本研究是對質子交換膜燃料電池建立二維之數學模式和實驗方法來分析電池之起動與加速性能，數值方法以有限元素分析法求解所建立之多重耦合非線性偏微分方程式。其中，燃料電池之方程式包含描述流體在多孔性薄膜的擴散層及觸媒層裡流動的Brinkman equation及兩極與交換膜之間電場反應的Charge equation，並使用在擴散及觸媒層裡因需要混合擴散係數而產生的Stefan-Maxwell組成方程式來表達組成之濃度變化。
本文之研究目的為先將流場採用逆向流和平行流去分析並討論其中的差異，選擇出性能較佳且較適合本研究之流場然後在啟動與加速過程裡以不同溫度、壓力和入口速度下實作與數值預測質子交換膜燃料電池的特性。並探討燃料電池啟動與加速過程內之濃度場與速度場分佈，以及在啟動與加速之瞬間電壓降與濃度、陰極與陽極之電流、與交換膜之間的影響。啟動前，因進入之燃料幾乎為零，而電流也跟著毫無變化；啟動瞬間，濃度瞬間加入；加速之後，系統已為穩態狀態，因此電流隨著不同的電壓穩定的輸出。
主要的結果為雖然平行流在流場有較好的溼潤度相較之下可以延長電池的壽命，但逆向流可以得到較佳的性能。在啟動與加速過程裡，較低的操作溫度(50℃)可以得到最大的電流密度和電壓降，假如操作溫度超過80℃時，則電池的膜可能會受損。而氣體進出口的壓力愈大所得到的電流密度和電壓降也相對的上昇，燃料入口速度愈大所得到的電池性能也相對的上昇。統合以上的結果可觀察到提昇背壓對燃料電池起動及加速有最顯著的影響，這可以成為日後在設計燃料電池上的參考。

This research is to build two-dimensional mathematical models and to conduct experiments, and to analyze the performance of transient condition of the proton exchange membrane fuel cell. In this model the finite element analytic method was used to solve the coupling multiple nonlinear partial differential equations. Equations of the fuel cell contain Brinkman equation describing fluid between the porosity thin film diffusion and the catalyst layers, and charge equation for the electric field response of the two-pole and the exchange membrane. Besides, the Stefan-Maxwell species equation resulted from the mixed diffusion coefficient that the process in the diffusion and catalyst layers needs is used to express specie concentration variations.
The research purpose of this article is to build a model where the flow field uses alternately the counter flow and parallel flow, and to discuss which one fits in this case and has better performance. Then predict the performance of the proton exchange membrane fuel cell in the start-up and the step-up process under different temperatures , pressures and inlet velocities. The concentration and velocity distributions as well as the instantaneous drop of voltage and the cathode and anode electric current and their variations between exchange membrane are also investigated in fuel cell start-up and step-up process. Before the start-up, the electric current is not changed due to the none of entering fuel; when started-up instantaneously, the concentration instantaneously joins. After the start-up, the system was already the stable state condition, and then electric current output is stable.
The main result is that parallel flow can get wetter so as to lengthen the life of the cell, but counter flow can get better performance. The fuel cell operating at the lower temperature(50℃) produces the highest electric current and drop of voltage. If it operated at over 80℃, the PEM of fuel cell might be hurt. The higher the pressure in the inlet and outlet is, the higher the electric current and drop of voltage become. And so is velocity, the higher the velocity in the fuel inlet is, the better performance can be gotten. Above all the result, increasing back pressure is the most obvious influence in start-up and step-up process of PEMFC. It can be an experience on the design a PEMFC in the future.

參考文獻

[1] 林昇佃、余子隆、張幼珍等，”燃料電池~新世紀能源”，滄海書局，2004。
[2] 黃鎮江，”燃料電池”，全華科技圖書股份有限公司，2003。
[3] Berning Torsten，”Three-Dimensional Computational Analysis of Transport Phenomena in a PEM Fuel Cell，1997.
[4] J. Larminie and A. Dicks，”Fuel Cell System Explained”，Wiley，Chichestwr，2000.
[5] A.J. Appleby and F. R. Foulkes，”Fuel Cell Handbook”，Krieger Publishing Company，Florida，1993.
[6] T.E. Springer，T. A. Zawodzinski and S. Gottesfeld，”Polymer Electrolyte Fuel Cell Model”，J. ectrochem. Society, 138(8): 334-2342， 1991.
[7] 顏維謀，”CFD在PEM燃料電池設計上之應用”，華梵大學機電工程學系，2004。
[8] Sergio Leonardo Garcia，”A Contribution to The Understanding of a PEM Fuel Cell Transient Model ”，Department of Electrical and Computer Engineering University of TORONTO，2001.
[9] Jay T. Pukrushpan，”Simulation and analysis of transient fuel cell system performance based on a dynamic reactant flow model”， American Society of Mechanical Engineers, Dynamic Systems and Control Division (Publication) DSC, p 637-648, 2002.
[10] Daniel B. Genevey，” Transient model of heat, mass, and charge transfer as well as electrochemistry in the cathode catalyst layer of a PEMFC”， American Society of Mechanical Engineers, Advanced Energy Systems Division (Publication) AES, v 42, 2002, p 393-406.
[11] 涂正輝，”質子交換膜燃料電池之三維流道設計與熱質傳分析 ”，國立成功大學機械研究所，2003。
[12] M. Grujicic，”Control of the transient behavior of polymer electrolyte membrane fuel cell systems”， Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, v 218, n 11, November, p 1239-1250, 2004.
[13] Helqe Weydahl，” Transient response of a proton exchange membrane fuel cell”， Meeting Abstracts, 2004 Joint International Meeting - 206th Meeting of the Electrochemical Society/2004 Fall Meeting of the Electrochemical Society of Japan, MA 2004-02, p 1980, 2004.
[14] Fang Ye，”Membrane and cathode catalyst layer numerical simulation of PEMFCs”，Kung Cheng Je Wu Li Hsueh Pao/Journal of Engineering Thermophysics, v 25, n 5, September, p 846-848, 2004.
[15] 邱冠銘，”質子交換膜燃料電池之暫態性能分析 ”，國立成功大學系統及船舶機電研究所，2006。
[16] P.R.Pathapati , X.Xue and J.Tang，” A new dynamic model for predicting transient phenomena in a PEM fuel cell system”，Renewable Energy，2006.
[17] 羅琨航，”質子交換膜單電池之輸送參數之實驗研究”，中華大學機械與航太工程研究所，2001。
[18] J.O’M Bockris and S. Srinivasan. Fuel Cells: Their Electrochemistry. McGrawHill，New York. 1969.
[19] J.J. Hwang，” Thermal-Electrochemical Modeling of a Proton Exchange Membrane Fuel Cell”，The Electrochemical Society，2005.
[20] M.F.Serincan and S.Yesilyurt，” Transient Analysis of Proton Electrolyte Membrane Fuel Cells (PEMFC) at Start-Up and Failure”，Fuel Cells，2006.
[21] A.Schmitz，C.Ziegler，J.O.Schumacher，M.Tranitz,E.Fontes and C.Hebling，” Modelling Approach for Planar Self-Breathing PEMFC and Comparison with Experimental Results”，Fuel Cells，2004.
[22] ” Chemical Engineering Module Model Library，COMSOL，2005.
[23] 顏維謀，”入口氣體濕度對二為質子交換膜燃料電池性能之影響”， 華梵大學機電工程學系，2004。
[24] 洪翊軒，”燃料電池系統性能提升之技術”， 智慧車輛與動力技術專輯，2005。
[25] ADRIAN Bejan，”Convection Heat Transfer”，Department of Mechanical Engineering and Materials Science Duke University，1984。
[26] 黃煥勝，”PEM燃料電池之組裝與性能測試”，中華大學機械與航太工程研究所，2000。
[27] J.J. Hwang，C.K. Chen，R.F. Savinell，C.C. Liu and J.Wainright，”A three-dimensional numerical simulation of the transport phenomena in the cathodic side of a PEMFC ”，Journal of Applied Electrochemistry，2004.
[28] J.A. Kolde，B. Bahar，M.S. Wilson，T.A. Zawodzinski and S. Gottesfeld，”Advanced Composite Polymer Electrolyte Fuel Cell Membranes”， Proc.Electrochem.Society,23:193-201，1995.
[29] R.E. De La Rue and C.W. Tobias. “On the Conductivity of Dispersions”. J. Electrochem. Soc.，106:827-836，1959.
[30] A. Greenbaum，”Iterative Methods for Linear Systems”，Frontiers in Applied Mathematics 17，SIAM，1997.
[31] Y. Sadd and M. H. Schultz，”GMRES:A generalized minimal residual algorithm for solving nonsystemmetric linear systems”，SIAM J. Sci. Statist. Comput.，7，PP.856-869，1986.