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Table 1: Geometrical parameters of the 1D-2D VRFB model

Table 1 Geometrical parameters of the 1D-2D VRFB model

Related Figures (10)

Figure 1: Schematic diagram of a VRFB (collectors + porous electrodes + polymeric membrane) interfaced to the electrical grid by a DC/AC converter. Electrolytes, stored in separated tanks, are pumped to the VRFB. AEE AEN MM MMe Se MMe Scie che ee Re SM Es el Se RE EM eR eee SAAR, ee Bets enhanced version of this model, with concentration dependent kinetics, was presented in [5]. Starting from this work, a novel 1D steady-state finite-element model of an all-vanadiun redox flow battery is here proposed. A typical VRFB cell (Fig.1) consists of: the positive anc the negative porous layers where chemical half-reactions occur, the separation polyme membrane for proton conduction, and the current collectors which convey the electron: co/from the external circuit. The FEM model incorporates the following multiphysic: aquations: momentum, charge and species conservation, mass transport (Nemst-Plank aquation), electric conduction, charge generation (Butler-V olmer equation) inside the porou: alectrodes, and the proton conduction inside the membrane. In particular, the effect of mas: ransport on the charge generation is taken into account by considering the electrode surface concentrations, which differ from bulk concentrations. Differently from [5], the 1D model i: implemented within a commercial software package (COMSOL) and takes into account the behaviour of the current collectors in order to achieve a more accurate representation of the Jevice. The independent variables of the model are the electrode and electrolyte potential: and the ionic species concentrations in the electrodes. The cell voltage is obtained from the aactrnde notential ac a fiinction of the State of Charade (SoC).
Figure 1: Schematic diagram of a VRFB (collectors + porous electrodes + polymeric membrane) interfaced to the electrical grid by a DC/AC converter. Electrolytes, stored in separated tanks, are pumped to the VRFB. AEE AEN MM MMe Se MMe Scie che ee Re SM Es el Se RE EM eR eee SAAR, ee Bets enhanced version of this model, with concentration dependent kinetics, was presented in [5]. Starting from this work, a novel 1D steady-state finite-element model of an all-vanadiun redox flow battery is here proposed. A typical VRFB cell (Fig.1) consists of: the positive anc the negative porous layers where chemical half-reactions occur, the separation polyme membrane for proton conduction, and the current collectors which convey the electron: co/from the external circuit. The FEM model incorporates the following multiphysic: aquations: momentum, charge and species conservation, mass transport (Nemst-Plank aquation), electric conduction, charge generation (Butler-V olmer equation) inside the porou: alectrodes, and the proton conduction inside the membrane. In particular, the effect of mas: ransport on the charge generation is taken into account by considering the electrode surface concentrations, which differ from bulk concentrations. Differently from [5], the 1D model i: implemented within a commercial software package (COMSOL) and takes into account the behaviour of the current collectors in order to achieve a more accurate representation of the Jevice. The independent variables of the model are the electrode and electrolyte potential: and the ionic species concentrations in the electrodes. The cell voltage is obtained from the aactrnde notential ac a fiinction of the State of Charade (SoC).
Due to the generality of PDEs defined in the fully coupled model, “General Form PDE” study nodes were used to implement both conduction and advection-diffusion equations in COMSOL. In particular, (8) was implemented as a diffusion-adsorption equation in order to account for the concentration gradient approximation. The degrees of freedom (DoF) of the discrete algebraic system are concentrations cy,4,cys,Cy+ (positive electrode) cyz,cy3,Cy+ (negative electrode), the electrolyte potential @, (membrane and electrodes), and solid phase potential @, (electrodes and collectors). These equations, discretized with quadratic finite elements (for both 1D and 2D) defined on structured meshes, were solved by the Newton- Raphson method with a fixed tolerance of 10~°. The 1D redox flow battery model is constructed from the previous non-linear equations: momentum, charge and species conservation, mass transport (Nerst-Plank equation), electric conduction, charge generation (Butler-V olmer equation) inside the porous electrodes, and the proton conduction inside the membrane. The basic assumption of the model regards the derivation of equation (8), and consists in approximating the concentration gradient inside the porous electrode with a finite difference. The partial differential equations (PDEs) for the 1D model are then simply expressed by substituting the gradient operator with 0, (derivative along the horizontal x-axis in Fig. 2) where electrical conduction and species diffusion occur. The numerical model is implemented in COMSOL®, which provides a robust simulation environment for multiphysics problems. This software, based on the finite element method (FEM) for the discretization of 1D, 2D, 3D PDEs, provides different non-linear solvers. In order to assess the validity and the accuracy of the dimensional reduction numerical
Due to the generality of PDEs defined in the fully coupled model, “General Form PDE” study nodes were used to implement both conduction and advection-diffusion equations in COMSOL. In particular, (8) was implemented as a diffusion-adsorption equation in order to account for the concentration gradient approximation. The degrees of freedom (DoF) of the discrete algebraic system are concentrations cy,4,cys,Cy+ (positive electrode) cyz,cy3,Cy+ (negative electrode), the electrolyte potential @, (membrane and electrodes), and solid phase potential @, (electrodes and collectors). These equations, discretized with quadratic finite elements (for both 1D and 2D) defined on structured meshes, were solved by the Newton- Raphson method with a fixed tolerance of 10~°. The 1D redox flow battery model is constructed from the previous non-linear equations: momentum, charge and species conservation, mass transport (Nerst-Plank equation), electric conduction, charge generation (Butler-V olmer equation) inside the porous electrodes, and the proton conduction inside the membrane. The basic assumption of the model regards the derivation of equation (8), and consists in approximating the concentration gradient inside the porous electrode with a finite difference. The partial differential equations (PDEs) for the 1D model are then simply expressed by substituting the gradient operator with 0, (derivative along the horizontal x-axis in Fig. 2) where electrical conduction and species diffusion occur. The numerical model is implemented in COMSOL®, which provides a robust simulation environment for multiphysics problems. This software, based on the finite element method (FEM) for the discretization of 1D, 2D, 3D PDEs, provides different non-linear solvers. In order to assess the validity and the accuracy of the dimensional reduction numerical
Figure 4: Electrolyte (Je) and electrode (Js) current density in electrode + membrane region.
Figure 4: Electrolyte (Je) and electrode (Js) current density in electrode + membrane region.
Figure 6: Negative electrode species concentrations Cy2, Cy3 during charge phase (SoC = 0.5).
Figure 6: Negative electrode species concentrations Cy2, Cy3 during charge phase (SoC = 0.5).
Figure 5: Positive electrode species concentrations Cy4, Cys during charge phase (SoC = 0.5). Figure 3: VRFB cell voltage vs. State of Charge.
Figure 5: Positive electrode species concentrations Cy4, Cys during charge phase (SoC = 0.5). Figure 3: VRFB cell voltage vs. State of Charge.
figure 9: Cell voltage time profile during charge (At.p, = 2200 s) and discharge phases.
figure 9: Cell voltage time profile during charge (At.p, = 2200 s) and discharge phases.
Figure 7: Reactant concentration cy,, cy; distributions during the charge phase (2D model, SoC = 0.5). Figure 8: Product concentration cy;, cy, distributions during the charge phase (2D model, SoC = 0.5).
Figure 7: Reactant concentration cy,, cy; distributions during the charge phase (2D model, SoC = 0.5). Figure 8: Product concentration cy;, cy, distributions during the charge phase (2D model, SoC = 0.5).
lable 2: Physical parameters of the 1D-2D VRFB model
lable 2: Physical parameters of the 1D-2D VRFB model
Related topics:
Electrical EngineeringChemical EngineeringEnergy Storage (in Engineering)Electrochemical Energy Storage DeviceRedox Flow BatteriesFlow Batteries
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