Introduction
Experimental
Electrodes
Pressure drop measurements
Fig.1 Electrodes and flow system for hydrodynamic studies. (a) Planar electrode+ TP, which comprises a stack of three pieces of polypropylene mesh. The circular insert depicts part of one TP next to the planar electrode. (b) Expanded metal mesh electrode consisting of a welded stack of three pieces of mesh. In these images, the general direction of fluid flow is from left to right. (c) A computer-assisted design (CAD) cut view of the 23 cm high flow cell employed for pressure drop measurements. (d) Experimental arrangement of the flow circuit used for the same studies. |
Numerical simulation
Turbulent flow approach
Free flow-Brinkman approach
Subdomains and simulation details
Fig.2 3D CAD subdomains for the half-cell flow channels considered in the simulations. For the RANS approach: (a) Plate+ TP electrode and (c) mesh electrode. The geometry of the electrode structure interacts directly with the fluid flow. For the free flow-Brinkman approach: (b) Plate+ TP electrode and (d) mesh electrode. A uniform subdomain represents the macroscopic characteristics of the porous media. In this perspective, the proton exchange membrane and negative half-cell would be placed adjacent and on top of the visible electrode channel, while the current collector would be placed below it. |
Tab.1 Electrolyte and electrode structure properties used in the numerical simulation considering a 0.1 mol·dm−3 Ce(IV) ions and 0.7 mol·dm−3 Ce(III) ions solution at 25°C |
Property | Value | Ref. |
---|---|---|
Density, r/(kg·m−3) | 1370 | [15] |
Kinematic viscosity, v/(m2·s−1) | 0.039 | [15] |
Porosity of TP, ξ/dimensionless | 0.78 | [16] |
Porosity of expanded mesh, ξ/dimensionless | 0.71 | [16] |
Permeability of TP, K/m2 | 3.9 × 10−9 | [16] |
Permeability of expanded mesh, K/m2 | 7.1 × 10−9 | [16] |
Fig.3 Grid independence analysis showing mesh refinement at the corners. (a) 3D computational subdomains consisting of approximately 250000, 600000 and 1300000 elements (also called “coarse”, “normal” and “fine” mesh, respectively); (b) Plot of calculated velocity magnitude as a function of the number of grid elements at the exit manifold of the flow cell. |
Results and discussion
Hydrodynamic simulation of electrolyte velocity
Fig.4 Electrolyte flow through the channel containing the plate+ TP electrode for a mean linear velocity of 0.1 m·s−1: (a) Electrolyte velocity fields calculated using the RANS approach, (b) electrolyte velocity fields calculated using the Brinkman approach, (c) typical flow line diagram generated using the RANS approach (d) typical flow line diagram generated using the Brinkman approach. The colour scale is valid for the velocity fields and not for the line diagrams. |
Fig.5 Electrolyte flow through the channel containing the expanded mesh electrode for a mean linear velocity of 0.08 m·s−1: (a) Electrolyte velocity fields calculated using the RANS approach, (b) electrolyte velocity fields calculated using the Brinkman approach, (c) typical flow line diagram generated using the RANS approach, (d) typical flow line diagram generated using the Brinkman approach. The colour scale is valid for the velocity fields and not for the line diagrams. |
Fig.6 Electrolyte velocity profiles as a function of x-coordinate (width) for the mesh electrode at different inlet velocities at its middle section, y-coordinate (length) = 0.03 m: (a) Calculated by RANS equations, where fluid flow interacts with the electrode structure, (b) calculated by Brinkman equations, where the electrode subdomain is considered to have a homogeneous porous behaviour. Values of x with no data corresponding to the void velocity subdomain where the mesh electrode is present. |
Simulated pressure drop and its validation
Fig.7 Electrolyte velocity profiles as a function of x-coordinate (width) for the mesh electrode at different inlet velocities at its middle section, y-coordinate (length) = 0.03 m: (a) Calculated by RANS equations, where fluid flow interacts with the electrode structure, (b) calculated by Brinkman equations, where the electrode subdomain is considered to have a homogeneous porous behaviour. Values of x with no data corresponding to the void velocity subdomain where the mesh electrode is present. |