Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 738207, 11 pages

http://dx.doi.org/10.1155/2015/738207

## Simulation and Optimization of Air-Cooled PEMFC Stack for Lightweight Hybrid Vehicle Application

Department of Automotive Engineering, Guangdong Polytechnic Institute, Guangzhou 510091, China

Received 4 April 2015; Revised 27 June 2015; Accepted 5 July 2015

Academic Editor: Mohsen Torabi

Copyright © 2015 Jingming Liang and Zefeng Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A model of 2 kW air-cooled proton exchange membrane fuel cell (PEMFC) stack has been built based upon the application of lightweight hybrid vehicle after analyzing the characteristics of heat transfer of the air-cooled stack. Different dissipating models of the air-cooled stack have been simulated and an optimal simulation model for air-cooled stack called convection heat transfer (CHT) model has been figured out by applying the computational fluid dynamics (CFD) software, based on which, the structure of the air-cooled stack has been optimized by adding irregular cooling fins at the end of the stack. According to the simulation result, the temperature of the stack has been equally distributed, reducing the cooling density and saving energy. Finally, the 2 kW hydrogen-air air-cooled PEMFC stack is manufactured and tested by comparing the simulation data which is to find out its operating regulations in order to further optimize its structure.

#### 1. Introduction

Air-cooled PEMFC is applied in some vehicles whose power requirements are not demanding because of its compact structure, low cost, and convenience to use. Most of its stack power is between 500 W and 5 kW; supposing power higher than 5 kW, the stack requires water cooling to dissipate heat. Due to its power limit, it is mostly applied in compact vehicles, such as golf carts, tour buses, and factory forklift trucks.

Currently, there are two kinds of air-cooled stack research orientations: one is to design various radiators, say, Boyd and Hooman [1], who study medal bubble micropore heat exchanger, whose simulation result shows that the temperature is uniform in the stack whose effect is similar to that of the water-cooled with small volume; Wan Mohamed et al. [2] designed some extending ribs in its superficial area to lose heat, whose heat dissipating efficiency can be improved by 30%. The other is the simulation and testing analysis of the flow field. Akbari et al. [3], diffusion layer and different Renaults are applied to evaluate air-cooled convection heat dissipating efficiency, whose results show that the former is less influential, yet, the range of temperature changes dramatically as the Renaults reduce. Adzakpa et al. built air-cooled model [4], whose simulation results show that different voltage distribution causes the decline of the whole stack power.

Based on the previous studies, this paper aims to further optimize the heat dissipating structure of the air-cooled stack and to make the stack temperature distribution more reasonable, including the following: (1) the stack temperature distribution is simulated and analyzed in different surface heat dissipation models; (2) the structure of heat dissipating outlet in air-cooled stack is optimized; (3) 2 kW air-cooled stack is designed and manufactured, which is applied to test and analyze in lightweight vehicle.

#### 2. Air-Cooled Stack Heat Transfer and Heat Dissipation Model

##### 2.1. The Generation of Stack Heat

More than half of the consuming energy produced in the PEMFC electrochemistry reaction dissipates in the form of heat energy [5]; in this case, in order to keep the stack operate within reasonable temperature, it is required to have the nature of heat dissipation.

These heat energies mainly embrace chemistry respondent heat, ohm heat, phase change heat, and entropy increasing heat, of which the first one is irreversible, whereas the last one is reversible; in addition, some sensible heat forms the temperature difference between the inlet gas and the outlet one. Therefore, the necessary dissipating heat of every single cell is composed of reversible heat, irreversible heat, and sensible heat, which can be expressed as below [4, 6]: where is reversible heat, J; is irreversible heat, J; and is sensible heat, J: where is stack current, A; is stack average temperature, K; is stack voltage, V; is Gibbs free energy, kJ/mol; is Faraday constant, C/mol; and and are total entropy and total enthalpy of the supplying gas:where and are the inlet and outlet sensible heat of total reactant gas, J:

Accordingly, the heat produced in a single cell is the total power of the electrochemistry; respondent subtracts the power that the cell gives out and adds the total sensible heat of the inlet and outlet gas, whose expression is shown in (4). The heat generation of stack is the total heat generated from every single cell:

##### 2.2. The Heat Dissipation of Stack

The air-cooled stack requires to discontinuously dissipate heat so as to maintain its steady operation. The main approaches of heat dissipation include forcing convection heat dissipation whose heat is dissipated by the air of the cooling plate and natural convection and radiation on the stack surface; yet, radiation merely dissipates a little heat due to the low operation temperature of the stack; in addition, the inlet and outlet of the respondent gas also dissipate some heat; heat conduction loses less heat, which can be neglected; therefore, the stack heat dissipation can be expressed as [7]where is some kind of reactant gas; and are the quality flow of the outlet and inlet reactant, kg/s; and is the temperature, K.

Single cell and cooling border to conduct convection heat exchange can be expressed aswhere forcing convection can be expressed aswhere is blades’ modulus and is the forcing convection modulus, W/(m^{2}·K), where natural convection can be expressed aswhere is the natural convection modulus, W/(m^{2}·K) and is the surrounding atmosphere temperature, K.

Radiation heat can be expressed aswhere is stack blackness; is Stefan-Boltzmann constant; and is the stack radiation area, m^{2}.

The convection exchange heat modulus is obtained according to the equationwhere is the air heat conduction modulus, W/m^{2}·K; is the hydraulic diameter, m; Pr is the Prandtl number; is the length of the water hose, m; and Re is the Reynolds number:

##### 2.3. The Simulation Model of Different Heat Dissipation for Air-Cooled Stack

When CFD software is applied to simulate PEMFC, the surface heat dissipating models can be categorized to be five [8]: specified heat flux, specified temperature (ST), CHT, external radiation, combined external radiation, and external convective heat transfer. The latter three heat dissipating models have been analyzed from (8) to (10); the first model is usually applied in the insulation layer, whose heat flow is set to be zero that can be skipped. The ST dissipating model can be divided into fluid surface and solid surface, which can be expressed as follows.

For fluid surface, considerwhere is fluid-side local heat transfer coefficient and and are wall surface temperature and local fluid temperature, respectively, K.

For solid surface, considerwhere is thermal conductivity of the solid, ; is local solid temperature, K; and is distance between wall surface and the solid cell center, m.

The ST heat dissipating model is usually used in the simulation of the water-cooled PEMFC stack; references [8–10] use this model to analyze. In addition, different flow fields are analyzed, such as parallel, interdigital, and serpentine ones [11–14]. ST model is also applied to compare their advantages and disadvantages, so as to find out the distributions of the temperature and the current density. However, as for the air-cooled PEMFC stack, ST model cannot work properly, as air-cooled intensity is lower than that of the water-cooled one. Generally, straight flow path is employed to dissipate heat, which is not uniform. Figure 1 is the surface cooling model: (a) is ST model and (b) is CHT model; seeing from the outer surface of the two models, the former can make the face temperature uniform, whereas temperature grads emerge in the latter; in this case, CHT model is similar to that of the air-cooled stack.