# Numerical Study on Effects of Flow Channel Length on Solid Oxide Fuel Cell-Integrated System Performances

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Description of SOFC-Integrated System

#### 2.1. Description of the SOFC Model

_{2}) and 8% yttrium-stabilized zirconia (YSZ). This model is established on the COMSOL 6.1 platform, which includes a fuel cell electrochemical model, a porous material transport model, and a heat transfer model. In a bid to better analyze its main issues, this study proposes the following methodology [26,27]:

- (1)
- The SOFC unit cell operates steadily, and the electrochemical reactions reach equilibrium.
- (2)
- The cathode and anode are constructed from homogeneous and isotropic porous materials.
- (3)
- In the anodic electrochemical reaction, only hydrogen gas participates.
- (4)
- SOFCs maintain consistent flow rates at the cathode and anode inlets over different lengths, and the inlet gas pressure is supplied by a compressor.
- (5)
- Gas pressure at the anode and cathode outlet is equivalent to the standard atmospheric pressure in the SOFC. Furthermore, the model operates at standard atmospheric pressure.
- (6)
- The SOFC gas inlet temperature and operating temperature are both set at 800 °C.
- (7)
- Anode and cathode outlet temperatures are computed from the model.
- (8)
- All gases are ideal gases in SOFC.

#### 2.1.1. Electrochemical Reaction

_{r}is the SOFC reversible voltage, V

_{cell}is the SOFC actual voltage, V

_{pol}is the total polarization voltage, V

_{act}is the activation voltage, V

_{con}is the concentration voltage, and V

_{ohm}is the ohmic voltage.

_{0}is the standard electromotive force at atmospheric pressure, R

_{g}is the gas constant (R

_{g}= 8.314 J/(mol·K)), T is the SOFC operating temperature (T = 800 °C), F is the Faraday constant (F = 96485 C/mol), and p is the fractional pressure for each gas component. n

_{e}is the number of electrons that are transferred (n

_{e}= 2).

_{an}and i

_{ca}represent the anodic and cathodic current densities. ${\alpha}_{a}^{a}$ and ${\alpha}_{c}^{a}$ represent the anodic transfer coefficient of the anode and cathode. V

_{an,act}and V

_{ca,act}represent anode and cathode activation polarization. i

_{0,an}and i

_{0,ca}represent the exchange current densities at the anode and cathode. The cell exchange current density is governed by the mass action law and is expressed as follows:

_{an}and E

_{ca}represent the anodic and cathodic preindex factor. K

_{an}and K

_{ca}represent the anodic and cathodic activation energy.

_{ohm}represents the approximate total resistance.

_{cell}is the amount of SOFC cells in the stack; Δv

_{fuel}is electrochemical reaction level (in mol/s); A

_{cell}is the active area of a single cell (in m

^{2}).

_{fuel}is the SOFC fuel utilization rate; v

_{fuel}is the hydrogen molar flow rate at the anode (in mol/s).

_{LHV}is the hydrogen’s lower heating value (241.8 kJ∙mol

^{−1}).

#### 2.1.2. Model Parameter Settings

#### 2.1.3. SOFC Model Validation

#### 2.2. Description of Other Equipment Models in the Integrated System

_{c}and C

_{min}represent the gas-specific heat capacity in the cold stream and the gas-specific heat capacity of the smaller fluid between the hot and cold streams at constant pressure (in J/g·K). $\dot{M}$ is the gas mass flow rate (in g/s). T

_{in,c}and T

_{out,c}represent the temperatures of the cold inlet stream and outlet stream of the compressor (in °C). T

_{in,h}represents the temperature of the hot inlet stream of the compressor. Additionally, when heating water, the latent heat of vaporization for water is considered.

_{h}represents the heat transfer area of the heat exchanger (in m

^{2}) and U

_{h}is the convective heat transfer coefficient (in W/(m

^{2}∙K)).

_{2}represents the compressor outlet pressure (in Pa) and p

_{1}represents the compressor inlet pressure. π

_{C}represents compressor pressure ratio.

_{c}is the compressor isentropic efficiency, T

_{2}

^{*}is the ideal outlet temperature of the compressor, T

_{1}is the compressor inlet temperature, and T

_{2}is the compressor outlet temperature. The ideal outlet temperature can be calculated using Equation (23).

_{h}

_{2o}is the water mass flow rate (in kg/s); P

_{out}and P

_{in}refer to the outlet and inlet pressures of the water pump (in Pa); η is the water pump efficiency; v is the specific volume of water (in m

^{3}/kg).

_{cell}between 0.4 V and 0.9 V and an L

_{cell}between 6 cm and 18 cm.

## 3. System Performance Evaluation Indicators

## 4. Results and Analysis

_{cell}ranging from 6 to 18 cm, and analyzes their cell performance at V

_{cell}ranging from 0.4 V to 0.9 V. The method of controlling variables was used to conduct analysis and discussion, ensuring the validity of the performance evaluation.

#### 4.1. Influence of Different Flow Channel Lengths on SOFC Stack

#### 4.2. Influence of Different Flow Channel Lengths on Compressor

#### 4.3. Influence of Different Flow Channel Lengths on Heat Exchangers

#### 4.4. System Performances Analysis

#### 4.4.1. Maximum Net Electrical Power of the System

#### 4.4.2. Maximum Net Electrical Efficiency of the System

#### 4.4.3. Maximum Thermoelectric Efficiency of the System

## 5. Summary

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Specific structure of SOFC; (

**b**) dimensions and boundary conditions. The blue arrow at the top indicates the air inlet, and the blue arrow at the bottom indicates the fuel outlet.

**Figure 7.**(

**a**) Effect of flow channel length and cell voltage on the pressure ratio of the air compressor; (

**b**) effect of flow channel length and cell voltage on the power of the air compressor.

**Figure 8.**(

**a**) Effect of flow channel length and cell voltage on the pressure ratio of the fuel compressor; (

**b**) effect of flow channel length and cell voltage on the power of the fuel compressor.

**Figure 9.**(

**a**) Effect of flow channel length and cell voltage on the power of the air heat exchanger; (

**b**) Effect of flow channel length and cell voltage on the power of the water heat exchanger; (

**c**) effect of flow channel length and cell voltage on the power of the hydrogen heat exchanger.

**Figure 10.**(

**a**) Air compressor outlet gas temperature at different flow channel lengths; (

**b**) fuel compressor outlet gas temperature at different flow channel lengths.

**Figure 11.**(

**a**) Effect of flow channel length and cell voltage on BOP power consumption; (

**b**) effect of flow channel length and cell voltage on net electrical power.

Parameter | Value | Unit | Symbol |
---|---|---|---|

Channel width | 2 | mm | w_{ch} |

Rib width | 2 | mm | w_{rib} |

Anode thickness | 0.15 | mm | t_{an} |

Electrolyte thickness | 0.1 | mm | t_{el} |

Cathode thickness | 0.1 | mm | t_{ca} |

Gas channel height | 2 | mm | h_{ch} |

Flow channel length | 60–180 | mm | L_{cell} |

Number of cells | 1000 | - | N_{cell} |

Parameter | Value | Unit |
---|---|---|

Anode electric potential | 0 | V |

Cathode electric potential | 0.4–0.9 | V |

Anode air velocity | 0.8 | m/s |

Cathode air velocity | 3 | m/s |

Anode mass fraction | H_{2}:H_{2}O = 0.4:0.6 | - |

Cathode mass fraction | O_{2}:N_{2} = 0.15:0.85 | - |

Anode fuel outlet | 0 | Pa |

Cathode fuel outlet | 0 | Pa |

Cell operating temperature | 800 | ℃ |

Cell operating pressure | 101.32 | kPa |

Parameter | Value | Unit | Symbol | References |
---|---|---|---|---|

Anode electronic conductivity | 2149.2 | S/m | ${\sigma}_{s,a}$ | [39] |

Cathode electronic conductivity | 5093 | S/m | ${\sigma}_{s,c}$ | [39] |

Electrolyte ionic conductivity | 2.2669 | S/m | ${\sigma}_{ion,l}$ | [39] |

Anodic transfer coefficient of anode | 0.5 | ${\alpha}_{a}^{a}$ | [40] | |

Anodic transfer coefficient of cathode | 3.5 | ${\alpha}_{c}^{a}$ | [40] | |

Anode activation energy | 6.54 × 1011 | 1/(Ω∙m^{2}) | ${K}_{an}$ | [26,41] |

Cathode activation energy | 2.35 × 1011 | 1/(Ω∙m^{2}) | ${K}_{ca}$ | [26,41] |

Exchange current density of anode | 4637.4 | A/m^{2} | ${i}_{0,an}$ | [26] |

Exchange current density of cathode | 1166.2 | A/m^{2} | ${i}_{0,ca}$ | [26] |

The specific surface area of anode | 102,500 | 1/m | ${S}_{an}$ | [42] |

The specific surface area of cathode | 102,500 | 1/m | ${S}_{ca}$ | [42] |

Electrolyte volume fraction | 0.7 | - | $\theta $ | [43] |

porosity | 0.4 | - | $\epsilon $ | [26,44] |

Parameter | Value | Unit | References |
---|---|---|---|

Porosity of anode | 0.4 | - | [26,44] |

Porosity of cathode | 0.4 | - | [26,44] |

Permeability of anode | 1.76 × 10^{−11} | m^{2} | [26] |

Permeability of cathode | 1.76 × 10^{−11} | m^{2} | [26] |

Parameter | Value | Unit | References |
---|---|---|---|

Anode heat capacity | 450 | J/(kg∙k) | [43] |

Cathode heat capacity | 430 | J/(kg∙k) | [43] |

Electrolyte heat capacity | 470 | J/(kg∙k) | [43] |

Anode density | 3310 | kg/m^{2} | [45] |

Cathode density | 3030 | kg/m^{2} | [45] |

Electrolyte density | 5160 | kg/m^{2} | [45] |

Thermal conductivity of the anode | 11 | W/(m∙k) | [43] |

Thermal conductivity of the cathode | 6 | W/(m∙k) | [43] |

Thermal conductivity of electrolyte | 2.7 | W/(m∙k) | [43] |

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**MDPI and ACS Style**

Liu, Y.; Liu, J.; Fu, L.; Wang, Q.
Numerical Study on Effects of Flow Channel Length on Solid Oxide Fuel Cell-Integrated System Performances. *Sustainability* **2024**, *16*, 1643.
https://doi.org/10.3390/su16041643

**AMA Style**

Liu Y, Liu J, Fu L, Wang Q.
Numerical Study on Effects of Flow Channel Length on Solid Oxide Fuel Cell-Integrated System Performances. *Sustainability*. 2024; 16(4):1643.
https://doi.org/10.3390/su16041643

**Chicago/Turabian Style**

Liu, Yuhang, Jinyi Liu, Lirong Fu, and Qiao Wang.
2024. "Numerical Study on Effects of Flow Channel Length on Solid Oxide Fuel Cell-Integrated System Performances" *Sustainability* 16, no. 4: 1643.
https://doi.org/10.3390/su16041643