# Effect of Groove Shape on Head Loss and Filtration Performance of Disc Filters

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Shape of Disc Groove

#### 2.2. Experimental Set-Up

#### 2.3. Head Loss Test

^{3}/h, and $k$ and $n$ are empirical constants that are determined by various structural features of the disc filter. In the head loss graph depicted in a logarithmic scale of general disc filters, $n$ is indicated by the slope of a straight line, which varies depending on the type of disc filter.

#### 2.4. Analysis of Head Loss Considering the Disc Groove Shape

#### 2.5. Filtration Performance Test

## 3. Results and Discussion

#### 3.1. Analysis of Disc Groove

^{2}and 49,285.4 μm

^{2}for the semi-elliptic and trapezoidal groove disc filters, respectively. Unlike the geometrical features of discs that could be observed with the naked eye, the shape of the grooves showed a difference of up to 57.6% in their sectional area. Additionally, the shape of the grooves on the upper and lower parts of the semi-elliptic groove disc was similar, whereas in the trapezoidal groove disc filter, the grooves on the upper and lower parts were different. The difference in hydraulic diameter according to the type of disc filter was small compared to the difference in the sectional area because the semi-elliptical groove shape in the proposed disc filter had a relatively large hydraulic diameter even in a small area. In other words, for the same sectional area, the elliptical shape provided a greater hydraulic diameter compared to other shapes.

#### 3.2. Head Loss Test Result

^{3}/h measured in the experiment, the head loss in the semi-elliptic groove filter was greater than that of the trapezoidal groove filter because the total number of grooves in the traditional disc filter was higher, and their average sectional area was approximately 1.8 times larger than that of the proposed disc filter. However, as the flow rate increased, the head loss of the trapezoidal groove filter increased more steeply, and it was estimated to be greater than that of the semi-elliptic groove filter at the flow rates exceeding 52.4 m

^{3}/h.

#### 3.3. Analysis of Head Loss According to the Groove Type

^{−6}m

^{2}/s, as shown in Table 3. The Reynolds number was less than 2100 in the majority of flow rates less than 63.9 m

^{3}/h and 98.8 m

^{3}/h in the semi-elliptic and trapezoidal groove filters, respectively. Accordingly, the flow inside the disc groove was considered to be laminar.

^{3}/h, the head loss in the trapezoidal disc groove with an adjusted area was greater than that of the semi-elliptic disc groove. In the range of 12–25 m

^{3}/h, which is the recommended flow rate provided in the product manual for disc filters, the head loss in a groove in two filters differed by 48–58%. Although the total head loss of the trapezoidal groove filter was smaller than that of the semi-elliptic groove filter in the head loss test, it was found that the head loss of the semi-elliptic groove filter was smaller when the sectional areas of the grooves were same. In other words, it is estimated that the hydraulically efficient cross section to reduce the head loss is elliptical because it increases the hydraulic diameter.

#### 3.4. Filtration Performance Test Results

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 3.**FESEM images showing the cross section of disc groove: (

**a**) Semi-elliptic groove disc magnified at 150×; (

**b**) Upper and (

**c**) lower part of semi-elliptic groove disc at 250×; (

**d**) Trapezoidal groove disc magnified at 150×; (

**e**) Upper and (

**f**) lower part of trapezoidal groove disc at 250×.

**Figure 4.**Relationship between head loss and flow rate: Semi-elliptic groove disc filter is presented by circle with black trend line and trapezoidal groove disc filter is presented by square with dotted trend line.

**Figure 5.**Maximum particle size that can pass through the disc groove: (

**a**) Semi-elliptic groove; (

**b**) Trapezoidal groove.

Specification | Semi-Elliptic Groove Disc Filter | Trapezoidal Groove Disc Filter |
---|---|---|

Number of stacked discs | 240 | 280 |

External diameter (mm) | 117.50 | 115.00 |

Internal diameter (mm) | 91.00 | 85.00 |

Number of grooves on a disc | 518 | 480 |

Total number of grooves | 248,640 | 268,800 |

Groove length (mm) | 14.76 | 15.70 |

Type Of Disc Filter | Disc Part | Width (μm) | Depth (μm) | Wetted Perimeter (μm) | Sectional Area (μm ^{2}) | Hydraulic Diameter (μm) | |
---|---|---|---|---|---|---|---|

Semi-elliptic groove | Upper | 361.0 | 98.4 | 817.7 | 27,899.2 | 136.5 | |

Lower | 363.3 | 95.5 | 819.2 | 27,249.5 | 133.1 | ||

Trapezoidal groove | Upper | 437.7 | 103.1 | 243.2 | 1131.2 | 65,761.3 | 232.5 |

Lower | 409.0 | 265.4 | 97.3 | 916.2 | 32,809.6 | 143.2 |

Flow Rate (m ^{3}/h) | Semi-Elliptic Groove Disc Filter | Trapezoidal Groove Disc Filter | ||||
---|---|---|---|---|---|---|

Flow Rate in a Groove (10 ^{−5} m^{3}/h) | Flow Velocity in a Groove (m/s) | Reynolds Number | Flow Rate in a Groove (10 ^{−5} m^{3}/h) | Flow Velocity in a Groove (m/s) | Reynolds Number | |

1 | 0.4022 | 0.0405 | 32.83 | 0.3720 | 0.0210 | 21.25 |

3 | 1.2066 | 0.1215 | 98.49 | 1.1161 | 0.0629 | 63.76 |

5 | 2.0109 | 0.2026 | 164.16 | 1.8601 | 0.1048 | 106.26 |

10 | 4.0219 | 0.4052 | 328.32 | 3.7202 | 0.2097 | 212.52 |

30 | 12.0656 | 1.2155 | 984.95 | 11.1607 | 0.6290 | 637.56 |

50 | 20.1094 | 2.0258 | 1641.58 | 18.6012 | 1.0484 | 1062.60 |

100 | 40.2188 | 4.0515 | 3283.16 | 37.2024 | 2.0968 | 2125.21 |

Flow Rate (m ^{3}/h) | Semi-Elliptic Groove Disc Filter | Trapezoidal Groove Disc Filter | ||
---|---|---|---|---|

$\mathbf{Head}\mathbf{Loss},\mathbf{\Delta}\mathit{H}$ (bar) | Head Loss in $\mathbf{a}\mathbf{Groove},\mathbf{\Delta}{\mathit{H}}_{\mathit{g}}$ (10 ^{−7} bar) | $\mathbf{Head}\mathbf{Loss},\mathbf{\Delta}\mathit{H}$ (bar) | Head Loss in a Groove with Adjusted Area, $\mathbf{\Delta}{\mathit{H}}_{\mathit{g}}{}^{\prime}$ (10 ^{−7} bar) | |

1 | 0.0306 | 1.2307 | 0.0098 | 1.1647 |

3 | 0.0596 | 2.3965 | 0.0262 | 3.1107 |

5 | 0.0812 | 3.2670 | 0.0413 | 4.9118 |

10 | 0.1237 | 4.9745 | 0.0768 | 9.1290 |

30 | 0.2408 | 9.6866 | 0.2051 | 24.3817 |

50 | 0.3283 | 13.2052 | 0.3239 | 38.4983 |

100 | 0.4999 | 20.1071 | 0.6020 | 71.5521 |

**Table 5.**Filtration performance test to evaluate the particle removal efficiency of the disc filters.

Type of Disc Filter | Particle Size (μm) | Inserted Particle Weight (g) | Weight of Sieve (g) | Weight of Sieve with Captured Particle (g) | Weight of Unfiltered Particle (g) | Particle Removal Efficiency (%) |
---|---|---|---|---|---|---|

Semi-elliptic groove | 212– | 5.00 | 362.47 | 362.51 | 0.04 | 99.2 |

180–212 | 5.00 | 348.99 | 349.09 | 0.10 | 98.0 | |

150–180 | 5.00 | 337.31 | 337.43 | 0.12 | 97.6 | |

125–150 | 5.00 | 341.81 | 341.95 | 0.14 | 97.2 | |

106–125 | 5.00 | 333.80 | 334.05 | 0.25 | 95.0 | |

Trapezoidal groove | 212– | 5.00 | 362.60 | 362.76 | 0.16 | 96.8 |

180–212 | 5.00 | 349.03 | 349.14 | 0.11 | 97.8 | |

150–180 | 5.00 | 337.31 | 337.51 | 0.20 | 96.0 | |

125–150 | 5.00 | 341.78 | 342.25 | 0.47 | 90.6 | |

106–125 | 5.00 | 333.72 | 334.76 | 1.04 | 79.2 |

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**MDPI and ACS Style**

Lee, S.-i.; Choi, J.-Y.; Choi, W. Effect of Groove Shape on Head Loss and Filtration Performance of Disc Filters. *Water* **2021**, *13*, 1683.
https://doi.org/10.3390/w13121683

**AMA Style**

Lee S-i, Choi J-Y, Choi W. Effect of Groove Shape on Head Loss and Filtration Performance of Disc Filters. *Water*. 2021; 13(12):1683.
https://doi.org/10.3390/w13121683

**Chicago/Turabian Style**

Lee, Sang-ik, Jin-Yong Choi, and Won Choi. 2021. "Effect of Groove Shape on Head Loss and Filtration Performance of Disc Filters" *Water* 13, no. 12: 1683.
https://doi.org/10.3390/w13121683