{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
Please cite us if you use the software
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Padulles-Amphlett Dynamic Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Version 1.2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n",
"The Padulles dynamic model can predict the transient response of cell voltage, temperature of the cell, hydrogen/oxygen out flow rates and cathode and anode channel temperatures/pressures under sudden change in load current. Hence, a dynamic fuel cell simulation is developed in this model, which incorporates the dynamics of flow and pressure in the anode and cathode channels and mass/ heat transfer transient features in the fuel cell body.\n",
"
This model is based on several assumptions: \n",
"
\n", "This model is an integration of Padulles-Hauer dynamic model with Amphlett static model. The advantage of this dynamic model is using Amphlett equation for simulating the polarization values. Amphlett model as the most complicated and preferable static model, but the most precise. Based on this model, the obtained polarization voltage is identical to the experimental results. \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fig1. Padulles-Amphlett Dynamic Model Block Diagram
\n", " \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", "
$$T$$ | \n", "Fuel cell temperature | \n", "$$K$$ | \n", "$$User$$ | \n", "
$$N_0$$ | \n", "Number of cells | \n", "$$--$$ | \n", "$$User$$ | \n", "
$$E_0$$ | \n", "No load voltage | \n", "$$V$$ | \n", "$$User$$ | \n", "
$$K_{H_2}$$ | \n", "Hydrogen valve constant | \n", "$$kmol.s^{-1}.atm^{-1}$$ | \n", "$$User$$ | \n", "
$$K_{H_2O}$$ | \n", "Water valve constant | \n", "$$kmol.s^{-1}.atm^{-1}$$ | \n", "$$User$$ | \n", "
$$K_{O_2}$$ | \n", "Oxygen valve constant | \n", "$$kmol.s^{-1}.atm^{-1}$$ | \n", "$$User$$ | \n", "
$$\\tau_{H_2}^{(s)}$$ | \n", "Hydrogen time constant | \n", "$$s$$ | \n", "$$User$$ | \n", "
$$\\tau_{H_2O}^{(s)}$$ | \n", "Water time constant | \n", "$$s$$ | \n", "$$User$$ | \n", "
$$\\tau_{O_2}^{(s)}$$ | \n", "Oxygen time constant | \n", "$$s$$ | \n", "$$User$$ | \n", "
$$l$$ | \n", "Membrane thickness | \n", "$$cm$$ | \n", "$$User$$ | \n", "
$$A$$ | \n", "Active area | \n", "$$cm^2$$ | \n", "$$User$$ | \n", "
$$\\tau_{1}^{(s)}$$ | \n", "Reformer time constant | \n", "$$s$$ | \n", "$$User$$ | \n", "
$$\\tau_{2}^{(s)}$$ | \n", "Reformer time constant | \n", "$$s$$ | \n", "$$User$$ | \n", "
$$CV$$ | \n", "Conversion factor | \n", "$$--$$ | \n", "$$User$$ | \n", "
$$B$$ | \n", "An empirical constant\n", "depending on the cell and its\n", "operation state | \n", "$$V$$ | \n", "$$User$$ | \n", "
$$R_{electronic}$$ | \n", "R-Electronic | \n", "$$\\Omega$$ | \n", "$$User$$ | \n", "
$$\\lambda$$ | \n", "An adjustable parameter with a possible minimum value of 14 and a maximum value of 23 | \n", "$$--$$ | \n", "$$User$$ | \n", "
$$J_{Max}$$ | \n", "Maximum current density of the cell | \n", "$$Acm^{-2}$$ | \n", "$$User$$ | \n", "
$$r_{h-o}$$ | \n", "Hydrogen-Oxygen flow ratio | \n", "$$--$$ | \n", "$$User$$ | \n", "
$$q_{methanol}$$ | \n", "Molar flow of methanol | \n", "$$kmol.s^{-1}$$ | \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", "
$$P_{H_2}$$ | \n", "Hydrogen partial pressure | \n", "$$atm$$ | \n", "$$System$$ | \n", "
$$P_{H_2O}$$ | \n", "Water partial pressure | \n", "$$atm$$ | \n", "$$System$$ | \n", "
$$P_{O_2}$$ | \n", "Oxygen partial pressure | \n", "$$atm$$ | \n", "$$System$$ | \n", "
$$K_r$$ | \n", "Modeling constant | \n", "$$kmol.s^{-1}.A^{-1}$$ | \n", "$$System$$ | \n", "
$$q_{O_2}^{(inlet)}$$ | \n", "Molar flow of oxygen | \n", "$$kmol.s^{-1}$$ | \n", "$$System$$ | \n", "
$$q_{H_2O}^{(inlet)}$$ | \n", "Molar flow of water | \n", "$$kmol.s^{-1}$$ | \n", "$$System$$ | \n", "
$$q_{H_2}^{(inlet)}$$ | \n", "Molar flow of hydrogen | \n", "$$kmol.s^{-1}$$ | \n", "$$System$$ | \n", "
$$J$$ | \n", "Actual current density of the cell | \n", "$$Acm^{-2}$$ | \n", "$$System$$ | \n", "
$$C_{O_2}$$ | \n", "Concentration of oxygen in the catalytic interface of the cathode | \n", "$$molcm^{-3}$$ | \n", "$$System$$ | \n", "
$$C_{H_2}$$ | \n", "Concentration of hydrogen in the catalytic interface of the anode | \n", "$$molcm^{-3}$$ | \n", "$$System$$ | \n", "
$$R_{Proton}$$ | \n", "Resistance to proton flow | \n", "$$\\Omega$$ | \n", "$$System$$ | \n", "
$$\\xi_2$$ | \n", "Parametric coefficients for cell model | \n", "$$--$$ | \n", "$$System$$ | \n", "
$$\\xi_1$$ | \n", "Parametric coefficients for cell model | \n", "$$--$$ | \n", "$$-0.948$$ | \n", "
$$\\xi_3$$ | \n", "Parametric coefficients for cell model | \n", "$$--$$ | \n", "$$7.6\\times10^{-5}$$ | \n", "
$$\\xi_4$$ | \n", "Parametric coefficients for cell model | \n", "$$--$$ | \n", "$$-1.93\\times10^{-4}$$ | \n", "
$$\\mu_F$$ | \n", "The fuel utilization | \n", "$$--$$ | \n", "$$0.95$$ | \n", "
$$HHV$$ | \n", "Higher heating value potential | \n", "$$V$$ | \n", "$$1.482$$ | \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", "
$$E_{th}$$ | \n", "Theoretical potential | \n", "$$V$$ | \n", "$$1.23$$ | \n", "
\n", "1- J. Padulles, G.W. Ault, J.R. McDonald. 2000. \"An integrated SOFC plant dynamic model for power systems\n", "simulation.\" Journal of Power Sources (Elsevier) 86 (1-2): 495-500. doi:10.1016/S0378-7753(99)00430-9\n", "\n", "
\n", "2- Hauer, K.-H. 2001. \"Analysis tool for fuel cell vehicle hardware and software (controls) with an application\n", "to fuel economy comparisons of alternative system designs.\" Ph.D. dissertation, Transportation Technology\n", "and Policy, University of California Davis.\n", "\n", "
\n", "3- J. C. Amphlett, R. M. Baumert, R. F. Mann, B. A. Peppley, and P. R. Roberge. 1995. \"Performance Modeling\n", "of the Ballard Mark IV Solid Polymer Electrolyte Fuel Cell.\" J. Electrochem. Soc. (The Electrochemical Society,\n", "Inc.) 142 (1): 9-15. doi: 10.1149/1.2043959.\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" } }, "nbformat": 4, "nbformat_minor": 2 }