A novel methodology for simulating contact-line behavior in capillary-driven flows

Despite the wide swath of applications where multiphase fluid contact lines exist, there is still no consensus on an accurate and general simulation methodology. Most prior numerical work has imposed one of the many dynamic contact-angle theories at solid walls. Such approaches are inherently limited by the theory accuracy. In fact, when inertial effects are important, the contact angle may be history dependent and, thus, any single mathematical function is inappropriate. Given these limitations, the present work has two primary goals: 1) create a numerical framework that allows the contact angle to evolve naturally with appropriate contact-line physics and 2) develop equations and numerical methods such that contact-line simulations may be performed on coarse computational meshes.

Fluid flows affected by contact lines are dominated by capillary stresses and require accurate curvature calculations. The level set method was chosen to track the fluid interfaces because it is easy to calculate interface curvature accurately. Unfortunately, the level set reinitialization suffers from an ill-posed mathematical problem at contact lines: a ``blind spot'' exists. Standard techniques to handle this deficiency are shown to introduce parasitic velocity currents that artificially deform freely floating (non-prescribed) contact angles. As an alternative, a new relaxation equation reinitialization is proposed to remove these spurious velocity currents and its concept is further explored with level-set extension velocities.

To capture contact-line physics, two classical boundary conditions, the Navier-slip velocity boundary condition and a fixed contact angle, are implemented in direct numerical simulations (DNS). DNS are found to converge only if the slip length is well resolved by the computational mesh. Unfortunately, since the slip length is often very small compared to fluid structures, these simulations are not computationally feasible for large systems. To address the second goal, a new methodology is proposed which relies on the volumetric-filtered Navier-Stokes equations. Two unclosed terms, an average curvature and a viscous shear VS, are proposed to represent the missing microscale physics on a coarse mesh.

All of these components are then combined into a single framework and tested for a water droplet impacting a partially-wetting substrate. Very good agreement is found for the evolution of the contact diameter in time between the experimental measurements and the numerical simulation. Such comparison would not be possible with prior methods, since the Reynolds number Re and capillary number Ca are large. Furthermore, the experimentally approximated slip length ratio is well outside of the range currently achievable by DNS. This framework is a promising first step towards simulating complex physics in capillary-dominated flows at a reasonable computational expense.

Low cost 3D global instability analysis and flow sensitivity based on dynamic mode decomposition and high-order numerical tools

We explore the recently developed snapshot-based dynamic mode decomposition (DMD) technique, a matrix-free Arnoldi type method, to predict 3D linear global flow instabilities. We apply the DMD technique to flows confined in an L-shaped cavity and compare the resulting modes to their counterparts issued from classic, matrix forming, linear instability analysis (i.e. BiGlobal approach) and direct numerical simulations. Results show that the DMD technique, which uses snapshots generated by a 3D non-linear incompressible discontinuous Galerkin Navier?Stokes solver, provides very similar results to classical linear instability analysis techniques. In addition, we compare DMD results issued from non-linear and linearised Navier?Stokes solvers, showing that linearisation is not necessary (i.e. base flow not required) to obtain linear modes, as long as the analysis is restricted to the exponential growth regime, that is, flow regime governed by the linearised Navier?Stokes equations, and showing the potential of this type of analysis based on snapshots to general purpose CFD codes, without need of modifications. Finally, this work shows that the DMD technique can provide three-dimensional direct and adjoint modes through snapshots provided by the linearised and adjoint linearised Navier?Stokes equations advanced in time. Subsequently, these modes are used to provide structural sensitivity maps and sensitivity to base flow modification information for 3D flows and complex geometries, at an affordable computational cost. The information provided by the sensitivity study is used to modify the L-shaped geometry and control the most unstable 3D mode.

Flow around a hemisphere-cylinder at high angle of attack and low Reynolds number. Part I: Experimental and numerical investigation

Three-dimensional Direct Numerical Simulations combined with Particle Image Velocimetry experiments have been performed on a hemisphere-cylinder at Reynolds number 1000 and angle of attack 20◦. At these flow conditions, a pair of vortices, so-called “horn” vortices, are found to be associated with flow separation. In order to understand the highly complex phenomena associated with this fully threedimensional massively separated flow, different structural analysis techniques have been employed: Proper Orthogonal and Dynamic Mode Decompositions, POD and DMD, respectively, as well as criticalpoint theory. A single dominant frequency associated with the von Karman vortex shedding has been identified in both the experimental and the numerical results. POD and DMD modes associated with this frequency were recovered in the analysis. Flow separation was also found to be intrinsically linked to the observed modes. On the other hand, critical-point theory has been applied in order to highlight possible links of the topology patterns over the surface of the body with the computed modes. Critical points and separation lines on the body surface show in detail the presence of different flow patterns in the base flow: a three-dimensional separation bubble and two pairs of unsteady vortices systems, the horn vortices, mentioned before, and the so-called “leeward” vortices. The horn vortices emerge perpendicularly from the body surface at the separation region. On the other hand, the leeward vortices are originated downstream of the separation bubble, as a result of the boundary layer separation. The frequencies associated with these vortical structures have been quantified.

AN INVESTIGATION OF VARIABLE VALVE TIMING EFFECTS ON HCCI ENGINE PERFORMANCE

The Homogeneous Charge Compression Ignition (HCCI) engine is a promising combustion concept for reducing NOx and particulate matter (PM) emissions and providing a high thermal efficiency in internal combustion engines. This concept though has limitations in the areas of combustion control and achieving stable combustion at high loads. For HCCI to be a viable option for on-road vehicles, further understanding of its combustion phenomenon and its control are essential. Thus, this thesis has a focus on both the experimental setup of an HCCI engine at Michigan Technological University (MTU) and also developing a physical numerical simulation model called the Sequential Model for Residual Affected HCCI (SMRH) to investigate performance of HCCI engines. The primary focus is on understanding the effects of intake and exhaust valve timings on HCCI combustion. For the experimental studies, this thesis provided the contributions for development of HCCI setup at MTU. In particular, this thesis made contributions in the areas of measurement of valve profiles, measurement of piston to valve contact clearance for procuring new pistons for further studies of high geometric compression ratio HCCI engines. It also consists of developing and testing a supercharging station and the setup of an electrical air heater to extend the HCCI operating region. The HCCI engine setup is based on a GM 2.0 L LHU Gen 1 engine which is a direct injected engine with variable valve timing (VVT) capabilities. For the simulation studies, a computationally efficient modeling platform has been developed and validated against experimental data from a single cylinder HCCI engine. In-cylinder pressure trace, combustion phasing (CA10, CA50, BD) and performance metrics IMEP, thermal efficiency, and CO emission are found to be in good agreement with experimental data for different operating conditions. Effects of phasing intake and exhaust valves are analyzed using SMRH. In addition, a novel index called Fuel Efficiency and Emissions (FEE) index is defined and is used to determine the optimal valve timings for engine operation through the use of FEE contour maps.

The Influence of Healed Intrablock Rockmass Structure on the Behaviour of Deep Excavations in Complex Rockmasses

Conventional rockmass characterization and analysis methods for geotechnical assessment in mining, civil tunnelling, and other excavations consider only the intact rock properties and the discrete fractures that are present and form blocks within rockmasses. Field logging and classification protocols are based on historically useful but highly simplified design techniques, including direct empirical design and empirical strength assessment for simplified ground reaction and support analysis. As modern underground excavations go deeper and enter into more high stress environments with complex excavation geometries and associated stress paths, healed structures within initially intact rock blocks such as sedimentary nodule boundaries and hydrothermal veins, veinlets and stockwork (termed intrablock structure) are having an increasing influence on rockmass behaviour and should be included in modern geotechnical design. Due to the reliance on geotechnical classification methods which predate computer aided analysis, these complexities are ignored in conventional design. Given the comparatively complex, sophisticated and powerful numerical simulation and analysis techniques now practically available to the geotechnical engineer, this research is driven by the need for enhanced characterization of intrablock structure for application to numerical methods. Intrablock structure governs stress-driven behaviour at depth, gravity driven disintegration for large shallow spans, and controls ultimate fragmentation. This research addresses the characterization of intrablock structure and the understanding of its behaviour at laboratory testing and excavation scales, and presents new methodologies and tools to incorporate intrablock structure into geotechnical design practice. A new field characterization tool, the Composite Geological Strength Index, is used for outcrop or excavation face evaluation and provides direct input to continuum numerical models with implicit rockmass structure. A brittle overbreak estimation tool for complex rockmasses is developed using field observations. New methods to evaluate geometrical and mechanical properties of intrablock structure are developed. Finally, laboratory direct shear testing protocols for interblock structure are critically evaluated and extended to intrablock structure for the purpose of determining input parameters for numerical models with explicit structure.

Influence de la taille et de la gradation des particules sur la résistance au cisaillement et le comportement dilatant des matériaux granulaires

Résumé : Cette étude examine l'impact de la taille et de la gradation de particules sur les corrélations théoriques et empiriques existantes les plus connues entre la résistance au cisaillement et le comportement dilatatant des matériaux granulaires en condition de déformation plane et en compression triaxiale drainée. À cette fin, 276 tests de cisaillements symétriques directs et 35 tests de compressions triaxiales drainées ont été menés sur des échantillons composés de billes de basalte (particules rondes), et de sables constitués de particules angulaires (sable de Péribonka et sable d'Eastmain) sur une échelle de 63 µm à 2000 µm afin d'évaluer leur résistance au cisaillement et leur comportement de dilatance sur une vaste échelle de pressions normales et de densités relatives initiales. Premièrement, la fiabilité et l'applicabilité des limites de mesure à l’aide de tests physiques de cisaillements symétriques directs dans l'interprétation de la résistance au cisaillement frictionnel en déformation plane des matériaux granulaires ont été discutées et confirmées par l'usage du code informatique DEM, SiGran. L'accent a été particulièrement mis sur la validation du modèle DEM au moyen de comparaison des résultats des simulations DEM avec leurs équivalents physiques à une échelle macro. Les résultats virtuels DSA sont abordés du point de vue de la coaxialité entre les principales tensions et les principales directions des paliers de pression ainsi que de la déviation de la direction d'extension nulle à partir de la direction horizontale. Les résultats numériques fournissent également des données quantitatives sur les différentes formes d'énergie consommées durant le cisaillement confirmées par d'autres résultats physiques et numériques publiés. Sur la base des postulats précédents, un examen minutieux des résultats des essais de cisaillements directs et de données issues de la littérature a été accompli afin d'évaluer la fiabilité des formules empiriques bien connues de Bolton et Collins et al. avec leurs constantes couramment employées en condition de déformation plane. L'étude montre qu'une application des relations empiriques de force-dilatation de cisaillement avec les constantes proposées par Bolton (1986) et Collins et al. (1992) aux sables ayant une distribution de taille de particules différente peut conduire à surestimer leurs valeurs en terme de force de cisaillement. Dans cette étude, les coefficients des équations de Bolton et Collins et al. ont donc été ajustée afin de prendre en compte les caractéristiques des particules, en particulier le diamètre médian, D50. De manière analogue, les effets microstructuraux imposés par la géométrie interne des particules (par exemple la taille, la forme et la gradation des particules) sur la relation tension-dilatation très connue, celle de Rowe (1962), et son ajustement empirique en condition triaxiale drainée ont été examinés dans cette étude. Une comparaison des prédictions des formules proposées avec les données de force de cisaillement issues de la littérature fournit de nombreuses preuves en faveur des contraintes mises en place au sein des relations existantes de force-dilatation de cisaillement en condition de déformation plane et triaxiale. Ces comparaisons prouvent également que la prise en compte de la taille des grains conduit à des résultats plus tangibles que lorsque la taille de la particule n'est pas considérée. Les formules de force-dilatation ajustées peuvent se révéler avantageuses pour évaluer indépendamment la cohérence des forces de cisaillement déterminées expérimentalement et pour introduire des lois d’écoulement plus précises dans les analyses géotechniques analytiques et numériques.

Numerical modelling of braided fibres for reinforced concrete

Fire has been always a major concern for designers of steel and concrete structures. Designing fire-resistant structural elements is not an easy task due to several limitations such as the lack of fire-resistant construction materials. Concrete reinforcement cover and external insulation are the most commonly adopted systems to protect concrete and steel from overheating, while spalling of concrete is minimised by using HPFRC instead of standard concrete. Although these methodologies work very well for low rise concrete structures, this is not the case for high-rise and inaccessible buildings where fire loading is much longer. Fire can permanently damage structures that cost a lot of money. This is unsafe and can lead to loss of life. In this research, the author proposes a new type of main reinforcement for concrete structures which can provide better fire-resistance than steel or FRP re-bars. This consists of continuous braided fibre rope, generally made from fire-resistant materials such as carbon or glass fibre. These fibres have excellent tensile strengths, sometimes in excess of ten times greater than steel. In addition to fire-resistance, these ropes can produce lighter and corrosive resistant structures. Avoiding the use of expensive resin binders, fibres are easily bound together using braiding techniques, ensuring that tensile stress is evenly distributed throughout the reinforcement. In order to consider braided ropes as a form of reinforcement it is first necessary to establish the mechanical performance at room temperature and investigate the pull-out resistance for both unribbed and ribbed ropes. Ribbing of ropes was achieved by braiding the rope over a series of glass beads. Adhesion between the rope and concrete was drastically improved due to ribbing, and further improved by pre-stressing ropes and reducing the slacked fibres. Two types of material have been considered for the ropes: carbon and aramid. An implicit finite element approach is proposed to model braided fibres using Total Lagrangian formulation, based on the theory of small strains and large rotations. Modelling tows and strands as elastic transversely isotropic materials was a good assumption when stiff and brittle fibres such as carbon and glass fibres are considered. The rope-to-concrete and strand-to-strand bond interaction/adhesion was numerically simulated using newly proposed hierarchical higher order interface elements. Elastic and linear damage cohesive models were used effectively to simulate non-penetrative 'free' sliding interaction between strands, and the adhesion between ropes and concrete respectively. Numerical simulation showed similar de-bonding features when compared with experimental pull-out results of braided ribbed rope reinforced concrete.

Numerical and experimental analysis of 3D printed smart structures and systems

Three dimensional (3D) printers of continuous fiber reinforced composites, such as MarkTwo (MT) by Markforged, can be used to manufacture such structures. To date, research works devoted to the study and application of flexible elements and CMs realized with MT printer are only a few and very recent. A good numerical and/or analytical tool for the mechanical behavior analysis of the new composites is still missing. In addition, there is still a gap in obtaining the material properties used (e.g. elastic modulus) as it is usually unknown and sensitive to printing parameters used (e.g. infill density), making the numerical simulation inaccurate. Consequently, the aim of this thesis is to present several work developed. The first is a preliminary investigation on the tensile and flexural response of Straight Beam Flexures (SBF) realized with MT printer and featuring different interlayer fiber volume-fraction and orientation, as well as different laminate position within the sample. The second is to develop a numerical analysis within the Carrera' s Unified Formulation (CUF) framework, based on component-wise (CW) approach, including a novel preprocessing tool that has been developed to account all regions printed in an easy and time efficient way. Among its benefits, the CUF-CW approach enables building an accurate database for collecting first natural frequencies modes results, then predicting Young' s modulus based on an inverse problem formulation. To validate the tool, the numerical results are compared to the experimental natural frequencies evaluated using a digital image correlation method. Further, we take the CUF-CW model and use static condensation to analyze smart structures which can be decomposed into a large number of similar components. Third, the potentiality of MT in combination with topology optimization and compliant joints design (CJD) is investigated for the realization of automated machinery mechanisms subjected to inertial loads.

Numerical prediction of the lateral displacement capacity of flexural reinforced concrete shear walls

Previous earthquakes showed that shear wall damage could lead to catastrophic failures of the reinforced concrete building. The lateral load capacity of shear walls needs to be estimated to minimize associated losses during catastrophic events; hence it is necessary to develop and validate reliable and stable numerical methods able to converge to reasonable estimations with minimum computational effort. The beam-column 1-D line element with fiber-type cross-section model is a practical option that yields results in agreement with experimental data. However, shortcomings of using this model to predict the local damage response may come from the fact that the model requires fine calibration of material properties to overcome regularization and size effects. To reduce the mesh-dependency of the numerical model, a regularization method based on the concept of post-yield energy is applied in this work to both the concrete and the steel material constitutive laws to predict the nonlinear cyclic response and failure mechanism of concrete shear walls. Different categories of wall specimens known to produce a different response under in plane cyclic loading for their varied geometric and detailing characteristics are considered in this study, namely: 1) scaled wall specimens designed according to the European seismic design code and 2) unique full-scale wall specimens detailed according to the U.S. design code to develop a ductile behavior under cyclic loading. To test the boundaries of application of the proposed method, two full-scale walls with a mixed shear-flexure response and different values of applied axial load are also considered. The results of this study show that the use of regularized constitutive models considerably enhances the response predictions capabilities of the model with regards to global force-drift response and failure mode. The simulations presented in this thesis demonstrate the proposed model to be a valuable tool for researchers and engineers.

Numerical modeling on the short-term response of fiber-reinforced concrete round panels

Fiber-reinforced concrete is a composite material consisting of discrete, discontinuous, and uniformly distributed fibers in plain concrete primarily used to enhance the tensile properties of the concrete. FRC performance depends upon the fiber, interface, and matrix properties. The use of fiber-reinforced concrete has been increasing substantially in the past few years in different fields of the construction industry such as ground-level application in sidewalks and building floors, tunnel lining, aircraft parking, runways, slope stabilization, etc. Many experiments have been performed to observe the short-term and long-term mechanical behavior of fiber-reinforced concrete in the last decade and numerous numerical models have been formulated to accurately capture the response of fiber-reinforced concrete. The main purpose of this dissertation is to numerically calibrate the short-term response of the concrete and fiber parameters in mesoscale for the three-point bending test and cube compression test in the MARS framework which is based on the lattice discrete particle model (LDPM) and later validate the same parameters for the round panels. LDPM is the most validated theory in mesoscale theories for concrete. Different seeds representing the different orientations of concrete and fiber particles are simulated to produce the mean numerical response. The result of numerical simulation shows that the lattice discrete particle model for fiber-reinforced concrete can capture results of experimental tests on the behavior of fiber-reinforced concrete to a great extent.

Modelagem matemática e simulação numérica do resfriamento rápido de morango com ar forçado

This work approaches the forced air cooling of strawberry by numerical simulation. The mathematical model that was used describes the process of heat transfer, based on the Fourier's law, in spherical coordinates and simplified to describe the one-dimensional process. For the resolution of the equation expressed for the mathematical model, an algorithm was developed based on the explicit scheme of the numerical method of the finite differences and implemented in the scientific computation program MATLAB 6.1. The validation of the mathematical model was made by the comparison between theoretical and experimental data, where strawberries had been cooled with forced air. The results showed to be possible the determination of the convective heat transfer coefficient by fitting the numerical and experimental data. The methodology of the numerical simulations was showed like a promising tool in the support of the decision to use or to develop equipment in the area of cooling process with forced air of spherical fruits.

Reaction-diffusion stochastic lattice model for a predator-prey system

We have the purpose of analyzing the effect of explicit diffusion processes in a predator-prey stochastic lattice model. More precisely we wish to investigate the possible effects due to diffusion upon the thresholds of coexistence of species, i. e., the possible changes in the transition between the active state and the absorbing state devoid of predators. To accomplish this task we have performed time dependent simulations and dynamic mean-field approximations. Our results indicate that the diffusive process can enhance the species coexistence.

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.

Gravitational quasinormal modes of AdS black branes in d spacetime dimensions

The AdS/CFT duality has established a mapping between quantities in the bulk AdS black-hole physics and observables in a boundary finite-temperature field theory. Such a relationship appears to be valid for an arbitrary number of spacetime dimensions, extrapolating the original formulations of Maldacena`s correspondence. In the same sense properties like the hydrodynamic behavior of AdS black-hole fluctuations have been proved to be universal. We investigate in this work the complete quasinormal spectra of gravitational perturbations of d-dimensional plane-symmetric AdS black holes (black branes). Holographically the frequencies of the quasinormal modes correspond to the poles of two-point correlation functions of the field-theory stress-energy tensor. The important issue of the correct boundary condition to be imposed on the gauge-invariant perturbation fields at the AdS boundary is studied and elucidated in a fully d-dimensional context. We obtain the dispersion relations of the first few modes in the low-, intermediate- and high-wavenumber regimes. The sound-wave (shear-mode) behavior of scalar (vector)-type low- frequency quasinormal mode is analytically and numerically confirmed. These results are found employing both a power series method and a direct numerical integration scheme.

Hybrid modeling of convective laminar flow in a permeable tube associated with the cross-flow process

The confined flows in tubes with permeable surfaces arc associated to tangential filtration processes (microfiltration or ultrafiltration). The complexity of the phenomena do not allow for the development of exact analytical solutions, however, approximate solutions are of great interest for the calculation of the transmembrane outflow and estimate of the concentration, polarization phenomenon. In the present work, the generalized integral transform technique (GITT) was employed in solving the laminar and permanent flow in permeable tubes of Newtonian and incompressible fluid. The mathematical formulation employed the parabolic differential equation of chemical species conservation (convective-diffusive equation). The velocity profiles for the entrance region flow, which are found in the connective terms of the equation, were assessed by solutions obtained from literature. The velocity at the permeable wall was considered uniform, with the concentration at the tube wall regarded as variable with an axial position. A computational methodology using global error control was applied to determine the concentration in the wall and concentration boundary layer thickness. The results obtained for the local transmembrane flux and the concentration boundary layer thickness were compared against others in literature. (C) 2007 Elsevier B.V. All rights reserved.