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Section 2.12 Modeling of the hydraulic circuit 2.12 Modeling of the hydraulic circuit The energy demand required for transporting the electrolyte in and out of the stacks, is a significant source of power loss in a flow battery. Furthermore, hydraulic, electric and electrochemical subsystems are closely interrelated. A higher flow rate decreases the concentration overpotential but increases the pump power demand. Long and narrow inlet and outlet channels of the cells reduce shunt currents, but increase the hydraulic resistance and thus again the pump power demand. Hence, the hydraulic circuit compellingly needs to be included into the design and optimization considerations. The pressure drop in the stack manifolds has to remain small, to enable an equal supply of all connected cells. Consequently, it is neglected in this work. The pressure drop in the cell, which consists of input channel, distribution funnel, porous flow-through electrode, collection funnel and output channel is derived using computational fluid dynamic (CFD) simulations. The cell model set up in ANSYS Maxwell to determine the channel geometry factor is linked to the CFD software ANSYS Fluent. Hence, the geometry does not have to be modelled again. The elements of the external hydraulic circuit such as pipes, tubes and orifices, namely T-junctions, 90° bends, and sensors, are modelled as follows. Also, a flow rate dependent pump efficiency is considered. 2.12.1 Pressure drop in the porous graphite felt electrode For the porous flow-through electrode, ANSYS Fluent applies Darcy’s law, as shown in Eq. (2-78) [71]. ∆p μElhE Q E κEwEE C (2-78) Wherein: ΔpE Pressure drop in the electrode μEl Electrolyte dynamic viscosity κE Permeability of the porous electrode (m2) hE Electrode height (m) wE Electrode width (m) δE Electrode thickness (m) QC Cell volumetric flow rate (m3s-1) The permeability of the porous electrode, κE, is derived using the Kozeny-Carman relation, as shown in Eq. (2-79) [71]. κE d2F 16KKC Wherein: dF Fiber diameter of the graphite felt KKC Kozeny-Carman constant εE Porosity of the graphite felt electrode ε3E 1 εE2 (m) 4.28 0.93 (2-79) (Pa) (Pas) 49PDF Image | Model-based Design Vanadium Redox Flow Batteries
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