# Experimental Study on the Influence of Barrier Structures on Water Renewal Capacity in Slow-Flow Water Bodies

^{1}

^{2}

^{3}

^{4}

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Methods

#### 2.1. Experimental Facility and Instrumentation

#### 2.2. Experimental Similarity Rule and Data Processing

_{ni}is the dimensionless velocity; v

_{i}is the surface velocity of each point in the flow field (m/s).

^{2}), and S

_{0}is the total area of the stagnant water area (cm

^{2}), $\overline{v}$ is the average velocity (dimensionless); v

_{ni}is the normalized velocity at each point in the flume. Water with a surface velocity lower than 0.2 cannot be purified effectively, which is called the stagnant water area. Two conditions are randomly selected to show the distribution of the stagnant water area, and S

_{0}is shown in Figure 2. Note that the white area is due to the fact that the vector arrow, whose speed is below the critical speed, is not displayed.

_{i}is the probability of a symbol showing up in a given system of symbols, and the use of the logarithm base two corresponds to the expression of information entropy in terms of bits. In entropy calculations, the dimensionless velocities of each point in the two-dimensional flow field processed by the PIV system are obtained. The maximum dimensionless velocity in all conditions is 1.64. The velocity values of the flow field are divided into the following nine intervals: v

_{n}

_{1}(0–0.164), v

_{n}

_{2}(0.164–0.328), v

_{n}

_{3}(0.328–0.492), v

_{n}

_{4}(0.492–0.656), v

_{n}

_{5}(0.656–0.820), v

_{n}

_{6}(0.820–0.984), v

_{n}

_{7}(0.984–1.148), v

_{n}

_{8}(1.148–1.312), v

_{n}

_{9}(1.312–1.64), and the corresponding P

_{1}, P

_{2}, P

_{3}, P

_{4}, P

_{5}, P

_{6}, P

_{7}, P

_{8}, P

_{9}values, respectively For the selected two-dimensional system, the total grid number N of the flow field and N

_{i}(i = 1–9) that corresponds to each interval v

_{ni}are calculated, respectively. Then, P

_{i}= N

_{i}/N is calculated. Finally, the information entropy of the velocity composition under different conditions is calculated according to Formula (5).

#### 2.3. Experimental Conditions

## 3. Experimental Results

#### 3.1. Flow Field Distribution

#### 3.2. Velocity Variation

#### 3.3. Water Exchange Rate and Average Velocity

#### 3.4. Information Entropy Analysis

## 4. Discussion

^{2}= 0.94. However, the correlation between H and average velocity is relatively weak, as R

^{2}= 0.68. When H increases, the proportion of each velocity interval becomes more uniform. When H is small, the low-velocity interval (especially 0–0.164 or 0.164–0.328) demonstrates obvious dominance, and the average velocity is relatively small. As H increases, it indicates that the corresponding proportion of other high-velocity intervals increases, and the average velocity should increase. Therefore, the two parameters also present a positive correlation.

## 5. Conclusions

- There is a good positive correlation between η and average velocity (R
^{2}= 0.94). Compared with η of 21.61–44.43% of water with no structures, placing barrier structures in the water can significantly improve the water exchange rate (up to twice its value). The results are of practical significance for designing and adjusting structures in water to improve water quality. - The location parameter l changes the deflection mainstream velocity and direction, and its influence on η is non-monotonic. With the increase in l, circulation gradually appears and the area gradually expands. The deflection angle and the ratio of lateral velocity to streamwise velocity decrease, and the deflection effect of the structure weakens. The flow field for a large l (0.69) is similar to that with no structures. To achieve a higher η by placing structures in the water, the optimal l that corresponds to the triangular prism, rectangular column, and semi-cylinder is 0.2–0.3, 0.2–0.3, and 0.3–0.55, respectively.
- Structures have different effects on the flow field due to the different interaction surfaces, and the resistance effect of the rectangular column is the strongest. The deflection angles for the triangular prism and semi-cylinder are about 30°–45° at various flow rates, and these will be smaller for a larger l. The deflection angle of the rectangular column can be 90° for a smaller l, and the influence on the flow field is more obvious. In all cases, η for the rectangular column is relatively large, while that for the semi-cylinder is relatively small. A larger interaction area between the flow and structures generally results in a higher η.
- The flow rate Q is an important factor that affects water renewal capacity, changing the interaction intensity between the flow and structures. The average velocity and η increase with the increase in Q, and the flow rate that corresponds to the maximum η is generally 6.8 L/min.
- The information entropy H varies positively with the average velocity (R
^{2}= 0.68). H for the rectangular column is larger, indicating that the rectangular column plays a more obvious role in adjusting the velocity composition, while H for the semi-cylinder is relatively smaller.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Experimental installation: (

**a**) side view of the flume; (

**b**) top view of the flume (point O is the axis origin, and the unit of the numbers in the figure is cm, except for those already indicated).

**Figure 2.**Distribution of the stagnant water area: (

**a**) rectangular column, Q = 6.8 L/min, l = 0.44; (

**b**) triangular prism, Q = 6.8 L/min, l = 0.44.

**Figure 3.**Schematic diagram of barrier structures in water body: (

**a**) structure location; (

**b**) triangular prism; (

**c**) semi-cylinder; (

**d**) rectangular column.

**Figure 4.**Vector distribution of the flow field under the influence of the rectangular column for Q = 3.7 L/min and 6.8 L/min, respectively: (

**a**–

**f**) for 3.7 L/min; (

**a1**–

**f1**) for 6.8 L/min. Vector distribution (

**a**,

**a1**) for no structure; (

**b**,

**b1**) for l = 0.19; (

**c**,

**c1**) for l = 0.31; (

**d**,

**d1**) for l = 0.44; (

**e**,

**e1**) for l = 0.56; (

**f**,

**f1**) for l = 0.69.

**Figure 5.**Vector distribution of the flow field under the influence of the triangular prism for Q = 3.7 L/min and 6.8 L/min, respectively: (

**a**–

**f**) for 3.7 L/min; (

**a1**–

**f1**) for 6.8 L/min. Vector distribution (

**a**,

**a1**) for no structure; (

**b**,

**b1**) for l = 0.19; (

**c**,

**c1**) for l = 0.31; (

**d**,

**d1**) for l = 0.44; (

**e**,

**e1**) for l = 0.56; (

**f**,

**f1**) for l = 0.69.

**Figure 6.**Vector distribution of the flow field under the influence of the semi-cylinder for Q = 3.7 L/min and 6.8 L/min, respectively: (

**a**–

**f**) for 3.7 L/min; (

**a1**–

**f1**) for 6.8 L/min. Vector distribution (

**a**,

**a1**) for no structure; (

**b**,

**b1**) for l = 0.19; (

**c**,

**c1**) for l = 0.31; (

**d**,

**d1**) for l = 0.44; (

**e**,

**e1**) for l = 0.56; (

**f**,

**f1**) for l = 0.69.

**Figure 7.**Straight line of the mainstream center (black line): (

**a**) semi-cylinder, Q = 6.8 L/min, l = 0.31; (

**b**) triangular prism, Q = 6.8 L/min, l = 0.31; (

**c**) rectangular column, Q = 6.8 L/min, l = 0.31.

**Figure 8.**Variation in the velocity along the deflection mainstream center: (

**a**) l = 0.31; (

**b**) l = 0.56 (a is the straight-line distance from each point of the deflected mainstream to the structure).

**Figure 9.**Calculation results for the triangular prism: (

**a**) water exchange rate; (

**b**) average velocity.

**Figure 10.**Calculation results for the semi-cylinder: (

**a**) water exchange rate; (

**b**) average velocity.

**Figure 11.**Calculation results for the rectangular column: (

**a**) water exchange rate; (

**b**) average velocity.

**Figure 12.**Calculation results of the information entropy of the two-dimensional flow field: (

**a**) triangular prism; (

**b**) semi-cylinder; (

**c**) rectangular column.

**Figure 13.**Fitting diagram of three parameters: (

**a**) water exchange rate and average velocity; (

**b**) information entropy and average velocity.

**Table 1.**Experimental conditions (C for semi-cylinder, R for rectangular column; T for triangular prism).

Experiment Conditions | Q (L/min) | l | Structural Shape | Experiment Conditions | Q (L/min) | l | Structural Shape |
---|---|---|---|---|---|---|---|

R1-0-0 | 3.7 | — | — | R3-3-2 | T | ||

R1-1-1 | 0.19 | R | R3-3-3 | C | |||

R1-1-2 | T | R3-4-1 | 0.56 | R | |||

R1-1-3 | C | R3-4-2 | T | ||||

R1-2-1 | 0.31 | R | R3-4-3 | C | |||

R1-2-2 | T | R3-5-1 | 0.69 | R | |||

R1-2-3 | C | R3-5-2 | T | ||||

R1-3-1 | 0.44 | R | R3-5-3 | C | |||

R1-3-2 | T | R4-0-0 | 6.0 | — | — | ||

R1-3-3 | C | R4-1-1 | 0.19 | R | |||

R1-4-1 | 0.56 | R | R4-1-2 | T | |||

R1-4-2 | T | R4-1-3 | C | ||||

R1-4-3 | C | R4-2-1 | 0.31 | R | |||

R1-5-1 | 0.69 | R | R4-2-2 | T | |||

R1-5-2 | T | R4-2-3 | C | ||||

R1-5-3 | C | R4-3-1 | 0.44 | R | |||

R2-0-0 | 4.5 | — | — | R4-3-2 | T | ||

R2-1-1 | 0.19 | R | R4-3-3 | C | |||

R2-1-2 | T | R4-4-1 | 0.56 | R | |||

R2-1-3 | C | R4-4-2 | T | ||||

R2-2-1 | 0.31 | R | R4-4-3 | C | |||

R2-2-2 | T | R4-5-1 | 0.69 | R | |||

R2-2-3 | C | R4-5-2 | T | ||||

R2-3-1 | 0.44 | R | R4-5-3 | C | |||

R2-3-2 | T | R5-0-0 | 6.8 | — | — | ||

R2-3-3 | C | R5-1-1 | 0.19 | R | |||

R2-4-1 | 0.56 | R | R5-1-2 | T | |||

R2-4-2 | T | R5-1-3 | C | ||||

R2-4-3 | C | R5-2-1 | 0.31 | R | |||

R2-5-1 | 0.69 | R | R5-2-2 | T | |||

R2-5-2 | T | R5-2-3 | C | ||||

R2-5-3 | C | R5-3-1 | 0.44 | R | |||

R3-0-0 | 5.3 | — | — | R5-3-2 | T | ||

R3-1-1 | 0.19 | R | R5-3-3 | C | |||

R3-1-2 | T | R5-4-1 | 0.56 | R | |||

R3-1-3 | C | R5-4-2 | T | ||||

R3-2-1 | 0.31 | R | R5-4-3 | C | |||

R3-2-2 | T | R5-5-1 | 0.69 | R | |||

R3-2-3 | C | R5-5-2 | T | ||||

R3-3-1 | 0.44 | R | R5-5-3 | C |

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## Share and Cite

**MDPI and ACS Style**

Pan, L.; Yang, X.; Yang, Y.-b.; Zhou, H.; Jiang, R.; Cai, J.; Li, N.; Wang, J.
Experimental Study on the Influence of Barrier Structures on Water Renewal Capacity in Slow-Flow Water Bodies. *Water* **2022**, *14*, 3757.
https://doi.org/10.3390/w14223757

**AMA Style**

Pan L, Yang X, Yang Y-b, Zhou H, Jiang R, Cai J, Li N, Wang J.
Experimental Study on the Influence of Barrier Structures on Water Renewal Capacity in Slow-Flow Water Bodies. *Water*. 2022; 14(22):3757.
https://doi.org/10.3390/w14223757

**Chicago/Turabian Style**

Pan, Longyang, Xingguo Yang, Yeong-bin Yang, Hongwei Zhou, Rui Jiang, Junyi Cai, Niannian Li, and Jiamei Wang.
2022. "Experimental Study on the Influence of Barrier Structures on Water Renewal Capacity in Slow-Flow Water Bodies" *Water* 14, no. 22: 3757.
https://doi.org/10.3390/w14223757