A Lattice-Boltzmann Model of Mass Transport in the Diffusion Layers of Vanadium Redox Flow Batteries

During the last years all-Vanadium Redox Flow Batteries (VRFBs) have gained attention as a way to store energy due to their high energy efficiency, long cycle life, independently tuneable power/energy size, and lack of contamination from cross-mixing of electrolytes [1]. However, in order to improve VRFBs performance, some conceptual and technological issues are still open. In particular, a properly designed geometry of flow channels and porous medium, which guarantees a uniform distribution of the reacting species all along the electrode, is still under investigation [2]. The ideal configuration aims to minimize the drag and maximize the mixing. In the present work a Lattice Boltzmann tri-dimensional multi-relaxation-time model has been used to better understand the dependence of mass and momentum transports on the porosity and carbon fiber preferential orientation in a typical VRFB porous medium. The model has been successfully validated against theoretical solutions of the Volume Averaged Navier-Stokes Equations [3]. The typical porosity used in VRFB,  f=0.9±0.1, is considered in a triperiodic box (left panel of Fig. 1). The flow is driven along the x direction by a mean pressure gradient DP/Dx which imposes the Reynolds number Re_p=rd_pU/(m (1-f)) with U the bulk velocity, d_p the fiber diameter, r and m the fluid density and dynamic viscosity, respectively. Different fiber orientations and distributions have been analyzed, from random isotropic cases to a completely oriented medium. Results show that the drag measured by the friction factor f_p=(f³/1-f)(DP/Dx)/(rU²) is well captured by the semi-empirical Ergun formula fe=1.75+150/Re_p when the medium is isotropic or preferentially oriented in directions transversal to the flow (right panel of Fig. 1). Conversely, when the medium is preferentially oriented along the flow direction the drag is appreciably reduced differing from the standard predictions. The fiber orientation also affects the mixing in the porous medium that needs to be enhanced to optimize the VRFB performance. The mass transport shows anomalous dispersion properties. Super-diffusive and sub-diffusive behaviors can be observed depending on the considered direction and fiber preferential orientation. A detailed analysis of mixing and drag properties of the porous media will be discussed in the final contribution in order to highlight the optimal configurations for VRFB.

References

[1]      P. Alotto, M. Guarnieri and F. Moro, “Redox flow batteries for the storage of renewable energy: A review”, Renew. Sust. Energ. Rev., 29, (2014): 325–335.

[2]      A. Tang, J. Bao, M. Skyllas-Kazacos, “Studies on pressure losses and flow rate optimization in vanadium redox flow batteries,” J. Power Sources, 248, (2014): 154-162.

[3]      D. Maggiolo, P. Alotto, A. Marion, M. Guarnieri, “Lattice-Boltzmann-based model for the channel-porous interface of PEMFC,” Proc. EFC2013 - Fifth European Fuel Cell Technology and Applications Conference - Piero Lunghi Conference, EFC13236, (2013): 379-380.