﻿ 燃料电池–高压压气机–涡轮系统仿真计算 Simulation and Calculation of Fuel Cell-High Pressure Compressor-Turbine System

Dynamical Systems and Control
Vol. 08  No. 02 ( 2019 ), Article ID: 29603 , 12 pages
10.12677/DSC.2019.82017

Simulation and Calculation of Fuel Cell-High Pressure Compressor-Turbine System

Long Li, Qianchao Liang*

College of Power Engineering, Naval University of Engineering, Wuhan Hubei

Received: Mar. 13th, 2019; accepted: Mar. 24th, 2019; published: Apr. 8th, 2019

ABSTRACT

The fuel cell is a highly efficient, green, non-polluting device that converts chemical energy into electrical energy. In order to study the influence of temperature and oxygen excess ration on fuel cell output performance, this paper designed a high-pressure specific compressor-turbine device for providing air to the cathode of the fuel cell and recovering exhaust gas. The model was built and simulated by Simulink software. According to the simulation results, it can be shown that increasing the temperature and oxygen excess ratio can improve the output performance of the fuel cell. This has certain guiding significance for the system design of the fuel cell.

Keywords:Fuel Cell System, Temperature, Oxygen Excess Ratio, Simulink Modeling Simulation, Residual Pressure Recovery

1. 前言

2. PEMFC系统

2.1. 系统模型的设计

PEMFC系统主要包括供气系统、电池系统、冷却系统、尾气回收系统。本文设计的PEMFC系统模型可见图1

Figure 1. The model of PEMFC system

2.2.1. PEMFC模块

Figure 2. The polarization curve of PEMFC

${V}_{cell}={E}_{Nerst}-{V}_{act}-{V}_{ohm}-{V}_{con}$ (2-1)

1) 热力学电动势

 (2-2)

${E}_{Nerst}=1.229-8.5×{10}^{-4}×\left(T-298.15\right)+4.308×{10}^{-5}T×\left(\mathrm{ln}{P}_{{H}_{2}}+0.5\mathrm{ln}{P}_{{O}_{2}}\right)$ (2-3)

2) 活化过电势

(2-4)

$\left\{\begin{array}{l}{V}_{act}={\delta }_{1}+\sigma T+{\delta }_{3}T\mathrm{ln}{C}_{O2}+{\delta }_{4}T\mathrm{ln}I\\ \sigma ={\delta }_{2}+2×{10}^{-4}\mathrm{ln}A+4.3×{10}^{-5}\mathrm{ln}{C}_{H2}\\ {C}_{O2}=1.97×{10}^{-7}×{P}_{{O}_{2}}×\mathrm{exp}\left(498/T\right)\\ {C}_{H2}=9.17×{10}^{-7}×{P}_{{H}_{2}}×\mathrm{exp}\left(-77/T\right)\end{array}$ (2-5)

3) 欧姆过电势

 (2-6)

4) 浓差过电势

PEMFC燃料电池在反应过程中需要燃料与氧化剂，并且在会生成一定量的水。这就会导致催化层内的生成物与反应物的浓度会发生变化，这就会产生浓差损失影响电池的输出性能。

${V}_{con}=-m\mathrm{exp}\left(ni\right)$ (2-7)

2.2.2. 其余子模块

1) 高压压气机

Figure 3. The mathematical model of a battery cell

$\text{π}={f}_{1}\left({G}_{in}\frac{{P}_{0}\sqrt{{T}_{in}}}{{P}_{in}\sqrt{{T}_{0}}},{n}_{c}\frac{\sqrt{{T}_{0}}}{\sqrt{{T}_{in}}}\right)$ (2-8)

 (2-9)

Figure 4. The characteristic curve of $\text{π}-{G}^{\prime }$

Figure 5. .The characteristic curve of $P-{n}^{\prime }$

${N}_{{e}_{C}}={c}_{pa}{T}_{1}\left({\pi }^{{m}_{a}}-1\right)/\eta$ (2-10)

${m}_{a}=\left({\lambda }_{a}-1\right)/{\lambda }_{a}$ (2-11)

${T}_{2}={T}_{1}\left[1+\left({\text{π}}^{{m}_{a}}-1\right)/\eta \right]$ (2-12)

2) 管道模型

 (2-13)

$\frac{\text{d}{P}_{sm}}{\text{d}t}=\frac{\gamma {R}_{a}}{{V}_{sm}}\left({F}_{cp}{T}_{cp,\text{out}}-{F}_{sm,\text{out}}{T}_{sm}\right)$ (2-14)

${F}_{sm,\text{out}}={k}_{sm,\text{out}}\left({P}_{sm}-{P}_{ca}\right)$ (2-15)

$\frac{\text{d}{p}_{rm}}{\text{d}t}=\frac{{R}_{a}{T}_{rm}}{{V}_{rm}}\left({F}_{ca,\text{out}}-{F}_{rm}\right)$ (2-16)

${F}_{rm}=\frac{{C}_{D,rm}{A}_{T,rm}{p}_{rm}}{\sqrt{R{T}_{rm}}}{\gamma }^{\frac{1}{2}}{\left(\frac{2}{\gamma +1}\right)}^{\frac{\gamma +1}{2\left(\gamma -1\right)}}，\frac{{p}_{atm}}{{p}_{rm}}\le {\left(\frac{2}{\gamma +1}\right)}^{\frac{\gamma }{\gamma -1}}$ (2-17)

3) 涡轮模型

 (2-18)

4) 阴极空气动态压力模型

$\frac{\text{d}{m}_{{O}_{2}}}{\text{d}t}={F}_{{O}_{2,\text{in}}}-{F}_{{O}_{2,\text{out}}}-{F}_{{O}_{2,rec}}$ (2-19)

$\frac{\text{d}{m}_{{N}_{2}}}{\text{d}t}={F}_{{N}_{2,\text{in}}}-{F}_{{N}_{2,\text{out}}}$ (2-20)

${F}_{{O}_{2,\text{in}}}=\frac{0.21{M}_{{O}_{2}}}{{M}_{air}}\cdot \frac{{F}_{sm,\text{out}}}{1+{\Omega }_{\text{atm}}}$ (2-21)

${F}_{{O}_{2,\text{in}}}=\frac{0.79{M}_{{N}_{2}}}{{M}_{air}}\cdot \frac{{F}_{sm,\text{out}}}{1+{\Omega }_{\text{atm}}}$ (2-22)

(2-23)

${P}_{{N}_{2}}=\frac{{n}_{{N}_{2}}{R}_{{N}_{2}}T}{{V}_{ca}}$ (2-24)

${P}_{ca}={P}_{{O}_{2}}+{P}_{{N}_{2}}$ (2-25)

 (2-26)

${F}_{{N}_{2,\text{out}}}=\frac{{m}_{{N}_{2}}}{{m}_{ca}}{F}_{ca,\text{out}}$ (2-27)

${m}_{ca}={m}_{{O}_{2}}+{m}_{{N}_{2}}$ (2-28)

${F}_{{O}_{2,rec}}=\frac{{M}_{{O}_{2}}nI}{4F}$ (2-29)

5) 废气利用率

(2-30)

Figure 6. The model of PEMFC system

3. 仿真结果分析

3.1. 仿真分析

Figure 7. The change of current

Figure 8. The change of a battery cell’s voltage

Figure 9. The change of oxygen pressure

Figure 10. The utilization rate of exhaust gas

3.2. 探究影响PEMFC输出性能的因素

1) 温度对PEMFC输出性能的影响

Figure 11. The output voltage of stack at different temperature

2) 氧气过量系数对PEMFC输出性能的影响

Figure 12. The oxygen pressure at different oxygen excess ratio

Figure 13. The output voltage of stack at different oxygen excess ratio

4. 结论

Simulation and Calculation of Fuel Cell-High Pressure Compressor-Turbine System[J]. 动力系统与控制, 2019, 08(02): 148-159. https://doi.org/10.12677/DSC.2019.82017

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9. NOTES

*通讯作者。