# Research on Solid Oxide Fuel Cell System Model Building and 3D Testing Based on the Nodal Idea

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## Abstract

**:**

## 1. Introduction

#### 1.1. SOFC Power Generation Principle and Characteristics

#### 1.2. SOFC Modeling at Home and Abroad

## 2. SOFC Model Building

#### 2.1. SOFC System Composition

#### 2.2. Modeling Methods and Processes

#### 2.2.1. General Model Equation

- (1)
- All the gases involved meet the ideal gas equation of state.
- (2)
- All characteristic parameters of the gas are uniformly distributed during gas flow.
- (3)
- The SOFC system is absolutely independent and sealed, and there is no heat transfer with the external environment.
- (4)
- There is no material accumulation and precipitation in the reactor, combustion chamber, or other devices.
- (5)
- The SOFC has a 100% current efficiency rate.
- (6)
- The hysteresis characteristics of the gas in each gas supply pipeline are replaced with an inertia link and a delay link.

- (1)
- Temperature characteristics

- (2)
- Velocity characteristics

- (3)
- Mole fraction properties

#### 2.2.2. Model of Each System Component

- (1)
- Heat exchanger model

- (2)
- Reactor model

- (3)
- Combustion chamber model

- (4)
- Lag model of the gas supply system

#### 2.3. Integration of SOFC Models

## 3. SOFC Performance Testing and Verification

#### 3.1. SOFC Performance Indicators

#### 3.1.1. Operation Parameters and Their Ranges

- (1)
- Fuel utilization rate ($FU$).$$FU=\frac{{R}_{{\mathrm{H}}_{2}}}{{\dot{N}}_{{\mathrm{H}}_{2}}}=\frac{n{I}_{s}}{2F{\dot{N}}_{{\mathrm{H}}_{2}}}.$$

- (2)
- Air excess ratio ($AR$).$$AR=\frac{{\dot{N}}_{{\mathrm{O}}_{2}}}{{R}_{{\mathrm{O}}_{2}}}=\frac{4F{X}_{{\mathrm{O}}_{2}}{\dot{N}}_{air}}{n{I}_{s}}.$$

- (3)
- Bypass valve opening ($BP$).$$BP=\frac{{\dot{N}}_{air,by}}{{\dot{N}}_{air}}.$$

- (4)
- Reactor current (${I}_{s}$):

#### 3.1.2. SOFC Static Performance Tests

#### 3.2. Thermal Output Characteristics and Their Ranges

#### 3.2.1. Thermal Output Characteristic Parameters

- (1)
- Maximum operating temperature of PEN($Max.{T}_{PEN}$).

- (2)
- Maximum operating temperature gradient of PEN($Max.|\Delta {T}_{PEN}|$).

- (3)
- Gas temperature difference at the reactor inlet ($\Delta {T}_{inlet}$):

- (4)
- Combustion chamber temperature (${T}_{B}$).

#### 3.2.2. One-Dimensional Test and Verification of Heat Output Characteristics

#### 3.2.3. Two-Dimensional Test and Verification of Heat Output Characteristics

#### 3.2.4. Three-Dimensional Test and Verification of Heat Output Characteristics

#### 3.3. Electrical Output Characteristics and Their Ranges

#### 3.3.1. Electrical Output Characteristic Parameters

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#### 3.3.2. One-Dimensional Test and Verification of Electrical Output Characteristics

#### 3.3.3. Two-Dimensional Test and Verification of Electrical Output Characteristics

#### 3.3.4. Three-Dimensional Test and Verification of Electrical Output Characteristics

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 5.**Validation of SOFC experiments (E) against model simulations and (S) through curve fitting.

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## Share and Cite

**MDPI and ACS Style**

Li, M.; Zhu, K.; Rao, M.; Chen, Z.; Xiong, K.; Hou, L.; Wang, X.; Chen, C.; Li, S.; Li, X.
Research on Solid Oxide Fuel Cell System Model Building and 3D Testing Based on the Nodal Idea. *Atmosphere* **2023**, *14*, 1261.
https://doi.org/10.3390/atmos14081261

**AMA Style**

Li M, Zhu K, Rao M, Chen Z, Xiong K, Hou L, Wang X, Chen C, Li S, Li X.
Research on Solid Oxide Fuel Cell System Model Building and 3D Testing Based on the Nodal Idea. *Atmosphere*. 2023; 14(8):1261.
https://doi.org/10.3390/atmos14081261

**Chicago/Turabian Style**

Li, Mingfei, Kanglin Zhu, Mumin Rao, Zhengpeng Chen, Kai Xiong, Longtong Hou, Xiabin Wang, Chuangting Chen, Shujun Li, and Xi Li.
2023. "Research on Solid Oxide Fuel Cell System Model Building and 3D Testing Based on the Nodal Idea" *Atmosphere* 14, no. 8: 1261.
https://doi.org/10.3390/atmos14081261