{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
Please cite us if you use the software
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Larminie-Dicks Static Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Version 1.4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Larminie-Dicks model is obtained for large variation of the load parameters. In this model, the fuel cell is represented by means of its voltage–current characteristic obtained in static operating mode. In fact, Larminie-Dicks static model presents the fuel cell voltage as a function of the current magnitude. The obtained polarization curve is composed of three main regions corresponding to the predominance of electrochemical activation phenomena (region I), a linear part (region II) where the voltage drop is mainly due to electronic and ionic internal resistances and the last region where the diffusion kinetics of gases through the electrodes becomes the limiting factor (region III). This last zone is characterized by a rapid voltage fall.\n", "It has to be noted that this curve is common to all fuel cells and consequently no units are depicted on it.\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fig1. Graphical Abstract of Static Models
\n", "$$Parameter$$ | \n", "$$Description$$ | \n", "$$Unit$$ | \n", "
$$V_0$$ | \n", "Intercept of the curve obtained by linear approximation | \n", "$$V$$ | \n", "
$$k$$ | \n", "Slope of the curve obtained by linear approximation | \n", "$$A^{-1}$$ | \n", "
$$P_{max}$$ | \n", "Maximum power obtained by linear approximation | \n", "$$W$$ | \n", "
$$V_{FC}|P_{max}$$ | \n", "Cell voltage at maximum power obtained by linear approximation | \n", "$$V$$ | \n", "
$$Parameter$$ | \n", "$$Description$$ | \n", "$$Unit$$ | \n", "
$$\\eta|P_{Max}$$ | \n", "Cell efficiency at maximum power | \n", "$$--$$ | \n", "
$$P_{Max}$$ | \n", "Maximum power | \n", "$$W$$ | \n", "
$$P_{Elec} $$ | \n", "Total electrical power | \n", "$$W$$ | \n", "
$$P_{Thermal} $$ | \n", "Total thermal power | \n", "$$W$$ | \n", "
$$V_{FC}|P_{Max}$$ | \n", "Cell voltage at maximum power | \n", "$$V$$ | \n", "
$$Parameter$$ | \n", "$$Description$$ | \n", "$$Unit$$ | \n", "$$Value$$ | \n", "
$$E_0$$ | \n", "Fuel cell reversible no loss voltage | \n", "$$V$$ | \n", "$$User$$ | \n", "
$$T$$ | \n", "Cell operation temperature | \n", "$$K$$ | \n", "$$User$$ | \n", "
$$A$$ | \n", "The slope of the Tafel line | \n", "$$V$$ | \n", "$$User$$ | \n", "
$$i_n$$ | \n", "Internal current | \n", "$$A$$ | \n", "$$User$$ | \n", "
$$i_0$$ | \n", "Exchange current at which the overvoltage begins to move\n", "from zero | \n", "$$A$$ | \n", "$$User$$ | \n", "
$$i_L$$ | \n", "Limiting current | \n", "$$A$$ | \n", "$$User$$ | \n", "
$$R_m$$ | \n", "The membrane and contact resistances | \n", "$$\\Omega$$ | \n", "$$User$$ | \n", "
$$N$$ | \n", "Number of single cells | \n", "$$--$$ | \n", "$$User$$ | \n", "
$$i_{start}$$ | \n", "Cell operating current start point | \n", "$$A$$ | \n", "$$User$$ | \n", "
$$i_{step}$$ | \n", "Cell operating current step | \n", "$$A$$ | \n", "$$User$$ | \n", "
$$i_{stop}$$ | \n", "Cell operating current end point | \n", "$$A$$ | \n", "$$User$$ | \n", "
$$B$$ | \n", "Constant in the mass transfer term | \n", "$$V$$ | \n", "$$System$$ | \n", "
$$R$$ | \n", "Universal gas constant | \n", "$$J.kmol^{-1}.K^{-1}$$ | \n", "$$8314.47$$ | \n", "
$$F$$ | \n", "Faraday’s constant | \n", "$$C.kmol^{-1}$$ | \n", "$$96484600$$ | \n", "
$$n$$ | \n", "Number of moles of electrons transferred in the balanced equation occurring in the fuel cell | \n", "$$--$$ | \n", "$$2$$ | \n", "
$$\\mu_F$$ | \n", "The fuel utilization | \n", "$$--$$ | \n", "$$0.95$$ | \n", "
$$HHV$$ | \n", "Higher heating value potential | \n", "$$V$$ | \n", "$$1.482$$ | \n", "
$$E_{th}$$ | \n", "Theoretical potential | \n", "$$V$$ | \n", "$$1.23$$ | \n", "
\n", "1-I. Sadli, P. Thounthong, J.-P. Martin, S. Rael, B. Davat. 2006.\n", "\"Behaviour of a PEMFC supplying a low voltage static converter.\"\n", "Journal of Power Sources (Elsevier) 156: 119–125.\n", "doi:10.1016/j.jpowsour.2005.08.021.\n", "\n", "
\n", "2-Larminie, J., Dicks, A., & McDonald, M. S. 2003. Fuel cell systems explained (Vol. 2, pp. 207-225). Chichester, UK: J. Wiley. doi: 10.1002/9781118706992.\n", "" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "OPEM", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }