## Abstract

Supersaturated total dissolved gas (TDG) generation in rivers poses great harm to aquatic organisms. In this paper, 30 groups of supersaturated TDG dissipation experiments with aeration were carried out. These results showed that aeration actively promoted the dissipation of supersaturated TDG. The aeration rate decreased by 34.94% from 1.0 m^{3}/h to 5.0 m^{3}/h, the reduced proportion of aeration aperture was 35.51% from 215 mm to 260 mm, whereas the aeration depth increased by 16.93% from 0.4 m to 1.2 m for the TDG dissipation time required, resulting in corresponding the variation of TDG dissipation coefficients were 86.26%, 23.74% and -5.39%, respectively. In general, the effect on TDG dissipation is that the aeration rate is the largest, followed by the aeration aperture, and the aeration depth is the smallest. A quantitative relationship was established between TDG dissipation coefficient and aeration conditions, and followed a power function, while the aeration depth inhibited its dissipation. Moreover, what matters was that a numerical model was presented for predicting the TDG dissipation in Eulerian-Eulerian. When the parameter was β = 10.52, the error between the original experimental data and the simulated of a multiphase TDG dissipation model was 0.2%. The study provides essential scientific data for mitigating the harms of supersaturated TDG.

## HIGHLIGHTS

The effect of aeration on supersaturated TDG is analysed.

The TDG dissipation coefficient and aeration conditions are established.

When the critical TDG source treatment sensitivity parameter

*β*= 10.52, the error between the actual supersaturated TDG dissipation process and the TDG dissipation model is 0.2%, and the experimental data and simulation values are similar.

## INTRODUCTION

Hydropower engineering constructed by humans plays a crucially important role in hydropower development, flood control, urban water supply, water storage and shipping safety, which is closely related to numerous river basins with abundant resources (Altinbilek 2002; Jellyman & Harding 2012; Chu *et al.* 2019; Shi *et al.* 2019; Paşa *et al.* 2023). Supersaturation of total dissolved gas (TDG) produced by dam discharge, a sudden rise in water temperature and excess oxygen from plant photosynthesis generation in water have a potentially significant impact on the biodiversity of fish, especially leading to gas bubble disease (GBD) and even death of fish (Ebel 1969; Don & Max 1980; Tan *et al.* 2006; Evan *et al.* 2009; Kirk & Wesley 2011; Algera *et al.* 2022). In recent years, supersaturated TDG has become a potential research topic because of its profound negative impact on the water environment in many places. For example, fish death was found on the downstream water surface of multiple dams in China's Three Gorges Project, high dams in the western region and the Columbia River and its tributary Snake River in the United States (Ebel 1969; Cheng *et al.* 2005; Jiang *et al.* 2008; Qin & Li 2008; Politano *et al.* 2011; Stewart *et al.* 2015; Wang *et al.* 2017; Zou *et al.* 2021).

There are two main ways to mitigate the harm of supersaturated TDG: one is to reduce the generation of supersaturated TDG, and the other is to accelerate the dissipation of supersaturated TDG. The earliest research on measures to mitigate TDG originated from the treatment of low-flow aquaculture water sources, including the siphon method (Colt 1983), packing column method (Politano *et al.* 2009), activated carbon adsorption (Niu *et al.* 2015; Huang *et al.* 2017) and planting aquatic plants (Yuan *et al.* 2018). Some engineering measures are designed to reduce the generation of supersaturated TDG, such as setting spillway deflectors (Environmental U.S. & Tribe 2004), stepped and baffle spillways (Wang *et al.* 2019), auxiliary energy dissipation pier (Huang *et al.* 2021a, 2021b), optimizing discharge structures (Feng *et al.*2014a) and dispersing discharge (Politano *et al.* 2012). However, the supersaturated TDG produced by the dam discharge has the characteristics of high saturation, slow dissipation speed, prominent cascade cumulative impact, and significant and sensitive impact on fish biodiversity in the dam downstream area (Li *et al.* 2009a, 2009b, 2013a, 2013b; Tanner *et al.* 2010; Feng *et al.* 2013, 2014a, 2014b). A single TDG mitigation measure can no longer solve the problem of supersaturated TDG hazards in the downstream area of the dam, and multiple mitigation methods should be needed to explore the TDG mitigation measure further.

In the past, aeration was mainly used for water quality treatment, river pollution treatment, environmental pollution treatment, aquaculture and separation of heavy metal pollution in numerous research literatures. Li *et al.* (2017) and Wang *et al.* (2013) summarized that micro-nanometer bubbles generated by aeration can degrade different types of organic pollutants, generate efficient free radicals and turbulence, remove solid surface pollutants and restore the water environment. Zhang *et al.* (2012a, 2012b) and Hong *et al.* (2011) found that different aeration conditions had a positive effect on removing black and odorous water in rivers. Zhu *et al.* (2023) and Qiao *et al.* (2023) found that aeration removed impurities and separated metal ions from wastewater. There is relatively little research on the effect of aeration on supersaturated TDG, where aeration may also be an important measure to slow down the dissipation of supersaturated TDG.

Based on the gas–liquid mass transfer mechanism (Li *et al.* 2020), aeration positively promoted the dissipation of supersaturated TDG (Ou *et al.* 2016; Liang *et al.* 2022; Yao *et al.* 2022a, 2022b, 2023) and dissolved oxygen (DO) (Chern & Yu 1997, 1999; Chern *et al.* 2001; Chern & Yang 2003; Huang *et al.* 2016; Wang *et al.* 2023), and increased oxygen in aquaculture (Cheng *et al.* 2013, 2014, 2015) and treated pollutants in rivers (Hong *et al.* 2011; Zhang *et al.* 2012a, 2012b). Ou *et al.* (2016) found that gas flow rate with aeration promoted the dissipation of supersaturated TDG. Huang *et al.* (2016) established relationships between gas flow rate, aeration depth and DO dissipation coefficient. Wang *et al.* (2023) found that smaller pinholes with aeration were more effective in promoting the dissipation of supersaturated DO. Zhan found that pinholes with aeration promoted the dissipation of supersaturated TDG. Cheng *et al.* (2013) found airflow pipe with aeration increased the oxygen content and established a relationship between the oxygen mass transfer coefficient and experimental conditions. Previous researchers were limited to analyzing the effect of aeration on reducing supersaturated TDG, whereas more aeration studies have focused on the transition of oxygen from an unsaturated state to a stable equilibrium state. Therefore, it is necessary to quantitatively analyze the impact of aeration on supersaturated TDG and solve the suppression problem of equipment deceleration.

Furthermore, for the multiphase aeration TDG model and numerical dam discharge TDG model, many researchers' findings were limited to the size of bubbles and their plumes in DO (Cheng *et al.* 2001, 2008; Fayolle *et al.* 2007; Xiao *et al.* 2012a, 2012b, 2014). Qin & Li (2008) found that the supersaturation of dissolved gas downstream of Gezhou Dam led to fish death and proposed a numerical model for supersaturated TDG. Cheng *et al.* (2009) found that supersaturated DO in the downstream of the Three Gorges Project posed a threat to the survival environment and life of fish and simulated the changes in DO. Politano *et al.* (2012, 2019) developed a numerical model of TDG changes for dam discharge in the United States. Exploring the application of supersaturated TDG dissipation models in aeration plays a positive role in protecting river ecology and the sustainable development of hydropower engineering.

Taking these results together indicates that the aeration measures to mitigate the harm of supersaturated TDG in the existing high-concentration supersaturated TDG watershed have not been found in the fish habitats. This paper focuses on the quantitative analysis of aeration on supersaturated TDG dissipation, the relationship between aeration conditions and TDG dissipation coefficient and its multiphase model in aeration experiments. The results provide an essential scientific basis for constructing suitable fish habitats with low levels of TDG concentration.

## MATERIALS AND METHODS

### Laboratory instrumentation

*et al.*(2022a, 2022b), and the experimental sketch is shown in Figure 1. The main equipment is a square aeration water tank of 2.0 m in height and 0.4 m in diameter. The aeration distributor is placed at a 0.3 m distance from the column bottom, which contains two microporous aeration distributors with diameters of 215 and 260 mm. The range of the barometer is 1.0～5.0 m

^{3}/h. The measuring range of the TGP is 0～600% of saturation with ±1% accuracy.

### Experimental methods

*et al.*2022a, 2022b). The supersaturated water is produced by the supersaturated TDG generation system and injected into the predetermined height of the circular water tank. And we input the set aeration rate into the supersaturated water and use the TGP meter to start recording the dissipation process of supersaturated TDG until the TDG concentration reaches about 100%, then stop recording and cycle this operation method. There are a total of 30 experiments, as shown in Figure 2.

## DISSCUSSION AND ANALYSIS OF SUPERSATURATED TDG DISSIPATION

### Dissipation of supersaturated TDG in aeration-free conditions

*H*= 0.4 m,

*H*= 0.8 m and

*H*= 1.2 m, the time required for supersaturated TDG to dissipate has reached more than 4 h. The dissipation rate is relatively slow, as shown in Figure 3. The dissipation coefficient

*K*

_{TDG,0}is calculated by the first-order dynamic Equation (1) (U.S Army Corps of Engineers 2005) and decreases with the increase of water depth, and the correlation coefficient

*R*

^{2}is greater than 0.983, as shown in Table 1.where

*G*is the TDG saturation (%),

*G*

_{eq}is the equilibrium saturation of TDG (usually 100%),

*G*

_{0}is the initial TDG concentration (%),

*K*

_{TDG}is the dissipation coefficient (h

^{−1}),

*t*is the dissipation time (h).

Group number . | H (m)
. | Q (m^{3}/h)
. | θ (m)
. | R^{2}
. | K_{TDG,0}
. | R^{2}
. |
---|---|---|---|---|---|---|

1 | 0.4 | – | – | 0.976 | 0.00806 ± 0.00 | 0.995 |

2 | 0.8 | – | – | 0.976 | 0.00734 ± 0.00 | 0.993 |

3 | 1.2 | – | – | 0.987 | 0.00636 ± 0.00 | 0.983 |

Group number . | H (m)
. | Q (m^{3}/h)
. | θ (m)
. | R^{2}
. | K_{TDG,0}
. | R^{2}
. |
---|---|---|---|---|---|---|

1 | 0.4 | – | – | 0.976 | 0.00806 ± 0.00 | 0.995 |

2 | 0.8 | – | – | 0.976 | 0.00734 ± 0.00 | 0.993 |

3 | 1.2 | – | – | 0.987 | 0.00636 ± 0.00 | 0.983 |

### Dissipation of supersaturated TDG in aeration

#### Dissipation process of supersaturated TDG

^{3}/h, the average time required for supersaturated TDG dissipation reduction is 34.94%. When the aeration aperture increases from 215 to 260 mm, the average reduction of time required for supersaturated TDG dissipation is 35.51%. When the aeration depth increases from 0.4 to 0.8 m, the average increase of time required for supersaturated TDG release is 16.93%. So, from the average time required for the supersaturated TDG dissipation, it can be seen that the aeration aperture has the greatest effect on the supersaturated TDG dissipation, followed by the aeration rate, and the aeration depth has the smallest effect, that is

*T*>

_{θ}*T*>

_{Q}*T*. As shown in Figure 1, the reasons are: (1) The gas–liquid interface is implicated in momentum, heat and mass transfer (Gualtieri & Doria 2012) and the gas flow rate can change the comfort of material surfaces and improve their overall energy performance (Barton

_{H}*et al.*2002; Mohammad

*et al.*2014). In aeration, a large number of bubbles become more and more with the increase of aeration rate, the supersaturated TDG dissipation process is mainly driven by a certain amount of turbulence generated by the aeration rate in which a large number of bubbles are constantly moving and bubbles in supersaturated water are constantly renewed and rise to the water surface (Chanson 2008). These results can enhance the mass transfer process at the gas–liquid interface and water surface to reduce the supersaturated TDG concentration (Yao

*et al.*2022a, 2022b). (2) With the increase of aeration depth, a large number of bubbles generated by air compressor conveying gas stagnate in supersaturated water for a relatively long time, resulting in the relative weakening of turbulence intensity caused by bubbles and the reduction of the contact area of gas–liquid interface, which inhibits the dissipation of supersaturation TDG (Brooks 1998; Cheng

*et al.*2005, 2014; Li

*et al.*2007). (3) The aeration aperture determines the size of bubbles. Some scholars have shown that a smaller bubble diameter is beneficial for the contact area of the gas–liquid interface and mass transfer between the gas–bubble interface and the water surface (Lehr

*et al.*2002; Li 2007). The increase of the aeration aperture leads to the increase in the number of bubbles in the same aeration rate, which enhances the mass transfer of supersaturated TDG at the gas–liquid interface (Laakkonen

*et al.*2007; Prince & Blanch 2010; Ashutosh

*et al.*2011).

Researchers . | Mitigation measure . | The time required for supersaturated TDG dissipation . |
---|---|---|

— | Aeration distributor | 165～100%/(0.07～0.17)h |

Feng et al. (2012, 2016) | Sediment | 130～105%/(0.18～1.10)h |

Feng et al. (2017) | Water blocking medium | 135～(4.1～9.6%)/(6.14～8.17)s |

Liu et al. (2015) | Wind speed | 135～115%/(2～4)h |

Ou et al. (2016) | Pinhole aeration | 132～105%/(0.22～0.43)h |

Zhang (2021) | Pinhole aeration | 140～95%/(0.13～0.53)h |

Yao et al. (2022a, 2022b) | Swirling aeration | 170～100%/(0.13～0.4)h |

Liang et al. (2022) | Pinhole aeration | 140～110%/(0.25～0.53)h |

Wang et al. (2023) | Pinhole aeration | 170～105%/(0.08～0.18)h |

Researchers . | Mitigation measure . | The time required for supersaturated TDG dissipation . |
---|---|---|

— | Aeration distributor | 165～100%/(0.07～0.17)h |

Feng et al. (2012, 2016) | Sediment | 130～105%/(0.18～1.10)h |

Feng et al. (2017) | Water blocking medium | 135～(4.1～9.6%)/(6.14～8.17)s |

Liu et al. (2015) | Wind speed | 135～115%/(2～4)h |

Ou et al. (2016) | Pinhole aeration | 132～105%/(0.22～0.43)h |

Zhang (2021) | Pinhole aeration | 140～95%/(0.13～0.53)h |

Yao et al. (2022a, 2022b) | Swirling aeration | 170～100%/(0.13～0.4)h |

Liang et al. (2022) | Pinhole aeration | 140～110%/(0.25～0.53)h |

Wang et al. (2023) | Pinhole aeration | 170～105%/(0.08～0.18)h |

#### Dissipation coefficient of supersaturated TDG

In order to further study the effect of aeration on supersaturated TDG, a first-order kinetic Equation (1) was introduced to express the dissipation rate of supersaturated TDG (U.S Army Corps of Engineers 2005). The results are shown in Table 3.

Group number . | H (m)
. | θ (mm)
. | Q (m^{3}/h)
. | K_{TDG} (h^{−1})
. | ψ = K_{TDG}/K_{TDG,0}
. | R^{2}
. |
---|---|---|---|---|---|---|

1 | 0.4 | 215 | 1.0 | 0.265 ± 0.00 | 32.88 | 0.987 |

2 | 0.4 | 215 | 2.0 | 0.703 ± 0.02 | 87.22 | 0.975 |

3 | 0.4 | 215 | 3.0 | 1.030 ± 0.06 | 127.79 | 0.929 |

4 | 0.4 | 215 | 4.0 | 1.138 ± 0.06 | 141.19 | 0.958 |

5 | 0.4 | 215 | 5.0 | 1.141 ± 0.03 | 141.56 | 0.958 |

6 | 0.4 | 260 | 1.0 | 0.118 ± 0.00 | 14.64 | 0.932 |

7 | 0.4 | 260 | 2.0 | 0.104 ± 0.01 | 12.90 | 0.737 |

8 | 0.4 | 260 | 3.0 | 0.746 ± 0.06 | 92.56 | 0.856 |

9 | 0.4 | 260 | 4.0 | 0.804 ± 0.02 | 99.75 | 0.978 |

10 | 0.4 | 260 | 5.0 | 1.795 ± 0.13 | 222.70 | 0.932 |

11 | 0.8 | 215 | 1.0 | 0.235 ± 0.00 | 32.02 | 0.994 |

12 | 0.8 | 215 | 2.0 | 0.459 ± 0.00 | 62.53 | 0.983 |

13 | 0.8 | 215 | 3.0 | 0.543 ± 0.00 | 73.98 | 0.989 |

14 | 0.8 | 215 | 4.0 | 1.102 ± 0.05 | 150.14 | 0.959 |

15 | 0.8 | 215 | 5.0 | 1.169 ± 0.05 | 159.26 | 0.969 |

16 | 0.8 | 260 | 1.0 | 0.183 ± 0.00 | 24.93 | 0.997 |

17 | 0.8 | 260 | 2.0 | 0.594 ± 0.01 | 80.93 | 0.992 |

18 | 0.8 | 260 | 3.0 | 0.714 ± 0.02 | 97.28 | 0.985 |

19 | 0.8 | 260 | 4.0 | 0.873 ± 0.01 | 118.94 | 0.959 |

20 | 0.8 | 260 | 5.0 | 1.225 ± 0.03 | 166.89 | 0.986 |

21 | 1.2 | 215 | 1.0 | 0.097 ± 0.00 | 15.25 | 0.845 |

22 | 1.2 | 215 | 2.0 | 0.300 ± 0.01 | 47.17 | 0.951 |

23 | 1.2 | 215 | 3.0 | 0.308 ± 0.02 | 48.43 | 0.881 |

24 | 1.2 | 215 | 4.0 | 0.445 ± 0.02 | 69.97 | 0.890 |

25 | 1.2 | 215 | 5.0 | 0.462 ± 0.02 | 72.64 | 0.869 |

26 | 1.2 | 260 | 1.0 | 0.273 ± 0.01 | 42.92 | 0.968 |

27 | 1.2 | 260 | 2.0 | 0.335 ± 0.02 | 52.67 | 0.903 |

28 | 1.2 | 260 | 3.0 | 0.719 ± 0.02 | 113.05 | 0.982 |

29 | 1.2 | 260 | 4.0 | 0.763 ± 0.03 | 119.97 | 0.968 |

30 | 1.2 | 260 | 5.0 | 0.811 ± 0.05 | 127.52 | 0.909 |

Group number . | H (m)
. | θ (mm)
. | Q (m^{3}/h)
. | K_{TDG} (h^{−1})
. | ψ = K_{TDG}/K_{TDG,0}
. | R^{2}
. |
---|---|---|---|---|---|---|

1 | 0.4 | 215 | 1.0 | 0.265 ± 0.00 | 32.88 | 0.987 |

2 | 0.4 | 215 | 2.0 | 0.703 ± 0.02 | 87.22 | 0.975 |

3 | 0.4 | 215 | 3.0 | 1.030 ± 0.06 | 127.79 | 0.929 |

4 | 0.4 | 215 | 4.0 | 1.138 ± 0.06 | 141.19 | 0.958 |

5 | 0.4 | 215 | 5.0 | 1.141 ± 0.03 | 141.56 | 0.958 |

6 | 0.4 | 260 | 1.0 | 0.118 ± 0.00 | 14.64 | 0.932 |

7 | 0.4 | 260 | 2.0 | 0.104 ± 0.01 | 12.90 | 0.737 |

8 | 0.4 | 260 | 3.0 | 0.746 ± 0.06 | 92.56 | 0.856 |

9 | 0.4 | 260 | 4.0 | 0.804 ± 0.02 | 99.75 | 0.978 |

10 | 0.4 | 260 | 5.0 | 1.795 ± 0.13 | 222.70 | 0.932 |

11 | 0.8 | 215 | 1.0 | 0.235 ± 0.00 | 32.02 | 0.994 |

12 | 0.8 | 215 | 2.0 | 0.459 ± 0.00 | 62.53 | 0.983 |

13 | 0.8 | 215 | 3.0 | 0.543 ± 0.00 | 73.98 | 0.989 |

14 | 0.8 | 215 | 4.0 | 1.102 ± 0.05 | 150.14 | 0.959 |

15 | 0.8 | 215 | 5.0 | 1.169 ± 0.05 | 159.26 | 0.969 |

16 | 0.8 | 260 | 1.0 | 0.183 ± 0.00 | 24.93 | 0.997 |

17 | 0.8 | 260 | 2.0 | 0.594 ± 0.01 | 80.93 | 0.992 |

18 | 0.8 | 260 | 3.0 | 0.714 ± 0.02 | 97.28 | 0.985 |

19 | 0.8 | 260 | 4.0 | 0.873 ± 0.01 | 118.94 | 0.959 |

20 | 0.8 | 260 | 5.0 | 1.225 ± 0.03 | 166.89 | 0.986 |

21 | 1.2 | 215 | 1.0 | 0.097 ± 0.00 | 15.25 | 0.845 |

22 | 1.2 | 215 | 2.0 | 0.300 ± 0.01 | 47.17 | 0.951 |

23 | 1.2 | 215 | 3.0 | 0.308 ± 0.02 | 48.43 | 0.881 |

24 | 1.2 | 215 | 4.0 | 0.445 ± 0.02 | 69.97 | 0.890 |

25 | 1.2 | 215 | 5.0 | 0.462 ± 0.02 | 72.64 | 0.869 |

26 | 1.2 | 260 | 1.0 | 0.273 ± 0.01 | 42.92 | 0.968 |

27 | 1.2 | 260 | 2.0 | 0.335 ± 0.02 | 52.67 | 0.903 |

28 | 1.2 | 260 | 3.0 | 0.719 ± 0.02 | 113.05 | 0.982 |

29 | 1.2 | 260 | 4.0 | 0.763 ± 0.03 | 119.97 | 0.968 |

30 | 1.2 | 260 | 5.0 | 0.811 ± 0.05 | 127.52 | 0.909 |

Table 3 shows that under aeration conditions, the supersaturated TDG dissipation coefficient is larger than that of pinhole aeration (Ou *et al.* 2016; Liang *et al.* 2022) and swirling aeration (Yao *et al.* 2023). When the aeration rate increases from 1.0 to 5.0 m^{3}/h, the average increase of supersaturated TDG dissipation coefficient is 86.26%. When the aeration depth increases from 0.4 to 0.8 m, the average increase of supersaturated TDG dissipation coefficient is 5.39%. And when the aeration aperture increases from 215 to 260 mm, the average reduction of supersaturated TDG dissipation coefficient is 23.74%. From the average value of supersaturated TDG dissipation coefficient, the effect of aeration rate on supersaturated TDG dissipation coefficient is the largest, followed by the effect of aeration aperture, and the effect of aeration depth is the smallest, that is *K _{Q}* >

*K*>

_{θ}*K*. Therefore, it is further verified that this aeration method can significantly promote supersaturated TDG dissipation.

_{H}^{3}/h, the maximum supersaturated TDG dissipation coefficient is 1.795 h

^{−1}, which is 222.7 times of the supersaturated TDG dissipation coefficient in no aeration. In order to more directly express the effect of aeration on supersaturated TDG dissipation, a relative dissipation coefficient (ψ=K

_{TDG}/K

_{TDG,0}) which is the ratio of the TDG dissipation coefficient (

*K*

_{TDG}) for different aeration to the TDG dissipation coefficient

*K*

_{TDG,0}without aeration is introduced. Then their relationship is shown in Figure 5, and Equation (2) and its correlation is shown in Table 4.where

*β*is the relative dissipation coefficient,

*Q*is the aeration rate (m

^{3}/h),

*α*

_{1},

*α*

_{2}are fitting parameters.

Parameters . | θ = 215 mm. | θ = 260 mm. | ||||
---|---|---|---|---|---|---|

0.4 . | 0.8 . | 1.2 . | 0.4 . | 0.8 . | 1.2 . | |

51.45 ± 10.69 | 4.73 ± 3.57 | 27.54 ± 8.06 | 34.04 ± 6.27 | 22.88 ± 4.64 | 42.10 ± 9.35 | |

0.69 ± 0.15 | 2.37 ± 0.49 | 1.12 ± 0.21 | 0.97 ± 0.13 | 0.75 ± 0.16 | 0.73 ± 0.16 | |

0.947 | 0.949 | 0.955 | 0.976 | 0.951 | 0.943 |

Parameters . | θ = 215 mm. | θ = 260 mm. | ||||
---|---|---|---|---|---|---|

0.4 . | 0.8 . | 1.2 . | 0.4 . | 0.8 . | 1.2 . | |

51.45 ± 10.69 | 4.73 ± 3.57 | 27.54 ± 8.06 | 34.04 ± 6.27 | 22.88 ± 4.64 | 42.10 ± 9.35 | |

0.69 ± 0.15 | 2.37 ± 0.49 | 1.12 ± 0.21 | 0.97 ± 0.13 | 0.75 ± 0.16 | 0.73 ± 0.16 | |

0.947 | 0.949 | 0.955 | 0.976 | 0.951 | 0.943 |

Equation (2) shows a power function relationship. And the water continuously generates strong turbulence during the aeration rate, and the increase of aeration rate causes the increase of water flow velocity gradient in the gas–liquid interface and then leads to the increase of turbulent kinetic energy and its dissipation rate (Geldert *et al.* 1998; Takemura & Yabe 1998; Shae *et al.* 2008). This greatly enhances the dissipation rate of supersaturated TDG at the gas–liquid interface, thus increasing in the supersaturated TDG dissipation coefficient (Gresch *et al.* 2011; Liu *et al.* 2015).

### The effect and quantitative relationship of aeration conditions on the dissipation of supersaturated TDG

Cheng *et al.* (2013) found that the relationship between the reaeration coefficient and aeration rate did not increase linearly in aeration. It is necessary to analyze further the relationship between aeration rate, aeration depth, aeration aperture and supersaturated TDG dissipation coefficient.

#### The effect of aeration rate

*K*

_{TDG,Q}is the supersaturated TDG dissipation (h

^{−1}),

*Q*is the aeration rate (m

^{3}/h), and

*α*,

*β*are fitting parameters.

Parameters . | θ = 215 mm. | θ = 260 mm. | ||||
---|---|---|---|---|---|---|

0.4 . | 0.8 . | 1.2 . | 0.4 . | 0.8 . | 1.2 . | |

0.440 ± 0.17 | 0.194 ± 0.11 | 0.153 ± 0.06 | 0.1602 ± 0.16 | 0.222 ± 0.26 | 0.269 ± 0.12 | |

0.668 ± 0.21 | 1.136 ± 0.33 | 0.731 ± 0.20 | 1.152 ± 0.58 | 0.9484 ± 0.66 | 0.699 ± 0.24 | |

0.948 | 0.956 | 0.956 | 0.879 | 0.782 | 0.935 |

Parameters . | θ = 215 mm. | θ = 260 mm. | ||||
---|---|---|---|---|---|---|

0.4 . | 0.8 . | 1.2 . | 0.4 . | 0.8 . | 1.2 . | |

0.440 ± 0.17 | 0.194 ± 0.11 | 0.153 ± 0.06 | 0.1602 ± 0.16 | 0.222 ± 0.26 | 0.269 ± 0.12 | |

0.668 ± 0.21 | 1.136 ± 0.33 | 0.731 ± 0.20 | 1.152 ± 0.58 | 0.9484 ± 0.66 | 0.699 ± 0.24 | |

0.948 | 0.956 | 0.956 | 0.879 | 0.782 | 0.935 |

#### The effect of aeration depth

*K*

_{TDG,H}is the supersaturated TDG dissipation (h

^{−1}),

*H*is the aeration depth (m).

Parameters . | Values . | Correlation coefficients . |
---|---|---|

0.811 | 1.000 | |

0.401 | 0.687 | |

0.4 m | – |

Parameters . | Values . | Correlation coefficients . |
---|---|---|

0.811 | 1.000 | |

0.401 | 0.687 | |

0.4 m | – |

#### The effect of aeration aperture

*et al.*1998). This element solves a critical problem in that aeration aperture suppresses the dissipation of supersaturated TDG (Ou

*et al.*2016; Yao

*et al.*2023). And a relationship between supersaturated TDG dissipation coefficient and aeration aperture is a power function relationship and a positive correlation relationship as shown in Equation (5). Its optimal parameters are shown in Table 7.where

*K*

_{TDG,θ}is the supersaturated TDG dissipation (h

^{−1}) and

*θ*is the aeration aperture (mm).

Parameter . | Values . | Correlation coefficients . |
---|---|---|

0.670 | 1.000 | |

0.357 | 0.683 | |

260 mm | – |

Parameter . | Values . | Correlation coefficients . |
---|---|---|

0.670 | 1.000 | |

0.357 | 0.683 | |

260 mm | – |

#### A quantitative relationship between the dissipation coefficients of supersaturated TDG and aeration conditions

*et al.*2016; Wang

*et al.*2023; Yao

*et al.*2023).According to mathematical regression analysis, we obtained the parameters of Equation (6) as shown in Equation (7), and the optimal parameters are shown in Table 8.where

*K*

_{TDG}is the supersaturated TDG dissipation coefficient (h

^{−1}),

*Q*is the aeration rate (m

^{3}/h),

*H*is the aeration depth (m) and

*θ*is the aeration aperture (mm).

Parameter . | Values . | Correlation coefficients . |
---|---|---|

1.494 | 1.000 | |

1.093 | 0.411 | |

0.449 | 0.508 | |

0.487 | 0.510 | |

5.0 m^{3}/h | – | |

0.4 m | – | |

260 mm | – |

Parameter . | Values . | Correlation coefficients . |
---|---|---|

1.494 | 1.000 | |

1.093 | 0.411 | |

0.449 | 0.508 | |

0.487 | 0.510 | |

5.0 m^{3}/h | – | |

0.4 m | – | |

260 mm | – |

#### Comparison between experimental data and calculated values

*et al.*2013a, 2013b; Cheng

*et al.*2014, 2015; Alomar

*et al.*2020), the results are shown in Figure 9 and the error value as shown in Table 9.where RMSE is the root mean square value, AME is the absolute mean value, is the calculated value, is the experimental data.

Parameters . | TDG . | |
---|---|---|

RMSE (%) . | AME (%) . | |

Equation (3) | 24.98 | 18.06 |

Equation (4) | 38.48 | 30.72 |

Equation (5) | 40.38 | 32.93 |

Equation (7) | 19.10 | 12.17 |

The lower comparison of the experimental data and calculated values shows that the established mathematical model of supersaturated TDG dissipation has particular applicability. It does not need to measure the characteristic dissipation coefficient under specific aeration conditions. However, it can directly predict the dissipation rate of supersaturated TDG in water under this condition by obtaining easily obtained parameters such as aeration rate, aeration depth and aeration aperture. These TDG mass transfer equations have high operability in practical environmental applications.

## SUPERSATURATED TDG DISSIPATION

Based on gas–liquid computational fluid dynamics (CFD) in Eulerian–Eulerian approach (Xia & Sun 2002; Henderson *et al.* 2007), we compiled the source term (*S*_{c}) of TDG transport diffusion equation with self-designed C Language to form a User Defined Function (UDF) file. We selected one of the aeration experiments where *Q* = 1.0 m^{3}/h, *H* = 0.8 m, *θ* = 260 mm, initial TDG concentration (*G* = 147.4%) and *K*_{TDG} = 0.183 as a vital model parameter. The supersaturated TDG dissipation model and its essential sensitivity parameters will be obtained, which are used to evaluate the error between the TDG dissipation process in the aeration experiment and the TDG dissipation model in the multiphase model (Cheng *et al.* 2009; Politano *et al.* 2009, 2011, 2012; Fu *et al.* 2010; Huang *et al.* 2021a, 2021b). Therefore, the calculation of the supersaturated TDG dissipation model includes a mathematical model, turbulent model and TDG transport diffusion equation as follows, and we also consider the effects of buoyancy, pressure, drag, turbulent dispersion and other forces on the supersaturated TDG dissipation (Manninen *et al.* 1996).

### Mathematical model

#### Mass and momentum conservation equation

*i*is the phase (gas or liquid), is the volume fraction of phase, is the phase density, is the effective density, is the phase velocity, is the correction pressure, is the force of gas and liquid and is the phase effective viscosity.

#### Effective viscosity of gas–liquid

*et al.*1997).where is the effective viscosity of the liquid phase and is the turbulent viscosity of the liquid phase.

### Turbulent model

*Κ* and *ε* equation, liquid phase turbulence coefficient

*κ*-

*ε*turbulence model to turbulence model to describe the turbulence of the liquid phase in an aeration system. The core of the RNG

*κ*-

*ε*turbulence model applies to the turbulence calculation of higher Re number and not only saves the calculation amount but also has good results in engineering applications, expressed by Equations (14)–(16) and their model parameters are shown in Table 10 (Wei

*et al.*2015; Guo

*et al.*2017).where is the density, is the viscosity coefficient.

Parameters . | . | . | . | . | . | . |
---|---|---|---|---|---|---|

4.38 | 0.012 | 0.085 | 1.68 | 0.7179 | 0.7179 |

Parameters . | . | . | . | . | . | . |
---|---|---|---|---|---|---|

4.38 | 0.012 | 0.085 | 1.68 | 0.7179 | 0.7179 |

#### Gas–liquid interaction forces

##### Drag force

##### Lift of bubbles

*C*

_{L}is the bubble lift coefficient.

##### Wall lubricating force

*et al.*1991).where

*C*

_{W}is the wall lubrication force coefficient.

##### Turbulent dissipation force

*et al.*1993; Li

*et al.*2009a, 2009b).where

*C*

_{TD}is the turbulent diffusion coefficient.

### TDG transport diffusion equation

*et al.*2009). The TDG dissipation source treatment in the equation is mainly known for the mass transfer at the gas–liquid interface (

*S*

_{C,G}) and the mass transfer at the water free-interface (

*S*

_{C,W}).where

*C*is the TDG saturation (%), is the molecular diffusion coefficient, is the Schmidt number, is the turbulent diffusion coefficient of gas gas–liquid mixed liquid, is the water flow velocity (m/s).

#### TDG dissipation source treatment

*et al.*2009, 2012, 2019; Qin & Li 2008) have used Equations (22) and (23) to represent gas–liquid interface mass transfer and water free-surface surface mass transfer, which better simulate the distribution of TDG saturation in practical engineering.where

*K*

_{L,B}is the gas–liquid interface mass transfer coefficient,

*K*

_{L,S}is the water free-surface surface mass transfer coefficient, is the specific surface area of bubbles (mm), is the specific surface area of free water surface (mm),

*C*

_{S}is the TDG concentration at atmospheric pressure (100%),

*C*

_{se}is the TDG equilibrium saturation within the bubble at a certain water depth (%).

#### TDG equilibrium saturation within the bubble

*et al.*2003).where Δ

*P*is the relative pressure of bubbles at depths of water (Pa),

*γ*is the water weight (kg/m

^{3}), and

*h*is the water depth (m).

#### Gas–liquid interfacial mass transfer coefficient and its mass transfer area

*μ*= 3.0 mm and the standard deviation

*σ*= 0.5, that is

*μ*～

*σ*(3.0, 0.5

^{2}).where

*R*is the diameter of the bubble (mm), Pe is the Peclet number (Pe = 2

*RV*

_{r}/

*D*

_{m}), Re is the Reynolds number (Re = 2

*R*[(2

*κ*/3)

^{1/2}]/

*V*

_{t}),

*V*

_{r}is the bubble rise velocity (m/s),

*D*

_{m}is the molecular diffusivity coefficient (

*D*

_{m}= 2.5*10

^{−9}m

^{2}/s),

*V*

_{t}is the turbulent diffusion coefficient,

*β*is the TDG source treatment sensitivity parameter.

#### Water free-surface mass transfer coefficient and its mass transfer area

*et al.*2009), and its mass transfer area is represented by Equation (28).where

*V*is the volume of the model (m

^{3}), Δ

*Z*is the surface grid size of the model.

### Determination of TDG source treatment sensitivity parameters

*β*= 7.78,

*β*= 9.48,

*β*= 10.52,

*β*= 11.78 and

*β*= 12.95. And the comparison of the supersaturated TDG dissipation obtained from the TDG source treatment sensitivity parameters with the original experimental data is shown in Figure 10. We see that when

*β*= 10.52, the experimental data and calculated values are relatively similar.

### TDG dissipation model in aeration

*β*= 10.52, this further explains that the experimental data and calculated values are relatively similar, the corresponding difference is 0.2%.

## CONCLUSIONS

In order to explore necessary measures to mitigate the harm of supersaturated TDG. Based on the gas–liquid mass transfer mechanism, indoor mechanism experiments and numerical simulation of methods, this paper profoundly aims to investigate the effect of aeration measures on water environments containing high concentrations of supersaturated TDG.

Experimental results indicate that aeration is one of the essential measures to mitigate the harm of supersaturated TDG and plays an active role in the dissipation process of supersaturated TDG and has a significant promoting effect on the gas–liquid interface mass transfer. And the time required for the supersaturated TDG dissipation process decreases with the increase of aeration rate and aeration aperture but is elevated with the increase of aeration depth, that is *T _{θ}* >

*T*>

_{Q}*T*, and TDG dissipation coefficients are elevated with the increase of aeration rate and aeration aperture, but are diminished with the increase of aeration depth, namely that of

_{H}*K*>

_{Q}*K*>

_{θ}*K*. Compared to the pinhole aeration method, this aeration method's larger aeration aperture has a promoting effect on the dissipation of supersaturated TDG. Besides, the relationship between the relative TDG dissipation coefficient and aeration rate is established, which is a power function and positively correlated. And a crucial quantitative relationship between supersaturated TDG dissipation coefficient and aeration conditions (aeration rate, aeration depth and aeration aperture) is established, that is, the TDG dissipation coefficient is positively correlated with aeration rate and aeration aperture in a power function, and negatively correlated with aeration depth in a power function. Their relative errors are within the controllable range. Moreover, one of the aeration data is selected for numerical simulation. When the critical TDG source treatment sensitivity parameter

_{H}*β*= 10.52, the error between the actual supersaturated TDG dissipation process and the TDG dissipation model is 0.2%, and the experimental data and simulation values are close.

This study provides essential scientific data and guiding suggestions for promoting the dissipation of supersaturated TDG and mitigating its harm and also indicates that aeration is likely to be one of the critical mitigating measures for TDG basins with high concentrations of local areas in the future. In future work, we should consider the impact of temperature, salinity, density and dynamic viscosity on supersaturated TDG, and for practical engineering applications, we will actively explore the application of aeration measures in basins with a high concentration of supersaturated TDG.

## ACKNOWLEDGEMENTS

The article is supported by: National Natural Science Foundation of China (Grant No.51709053) and the Science and Technology Fund of Guizhou Province (No.QKHJ-2019-1117).

## AUTHOR'S CONTRIBUTION

Y. Y. conceptualized the whole article, developed the methodology, investigated the article, rendered support in formal analysis, prepared the experiment, wrote the original draft and edited the article. H. Y. brought the resources, supervised the article, rendered support in funding supply, and reviewed the article. Y. W. prepared the experiment.

## DATA AVAILABILITY STATEMENT

All relevant data are included in the paper or its Supplementary Information.

## CONFLICT OF INTEREST

The authors declare there is no conflict.

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