A finite-volume shallow layer method for the MHD instabilities in an aluminium production cell

An electrolytic cell for Aluminium production contains molten metal and molten electrolyte, which are subject to high dc-currents and magnetic fields. Lorentz forces arising from the cross product of current and magnetic field may amplify natural gravity waves at the interface between the two fluids, leading to short circuits in extreme cases. The external magnetic field and current distribution in the production cell is computed through a detailed finite element analysis at Torino Polytechnic. The results are then used to compute the magnetohydrodynamic and thermal effects in the aluminium/electrolyte bath. Each cell has lateral dimensions of 6m x 2m, whilst the bath depth is only 30cm. the electrically resistive electrolyte path, which is critical in the operation of the cell, has layer depth of only a few centimetres below each carbon anode. Because the shallow dimensions of the liquid layer a finite-volume shallow-layer technique has been used at Greenwich to compute the resulting flow-field and interface perturbations. The information obtained from this method, i.e. depth averaged velocities and aluminium/electrolyte interface position is then embedded in the three-dimensional finite volume code PHYSICA and will be used to compute the heat transfer and phase change in the cell.

Airframe sound simulation based on staggered-grid higher order schemes and finite volume CFD methods

Abstract not available

DEVELOPMENT OF A 2-DIMENSIONAL FINITE VOLUME MODEL TO ASSESS HYDRODYNAMIC AND MICROBIAL CONTROLS ON DNAPL DISSOLUTION AND DETOXIFICATION

Tetrachloroethene (PCE) and trichloroethene (TCE) form dense non-aqueous phase liquids (DNAPLs), which are persistent groundwater contaminants. DNAPL dissolution can be "bioenhanced" via dissolved contaminant biodegradation at the DNAPL-water interface. This research hypothesized that: (1) competitive interactions between different dehalorespiring strains can significantly impact the bioenhancement effect, and extent of PCE dechlorination; and (2) hydrodynamics will affect the outcome of competition and the potential for bioenhancement and detoxification. A two-dimensional coupled flowtransport model was developed, with a DNAPL pool source and multiple microbial species. In the scenario presented, Dehalococcoides mccartyi 195 competes with Desulfuromonas michiganensis for the electron acceptors PCE and TCE. Simulations under biostimulation and low velocity (vx) conditions suggest that the bioenhancement with Dsm. michiganensis alone was modestly increased by Dhc. mccartyi 195. However, the presence of Dhc. mccartyi 195 enhanced the extent of PCE transformation. Hydrodynamic conditions impacted the results by changing the dominant population under low and high vx conditions.

Galerkin finite element method for incompressible thermofluid flows framed within the bond graph theory

In this paper a bond graph methodology is used to model incompressible fluid flows with viscous and thermal effects. The distinctive characteristic of these flows is the role of pressure, which does not behave as a state variable but as a function that must act in such a way that the resulting velocity field has divergence zero. Velocity and entropy per unit volume are used as independent variables for a single-phase, single-component flow. Time-dependent nodal values and interpolation functions are introduced to represent the flow field, from which nodal vectors of velocity and entropy are defined as state variables. The system for momentum and continuity equations is coincident with the one obtained by using the Galerkin method for the weak formulation of the problem in finite elements. The integral incompressibility constraint is derived based on the integral conservation of mechanical energy. The weak formulation for thermal energy equation is modeled with true bond graph elements in terms of nodal vectors of temperature and entropy rates, resulting a Petrov-Galerkin method. The resulting bond graph shows the coupling between mechanical and thermal energy domains through the viscous dissipation term. All kind of boundary conditions are handled consistently and can be represented as generalized effort or flow sources. A procedure for causality assignment is derived for the resulting graph, satisfying the Second principle of Thermodynamics. (C) 2007 Elsevier B.V. All rights reserved.

EFFECT – Efficient finite element code

The theme of this dissertation is the finite element method applied to mechanical structures. A new finite element program is developed that, besides executing different types of structural analysis, also allows the calculation of the derivatives of structural performances using the continuum method of design sensitivities analysis, with the purpose of allowing, in combination with the mathematical programming algorithms found in the commercial software MATLAB, to solve structural optimization problems. The program is called EFFECT – Efficient Finite Element Code. The object-oriented programming paradigm and specifically the C ++ programming language are used for program development. The main objective of this dissertation is to design EFFECT so that it can constitute, in this stage of development, the foundation for a program with analysis capacities similar to other open source finite element programs. In this first stage, 6 elements are implemented for linear analysis: 2-dimensional truss (Truss2D), 3-dimensional truss (Truss3D), 2-dimensional beam (Beam2D), 3-dimensional beam (Beam3D), triangular shell element (Shell3Node) and quadrilateral shell element (Shell4Node). The shell elements combine two distinct elements, one for simulating the membrane behavior and the other to simulate the plate bending behavior. The non-linear analysis capability is also developed, combining the corotational formulation with the Newton-Raphson iterative method, but at this stage is only avaiable to solve problems modeled with Beam2D elements subject to large displacements and rotations, called nonlinear geometric problems. The design sensitivity analysis capability is implemented in two elements, Truss2D and Beam2D, where are included the procedures and the analytic expressions for calculating derivatives of displacements, stress and volume performances with respect to 5 different design variables types. Finally, a set of test examples were created to validate the accuracy and consistency of the result obtained from EFFECT, by comparing them with results published in the literature or obtained with the ANSYS commercial finite element code.

Improvign mixing processes with the help of numerical tools

In several industrial applications, highly complex behaviour materials are used together with intricate mixing processes, which difficult the achievement of the desired properties for the produced materials. This is the case of the well-known dispersion of nano-sized fillers in a melt polymer matrix, used to improve the nanocomposite mechanical and/or electrical properties. This mixing is usually performed in twin-screw extruders, that promote complex flow patterns, and, since an in loco analysis of the material evolution and mixing is difficult to perform, numerical tools can be very useful to predict the evolution and behaviour of the material. This work presents a numerical based study to improve the understanding of mixing processes. Initial numerical studies were performed with generalized Newtonian fluids, but, due to the null relaxation time that characterize this type of fluids, the assumption of viscoelastic behavior was required. Therefore, the polymer melt was rheologically characterized, and, a six mode Phan-Thien-Tanner and Giesekus models were used to fit the rheological data. These viscoelastic rheological models were used to model the process. The conclusions obtained in this work provide additional and useful data to correlate the type and intensity of the deformation history promoted to the polymer nanocomposite and the quality of the mixing obtained.

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

Red blood cell structure and dynamics explored with digital holographic microspcopy

Digital holographic microscopy (DHM) is a technique that allows obtaining, from a single recorded hologram, quantitative phase image of living cell with interferometric accuracy. Specifically the optical phase shift induced by the specimen on the transmitted wave front can be regarded as a powerful endogenous contrast agent, depending on both the thickness and the refractive index of the sample. Thanks to a decoupling procedure cell thickness and intracellular refractive index can be measured separately. Consequently, Mean corpuscular volume (MCV) and mean corpuscular hemoglobin concentration (MCHC), two highly relevant clinical parameters, have been measured non-invasively at a single cell level. The DHM nanometric axial and microsecond temporal sensitivities have permitted to measure the red blood cell membrane fluctuations (CMF) on the whole cell surface. ©2009 COPYRIGHT SPIE--The International Society for Optical Engineering.

Finite energy Dirac-Born-Infeld monopoles and string junctions

It is shown that the world volume field theory of a single D3-brane in a supergravity D3-brane background admits finite energy, and non-singular, Abelian monopoles and dyons preserving 1/2 or 1/4 of the N=4 supersymmetry and saturating a Bogomolnyi-type bound. The 1/4 supersymmetric solitons provide a world volume realization of string-junction dyons. We also discuss the dual M-theory realization of the 1/2 supersymmetric dyons as finite tension self-dual strings on the M5-brane, and of the 1/4 supersymmetric dyons as their intersections.

Holographic phase transitions with fundamental matter

The holographic dual of a finite-temperature gauge theory with a small number of flavors typically contains D-brane probes in a black hole background. At low temperature, the branes sit outside the black hole and the meson spectrum is discrete and possesses a mass gap. As the temperature increases, the branes approach a critical solution. Eventually, they fall into the horizon and a phase transition occurs. In the new phase, the meson spectrum is continuous and gapless. At large Nc and large't Hooft coupling, we show that this phase transition is always first order. In confining theories with heavy quarks, it occurs above the deconfinement transition for the glue.

Cell morphology and intracellular ionic homeostasis explored with a multimodal approach combining epifluorescence and digital holographic microscopy.

The authors have developed a live-cell multimodality microscope combining epifluorescence with digital holographic microscopy; it has been implemented with a decoupling procedure allowing to separately measure from the quantitative phase important cell parameters including absolute volume, shape and integral intracellular refractive index. In combination with the numerous different specific fluorescent cellular probes, this multimodality microscopy can address important issues in cell biology. This is demonstrated by the study of intracellular calcium homeostasis associated with the change in cell volume, which play a critical role in the excitotoxicity-induced neuronal death.

Investigation of Two Bridge Alternatives for Low Volume Roads, Volume 1 of 2 Concept 1: Precast Steel Beam Units, HR-382, 1997

Recent reports have indicated that 23.5% of the nation's highway bridges are structurally deficient and 17.7% are functionally obsolete. A significant number of these bridges are on the Iowa secondary road system where over 86% of the rural bridge management responsibilities are assigned to the counties. Some of the bridges can be strengthened or otherwise rehabilitated, but many more are in need of immediate replacement. In a recent investigation (HR-365 "Evaluation of Bridge Replacement Alternatives for the County Bridge System") several types of replacement bridges that are currently being used on low volume roads were identified. It was also determined that a large number of counties (69%) have the ability and are interested in utilizing their own forces to design and construct short span bridges. In reviewing the results from HR-365, the research team developed one "new" bridge replacement concept and a modification of a replacement system currently being used. Both of these bridge replacement alternatives were investigated in this study, the results of which are presented in two volumes. This volume (Volume 1) presents the results of Concept 1 - Steel Beam Precast Units. Concept 2 - Modification of the Beam-in-Slab Bridge is presented in Volume 2. Concept 1, involves the fabrication of precast units (two steel beams connected by a concrete slab) by county work forces. Deck thickness is limited so that the units can be fabricated at one site and then transported to the bridge site where they are connected and the remaining portion of the deck placed. Since Concept 1 bridge is primarily intended for use on low-volume roads, the precast units can be constructed with new or used beams. In the experimental part of the investigation, there were three types of static load tests: small scale connector tests, "handling strength" tests, and service and overload tests of a model bridge. Three finite element models for analyzing the bridge in various states of construction were also developed. Small scale connector tests were completed to determine the best method of connecting the precast double-T (PCDT) units. "Handling strength" tests on an individual PCDT unit were performed to determine the strength and behavior of the precast unit in this configuration. The majority of the testing was completed on the model bridge [L=9,750 mm (32 ft), W=6,400 mm (21 ft)] which was fabricated using the precast units developed. Some of the variables investigated in the model bridge tests were number of connectors required to connect adjacent precast units, contribution of diaphragms to load distribution, influence of position of diaphragms on bridge strength and load distribution, and effect of cast-in-place portion of deck on load distribution. In addition to the service load tests, the bridge was also subjected to overload conditions. Using the finite element models developed, one can predict the behavior and strength of bridges similar to the laboratory model as well as design them. Concept 1 has successfully passed all laboratory testing; the next step is to field test it.

Investigation of Two Bridge Alternatives for Low Volume Roads Volume 2 of 2 Concept 2: Beam In Slab Bridge, HR-382, 1997

Recent reports have indicated that 23.5% of the nation's highway bridges are structurally deficient and 17.7% are functionally obsolete. A significant number of these bridges are on the Iowa secondary road system where over 86% of the rural bridge management responsibilities are assigned to the counties. Some of the bridges can be strengthened or otherwise rehabilitated, but many more are in need of immediate replacement. In a recent investigation (HR-365 "Evaluation of Bridge Replacement Alternatives for the County Bridge System") several types of replacement bridges that are currently being used on low volume roads were identified. It was also determined that a large number of counties (69%) have the ability and are interested in utilizing their own forces to design and construct short span bridges. After reviewing the results from HR-365, the research team developed one "new" bridge replacement concept and a modification of a replacement system currently being used. Both of these bridge replacement alternatives were investigated in this study, the results of which are presented in two volumes. This volume (Volume 2) presents the results of Concept 2 - Modification of the Beam-in-Slab Bridge. Concept 1 - Steel Beam Precast Units is presented in Volume 1. Concept 2 involves various laboratory tests of the Beam-in-Slab bridge (BISB) currently being used by Benton County and several other Iowa counties. In this investigation, the behavior and strength of the BISB were determined; a new method of obtaining composite action between the steel beams and concrete was also tested. Since the Concept 2 bridge is primarily intended for use on low-volume roads, the system can be constructed with new or used beams. In the experimental part of the investigation, there were three types of laboratory tests: push-out tests, service and ultimate load tests of models of the BISB, and composite beam tests utilizing the newly developed shear connection. In addition to the laboratory tests, there was a field test in which an existing BISB was service load tested. An equation was developed for predicting the strength of the shear connection investigated; in addition, a finite element model for analyzing the BISB was also developed. Push-out tests were completed to determine the strength of the recently developed shear connector. A total of 36 specimens were tested, with variables such as hole diameter, hole spacing, presence of reinforcement, etc. being investigated. In the model tests of the BISB, two and four beam specimens [L=9,140 mm (30 ft)] were service load tested for behavior and load distribution data. Upon completion of these tests, both specimens were loaded to failure. In the composite beam tests, four beams, one with standard shear studs and three using the shear connection developed, were tested. Upon completion of the service load tests, all four beams were loaded to failure. The strength and behavior of the beams with the new shear connection were found to be essentially the same as that of the specimen with standard shear studs.

The number of planar central configurations for the 4-body problem is finite when 3 mass positions are fixed

In the n{body problem a central con guration is formed when the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration vector. Lindstrom showed for n = 3 and for n > 4 that if n ? 1 masses are located at xed points in the plane, then there are only a nite number of ways to position the remaining nth mass in such a way that they de ne a central con guration. Lindstrom leaves open the case n = 4. In this paper we prove the case n = 4 using as variables the mutual distances between the particles.

Fly Ash Soil Stabilization for Non-Uniform Subgrade Soils, Volume II: Influence of Subgrade Non-Uniformity on PCC Pavement Performance, TR-461, 2005

To provide insight into subgrade non-uniformity and its effects on pavement performance, this study investigated the influence of non-uniform subgrade support on pavement responses (stress and deflection) that affect pavement performance. Several reconstructed PCC pavement projects in Iowa were studied to document and evaluate the influence of subgrade/subbase non-uniformity on pavement performance. In situ field tests were performed at 12 sites to determine the subgrade/subbase engineering properties and develop a database of engineering parameter values for statistical and numerical analysis. Results of stiffness, moisture and density, strength, and soil classification were used to determine the spatial variability of a given property. Natural subgrade soils, fly ash-stabilized subgrade, reclaimed hydrated fly ash subbase, and granular subbase were studied. The influence of the spatial variability of subgrade/subbase on pavement performance was then evaluated by modeling the elastic properties of the pavement and subgrade using the ISLAB2000 finite element analysis program. A major conclusion from this study is that non-uniform subgrade/subbase stiffness increases localized deflections and causes principal stress concentrations in the pavement, which can lead to fatigue cracking and other types of pavement distresses. Field data show that hydrated fly ash, self-cementing fly ash-stabilized subgrade, and granular subbases exhibit lower variability than natural subgrade soils. Pavement life should be increased through the use of more uniform subgrade support. Subgrade/subbase construction in the future should consider uniformity as a key to long-term pavement performance.