Channel shape optimization of solid oxide fuel cells using advanced numerical techniques

Shape optimization of fuel channels in solid oxide fuel cells (SOFC) is presented. A three-dimensional, implicit, multi-species fuel cell solver is developed to compute the baseline solution. Sensitivity derivatives required for the optimization are computed using the discrete adjoint method. A gradient-based optimizer is utilized to update the design variables. The geometry of the fuel channel is parameterized to obtain meaningful design variables using a recently developed technique that is applicable for multi-disciplinary design optimization. During the design process, the mesh is continually modified to reflect the changes in the underlying geometry. An automated environment to sequentially execute the aforementioned processes is developed. Cost functions representating the cell voltage and uniform distribution of fuel among all channels are optimized with respect to the shape of the fuel channels.     

Data-driven predictive control for solid oxide fuel cells

This paper is concerned with predictive control of solid oxide fuel cells (SOFC) based on a benchmark model commonly studied in the dynamic SOFC modeling/control literature. It has been shown in previous studies that control of SOFC is challenging owing to the slow response and tight operating constraints. In this paper, we apply a data-driven predictive control approach to solving the control problem of the SOFC system. The predictive control applied is completely data based. In addition, unlike other data-driven predictive control designs, the proposed approach can deal with systems without complete on-line measurement of all output variables. Simulation results have demonstrated the feasibility of the control application.     

Feedforward based transient control in solid oxide fuel cells

In SOFCs, transient control of fuel utilization is achievable via input-shaping. In this paper, the approach is generalized to a feedforward control problem for second-order LTI systems with two inputs and one output. One is a measurable, time-varying, exogenous input and the other is a control input. The problem studied is exact tracking of a constant reference using the plant's DC gain vector. The problem considers plant models that can be divided into known and unknown parts, and where feedback is unavailable. Although SOFCs have nonlinear dynamics, the linear abstraction nevertheless helps predict the observed effectiveness of input-shaping.     

Mathematical modeling and steady-state analysis of a proton-conducting solid oxide fuel cell

This paper presents a study of mathematical modeling and steady-state analysis of a proton-conducting solid oxide fuel cell (SOFC). The SOFC has a SrCe_0.95Yb_0.05O_3?α (SCY) electrolyte and two platinum electrodes. A mathematical model of the SOFC is first developed. The model captures electrochemical processes as well as the transport phenomena. The existence of steady-state multiplicity in the cell under three modes of constant ohmic load, potentiostatic and galvanostatic operations is studied. Simulation results show that a multiple steady-states region exists at low inlet fuel and air temperatures under constant ohmic load and potentiostatic operations. The occurrence of ignition and extinction in the cell solid (electrolyte, anode and cathode) temperature is reported. This result is in agreement with those for oxygen ion-conducting solid oxide fuel cells in which the existence of steady-state multiplicity has been attributed to the dependence of the electrolyte oxygen-ion conductivity on temperature. This work shows that concentration and temperature multiplicities coexist.     

两种固体氧化物燃料电池系统的故障建模与仿真对比研究

固体氧化物燃料电池(SOFC)系统的建模方式较多,而基于机理模型的故障诊断是能够通过系统的动态趋势辨别故障的有效手段之一,但该方法对机理模型的准确性有要求.此外,不同的燃料供给系统采用的系统结构也是有差异的,进而导致在相同故障下SOFC系统的动态响应也是不同的.因此,本文基于两种燃料供应方式,提出了分别以纯氢气和天然气作为燃料的SOFC系统结构,并基于原有机理知识进行MATLAB/Simulink系统建模.经与真实SOFC系统实验对比,搭建的系统模型能够有效模拟系统在无故障状态下的动态变化;另外,在无故障模型的基础上,分别加入两类常见故障,其一为风机故障,其二为燃料供应管路泄露.最后通过仿真分析,明确了所搭建模型的合理性,且发现了两种燃料供应对SOFC系统热响应特性是不同的,对SOFC系统故障的检测和设备选型具有重要意义.     

An adaptive non-linear observer for the estimation of temperature distribution in the planar solid oxide fuel cell

Minimising the thermal gradients is extremely important in a planar solid oxide fuel cell (SOFC) for improving the cell life. The estimation of the temperature distribution in the cell is necessary to achieve this objective through suitable control, since they are not generally measurable. In this work, we have designed a non-linear adaptive observer for estimating the temperatures inside the hydrogen fed planar SOFC. The observer design is based on a lumped parameter model of the SOFC. The stability of the proposed observer is proven using the Lyapunov function method and is based on the concept of input-to-state stability for cascaded systems. The simulations show that the developed observer can track the temperature and species concentration profiles in the planar SOFC during step changes in the cell current. The adaptive observer presented is valid for a wide operating range, requires fewer variables to be measured, and is robust to fluctuations in the inlet flows.     

CUIRRE: An open-source library for load balancing and characterizing irregular applications on GPUs

While Graphics Processing Units (GPUs) show high performance for problems with regular structures, they do not perform well for irregular tasks due to the mismatches between irregular problem structures and SIMD-like GPU architectures. In this paper, we introduce a new library, CUIRRE, for improving performance of irregular applications on GPUs. CUIRRE reduces the load imbalance of GPU threads resulting from irregular loop structures. In addition, CUIRRE can characterize irregular applications for their irregularity, thread granularity and GPU utilization. We employ this library to characterize and optimize both synthetic and real-world applications. The experimental results show that a 1.63× on average and up to 2.76× performance improvement can be achieved with the centralized task pool approach in the library at a 4.57% average overhead with static loading ratios. To avoid the cost of exhaustive searches of loading ratios, an adaptive loading ratio method is proposed to derive appropriate loading ratios for different inputs automatically at runtime. Our task pool approach outperforms other load balancing schemes such as the task stealing method and the persistent threads method. The CUIRRE library can easily be applied on many other irregular problems.     

Dynamic modeling,simulation, and MIMO predictive control of a tubular solid oxide fuel cell

Solid oxide fuel cells are a promising option for distributed energy stationary power generation that offers efficiencies up to 50% in stand-alone applications, 70% in hybrid gas turbine applications and 80% in cogeneration. To advance SOFC technology sufficiently for widespread market penetration, the SOFC must demonstrate improved cell lifetime from the status quo. Much research has been performed to improve SOFC lifetime using advanced geometries and materials, and in this research, we suggest further improving lifetime by designing an advanced control algorithm based upon preexisting mechanical stress analysis [1]. Control algorithms commonly address SOFC lifetime related operability objectives using unconstrained, SISO control algorithms that seek to minimize thermal transients. While thermal fatigue may be one thermal stress driver, these studies often do not consider maximum radial thermal gradients or critical absolute temperatures in the SOFC. In addition, researchers often discuss hot-spots as a critical lifetime reliability issue, but as previous stress work demonstrates, the minimum cell temperature is the primary thermal stress driver in tubular SOFCs modeled after the Siemens Power Generation, Inc. design. In this work, we present a dynamic, quasi-two-dimensional model for a high-temperature tubular SOFC combined with ejector and prereformer models. The model captures dynamics of critical thermal stress drivers and is used as the physical plant for closed-loop simulations with a constrained, MIMO model predictive control algorithm. Closed-loop simulation results demonstrate effective load-following, operability constraint satisfaction, and disturbance rejection.     

An improved numerical process for solution of solid mechanics problems

This paper gives an overview of the development and status of an improved numerical process for the solution of solid mechanics problems. The proposed process uses a mixed formulation with the fundamental unknowns consisting of both stress and displacement parameters. The problem is formulated either by means of first-order partial differential equations or in a variational form by using a Hellinger-Reissner-type mixed variational principle.

For presentation purposes, the components of a numerical process are characterized and the criteria for an ideal process are outlined. Commonly used finite-difference and finite-element procedures arc examined in the light of these criteria and it is shown that they fall short in a number of ways. The proposed numerical process, on the other hand, satisfies most of the optimality criteria and appears to be particularly suited for use with the forthcoming generation computers (e.g. STAR-100 computer).

The paper includes a number of examples showing application of the proposed process to a broad spectrum of solid mechanics problems. These examples demonstrate the versatility and high accuracy of the numerical process obtained by using mixed formulations in conjunction with improved discretization techniques.     

A 2D model for shape optimization of solid oxide fuel cell cathodes

A topology optimization method is used to identify the optimal shape of the nano-composite cathode of a solid oxide fuel cell (SOFC). A simplified analysis model is used in computations aimed at reducing ohmic losses by optimizing the shape of the cathode to minimize resistance. The model of the SOFC is reduced to a periodic, 2D conduction problem with design-dependent ionic transfer boundary conditions. Special techniques are introduced to avoid physically inadmissible designs that would otherwise be allowed by the 2D model. Isoperimetric constraints on the perimeter and the amount of material are used in the problem. Numerical examples are provided to discuss the effect of material properties and the resource restrictions introduced by the constraints. The methodology discussed can be applied to similar problems involving design-dependent boundary conditions.     

Measurement of thermodynamic activity of zirconia in yttria-stabilized zirconia electrolyte for solid oxide fuel cell application

The Knudsen effusion mass spectrometry technique was applied to determine the activity of ZrO₂ in 8 mol% yttria-stabilized zirconia (8YSZ) in the temperature range from 2200 K to 2500 K. The minor ZrO₂⁺ ion current was used in calculations instead of the prevailing ZrO⁺ signal. The phase stability of the samples and their negligible interaction with the cell material was proved by XRD-analysis. The activity of ZrO₂ was obtained to be 0.84 ± 0.04 independent of temperature. This fact allows estimating the same value of activity in the operating temperature range of solid oxide fuel cells (SOFCs).     

固体氧化物燃料电池温度特性的T-S模糊建模

固体氧化物燃料电池（SOFC）工作温度对于其输出电特性的性能起着重要的作用。由于电池在电化学反应过程中,温度特性呈现强非线性等特性,采用常规机理建模后难以在该模型的基础上较好地管理温度特性。为此,设计了面向控制的改进型T-S模型的模糊建模方法来解决此难题。实验仿真结果表明该模糊模型能精确拟合温度动态响应的映射特性,为下一步控制算法的实现奠定了良好的基础。     

An object-oriented approach to the solid modeling of empirical data

An object-oriented approach to the construction, manipulation, and display of complex geometric models of oil reservoirs is described. The authors have extended the traditional constructive solid geometry modeling techniques to accommodate the requirements for reservoir models. Both the user interface and the model building are implemented in Strobe, an object-oriented extension to Interlisp. The geometric model is specified through a CSG-graph editor built using an object-oriented toolkit for graphical interfaces. This editor proves to be an invaluable tool with which to build, maintain and manipulate large, complicated geometric models     

Control‐oriented fault detection of solid oxide fuel cell system unknown input on fuel supply

As the solid oxide fuel cell (SOFC) system work environment is a high‐temperature environment for a long time, it is difficult to obtain the SOFC stack internal state change directly. When the fault occurs, it is difficult to determine where the fault occurs. Moreover, the existing literature ignores the impact of faults, which creates many problems for SOFC system control. Therefore, a state observer‐based fault detection method, which is used to detect the input flow sensor fault and the fuel input fault, is proposed. Their advantage is that they do not need data processing. To realize the fault detection, the observer is used to track the changes of SOFC stack chamber temperature. To obtain the observer estimation parameter, an approach from the actual stack structure parameters is employed to approximate the observer parameters. The results show the proposed fault detect method can judge fuel input fault type quickly and shield the disturbances signals from the sensor effectively. The proposed method also can be used to other operating points or air input fault.     

Fragmentation of numerical algorithms for parallel subroutines library

Fragmentation is a well-known method of the parallelization of numerical algorithms and programs. Algorithm fragmentation allows creating fragmented parallel programs that can be executed on parallel computers of different types (multiprocessors and/or multicomputers) and can be dynamically tuned to all the available resources. Fragmentation of the often used numerical algorithms, their representation for inclusion into the library of parallel numerical subroutines and properties of the runtime system are considered.     

An application of algebraic topology to solid modeling in molecular biology

A recurring problem in solid modeling, computer graphics, and molecular modeling is the computation of the intersection of two objects. A general solution to this problem is obtained by applying two ideas of algebraic topology: (1) a chain complex, and (2) a boundary formula for the intersection of two objects. A general data structure for a chain complex made up of piecewise polynomial cells is described, as are algorithms for connectivity, containment and intersection. The basic ideas of this work are abstract, topological, and for the most part, independent of the shape and dimensionality of the objects. An application to structural molecular biology is presented. The application identifies convex and concave features of protein surfaces.     

Optimization and control of a stand-alone hybrid solid oxide fuel cells/gas turbine system coupled with dry reforming of methane

This paper presents the hybrid solid oxide fuel cells (SOFC)/gas turbine (GT) system coupled with dry reforming of methane (DRM). The DRM is a syngas producer by consuming greenhouse gas. The stand-alone (off-the-grid) power system is developed by using a combination of a post-burner, recuperators and pressurized recycles in place of external energy supplies. To address the stand-alone operation and meet the complete combustion condition for the burner, the optimal operating conditions are initially determined by solving a constrained optimization algorithm for maximizing the hybrid power efficiency, and the dynamic control loops are implemented in a plantwide environment. In the proposed plantwide control strategy, the inventory control framework is added to regulate the plant component inventory, an air/fuel cross-limiting combustion control is added to ensure complete combustion and reduce heat loss, and the power and CO₂ emission control configuration is added to achieve the quality control performance. Finally, the simulation shows that the IMC-based multi-loop control scheme can efficiently regulate the total system power and control CO₂ emissions per kWh of electricity as well.     

QuTiP: An open-source Python framework for the dynamics of open quantum systems

We present an object-oriented open-source framework for solving the dynamics of open quantum systems written in Python. Arbitrary Hamiltonians, including time-dependent systems, may be built up from operators and states defined by a quantum object class, and then passed on to a choice of master equation or Monte Carlo solvers. We give an overview of the basic structure for the framework before detailing the numerical simulation of open system dynamics. Several examples are given to illustrate the build up to a complete calculation. Finally, we measure the performance of our library against that of current implementations. The framework described here is particularly well suited to the fields of quantum optics, superconducting circuit devices, nanomechanics, and trapped ions, while also being ideal for use in classroom instruction.Program summaryProgram title: QuTiP: The Quantum Toolbox in PythonCatalogue identifier: AEMB_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEMB_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 16 482No. of bytes in distributed program, including test data, etc.: 213 438Distribution format: tar.gzProgramming language: PythonComputer: i386, x86-64Operating system: Linux, Mac OSX, WindowsRAM: 2+ GigabytesClassification: 7External routines: NumPy (http://numpy.scipy.org/), SciPy (http://www.scipy.org/), Matplotlib (http://matplotlib.sourceforge.net/)Nature of problem: Dynamics of open quantum systems.Solution method: Numerical solutions to Lindblad master equation or Monte Carlo wave function method.Restrictions: Problems must meet the criteria for using the master equation in Lindblad form.Running time: A few seconds up to several tens of minutes, depending on size of underlying Hilbert space.