Effective cell-centred time-domain Maxwell's equations numerical solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed. © 2004 Elsevier Inc. All rights reserved.

Simultaneous biochemical reaction and separation in a continuous rotating annular chromatograph

The aim of this work has been to investigate the behaviour of a continuous rotating annular chromatograph (CRAC) under a combined biochemical reaction and separation duty. Two biochemical reactions have been employed, namely the inversion of sucrose to glucose and fructose in the presence of the enzyme invertase and the saccharification of liquefied starch to maltose and dextrin using the enzyme maltogenase. Simultaneous biochemical reaction and separation has been successfully carried out for the first time in a CRAC by inverting sucrose to fructose and glucose using the enzyme invertase and collecting continuously pure fractions of glucose and fructose from the base of the column. The CRAC was made of two concentric cylinders which form an annulus 140 cm long by 1.2 cm wide, giving an annular space of 14.5 dm3. The ion exchange resin used was an industrial grade calcium form Dowex 50W-X4 with a mean diameter of 150 microns. The mobile phase used was deionised and dearated water and contained the appropriate enzyme. The annular column was slowly rotated at speeds of up to 240°h-1 while the sucrose substrate was fed continuously through a stationary feed pipe to the top of the resin bed. A systematic investigation of the factors affecting the performance of the CRAC under simultaneous biochemical reaction and separation conditions was carried out by employing a factorial experimental procedure. The main factors affecting the performance of the system were found to be the feed rate, feed concentrations and eluent rate. Results from the experiments indicated that complete conversion could be achieved for feed concentrations of up to 50% w/v sucrose and at feed throughputs of up to 17.2 kg sucrose per m3 resin/h. The second enzymic reaction, namely the saccharification of liquefied starch to maltose employing the enzyme maltogenase has also been successfully carried out on a CRAC. Results from the experiments using soluble potato starch showed that conversions of up to 79% were obtained for a feed concentration of 15.5% w/v at a feed flowrate of 400 cm3/h. The product maltose obtained was over 95% pure. Mathematical modelling and computer simulation of the sucrose inversion system has been carried out. A finite difference method was used to solve the partial differential equations and the simulation results showed good agreement with the experimental results obtained.

Bioreaction and separation in batch chromatographic columns

The objective of this work has been to study the behaviour and performance of a batch chromatographic column under simultaneous bioreaction and separation conditions for several carbohydrate feedstocks. Four bioreactions were chosen, namely the hydrolysis of sucrose to glucose and fructose using the enzyme invertase, the hydrolysis of inulin to fructose and glucose using inulinase, the hydrolysis of lactose to glucose and galactose using lactase and the isomerization of glucose to fructose using glucose isomerase. The chromatographic columns employed were jacketed glass columns ranging from 1 m to 2 m long and the internal diameter ranging from 0.97 cm to 1.97 cm. The stationary phase used was a cation exchange resin (PUROLITE PCR-833) in the Ca2+ form for the hydrolysis and the Mg2+ form for the isomerization reactions. The mobile phase used was a diluted enzyme solution which was continuously pumped through the chromatographic bed. The substrate was injected at the top of the bed as a pulse. The effect of the parameters pulse size, the amount of substrate solution introduced into the system corresponding to a percentage of the total empty column volume (% TECV), pulse concentration, eluent flowrate and the enzyme activity of the eluent were investigated. For the system sucrose-invertase complete conversions of substrate were achieved for pulse sizes and pulse concentrations of up to 20% TECV and 60% w/v, respectively. Products with purity above 90% were obtained. The enzyme consumption was 45% of the amount theoretically required to produce the same amount of product as in a conventional batch reactor. A value of 27 kg sucrose/m3 resin/h for the throughput of the system was achieved. The systematic investigation of the factors affecting the performance of the batch chromatographic bioreactor-separator was carried out by employing a factorial experimental procedure. The main factors affecting the performance of the system were the flowrate and enzyme activity. For the system inulin-inulinase total conversions were also obtained for pulses sizes of up to 20 % TECV and a pulse concentration of 10 % w/v. Fructose rich fractions with 100 % purity and representing up to 99.4 % of the total fructose generated were obtained with an enzyme consumption of 32 % of the amount theoretically required to produce the same amount of product in a conventional batch reactor. The hydrolysis of lactose by lactase was studied in the glass columns and also in an SCCR-S unit adapted for batch operation, in co-operation with Dr. Shieh, a fellow researcher in the Chemical Engineering and Applied Chemistry Department at Aston University. By operating at up to 30 % w/v lactose feed concentrations complete conversions were obtained and the purities of the products generated were above 90%. An enzyme consumption of 48 % of the amount theoretically required to produce the same amount of product in a conventional batch reactor was achieved. On working with the system glucose-glucose isomerase, which is a reversible reaction, the separation obtained with the stationary phase conditioned in the magnesium form was very poor although the conversion obtained was compatible with those for conventional batch reactors. By working with a mixed pulse of enzyme and substrate, up to 82.5 % of the fructose generated with a purity of 100 % was obtained. The mathematical modelling and computer simulation of the batch chromatographic bioreaction-separation has been performed on a personal computer. A finite difference method was used to solve the partial differential equations and the simulation results showed good agreement with the experimental results.

A Note on the “Constructing” of Nonstationary Methods for Solving Nonlinear Equations with Raised Speed of Convergence

This paper is partially supported by project ISM-4 of Department for Scientific Research, “Paisii Hilendarski” University of Plovdiv.

A Gradient-Type Optimization Technique for the Optimal Control for Schrodinger Equations

In this paper, we are considered with the optimal control of a schrodinger equation. Based on the formulation for the variation of the cost functional, a gradient-type optimization technique utilizing the finite difference method is then developed to solve the constrained optimization problem. Finally, a numerical example is given and the results show that the method of solution is robust.

Simulação da destilação molecular de filme descendente para o petróleo

The heavy part of the oil can be used for numerous purposes, e.g. to obtain lubricating oils. In this context, many researchers have been studying alternatives such separation of crude oil components, among which may be mentioned molecular distillation. Molecular distillation is a forced evaporation technique different from other conventional processes in the literature. This process can be classified as a special distillation case under high vacuum with pressures that reach extremely low ranges of the order of 0.1 Pascal. The evaporation and condensation surfaces must have a distance from each other of the magnitude order of mean free path of the evaporated molecules, that is, molecules evaporated easily reach the condenser, because they find a route without obstacles, what is desirable. Thus, the main contribution of this work is the simulation of the falling-film molecular distillation for crude oil mixtures. The crude oil was characterized using UniSim® Design and R430 Aspen HYSYS® V8.5. The results of this characterization were performed in spreadsheets of Microsoft® Excel®, calculations of the physicochemical properties of the waste of an oil sample, i.e., thermodynamic and transport. Based on this estimated properties and boundary conditions suggested by the literature, equations of temperature and concentration profiles were resolved through the implicit finite difference method using the programming language Visual Basic® (VBA) for Excel®. The result of the temperature profile showed consistent with the reproduced by literature, having in their initial values a slight distortion as a result of the nature of the studied oil is lighter than the literature, since the results of the concentration profiles were effective allowing realize that the concentration of the more volatile decreases and of the less volatile increases due to the length of the evaporator. According to the transport phenomena present in the process, the velocity profile tends to increase to a peak and then decreases, and the film thickness decreases, both as a function of the evaporator length. It is concluded that the simulation code in Visual Basic® language (VBA) is a final product of the work that allows application to molecular distillation of petroleum and other similar mixtures.

Surface quality and surface waves on subwavelength-structured silver films

We analyze the physical-chemical surface properties of single-slit, single-groove subwavelength-structured silver films with high-resolution transmission electron microscopy and calculate exact solutions to Maxwell’s equations corresponding to recent far-field interferometry experiments using these structures. Contrary to a recent suggestion the surface analysis shows that the silver films are free of detectable contaminants. The finite-difference time-domain calculations, in excellent agreement with experiment, show a rapid fringe amplitude decrease in the near zone (slit-groove distance out to 3–4 wavelengths). Extrapolation to slit-groove distances beyond the near zone shows that the surface wave evolves to the expected bound surface plasmon polariton (SPP). Fourier analysis of these results indicates the presence of a distribution of transient, evanescent modes around the SPP that dephase and dissipate as the surface wave evolves from the near to the far zone.

Particle positions of numerical experiments 1 to 4

In mixed sediment beds, erosion resistance can change relative to that of beds composed of a uniform sediment because of varying textural and/or other grain-size parameters, with effects on pore water flow that are difficult to quantify by means of analogue techniques. To overcome this difficulty, a three-dimensional numerical model was developed using a finite difference method (FDM) flow model coupled with a distinct element method (DEM) particle model. The main aim was to investigate, at a high spatial resolution, the physical processes occurring during the initiation of motion of single grains at the sediment-water interface and in the shallow subsurface of simplified sediment beds under different flow velocities. Increasing proportions of very fine sand (D50=0.08 mm) were mixed into a coarse sand matrix (D50=0.6 mm) to simulate mixed sediment beds, starting with a pure coarse sand bed in experiment 1 (0 wt% fines), and proceeding through experiment 2 (6.5 wt% fines), experiment 3 (10.5 wt% fines), and experiment 4 (28.7 wt% fines). All mixed beds were tested for their erosion behavior at predefined flow velocities varying in the range of U 1-5=10-30 cm/s. The experiments show that, with increasing fine content, the smaller particles increasingly fill the spaces between the larger particles. As a consequence, pore water inflow into the sediment is increasingly blocked, i.e., there is a decrease in pore water flow velocity and, hence, in the flow momentum available to entrain particles. These findings are portrayed in a new conceptual model of enhanced sediment bed stabilization.

Inversion of ambient seismic noise HVSR to evaluate velocity and structural models of the Lower Tagus Basin, Portugal

During its history, several significant earthquakes have shaken the Lower Tagus Valley (Portugal). These earthquakes were destructive; some strong earthquakes were produced by large ruptures in offshore structures located southwest of the Portuguese coastline, and other moderate earthquakes were produced by local faults. In recent years, several studies have successfully obtained strong-ground motion syntheses for the Lower Tagus Valley using the finite difference method. To confirm the velocity model of this sedimentary basin obtained from geophysical and geological data, we analysed the ambient seismic noise measurements by applying the horizontal to vertical spectral ratio (HVSR) method. This study reveals the dependence of the frequency and amplitude of the low-frequency (HVSR) peaks (0.2–2 Hz) on the sediment thickness. We have obtained the depth of the Cenozoic basement along a profile transversal to the basin by the inversion of these ratios, imposing constraints from seismic reflection, boreholes, seismic sounding and gravimetric and magnetic potentials. This technique enables us to improve the existing three-dimensional model of the Lower Tagus Valley structure. The improved model will be decisive for the improvement of strong motion predictions in the earthquake hazard analysis of this highly populated basin. The methodology discussed can be applied to any other sedimentary basin.

Confirmação do modelo da estrutura 3D do vale inferior do Tejo a partir de dados de ruído sísmico ambiente

Ao longo de sua história a região do Vale Inferior do Tejo VIT foi abalada por vários sismos consideravelmente destrutivas, tendo alguns deles produzido significativas deformações nas estruturas marítimas localizadas no litoral a sudoeste do território Português; outros, moderados, foram produzidos por fontes locais, como os de 1344, 1531 e 1909. Nos últimos anos, devido à melhoria dos modelos de estrutura 3D e o desenvolvimento dos métodos numéricos, foram elaborados vários estudos de síntese de movimento forte do solo para a região do Baixo Tejo utilizando o método de diferenças finitas. Para confirmar o modelo de velocidades desta bacia usámos medidas de ruído sísmico, aplicámos um método baseado na razão espectral H/V, e, a partir destas curvas, por inversão, obtivemos um modelo de velocidades para a região estudada. Os resultados revelam uma boa concordância entre o modelo obtido e os dados geofísicos e geológicos recolhidos na mesma área._ ABSTRACT: Along his history the Lower Tagus Valley (LTV) area was shaken by several earthquakes. The largest reported had their origin in the southwestern part of Iberia. Other moderate earthquakes were produced by local sources such as the 1344, 1531 and the 1909. ln the last years, due to 3D structural model improvement and development in numerical methods, several studies have successful obtained strong-ground motion synthesis for the LVT region using finite difference method. To confirm the velocity model of the LTV sedimentary basin obtained by geophysical and geological data, we use broad-band microtremor measurements and application of the horizontal to vertical (H/V) spectral ratio method. We have obtained a velocity model for the studied region by inversion of the H/V curve. The results have good agreement geological and geophysical data.

Models for reliability estimation of HVDC cable systems

The work carried out in this thesis aims at: - studying – in both simulative and experimental methods – the effect of electrical transients (i.e., Voltage Polarity Reversals VPRs, Temporary OverVoltages TOVs, and Superimposed Switching Impulses SSIs) on the aging phenomena in HVDC extruded cable insulations. Dielectric spectroscopy, conductivity measurements, Fourier Transform Infra-Red FTIR spectroscopy, and space charge measurements show variation in the insulating properties of the aged Cross-Linked Polyethylene XLPE specimens compared to non-aged ones. Scission in XLPE bonds and formation of aging chemical bonds is also noticed in aged insulations due to possible oxidation reactions. The aged materials show more ability to accumulate space charges compared to non-aged ones. An increase in both DC electrical conductivity and imaginary permittivity has been also noticed. - The development of life-based geometric design of HVDC cables in a detailed parametric analysis of all parameters that affect the design. Furthermore, the effect of both electrical and thermal transients on the design is also investigated. - The intrinsic thermal instability in HVDC cables and the effect of insulation characteristics on the thermal stability using a temperature and field iterative loop (using numerical methods – Finite Difference Method FDM). The dielectric loss coefficient is also calculated for DC cables and found to be less than that in AC cables. This emphasizes that the intrinsic thermal instability is critical in HVDC cables. - Fitting electrical conductivity models to the experimental measurements using both models found in the literature and modified models to find the best fit by considering the synergistic effect between field and temperature coefficients of electrical conductivity.

An Eulerian Immersed Boundary Method for flow simulations over stationary and moving rigid bodies

The fluid flow over bodies with complex geometry has been the subject of research of many scientists and widely explored experimentally and numerically. The present study proposes an Eulerian Immersed Boundary Method for flows simulations over stationary or moving rigid bodies. The proposed method allows the use of Cartesians Meshes. Here, two-dimensional simulations of fluid flow over stationary and oscillating circular cylinders were used for verification and validation. Four different cases were explored: the flow over a stationary cylinder, the flow over a cylinder oscillating in the flow direction, the flow over a cylinder oscillating in the normal flow direction, and a cylinder with angular oscillation. The time integration was carried out by a classical 4th order Runge-Kutta scheme, with a time step of the same order of distance between two consecutive points in x direction. High-order compact finite difference schemes were used to calculate spatial derivatives. The drag and lift coefficients, the lock-in phenomenon and vorticity contour plots were used for the verification and validation of the proposed method. The extension of the current method allowing the study of a body with different geometry and three-dimensional simulations is straightforward. The results obtained show a good agreement with both numerical and experimental results, encouraging the use of the proposed method.

Verification of a mixed high-order accurate DNS code for laminar turbulent transition by the method of manufactured solutions

This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high-order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier-Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity-velocity formulation for a two-dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high-order compact and non-compact finite-differences from fourth-order to sixth-order of accuracy. The other scheme used spectral methods instead of finite-difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed-order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright (C) 2009 John Wiley & Sons, Ltd.

Matrix Method for Acoustic Levitation Simulation

A matrix method is presented for simulating acoustic levitators. A typical acoustic levitator consists of an ultrasonic transducer and a reflector. The matrix method is used to determine the potential for acoustic radiation force that acts on a small sphere in the standing wave field produced by the levitator. The method is based on the Rayleigh integral and it takes into account the multiple reflections that occur between the transducer and the reflector. The potential for acoustic radiation force obtained by the matrix method is validated by comparing the matrix method results with those obtained by the finite element method when using an axisymmetric model of a single-axis acoustic levitator. After validation, the method is applied in the simulation of a noncontact manipulation system consisting of two 37.9-kHz Langevin-type transducers and a plane reflector. The manipulation system allows control of the horizontal position of a small levitated sphere from -6 mm to 6 mm, which is done by changing the phase difference between the two transducers. The horizontal position of the sphere predicted by the matrix method agrees with the horizontal positions measured experimentally with a charge-coupled device camera. The main advantage of the matrix method is that it allows simulation of non-symmetric acoustic levitators without requiring much computational effort.