random disturbances, or small environments. Moreover, it is the only reliable approach when one wants to track exactly the position of a few walkers. On the other hand, it may not be convenient to use a microscopic approach to model pedestrian .ow in large environments, due to the high com- putational e¤ort required. A macroscopic approach may be preferable to address optimization problems and analytical issues, as well as to handle experimental data. Nonetheless, despite the fact that self-organization phenomena are often visible only in large crowds, they are a consequence of strategical behaviors devel- oped by individual pedestrians. The two scales may reproduce the same features of the group behavior, thus providing a perfect matching between the results of the simulations for the micro- scopic and the macroscopic model in some test cases. This motivated the multiscale approach proposed by Cristiani, Piccoli and Tosin. Such an approach allows one to keep a macroscopic view without losing the right amount of .granularity,.which is crucial for the emergence of some self-organized patterns. Furthermore, the method allows one to introduce in a macroscopic (averaged) context some micro- scopic e¤ects, such as random disturbances or di¤erences among the individuals, in a fully justi.able manner from both the physical and the mathematical perspec- tive. In the model, microscopic and macroscopic scales coexist and continuously share information on the overall dynamics. More precisely, the microscopic part tracks the trajectories of single pedestrians and the macroscopic part the density of pedestrians using the same evolution equation duly interpreted in the sense of measures. In this respect, the two scales are indivisible. Starting from model of Cristiani, Piccoli and Tosin we have implemented algo- rithms to simulate the pedestrians motion toward a target to reach in a bounded area, with one or more obstacles inside. In this work di¤erent scenarios have been analyzed in order to .nd the obstacle con.guration which minimizes the pedes- trian average exit time. The optimization is achieved using to algorithms. The .rst one is based on the exhaustive exploration of all positions: the average exit time for all scenarios is computed and then the best one is chosen. The second algorithm is of steepest descent type according to which the obstacle con.guration corresponding to the minimum exit time is found using an iterative method. A variant has been introduced to the algorithm so to obtain a more e¢ cient proce- dure. The latter allows to .nd better solutions in few steps than other algorithms. Finally we performed other simulations with bounded domains like a classical .at with .ve rooms and two exits, comparing the results of three di¤erent scenario changing the positions of exit doors. [edited by author]
X n.s.

Suspensions and dispersions are an important class of complex fluids frequently encountered in a variety of industrial processes and are prominent in many consumer products such as beauty creams and food dressing. The extensive use of suspensions can be partly attributed to their unique rheological properties such as shear-induced normal stresses, yield stress, time-dependent viscosity and shear thinning. These rheological properties are a direct result of the interplay between the suspension microstructure and flow and have consequences for material processing. The quantitative understanding of suspension rheology so far has been dominated by empirical models. However, such models are either very specialized to particular flows, involve numerous/unphysical parameters, or are inadequate to describe rheological phenomena such as normal stresses. Alternatively, microscopic approaches have primarily been successful in addressing idealized cases and/or small length/time scales. Therefore, the goal of this thesis is to develop new and improved classes of continuum models that clearly connect the suspension microstructure under flow to the observed macroscopic rheology.

In this thesis, new, generally multiscale methods are applied towards developing robust constitutive models for suspension rheology. Two primary modeling approaches are employed to advance the modeling of suspension rheology in this thesis. First is a bottom-up approach that starts from a microscopic description of the suspension microstructure (e.g., the evolving aggregate size distribution) that is then coupled to an empirical/phenomenological equation to allow for the evaluation of the shear stress. The shortcoming of using a phenomenological stress expression is counterbalanced by the accurate microstructure picture provided by a microscopic framework. The second technique is a top-down approach that starts from a macroscopic description of the system through the use of state variables whose dynamic equations are developed within the Hamiltonian-enhanced Non-Equilibrium Thermodynamics framework. The key benefit of this latter approach is that the expressions for the stress tensor and microstructure, with the latter represented by a second rank tensor, emerge self-consistently from the framework. Moreover, the generated equations are applicable to general flows. The multiscale nature of suspension microstructure implies that depending on the phenomena of interest, one or the other or a combination of the two approaches may be favored. Regardless of the approach taken, a recurrent theme in this work is the clear association of the observed macroscopic rheological behavior with an underlying microscopic picture. Finally, for all the suspensions emphasized in this thesis i.e., thixotropic, polydisperse, noncolloidal and emulsions, the corresponding rheological models developed are validated against experimental/simulation data revealing their predictive capability.

A number of important specific accomplishments are achieved in this thesis. To begin with, a population balance-based constitutive model for thixotropic suspensions is developed. Unlike alternative phenomenological models currently in use, a population balance-based model incorporates parameters with clear physical meaning. As a result, the resultant model holds promise for inverse design of thixotropic materials such as pastes that are used in many industrial processes. Next, the use of a conformation tensor as an internal variable to represent changes in suspension microstructure during material deformation is also demonstrated. For the first time, a comprehensive conformation tensor-based framework for suspensions, with a rigor approaching that performed previously for polymeric system, is realized. When applied to dilute emulsions, the conformation tensor-based rheological model that results is in exact agreement with existing asymptotic microscopic theory. In the same emulsion system, effects of microinertia and Ostwald ripening have also been included within a conformation tensor-based model for the first time. In concentrated suspensions, the conformation based theory has been shown to be capable of describing emerging secondary structure in the particle configuration leading to first and second normal stress differences that are both negative. Additional advances have also been made to develop self-consistent approximations for polydisperse suspension viscosity and testing them against prototype experiments. On a broader level, this work provides a number of methodologies for systematic constitutive model development in complex fluids. From an engineering perspective, the results of this thesis can be used to improve upon existing numerical tools, e.g., computational fluid dynamics, to allow for accurate simulation of industrial processes such as extrusion and screen printing of thixotropic pastes, suspensions and emulsions.

We determined genetic variance and gene flow across multiple scales (reaches, headwater segments, and catchments) to examine the dispersal ability of the flatworm Polycelis coronata along the Wasatch Mountains of Utah. Multiple models predict patterns of genetic differentiation in stream invertebrates based on dispersal traits and the spatial connectivity of the habitat. The stream hierarchy model predicts genetic differentiation to be low and gene flow to be high between reaches nested in segments, moderate among segments within catchments, and differentiation to be highest and gene flow lowest among catchments, whereas the headwater model predicts the greatest differentiation between headwater segments. Our objective was to determine which model best described genetic patterns observed in P. coronata. Using a nested hierarchical sampling design ensured that if limitations to dispersal had an effect on genetic differentiation, we would be able to identify at what scale these processes operate. We hypothesized genetic variation would be small within headwater segments and reach maximum levels between headwater segments with no increase in differentiation with increasing distance between headwater patches or between drainages. We do not expect high dispersal along the stream network or across the terrestrial environment (actively or passively).We generated DNA sequence data (mitochondrial COI) from 50 sites nested within 24 segments, which were nested in four adjacent catchments. We identified 134 haplotypes from 506 individuals using a 763 bp fragment of mtDNA. Genetic patterns did not conform to the SH model. Evidence from one drainage (Provo River) was consistent with the headwater model. However, high differentiation within sites suggested that the genetic patterns we uncovered may be representative of high ancestral polymorphism among pre-fragmented populations that were historically widespread. Large effective population sizes and no evidence of bottleneck events suggest incomplete lineage cannot be discounted as an explanation of high differentiation at the smallest scales.

In this dissertation, we present multiscale analytical solutions, in the weak sense, to the generalized Laplace's equation in Ω ⊂ Rⁿ, subject to periodic and nonperiodic boundary conditions. They are called multiscale solutions since they depend on a coefficient which takes a wide possible range of scales. We define forms of nonseparable coefficient functions in Lᵖ(Ω) such that the solutions are valid for the periodic and nonperiodic cases. In the periodic case, one such solution corresponds to the auxiliary cell problem in homogenization theory. Based on the proposed analytical solution, we were able to write explicitly the analytical form for the upscaled equation with an effective coefficient, for linear and nonlinear cases including the one with body forces. This was done by performing the two-scale asymptotic expansion for linear and nonlinear equations in divergence form with periodic coefficient. We proved that the proposed homogenized coefficient satisfies the Voigt-Reiss inequality. By performing numerical experiments and error analyses, we were able to compare the heterogeneous equation and its homogenized approximation in order to define criteria in terms of allowable heterogeneity in the domain to obtain a good approximation. The results presented, in this dissertation, have laid mathematical groundwork to better understand and apply multiscale processes under a deterministic point of view.

Thesis (Ph. D.)--University of Kentucky, 2006.
Title from document title page (viewed on January 25, 2007). Document formatted into pages; contains: xiii, 162 p. : ill. (some col.). Includes abstract and vita. Includes bibliographical references (p. 151-157).

An imaging-based computational framework for simulation of airflow in subject specific breathing human lungs is established. The three-dimensional (3D) airways of up to 9 generations and lobes are segmented and reconstructed from computed tomography (CT) images. Beyond the CT-resolved 3D airways, a volume filling method is applied to generate the one-dimensional (1D) conducting airway tree that bridges the central airway with the lung parenchyma. Through 3D-1D airway coupling, a novel image-registration-based boundary condition (BC) is proposed to derive physiologically-consistent regional ventilation for the whole lung and provide flow-rate fractions needed for the 3D airway model via the 1D-tree connectivity and the mass conservation. The in-house parallel finite-element large-eddy simulation (LES) code enables to capture genuinely complex airflow characteristics in a computationally-efficient manner. The 3D-1D coupling framework is multiscale because it can not only predict detailed flows in the 3D central airways at a local level, but also yields subject-specific physiologically-consistent regional ventilation at the whole lung level. The framework has been applied to investigate pulmonary airflow and lung physiology. For example, the study of intra- and inter-subject variability provides insight into the effect of airway geometry on airflow structure. The relations between airflow structure, energy dissipation, and airway resistance under normal breathing condition have also been studied, showing similarity behaviors for inspiratory and expiratory flows. In the study of high-frequency oscillatory ventilation, we have compared counter-flow structures near flow reversal (namely phase change between inspiration and expiration) and quantified associated convective mixing in both idealized and CT-based airway models. Furthermore, the image-registration-derived displacement field is used to deform 3D-1D airway models for breathing lung simulation and estimate diameter changes of 1D airway segments during deformation. In conjunction with an arbitrary Lagrangian Eulerian method, airflow in a breathing lung has been simulated and compared with that of a rigid airway model. The results show that the proposed computational framework is promising in better understanding the human lung physiology and improving the treatment of diseased lung.

The groundwater specialists and the reservoir engineers share the same interest in simulating multiphase flow in soil with heterogeneous intrinsic properties. They also both face the challenge of going from a well-modeled micrometer scale to the reservoir scale with a controlled loss of information. This upscaling process is indeed worthy to make simulation over an entire reservoir manageable and stochastically repeatable. Two upscaling steps can be defined: one from the micrometer scale to the Darcy scale, and another from the Darcy scale to the reservoir scale. In this thesis, a new second upscaling multiscale algorithm Finite Volume Mixed Hybrid Multiscale Methods (Fv-MHMM) is investigated. Extension to a two-phase flow system is done by weakly and sequentially coupling saturation and pressure via IMPES-like method.

In this dissertation we develop and analyze numerical method to solve general elliptic boundary value problems with many scales. The numerical method presented is intended to capture the small scales effect on the large scale solution without resolving the small scale details, which is done through the construction of a multiscale map. The multiscale method is more effective when the coarse element size is larger than the small scale length. To guarantee a numerical conservation, a finite volume element method is used to construct the global problem. Analysis of the multiscale method is separately done for cases of linear and nonlinear coefficients. For linear coefficients, the multiscale finite volume element method is viewed as a perturbation of multiscale finite element method. The analysis uses substantially the existing finite element results and techniques. The multiscale method for nonlinear coefficients will be analyzed in the finite element sense. A class of correctors corresponding to the multiscale method will be discussed. In turn, the analysis will rely on approximation properties of this correctors. Several numerical experiments verifying the theoretical results will be given. Finally we will present several applications of the multiscale method in the flow in porous media. Problems that we will consider are multiphase immiscible flow, multicomponent miscible flow, and soil infiltration in saturated/unsaturated flow.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Nuclear Science and Engineering, 2018.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 176-181).
In the fuel assemblies of a boiling water reactor (BWR) the steam quality increases along the assembly's length as heat is transferred from the fuel rods to the water coolant. Nucleate boiling is the dominant heat transfer mechanism at low and intermediate steam qualities (typical of the bubbly and slug/churn flow regimes), while forced convective evaporation dominates at higher steam quality in the annular flow regime. The transition of the heat transfer mechanism, also called suppression of nucleate boiling (SNB), affects the local heat transfer coefficient (HTC), the stability of the liquid film, and the entrainment dynamics. To support the efficient design and safe operation of future BWRs with higher power density, a thorough understanding of the thermohydraulic mechanisms and an accurate prediction of the transition conditions for SNB in annular flow is quite desirable. An innovative diagnostic technique combining synchronized infrared thermography and an electrical conductance-based liquid film thickness sensor was utilized here to investigate the details of the SNB phenomena with high spatial and temporal resolutions. The main control parameters of the tests included: the mass flux from 700 to 1400 kg-m⁻²-s⁻¹, steam quality from 0.01 to 0.08, and heat flux from 100 to 2000 kW-m⁻². The system pressure was held close to atmospheric pressure. At each set of conditions, the local distributions of the 2D surface temperature, 2D heat flux, and quasi-2D liquid film thickness were measured. From the measured data, the SNB heat flux, the SNB wall superheat, and the hydrodynamic properties of the disturbance waves were extracted. The experimental observations show for the first time the multiscale interaction of the extremely thin film and small nucleation cavities (on the scale of 10 micron), with the large disturbance waves and their associated temperature oscillations (with wavelengths of ~10 cm). A first of a kind 1D mechanistic model was developed to accurately capture this unique transient effect of the disturbance waves on the local heat transfer. The experimental results also suggest a strong dependency of the SNB heat flux and wall superheat on steam quality, with a second-order, weaker dependency on total mass flux. The same dependency is also found for the disturbance wave properties. A complete set semi-empirical correlations was proposed for predicting the time-averaged film thickness and SNB thermal conditions. Good agreement is found between the semi-empirical correlations and the experimental results. The database generated in this project can be further used for development and validation of CFD models of SNB and two-phase heat transfer in annular flow.
by Guanyu Su.
Ph. D.

This thesis presents an experimental investigation into the wake of a lifting wing with multiscale cut-in trailing edge serrations. More specifically, it looks into how the wake is affected by the serration patterns, both in terms of mean properties and dynamic and spectral information. The flow is investigated by means of particle image velocimetry and hot-wire anemometry to combine the dynamic and spatial strengths of the two experimental techniques. The response of a wing fitted with such serrations and subjected to unsteady inflows is studied by means of lift measurement and hot-wire anemometry in the wake. Cut-in trailing edges are found to generate a strong secondary flow from below the peaks towards the troughs. Such a flow pattern increases the velocity deficit behind the peaks while re-energising the wake behind the troughs, giving rise to span-wise inhomogeneity of the velocity deficit and wake width which persists far downstream. The introduction of cut-in serrations exhibits bluntness that in turn generates vortex shedding that locks into a bent cell structure. The use of multiscale patterns weakens the cell structures which translates into a reduction of vortex shedding intensity as well as a reduction of span-wise correlation at both vortex shedding and low frequencies. The use of an alternative sharp approach offers a compromise that gives less coherence reduction on the edges of the wake but avoids the introduction of a clear vortex shedding signal. Under unsteady inflow conditions, the 2-iteration multiscale pattern provide the strongest overall reduc- tion of coherence. Statistical analysis of lift fluctuations under unsteady and intermittent inflow conditions reveals that the single tone sinusoidal pattern has the strongest reduction of the distribution’s tails. Finally, the multiscale patterns are found to smooth the time-evolution of the lift fluctuations when the wing is submitted to a sinusoidal variation of the flow incidence.

Most applications in computer vision suffer from two major difficulties. The first is they are notoriously ridden with sub-optimal local minima. The second is that they typically require high computational cost to be solved robustly. The reason for these two drawbacks is that most problems in computer vision, even when well-defined, typically require finding a solution in a very large high-dimensional space. It is for these two reasons that multiscale methods are particularly well-suited to problems in computer vision. Multiscale methods, by way of looking at the coarse scale nature of a problem before considering the fine scale nature, often have the ability to avoid sub-optimal local minima and obtain a more globally optimal solution. In addition, multiscale methods typically enjoy reduced computational cost. This thesis applies novel multiscale active contour methods to several problems in computer vision, especially in simultaneous segmentation and reconstruction of tomography images. In addition, novel multiscale methods are applied to contour registration using minimal surfaces and to the computation of non-linear rotationally invariant optical flow. Finally, a methodology for fast robust image segmentation is presented that relies on a lower dimensional image basis derived from an image scale space. The specific advantages of using multiscale methods in each of these problems is highlighted in the various simulations throughout the thesis, particularly their ability to avoid sub-optimal local minima and their ability to solve the problems at a lower overall computational cost.

Améliorer la gestion et l’organisation des blocs opératoires est une tâche critique dans les hôpitaux modernes, principalement à cause de la diversité et l’urgence des activités impliquées. Contrairement à l’aviation civile, qui a su optimiser organisation et sécurité, le management de bloc opératoire est plus délicat. Le travail ici présenté abouti au développement et à l’installation de nouvelles technologies assistées par ordinateur résolvant les problèmes quotidiens des blocs opératoires. La plupart des systèmes existants modélisent le flux chirurgical et sont utilisés seulement pour planifier. Ils sont basés sur des procédés stochastiques, n’ayant pas accès à des données sûres. Nous proposons une structure utilisant un modèle multi-agent qui comprend tous les éléments indispensables à une gestion efficace et au maintien de la sécurité dans les blocs opératoires, allant des compétences communicationnelles du staff, au temps nécessaire à la mise en place du service de nettoyage. Nous pensons que la multiplicité des ressources humaines engagées dans cette structure cause des difficultés dans les blocs opératoires et doit être prise en compte dans le modèle. En parallèle, nous avons construit un modèle mathématique de flux d’air entre les blocs opératoires pour suivre et simuler la qualité de l’environnement de travail. Trois points sont nécessaires pour la construction et le bon fonctionnement d’un ensemble de bloc opératoire : 1) avoir accès au statut du système en temps réel grâce au placement de capteurs 2) la construction de modèles multi-échelles qui lient tous les éléments impliqués et leurs infrastructures 3) une analyse minutieuse de la population de patients, du comportement des employés et des conditions environnementales. Nous avons développé un système robuste et invisible qui permet le suivi et la détection automatique d’événements dans les blocs. Avec ce système nous pouvons suivre l’activité à la porte d’entrée des blocs, puis l’avancement en temps réel de la chirurgie et enfin l’état général du bloc. Un modèle de simulation numérique de mécanique des fluides de plusieurs blocs opératoires est utilisé pour suivre la dispersion de fumée chirurgicale toxique, ainsi qu’un modèle multi-domaine qui évalue les risques de propagation de maladie nosocomiale entre les blocs. La combinaison de ces trois aspects amène une nouvelle dimension de sensibilisation à l’environnent des blocs opératoires et donne au staff un système cyber-physique capable de prédire des événements rares impactant la qualité, l’efficacité, la rentabilité et la sécurité dans l’hôpital
Improving operating room management is a constant issue for modern large hospital systems who have to deal with the reality of day to day clinical activity. As opposed to other industrial sectors such as air civil aviation that have mastered the topic of industry organization and safety, progress in surgical flow management has been slower. The goal of the work presented here is to develop and implement technologies that leverage the principles of computational science to the application of OR suite problems. Most of the currently available models of surgical flow are used for planning purposes and are essentially stochastic processes due to uncertainties in the available data. We propose an agent-based model framework that can incorporate all the elements, from communication skills of the staff to the time it takes for the janitorial team to go clean an OR. We believe that human factor is at the center of the difficulty of OR suite management and should be incorporated in the model. In parallel, we use a numerical model of airflow at the OR suite level to monitor and simulate environment conditions inside the OR. We hypothesize that the following three key ingredients will provide the level of accuracy needed to improve OR management : 1) Real time updates of the model with ad hoc sensors of tasks/stages 2) Construction of a multi-scale model that links all key elements of the complex surgical infrastructure 3) Careful analysis of patient population factors, staff behavior, and environment conditions. We have developed a robust and non-obtrusive automatic event tracking system to make our model realistic to clinical conditions. Not only we track traffic through the door and the air quality inside the OR, we can also detect standard events in the surgical process. We propose a computational fluid dynamics model of a part of an OR suite to track dispersion of toxic surgical smoke and build in parallel a multidomain model of potential nosocomial contaminant particles flow in an OR suite. Combining the three models will raise the awareness of the OR suite by bringing to the surgical staff a cyber-physical system capable of prediction of rare events in the workflow and the safety conditions

We determined genetic variance and gene flow across multiple scales (reaches, tributaries, and catchments) to examine the dispersal ability of the caddisfly, Neothremma alicia in streams along the Wasatch Range in the Rocky Mountains of Utah. Neothremma alicia is one of the most abundant caddisflies in this region. We generated DNA sequence data (mitochondrial COI) from 34 reaches, nested in 15 tributaries distributed across 3 adjacent catchments. We identified 47 haplotypes from a total of 486 individuals. The most abundant haplotype (H1) was found at all sites/reaches and comprised 44% of the total number of individuals sequenced. The remaining rare haplotypes (46) were recently derived from the dominant, H1 haplotype. All of the rare haplotypes were restricted to a single catchment with 81 % restricted to either a single tributary or to two adjacent tributaries. We found the largest FST values among tributaries and the smallest FST values between reaches within tributaries suggesting that dispersal and gene flow is largely confined to within tributaries. This result supports the observation that aerial adults commonly crawl and fly along the stream corridor, especially in deeply incised valleys of mountainous regions. Our analyses show that this population has experienced a bottleneck that may have reduced population genetic variance from many haplotypes to one single dominant haplotype, H1. The rare haplotypes may have diverged since the bottleneck from the H1 haplotype and thus, have not had time to disperse outside their catchment and in most cases outside their specific tributary. Our analyses indicated that the bottleneck took place between 1,000 and 10,000 years ago. Thus, it appears that most rare haplotypes have been unable to colonize outside of the tributary they originated in for around 1,000 years.

For simple fluids, or Newtonian fluids, the study of the Navier-Stokes equations in the high Reynolds number limit brings about two fundamental research subjects, the Euler equations and the Prandtl's system. The consideration of infinite Reynolds number reduces the Navier-Stokes equations to the Euler equations, both of which are dealing with the entire flow region. Prandtl's system consists of the governing equations of the boundary layer, a thin layer formed at the wall boundary where viscosity cannot be neglected. In this dissertation, we investigate the upper convected Maxwell(UCM) model for complex fluids, or non-Newtonian fluids, in the high Weissenberg number limit. This is analogous to the Newtonian fluids in the high Reynolds number limit. We present two well-posedness results. The first result is on an initial-boundary value problem for incompressible hypoelastic materials which arise as a high Weissenberg number limit of viscoelastic fluids. We first assume the stress tensor is rank-one and develop energy estimates to show the problem is locally well-posed. Then we show the more general case can be handled in the same spirit. This problem is closely related to the incompressible ideal magneto-hydrodynamics (MHD) system. The second result addresses the formulation of a time-dependent elastic boundary layer through scaling analysis. We show the well-posedness of this boundary layer by transforming to Lagrangian coordinates. In contrast to the possible ill-posedness of Prandtl's system in Newtonian fluids, we prove that in non-Newtonian fluids the stress boundary layer problem is well-posed.
Ph. D.

Management of invasive species is notoriously difficult and often expensive. The aim of this study was to inform feral pig management practises in far-north Queensland by utilising molecular markers and geographic information systems to evaluate the affect of landscape features on feral pig population structure. This thesis evaluated landscape features at multiple spatial scales to identify landscape features that are a barrier or facilitator of feral pig movement and makes recommendations for future management strategies.

We address two computational challenges for numerical simulations of Darcy flow problems: rough and uncertain data. The rapidly varying and possibly high contrast permeability coefficient for the pressure equation in Darcy flow problems generally leads to irregular solutions, which in turn make standard solution techniques perform poorly. We study methods for numerical homogenization based on localized computations. Regarding the challenge of uncertain data, we consider the problem of forward propagation of uncertainty through a numerical model. More specifically, we consider methods for estimating the failure probability, or a point estimate of the cumulative distribution function (cdf) of a scalar output from the model. The issue of rough coefficients is discussed in Papers I–III by analyzing three aspects of the localized orthogonal decomposition (LOD) method. In Paper I, we define an interpolation operator that makes the localization error independent of the contrast of the coefficient. The conditions for its applicability are studied. In Paper II, we consider time-dependent coefficients and derive computable error indicators that are used to adaptively update the multiscale space. In Paper III, we derive a priori error bounds for the LOD method based on the Raviart–Thomas finite element. The topic of uncertain data is discussed in Papers IV–VI. The main contribution is the selective refinement algorithm, proposed in Paper IV for estimating quantiles, and further developed in Paper V for point evaluation of the cdf. Selective refinement makes use of a hierarchy of numerical approximations of the model and exploits computable error bounds for the random model output to reduce the cost complexity. It is applied in combination with Monte Carlo and multilevel Monte Carlo methods to reduce the overall cost. In Paper VI we quantify the gains from applying selective refinement to a two-phase Darcy flow problem.

The study and modelling of two-phase flow, even the simplest ones such as the bubbly flow, remains a challenge that requires exploring the physical phenomena from different spatial and temporal resolution levels. CFD (Computational Fluid Dynamics) is a widespread and promising tool for modelling, but nowadays, there is no single approach or method to predict the dynamics of these systems at the different resolution levels providing enough precision of the results. The inherent difficulties of the events occurring in this flow, mainly those related with the interface between phases, makes that low or intermediate resolution level approaches as system codes (RELAP, TRACE, ...) or 3D TFM (Two-Fluid Model) have significant issues to reproduce acceptable results, unless well-known scenarios and global values are considered. Instead, methods based on high resolution level such as Interfacial Tracking Method (ITM) or Volume Of Fluid (VOF) require a high computational effort that makes unfeasible its use in complex systems. In this thesis, an open-source simulation framework has been designed and developed using the OpenFOAM library to analyze the cases from microescale to macroscale levels. The different approaches and the information that is required in each one of them have been studied for bubbly flow. In the first part, the dynamics of single bubbles at a high resolution level have been examined through VOF. This technique has allowed to obtain accurate results related to the bubble formation, terminal velocity, path, wake and instabilities produced by the wake. However, this approach has been impractical for real scenarios with more than dozens of bubbles. Alternatively, this thesis proposes a CFD Discrete Element Method (CFD-DEM) technique, where each bubble is represented discretely. A novel solver for bubbly flow has been developed in this thesis. This includes a large number of improvements necessary to reproduce the bubble-bubble and bubble-wall interactions, turbulence, velocity seen by the bubbles, momentum and mass exchange term over the cells or bubble expansion, among others. But also new implementations as an algorithm to seed the bubbles in the system have been incorporated. As a result, this new solver gives more accurate results as the provided up to date. Following the decrease on resolution level, and therefore the required computational resources, a 3D TFM have been developed with a population balance equation solved with an implementation of the Quadrature Method Of Moments (QMOM). The solver is implemented with the same closure models as the CFD-DEM to analyze the effects involved with the lost of information due to the averaging of the instantaneous Navier-Stokes equation. The analysis of the results with CFD-DEM reveals the discrepancies found by considering averaged values and homogeneous flow in the models of the classical TFM formulation. Finally, for the lowest resolution level approach, the system code RELAP5/MOD3 is used for modelling the bubbly flow regime. The code has been modified to reproduce properly the two-phase flow characteristics in vertical pipes, comparing the performance of the calculation of the drag term based on drift-velocity and drag coefficient approaches.
El estudio y modelado de flujos bifásicos, incluso los más simples como el bubbly flow, sigue siendo un reto que conlleva aproximarse a los fenómenos físicos que lo rigen desde diferentes niveles de resolución espacial y temporal. El uso de códigos CFD (Computational Fluid Dynamics) como herramienta de modelado está muy extendida y resulta prometedora, pero hoy por hoy, no existe una única aproximación o técnica de resolución que permita predecir la dinámica de estos sistemas en los diferentes niveles de resolución, y que ofrezca suficiente precisión en sus resultados. La dificultad intrínseca de los fenómenos que allí ocurren, sobre todo los ligados a la interfase entre ambas fases, hace que los códigos de bajo o medio nivel de resolución, como pueden ser los códigos de sistema (RELAP, TRACE, etc.) o los basados en aproximaciones 3D TFM (Two-Fluid Model) tengan serios problemas para ofrecer resultados aceptables, a no ser que se trate de escenarios muy conocidos y se busquen resultados globales. En cambio, códigos basados en alto nivel de resolución, como los que utilizan VOF (Volume Of Fluid), requirieren de un esfuerzo computacional tan elevado que no pueden ser aplicados a sistemas complejos. En esta tesis, mediante el uso de la librería OpenFOAM se ha creado un marco de simulación de código abierto para analizar los escenarios desde niveles de resolución de microescala a macroescala, analizando las diferentes aproximaciones, así como la información que es necesaria aportar en cada una de ellas, para el estudio del régimen de bubbly flow. En la primera parte se estudia la dinámica de burbujas individuales a un alto nivel de resolución mediante el uso del método VOF (Volume Of Fluid). Esta técnica ha permitido obtener resultados precisos como la formación de la burbuja, velocidad terminal, camino recorrido, estela producida por la burbuja e inestabilidades que produce en su camino. Pero esta aproximación resulta inviable para entornos reales con la participación de más de unas pocas decenas de burbujas. Como alternativa, se propone el uso de técnicas CFD-DEM (Discrete Element Methods) en la que se representa a las burbujas como partículas discretas. En esta tesis se ha desarrollado un nuevo solver para bubbly flow en el que se han añadido un gran número de nuevos modelos, como los necesarios para contemplar los choques entre burbujas o con las paredes, la turbulencia, la velocidad vista por las burbujas, la distribución del intercambio de momento y masas con el fluido en las diferentes celdas por cada una de las burbujas o la expansión de la fase gaseosa entre otros. Pero también se han tenido que incluir nuevos algoritmos como el necesario para inyectar de forma adecuada la fase gaseosa en el sistema. Este nuevo solver ofrece resultados con un nivel de resolución superior a los desarrollados hasta la fecha. Siguiendo con la reducción del nivel de resolución, y por tanto los recursos computacionales necesarios, se efectúa el desarrollo de un solver tridimensional de TFM en el que se ha implementado el método QMOM (Quadrature Method Of Moments) para resolver la ecuación de balance poblacional. El solver se desarrolla con los mismos modelos de cierre que el CFD-DEM para analizar los efectos relacionados con la pérdida de información debido al promediado de las ecuaciones instantáneas de Navier-Stokes. El análisis de resultados de CFD-DEM permite determinar las discrepancias encontradas por considerar los valores promediados y el flujo homogéneo de los modelos clásicos de TFM. Por último, como aproximación de nivel de resolución más bajo, se investiga el uso uso de códigos de sistema, utilizando el código RELAP5/MOD3 para analizar el modelado del flujo en condiciones de bubbly flow. El código es modificado para reproducir correctamente el flujo bifásico en tuberías verticales, comparando el comportamiento de aproximaciones para el cálculo del término d
L'estudi i modelatge de fluxos bifàsics, fins i tot els més simples com bubbly flow, segueix sent un repte que comporta aproximar-se als fenòmens físics que ho regeixen des de diferents nivells de resolució espacial i temporal. L'ús de codis CFD (Computational Fluid Dynamics) com a eina de modelatge està molt estesa i resulta prometedora, però ara per ara, no existeix una única aproximació o tècnica de resolució que permeta predir la dinàmica d'aquests sistemes en els diferents nivells de resolució, i que oferisca suficient precisió en els seus resultats. Les dificultat intrínseques dels fenòmens que allí ocorren, sobre tots els lligats a la interfase entre les dues fases, fa que els codis de baix o mig nivell de resolució, com poden ser els codis de sistema (RELAP,TRACE, etc.) o els basats en aproximacions 3D TFM (Two-Fluid Model) tinguen seriosos problemes per a oferir resultats acceptables , llevat que es tracte d'escenaris molt coneguts i se persegueixen resultats globals. En canvi, codis basats en alt nivell de resolució, com els que utilitzen VOF (Volume Of Fluid), requereixen d'un esforç computacional tan elevat que no poden ser aplicats a sistemes complexos. En aquesta tesi, mitjançant l'ús de la llibreria OpenFOAM s'ha creat un marc de simulació de codi obert per a analitzar els escenaris des de nivells de resolució de microescala a macroescala, analitzant les diferents aproximacions, així com la informació que és necessària aportar en cadascuna d'elles, per a l'estudi del règim de bubbly flow. En la primera part s'estudia la dinàmica de bambolles individuals a un alt nivell de resolució mitjançant l'ús del mètode VOF. Aquesta tècnica ha permès obtenir resultats precisos com la formació de la bambolla, velocitat terminal, camí recorregut, estela produida per la bambolla i inestabilitats que produeix en el seu camí. Però aquesta aproximació resulta inviable per a entorns reals amb la participació de més d'unes poques desenes de bambolles. Com a alternativa en aqueix cas es proposa l'ús de tècniques CFD-DEM (Discrete Element Methods) en la qual es representa a les bambolles com a partícules discretes. En aquesta tesi s'ha desenvolupat un nou solver per a bubbly flow en el qual s'han afegit un gran nombre de nous models, com els necessaris per a contemplar els xocs entre bambolles o amb les parets, la turbulència, la velocitat vista per les bambolles, la distribució de l'intercanvi de moment i masses amb el fluid en les diferents cel·les per cadascuna de les bambolles o els models d'expansió de la fase gasosa entre uns altres. Però també s'ha hagut d'incloure nous algoritmes com el necessari per a injectar de forma adequada la fase gasosa en el sistema. Aquest nou solver ofereix resultats amb un nivell de resolució superior als desenvolupat fins la data. Seguint amb la reducció del nivell de resolució, i per tant els recursos computacionals necessaris, s'efectua el desenvolupament d'un solver tridimensional de TFM en el qual s'ha implementat el mètode QMOM (Quadrature Method Of Moments) per a resoldre l'equació de balanç poblacional. El solver es desenvolupa amb els mateixos models de tancament que el CFD-DEM per a analitzar els efectes relacionats amb la pèrdua d'informació a causa del promitjat de les equacions instantànies de Navier-Stokes. L'anàlisi de resultats de CFD-DEM permet determinar les discrepàncies ocasionades per considerar els valors promitjats i el flux homogeni dels models clàssics de TFM. Finalment, com a aproximació de nivell de resolució més baix, s'analitza l'ús de codis de sistema, utilitzant el codi RELAP5/MOD3 per a analitzar el modelatge del fluxos en règim de bubbly flow. El codi és modificat per a reproduir correctament les característiques del flux bifàsic en canonades verticals, comparant el comportament d'aproximacions per al càlcul del terme de drag basades en velocitat de drift flux model i de les basades en coe
Peña Monferrer, C. (2017). Computational fluid dynamics multiscale modelling of bubbly flow. A critical study and new developments on volume of fluid, discrete element and two-fluid methods [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/90493
TESIS

This thesis describes the unstable dynamics of a gas jet impinging on a falling liquid film. This flow configuration is encountered in the jet wiping process, used in continuous coating applications such as the hot-dip galvanizing to control the thickness of a liquid coat on a moving substrate. The interaction between these flows generates a non-uniform coating layer, of great concern for the quality of industrial products, and results from a complex coupling between the interface instabilities of the liquid film and the confinement-driven instabilities of the impinging jet.Combining experimental and numerical methods, this thesis studied the dynamics of these flows on three simplified flow configurations, designed to isolate the key features of their respective instabilities and to provide complementary information on their mutual interaction. These configurations include the gas jet impingement on a falling liquid film perturbed with controlled flow rate pulsation, the gas jet impingement on a solid interface reproducing stable and unstable liquid film interfaces and a laboratory scaled model of the jet wiping process. Each of these configurations was reproduced on dedicated experimental set-up, instrumented for non-intrusive measurement techniques such as High-Speed Flow Visualization (HSFV) and Time-resolved Particle Image Velocimetry (TR-PIV) for the gas jet flow analysis, Laser Induced Fluorescence (LIF) tracking of the liquid interface, and 3D Light Absorption (LAbs) measurement of the liquid film thickness. To optimize the performances of these measurement techniques, several advanced data processing routines were developed, including a novel image pre-processing method for background removal in PIV and a dynamic feature tracking for the automatic detection of the jet flow and the liquid film interface from HSFV, LIF, and PIV videos.To identify the flow structures driving the unstable response of the jet flow, a novel data-driven modal decomposition was developed. This decomposition, referred to as Multiscale Proper Orthogonal Decomposition (mPOD), was validated on synthetic, numerical and experimental test cases and allowed for better feature extraction than classical alternatives such as Proper Orthogonal Decomposition (POD) or Dynamic Mode Decomposition (DMD).The experimental work on these laboratory models was complemented with the analysis of several numerical simulations, including a classical 2D Unsteady Reynolds Averaged Navier Stokes (URANS) modeling of the gas jet impingement on a fixed interface, a 2D Variational Multiscale Simulation (VMS) with anisotropic mesh refinement of the gas jet impingement on a pulsing interface, and a 3D simulation of the jet wiping process combining Large Eddy Simulation (LES) on the gas side with Volume of Fluid (VOF) treatment of the liquid film flow. The experimental modal analysis on the dynamic response of the gas jet and the characterization of the pressure-velocity coupling in the numerical investigation allowed for a complete picture of the mechanism driving the jet oscillation and its possible impact on the liquid film.In parallel, several flow control strategies to prevent the jet oscillation were developed, tested numerically and experimentally in simplified conditions, and later implemented on the design of a new nozzle for the jet wiping process. This new nozzle was finally tested on a laboratory scale of the wiping process and its performances compared to single jet and multiple jet wiping configurations. In these three cases, the experimental work presents the modal analysis of the gas field using TR-PIV and mPOD, the liquid interface tracking via LIF, and the final coating thickness characterization via LAbs.The large spatiotemporally resolved experimental database allowed to give a detailed description of the jet wiping instability and to provide new insights on this fascinating fundamental and applied problem of fluid dynamics.
Doctorat en Sciences de l'ingénieur et technologie
info:eu-repo/semantics/nonPublished

Au cours des dernières décennies, les plasmas créés par une décharge micro-ondes ont de plusen plus attiré l’attention de la communauté scientifique aérospatiale sur le sujet du contrôled’écoulements. En effet, il a été démontré expérimentalement que le dépôt d’énergie obtenu parle plasma peut modifier les propriétés aérodynamiques de l’écoulement autour d’un objet telleque la trainée de frottement. Or, la conception et l’optimisation de ces actionneurs plasma entant que technique de contrôle d’écoulements nécessitent une compréhension approfondie de laphysique sous-jacente que les seules expériences sont incapables de fournir.Dans ce contexte, nous nous intéressons à la modélisation numérique de l’interaction desondes électromagnétiques avec un plasma et le gaz afin de mieux comprendre la nature desdécharges micro-ondes et leur applicabilité. La modélisation de ces phénomènes présente desdifficultés importantes en raison du couplage multi-physique et donc de la multitude des échellesspatiales et temporelles qui apparaissent. Ce travail de thèse traite des questions de physiqueet de mathématiques appliquées soulevées par la modélisation numérique de ces plasmas.La première partie du travail se focalise sur les questions de validité du modèle physique duclaquage micro-onde fondé sur l’approximation de champ effectif local. En raison des gradientsde densité du plasma très élevés, la validité du concept de champ effectif local peut être misen doute. Pour cela, un modèle fluide du second ordre est développé en incluant une equationd’énergie électronique non-locale. Cette modélisation permet de décrire de façon plus précisele dépôt d’énergie par plasma induisant la formation d’ondes de choc dans le gaz. Une analysedimensionnelle du système d’équations fluide permet de caractériser la non-localité en espace dubilan d’énergie électronique en fonction du champ électrique réduit et de la fréquence de l’onderéduite. Une discussion est également menée sur d’autres approximations des coefficients detransport électronique. Dans une deuxième partie, la construction et l’analyse d’une méthode multi-échelles derésolution numérique du problème de propagation des ondes électromagnétiques dans le plasmasont réalisées. Il s’agit du couplage entre les équations de Maxwell dans le domaine temporel avecune équation de quantité de mouvement pour les électrons. L’approche s’appuie sur la méthodede décomposition de domaine de type Schwartz, basée sur une formulation variationnelle duschéma de Yee et utilisant deux niveaux de grilles Cartésiennes emboitées. Une grille locale,appelée patch, est utilisée pour calculer de manière itérative la solution dans la région du plasmaoù une meilleure précision est requise. La méthode proposée permet le raffinement local etdynamique du maillage spatial tout en conservant l’énergie du système. Une analyse théorique dela convergence de l’algorithme pour les résolutions temporelles explicite et implicite est égalementréalisée. Dans la dernière partie, des simulations numériques sur le claquage micro-ondes et la formation de structures filamentaires de plasma sont conduites. Les effets de différents types d’approximations sur le modèle physique du plasma sont analysés. Puis, ces expériences numériques démontre la précision et l’efficacité, en terme de temps de calcul, de la méthode multi-échelleproposée. Enfin, on étudie les effets de chauffage du gaz sur la formation et l’entretien de structures filamentaires dans l’air à pression atmosphérique. Pour cela, le modèle micro-onde-plasma développé est couplé avec les équations de Navier-Stokes instationnaires pour les écoulements compressibles. Les simulations montrent des caractéristiques intéressantes de la dynamique deces structures plasma pendant le processus de chauffage du gaz, qui sont en accord étroit avec les données expérimentales
In recent decades, microwave discharge plasmas have attracted increasing attention of aerospace scientific community to the subject of aerodynamic flow control because of their capability of sub- stantially modifying the properties of the flow around bodies by effective energy deposition. The design and optimization of these plasma actuators as flow control technique require a compre- hensive understanding of the complex physics involved that the sole experiments are incapable to provide.In this context, we have interest in the numerical modeling of the mutual interaction of elec- tromagnetic waves with plasma and gas in order to better understand the nature of microwave discharges and their applicability. A challenging problem arises when modeling such phenomena because of the coupling of different physics and therefore the multiplicity of spatial and tempo- ral scales involved. A solution is provided by this thesis work which addresses both physics and applied mathematics questions related to microwave plasma modeling.The first part of this doctorate deals with validity matters of the physical model of microwave breakdown based on the local effective field concept. Because of large plasma density gradients, the local effective field approximation is questionable and thus a second-order plasma fluid model is developed, where the latter approximation is replaced by the local mean energy approximation. This modeling approach enables to take into account the non-locality in space of the electron energy balance that provides a more accurate description of the energy deposition by microwave plasma leading to the shock waves formation into the gas. A dimensionless analysis of the plasma fluid system is performed in order to theoretically characterize the non-locality of the introduced electron energy equation as function of the reduced electric field and wave frequency. It also discusses other approximations related to the choice and method of calculation of electron transport coefficients.Concerning the mathematical aspects, the thesis work focuses on the design and the analysis of a multiscale method for numerically solving the problem of electromagnetic wave propagation in microwave plasma. The system of interest consists of time-dependent Maxwell’s equations coupled with a momentum transfer equation for electrons. The developed approach consists of a Schwartz type domain decomposition method based on a variational formulation of the standard Yee’s scheme and using two levels of nested Cartesian grids. A local patch of finite elements is used to calculate in an iterative manner the solution in the plasma region where a better precision is required. The proposed technique enables a conservative local and dynamic refinement of the spatial mesh. The convergence behavior of the iterative resolution algorithm both in an explicit and implicit time-stepping formulation is then analyzed.In the last part of the doctorate, a series of numerical simulations of microwave breakdown and the filamentary plasma array formation in air are performed. They allow to study in detail the consequences of the different types of physical approximations adopted in the plasma fluid model. Then, these numerical experiments demonstrate the accuracy and the computational efficiency of the proposed patch correction method for the problem of interest. Lastly, a numerically investigation of the effects of gas heating on the formation and sustaining of the filamentary plasma array in atmospheric-pressure air is carried out. For doing this, the developed microwave-plasma model is coupled with unsteady Navier-Stokes equations for compressible flows. The simulations provide interesting features of the plasma array dynamics during the process of gas heating, in close agreement with experimental data

This research is aimed to develop a homogenized model for practical applications of the fluid flow over and through the microstructured surfaces, which prescribed reliable estimates of the linear response of overall structures. The up-scaling method based on asymptotic theories is used to treat the fluid flow problems where various spatial scales (microscopic and macroscopic) are present. The goal of this work is to provide an in-expensive high-order homogenized framework for the flows over complex textures such as elastic and rigid rough surfaces, isotropic and orthotropic porous media, with periodic internal distributions, independent of the material properties and the constituent's geometrical arrangement in a reliable way. The framework includes effective conditions corrected up to the high-order as a replacement of the micro-textured surfaces, producing sizeable effects on the overlaying flow as compared to the classical Navier's conditions. These effective conditions contain parameters that are non-empirical and stems from the numerical solution of auxiliary Stokes-like problems. These conditions developed for different applications are tested on the classical problems such as Hiemenz stagnation point flow over a rough plate, Hiemenz stagnation point flow over isotropic and orthotropic porous bed, backward-facing step with porous step region, and flow over the permeable channel, to test the accuracy and working capability of the framework for different flow situations. For simulation purposes, commercial software COMSOL academic version 5.4, open-source solver FreeFEM, and commercial software Star-CCM+ by are used. The outcomes of the model simulations are compared with exact simulations of our own and with literature. The overall results suggested that the homogenized model is computationally inexpensive compared to the feature-resolving simulations and can provide a quick design of drag-altering micro-textured surfaces. Moreover, the present model is flexible for further amendments to tackle complex engineered and industrial fluid flow problems.

Helicopter performance is greatly influenced by its drag. Pylons, fuselage, landing gear, and especially the rotor hub of a helicopter experience large separated flow regions, even under steady level flight conditions the vehicle has been designed for, contributing to the helicopter drag. Several passive and active flow control concepts have been studied for reducing helicopter drag. While passive flow control methods reduce drag, they do so at one optimized design condition. Therefore, passive drag reduction methods may not work for helicopters that operate under widely varying flight conditions. Active flow control (AFC) methods overcome this disadvantage and consequently are widely being pursued. The present investigator has studied some of these AFC methods using computational fluid dynamics (CFD) techniques and has found synthetic (or pulsed) jets as one of the more effective drag reduction devices. Two bluff bodies, representative of helicopter components, have been studied and the mechanism behind drag reduction has been analyzed. It was found that the increase in momentum due to the jet, and a resultant reduction in the separated flow region, is the main reason for drag reduction in these configurations. In comparison with steady jets, synthetic jets were found to use less power for a greater drag reduction. The flow inside these synthetic jet devices is incompressible. It is computationally inefficient to use compressible flow solvers in incompressible regions. In such regions, using Lattice Boltzmann equations (LBE) is more suitable compared to solving the incompressible Navier-Stokes equations. The length scales close to the synthetic jet devices are very small. LBE may be used to better resolve these small length scale regions. However, using LBE throughout the whole domain would be computationally expensive since the grid spacing in the LBE solver has to be of the order of the mean free path. To address this need, a coupled Lattice Boltzmann-Navier-Stokes (LB-NS) methodology has been developed. The LBE solver has been successfully validated in a standalone manner for several benchmark cases. The solver has also been shown to be of second order accuracy. This LBE solver has been subsequently coupled with an existing Navier-Stokes (NS) solver. Validation of the coupled methodology has been done for analytical problems with known closed form solution. This LB-NS methodology is further used to simulate the flow past a cylinder where synthetic jet devices have been used to reduce drag. The LBE solver is used in the cavity of the synthetic jet nozzle while the NS solver is employed in the rest of the domain. The cylinder configuration was chosen to demonstrate drag reduction on helicopter hub shape geometries. Significant drag reduction is observed when synthetic jets are used, compared to the baseline no flow control case.

Les phénomènes interfaciaux suscitent un intérêt croissant dans divers domaines industriels et fondamentaux tels que les industries pétrolière, alimentaire, cosmétique ou l'imprimerie, etc. Cette thèse se concentre particulièrement sur les phénomènes impliquant des gouttes et des bulles, notamment leur coalescence, étalement, drainage et éclatement dans des fluides non newtoniens. Plusieurs méthodes expérimentales ont été utilisées, incluant un système d'acquisition électrique DC ultra-rapide, une caméra rapide et un micro-PIV à grande vitesse. La première partie de l'étude explore le contact initial et l'étalement (coalescence) d'une goutte non newtonienne sur une surface solide ou liquide. L'évolution de la conductance électrique, en corrélation avec la largeur d'étalement de la goutte, a été détectée dans les premières microsecondes. L'étalement d'une dispersion opaque de nanoparticules a été entrepris, révélant les mécanismes sous-jacents et les régimes par une loi d’échelle sans dimension. La quantification des champs de vitesse à l'intérieur de la goutte a également été réalisée. La deuxième partie compare la durée de vie et l'éclatement d'une bulle unique à différentes surfaces liquides, y compris celles chargées de particules superhydrophobes. L'épaisseur de la calotte de la bulle a été mesurée grâce à l'imagerie à grande vitesse. Les champs de vitesse autour de la cavité de bulle ont été mesurés, montrant le rôle de la couche de particules et la viscoélasticité des fluides dans la transition d'une rupture rapide à une disparition lente de la bulle. Enfin, la troisième partie examine la coalescence d'une goutte non newtonienne avec une phase liquide de la même nature à travers des interfaces air-liquide chargées de particules. Les champs de vitesse au sein de la goutte et dans le liquide ont été évalués, et une analyse du signal électrique a mis en évidence la différence avec la coalescence à des surfaces sans particules. Le rôle complexe de la couche de particules comme barrière et pont a été dévoilé, ainsi que sa relation avec la viscoélasticité du fluide
Interfacial phenomena as a research domain have attracted focus and resources from areas of industrial and fundamental interests: cosmetics, printing, food industries, and glass productions, etc. What charms the defender most is the phenomena with drops and bubbles - their processes of coalescing, spreading, draining, and bursting - involving non-Newtonian fluids. Multiple experimental methods such as ultra-high-speed DC electrical acquisition system, high-speed camera and high-speed micro-PIV were jointly adopted for the investigation. The first part focused on experimental research on initial contact and spreading (coalescing) of a non-Newtonian drop on a solid (liquid) planar surface. The evolution of the electrical conductance in close relation with the drop spreading (coalescing) width was detected at first microseconds. Spreading (coalescing) behaviors of an opaque dispersion of nanoparticles was examined. Regimes and mechanism behind were revealed via dimensionless scaling. The quantification of flow fields inside a spreading (coalescing) drop was performed. The second part comparatively investigated the lifetime and bursting behavior of a single bubble at different liquid surfaces and through particle-laden liquid surfaces. Bubble cap thickness was quantitatively compared based on the high-speed imaging results. Velocity fields and profiles around bubble cavity were drafted and analyzed. The role of particle layer, together with fluids’ viscoelasticity, was confirmed in the shift for a bubble from a quick rupture death to a slow shrinking disappearance. The last part studied the coalescence of a non-Newtonian drop with its bulk phase through particle-laden air-liquid surfaces. A characteristic evaluation of speed fields within the drop and the bulk was conducted. An electrical signal analysis was carried out to highlight the difference with the coalescence of a drop with particle-free surfaces. The complicate role of particle layer as a barrier and bridge at the same time was confirmed and its relationship with fluid’s viscoelasticity was demonstrated

Cette thèse est consacrée à la modélisation mathématique de la coagulation sanguine et de la formation de thrombus dans des conditions normales et pathologiques. La coagulation sanguine est un mécanisme défensif qui empêche la perte de sang suite à la rupture des tissus endothéliaux. C'est un processus complexe qui est règlementé par différents mécanismes mécaniques et biochimiques. La formation du caillot sanguin a lieu dans l'écoulement sanguin. Dans ce contexte, l'écoulement à faible taux de cisaillement stimule la croissance du caillot tandis que la circulation sanguine à fort taux de cisaillement la limite. Les désordres qui affectent le système de coagulation du sang peuvent provoquer différentes anomalies telles que la thrombose (coagulation exagérée) ou les saignements (insuffisance de coagulation). Dans la première partie de la thèse, nous présentons un modèle mathématique de coagulation sanguine. Le modèle capture la dynamique essentielle de la croissance du caillot dans le plasma et le flux sanguin quiescent. Ce modèle peut être réduit à un modèle qui consiste en une équation de génération de thrombine et qui donne approximativement les mêmes résultats. Nous avons utilisé des simulations numériques en plus de l'analyse mathématique pour montrer l'existence de différents régimes de coagulation sanguine. Nous spécifions les conditions pour ces régimes sur différents paramètres pathophysiologiques du modèle. Ensuite, nous quantifions les effets de divers mécanismes sur la croissance du caillot comme le flux sanguin et l'agrégation plaquettaire. La partie suivante de la thèse étudie certaines des anomalies du système de coagulation sanguine. Nous commençons par étudier le développement de la thrombose chez les patients présentant une carence en antihrombine ou l'une des maladies inflammatoires. Nous déterminons le seuil de l'antithrombine qui provoque la thrombose et nous quantifions l'effet des cytokines inflammatoires sur le processus de coagulation. Puis, nous étudions la compensation de la perte du sang après un saignement en utilisant un modèle multi-échelles qui décrit en particulier l'érythropoïèse et la production de l'hémoglobine. Ensuite, nous évaluons le risque de thrombose chez les patients atteints de cancer (le myélome multiple en particulier) et le VIH en combinant les résultats du modèle de coagulation sanguine avec les produits des modèles hybrides (discret-continues) multi-échelles des systèmes physiologiques correspondants. Finalement, quelques applications cliniques possibles de la modélisation de la coagulation sanguine sont présentées. En combinant le modèle de formation du caillot avec les modèles pharmacocinétiques pharmacodynamiques (PK-PD) des médicaments anticoagulants, nous quantifions l'action de ces traitements et nous prédisons leur effet sur des patients individuels
This thesis is devoted to the mathematical modelling of blood coagulation and clot formation under flow in normal and pathological conditions. Blood coagulation is a defensive mechanism that prevents the loss of blood upon the rupture of endothelial tissues. It is a complex process that is regulated by different mechanical and biochemical mechanisms. The formation of the blood clot takes place in blood flow. In this context, low-shear flow stimulates clot growth while high-shear blood circulation limits it. The disorders that affect the blood clotting system can provoke different abnormalities such thrombosis (exaggerated clotting) or bleeding (insufficient clotting). In the first part of the thesis, we introduce a mathematical model of blood coagulation. The model captures the essential dynamics of clot growth in quiescent plasma and blood flow. The model can be reduced to a one equation model of thrombin generation that gives approximately the same results. We used both numerical simulations and mathematical investigation to show the existence of different regimes of blood coagulation. We specify the conditions of these regimes on various pathophysiological parameters of the model. Then, we quantify the effects of various mechanisms on clot growth such as blood flow and platelet aggregation. The next part of the thesis studies some of the abnormalities of the blood clotting system. We begin by investigating the development of thrombosis in patients with antihrombin deficiency and inflammatory diseases. We determine the thrombosis threshold on antithrombin and quantify the effect of inflammatory cytokines on the coagulation process. Next, we study the recovery from blood loss following bleeding using a multiscale model which focuses on erythropoiesis and hemoglobin production. Then, we evaluate the risk of thrombosis in patients with cancer (multiple myeloma in particular) and HIV by combining the blood coagulation model results with the output of hybrid multiscale models of the corresponding physiological system. Finally, possible clinical applications of the blood coagulation modelling are provided. By combining clot formation model with pharmacokinetics-pharmacodynamics (PK-PD) models of anticoagulant drugs, we quantify the action of these treatments and predict their effect on individual patients

Thesis (M.S. in Mechanical Engineering)--Naval Postgraduate School, December 2007.
Thesis Advisor(s): Kwon, Young W. "December 2007." Description based on title screen as viewed on January 17, 2008. Includes bibliographical references (p. 77-78). Also available in print.

Multiscale mathematical modeling of flows containing particles is conducted in this study using computational fluid dynamics and molecular dynamics. The first study considered continuous media interaction of macro-scale fluid and micro-scale solid particles using computational fluid dynamics and rigid particle dynamics. This study investigates the potential enhancement of heat transfer properties of particulate fluid as well as the effect of injected particles on fluid profiles, and pressure on walls under different particle injection conditions. In the second part of this research, the molecular dynamics simulation was performed to simulate solid-liquid interaction at the molecular level (nanotechnology) to understand their behaviors. The results from two different scales were compared qualitatively.

Cette thèse se concentre sur le développement d'une méthode précise et efficace pour la simulation des grandes échelles (LES) des écoulements turbulents. Une approche de la LES basée sur la méthode variationnelle multi-échelles (VMS) est considérée. La VMS applique aux équations de la dynamique des fluides une séparation d'échelles a priori sans recours à des hypothèses sur les conditions aux limites ou sur l'uniformité du maillage. Afin d'assurer effectivement une séparation d'échelles dans l'espace des nombres d'onde associé, nous choisissons d'utiliser les ondelettes de deuxième génération (SGW), une base polynomiale qui présente des propriétés de localisation spatiale-fréquence optimales. A partir de la séparation d'échelles ainsi réalisée, l'action du modèle sous-maille est limitée à un intervalle de nombres d'onde proche de la coupure spectrale. Cette approche VMS-LES basée sur les ondelettes est désignée par WAVVMS-LES. Elle est incorporée dans un solveur d'ordre élevé pour la simulation des écoulements incompressibles sur la base d'une méthode de Galerkin discontinue (DG-FEM) stabilisée pour la pression. La méthode est évaluée par réalisation de LES sur des maillages fortement sous-résolus pour le cas test du tourbillon de Taylor-Green 3D à deux nombres de Reynolds différents
This thesis focuses on the development of an accurate and efficient method for performing Large-Eddy Simulation (LES) of turbulent flows. An LES approach based upon the Variational Multiscale (VMS) method is considered. VMS produces an a priori scale-separation of the governing equations, in a manner which makes no assumptions on the boundary conditions and mesh uniformity. In order to ensure that scale-separation in wavenumber is achieved, we have chosen to make use of the Second Generation Wavelets (SGW), a polynomial basis which exhibits optimal space-frequency localisation properties. Once scale-separation has been achieved, the action of the subgrid model is restricted to the wavenumber band closest to the cutoff. We call this approach wavelet-based VMS-LES (WAV-VMS-LES). This approach has been incorporated within the framework of a high-order incompressible flow solver based upon pressure-stabilised discontinuous Galerkin FEM (DG-FEM). The method has been assessed by performing highly under-resolved LES upon the 3D Taylor-Green Vortex test case at two different Reynolds numbers

The extraordinary complexity of turbulence has motivated the study of some of its key features in flows with similar structure but simpler or even trivial dynamics. Recently, a novel class of such flows has been developed in the laboratory by applying multiscale electromagnetic forcing to a thin layer of conducting fluid. In spite of being stationary, planar, and laminar these flows have been shown to resemble turbulent ones in terms of energy spectra and particle dispersion. In this thesis, some extensions of these flows are investigated through simulations of a layer-averaged model carried out using a bespoke semi-Lagrangian spline code. The selected forcings generalise the experimental ones by allowing for various kinds of self-similarity and planetary motion of the multiple scales. The spatiotemporal structure of the forcings is largely reflected on the flows, since they mainly arise from a linear balance between forcing and bottom friction. The exponents of the approximate power laws found in the wavenumber spectra can thus be related to the scaling and geometrical forcing parameters. The Eulerian frequency spectra of the unsteady flows exhibit similar power laws originating from the sweeping of the multiple flow scales by the forcing motions. The disparity between fluid and sweeping velocities makes it possible to justify likewise the observed Lagrangian power laws, but precludes a proper analogy with turbulence. In the steady case, the absolute dispersion of tracer particles presents ballistic and diffusive stages, while relative dispersion shows a superquadratic intermediate stage dominated by separation bursts due to the various scales. In the unsteady case, the absence of trapping by fixed streamlines leads to appreciable enhancement of relative dispersion at low and moderate rotation frequency. However, the periodic reversals of the large scale give rise to subdiffusive absolute dispersion and severely impede relative dispersion at high frequency.

We develop, validate, and apply an efficient multiscale method for the simulation of a large class of low-speed internal rarefied gas flows, which are critical to a range of future technologies. The method is based on an existing multiscale approach for the simulation of small-scale dense-fluid flows of high-aspect ratio, but has been extended to support fluid compressibility, non-isothermal conditions, three dimensional domains, and transience. Furthermore, the method is able to treat a broader range of flows: periodic, non-periodic, body-force-driven, pressure-driven, thermally-driven, and shear-driven. It also incorporates pseudospectral methods, and so boasts excellent convergence characteristics and accuracy. All verification cases presented herein are designed to be amenable to solution by a full molecular treatment (where scale separation is not exploited). The computationally demanding simulation technique known as direct simulation Monte Carlo (DSMC) is employed to obtain reference solutions, allowing for comparison with those computed by the multiscale method: excellent agreement is observed throughout. The unsteady (time-marching) implementation of the method, which allows for the resolution of transient flows, is validated by comparison with time dependent experimental data. Again, agreement is excellent. The computational efficiency of the multiscale method is exceptional. It provides efficiency gains of multiple orders of magnitude, relative to full molecular simulations (by the DSMC method); in some cases, the multiscale method allows for the solution of otherwise computationally intractable problems. Note, highly scale-separated systems are simulated with even greater efficiency. Following the experimental validation of the method, it is applied to the study of thermal-transpiration compressors (and implicitly Knudsen compressors). We characterise the effectiveness of these devices by considering the maximum pressure difference attainable for various combinations of (realistic) thermodynamic and geometric conditions. The development time required to obtain this pressure difference, which is also considered as a performance indicator, is also computed.

Mass transfer and reaction in the liquid phase of gas-liquid multiphase flows usually takes place at a considerably slower rate than the transfer of momentum, so mass flux boundary layers are much thinner than momentum boundary layers. In Direct Numerical Simulations (DNS) the resolution requirement for flows with mass transfer are therefore significantly higher than for flow without mass transfer and reaction. In this work we develop a multi-scale approach and demonstrate its implementation in 2D to compute the mass transfer from buoyant bubbles, using a boundary-layer approximation next to the bubble and a relatively coarse grid for the rest of the flow. This approach greatly reduces the overall grid resolution required. Then we implement our method in 3D and perform validation of the approach by comparing to experimental data and semi-empirical correlations from the literature. We study the effect of void fraction and bubble interactions on the mass transfer from many bubbles using a 3D implementation of the code. Specifically, we do simulations of single bubbles in periodic boxes and we compare it to the simulation of several bubbles in a larger domain with the same void fraction. Comparisons shows that even though the average Reynolds number of freely moving bubbles drops after a while the mass transfer from the bubbles for most case studies increases slightly when bubbles start wobbling which increases bubble interactions. We also develop a film model to recover the under-resolved viscous forces between colliding non-coalescing droplet.