Discontinuous Source Research Articles

New Membranes for Redox Flow Batteries Based on Heteropoly Acid-Polymer Composites

Redox flow batteries (RFBs) remain one of the most promising technologies that are actively explored for grid-scale energy storage from discontinuous power sources such as wind and solar.[1] Proliferation of RFB technology has resulted in a need for continued development and understanding of new redox couples and improved separator membranes for RFB operation, while reducing cost. Membranes employed in RFB technology are largely comprised of the perfluorosulfonic acid (PFSA) family (e.g. Nafion, Aquivion, and 3M PFSA) which own their functionality to the phase separated structure composed of ionically conductive hydrophilic domains distributed within an inert and mechanically stable hydrophobic matrix.[2] PFSA membranes are also susceptible to high crossover of redox active species, leading to parasitic losses in capacity that can only be solved by the development of highly selective separator membranes. In this work, we report our progress in developing membranes that exhibit high selectivity by employing heteropoly acid (HPA) ion conductors that have been covalently tethered to the backbone of a polymer support. HPA-loaded membranes are promising due to the highly mobile protons associated with the HPA molecule[3] alongside the hydrophobic polymer that provides mechanical strength that is capable of preventing crossover. PFSA membranes were used as a baseline to access the quality of the newly developed HPA-loaded membranes by measuring the selectivity which involves measurement of the membrane conductivity and permeability. The HPA-loading was varied on a mass base in order to evaluate the trade-offs between increased membrane conductivity, which tends to occur with increased permeability of redox active species. Selected membranes were subjected to cell testing in a RFB based on the iron-hydrogen to gauge cell performance.

A gradient recovery–based adaptive finite element method for convection‐diffusion‐reaction equations on surfaces

SummaryIn this paper, we present an adaptive mesh refinement method for solving convection‐diffusion‐reaction equations on surfaces, which is a fundamental subproblem in many models for simulating the transport of substances on biological films and solid surfaces. The method considered is a combination of well‐known techniques: the surface finite element method, streamline diffusion stabilization, and the gradient recovery–based Zienkiewicz‐Zhu error estimator. The streamline diffusion method overcomes the instability issue of the finite element method for the dominance of the convection. The gradient recovery–based adaptive mesh refinement strategy enables the method to provide high‐resolution numerical solutions by relatively fewer degrees of freedom. Moreover, the implementation detail of a surface mesh refinement technique is presented. Various numerical examples, including the convection‐dominated diffusion problems with large variations of solutions, nearly singular solutions, discontinuous sources, and internal layers on surfaces, are presented to demonstrate the efficacy and accuracy of the proposed method.

Robin boundary value problems for a singularly perturbed weakly coupled system of convection–diffusion equations having discontinuous source term

In this paper, we consider a weakly coupled system of convection–diffusion equations subject to Robin boundary conditions, and having boundary and interior layers. The diffusion term of each equation is multiplied by a small singular perturbation parameter, but these parameters are assumed to be different in magnitude, and the source term is having a discontinuity at a point in the interior of the domain. An upwind scheme is used for the considered problem in conjunction with piecewise uniform Shishkin mesh. It is proved that the numerical approximations produced by this method are almost first order uniformly convergent with respect to both small parameters. Numerical results are presented to validate the theoretical results.

Hybridizable Discontinuous Galerkin Method Contrast Source Inversion of 2-D and 3-D Dielectric and Magnetic Targets

We present a microwave imaging algorithm capable of simultaneously reconstructing electric and magnetic targets from both electric and magnetic field measurement data, with support for arbitrary imaging system boundaries and inhomogeneous background media. A high-order time-harmonic discontinuous Galerkin method (DGM) forward solver is adopted within a contrast source inversion (CSI) algorithm formulated for electric and magnetic targets. Due to its high-order capabilities, the DGM forward solver effectively decouples the contrast and field discretizations without introducing a dual mesh. The drawback of standard DGM forward solvers, namely, their high computational cost, is addressed by a hybridizable DGM (HDGM) formulation. Synthetic and experimental results for both DGM-CSI and HDGM-CSI are presented for a variety of 2-D and 3-D measurement configurations and both dielectric and magnetic targets. HDGM-CSI is shown to have imaging performance comparable to FEM-CSI for dielectric targets, and significant additional flexibility that will enable future electromagnetic imaging applications and system design.

Asymptotic Stability of a Stationary Solution of a Multidimensional Reaction–Diffusion Equation with a Discontinuous Source

A two-dimensional reaction–diffusion equation in a medium with discontinuous characteristics is considered; the existence, local uniqueness, and asymptotic stability of its stationary solution, which has a large gradient at the interface, is proved. This paper continues the authors’ works concerning the existence and stability of solutions with internal transition layers of boundary value problems with discontinuous terms to multidimensional problems. The proof of the existence and stability of a solution is based on the method of upper and lower solutions. The methods of analysis proposed in this paper can be generalized to equations of arbitrary dimension of the spatial variables, as well as to more complex problems, e.g., problems for systems of equations. The results of this work can be used to develop numerical algorithms for solving stiff problems with discontinuous coefficients.

Solute transport model for groundwater contamination in Wadi Bani Malik, Jeddah, Saudi Arabia

Groundwater is susceptible to pollutants. Contamination occurs when human products such as gasoline, oil, and sewage get into the groundwater and cause it to become unsafe for human use. In the last 15 years, Wadi Bani Malik has become a highly polluted area due to the disposal of sewage water in the Al-Musk area. This area has been subjected to environmental hazards, and the groundwater is the most vulnerable to the pollution. The degree of pollution can be determined from the analysis of arsenic (As). In this investigation, solute transport modeling is conducted using the finite difference method implicitly with the backward in time and center space (BTCS) technique. The model solution is in good agreement with the analytical solution. More importantly, when the model is compared with the observed As samples, it shows a strong correlation > 0.8. The model predicts the movement of the contaminants in the groundwater beginning from the starting day of installation of the land fill, showing that the plume will only travel about 16–20 km in 40 years. By that time, less than about 30% of the concentration in groundwater will be subjected to decay (diluted). However, it is difficult to fully explain the real concentration rate of change in the Al-Musk area towards the groundwater because between 2000 and 2011, the pollution was considered as a continuous source, but after that, the disposal of sewage in Al-Musk Lake has mainly stopped. So, the behavior of the lake is now defined as a discontinuous point source function.

Thermal energy storage for waste heat recovery in the steelworks: The case study of the REslag project

This work attempts to find a technological solution for heat recovery from the exhaust gases at high temperature exiting in the electric arc furnace of a steelmaking plant. A thermal energy storage system based on a dual-media packed bed is proposed as low-cost and suitable technology, using a by-product produced in the same plant, the steel slag, as filler material. The main objective of this system is to achieve a continuous heat supply from the inherent batch operation of the steel furnace. This implementation strategy presents great advantages. Among them, the added value of a continuous heat source can be highlighted as it opens a wide number of applications for the recovered heat, not accessible for discontinuous sources. The obtained results have revealed the large pressure drop values induced by the packed bed as the critical design parameter. This phenomenon is associated to the large amount of released energy from the furnace, together with the short times for its capture and storage. Besides, the influence of the idle period, inherent to the batch operation of the furnace has also been investigated. In this case, the short time of static operation together with the thermal stratification behavior have demonstrated the negligible impact of this idle period in the thermal energy storage unit operation. Finally, the research carried out has shown that, after an appropriate optimization process, efficiency values above 65% and 85% could be achieved for the cycle and filler material usage, respectively. These values show the great waste recovery potential of the proposed solution. It should be noted that, the definition of the design and operation parameters of a demonstration plant, to be constructed in a steelwork, is the final target of the presented work.

An Inductor-Less, Discontinuous Current Source Gate Driver for SiC Devices

EMI has remained a limiting factor in driving the SiC MOSFETs to its maximum potential and achieving a trade-off between EMI and switching losses is a major challenge for the designers. In this paper, an inductor-less, discontinuous current source gate driver (DCSD) is proposed. Exclusion of inductor results in a compact footprint and easy integration in IC form. The absence of predriver for proposed DCSD reduces the complexity of the driver, making it easier to control and implement. In addition, very low propagation delay is attained with the proposed DCSD which allows SiC MOSFETs to switch at higher switching frequencies with low losses. The proposed DCSD is compared with a commercially available reference gate driver for SiC MOSFET, and the results are analyzed and validated with hardware prototype. A better trade-off between switching losses and EMI is obtained with the proposed driver, where during turn-off, a 65% reduction in $dV_{ds}/dt$ and 45% reduction in $dI_{d}/dt$ is achieved at the cost of 33% increase in the total switching loss.

A New Parareal Algorithm for Problems with Discontinuous Sources

The Parareal algorithm allows to solve evolution problems exploiting parallelization in time. Its convergence and stability have been proved under the assumption of regular (smooth) inputs. We present and analyze here a new Parareal algorithm for ordinary differential equations which involve discontinuous right-hand sides. Such situations occur in various applications, e.g., when an electric device is supplied with a pulse-width-modulated signal. Our new Parareal algorithm uses a smooth input for the coarse problem with reduced dynamics. We derive error estimates that show how the input reduction influences the overall convergence rate of the algorithm. We support our theoretical results by numerical experiments, and also test our new Parareal algorithm in an eddy current simulation of an induction machine.

具有不连续源项的二阶半线性系统边值问题的奇摄动

具有不连续源项的二阶半线性系统边值问题的奇摄动

Domain decomposition methods with fundamental solutions for Helmholtz problems with discontinuous source terms

The direct application of the classical method of fundamental solutions (MFS) is restricted to homogeneous linear partial differential equations (PDEs). The use of fundamental solutions with different frequencies allowed the extension of the MFS to non-homogeneous PDEs, in particular, for Poisson or Helmholtz equations and for elastostatic or elastodynamic problems. This method has been called method of fundamental solutions for domains (MFS-D), but it faces an approximation problem when the non-homogeneous term presents discontinuities, because the fundamental solutions are analytic functions outside the source point set. In this paper we analyze two domain decomposition techniques for overcoming this approximation problem. The problem is set in the context of the modified Helmholtz equation, and we also establish the missing density results that justify both the MFS and the MFS-D approximations. Numerical results are presented comparing a direct and an iterative domain decomposition technique, with simulations in non-trivial domains.

Parameter-uniform convergence of a numerical method for a coupled system of singularly perturbed semilinear reaction–diffusion equations with boundary and interior layers

In this paper, we consider a coupled system of m ( ≥ 2 ) singularly perturbed semilinear reaction–diffusion equations with a discontinuous source term having a discontinuity at a point in the interior of the domain. The diffusion term of each equation is multiplied by small singular perturbation parameter, but these parameters are assumed to be different in magnitude. A numerical method is constructed on a variant of Shishkin mesh. The approximations generated by this method are shown to be almost second order uniformly convergent with respect to all perturbation parameters. Numerical results are in support of the theoretical results. • A coupled system of m ( ≥ 2 ) singularly perturbed semilinear reaction-diffusion equations is considered. • The source term is having a discontinuity at a point in the interior of the domain. • The diffusion term of each equation is multiplied by a small perturbation parameter. • All the perturbation parameters are different in magnitude. • The constructed numerical method has almost second parameter uniform convergence.

Towards a Harmonized Odour Guideline for Some Austrian Provinces

Currently some provinces in Austria attempt to set up a harmonized regulation for assessing odour nuisance. The Austrian laws do not stipulate that any nuisance is to be prevented, but only “unacceptable” nuisance. “Unacceptable” is not a scientific or medical term but needs to be interpreted in a legal context. In the new guideline different odour impact criteria (OIC) are set up with regard to the hedonic tone of odours. For each category a maximally allowed frequency is defined. Frequencies are to be assessed on the total number of hours of a year, where the computed 90th percentile within one hour is above a certain threshold concentration (e.g. 1 odour unit [ou] per m³). Such is termed an odour hour. Dispersion modelling is the major methodology for odour assessments. Unlike in Germany, no specific model is prescribed, but model developers need to prove the capability of their model to accurately simulate the 90th percentile odour concentration of an hour. For instance, the Lagrangian particle model GRAL, which is frequently used in Austria, offers a new module to compute the 90th percentile based on the work of Oettl and Ferrero (2017a). The 90th percentile is thereby a function of the three dimensional odour-concentration field and the atmospheric turbulence, thus, the model is able to take into account the effects of overlapping odour plumes, too. It could be demonstrated that modelled odour-hour frequencies using this novel approach are in very good agreement with observed odour hours assessed by field inspections following the new European standard EN 16841-1. Field inspections, therefore, may also be used for odour assessment, whenever modelling is not possible (e.g. unknown source strengths). OICs are derived upon dose-response relationships, which were established by evaluating historical citizen’s complaints using the dispersion model GRAL. Relationships between the percentage of annoyed residents and modelled odour-hour frequencies were found to be quite different for odorants having a very high potential of offensiveness and such with a moderate potential. Discontinuous odour sources are assessed by using OICs based on the 0.5th percentile evaluated for concentrations larger than 1 ou m-3. The corresponding concentration thresholds for the four distinguished hedonic tones were derived by matching the affected non-attainment areas resulting from the regulations for continuous sources with those resulting from the 0.5th percentile regulation.

Unified formulation of the momentum-weighted interpolation for collocated variable arrangements

Momentum-weighted interpolation (MWI) is a widely used discretisation method to prevent pressure–velocity decoupling in simulations of incompressible and low Mach number flows on meshes with a collocated variable arrangement. Despite its popularity, a unified and consistent formulation of the MWI is not available at present. In this work, a discretisation procedure is devised following an in-depth analysis of the individual terms of the MWI, derived from physically consistent arguments, based on which a unified formulation of the MWI for flows on structured and unstructured meshes is proposed, including extensions for discontinuous source terms in the momentum equations as well as discontinuous changes of density. As shown by the presented analysis and numerical results, the MWI enforces a low-pass filter on the pressure field, which suppresses oscillatory solutions. Furthermore, the numerical dissipation of kinetic energy introduced by the MWI is shown to converge with third order in space and is independent of the time-step, if the MWI is derived consistently from the momentum equations. In the presence of source terms, the low-pass filter on the pressure field can be shaped by a careful choice of the interpolation coefficients to ensure the filter only acts on the driving pressure gradient that is associated with the fluid motion, which is shown to be vitally important for the accuracy of the numerical solution. To this end, a force-balanced discretisation of the source terms is proposed, that precisely matches the discretisation of the pressure gradients and preserves the force applied to the flow. Using representative test cases of incompressible and low Mach number flows, including flows with discontinuous source terms and two-phase flows with large density ratios, the newly proposed formulation of the MWI is favourably compared against existing formulations and is shown to significantly reduce, or even eliminate, solution errors, with an increased stability for flows with large density ratios.

Influence of the Supporting Electrolyte on the Structure-Transport Properties of PFSA Membranes for Redox Flow Batteries

Redox flow batteries (RFBs) are poised at becoming one of the most promising technologies that are being explored for grid-scale energy storage from discontinuous power sources such as wind and solar.[1] This has resulted in a need for continued development and understanding of new redox couples and their supporting electrolyte counterparts, as well as improving membranes for RFB operation while reducing cost. Membranes employed in RFB technology are largely comprised of the perfluorosulfonic acid (PFSA) family (e.g. Nafion, Aquivion, and 3M PFSA) which exhibit different material properties depending on the surrounding environment, such as transport properties.[2] The structure-property relationships of PFSAs are well-known and studied,[3] providing the initial framework for our understanding; however, much of this work has been performed in either vapor or liquid water. Thus, it is of interest to elucidate how the structure and transport properties of PFSAs change in various electrolytes used in RFBs. In this work, we discuss our progress in linking the electrolyte concentration-dependent nanostructure to the transport of ions in PFSA membranes. Sulfuric acid and hydrochloric acid represent the majority of supporting electrolytes used in RFB applications and are therefore the primary focus of this study. The polymer’s nanostructure in electrolytes is analyzed using small angle X-ray scattering (SAXS) in-situ, in order to understand the influence of the type and concentration of the supporting electrolytes on the characteristic morphological features of the membrane. Then, nanostructural information is linked to the ion transport through the membrane, via conductivity. Linking the conductivity and polymer morphology provides a better understanding of the structure-transport relationships of PFSAs in electrolytes, and their implications for membrane performance in a RFB cell. Perry, M.L. and A.Z. Weber, Advanced Redox-Flow Batteries: A Perspective. Journal of the Electrochemical Society, 2016. 163(1): p. A5064-A5067.Tang, Z., et al., Composition and Conductivity of Membranes Equilibrated with Solutions of Sulfuric Acid and Vanadyl Sulfate. Journal of the Electrochemical Society, 2013. 160(9): p. F1040-F1047.Kusoglu, A. and A.Z. Weber, New Insights into Perfluorinated Sulfonic-Acid Ionomers. Chem Rev, 2017. 117(3): p. 987-1104.

2D well-balanced augmented ADER schemes for the Shallow Water Equations with bed elevation and extension to the rotating frame

In this work, an arbitrary order augmented WENO-ADER scheme for the resolution of the 2D Shallow Water Equations (SWE) with geometric source term is presented and its application to other shallow water models involving non-geometric sources is explored. This scheme is based in the 1D Augmented Roe Linearized-ADER (ARL-ADER) scheme, presented by the authors in a previous work and motivated by a suitable compromise between accuracy and computational cost. It can be regarded as an arbitrary order version of the Augmented Roe solver, which accounts for the contribution of continuous and discontinuous geometric source terms at cell interfaces in the resolution of the Derivative Riemann Problem (DRP). The main novelty of this work is the extension of the ARL-ADER scheme to 2 dimensions, which involves the design of a particular procedure for the integration of the source term with arbitrary order that ensures an exact balance between flux fluctuations and sources. This procedure makes the scheme preserve equilibrium solutions with machine precision and capture the transient waves accurately. The scheme is applied to the SWE with bed variation and is extended to handle non-geometric source terms such as the Coriolis source term. When considering the SWE with bed variation and Coriolis, the most relevant equilibrium states are the still water at rest and the geostrophic equilibrium. The traditional well-balanced property is extended to satisfy the geostrophic equilibrium. This is achieved by means of a geometric reinterpretation of the Coriolis source term. By doing this, the formulation of the source terms is unified leading to a single geometric source regarded as an apparent topography. The numerical scheme is tested for a broad variety of situations, including some cases where the first order scheme ruins the solution.

Excitation of electromagnetic waves by a discontinuous electric line source

The radiation process of electromagnetic waves is investigated when a discontinuity on an electric line source is created. Three cases are taken into account. In the first case, an abrupt discontinuity is formed on the antenna geometry. The edge discontinuity of the line source is excluded from space as the second case. The third situation considers the isolation of the continuous part of the antenna. The excitation of current and charge densities are studied for the two situations. The magnetic vector and electric scalar potentials are evaluated from the sources and the electric and magnetic fields are obtained. Computational MATLAB simulations are given for the behaviors of the radiated electromagnetic waves in free space.

A new reconstruction method for a parabolic inverse source problem

ABSTRACTIn this paper, we focus on the detection of the shape and location of a discontinuous source term from the knowledge of boundary measurements. We propose a non-iterative reconstruction algorithm based on the Kohn-Vogelius formulation and the topological sensitivity analysis method. The inverse source problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from an energy-like cost function. The unknown shape of the term source support is reconstructed using a level-set curve of the topological gradient. The efficiency of our algorithm is illustrated by some numerical simulations.

Probing the Size-Exclusion Properties of Redox Flow Battery Separator Membranes Using Metal-Ligand Complexes

Redox flow batteries (RFBs) are among one of the most promising technologies being explored for grid-scale energy storage from discontinuous power sources such as wind and solar.1 This has resulted in a need for continued development and understanding of electrolytes and membranes employed in RFBs as a means of improving performance while reducing cost. New approaches in membrane design rely on size-exclusion to reduce parasitic losses resulting from water and electrolyte crossover that presently plagues ionomer membranes within the perfluorosulfonic acid (PFSA) family (e.g. Nafion, Aquivion, and 3M PFSA).2 The structure-property relationships of PFSAs are well-known and studied,3 providing the initial framework for utilization of ligands to understand transport through next-generation membranes. In this work, we discuss our efforts in developing a systematic approach towards probing the effective size-exclusion properties of the polymeric membranes by employing iron-ligand complexes. A series of aminopolycarboxylic acid ligands, shown in Figure 1, that strongly complex with iron were selected to explore the effect of molecule size on crossover in PFSAs with varying domain sizes, controlled via side chain length. We show decreases in permeability with increased size of the iron-ligand complex, providing information regarding the hydrophilic domain network of these ionomer membranes. By measuring the crossover of these complexes using diffusion cells, we explore the size-exclusion properties of PFSAs using relevant molecules for future iron RFB applications. Acknowledgements This work was funded as a sub-contract under the Integration and Optimization of Novel Ion-Conducting Solids program (IONICS), by the Advanced Research Projects Agency-Energy (ARPA-E), of the US Department of Energy under award number DE-AR0000773. Perry, M. L.; Weber, A. Z., Advanced Redox-Flow Batteries: A Perspective. J Electrochem Soc 2016, 163 (1), A5064-A5067.Darling, R.; Gallagher, K.; Xie, W.; Su, L.; Brushett, F., Transport Property Requirements for Flow Battery Separators. J Electrochem Soc 2015, 163 (1), A5029-A5040.Kusoglu, A.; Weber, A. Z., New Insights into Perfluorinated Sulfonic-Acid Ionomers. Chem Rev 2017, 117 (3), 987-1104. Figure 1

Assessment of the effects of discontinuous sources of contamination through biomarker analyses on caged mussels

The present study analysed potential adverse effects of discontinuous sources of contamination, namely the discharge of a combined sewer overflow (CSO) and of runoff in an urban area, the Bay of Santander (North Iberian Peninsula). Water samples and caged mussels were used to analyse concentrations of contaminants and biological responses. Mussels (Mytilus galloprovincialis) were transplanted to a marina receiving runoff from a petrol station and to a CSO discharge site. Samples were collected in synchrony with heavy rains along 62days. Lysosomal membrane stability (LMS) and acyl-CoA oxidase (AOX) activity were measured as core biomarkers and were analysed at all sampling times. Histopathology of digestive gland and gonads, transcription levels of vitellogenin gene, volume density of black silver deposits and micronuclei formation were measured at initial and final stages of the transplant. Chemical analyses of metals, polycyclic aromatic hydrocarbons (PAHs) and endocrine disruptors were performed in water samples and mussel flesh. Mussels accumulated low concentrations of contaminants, which is in accordance with results obtained from exposure biomarkers. AOX activity decreased in all transplanted mussels after the first heavy rain, but this change seems to be related to the seasonal pattern of the enzyme activity. Mussels located close to the CSO discharge site showed a reduction in LMS after the first rain event, when compared to mussels before the transplant and to mussels from the reference location. However, this was attributable to natural environmental changes rather than to pollution. Values of the rest of analysed biomarkers were below threshold values reported for the study area.