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 m3/h to 5.0 m3/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
Experimental methods
DISSCUSSION AND ANALYSIS OF SUPERSATURATED TDG DISSIPATION
Dissipation of supersaturated TDG in aeration-free conditions
Supersaturated TDG dissipation coefficient in different water depth (H/m) under the static condition
Group number . | H (m) . | Q (m3/h) . | θ (m) . | R2 . | KTDG,0 . | R2 . |
---|---|---|---|---|---|---|
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 (m3/h) . | θ (m) . | R2 . | KTDG,0 . | R2 . |
---|---|---|---|---|---|---|
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 process of supersaturated TDG under aeration-free conditions in water depths (H) of 0.4, 0.8 and 1.2 m.
Dissipation process of supersaturated TDG under aeration-free conditions in water depths (H) of 0.4, 0.8 and 1.2 m.
Dissipation of supersaturated TDG in aeration
Dissipation process of supersaturated TDG
Compare the time required for the supersaturated TDG dissipation between microporous aeration and other mitigation measures
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 process of supersaturated TDG under different aeration rates (Q = (1, 2, 3, 4, 5) m3/h), aeration depth (H = (0.4, 0.8, 1.2) m) and aeration aperture (θ = (215, 260) mm).
Dissipation process of supersaturated TDG under different aeration rates (Q = (1, 2, 3, 4, 5) m3/h), aeration depth (H = (0.4, 0.8, 1.2) m) and aeration aperture (θ = (215, 260) mm).
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.
Supersaturated TDG dissipation coefficient in different aeration depth (H/m) under the aeration conditions
Group number . | H (m) . | θ (mm) . | Q (m3/h) . | KTDG (h−1) . | ψ = KTDG/KTDG,0 . | R2 . |
---|---|---|---|---|---|---|
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 (m3/h) . | KTDG (h−1) . | ψ = KTDG/KTDG,0 . | R2 . |
---|---|---|---|---|---|---|
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 m3/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 KQ > Kθ > KH. Therefore, it is further verified that this aeration method can significantly promote supersaturated TDG dissipation.
Fitting results of parameters on the relationship of relative dissipation coefficient (β) varying with aeration rate
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 |
The relationship between relative dissipation coefficient (β) and aeration rate (Q/m3·h−1).
The relationship between relative dissipation coefficient (β) and aeration rate (Q/m3·h−1).
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
Fitting results of parameters on the relationship of supersaturated TDG dissipation coefficients (KTDG,Q) varying with aeration rate (Q/m3/h)
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 |
Relationship between the supersaturated TDG dissipation (KTDG,Q) and aeration rate (Q).
Relationship between the supersaturated TDG dissipation (KTDG,Q) and aeration rate (Q).
The effect of aeration depth
Parameter values and correlation coefficients
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 | – |
Relationship between the supersaturated TDG dissipation (KTDG,H) and aeration depth (H).
Relationship between the supersaturated TDG dissipation (KTDG,H) and aeration depth (H).
The effect of aeration aperture
Parameter values and correlation coefficients
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 | – |
Relationship between the supersaturated TDG dissipation (KTDG,θ) and aeration aperture (θ).
Relationship between the supersaturated TDG dissipation (KTDG,θ) and aeration aperture (θ).
A quantitative relationship between the dissipation coefficients of supersaturated TDG and aeration conditions
Parameter values and correlation coefficients
Parameter . | Values . | Correlation coefficients . |
---|---|---|
![]() | 1.494 | 1.000 |
![]() | 1.093 | 0.411 |
![]() | 0.449 | 0.508 |
![]() | 0.487 | 0.510 |
![]() | 5.0 m3/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 m3/h | – |
![]() | 0.4 m | – |
![]() | 260 mm | – |
Comparison between experimental data and calculated values


The calculated values of errors
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 (Sc) 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 m3/h, H = 0.8 m, θ = 260 mm, initial TDG concentration (G = 147.4%) and KTDG = 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







Effective viscosity of gas–liquid


Turbulent model
Κ and ε equation, liquid phase turbulence coefficient


Turbulent model parameters
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
Wall lubricating force
Turbulent dissipation force
TDG transport diffusion equation




TDG dissipation source treatment


TDG equilibrium saturation within the bubble
Gas–liquid interfacial mass transfer coefficient and its mass transfer area
Water free-surface mass transfer coefficient and its mass transfer area
Determination of TDG source treatment sensitivity parameters
Comparison of the supersaturated TDG dissipation obtained from the TDG source treatment sensitivity parameters with the original experimental data.
Comparison of the supersaturated TDG dissipation obtained from the TDG source treatment sensitivity parameters with the original experimental data.
TDG dissipation model in aeration
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 Tθ > TQ > TH, 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 KQ > Kθ > KH. 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 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.