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大功率质子交换膜燃料电池电堆膜电极一致性研究

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化工学报 2024年第2期75卷 637-646页

作者：陈宏江坤唐廷江黄易元池滨廖世军华南理工大学化学与化工学院广东广州510641 深圳市雄韬电源科技股份有限公司广东深圳518120 广东云韬氢能科技有限公司广东广州510080

随着燃料电池应用领域的拓宽以及应用规模的不断扩大,大功率燃料电池电堆的需求也不断上升。大功率燃料电池电堆的电压一致性是衡量或影响电堆性能的重要指标。对某公司生产的65 kW大功率电堆进行了单电池一致性的研究,考察不同运行条... 详细信息

随着燃料电池应用领域的拓宽以及应用规模的不断扩大,大功率燃料电池电堆的需求也不断上升。大功率燃料电池电堆的电压一致性是衡量或影响电堆性能的重要指标。对某公司生产的65 kW大功率电堆进行了单电池一致性的研究,考察不同运行条件对于电堆一致性的影响,并对其产生的可能原因进行了深入的研究和讨论。研究结果表明:在额定功率和给定的运行条件下,电堆表现出了较好的一致性;电堆输出功率、电堆温度和温差、反应气体计量比、气体湿度等对电堆膜电极一致性均有较大的影响。其中输出功率、空气计量比、气体湿度对于电堆一致性的影响最为强烈,输出功率增高、空气计量比和空气湿度降低均会大幅度降低电堆的一致性。在研究结果的基础上,提出了保持大功率燃料电池电堆一致性的运行条件的建议。可为改善大功率电堆的设计和优化大功率电堆的运行条件,及促进我国燃料电池技术及产业的发展提供参考。

关键词：质子交换膜燃料电池大功率电堆电压一致性运行条件影响

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A new non-perturbative approach in quantum mechanics for time-independent Schr?dinger equations

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Science China(Physics,Mechanics & Astronomy) 2020年第3期63卷 70-81页

作者： shijun liao Center of Advanced Computing School of Naval ArchitectureOcean and Civil EngineeringShanghai Jiao Tong UniversityShanghai 200240China School of Physics and Astronomy Shanghai Jiao Tong UniversityShanghai 200240China

A new non-perturbative approach is proposed to solve time-independent Schr?dinger equations in quantum *** is based on the homotopy analysis method(HAM)that was developed by the author in 1992 for highly nonlinear equations and has been widely applied in many *** perturbative methods,this HAM-based approach has nothing to do with small/large physical ***,convergent series solution can be obtained even if the disturbance is far from the known status.A nonlinear harmonic oscillator is used as an example to illustrate the validity of this approach for disturbances that might be one thousand times larger than the possible superior limit of the perturbative *** HAM-based approach could provide us rigorous theoretical results in quantum mechanics,which can be directly compared with experimental ***,this is of great benefit not only for improving the accuracy of experimental measurements but also for validating physical theories.

关键词： non-perturbative series homotopy analysis method quantum mechanics

NUMERICALLY SOLVING STRONGLY NONLINEAR PROBLEMS BY MEANS OF NO ITERATIONS

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Journal of Hydrodynamics 1998年第1期10卷 102-108页

作者： liao, shijun Shanghai Jiaotong Univ Shanghai China

Based on the Homotopy Analysis Method, a direct numerical method for strongly nonlinear problems was proposed. The 2-D laminar flow over semi-infinite plate was used. The method can give the accurate enough approximations of a strongly nonlinear problem by means of no iteration and can provide a family of iterative formulas with traditional approaches.

关键词： Iterative methods Laminar flow Nonlinear equations Numerical methods Viscous flow

Two kinds of peaked solitary waves of the KdV,BBM and Boussinesq equations

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Science China(Physics,Mechanics & Astronomy) 2012年第12期55卷 2469-2475页

作者： liao shijun Department of Mathematics&State Key Laboratory of Ocean Engineering School of Naval ArchitectureOcean and Civil EngineeringShanghai Jiao Tong UniversityShanghai 200240China

It is well-known that the celebrated Camassa-Holm equation has the peaked solitary waves,which have been not reported for other mainstream models of shallow water *** this letter,the closed-form solutions of peaked solitary waves of the KdV equation,the BBM equation and the Boussinesq equation are given for the first *** of them have either a peakon or an *** of them exactly satisfies the corresponding Rankine-Hogoniot jump condition and could be understood as weak ***,the peaked solitary waves might be common for most of shallow water wave models,no matter whether or not they are integrable and/or admit breaking-wave solutions.

关键词： solitary waves peaked crest progressive discontinuity weak solution

Clean numerical simulation:a new strategy to obtain reliable solutions of chaotic dynamic systems

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Applied Mathematics and Mechanics(English Edition) 2018年第11期39卷 1529-1546页

作者： Xiaoming LI shijun liao School of Naval Architecture Ocean and Civil EngineeringShanghai Jiao Tong UniversityShanghai 200240China State Key Laboratory of Ocean Engineering Shanghai 200240China Collaborative Innovative Center for Advanced Ship and Deep-Sea Exploration Shanghai 200240China Ministry-of-Education Key Laboratory of Scientific and Engineering Computing Shanghai 200240China

It is well-known that chaotic dynamic systems, e.g., three-body system and turbulent flow, have sensitive dependence on the initial conditions(SDIC). Unfortunately,numerical noises, i.e., truncation error and round-off error, always exist in practice. Thus,due to the SDIC, the long-term accurate prediction of chaotic dynamic systems is practically impossible. In this paper, a new strategy for chaotic dynamic systems, i.e., the clean numerical simulation(CNS), is briefly described, and applied to a few Hamiltonian chaotic systems. With negligible numerical noises, the CNS can provide convergent(reliable) chaotic trajectories in a long enough interval of time. This is very important for Hamiltonian systems, and thus should have many applications in various fields. It is found that the traditional numerical methods in double precision cannot give not only reliable trajectories but also reliable Fourier power spectra and autocorrelation functions(ACFs). In addition, even the statistic properties of chaotic systems cannot be correctly obtained by means of traditional numerical algorithms in double precision, as long as these statistics are time-dependent. The CNS results strongly suggest that one had better be very careful on the direct numerical simulation(DNS) results of statistically unsteady turbulent flows, although DNS results often agree well with experimental data when the turbulent flow is in a statistical stationary state.

关键词： chaos numerical noise clean numerical simulation(CNS) reliability of computation

Analytic approximations of Von Krmn plate under arbitrary uniform pressure—equations in integral form

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Science China(Physics,Mechanics & Astronomy) 2018年第1期61卷 57-67页

作者： XiaoXu Zhong shijun liao School of Naval Architecture Ocean and Civil Engineering Shanghai Jiao Tong University Collaborative Innovative Center for Advanced Ship and Deep-Sea Exploration State Key Laboratory of Ocean Engineering Ministry-of-Education Key Laboratory of Scientific and Engineering Computing

Analytic approximations of the Von Karman＇s plate equations in integral form for a circular plate under external uniform pressure to arbitrary magnitude are successfully obtained by means of the homotopy analysis method （HAM）, an analytic approximation technique for highly nonlinear problems. Two HAM-based approaches are proposed for either a given external uniform pressure Q or a given central deflection, respectively. Both of them are valid for uniform pressure to arbitrary magnitude by choosing proper values of the so-called convergence-control parameters c1 and c2 in the frame of the HAM. Besides, it is found that the HAM- based iteration approaches generally converge much faster than the interpolation iterative method. Furthermore, we prove that the interpolation iterative method is a special case of the first-order HAM iteration approach for a given external uniform pressure Q when c1= -0 and c2 = -1, where 0 denotes the interpolation iterative parameter. Therefore, according to the convergence theorem of Zheng and Zhou about the interpolation iterative method, the HAM-based approaches are valid for uniform pressure to arbitrary magnitude at least in the special case c1 = -0 and c2= -1. In addition, we prove that the HAM approach for the Von karman＇s plate equations in differential form is just a special case of the HAM for the Von karman＇s plate equations in integral form mentioned in this paper. All of these illustrate the validity and great potential of the HAM for highly nonlinear problems, and its superiority over perturbation techniques.

关键词： circular plate high nonlinearity homotopy analysis method

More than six hundred new families of Newtonian periodic planar collisionless three-body orbits

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Science China(Physics,Mechanics & Astronomy) 2017年第12期60卷 63-69页

作者： XiaoMing Li shijun liao School of Naval Architecture Ocean and Civil Engineering Shanghai Jiaotong University Shanghai 200240 China MoE Key Laboratory in Scientific and Engineering Computing Shanghai 200240 China

The famous three-body problem can be traced back to Isaac Newton in the 1680 s. In the 300 years since this "three-body problem"was first recognized, only three families of periodic solutions had been found, until 2013 when ˇSuvakov and Dmitraˇsinovi′c [***. Lett. 110, 114301(2013)] made a breakthrough to numerically find 13 new distinct periodic orbits, which belong to 11 new families of Newtonian planar three-body problem with equal mass and zero angular momentum. In this paper, we numerically obtain 695 families of Newtonian periodic planar collisionless orbits of three-body system with equal mass and zero angular momentum in case of initial conditions with isosceles collinear configuration, including the well-known figure-eight family found by Moore in 1993, the 11 families found by ˇSuvakov and Dmitraˇsinovi′c in 2013, and more than 600 new families that have never been reported, to the best of our knowledge. With the definition of the average period T = T=Lf, where Lf is the length of the so-called "free group element", these 695 families suggest that there should exist the quasi Kepler's third law T* ≈ 2:433 ± 0:075 for the considered case, where T*= T|E|^(3/2) is the scale-invariant average period and E is its total kinetic and potential energy,respectively. The movies of these 695 periodic orbits in the real space and the corresponding close curves on the "shape sphere"can be found via the website: http://***/three-body/***.

关键词： three-body problem periodic orbits clean numerical simulation(CNS)

On peaked solitary waves of the Degasperis-Procesi equation

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Science China(Physics,Mechanics & Astronomy) 2013年第2期56卷 418-422页

作者： liao shijun State Key Laboratory of Ocean Engineering Dept.of MathematicsSchool of Naval ArchitectureOcean and Civil EngineeringShanghai Jiao Tong University

The Degasperis-Procesi （DP） equation describing the propagation of shallow water waves contains a physical parameter co, and it is well-known that the DP equation admits solitary waves with a peaked crest when ω = 0. In this article, we illustrate, for the first time, that the DP equation admits peaked solitary waves even when ω≠ 0. This is helpful to enrich our knowledge and deepen our understandings about peaked solitary waves of the DP equation.

关键词： peaked solitary waves discontinuity Degasperis-Procesi equation

Avoiding Small Denominator Problems by Means of the Homotopy Analysis Method

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Advances in Applied Mathematics and Mechanics 2023年第2期15卷 267-299页

作者： shijun liao Center of Marine Numerical Experiment State Key Laboratory of Ocean EngineeringShanghai 200240China School of Naval Architecture Ocean and Civil EngineeringShanghai Jiaotong UniversityShanghai 200240China

The so-called“small denominator problem”was a fundamental problem of dynamics,as pointed out by Poincar´*** denominators appear most commonly in perturbative *** Duffing equation is the simplest example of a non-integrable system exhibiting all problems due to small *** this paper,using the forced Duffing equation as an example,we illustrate that the famous“small denominator problems”never appear if a non-perturbative approach based on the homotopy analysis method(HAM),namely“the method of directly defining inverse mapping”(MDDiM),is *** HAM-based MDDiM provides us great freedom to directly define the inverse operator of an undetermined linear operator so that all small denominators can be completely avoided and besides the convergent series of multiple limit-cycles of the forced Duffing equation with high nonlinearity are successfully ***,from the viewpoint of the HAM,the famous“small denominator problems”are only artifacts of perturbation ***,completely abandoning perturbation methods but using the HAM-based MDDiM,one would be never troubled by“small denominators”.The HAM-based MDDiM has general meanings in mathematics and thus can be used to attack many open problems related to the so-called“small denominators”.

关键词： Small denominator problem Duffing equation limit cycle homotopy analysis method(HAM) MDDiM