Numerical modeling can provide quantitative information and analysis to predict the battery behavior accurately. Solution to the governing equations is difficult because of coupling of the transport processes and the electrochemical reaction. Recently it is found that numerical modeling using computational fluid dynamics techniques can lead to remarkable capabilities and advantages in providing more quantitative information about the battery systems and their performance[28]. Shah et al. [29]
developed two-dimensional transient numerical model for the vanadium redox flow
batteries. As per best of our knowledge, this is the first published work on numerical modeling of the vanadium redox flow battery. The governing equations are solved by COMSOL Multiphysics package. The study has been done for the effects of the variations in the concentration, electrolyte flow rate and electrode porosity on the performance of the cell. The model is validated with the experimental result and it shows better agreement. Bayanov and Vanhaelst [14] developed a two-dimensional numerical model based on the conservation of mass, momentum and charge with reaction equations. They studied the battery performance for various electrode col- lectors for different current density. The numerical simulation study has been done for two cases like carbon plates electrode collectors and steel plates electrode collec- tors. The results show that even though the resistance of the electrode collectors is same for steel plate give better voltage current characteristics than the carbon plate collectors. The charge and discharge time are higher for the carbon plate electrode collectors than the steel plate electrode collectors. The numerical simulation results validated with the experimental results which shows good agreement. You et al. [13]
studied the two-dimensional stationary model for the vanadium redox flow battery based on the conservation laws coupled with electrochemical reactions. The equa- tions of the continuity, momentum, species conservation, charge with the reaction equations are solved using the COMSOL Multiphysics package. They studied the performance of the cell by varying the electrode porosity, applied current density and local mass transfer coefficient. The results shows that the bulk reaction rate depends on the applied current density, if the applied current density increases two times the initial value then the transfer current density and overpotential increase almost double. The variation of the mass transfer coefficient only affects value of the overpotential. Also results show that if mass transfer coefficient decreases, it results in increased polarization and rate of side reactions. Chen et al. [28] did the numerical simulation of the electrolyte flow distribution for all vanadium redox flow battery by solving steady equations of continuity and momentum equation using the commercial CFD package ANSYS FLUENT. The numerical simulation results show that electrolyte has concentrated distribution at the central area of the flow field of the cell and disturbed flow and vortex flow of the electrolyte in the inlet and outlet regions. The higher flux of electrolyte in the battery leads to uniform dis- tribution of electrolyte and minimizes the effect of flow irregularity on the battery.
Vynnycky [12] has developed two-dimensional time dependent single phase isother- mal numerical model for the operation of a single cell in a vanadium redox flow
2.4 Two-dimensional numerical study 15 battery. The model assumes that the membrane is fully humidified, only hydrogen ions can cross the membrane and the dilute solution approximation is valid. He also derived asymptotically reduced model, which decouples fluid mechanics from electrochemistry. This approach is proposed for accurate and computationally ef- ficient vanadium redox flow battery models. The important advantage of using asymptotically reduced model is, it preserve geometrical resolution without losing the accuracy. The governing equations with suitable assumptions and boundary conditions are solved by using the COMSOL Multiphysics package. These mathe- matical models are useful in optimizing the vanadium redox flow battery.
Chen et al. [30] extended the above model by adding advection term in species con- servation equations and proton concentrations in Nernst equation. This enhanced model is able to capture cell performance at different flow rates as evidenced by polarization curves. The optimal electrolyte flow rate can be determined by using power based round trip efficiencies. A quasi-steady state model was developed for VRFBs by Sharma et al. [31]. This model was more useful for rapid modeling, de- sign and optimization of VRFB stacks. One more model was developed by Turker et al. [32] based on the experimental data. The overall system efficiency with soc was studied for VRFB unit and soc was estimated by including the energy losses at stacks during electrochemical conversion process and by the power consumption of the hydraulic circuits as well as the power conversion systems. By employing this model, optimal number of modules for certain power levels while charging and discharging operations were calculated for megawatt scale operations. Viscosity of the electrolyte dependent model was developed for the VRFB [33]. In reality the viscosity of the electrolyte varies during charging and discharging process as the con- centrations of acid and vanadium ions in the electrolyte continuously change with the state of charge of VRFB. The results show that consideration of soc dependent electrolyte gives a more realistic simulation of the distributions of current density and overpotential in the electrodes. It results in more accurate estimations of system efficiency and pumping work of VRFBs. A model by Tian et al. [34] was proposed to reduce the pressure drop across the porous electrodes in VRFB. It was found that for lab-scale single electrode size, pressure drop can be minimized by introducing of channels in the flow cell and electrode designs. Also the proposed new design does not generate significant net power output loss.
A two-dimensional numerical model [35] was introduced by including the effects of electrode compression on voltage losses and hydraulics. The results show that reduc-
tion of the electrode thickness by compression reduces the porosity, the specific area resistance and hydraulic permeability, which results in increase in cell performance but also higher pressure drop. Also due to electrode compression reduces the ohmic losses leading to better performance. The VRFB model [36] based on the stack efficiency curves given by the manufacturer, the model includes mechanical model of the VRFB hydraulic circuit and pumps. Also the model takes into consideration of both the voltage and coulombic losses of the stack, therefore the performance of the model has a high degree of accuracy. Latha and Jayanthi [37] studied the electrolyte flow distribution for three sets of parallel, serpentine and interdigitated configurations for redox flow batteries. From the result it was showed that pressure drop in the interdigitated flow field is less than that in the serpentine for the same flow rate. Also interdigited flow fields show superior cell performance of RFBs. A model was developed by Rudolph et al. [38] to study the energy and efficiency losses during cyclic operation of the VRFB. It was observed that the capacity decrease is caused by the parasitic oxidation ofV2+ ions in the negative half-cells and the inter- nal resistance increase due to passivation of the negative graphite collector surface.
The hydrodynamics of serpentine flow fields were studied for the RFB applications [39]. It was shown that considerable effect on the predicted pressure drop on the performance of the redox flow batteries. Rudolph et al. [40] developed model to study the distribution of the electrolyte in the electrode with different inlet configu- rations. This model was useful to achieve optimal electrolyte flow rate which results to obtain the uniform distribution of the electrolyte flow to each half-cell.