In the numerical simulation of fluid flow and solute transport in porous media, finite element method (FEM) has long been utilized and has been proven to be efficient. In this work, an alternative approach called random walk particle tracking (RWPT) method is proposed. In this method, a finite number of particles represent the distribution of a solute mass. Each particle carries a certain fraction of the total mass and moves in the porous media according to the velocity field. The proposed RWPT model is established on a scientific software platform OpenGeoSys (OGS), which is an open source initiative for numerical simulation of thermo-hydro-mechanical-chemical (THMC) processes in porous media. The flow equation is solved using finite element method in OGS. The obtained hydraulic heads are numerically differentiated to obtain the velocity field. The particle tracking method does not solve the transport equation directly but deals with it in a physically stochastic manner by using the velocity field. Parallel computing concept is included in the model implementation to promote computational efficiency. Several benchmarks are developed for the particle tracking method in OGS to simulate solute transport in porous media and pore space. The simulation results are compared to analytical solutions and other numerical methods to test the presented method. The particle tracking method can accommodate Darcy flow as it is the main consideration in groundwater flow. Furthermore, other flow processes such as Forchheimer flow or Richards flow can be combined with as well. Two applications indicate the capability of the method to handle theoretical real-world problems. This method can be applied as a tool to elicit and discern the detailed structure of evolving contaminant plumes. / Bei der numerischen Simulation von Strömung und Stofftransport in porösen Medien hat die Nutzung der Finite-Elemente-Methode (FEM) eine lange Tradition und wird sich als effizient erweisen. In dieser Arbeit wird ein alternativer Ansatz, die random walk particle tracking (RWPT) Methode vorgeschlagen. Bei diesem Verfahren stellt eine endliche Anzahl von Partikeln die Verteilung eines gelösten Stoffes dar. Jedes Teilchen trägt einen bestimmten Bruchteil der Gesamtmasse und bewegt sich in den porösen Medien gemäß des Geschwindigkeitsfeldes. Das vorgeschlagene RWPT Modell basiert auf der wissenschaftlichen Softwareplattform OpenGeoSys (OGS), die eine Open-Source-Initiative für die numerische Simulation thermo-hydro-mechanisch-chemischen (THMC) in porösen Medien darstellt. Die Strömungsgleichung wird in OGS mit der Finite-Elemente-Methode gelöst. Der Grundwasserstand wird numerisch berechnet, um das Geschwindigkeitsfeld zu erhalten. Die Partikel-Tracking-Methode löst die Transportgleichung nicht direkt, sondern befasst sich mit ihr in einer physikalisch stochastische Weise unter Nutzung des Geschwindigkeitsfeldes. Zur Berücksichtigung der Recheneffizienz ist ein Parallel Computing-Konzept in der Modell-Implementierung enthalten. Zur Simulation des Stofftransports in porösen Medien und im Porenraum wurden mehrere Benchmarks für die Partikel-Tracking-Methode in OGS entwickelt. Die Simulationsergebnisse werden mit analytischen Lösungen und andere numerische Methoden verglichen, um die Aussagefähigkeit des vorgestellten Verfahrens zu bestätigen. Mit der Partikel-Tracking-Methode kann die Darcy-Strömung gelöst werden, die das wichtigste Kriterium in der Grundwasserströmung ist. Außerdem bewältigt die Methode auch andere Strömungsprozesse, wie die Forchheimer-Strömung und die Richards-Strömung. Zwei Anwendungen zeigen die Leistungsfähigkeit der Methode bei der prinzipiellen Handhabung von Problemen der realen Welt. Die Methode kann als ein Instrument zur Aufdeckung Erkennung der detaillierte Struktur von sich entwickelnden Schadstofffahnenangewendet werden.

Physical lab experiments have shown that the pressure caused by an impinging jet on a granular bed has the potential to form craters. This poses a danger to landing success and nearby spacecraft for future rocket missions. Current numerical simulations for this process do not accurately reproduce experimental results. Our goal is to produce improved simulations to more accurately and effi- ciently model the changes in pressure as gas flows through a porous medium. A two-dimensional model in space known as the nonlinear Porous Medium Equation as it is derived from Darcy’s law is used. An Alternating-Direction Implicit (ADI) temporal scheme is presented and implemented which reduces our multidimensional problem into a series of one-dimensional problems. We take advantage of explicit approximations for the nonlinear terms using extrapolation formulas derived from Taylor-series, which increases efficiency when compared to other common methods. We couple our ADI temporal scheme with different spatial discretizations including a second-order Finite Difference (FD) method, a fourth-order Orthogonal Spline Collocation (OSC) method, and an Nth-order Chebyshev Spectral method. Accuracy and runtime are compared among the three methods for comparison in a linear analogue of our problem. We see the best results for accuracy when using an ADI-Spectral method in the linear case, but discuss possibilities for increased effi- ciency using an ADI-OSC scheme. Nonlinear results are presented using the ADI-Spectral method and the ADI-FD method.

This study examines the local and averaged endwall heat transfer effects of a staggered array of porous pin fins within a rectangular channel. The porous pin fins were made from aluminum and had a pore density of 10 pores per inch (PPI). The pressure drop through the channel was also determined for several flow rates and presented in terms of the friction factor. Local heat transfer coefficients on the endwall were measured using Thermochromic Liquid Crystal (TLC) sheets recorded with a charge-coupled device (CCD) camera. Static and total pressure measurements were taken at the entrance and exit of the test section to determine the overall pressure drop through the channel and explain the heat transfer trends through the channel. Results are presented for Reynolds numbers between 25000 and 130000 and a blockage ratio (blocked channel area divided by open channel area) of 50%. All results were compared to the corresponding results obtained using solid pins. All experiments were carried out in a 150 mm by 500 mm channel with an X/D of 1.72, a Y/D of 2.0, and a Z/D of 1.72 for the porous pins. It was found that for the range of Reynold's numbers tested in this study, the porous pin array consistently resulted in a larger friction factor, and therefore greater losses than a geometrically similar array of solid pins. The friction factors for the solid pin array were between 9.5 and 10.5, similar to the results found in the literature. For the porous pins, however, the friction factors were significantly increased as the Reynold's number increased, reaching as high as 15.3 at the highest Reynold's number tested. The heat transfer enhancement for the porous pins was found to be between 150 and 170% while the solid pins resulted in a heat transfer enhancement between 190 and 230%.

<p dir="ltr">Low frequency noise has been a challenge to noise control strategies for a long time due to its relatively long wavelength compared with practical thicknesses of acoustical treatments. A series of studies have drawn increasing attention to the acoustical behavior of porous granular materials such as activated carbon due to their good performance at low frequency. To better characterize this type of material, a 1-dimensional poro-elastic model is introduced in this work, which accounts for both the inner particle structure and the elasticity of the granule stack, allowing a better match of resonance features between the model prediction and measurement results. This model was then extended to a 2-dimensional finite difference (2DFD) approach under an axisymmetric assumption, with the depth-dependent stiffness of the granule stack considered. The shape of the computational domain of this 2DFD approach is close to the realistic geometry of the cylindrical standing wave tube, and it provides flexibility in assigning different types of boundary conditions at the circumferential wall of the container. The model is validated by comparing the simulation output and measurements of the acoustic response of porous granular materials in a cylindrical standing wave tube with rigid backing. The comparison demonstrates that the proposed 2DFD model is able to closely match the test results even down to detailed features, thus providing a means of accurate acoustic characterization of granular materials. The application scenarios of porous granular materials are also discussed in this work. A hybrid model based on the classical Johnson-Champoux-Allard (JCA) model and the rigid model describing the multi-level porosity within the granules is proposed to predict the performance of composite materials made of non-woven fiber matrices and porous granular materials. The performance of other practical applications such as that of a sound absorber consisting of a membrane and a cavity partially filled with the porous granular material is also discussed. These applications are shown to be promising strategies of addressing the low frequency noise problems.</p>

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[pt] A natureza física do amortecimento nos solos e sua formulação matemática têm sido objeto de intensa pesquisa ao longo do último meio século. Estes vários ensaios para explicar os mecanismos de perda de energia durante os episódios de vibração surgem da importância do amortecimento no problema de propagação de ondas para fins de engenharia. O objetivo deste estudo é propor uma maneira alternativa de analisar o fenômeno do amortecimento em solos, considerando o problema de vibração como um problema matemático poromecânico acoplado onde deslocamentos relativos e velocidades entre as duas fases que compõem o material geológico, fluido e sólido, gera forças de interação nas interfaces e pode desempenhar um papel importante na perda de energia vibracional dos solos. Presume-se que o problema seja resolvido na escala de poros, concentrando-se nas condições cinéticas e dinâmicas na interface entre o esqueleto sólido e o fluido de saturação. Variáveis adimensionais que misturam propriedades fluidas e sólidas permitem o acoplamento do problema, resultando no surgimento de uma massa aparente, coeficientes de amortecimento e rigidez que serão introduzidos posteriormente nas equações de movimento. A equação proposta de amortecimento será então justaposta a testes de laboratório e uma comparação com os modelos mais importantes da literatura será feita usando o software DEEPSOIL para análise de propagação de ondas para verificar sua validade. / [en] The physical nature of damping in soils and its mathematical formulation attempts have been the subject of intensive researches along the last half century. These several trials to explain the mechanisms of energy loss during vibration episodes arise from the importance of damping in the wave propagation problem for engineering purposes. The aim of this study is to propose an alternative way to analyze the damping phenomenon in soils by looking at the vibration problem as a coupled poromechanical mathematical problem where relative displacements and velocities in between the two phases that compose the geological material, fluid and solid, generates interaction forces at the interfaces and can play an important role in the vibrational energy loss of soils. The problem is assumed to be solved at the pore scale, focusing on the kinetic and dynamic conditions at the interface in between the solid skeleton and the saturating fluid. Dimensionless variables that mixes fluid and solid properties allows the coupling of the problem, resulting on the rising of an apparent mass, damping and stiffness coefficients that will be introduced later in the equations of motion. The proposed equation of damping will thus be juxtaposed to laboratory tests data and a comparison with the most important models in the literature will be done further using the software DEEPSOIL for wave propagation analysis to check its validity.

<p dir="ltr">Microfluidic techniques have been widely adopted in biomedical research due to the pre- cise control of fluids, small volume requirement, low cost and etc, and have boosted the development of biomolecular interaction analysis, point-of-care diagnostics, and biosensors.</p><p dir="ltr">Protein-protein interaction plays a key role in biological, biomedical and pharmaceutical research. The technical development of biosensors, new drugs and vaccines, and disease diagnostics heavily rely on the characterization of protein-protein interaction kinetics. The current gold standard assays for measuring protein-protein interaction are surface plasmon resonance (SPR), and bio-layer interferometry (BLI). These commercial devices are accurate but expensive, however.</p><p dir="ltr">Here, I have developed new microfluidic techniques and models in protein-protein in- teraction kinetics measurement, rotational diffusion coefficient modeling, electrochemical impedance spectroscopy-based biosensors, and two-phase porous media flow models. Firstly, I applied particle diffusometry (PD) in the streptavidin-biotin binding kinetics measurement, utilizing a Y-junction microchannel. Secondly, to reduce solution volumes used in an analysis experiment, I designed a low-volume chip and coupled it with PD to measure the binding kinetics of human immunodeficiency virus p24 antibody-antigen interactions. Thirdly, con- sidering the Brownian motion of the non-symmetric particles, I developed a new model to efficiently compute particles’ rotational diffusion coefficients. Fourthly, to make economic biosensors to detect multiple biomarkers, I created a new chip, enabling hundreds of tests in a single droplet (∼ 50 μL) on one chip. Finally, to understand the liquid flow in porous media, such as nitrocellulose in lateral flow assays, I built a new two-phase porous media flow model based on the Navier-Stokes equation and compared it with experiments. These techniques and models underwent rigorous experimental and computational validation, demonstrating their effectiveness and performance.</p>

This investigation completed the verification of a three-dimensional resin transfer molding/resin film infusion (RTM/RFI) process simulation model. The model incorporates resin flow through an anisotropic carbon fiber preform, cure kinetics of the resin, and heat transfer within the preform/tool assembly. The computer model can predict the flow front location, resin pressure distribution, and thermal profiles in the modeled part. The formulation for the flow model is given using the finite element/control volume (FE/CV) technique based on Darcy's Law of creeping flow through a porous media. The FE/CV technique is a numerically efficient method for finding the flow front location and the fluid pressure. The heat transfer model is based on the three-dimensional, transient heat conduction equation, including heat generation. Boundary conditions include specified temperature and convection. The code was designed with a modular approach so the flow and/or the thermal module may be turned on or off as desired. Both models are solved sequentially in a quasi-steady state fashion. A mesh refinement study was completed on a one-element thick model to determine the recommended size of elements that would result in a converged model for a typical RFI analysis. Guidelines are established for checking the convergence of a model, and the recommended element sizes are listed. Several experiments were conducted and computer simulations of the experiments were run to verify the simulation model. Isothermal, non-reacting flow in a T-stiffened section was simulated to verify the flow module. Predicted infiltration times were within 12-20 percent of measured times. The predicted pressures were approximately 50 percent of the measured pressures. A study was performed to attempt to explain the difference in pressures. Non-isothermal experiments with a reactive resin were modeled to verify the thermal module and the resin model. Two panels were manufactured using the RFI process. One was a stepped panel and the other was a panel with two `T' stiffeners. The difference between the predicted infiltration times and the experimental times was 4 to 23 percent. / Master of Science

This dissertation presents a detailed account of the study undertaken on the subject of heat and mass transfer phenomena in porous media. The current work specifically targets the general reaction-diffusion systems arising in separation processes using porous sorbent particles. These particles are comprised of pore channels spanning length scales over almost three orders of magnitude while involving a variety of physical processes such as mass diffusion, heat transfer and surface adsorption-desorption. A novel methodology is proposed in this work that combines models that account for the multi-scale and multi-physics phenomena involved. Pore-resolving DNS calculations using an immersed boundary method (IBM) framework are used to simulate the macro-scale physics while the phenomena at smaller scales are modeled using a sub-pore modeling technique. The IBM scheme developed as part of this work is applicable to complex geometries on curvilinear grids, while also being very efficient, consuming less than 1% of the total simulation time per time-step. A new method of implementing the conjugate heat transfer (CHT) boundary condition is proposed which is a direct extension of the method used for other boundary conditions and does not involve any complex interpolations like previous CHT implementations using IBM. Detailed code verification and validation studies are carried out to demonstrate the accuracy of the developed method. The developed IBM scheme is used in conjunction with a stochastic reconstruction procedure based on simulated annealing. The developed framework is tested in a two-dimensional channel with two types of porous sections - one created using a random assembly of square blocks and another using the stochastic reconstruction procedure. Numerous simulations are performed to demonstrate the capability of the developed framework. The computed pressure drops across the porous section are compared with predictions from the Darcy-Forchheimer equation for media composed of different structure sizes. The developed methodology is also applied to CO2 diffusion studies in porous spherical particles of varying porosities. For the pore channels that are unresolved by the IBM framework, a sub-pore modeling methodology developed as part of this work which solves a one-dimensional unsteady diffusion equation in a hierarchy of scales represented by a fractal-type geometry. The model includes surface adsorption-desorption, and heat generation and absorption. It is established that the current framework is useful and necessary for reaction-diffusion problems in which the adsorption time scales are very small (diffusion-limited) or comparable to the diffusion time scales. Lastly, parametric studies are conducted for a set of diffusion-limited problems to showcase the powerful capability of the developed methodology. / Ph. D.

This thesis is concerned with developing porous materials from tyre shred residue and polyurethane binder for acoustic absorption and thermal insulation applications. The resultant materials contains a high proportion of open, interconnected cells that are able to absorb incident sound waves through viscous friction, inertia effects and thermal energy exchanges. The materials developed are also able to insulate against heat by suppressing the convection of heat and reduced conductivity of the fluid locked in the large proportion of close-cell pores. The acoustic absorption performance of a porous media is controlled by the number of open cells and pore size distribution. Therefore, this work also investigates the use of catalysts and surfactants to modify the pore structure and studies the influence of the various components in the chemical formulations used to produce these porous materials. An optimum type and amounts of catalyst are selected to obtain a high chemical conversion and a short expanding time for the bubble growth phase. The surfactant is used to reduce the surface tension and achieve a homogenous mixing between the solid particulates tyre shred residue, the water, the catalyst and the binder. It is found that all of the components significantly affect the resultant materials structure and its morphology. The results show that the catalyst has a particularly strong effect on the pore structure and the ensuing thermal and acoustical properties. In this research, the properties of the porous materials developed are characterized using standard experimental techniques and the acoustic and thermal insulation performance underpinned using theoretical models. The important observation from this research is that a new class of recycled materials with pore stratification has been developed. It is shown that the pore stratification can have a positive effect on the acoustic absorption in a broadband frequency range. The control of reaction time in the foaming process is a key function that leads to a gradual change in the pore size distribution, porosity, flow resistivity and tortuosity which vary as a function of sample depth. It is shown that the Pade approximation is a suitable model to study the acoustic behaviour of these materials. A good agreement between the measured data and the model was attained. / Ministry of Science and Technology of Thailand; Naresuan University, Phitsanulok, Thailand,