# Effect of Serpentine Flow Field Channel Dimensions and Electrode Intrusion on Flow Hydrodynamics in an All-Iron Redox Flow Battery

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{2}for different electrolyte flow rates were numerically validated. A computational fluid dynamics study was conducted for detailed flow analyses, velocity magnitude contours, flow distribution, and uniformity index for the intrusion effect of a graphite felt electrode bearing a thickness of 6 mm with a channel compressed to varying percentages of 50%, 60%, and 70%. Experimental pressure drops $\left(\Delta p\right)$ over the numerical value resulted in the maximum error approximated to 4%, showing good agreement. It was also reported that the modified version of the cross-split serpentine flow field, model D, had the lowest pressure drop, $\Delta p$, of 2223.4 pa, with a maximum uniformity index at the electrode midplane of 0.827 for CR 50%, across the active cell area. The pressure drop $\left(\Delta p\right)$ was predominantly higher for increased compression ratios, wherein intrusion phenomena led to changes in electrochemical activity; it was found that the velocity distribution was quite uniform for a volumetric uniformity index greater than 80% in the felt.

## 1. Introduction

## 2. Materials and Methods

^{2+}⇌ 2Fe

^{3+}+ 2e

^{−}E

^{0}= 0.77 V

^{2+}+ 2e

^{−}⇌ Fe

^{0}E

^{0}= −0.44 V

^{2+}⇌ Fe

^{0}+ 2Fe

^{3+}E

^{0}= 1.21 V

^{2}, with fixed inlet and outlet positions. Electrode graphite felt, a porous medium with a thickness of 6 mm, was specifically selected based on certain criteria such as electrical conductivity, surface area, pore size, pretreatment (thermal treatment), and electrochemical activity (cell resistance and cell efficiency). An electrolyte solution containing ferrous chloride tetrahydrate (FeCl

_{2}) was proportionately mixed with 2 moles of ammonium (NH

_{4}), 3.25 moles of chloride (Cl

_{2}), and 0.3 moles of ascorbic acid (C₆H₈O₆) to maintain ideal pH conditions [37].

#### 2.1. Flow Field without Felt Model

#### 2.2. Flow Field with Felt Model

#### 2.3. Circuit Analogy Model

_{1}and m

_{2}are split mass flow, i.e., correlating to vertical and horizontal channels of the model, respectively; and R

_{1}and R

_{2}are resistance values corresponding to the vertical and horizontal halves of the model, respectively. Henceforth, the analysis considered the mass flow to be equivalent to the current flow, and the resistance was equivalent to flow deceleration due to skin friction and bend losses in the passage.

^{2}[4 f L/D + N

_{b}K

_{b}]

_{b}is the number of bends, and K

_{b}is the bend loss coefficient.

_{m}= ∆p/L = αV + βV

^{2}

_{c}, and d

_{fi}are the original felt thickness, compressed felt thickness, and depth length of felt intrusion into the channel, respectively.

^{2}= 0.012(1 − ϕ) [ π/4ϕ

^{2}− 2 (π/4ϕ) + 1] [1 + 0.72ϕ/(0.89 − ϕ)

^{0.54}]

## 3. Experimental Study

^{2}, i.e., 135 mm length × 97 mm width, wherein 17 parallel channels are aligned along the longer length of the rectangular cell. Notably, all are square channels with a 2 mm hydraulic diameter, each placed at an equal distance, as depicted in Figure 5. Geometrical details of the flow field along with the felt are as follows: channel width of 2 mm, rib width of 2 mm, channel depth of 2 mm, and Rayon-based graphite felt electrode (AGFHT) with a thickness of 6 mm and subjected to electrode compression (change in original thickness) to 60% and graphite plate (isostatic grade) with a thickness of 10 mm.

^{2+}/Fe

^{3+}and Fe

^{2+}/Fe, acting as positive and negative electrolytes, respectively, as stated in Equations (1) and (2).

## 4. CFD Analysis

#### 4.1. Flow Field Model Analysis

#### 4.2. Flow Field with the Electrode Intrusion Model

_{ch}and Q

_{pm}, flowing through the channel and porous electrode medium. The properties of the selected electrode were a plane permeability of 1.498 × 10

^{-6}m

^{2}, porosity of 0.80, and a fiber diameter of 0.0155 mm. The electrolyte had a viscosity of 0.0013897 Pa-s. Electrode intrusion into the channel is a strong function of compression ratios, which reduce the hydraulic diameter of the channel and thereby increase the mean effective flow velocity, resulting in an increased pressure drop. Equation (10) shows the calculation of the intrusion depth in terms of the compression ratio (CR) and the uncompressed thickness of the graphite felt.

## 5. Results and Discussion

#### 5.1. Numerical Software Validation

^{2}. The experimental results of pressure drop, ∆p, obtained for the above cell area were compared with those of numerically analyzed values. The pressure drop curves were derived based on the analysis results of a 2 × 2 single-channel serpentine flow field (SCSFF) with an intrusion effect for varying Reynold’s numbers of 180, 360, 540, 720, and 899 at a 60% compression value, as depicted in Figure 10.

#### 5.2. Simulation Results

## 6. Conclusions

^{2}. The parameters measured experimentally, such as cell pressure drop $\left(\Delta p\right)$ through channels and with the presence of electrodes, were numerically validated using a CFD tool. The electrode felt channel intrusion behavior for both the flow fields, i.e., SCSFF and CSSFF at different CRs for various flow rates, was also numerically analyzed for flow velocity magnitude and flow distribution characteristics.

- A single-channel serpentine flow field (SCSFF) resulted in the highest pressure drop order of 31,815.35 Pa compared with a modified version of the cross-split serpentine flow field of Model D with 6941.12 Pa at CR 60% for a flow rate of 150 mL/min across an active cell area of 131 cm
^{2}. - The compression ratio (CR) was found to be a strong function of electrode felt channel intrusion, which resulted in a reduced effective hydraulic diameter of the channel, which, in turn, reduced the effective flow area, causing an increased mean flow velocity.
- We observed that skin friction is a function of the Reynolds number and gradually increased due to a reduction in the effective hydraulic diameter, which meant the flow velocity had increased.
- We also observed that even with an increase in the volumetric flow uniformity index of more than 80%, the flow velocity distribution over electrode felt was relatively uniform at different compression ratios, as shown in Figure 15.
- We also noticed that the influence of an intrusion effect was marginal on the flow distribution and uniformity throughout the electrode felt region.
- The CSSFF design was found to be the better choice over SCSFF in terms of volumetric flow uniformity through electrode mid and end planes, and might also reduce the mass transport polarization behavior, establishing an ideal ionic activity rate.
- In this study, Model D, a modified version of CSSFF, was found to be an optimal design suitable for the defined active cell area of 131 cm
^{2}, at different CRs, operating at a maximum flow rate of 150 mL/min.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 5.**The 2 × 2 single-channel serpentine flow field with electrode felt (SCSFF) CFD flow field model.

**Figure 6.**(

**a**) An Experimental Set Up of Battery Stack. (

**b**) U Tube Manometer to Measure Pressure Drop.

**Figure 8.**(

**a**) Graphite Electrode Felt Intrusion into Channels. (

**b**) Geometry Modeled for CFD Analysis.

**Figure 9.**(

**a**–

**c**) are Schematic Representations of the Flow Field with Electrode Felt Intrusion at Varying Compression Ratios (50, 60 and 70%).

**Figure 10.**Comparison of CFD and Experiment Pressure Drop (∆p) for the Single Channel Serpentine Flow Field (SCSFF) for Different Reynold’s Number.

**Figure 11.**(

**a**–

**c**) 2 × 2 single serpentine flow field (SCSFF) absolute total pressure drop with electrode felt intrusion, predicted velocity magnitude at channel mid plane without electrode felt and with electrode felt mid plane 60% CR at 150 mL/min.

**Figure 12.**(

**a**–

**c**) Comparison of experimental and CFD pressure drop values for model D of CSSFF with an electrode intrusion at CR (50%, 60%, and 70%) for flow rates of 30, 90, and 150 mL/min.

**Figure 13.**Predicted absolute pressure drop for Model D of the CSSFF with an electrode intrusion for a flow rate of 150mL/min at CRs: (

**a**) 50%; (

**b**) 60%; and (

**c**) 70%.

**Figure 14.**(

**a**–

**c**) Velocity magnitude at the mid-plane of Model D of the CSSFF channel for a flow rate of 150 mL/min.

**Figure 15.**Predicted velocity magnitude at an electrode mid-plane for Model D of CSSFF with an electrode intrusion for a flow rate of 150 mL/min at CRs: (

**a**) 50%; (

**b**) 60; (

**c**) 70%.

**Figure 16.**Uniformity index for Model D of CSSFF with an electrode intrusion at CRs of 50%, 60%, and 70% for a flow rate of 150 mL/min.

**Figure 17.**Predicted volumetric flow distribution at an electrode mid-plane for Model D of CSSFF with an electrode intrusion for a flow rate of 150mL/min at CRs: (

**a**) 50%; (

**b**) 60%; and (

**c**) 70%.

Models | Width (mm) | Channel Depth (mm) | No of Channels | No. of Bends (N _{b}) | Total Flow Path Length (mm) | Active Area (mm ^{2}) | Channel Hydraulic Diameter (mm) | ||
---|---|---|---|---|---|---|---|---|---|

Channel | Rib | Horizontal | Vertical | ||||||

A | 2 | 2 | 2 | 17 | 24 | 40 | 3037 | 2 | |

B | 2 | 2 | 3 | 17 | 24 | 40 | 3037 | 2.4 | |

C | 3 | 3 | 2 | 13 | 19 | 31 | 2364 | 2.4 | |

D | 3 | 3 | 3 | 13 | 19 | 31 | 2364 | 13,095 | 3 |

Boundary Condition | Flow Rate mL/min | Reynold’s (Re) | CFD Pressure Drop p [Pa] | Exp Pressure Drop p [Pa] |
---|---|---|---|---|

1 | 30 | 180 | 4898.61 | 5100.00 |

2 | 60 | 360 | 11,188.90 | 11,600.00 |

3 | 90 | 540 | 17,772.72 | 18,550.00 |

4 | 120 | 720 | 24,647.79 | 25,750.00 |

5 | 150 | 899 | 31,815.35 | 33,250.00 |

Case | Graphite Felt Actual Thickness (mm) | CR 50% | CR 60% | CR 70% |
---|---|---|---|---|

Compressed value | 6 | 3 | 2.4 | 1.8 |

Intrusion value | 1.78 | 2.14 | 2.49 |

**Table 4.**Compared experimental and CFD pressure drop values for Model D of the CSSFF at different CRs and for varying flow rates.

Flow Rates mL/min | Compression Ratio % | Experimental CSSFF Pressure Drop, Pa | CFD Model CSSFF Pressure Drop, Pa |
---|---|---|---|

30 | 50.00 | 1233 | 1002 |

60.00 | 3128 | 2789 | |

70.00 | 12,450 | 11,890 | |

90 | 50.00 | 1874 | 1560 |

60.00 | 4840 | 4150 | |

70.00 | 18,300 | 17,780 | |

150 | 50.00 | 2453 | 2223 |

60.00 | 7350 | 6941 | |

70.00 | 26,130 | 24,679 |

Compression Ratio Percentage | Uniformity Index (Felt Mid) | Uniformity Index (Felt Volume) |
---|---|---|

50 | 0.827 | 0.768 |

60 | 0.820 | 0.749 |

70 | 0.804 | 0.721 |

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## Share and Cite

**MDPI and ACS Style**

Krishnappa, R.B.; Subramanya, S.G.; Deshpande, A.; Chakravarthi, B.
Effect of Serpentine Flow Field Channel Dimensions and Electrode Intrusion on Flow Hydrodynamics in an All-Iron Redox Flow Battery. *Fluids* **2023**, *8*, 237.
https://doi.org/10.3390/fluids8080237

**AMA Style**

Krishnappa RB, Subramanya SG, Deshpande A, Chakravarthi B.
Effect of Serpentine Flow Field Channel Dimensions and Electrode Intrusion on Flow Hydrodynamics in an All-Iron Redox Flow Battery. *Fluids*. 2023; 8(8):237.
https://doi.org/10.3390/fluids8080237

**Chicago/Turabian Style**

Krishnappa, Rakesh Basavegowda, S. Gowreesh Subramanya, Abhijit Deshpande, and Bharatesh Chakravarthi.
2023. "Effect of Serpentine Flow Field Channel Dimensions and Electrode Intrusion on Flow Hydrodynamics in an All-Iron Redox Flow Battery" *Fluids* 8, no. 8: 237.
https://doi.org/10.3390/fluids8080237