Modeling Fluid Flow in the Gas Diffusion Layers in PEMFC Using the Multiple Relaxation‐time Lattice Boltzmann Method

The gas diffusion layers (GDLs) are key components in proton exchange membrane fuel cells and understanding fluid flow through them plays a significant role in improving fuel cell performance. In this paper we used a combination of multiple‐relaxation time lattice Boltzmann method and imaging technology to simulate fluid flow through the void space in a carbon paper GDL. The micro‐structures of the GDL were obtained by digitizing 3D images acquired by X‐ray computed micro‐tomography at a resolution of 1.76 μm, and fluid flow through the structures was simulated by applying pressure gradient in both through‐plane and in‐plane directions, respectively. The simulated velocity field at micron scale was then used to estimate the anisotropic permeability of the GDL. To test the method, we simulated fluid flow in a column packed with glass beads and the estimated permeability was found to be in good agreement with experimental measurements. The simulated results for the GDL revealed that the increase of permeability with porosity was well fitted by the model of Tomadakis–Sotirchos [48] without fitting parameters. The permeability calculated using fluids with different viscosities indicated that the multiple‐relaxation time lattice Boltzmann method provides robust solutions, giving a viscosity‐independent permeability. This is a significant improvement over the commonly used single‐time relaxation lattice Boltzmann model which was found to give rise to a unrealistic viscosity‐dependent permeability because of its inaccuracy in solving the fluid–solid boundaries.     

多孔介质内流体流动的格子Boltzmann模拟

采用格子Boltzmann方法模拟多孔介质内的流动过程,通过预测渗透率,比较了单松弛模型、多松弛模型和熵格子模型在多孔介质计算中的优劣,为研究多松弛模型中各自由参数的影响,选择了12种组合进行模拟,此外,还将大涡模拟与格子Boltzmann方法相结合模拟了多孔介质内高Reynolds数下的流动及流型的转变。结果表明：单松弛模型和熵格子模型预测的渗透率随黏度逐渐增大,而多松弛模型得到的结果随黏度变化很小,另外,多松弛模型中不同松弛参数的组合对结果有较大的影响,通过比较推荐了模拟多孔介质时的最佳组合,计算结果与经验公式吻合较好。大涡模拟与多松弛模型结合较好地预测了多孔介质内流型的转变,Reynolds数越大,多孔介质内的涡越多,并且变大。     

基于格子Boltzmann方法的单颗粒绕流数值模拟

采用格子Boltzmann方法（LBM）研究了单颗粒绕流流动过程。通过使用LBM中的LBGK（lattice Bhatnagar-Gross-Krook）模型和二阶精度的曲线边界条件处理方法，实现了对单颗粒绕流问题的定常及非定常流动过程中涡结构的模拟。采用动量交换法分别计算了Reynolds数在0.1～200范围内27个不同Reynolds数时的曳力系数，并将计算结果拟合得到基于LBM数值模拟的曳力曲线。计算结果表明，LBM在气固两相流的模拟计算中具有精确、可靠的优点，使用LBM模拟计算曳力曲线的方法经济、易行，并且可以克服由传统实验方法获得曳力曲线的局限性。     

格子波尔兹曼方法模拟外掠圆管的流动与换热

运用格子波尔兹曼方法(LBM)对流体外掠圆管的流动和换热进行了数值模拟,分析了不同雷诺数下流场和温度场的分布特点,并将Re为0.8时中心线速度分布的模拟结果以及Re为34时y方向上速度分布的模拟结果与Oseen理论解和实验数据分别进行了对比,具有很好的吻合度。此外,对曲面边界提出了固体内部节点选取方法,节点温度差分数值求解方法,使模拟方法具有良好的数值稳定性和精确性。数值计算结果表明格子波尔兹曼方法能有效模拟外掠圆管流体流动现象。     

Multiscale model for solid oxide fuel cell with electrode containing mixed conducting material

Solid oxide fuel cells (SOFCs) with electrodes that contain mixed conducting materials usually show very different relationships among microstructure parameters, effective electrode characteristics, and detailed working processes from conventional ones. A new multiscale model for SOFCs using mixed conducting materials, such as LSCF or BSCF, was developed. It consisted of a generalized percolation micromodel to obtain the electrode properties from microstructure parameters and a multiphysics single cell model to relate these properties to performance details. Various constraint relationships between the activation overpotential expressions and electric boundaries for SOFC models were collected by analyzing the local electrochemical equilibrium. Finally, taking a typical LSCF‐SDC/SDC/Ni‐SDC intermediate temperature SOFC as an example, the application of the multiscale model was illustrated. The accuracy of the models was verified by fitting 25 experimental I‐V curves reported in literature with a few adjustable parameters; additionally, and several conclusions were drawn from the analysis of simulation results. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3786–3803, 2015     

不可压热流体中气体传质扩散过程的数值模拟

控制流体流动中溶解的气体分子浓度能有效控制流动过程中的化学反应,而由热产生的自然对流能够加强气体分子的传递,因此研究气体分子在热流体流动中的扩散混合过程有重要意义。应用格子Boltzmann方法,耦合热效应和扩散效应,数值模拟了一个简化的容器中随着自然对流的发展,溶解的氧气分子在整个容器中的扩散过程。首先建立了二维9速模型的双扩散模型来模拟热量和质量的双扩散对流。为了考察不同自然对流流动对气体分子传递的影响,设计了3种不同给热条件,对不同热流动的形成过程和气体分子扩散过程进行了模拟,与文献结果吻合良好。通过详细分析热边界如何影响流动和传质过程,证实了模拟的速度场与文献数据差异的合理性,同时为控制气体传质过程提供给热条件的设计依据。     

耦合格子Boltzmann的聚合物结晶相场方法

在模拟枝晶生长的相场方法上,耦合多松弛格式的格子Boltzmann方法,建立了相场-格子动力学耦合模型,对聚合物结晶过程中出现的枝晶生长形貌进行了数值模拟。耦合模型规避了传统相场法需要高分辨率场精确解决固液界面的难点,其中高精确的解析度会严重影响时间步长的选取。运用LBM方法,提出了一种自适应的时间步长计算方法,允许在改变时间步长的同时不需要相应地改变网格大小,时间步长允许设置得较大而数值模拟结果不会出现发散现象,也避免了高精度差分格式的使用。使用FORTRAN语言对相场-格子动力学耦合模型进行了求解,通过对聚合物等规聚苯乙烯结晶的数值模拟,研究了在不同实验温度下等规聚苯乙烯晶体的数值模拟形貌,并与实验结果进行了比较,验证了模型的有效性。     

REV尺度多孔介质格子Boltzmann方法的数学模型及应用的研究进展

综述了多孔介质表征体元尺度(REV)格子Boltzmann模型的研究进展,根据对多孔介质处理方式主要分为部分反弹模型和阻力模型两类,分析归纳了各类模型的优缺点。由于阻力模型中渗流的广义格子Boltzmann方程(GLBE)的作用力是基于GUO等的作用力模型,可以准确得到宏观方程,不存在离散误差,且模型的平衡分布函数和作用力项中都包含反应介质特性的孔隙率,因而应用最为广泛。本文还重点介绍了REV尺度多孔介质LBE模型在流动、传热、传质、化学反应及相变等过程中的具体应用,认为REV尺度多孔介质内的三传一反数学模型中需要加入孔隙尺度因素,在更大工程尺度上应该考虑过程参数的各向异性,展望了REV尺度多孔介质LBE模型的发展和应用前景。     

The Use of Methane‐Containing Syngas in a Solid Oxide Fuel Cell: A Comparison of Kinetic Models and a Performance Evaluation

The nickel‐based anodes of solid oxide fuel cells (SOFCs) can catalytically reform hydrocarbons, which make natural gas, gasification syngas, etc., become potential fuels in addition to hydrogen. SR and water–gas shift (WGS) often occur inside SOFCs when operated on these fuels. Their reaction rates affect the partial pressures of hydrogen and carbon monoxide, the local temperatures and the related Nernst voltages. Consequently, the reaction rates affect the electrochemical reactions in the fuel cell. Three different kinetic models were used to characterize methane SR in a tubular SOFC; the results of each model were evaluated and compared. The polarizations of the fuel cell results of these models were validated against experimental data. The performance of a fuel cell operated with different fuels and based on a selected kinetic model was further studied in terms of the anode oxygen partial pressure, the thermo‐electrochemical distribution, and the system level performance.     

Validation of Simulation and Mass Transfer Coefficient Prediction with Interfacial Convection

Investigation of interfacial mass transfer by means of numerical simulation is a promising field. In the present work, the Rayleigh convection of the CO₂‐ethanol absorption process was simulated using a random‐disturbance model based on the lattice Boltzmann method and the results were compared with the Schlieren observation for validation. It was found that the simulation method was superior for capturing the characteristics of the absorption process. A correlation was then proposed to predict the mass transfer coefficient based on Reynolds mass flux, scalar fluctuation variance, and its dissipation rate, and the correlation was found to be superior to existing methods in terms of phase difference. In this correlation, the mass transfer coefficient was linked with computational mass transfer for the first time.     

基于格子Boltzmann方法模拟纳米流体强化传质过程

使用Boltzmann方法对纳米流体中的传质过程进行了模拟,给出了修改后的Boltzmann方程和计算纳米流体中扩散系数的方程,通过两种方法,基于有限体积颗粒的LBE方法和基于点源颗粒的LBE方法进行了模拟,并与宣益民的实验进行了对比。最后计算了CO2在纳米流体中的扩散系数,计算结果表明,纳米流体因为其纳米颗粒的微扰动对传质有着很大的强化效果,为CO2吸收提供了一种新思路,并且证明了纳米流体的强化传质主要是靠对流传质。     

Advances in modelling of biomimetic fluid flow at different scales

The biomimetic flow at different scales has been discussed at length. The need of looking into the biological surfaces and morphologies and both geometrical and physical similarities to imitate the technological products and processes has been emphasized. The complex fluid flow and heat transfer problems, the fluid-interface and the physics involved at multiscale and macro-, meso-, micro- and nano-scales have been discussed. The flow and heat transfer simulation is done by various CFD solvers including Navier-Stokes and energy equations, lattice Boltzmann method and molecular dynamics method. Combined continuum-molecular dynamics method is also reviewed.     

基于格子Boltzmann方法的封闭三角腔自然对流的数值模拟

建立了二维不可压缩D2G9格子Boltzmann模型,耦合二维TD2Q5热格子Boltzmann模型,在非平衡态外推的边界条件下,首先对不同Eckert数(Ec)和Prandtl数(Pr)时Couette流的温度场进行数值模拟,计算结果与解析解吻合良好,且在Ec变化很大的条件下,计算结果仍与解析解相符,验证了模型的准确性和稳定性. 然后对封闭三角空腔内不同Rayleigh数(Ra)下的自然对流流场和温度场进行了数值模拟,结果与文献计算值吻合良好,说明格子Boltzmann方法的TD2Q5热模型可用于高Ra时的空腔热流动模拟.     

Computational Studies for the Evaluation of Fuel Flexibility in Solid Oxide Fuel Cells: A Case with Biosyngas

The fuel flexibility of solid oxide fuel cells (SOFCs) is one of the advantages of this technology, and biosyngas produced from biomass is emerging as a new fuel. The fuelling of SOFCs with different fuels is always challenging because of the associated risks. Mathematical modeling tools are useful for predicting the operational safety constraints and designs of SOFCs that are suitable for different fuels. Using a single channel model that incorporates direct internal reforming (DIR), this work investigates the fuel flexibility of an anode‐supported intermediate temperature planar solid oxide fuel under co‐flow operation. The DIR reaction of methane, the water‐gas shift reaction (WGS) and the electrochemical reaction of hydrogen are the three reactions taken into account in this simulation work. Detailed comparisons of the gas concentrations, the current density distributions and the temperature change profiles are presented and discussed. These simulation results provide the initial data for performance analyses and safety predictions, which will be helpful for our future experimental investigations. The thermodynamic predictions of both nickel oxidation and carbon deposition are employed to check the operational safety of SOFCs fuelled with biosyngas.     

Investigation of the accuracy of the extrapolation method for the lattice Boltzmann simulation of viscous fluid flow in a Maxblend impeller system

This paper offers a thorough assessment on the performance of the extrapolation method for the lattice Boltzmann simulation of viscous mixing flows. This method appears to be well-suited for the treatment of the complex boundary conditions found in various mixing systems. Here, the ability to simulate accurate power consumption and pumping capacity is evaluated on several configurations of the Maxblend mixing system, which has proven efficient in a wide range of applications. First, the impact of the boundary conditions on the spatial convergence of the lattice Boltzmann method (LBM) is determined on the 3D Couette flow, clearly showing that small modifications of the boundary conditions may reduce the accuracy of the predicted shear rate and power. Second, a parallel LBM scheme was used to simulate fluid flow within a Maxblend mixing system. For the unbaffled configuration, the simulated power consumption and the pumping capacity are observed to be in good agreement with experimental data and finite element simulation results. The effect of the bottom clearance is also successfully evaluated, suggesting that the standard bottom clearance is not optimum in the transitional regime. Lastly, results for the most geometrically complex case (baffled configuration) indicate that the power consumption is affected by numerical perturbations appearing around the moving impeller. Overall, these results show that, when combined with the extrapolation method for the treatment of boundary conditions, the LBM is an efficient tool for the investigation of viscous flow in mixers of industrial relevance.     

Energy and drying time optimization of convective drying: Taguchi and LBM methods

In this study, a novel method for numerical simulation of drying is proposed and the process is optimized by Taguchi method. A 2D numerical solution is performed to analyze coupled heat and mass transfer occurring during drying of a rectangular moist object. The dryer section and the moist object are conjugately simulated where the coupled heat and mass transfer equations are solved together. The lattice Boltzmann method is employed to solve hydrodynamic, heat, and mass transfer equations. This study applied the Taguchi method to determine optimum conditions for drying so as to minimize the drying time and energy consumption. The control factors included temperature, air velocity, and thickness ratio (the moist object thickness to channel width). The following optimal conditions were obtained: temperature (T?=?60?°C), velocity (V?=?0.1 m/s), and thickness ratio (TR =0.1). The results of numerical solution are then compared to the measured data available in the literature, presenting a reasonable agreement.     

Three‐Dimensional Computational Fluid Dynamics Modeling of a Planar Solid Oxide Fuel Cell

A three‐dimensional computational fluid dynamics model was developed to study the performance of a planar solid oxide fuel cell (SOFC). The governing equations were solved with the finite volume method. The model was validated by comparing the simulation results with data from literature. Parametric simulations were performed to investigate the coupled heat/mass transfer and electrochemical reactions in a planar SOFC. Different from previous two‐dimensional studies the present three‐dimensional analyses revealed that the current density was higher at the center along the flow channel while lower under the interconnect ribs, due to slower diffusion of gas species under the ribs. The effects of inlet gas flow rate and electrode porosity on SOFC performance were examined as well. The analyses provide a better understanding of the working mechanisms of SOFCs. The model can serve as a useful tool for SOFC design optimization.     

Solid oxide fuel cells in combination with biomass gasification for electric power generation

Biomass, a source of renewable energy, represents an effective substitute to fossil fuels. Gasification is a process that organics are thermochemically converted into valuable gaseous products(e.g. biogas). In this work, the catalytic test demonstrated that the biogas produced from biomass gasification mainly consists of H_2,CH_4, CO,and CO_2, which were then be used as the fuel for solid oxide fuel cell(SOFC). Planar SOFCs were fabricated and adopted. The steam reforming of biogas was carried out at the anode of a SOFC to obtain a hydrogen-rich fuel.The performance of the SOFCs operating on generated biogas was investigated by I–V polarization and electrochemical impedance spectra characterizations. An excellent cell performance was obtained, for example,the peak power density of the SOFC reached 1391 mW·cm~(-2) at 750℃ when the generated biogas was used as the fuel. Furthermore, the SOFC fuelled by simulated biogas delivered a very stable operation.     

气液两相分离的免方程多尺度模拟方法

提出了一种用于模拟气液两相分离过程的免方程多尺度方法, 该方法以格子Boltzmann(LB)模型作为介观仿真器, LB模型进行少量演化步后运用二阶伸缩式投影方法对介观仿真器演化得到的结果进行有效的外推处理, 能够快速准确地获取后续演化步的结果, 从而实现对气液两相分离过程的多尺度模拟研究。对气液分离过程中饱和密度曲线和模型产生的伪速度大小的对比分析表明所提出的多尺度模拟方法能够快速准确地反映气液两相分离过程的宏观特性, 证明了所提方法的准确性和高效性。     

Film percolation for composite electrodes of solid oxide fuel cells

A film percolation model is proposed for composite electrodes of solid oxide fuel cells (SOFCs). The model is developed to predict the percolation properties of 2D-infinite structures which represent the structural characteristics of composite electrodes of electrochemical devices such as SOFCs. The model can be used to estimate electrode properties, such as percolation probability, active three-phase boundary length and interfacial polarization resistance. Compared with the classic percolation theory, which is particularly applicable to 3D-infinite bulks, the model can explicitly capture the effects of thinly layered nature of composite electrodes, and describes a cross-over between 2D-infinite films and 3D-infinite bulks. It also permits the prediction within whole electrode composition range, and can be easily applied in SOFC modeling.