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Modeling Vanadium Redox Flow Batteries Using OpenFOAM

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Book cover Electrochemical Cell Calculations with OpenFOAM

Part of the book series: Lecture Notes in Energy ((LNEN,volume 42))

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Abstract

This chapter establishes that OpenFOAM is applicable for analyzing the electrolyte flow in a vanadium redox flow battery (VFB) and the transport phenomena in these systems. The local porosity was controlled by inserting an extra layer of electrode at the inlet and outlet. The variations in electrochemical characteristics and energy conversion efficiency with porosity were obtained through VFB single cell experiments. Numerical analysis of the electrolyte flow and pressure distribution provided a theoretical explanation for the physical phenomenon, which depending on the local porosities. When the current density was 50 mA/cm2, the electrode with uniform porosity (UP) showed the best energy performance. However, at a high current density of 150 mA/cm2, the partial porosity-lowered electrode at inlet (designated as LPI) showed better efficiency than the UP electrode since the rate of electrochemical reaction increases, and the mass transfer of the reactant is enhanced accordingly. OpenFOAM is expected to contribute significantly to the optimization of this flow battery system. In the near future, it will also aid in achieving carbon neutrality by the virtue of collective intelligence.

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Change history

  • 17 December 2022

    .

Notes

  1. 1.

    In order to use concentration instead of activity in the Nernst equation, formal cell potential, E0’, is a more correct expression than standard cell potential, E0. Since the difference between the two values is usually not significant, E0’ and E0 are not distinguished in this chapter. (Allen and Bard 2001).

  2. 2.

    \(k \in \left\{f, s\right\}\), f and s represent the fluid phase and solid phase, respectively.

Abbreviations

UP:

uniform porosity

LPI:

low porosity at the inlet

LPO:

low porosity at the outlet

E eq :

equilibrium cell potential

E 0 :

standard cell potential

E 0' :

formal cell potential

C i :

concentration of the i species

\({{\textit{C}}_{{\textit{i}}}^{*}}\) :

bulk concentration of the i species

R :

ideal gas constant, 8.314 J/mol K

T :

cell temperature, K

F :

Faraday constant, 96,485 A s/mol

k 0 :

standard rate constant

i :

current at the electrodes

CE:

current efficiency, Coulomb efficiency

VE:

voltage efficiency

EE:

energy efficiency

I :

current

V :

voltage

t :

time

\({\vec{u}}\) :

flow velocity vector, m/s

p :

pressure, N/m2

\({\vec{f}}\) :

acceleration vector caused by body force, m/s2

S :

sink term of the momentum loss per unit volume, kg/m2s2

K :

permeability of the porous medium, m2

V f :

void volume occupied by fluid phase

V s :

void volume occupied by solid phase

V :

local representative elementary volume

REV:

representative elementary volume

<>:

superficial average or phase average (macroscopic)

\({\left\langle { } \right\rangle ^k}\) :

intrinsic phase average (microscopic)

u D :

Darcy velocity (flux), filtration (filter) velocity, superficial velocity

u p :

physical velocity, pore velocity, interstitial velocity

D p :

mean pore diameter, m

Fo:

Forchheimer number

Cf:

Forchhemier coefficient, inertia coefficient

Re:

Reynolds number

\({\alpha}\) :

transfer coefficient, symmetry factor, in Eqs. (8) and (9)

\({\alpha}\) :

viscous resistance coefficient, m–2, in Eqs. (29), (30), and (32)

\({\eta}\) :

overpotential

\({\rho}\) :

density, kg/m3

\({\rho_0}\) :

reference density or surface density, kg/m3

\({\varepsilon}\) :

porosity

\({\tau _{ij}}\) :

shear stress tensor, N/m2

\({\mu}\) :

dynamic viscosity, Pa·s

\({\mu_e}\) :

effective viscosity, Pa·s

\({\beta}\) :

inertial resistance coefficient, Forchhemier or non-Darcy coefficient, m–1

\({\psi_k}\) :

local microscopic property with k-phase

0:

standard state when activity is 1.0

':

formal state

*:

bulk solution

dis :

discharge

ch :

charge

+:

positive electrode

−:

negative electrode

f :

fluid phase

s :

solid phase

k :

phase, solid or fluid

D :

Darcy

p :

physical value or pore

e:

effective value

0:

reference or surface

References

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Acknowledgements

This research was supported by Korea Institute of Science and Technology (2E30993), Dongguk University research fund of 2021, the KRICT Core Research Program (KK2022-20) and Chung Ang University research fund of 2021.

Author information

Authors and Affiliations

  1. Korea Institute of Science and Technology Europe, Saarbrücken, Germany

    Sangwon Kim

  2. Transfercenter Sustainable Electrochemistry, Saarland University, Saarbrücken, Germany

    Sangwon Kim

  3. Department of Mechanical System Engineering, Dongguk University, Gyeongju, Republic of Korea

    Dong Hyup Jeon

  4. Advanced Material Division, Korea Research Institute of Chemical Technology, Daejeon, Republic of Korea

    Sang Jun Yoon

  5. School of Mechanical Engineering, Chung-Ang University, Seoul, Republic of Korea

    Dong Kyu Kim

Authors
  1. Sangwon Kim
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  2. Dong Hyup Jeon
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Corresponding author

Correspondence to Sangwon Kim .

Editor information

Editors and Affiliations

  1. Institute of Energy and Climate Research (IEK-14), Forschungszentrum Jülich GmbH, Jülich, Germany

    Steven Beale

  2. Institute of Energy and Climate Research (IEK-14), Forschungszentrum Jülich GmbH, Jülich, Germany

    Werner Lehnert

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Kim, S., Jeon, D.H., Yoon, S.J., Kim, D.K. (2022). Modeling Vanadium Redox Flow Batteries Using OpenFOAM. In: Beale, S., Lehnert, W. (eds) Electrochemical Cell Calculations with OpenFOAM. Lecture Notes in Energy, vol 42. Springer, Cham. https://doi.org/10.1007/978-3-030-92178-1_5

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  • DOI: https://doi.org/10.1007/978-3-030-92178-1_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92177-4

  • Online ISBN: 978-3-030-92178-1

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