# Effect of Structural Parameters and Operational Characteristic Analysis on Ejector Used in Proton Exchange Membrane Fuel Cell

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Ejector Structure Design

#### 2.1. Design Condition

#### 2.2. Thermodynamic Theory Design Procedure

^{−1}); ${M}_{{H}_{2}}$ is the molar weight of hydrogen.

**Remark.**

## 3. Numerical Modeling

^{+}independence is compared. Finally, the experiment validation procedure is explained.

#### 3.1. CFD Modeling and Convergence Criteria

^{−6}, and the remaining residuals are less than 10

^{−5}.

#### 3.2. Grid Independence Verification

#### 3.3. The y+ Independence

^{+}value which is recommended to be less than 1. However, this value will also change as the operating conditions change. The maximum y

^{+}of the grid used in this paper is less than 5. Comparing the results of different fine mesh grids in Table 4, it is shown that the relative deviation of ER is less than 0.1% when y

^{+}is between 1 and 5. Concerning the local data, it was shown that the wall pressure has almost no deviation in Figure 4. Therefore, it is concluded that y

^{+}has no noticeable impact on the performance of the ejector in this mesh number. This stems from the fact that the selected SST k-ω model uses y

^{+}insensitive wall treatment. In addition, this article assumes that the wall is insulated, and the boundary layer does not simulate heat transfer prediction, so the near-wall mesh is not deliberately refined.

#### 3.4. Model Validation

## 4. Single-Factor Analysis of the Performance of Ejector in PEMFC

#### 4.1. Effect of Nozzle Dimensions

_{t}is investigated in the range of 0.9~0.98 mm, while the other ejector geometric parameters were unchanged. Figure 6a indicates that the ejector performance is affected by the nozzle throat diameter on in PEMFC system, the entrainment ratio continuously falls while the nozzle throat diameter increases under full current condition. Especially at a low current, when the stack current is 110 A, the entrainment ratio decreases by 0.45 as the nozzle throat diameter increases from 0.9 to 0.98 mm. The entrainment ratio is negatively related with Dt, due to falling axial velocity of nozzle and suction chamber, as shown in Figure 6c. Similarly, Feng [19] analyzed a PEMFC ejector to obtain the effect of various nozzle diameters on entrainment ratio of hydrogen. Their results indicate that entrainment ratio is affected significantly by the diameter, and entrainment ratio becomes higher as the diameter decreases. Therefore, the nozzle diameter is classified as a crucial parameter of ejector design. In order to enhance the range of the ejector at low currents, the throat diameter should be as small as possible. However, a higher inlet pressure of the primary flow is needed as the diameter of the nozzle throat reduces, which is limited by the pressure regulating capacity of the proportional valve. There is a trade-off between operating range and primary inlet pressure, when the throat diameter is optimized. In this work, the primary pressure is higher than 8.5 bar when D

_{t}is less than 0.94 mm. So, the ejector nozzle diameter was supposed to be 0.94 mm.

#### 4.2. Effect of Suction Chamber Dimensions

#### 4.3. Effect of Mixing Tube Dimensions

_{m}up to 3 mm causes an increase of ER due to the enlargement of the effective area. Further enlargement of D

_{m}leads to a decreasing ER caused by the reduced effect of the shear mixing layer between the primary and secondary flow. In fact, each working condition corresponds to a unique optimal mixing tube diameter, a mixing tube diameter that makes optimal entrainment ratio at high currents may not fit well for the low current conditions [22]. If the mixing tube diameter is small, the secondary flow area is small in the mixing tube, and the velocity is increasing at sonic speed (namely, flow is chocked), mass flow rate of the secondary flow will be decreased. If the mixing tube diameter is too large, there may exist backflow in the mixing tube inner zone, which would reduce the entrainment ratio. In Figure 10a, entrainment ratios at medium and high currents increase continuously, the reason should be that the dimension change of mixing tube diameter is too small to be seen the optimal value. If the diameter is increased further, an optimum will appear at medium and high currents, respectively, similar to the low current case. As shown in Figure 10b, when D

_{m}= 2.2 mm, a vortex is not formed in the mixing tube, and the entrainment capacity is mainly limited by the flow cross-sectional area of the mixing tube. When D

_{m}is increased, a vortex is formed due to insufficient kinetic energy and wall viscous effect. When it increases from 2.6 to 3.8 mm, the size of vortex gradually increases, which further consumes the primary flow kinetic energy, and the entrainment ability is weakened. Thus, the mixing tube diameter was optimized to be 3 mm for ensuring PEMFC recirculation ratio (same as entrainment ratio in this study) of different operating conditions and taking into account the uniformity of the entrainment ratio.

#### 4.4. Effect of Diffuser Dimensions

## 5. Multi-Factor Analysis of the Performance of Ejector Using Taguchi Method

#### 5.1. Taguchi Experimental Design

_{n}(m

^{k}), which means m factor at k levels and n cases is required to run which. In this research, five factors that have crucial influence on the performance of PEMFC ejector are chosen according to above single-factor analysis results, namely nozzle divergent angle (θ

_{td}), nozzle throat length (L

_{t}), nozzle exit position (NXP), mixing tube diameter (D

_{m}), mixing tube length (L

_{m}). As showed in Table 5, each factor shall correspond to 5 levels at most, which ensures that performances of ejectors shall be optimal.

#### 5.2. Correlation Analysis of Factors

#### 5.3. Optimal Combination

#### 5.4. Comparison of the Optimized Result

## 6. Conclusions

- In the normal range, the nozzle convergence angle, suction chamber angle, and diffuser length are non-essential structural factors that hardly affect the performance of ejector. Nozzle divergent angle and nozzle throat length are important parameters of partial working conditions. Nozzle throat diameter, nozzle exit position, mixing tube diameter and mixing tube length are crucial for wide-range ejector design in PEMFC.
- Convergent nozzle outperforms convergent-divergent nozzle at entrainment ratio of PEMFC ejector. The optimal mixing tube diameter is 3 mm with the current is 110 A, and the optimal diameter as stack current increases. The optimal NXT is 1.5 mm with current is 110 A, while the optimal NXT is 3 mm and 4.5 mm when the current is 275 A and 412.5 A, respectively.
- Multi-factor analysis indicated that mixing tube diameter shall be the most significant parameter affecting performance of PEMFC ejectors except the nozzle diameter. In addition, the nozzle angle and length are more sensitive to the entrainment performance at low and medium currents, while the nozzle exit position is more sensitive at high currents.
- The ejector optimized based on multiple load condition can operate in a wider range, and the entrainment ratio is more uniform. Multi-factor analysis method rather than the single-factor analysis may lead to more effective improvement of operating range. Entrainment ratios of the ejector optimized by multi-factor is about 5% greater than single-factor.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

A | Area [m^{−2}] |

D | Diameter [m] |

ER | Entrainment ratio |

F | Faraday’s constant [C mol^{−1}] |

L | Length [m] |

T | Temperature [K] |

I | Current [A] |

m | mass flow rate [kg s^{−1}] |

M | molar weight [kg mol^{−1}] |

Ma | Much number |

N | number of single cell of PEMFC stack |

P | Pressure [Pa] |

R | gas constant [J mol^{−1} K^{−1}] |

S/N | signal-to-noise ratio |

V | Velocity [m s^{−1}] |

Greek letters | |

θ | Angle [°] |

λ | excess ratio |

γ | specific heat ratio |

ρ | Density [kg m^{3}] |

η | mean of S/N ratio |

φ | Efficiency [%] |

Subscript | |

p | primary flow |

s | secondary flow |

c | exit flow |

t | nozzle throat |

y | mixing tube inlet |

v | velocity distribution |

h_{2} | hydrogen |

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**Figure 5.**Comparison of simulated results and experimental data from [18]. (

**a**) Mass flow rate of primary and secondary flow. (

**b**) Deviation between simulation and experiment.

**Figure 6.**(

**a**) Effect of nozzle throat diameter (D

_{t}) on anode ejector; (

**b**) Effect of nozzle throat length (L

_{td}) on anode ejector entrainment ratio; (

**c**) Mach number of different nozzle throat diameter at 110 A; (

**d**) Mach number of different nozzle throat length at 110 A. (Dash red lines 1, 2, and 3 in figure are the nozzle exit, the mixing tube inlet and the mixing tube exit, respectively.)

**Figure 7.**(

**a**) Effect of nozzle convergence angle (θ

_{tc}) on anode ejector; (

**b**) Effect of nozzle divergent angle (θ

_{td}) on anode ejector; (

**c**) Mach number of different nozzle divergent angle at 110 A; (

**d**) Mach number of different nozzle divergent angle at 275 A.

**Figure 8.**Effect of NXP on PEMFC ejector. (

**a**) Entrainment ratio; (

**b**) Mach number of different NXP at 275 A; (

**c**) Velocity vector diagrams of different NXP at 110 A. (The black box shows an enlarged view of the local flow. The red circle represents the vortex generation zone.)

**Figure 9.**Effect of suction chamber angle (θ

_{s}) on PEMFC ejector. (

**a**) Entrainment ratio; (

**b**) Mach number of different suction chamber angle at 110 A.

**Figure 10.**Effect of mixing tube diameter (D

_{m}) on PEMFC ejector. (

**a**) Entrainment ratio; (

**b**) Velocity vector diagrams of different mixing tube diameter at 110 A.

**Figure 11.**Effect of mixing tube length (L

_{m}) on PEMFC ejector. (

**a**) Entrainment ratio; (

**b**) Velocity vector diagrams of different mixing tube length at 110A.

Current (A) | Power (kW) | Mass Flow Rate of Primary Flow (g/s) | Ejector Exit Pressure (bar) | Ejector Secondary Flow Pressure (bar) | H_{2} Mass Fraction of Secondary Flow(%) | Entrainment Ratio |
---|---|---|---|---|---|---|

55 | 3.8 | 0.05243 | 1.3 | 1.213 | 0.69 | 4.26 |

110 | 7.4 | 0.10336 | 1.52 | 1.42 | 0.65 | 2.68 |

165 | 10 | 0.15579 | 1.75 | 1.64 | 0.61 | 2.14 |

220 | 14 | 0.20672 | 1.96 | 1.845 | 0.58 | 1.90 |

275 | 16.5 | 0.25765 | 2.2 | 2.08 | 0.55 | 1.77 |

330 | 20 | 0.31009 | 2.2 | 2.07 | 0.55 | 1.77 |

385 | 22 | 0.36102 | 2.2 | 2.055 | 0.55 | 1.77 |

412.5 | 23.5 | 0.38798 | 2.2 | 2.039 | 0.55 | 1.77 |

Parameters | Value | Parameters | Value |
---|---|---|---|

Nozzle diameter (D_{t}) | 0.94 mm | Mixing tube length (L_{m}) | 20 mm |

Mixing tube diameter (D_{m}) | 3.2 mm | Suction chamber angle (θ_{s}) | 30° |

Nozzle convergence angle (θ_{tc}) | 11° | Nozzle exit position (NXP) | 3 mm |

Nozzle throat length (L_{td}) | 0.5 mm | Diffuser length (L_{d}) | 40 mm |

Nozzle divergent angle (θ_{td}) | 0° |

Model | Mesh Cells | ER | Relative Deviation |
---|---|---|---|

1 | 53,144 | 1.889706 | 6.78% |

2 | 96,729 | 1.982459 | 2.21% |

3 | 153,144 | 2.006531 | 1.02% |

4 | 199,549 | 2.017966 | 0.46% |

5 | 300,339 | 2.027254 | 0.00% |

y^{+}_{max} | Primary Flow (g·s ^{−1}) | Secondary Flow (g·s ^{−1}) | Relative Deviation |
---|---|---|---|

4.5 | 0.388 | 0.76183 | 0.021% |

2.25 | 0.388 | 0.76218 | 0.068% |

1 | 0.388 | 0.76167 | 0 |

level | θ_{td} (A) | L_{t} (B) | NXP (C) | D_{m} (D) | L_{m} (E) |
---|---|---|---|---|---|

1 | 0 | 0.5 | 1 | 2.2 | 12 |

2 | 1.5 | 1.5 | 2 | 2.6 | 15 |

3 | 3.5 | 2.5 | 3 | 3.0 | 18 |

4 | 4.5 | 3.5 | 4 | 3.4 | 21 |

5 | 6 | 4.5 | 5 | 3.8 | 24 |

L_{25}(5^{5}) | A | B | C | D | E |
---|---|---|---|---|---|

1 | 1 | 1 | 1 | 1 | 1 |

2 | 1 | 2 | 2 | 2 | 2 |

3 | 1 | 3 | 3 | 3 | 3 |

4 | 1 | 4 | 4 | 4 | 4 |

5 | 1 | 5 | 5 | 5 | 5 |

6 | 2 | 1 | 2 | 3 | 4 |

7 | 2 | 2 | 3 | 4 | 5 |

8 | 2 | 3 | 4 | 5 | 1 |

9 | 2 | 4 | 5 | 1 | 2 |

10 | 2 | 5 | 1 | 2 | 3 |

11 | 3 | 1 | 3 | 5 | 2 |

12 | 3 | 2 | 4 | 1 | 3 |

13 | 3 | 3 | 5 | 2 | 4 |

14 | 3 | 4 | 1 | 3 | 5 |

15 | 3 | 5 | 2 | 4 | 1 |

16 | 4 | 1 | 4 | 2 | 5 |

17 | 4 | 2 | 5 | 3 | 1 |

18 | 4 | 3 | 1 | 4 | 2 |

19 | 4 | 4 | 2 | 5 | 3 |

20 | 4 | 5 | 3 | 1 | 4 |

21 | 5 | 1 | 5 | 4 | 3 |

22 | 5 | 2 | 1 | 5 | 4 |

23 | 5 | 3 | 2 | 1 | 5 |

24 | 5 | 4 | 3 | 2 | 1 |

25 | 5 | 5 | 4 | 3 | 2 |

Objective | Combination | 110 A | 220 A | 412.5 A | |||
---|---|---|---|---|---|---|---|

S/N | λ | S/N | λ | S/N | λ | ||

Low current | A1B1C5D2E2 | 11.66 | 3.83 | 9.95 | 3.14 | 7.72 | 2.43 |

Middle current | A1B2C5D5E3 | 4.94 | 1.76 | 14.57 | 5.35 | 12.76 | 4.34 |

High current | A1B2C5D5E5 | 4.85 | 1.74 | 14.30 | 5.19 | 12.77 | 4.35 |

Operating range | A1B1C3D3E2 | 11.35 | 3.69 | 11.64 | 3.82 | 9.40 | 2.95 |

Structure | Initial Ejector | Optimized by Single-Factor | Optimized by Multi-Factor |
---|---|---|---|

Nozzle divergent angle | 0 | 0 | 0 |

Nozzle throat length | 0.5 | 6 | 0.5 |

NXP | 3 | 1.5 | 3 |

Mixing tube length | 20 | 18 | 15 |

Mixing tube diameter | 3.2 | 3 | 3 |

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## Share and Cite

**MDPI and ACS Style**

Li, C.; Sun, B.; Luo, Q.
Effect of Structural Parameters and Operational Characteristic Analysis on Ejector Used in Proton Exchange Membrane Fuel Cell. *Sustainability* **2022**, *14*, 9205.
https://doi.org/10.3390/su14159205

**AMA Style**

Li C, Sun B, Luo Q.
Effect of Structural Parameters and Operational Characteristic Analysis on Ejector Used in Proton Exchange Membrane Fuel Cell. *Sustainability*. 2022; 14(15):9205.
https://doi.org/10.3390/su14159205

**Chicago/Turabian Style**

Li, Chao, Baigang Sun, and Qinghe Luo.
2022. "Effect of Structural Parameters and Operational Characteristic Analysis on Ejector Used in Proton Exchange Membrane Fuel Cell" *Sustainability* 14, no. 15: 9205.
https://doi.org/10.3390/su14159205