Eulerian Two-Fluid Model of Alkaline Water Electrolysis for Hydrogen Production
Abstract
:1. Introduction
2. Numerical Methods
2.1. Geometry and Mesh
2.2. Mathematical Formulation
2.2.1. The Bubble Dispersion Problem
2.2.2. Model
- The flow is Newtonian, viscous and incompressible;
- Due to the high heat transfer induced by the bubbles and the relatively low surface and volume inducing a low heat injection by ohmic and activation losses, the flow is considered isothermal
- At the same time, numerical simulations were carried out in order to highlight the influence of ions on the velocity and void fraction distribution. There were only very little differences when the ions distribution was taking into account. Thus, the electrolyte is considered as extremely well mixed. This hypothesis has been made also by Abdelouahed et al. [26] and Schillings et al. [14];
- Oxygen, hydrogen and electrolytes are three continuum media;
- Because the Reynolds number calculated via the data from Boissonneau et al. [15] is between 240 and 480, the flow is considered as laminar;
- The effect of the surface tension is neglected;
- Nagai et al. [28] observed a dependency of the diameter with respect with the current density and in addition to this dependency, Boissonneau et al. [15] observed that the bubble diameter increases with height. Schillings et al. [14] chose to make the diameter increase with the height and current density. In the current study and in other studies [12,13], it was decided that a constant bubble diameter is taken for a given current density. Although this hypothesis is made in a lot of studies, it does not reflect the reality. There is a distribution of the bubble diameter, but since it is not yet possible to model this distribution, we are forced to make this assumption;
2.3. Boundary Conditions
2.4. Numerical Procedure
3. Results
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Position | Boundary Conditions |
---|---|
x = 0 Helec < y < 2 Helec | |
x = 2h 0 < y <3 Helec | |
0 < x < 2h y = 0 | |
0 < x < 2h y = 3 Helec |
Name | Value |
---|---|
Geometry inputs | |
Helec (mm) | 40 |
L (mm) | 30 |
h (mm) | 1.5 |
HTot (mm) | 120 |
Physical Inputs | |
ρl (kg m−3) | 1040 |
ρO2 (kg m−3) | 1.3 |
ρH2 (kg m−3) | 0.08 |
υl (m2 s−1) | 9.97 × 10−7 |
Two-Phase Inputs | |
db (µm) | for 500 A m−2 db = 50 µm for 1000 A m−2 db = 58 µm for 2000 A m−2 db = 78 µm |
500 A m−2 | 1000 A m−2 | 2000 A m−2 |
---|---|---|
KO2/d = 10.5 | KO2/d = 9 | KO2/d = 5 |
KH2/d = 5 | KH2/d = 4 | KH2/d = 2.5 |
j (A m−2) | Model Comparaison | Zone | 60 mm | 75 mm |
---|---|---|---|---|
500 A m−2 | Boissonneau vs. Abdelouahed | H2 | 6.95 × 10−2 | 3.96 × 10−2 |
O2 | 2.48 × 10−1 | 1.47 × 10−1 | ||
Bulk | 2.91 × 10−1 | 2.91 × 10−1 | ||
Boissonneau vs. Schillings | H2 | 6.00 × 10−2 | 1.60 × 10−2 | |
O2 | 2.85 × 10−1 | 2.65 × 10−1 | ||
Bulk | 1.90 × 10−1 | 2.06 × 10−1 | ||
Boissonneau vs. Current Study | H2 | 1.76 × 10−1 | 4.55 × 10−2 | |
O2 | 2.01 × 10−1 | 7.40 × 10−2 | ||
Bulk | 2.48 × 10−1 | 2.36 × 10−1 | ||
1000 A m−2 | Boissonneau vs. Abdelouahed | H2 | 1.04 × 10−1 | 6.13 × 10−2 |
O2 | 3.48 × 10−1 | 2.69 × 10−1 | ||
Bulk | 3.83 × 10−1 | 3.51 × 10−1 | ||
Boissonneau vs. Schillings | H2 | 1.21 × 10−1 | 4.76 × 10−2 | |
O2 | 2.99 × 10−1 | 2.27 × 10−1 | ||
Bulk | 1.69 × 10−1 | 1.31 × 10−1 | ||
Boissonneau vs. Current Study | H2 | 1.04 × 10−1 | 7.95 × 10−2 | |
O2 | 2.35 × 10−1 | 6.37 × 10−2 | ||
Bulk | 2.50 × 10−1 | 1.99 × 10−1 | ||
2000 A m−2 | Boissonneau vs. Abdelouahed | H2 | 1.43 × 10−1 | 7.09 × 10−2 |
O2 | 2.69 × 10−1 | 3.58 × 10−1 | ||
Bulk | 3.51 × 10−1 | 3.70 × 10−1 | ||
Boissonneau vs. Schillings | H2 | 4.76 × 10−2 | 4.31 × 10−2 | |
O2 | 2.27 × 10−1 | 2.90 × 10−1 | ||
Bulk | 1.31 × 10−1 | 6.27 × 10−2 | ||
Boissonneau vs. Current Study | H2 | 7.95 × 10−2 | 7.44 × 10−2 | |
O2 | 6.37 × 10−2 | 1.71 × 10−1 | ||
Bulk | 1.99 × 10−1 | 2.57 × 10−1 |
j (A m−2) | Vmax liq cath (m s−1) | Vmax liq an (m s−1) | εmax cath | εmax an | δcath (µm) | δan (µm) | R(ε)/R |
---|---|---|---|---|---|---|---|
500 A m−2 | 7.8 × 10−2 | 4.8 × 10−2 | 0.23 | 0.13 | 515 | 600 | 1.032 |
1000 A m−2 | 9 × 10−2 | 6.8 × 10−2 | 0.28 | 0.16 | 566 | 677 | 1.043 |
2000 A m−2 | 1.25 × 10−1 | 9.1 × 10−2 | 0.33 | 0.19 | 690 | 800 | 1.057 |
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Le Bideau, D.; Mandin, P.; Benbouzid, M.; Kim, M.; Sellier, M.; Ganci, F.; Inguanta, R. Eulerian Two-Fluid Model of Alkaline Water Electrolysis for Hydrogen Production. Energies 2020, 13, 3394. https://doi.org/10.3390/en13133394
Le Bideau D, Mandin P, Benbouzid M, Kim M, Sellier M, Ganci F, Inguanta R. Eulerian Two-Fluid Model of Alkaline Water Electrolysis for Hydrogen Production. Energies. 2020; 13(13):3394. https://doi.org/10.3390/en13133394
Chicago/Turabian StyleLe Bideau, Damien, Philippe Mandin, Mohamed Benbouzid, Myeongsub Kim, Mathieu Sellier, Fabrizio Ganci, and Rosalinda Inguanta. 2020. "Eulerian Two-Fluid Model of Alkaline Water Electrolysis for Hydrogen Production" Energies 13, no. 13: 3394. https://doi.org/10.3390/en13133394