Film thickness measurement techniques applied to micro-scale two-phase flow systems

Recently semi-empirical models to estimate flow boiling heat transfer coefficient, saturated CHF and pressure drop in micro-scale channels have been proposed. Most of the models were developed based on elongated bubbles and annular flows in the view of the fact that these flow patterns are predominant in smaller channels. In these models, the liquid film thickness plays an important role and such a fact emphasizes that the accurate measurement of the liquid film thickness is a key point to validate them. On the other hand, several techniques have been successfully applied to measure liquid film thicknesses during condensation and evaporation under macro-scale conditions. However, although this subject has been targeted by several leading laboratories around the world, it seems that there is no conclusive result describing a successful technique capable of measuring dynamic liquid film thickness during evaporation inside micro-scale round channels. This work presents a comprehensive literature review of the methods used to measure liquid film thickness in macro- and micro-scale systems. The methods are described and the main difficulties related to their use in micro-scale systems are identified. Based on this discussion, the most promising methods to measure dynamic liquid film thickness in micro-scale channels are identified. (C) 2009 Elsevier Inc. All rights reserved.

Dual boundary element formulation applied to analysis of multi-fractured domains

This paper deals with analysis of multiple random crack propagation in two-dimensional domains using the boundary element method (BEM). BEM is known to be a robust and accurate numerical technique for analysing this type of problem. The formulation adopted in this work is based on the dual BEM, for which singular and hyper-singular integral equations are used. We propose an iterative scheme to predict the crack growth path and the crack length increment at each time step. The proposed scheme able us to simulate localisation and coalescence phenomena, which is the main contribution of this paper. Considering the fracture mechanics analysis, the displacement correlation technique is applied to evaluate the stress intensity factors. The propagation angle and the equivalent stress intensity factor are calculated using the theory of maximum circumferential stress. Examples of simple and multi-fractured domains, loaded up to the rupture, are considered to illustrate the applicability of the proposed scheme. (C) 2010 Elsevier Ltd. All rights reserved.

A BEM model applied to failure analysis of multi-fractured structures

Due to manufacturing or damage process, brittle materials present a large number of micro-cracks which are randomly distributed. The lifetime of these materials is governed by crack propagation under the applied mechanical and thermal loadings. In order to deal with these kinds of materials, the present work develops a boundary element method (BEM) model allowing for the analysis of multiple random crack propagation in plane structures. The adopted formulation is based on the dual BEM, for which singular and hyper-singular integral equations are used. An iterative scheme to predict the crack growth path and crack length increment is proposed. This scheme enables us to simulate the localization and coalescence phenomena, which are the main contribution of this paper. Considering the fracture mechanics approach, the displacement correlation technique is applied to evaluate the stress intensity factors. The propagation angle and the equivalent stress intensity factor are calculated using the theory of maximum circumferential stress. Examples of multi-fractured domains, loaded up to rupture, are considered to illustrate the applicability of the proposed method. (C) 2011 Elsevier Ltd. All rights reserved.

An alternative multi-region BEM technique for three-dimensional elastic problems

The main objective of this work is to present an alternative boundary element method (BEM) formulation for the static analysis of three-dimensional non-homogeneous isotropic solids. These problems can be solved using the classical boundary element formulation, analyzing each subregion separately and then joining them together by introducing equilibrium and displacements compatibility. Establishing relations between the displacement fundamental solutions of the different domains, the alternative technique proposed in this paper allows analyzing all the domains as one unique solid, not requiring equilibrium or compatibility equations. This formulation also leads to a smaller system of equations when compared to the usual subregion technique, and the results obtained are even more accurate. (C) 2008 Elsevier Ltd. All rights reserved.

A numerical model for the description of the nonlinear behaviour of multi-leaf masonry walls

A nonlinear finite element model was developed to simulate the nonlinear response of three-leaf masonry specimens, which were subjected to laboratory tests with the aim of investigating the mechanical behaviour of multiple-leaf stone masonry walls up to failure. The specimens consisted of two external leaves made of stone bricks and mortar joints, and an internal leaf in mortar and stone aggregate. Different loading conditions, typologies of the collar joints, and stone types were taken into account. The constitutive law implemented in the model is characterized by a damage tensor, which allows the damage-induced anisotropy accompanying the cracking process to be described. To follow the post-peak behaviour of the specimens with sufficient accuracy it was necessary to make the damage model non-local, to avoid mesh-dependency effects related to the strain-softening behaviour of the material. Comparisons between the predicted and measured failure loads are quite satisfactory in most of the studied cases. (c) 2007 Elsevier Ltd. All rights reserved.

Performance of the Equivalent Reservoir Modelling Technique for Multi-Reservoir Hydropower Systems

This paper investigates the validity of a simplified equivalent reservoir representation of a multi-reservoir hydroelectric system for modelling its optimal operation for power maximization. This simplification, proposed by Arvanitidis and Rosing (IEEE Trans Power Appar Syst 89(2):319-325, 1970), imputes a potential energy equivalent reservoir with energy inflows and outflows. The hydroelectric system is also modelled for power maximization considering individual reservoir characteristics without simplifications. Both optimization models employed MINOS package for solution of the non-linear programming problems. A comparison between total optimized power generation over the planning horizon by the two methods shows that the equivalent reservoir is capable of producing satisfactory power estimates with less than 6% underestimation. The generation and total reservoir storage trajectories along the planning horizon obtained by equivalent reservoir method, however, presented significant discrepancies as compared to those found in the detailed modelling. This study is motivated by the fact that Brazilian generation system operations are based on the equivalent reservoir method as part of the power dispatch procedures. The potential energy equivalent reservoir is an alternative which eliminates problems with the dimensionality of state variables in a dynamic programming model.

Full-scale anaerobic sequencing batch biofilm reactor for sulfate-rich wastewater treatment

This paper describes the performance and biofilm characteristics of a full-scale anaerobic sequencing batch biofilm reactor (ASBBR; 20 m(3)) containing biomass immobilized on an inert support (mineral coal) for the treatment of industrial wastewater containing a high sulfate concentration. The ASBBR reactor was operated during 110 cycles (48 h each) at sulfate loading rates ranging from 6.9 to 62.4 kgSO(4)(2-)/cycle corresponding to sulfate concentrations of 0.58-5.2 gSO(4)(2-)/L. Domestic sewage and ethanol were utilized as electron donors for sulfate reduction. After 71 cycles the mean sulfate removal efficiency was 99%, demonstrating a high potential for biological sulfate reduction. The biofilm formed in the reactor occurred in two different patterns, one at the beginning of the colonization and the other of a mature biofilm. These different colonization patterns are due to the low adhesion of the microorganisms on the inert support in the start-up period. The biofilm population is mainly made up of syntrophic consortia among sulfate-reducing bacteria and methanogenic archaea such as Methanosaeta spp.

Effect of Fill Time on the Performance of Pilot-scale ASBR and AnSBBR Applied to Sanitary Wastewater Treatment

Many lab-scale studies have been carried out regarding the effect of feed strategy on the performance of anaerobic sequencing batch reactors (ASBR); however, more detailed pilot-scale studies should be performed to assess the real applicability of this type of operation. Therefore, the objective of this work was to assess the effect of feed strategy or fill time in a 1-m(3) mechanically stirred pilot-scale sequencing batch reactor, treating 0.65 m(3) sanitary wastewater in 8-h cycles at ambient temperature. Two reactor configurations were used: one containing granular biomass (denominated ASBR) and the other immobilized biomass on polyurethane foam as inert support (denominated anaerobic sequencing batch biofilm reactor (AnSBBR)). The reactors were operated under five distinct feed strategies, namely: typical batch and fed-batch for 25%, 50%, 75%, and 100% of the cycle length. Stirring frequency in the ASBR was 40 rpm with two flat-blade turbine impellers and 80 rpm in the AnSBBR with two helix impellers. The results showed that both the ASBR and AnSBBR when operated under typical batch, fed-batch for 50% and 75% of the cycle length, presented improved organic matter removal efficiencies, without significant differences in performance, thus showing important operational flexibility. In addition, the reactors presented operation stability under all conditions.

The treatment of sulfate-rich wastewater using an anaerobic sequencing batch biofilm pilot-scale reactor

This paper presents the results from 92 cycles of an anaerobic sequencing batch biofilm reactor containing biomass immobilized on inert support (mineral coal) applied for the treatment of an industrial wastewater containing high sulfate concentration. The pilot-scale reactor, with a total volume of 1.2 m(3), was operated at sulfate loading rates ranging from 0.15 to 1.90 kgSO(4)(2-)/cycle (48 It - cycle) corresponding to sulfate concentrations of 0.25 to 3.0 gSO(4)(2-) l(-1). Domestic sewage and ethanol were utilized as electron donors for sulfate reduction. Influent sulfate concentrations were increased in order to evaluate the minimum COD/sulfate ratio at which high reactor performance could be maintained. The mean sulfate removal efficiency remained between the range of 88 to 92% at several sulfate concentrations. Temporal profiles along the 48 h cycles were carried out under stable operation at sulfate concentrations of 1.0, 2.0 and 3.0 gSO(4)(2-) l(-1). Sulfate removal reached 99% for cycle times of 15, 25, and 30 h, and the effluents sulfate concentrations were lower than 8 mgSO(4)(2-) l(-1). The results demonstrate the potential applicability of the anaerobic configuration for the biological treatment of sulfate-rich wastewaters. (C) 2009 Elsevier B.V. All rights reserved.

Bioremediation of gasoline-contaminated groundwater in a pilot-scale packed-bed anaerobic reactor

This work reports on the anaerobic treatment of gasoline-contaminated groundwater in a pilot-scale horizontal-flow anaerobic immobilized biomass reactor inoculated with a methanogenic consortium. BTEX removal rates varied from 59 to 80%, with a COD removal efficiency of 95% during the 70 days of in situ trial. BTEX removal was presumably carried out by microbial syntrophic interactions, and at the observed concentrations, the interactions among the aromatic compounds may have enhanced overall biodegradation rates by allowing microbial growth instead of co-inhibiting biodegradation. There is enough evidence to support the conclusion that the pilot-scale reactor responded similarly to the lab-scale experiments previously reported for this design. (C) 2009 Elsevier Ltd. All rights reserved.

Buckling and post-buckling of extensible rods revisited: A multiple-scale solution

An exact non-linear formulation of the equilibrium of elastic prismatic rods subjected to compression and planar bending is presented, electing as primary displacement variable the cross-section rotations and taking into account the axis extensibility. Such a formulation proves to be sufficiently general to encompass any boundary condition. The evaluation of critical loads for the five classical Euler buckling cases is pursued, allowing for the assessment of the axis extensibility effect. From the quantitative viewpoint, it is seen that such an influence is negligible for very slender bars, but it dramatically increases as the slenderness ratio decreases. From the qualitative viewpoint, its effect is that there are not infinite critical loads, as foreseen by the classical inextensible theory. The method of multiple (spatial) scales is used to survey the post-buckling regime for the five classical Euler buckling cases, with remarkable success, since very small deviations were observed with respect to results obtained via numerical integration of the exact equation of equilibrium, even when loads much higher than the critical ones were considered. Although known beforehand that such classical Euler buckling cases are imperfection insensitive, the effect of load offsets were also looked at, thus showing that the formulation is sufficiently general to accommodate this sort of analysis. (c) 2008 Elsevier Ltd. All rights reserved.

Hybrid and multi-field variational principles for geometrically exact three-dimensional beams

This paper addresses the development of several alternative novel hybrid/multi-field variational formulations of the geometrically exact three-dimensional elastostatic beam boundary-value problem. In the framework of the complementary energy-based formulations, a Legendre transformation is used to introduce the complementary energy density in the variational statements as a function of stresses only. The corresponding variational principles are shown to feature stationarity within the framework of the boundary-value problem. Both weak and linearized weak forms of the principles are presented. The main features of the principles are highlighted, giving special emphasis to their relationships from both theoretical and computational standpoints. (C) 2010 Elsevier Ltd. All rights reserved.

Planning and operation of large-scale water distribution systems with preemptive priorities

This paper describes the development of an optimization model for the management and operation of a large-scale, multireservoir water supply distribution system with preemptive priorities. The model considers multiobjectives and hedging rules. During periods of drought, when water supply is insufficient to meet the planned demand, appropriate rationing factors are applied to reduce water supply. In this paper, a water distribution system is formulated as a network and solved by the GAMS modeling system for mathematical programming and optimization. A user-friendly interface is developed to facilitate the manipulation of data and to generate graphs and tables for decision makers. The optimization model and its interface form a decision support system (DSS), which can be used to configure a water distribution system to facilitate capacity expansion and reliability studies. Several examples are presented to demonstrate the utility and versatility of the developed DSS under different supply and demand scenarios, including applications to one of the largest water supply systems in the world, the Sao Paulo Metropolitan Area Water Supply Distribution System in Brazil.

A comparison of the critical impeller speed for solids suspension in a bench-scale and a pilot-scale mechanical flotation cell

This paper compares the critical impeller speed results for 6 L Denver and Wemco bench-scale flotation cells with findings from a study by Van der Westhuizen and Deglon [Van der Westhuizen, A.P., Deglon, D.A., 2007. Evaluation of solids suspension in a pilot-scale mechanical flotation cell: the critical impeller speed. Minerals Engineering 20,233-240; Van der Westhuizen, A.P., Deglon, D.A., 2008. Solids suspension in a pilot scale mechanical flotation cell: a critical impeller speed correlation. Minerals Engineering 21, 621-629] conducted in a 125 L Batequip flotation cell. Understanding solids suspension has become increasingly important due to dramatic increases in flotation cell sizes. The critical impeller speed is commonly used to indicate the effectiveness of solids suspension. The minerals used in this study were apatite, quartz and hematite. The critical impeller speed was found to be strongly dependent on particle size, solids density and air flow rate, with solids concentration having a lesser influence. Liquid viscosity was found to have a negligible effect. The general Zwietering-type critical impeller speed correlation developed by Van der Westhuizen and Deglon [Van der Westhuizen, A.P., Deglon, D.A., 2008. Solids suspension in a pilot scale mechanical flotation cell: a critical impeller speed correlation. Minerals Engineering 21, 621-629] was found to be applicable to all three flotation machines. The exponents for particle size, solids concentration and liquid viscosity were equivalent for all three cells. The exponent for solids density was found to be less significant than that obtained by the previous authors, and to be consistent with values reported in the general literature for stirred tanks. Finally, a new dimensionless critical impeller speed correlation is proposed where the particle size is divided by the impeller diameter. This modified equation generally predicts the experimental measurements well, with most predictions within 10% of the experimental. (C) 2009 Elsevier Ltd. All rights reserved.

Recycling Krylov subspaces for efficient large-scale electrical impedance tomography

Electrical impedance tomography (EIT) captures images of internal features of a body. Electrodes are attached to the boundary of the body, low intensity alternating currents are applied, and the resulting electric potentials are measured. Then, based on the measurements, an estimation algorithm obtains the three-dimensional internal admittivity distribution that corresponds to the image. One of the main goals of medical EIT is to achieve high resolution and an accurate result at low computational cost. However, when the finite element method (FEM) is employed and the corresponding mesh is refined to increase resolution and accuracy, the computational cost increases substantially, especially in the estimation of absolute admittivity distributions. Therefore, we consider in this work a fast iterative solver for the forward problem, which was previously reported in the context of structural optimization. We propose several improvements to this solver to increase its performance in the EIT context. The solver is based on the recycling of approximate invariant subspaces, and it is applied to reduce the EIT computation time for a constant and high resolution finite element mesh. In addition, we consider a powerful preconditioner and provide a detailed pseudocode for the improved iterative solver. The numerical results show the effectiveness of our approach: the proposed algorithm is faster than the preconditioned conjugate gradient (CG) algorithm. The results also show that even on a standard PC without parallelization, a high mesh resolution (more than 150,000 degrees of freedom) can be used for image estimation at a relatively low computational cost. (C) 2010 Elsevier B.V. All rights reserved.