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Supersaturation of dissolved oxygen (DO) and total dissolved gas (TDG) is generated by high dam discharge, excess oxygen production in photosynthesis and increasing temperature in water, which may directly lead to fish suffering from ‘gas bubble disease’ or death. In this paper, under a series of experimental aeration conditions in standing water, it was concluded that aeration had a positively promoting effect on releases of supersaturated DO and TDG, while aeration aperture and aeration depth had inhibitory effects on them. For single factor analysis, aeration had the greatest effect on the release of DO and TDG, the second effect on DO was that of aeration depth and the smallest effect was that of aeration aperture, but the second effect on TDG was that of aeration aperture and the smallest effect was that of aeration depth. Most importantly, the release coefficient of DO was greater than that of TDG, and a quantitative relationship between the release coefficient of DO and TDG and aeration conditions, respectively, was established. An exponential function relationship of the release coefficients of DO and TDG was also established. The results of the research have important guiding significance and theoretical value for reducing the harm caused by supersaturated DO and TDG.

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  • The relationships between dissolved oxygen (DO) and total dissolved gas (TDG) and aeration, aeration depth and aeration aperture were established respectively.

  • A quantitative relationship between release coefficient (DO/TDG) and aeration conditions was established.

  • The root mean square error and the absolute average error were used for error analysis to judge the applicability of the equation. These equations were within 10%.

  • The relationship between dissolved oxygen (DO) and total dissolved gas (TDG) was established.

Graphical Abstract

Graphical Abstract
Graphical Abstract
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dissolved oxygen (DO), influence factor, release relationship, total dissolved gas (TDG)
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Supersaturation of total dissolved gas (TDG) mainly includes the supersaturation of dissolved oxygen (DO), dissolved nitrogen (DN) and other gases, which is generated by high discharge dam, excess oxygen production in photosynthesis and accumulation of water temperature and may directly cause fish to suffer from ‘gas bubble disease’ (GBD) and even death in water (Weitkamp & Katz 1980; Zhang et al. 2007; Qu et al. 2011; Chen et al. 2012). For research on dissolved oxygen (DO), Cheng et al. (2013) found that aeration can increase O2 content in water, and studied the mass transfer coefficient of DO, which was affected by aeration and temperature, linearly increasing with aeration, but inversely proportional to water depth. The conclusion is that the aeration method has the advantage of popularization for aquaculture, but the main influencing factors of DO are not clearly proposed. Huang et al. (2016) found that aeration can promote the recovery of supersaturated DO to the equilibrium state, and the relationship between DO release coefficient and aeration was established, but the relationship was not analyzed regarding whether the equation was applicable. Wan et al. (2017) concluded that the SPH method can simulate the DO concentration distribution of over-stepped spillways, and the simulation results were basically consistent with the data acquisition results. Monk et al. (1980) found that siphons can effectively remove gas from water. The results show that the degassing efficiency of various siphon designs depends on the gas content of the water, vacuum head, turbulence and the length of the siphon apex and that turbulence was the main factor in reducing the gas content in the water. Chen et al. (2022) found the distribution and change process of supersaturated dissolved gas at natural intersections under non-constant conditions by using prototype observation and numerical simulation, respectively. The results of the two comparisons were similar. Among them, the supersaturated DO increased with the increasing inflow DO level of the mainstream, but decreased with the increasing flow ratio of the branch. In the Three Gorges Project, Chen et al. (2009) analyzed that downstream water level and flow were important factors for DO and DO concentration increased with the increasing flow and downstream water level. Li & Qin (2012) measured the dissolved oxygen saturation in the discharge and its changes along the way at the Three Gorges Dam and Gezhou Dam, respectively, and also simulated the air–water transport process and DO concentration distribution through numerical simulation methods, and the measured values were close to the simulated values. Du et al. (2017) found that turbulence had a significant promoting effect on DO release, which had a positive correlation with its release coefficient under differing turbulence, but the installation method of the water pump had huge limitations.

For research on supersaturated TDG, Feng et al. (2014, 2018) found that reservoir operation can alleviate the hazard of supersaturated TDG, and simulation numerical results showed that optimum discharge structures combined with cascade joint operation can help reduce the duration of high flow discharge, thus reducing supersaturated TDG. Huang et al. (2017) found activated carbon with an adsorbent medium can significantly promote the release of supersaturated TDG, and the release effect of TDG was stronger with larger specific surface area of activated carbon, but the cost of the material was relatively high and it did not easily degrade. In terms of numerical models, Politano et al. (2012, 2017) summarized that the harm of supersaturated TDG can be reduced by dispersing flood discharge. She found that a two-fluid model can be used to calculate the bubble volume fraction and flow velocity of the dam and a poly-disperse model can be used to calculate the bubble size and established the TDG two-phase flow transport equation of the gas volume fraction and bubble size distribution (Politano et al. 2007). Based on mechanical principles, Politano et al. (2009) proposed an anisotropic two-phase flow model which can predict water entrainment, gas volume fraction, bubble size and TDG concentration. For the problem of unstable heat exchange between temperature and water, she also established an unsteady three-dimensional non-hydrostatic model which can predict the hydrodynamic and thermal forces in the fore-bay and turbine inlet, and its numerical results were consistent with the measured values (Politano et al. 2008). These models lay a foundation for finding ways to mitigate the harm of supersaturated TDG and better provide accurate TDG concentration location situation, facilitating the establishment of mitigation devices.

To sum up, in terms of research content, supersaturated DO and TDG are mostly caused by the high discharge dam, which may directly cause serious damage to fish. Meanwhile, in previous research, some scholars have summed up many methods to mitigate the damage of dissolved gas and the relationship between the influencing factors and the dissolved gas. However, there are certain limitations on the safety of the dam structure, the properties of the mitigation material and the complexity of the dissolved gas. Other scholars have established the dissolved gas concentration transport equation and the structure of its numerical model, but the applicable accuracy needs to be further verified. Therefore, under a series of experimental aeration conditions, this research explored the influencing scale of factors, the applicability of the concentration transport equation, and the release relationship between supersaturated DO and TDG, and these provided guidance and data value for alleviating the harm caused by dissolved gas.

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Laboratory instrumentation

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The laboratory instrumentation has a generation device and release device which are designed with reference to Li et al. (2010), 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 0.55 m in length and 0.44 m in width. The aeration distributor is placed at 0.4 m distance from the column bottom, which contains 63 steel pinholes with diameters of 0.6 mm and 0.9 mm. The range of the barometer is 0.5–6.0 m3/h. The measuring range of the TGP is 0%–600% of saturation with ±1% accuracy.
Figure 1
Sketch of the experimental setup.
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Sketch of the experimental setup.

Figure 1
Sketch of the experimental setup.
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Sketch of the experimental setup.

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Experimental methods

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The TGP (13) has the function of recording the concentration of DO and TDG. Before the aeration experiment, water and gas were transported by the water pump (3) and the air compressor (7) respectively, and then entered the pressure tank (10) together through the Venturi tube (5), which gradually formed supersaturated water. After the supersaturated water was prepared it was put into the water tank (11) equipped with the aeration distributor (14). When the predetermined aeration depth was reached and the concentration reached 140%, the TGP started to continuously measure supersaturated DO and TDG concentrations in the water, and the recording was stopped when the concentration was around 100%.

Different experimental aeration conditions are shown in Table 1. The aeration depths were 0.4 m, 0.8 m and 1.2 m, the aeration rates were 0.5 m3/h, 1.0 m3/h, 1.5 m3/h and 2.0 m3/h, and the diameters of the aeration aperture were 0.6 mm and 0.9 mm. There were 48 sets of experiments.

Table 1

Different experimental aeration conditions (48 sets of experiments)

Group numberMeasuring object (%)Aeration depth (H, m)Aeration aperture (D, mm)Aeration (Q, m3·h−1)
1 DO, TDG 0.4 0.6, 0.9 0.5, 1.0, 1.5, 2.0 
2 DO, TDG 0.8 0.6, 0.9 0.5, 1.0, 1.5, 2.0 
3 DO, TDG 1.2 0.6, 0.9 0.5, 1.0, 1.5, 2.0 
Group numberMeasuring object (%)Aeration depth (H, m)Aeration aperture (D, mm)Aeration (Q, m3·h−1)
1 DO, TDG 0.4 0.6, 0.9 0.5, 1.0, 1.5, 2.0 
2 DO, TDG 0.8 0.6, 0.9 0.5, 1.0, 1.5, 2.0 
3 DO, TDG 1.2 0.6, 0.9 0.5, 1.0, 1.5, 2.0 
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Experimental conditions

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The equation of saturation (Colt 1983):
(1)
where is the saturation of the dissolved gas i (%), is the actual solubility of the gas in water (⁠⁠), is the solubility of the gas i in water under certain temperature and pressure conditions (⁠⁠). Then > 100% is the supersaturated state, = 100% is the saturated state, and < 100% is the unsaturated state.
From Equation (1) and Figures 2 and 3, it can be seen that the concentration of DO and TDG in the experimental conditions exceeded 100%, which is a supersaturated state. Under the same aeration depth and aeration aperture, when the aeration increased from 0.5 m3/h to 2.0 m3/h, the time required for the release of supersaturated DO and TDG decreased by an average of 154.27%. Under the same aeration and aeration aperture, when the aeration depth was increased from 0.4 m to 1.2 m, the average increase in the time required for DO and TDG release was 11.36%. Under the same aeration and aeration depth, when the aeration aperture was increased from 0.6 mm to 0.9 mm, the average increase in time required for DO and TDG release was 12.47%. The results show that aeration can significantly promote the release of supersaturated DO and TDG, while large aeration depth and aeration aperture can inhibit their release. Therefore, in order to avoid the negative effect of large aeration aperture, a smaller aeration aperture can be further verified. The reasons for this are: (1) The air–water interface is affected by momentum, heat and mass transfer. Supersaturated DO and TDG are pushed by aeration which creates a little turbulence in standing water. The bubble density in the water tank increases with the increasing aeration, so that the turbulence intensity generated by aeration moves upward to the free surface in the deep area of the cylindrical water tank and the near-surface layers of flow in the gas transport process are constantly updated and the mass transfer process of the air–water interface is also strengthened (Chanson 2008; Gualtieri & Doria 2012). (2) The pressure and residence time of bubbles in the water are relatively long with increasing aeration depth, and the mass transfer of supersaturated dissolved gas mainly belongs to the bubble interface (Newbry 1998; Cheng et al. 2005, 2013). As the water depth increases, the turbulence intensity of water induced by bubbles is weakened, also decreasing the mass transfer effect of supersaturated dissolved gas at the air–water interface (Li et al. 2007). (3) Murphy et al. (1998) established a function of bubble radius and diffuser pore size, noting that bubble size decreases with decreasing diffuser pore size. Smaller bubbles can provide a larger contact area between the gas and DO/TDG, are less buoyant and may enhance the air–water interface mass transfer (Agarwal et al. 2011).
Figure 2
DO concentration vs time.
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DO concentration vs time.

Figure 2
DO concentration vs time.
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DO concentration vs time.

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Figure 3
TDG concentration vs time.
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TDG concentration vs time.

Figure 3
TDG concentration vs time.
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TDG concentration vs time.

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Release coefficients of DO and TDG

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In order to further study the effect of aeration on supersaturated DO and TDG, a first-order kinetic equation was introduced to express the release rate of DO and TDG (US Army Corps of Engineers 2005), the results are shown in Figures 4 and 5, and the slope is the release rate as shown in Table 2.
(2)
Table 2

Release coefficient and correlation coefficient

RunAeration aperture (mm)Aeration depth (m)Aeration (m3/h)
1 0.6 0.4 0.5 0.126 0.063 0.999 
2 0.6 0.4 1.0 0.177 0.074 0.968 
3 0.6 0.4 1.5 0.259 0.092 0.949 
4 0.6 0.4 2.0 0.357 0.245 0.998 
5 0.6 0.8 0.5 0.082 0.056 0.999 
6 0.6 0.8 1.0 0.143 0.067 0.990 
7 0.6 0.8 1.5 0.221 0.102 0.993 
8 0.6 0.8 2.0 0.327 0.103 0.996 
9 0.6 1.2 0.5 0.069 0.046 0.998 
10 0.6 1.2 1.0 0.123 0.062 0.998 
11 0.6 1.2 1.5 0.198 0.083 0.990 
12 0.6 1.2 2.0 0.293 0.136 0.993 
13 0.9 0.4 0.5 0.095 0.050 0.987 
14 0.9 0.4 1.0 0.132 0.067 0.977 
15 0.9 0.4 1.5 0.211 0.088 0.951 
16 0.9 0.4 2.0 0.295 0.226 0.995 
17 0.9 0.8 0.5 0.058 0.054 0.996 
18 0.9 0.8 1.0 0.112 0.067 0.999 
19 0.9 0.8 1.5 0.173 0.072 0.969 
20 0.9 0.8 2.0 0.272 0.198 0.997 
21 0.9 1.2 0.5 0.044 0.039 0.996 
22 0.9 1.2 1.0 0.085 0.060 0.996 
23 0.9 1.2 1.5 0.139 0.067 0.991 
24 0.9 1.2 2.0 0.190 0.151 0.990 
RunAeration aperture (mm)Aeration depth (m)Aeration (m3/h)
1 0.6 0.4 0.5 0.126 0.063 0.999 
2 0.6 0.4 1.0 0.177 0.074 0.968 
3 0.6 0.4 1.5 0.259 0.092 0.949 
4 0.6 0.4 2.0 0.357 0.245 0.998 
5 0.6 0.8 0.5 0.082 0.056 0.999 
6 0.6 0.8 1.0 0.143 0.067 0.990 
7 0.6 0.8 1.5 0.221 0.102 0.993 
8 0.6 0.8 2.0 0.327 0.103 0.996 
9 0.6 1.2 0.5 0.069 0.046 0.998 
10 0.6 1.2 1.0 0.123 0.062 0.998 
11 0.6 1.2 1.5 0.198 0.083 0.990 
12 0.6 1.2 2.0 0.293 0.136 0.993 
13 0.9 0.4 0.5 0.095 0.050 0.987 
14 0.9 0.4 1.0 0.132 0.067 0.977 
15 0.9 0.4 1.5 0.211 0.088 0.951 
16 0.9 0.4 2.0 0.295 0.226 0.995 
17 0.9 0.8 0.5 0.058 0.054 0.996 
18 0.9 0.8 1.0 0.112 0.067 0.999 
19 0.9 0.8 1.5 0.173 0.072 0.969 
20 0.9 0.8 2.0 0.272 0.198 0.997 
21 0.9 1.2 0.5 0.044 0.039 0.996 
22 0.9 1.2 1.0 0.085 0.060 0.996 
23 0.9 1.2 1.5 0.139 0.067 0.991 
24 0.9 1.2 2.0 0.190 0.151 0.990 
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Figure 4
DO release coefficient vs time.
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DO release coefficient vs time.

Figure 4
DO release coefficient vs time.
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DO release coefficient vs time.

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Figure 5
TDG release coefficient vs time.
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TDG release coefficient vs time.

Figure 5
TDG release coefficient vs time.
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TDG release coefficient vs time.

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Numerical integration:

where G is the TDG saturation (%), is the equilibrium saturation of TDG (usually 100%), is the release coefficient, t is the release time, and C is the intercept.

From Table 2, it is clearly seen that the release coefficient of DO is greater than that of TDG. TDG contains nitrogen (N2), oxygen (O2), carbon dioxide (CO2), hydrogen (H2) and other gases, and they are divided into polar molecules and non-polar molecules. The solubility of polar molecules is greater than that of non-polar molecules, such as N2, O2, CO2 and H2, which belong to the non-polar molecules that are hardly soluble in water, so they can easily reach a supersaturated state, while the solubility of the ammonium cation (⁠⁠) is relatively large and easily forms a compound with water, so the compound is in equilibrium (Tan et al. 2006).

As shown from Table 3, for single factor analysis, when aeration is from 0.5 m3·h−1 to 2.0 m3·h−1, the average increment of DO release coefficient is 287.41%, while that of TDG is 265.72%. When the aeration aperture is from 0.6 mm to 0.9 mm, the average reduction of DO release coefficient is 36.33%, while that of TDG is 70.77%. When the aeration depth is from 0.4 m to 1.2 m, the average reduction in DO release coefficient is 132.66%, while that of TDG concentration is 79.81%. Therefore, for DO release, aeration has the greatest effect on it, followed by aeration depth and the smallest effect is that of aeration aperture. For TDG release, the greatest effect is that of aeration, followed by aeration aperture and the smallest effect is that of aeration depth.

Table 3

Variation in the release coefficient of supersaturated DO and TDG

RunD (mm)H (m)Q (m3·h−1)Variation (⁠⁠)Variation (⁠⁠)
1 0.6 0.4 0.5–2.0 0.126–0.357 1.827 0.0632–0.245 2.874 
2 0.6 0.8 0.5–2.0 0.082–0.327 2.985 0.0556–0.172 2.075 
3 0.6 1.2 0.5–2.0 0.069–0.293 3.265 0.046–0.136 1.961 
4 0.9 0.4 0.5–2.0 0.095–0.295 2.115 0.050–0.226 3.528 
5 0.9 0.8 0.5–2.0 0.058–0.272 3.722 0.054–0.198 2.661 
6 0.9 1.2 0.5–2.0 0.044–0.190 3.330 0.039–0.151 2.844 
RunD (mm)H (m)Q (m3·h−1)Variation (⁠⁠)Variation (⁠⁠)
1 0.6 0.4 0.5–2.0 0.126–0.357 1.827 0.0632–0.245 2.874 
2 0.6 0.8 0.5–2.0 0.082–0.327 2.985 0.0556–0.172 2.075 
3 0.6 1.2 0.5–2.0 0.069–0.293 3.265 0.046–0.136 1.961 
4 0.9 0.4 0.5–2.0 0.095–0.295 2.115 0.050–0.226 3.528 
5 0.9 0.8 0.5–2.0 0.058–0.272 3.722 0.054–0.198 2.661 
6 0.9 1.2 0.5–2.0 0.044–0.190 3.330 0.039–0.151 2.844 
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According to the relevant research results of the effect of aeration on re-oxygenation mass transfer, the relationship between the re-oxygenation coefficient and aeration did not follow a linear increase (Cheng et al. 2013). It is necessary to further analyze the relationship equations between aeration, aeration depth and aeration aperture and the release coefficient of supersaturated DO/TDG.

The effect of aeration

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Figure 6 shows that the relationship between release coefficient and aeration is positively correlated. In addition, aeration and the release coefficient are fitted by a nonlinear fitting method in ORIGIN software, and the parameter values and correlation coefficients as shown in Table 4 are obtained. Therefore, their relationship can be expressed by Equation (3):
(3)
where is release coefficient, Q are aeration (m3/h) and are fitting parameters.
Table 4

Parameter values and correlation coefficients

RunDO
TDG
1 0.117 ± 0.047 −1.655 ± 0.374 0.999 0.0009 ± 0.000 −0.265 ± 0.052 0.999 
2 0.144 ± 0.060 −1.813 ± 0.426 0.999 0.0054 ± 0.006 −0.629 ± 0.191 0.999 
3 0.135 ± 0.061 −1.833 ± 0.473 0.999 0.0059 ± 0.008 −0.707 ± 0.306 0.997 
4 0.086 ± 0.039 −1.506 ± 0.356 0.996 0.0004 ± 0.000 −0.329 ± 0.061 0.996 
5 0.070 ± 0.040 −1.512 ± 0.346 0.999 0.0001 ± 0.000 −0.216 ± 0.065 0.995 
6 0.38 ± 0.499 −4.991 ± 5.178 0.999 0.0004 ± 0.000 −0.364 ± 0.107 0.981 
RunDO
TDG
1 0.117 ± 0.047 −1.655 ± 0.374 0.999 0.0009 ± 0.000 −0.265 ± 0.052 0.999 
2 0.144 ± 0.060 −1.813 ± 0.426 0.999 0.0054 ± 0.006 −0.629 ± 0.191 0.999 
3 0.135 ± 0.061 −1.833 ± 0.473 0.999 0.0059 ± 0.008 −0.707 ± 0.306 0.997 
4 0.086 ± 0.039 −1.506 ± 0.356 0.996 0.0004 ± 0.000 −0.329 ± 0.061 0.996 
5 0.070 ± 0.040 −1.512 ± 0.346 0.999 0.0001 ± 0.000 −0.216 ± 0.065 0.995 
6 0.38 ± 0.499 −4.991 ± 5.178 0.999 0.0004 ± 0.000 −0.364 ± 0.107 0.981 
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Figure 6
Relationship between release coefficient and aeration.
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Relationship between release coefficient and aeration.

Figure 6
Relationship between release coefficient and aeration.
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Relationship between release coefficient and aeration.

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The effect of aeration depth

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Figures 7 and 8 show that the relationship between release coefficient and aeration depth is negatively correlated. Their relationship is fitted into Equations (4) and (5) by a multivariate nonlinear regression analysis in SPSS software:
(4)
(5)
where is DO release coefficient, is TDG release coefficient, is aeration depth (m).
Figure 7
Relationship between DO release coefficient and aeration depth.
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Relationship between DO release coefficient and aeration depth.

Figure 7
Relationship between DO release coefficient and aeration depth.
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Relationship between DO release coefficient and aeration depth.

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Figure 8
Relationship between TDG release coefficient and aeration depth.
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Relationship between TDG release coefficient and aeration depth.

Figure 8
Relationship between TDG release coefficient and aeration depth.
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Relationship between TDG release coefficient and aeration depth.

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The effect of aeration aperture

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Figures 9 and 10 show that the relationship between release coefficient and aeration aperture is negatively correlated. Their relationship is fitted into Equations (6) and (7) by a multivariate nonlinear regression analysis in SPSS software:
(6)
(7)
where is DO release coefficient, is TDG release coefficient, D is aeration aperture (mm).
Figure 9
Relationship between DO release coefficient and aeration aperture.
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Relationship between DO release coefficient and aeration aperture.

Figure 9
Relationship between DO release coefficient and aeration aperture.
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Relationship between DO release coefficient and aeration aperture.

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Figure 10
Relationship between TDG release coefficient and aeration aperture.
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Relationship between TDG release coefficient and aeration aperture.

Figure 10
Relationship between TDG release coefficient and aeration aperture.
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Relationship between TDG release coefficient and aeration aperture.

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A quantitative relationship between release coefficient and aeration conditions

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In the experiments, three factors act together on the release coefficient, and the relational Equation (8) of the joint action of the three factors is obtained by combining Equations (3)–(7):
(8)
where is release coefficient, is aeration (m3/h), is aeration aperture (mm), is aeration depth (m) and are the fitting parameters of the equation.

These parameters (⁠⁠, ⁠, and ⁠) are obtained by using a multivariate nonlinear regression analysis method in SPSS software, as shown in Table 5.

Table 5

Parameter values and correlation coefficients

RunDO
TDG
ParametersValuesCorrelation coefficientsParametersValuesCorrelation coefficients
1  2.0 m3/h —  2.0 m3/h — 
2  0.4 m —  0.4 m — 
3  0.6 mm —  0.6 mm — 
4  0.371 1.000  0.196 1.000 
5  1.033 0.390  1.340 0.343 
6  0.274 0.588  0.377 0.520 
7  0.635 0.433  −0.122 0.567 
RunDO
TDG
ParametersValuesCorrelation coefficientsParametersValuesCorrelation coefficients
1  2.0 m3/h —  2.0 m3/h — 
2  0.4 m —  0.4 m — 
3  0.6 mm —  0.6 mm — 
4  0.371 1.000  0.196 1.000 
5  1.033 0.390  1.340 0.343 
6  0.274 0.588  0.377 0.520 
7  0.635 0.433  −0.122 0.567 
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Table 5 clearly shows the values of the parameter and the correlation coefficient, so the equations for obtaining DO and TDG are (9) and (10):
(9)
(10)

Comparison between experimental data and calculated values

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Cheng et al. (2015) carried out experimental analysis of microporous aeration at the bottom of a pond to study the effect of aeration rate and aeration pipe length on DO mass transfer, and when she established the DO mass transfer prediction equation, the root mean square error (11) and the absolute average error (12) were used for error analysis to judge the applicability of the equation. So, for the comparison of experimental data and calculated values of Equations (3)–(10), the calculation method here is the same as hers.
(11)
(12)
where RMSE is the root mean square value, AME is the absolute mean value, is the calculated value, is the experimental value.
Figure 11 clearly shows the comparison between experimental data and calculated values, and the calculated values of errors are shown in Table 6.
Table 6

The calculated values of errors

ParametersDO
ParametersTDG
RMSEAMERMSEAME
Equation (3) 3.86% 2.94% Equation (3) 3.29% 2.53% 
Equation (4) 9.46% 7.48% Equation (5) 5.37% 4.22% 
Equation (6) 8.42% 7.13% Equation (7) 5.54% 4.16% 
Equation (9) 1.62% 2.94% Equation (10) 2.74% 2.25% 
ParametersDO
ParametersTDG
RMSEAMERMSEAME
Equation (3) 3.86% 2.94% Equation (3) 3.29% 2.53% 
Equation (4) 9.46% 7.48% Equation (5) 5.37% 4.22% 
Equation (6) 8.42% 7.13% Equation (7) 5.54% 4.16% 
Equation (9) 1.62% 2.94% Equation (10) 2.74% 2.25% 
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Figure 11
Comparison between experimental data and calculated values.
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Comparison between experimental data and calculated values.

Figure 11
Comparison between experimental data and calculated values.
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Comparison between experimental data and calculated values.

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Both RMSE and AME are within 10%, and these equations are reasonable (Cheng et al. 2015; Ou et al. 2016). In addition, the objective Equation (13) is a function of measuring AME:
(13)
where is the target value of AME, is the maximum of the experimental value, is the minimum of the experimental value.

For DO, ⁠. For TDG, ⁠. The error of AME is lower than that of Target, which further shows that these equations are feasible.

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Ma et al. (2013) detected the concentration of DO and TDG in rivers in southwest China and found that the concentration of DO and TDG was a linear relationship, but did not fit the relationship equation of their release coefficients. Therefore, based on the previous relationship between the release coefficient and aeration conditions, experimental data and calculated values are used to represent the release relationship of DO and TDG.

According to the distribution of the release coefficient in Figure 12, we tried to use linear fitting, exponential function, power function and other forms of function to express the relationship between the two, but only the form of the exponential function was more consistent. The release relationship between DO and TDG is Equation (14), and the equation parameters are shown in Table 7.
(14)
where is the TDG release coefficient, is the DO release coefficient and are the equation parameters.
Table 7

Equation parameters and correlation coefficients

ParametersExperimental datak–Qk–Hk–Dk–Q,H,D
 0.559 ± 0.144 0.748 ± 0.000 0.716 ± 0.000 0.089 ± 0.000 0.627 ± 0.100 
 1.027 ± 0.174 1.213 ± 0.000 0.994 ± 0.000 −0.033 ± 0.000 1.109 ± 0.110 
 0.671 1.000 1.000 1.000 0.883 
ParametersExperimental datak–Qk–Hk–Dk–Q,H,D
 0.559 ± 0.144 0.748 ± 0.000 0.716 ± 0.000 0.089 ± 0.000 0.627 ± 0.100 
 1.027 ± 0.174 1.213 ± 0.000 0.994 ± 0.000 −0.033 ± 0.000 1.109 ± 0.110 
 0.671 1.000 1.000 1.000 0.883 
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Figure 12
Release coefficient distribution and nonlinear fitting of DO and TDG.
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Release coefficient distribution and nonlinear fitting of DO and TDG.

Figure 12
Release coefficient distribution and nonlinear fitting of DO and TDG.
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Release coefficient distribution and nonlinear fitting of DO and TDG.

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Supersaturated dissolved gas (DO and TDG) is mainly produced by excessive flood discharge from spillways, excess oxygen production in photosynthesis and water temperature accumulation, which may directly cause great harm to fish. This phenomenon has become a hot issue of social focus.

In this paper, under a series of aeration conditions, the release coefficient of supersaturated DO was larger than that of supersaturated TDG. Single factor analysis showed that aeration had the greatest effect on DO release, followed by aeration depth, and aeration aperture was the smallest. For TDG release, aeration had the greatest effect on it, followed by aeration aperture and aeration depth had the smallest effect. In addition, aeration can obviously promote dissolved gas, while aeration depth and aeration aperture can inhibit it.

A quantitative release relationship between dissolved gas (DO, TDG) and aeration conditions (aeration, aeration depth and aeration aperture) was established, respectively. These equations were feasible and their errors were all within 10%, as follows:

Relationship between k and Q:

Relationship between k and H: ⁠,

Relationship between k and D: ⁠,

Relationship between k and

Most importantly, the release relationship between supersaturated TDG and supersaturated DO is established, as shown to be ⁠.

This research has important research value for alleviating the harm caused by supersaturated dissolved gas. In order to apply this relationship to practical projects, the effects of water temperature and hydrodynamic parameters should be further studied.

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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).

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

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The authors declare there is no conflict.

Chanson
H.
2008
Advective diffusion of air bubbles in turbulent water flows
. In:
Fluid Mechanics of Environmental Interfaces
(C. Gualtieri & D. T. Mihailović, eds), Taylor & Francis, London, UK, pp. 163–198
.
Google Scholar
 
Chen
Y. C.
,
Fu
J.
,
Liu
Z. W.
,
Cheng
X. J.
 &
Zhu
D. J.
2009
Analysis of dissolved oxygen variation characteristics and influencing factors downstream of the Three Gorges Dam
.
Advances in Water Science
20
(
4
),
526
–
530
(in Chinese)
.
Google Scholar
 
Chen
S. C.
,
Liu
X. Q.
,
Jiang
W.
,
Li
K. F.
,
Du
J.
,
Shen
D. Z.
 &
Gong
Q.
2012
Effects of total dissolved gas supersaturated water on lethality and catalase activity of Chinese sucker (Myxocyprinus asiaticus Bleeker)
.
Journal of Zhejiang University Science B
13
(
10
),
791
–
796
.
Google Scholar
Crossref
Search ADS
PubMed
 
Chen
Z.
,
Feng
J.
,
Li
R.
,
Wang
Y.
,
Peng
F.
 &
Li
K.
2022
Field observation and numerical modelling of supersaturated dissolved gas at river confluence
.
Ecological Modelling
471
,
110017
.
Google Scholar
Crossref
Search ADS
 
Cheng
X. J.
,
Chen
Y. C.
,
Gao
Q. H.
 &
Chen
Y.
2005
Analysis of supersaturated reoxygenation of discharge from the dam body of the Three Gorges Reservoir
.
Journal of Hydroelectric Power Generation
24
(
6
),
62
–
67
(in Chinese)
.
Google Scholar
 
Cheng
X. J.
,
Xie
J.
,
Yu
D. G.
 &
Zeng
Y. X.
2013
Computational analysis of oxygen mass transfer at the microbubble–water interface and water surface by aeration and oxygenation
.
Chinese Journal of Agricultural Engineering
29
(
13
),
190
–
199
(in Chinese)
.
Google Scholar
 
Cheng
X. J.
,
Zeng
Y. X.
 &
Xie
Y. N.
2015
Experiment and analysis of microporous aeration and oxygenation at the bottom of pond
.
Journal of Chinese Academy of Water Resources and Hydropower Science
13
(
5
),
339
–
343 + 351
(in Chinese)
.
Google Scholar
 
Du
K. K.
,
Li
Y. F.
,
Liu
L.
,
Ru
H. J.
,
Sheng
Q.
,
Wu
X. X.
,
Zhang
Y.
,
Liu
X. J.
 &
Ni
C. H.
2017
A preliminary study on the effect of turbulence on the release of dissolved oxygen from supersaturated water
.
Freshwater Fisheries
47
(
5
),
21
–
25
(in Chinese)
.
Google Scholar
 
Gualtieri
C.
 &
Doria
G. P.
2012
Gas-transfer at unsheared free-surfaces. In: Fluid Mechanics of Environmental Interfaces (C. Gualtieri & D. T. Mihailović, eds), CRC Press, Boca Raton, FL, USA, pp. 145–179
.
Huang
Y. H.
,
Li
R.
,
Feng
J. J.
,
Qu
L.
 &
Niu
J. L.
2016
Experimental study on the recovery of dissolved oxygen supersaturated water by aeration
.
Chinese Journal of Hydroelectric Power
35
(
6
),
80
–
86
(in Chinese)
.
Google Scholar
 
Huang
Y. N.
,
Li
R.
,
Li
J. L.
 &
Huang
Y. H.
2017
Experimental study of specific surface area promoting the release of dissolved oxygen from supersaturated water
.
Hydropower and Energy Science
35
(
4
),
45
–
48
(in Chinese)
.
Google Scholar
 
Li
L.
 &
Qin
C. L.
2012
Analysis of the cumulative effect of dissolved oxygen in the water body of the Three Gorges Cascade Power Station
.
Journal of Hydropower Generation
31
(
1
),
189
–
194
(in Chinese)
.
Google Scholar
 
Li
E.
,
Zeng
X. Y.
 &
Fan
Y. H.
2007
Determination of optimal bubble group for microporous aeration
.
Water Treatment Technology
33
(
7
),
21
–
24 + 52
(in Chinese)
.
Google Scholar
 
Li
R.
,
Huang
X.
,
Li
K. F.
,
Yi
W. M.
,
Li
J.
,
Deng
Y.
,
Feng
J. J.
,
Qu
L.
 &
Liang
R. F.
2010
A device for the study of total dissolved gas supersaturation in water and its impact on fish, China Patent No. ZL 2009 1 0164299.3. Authorized Announcement 2011, pp. 7-20 (in Chinese)
.
Ma
Q.
,
Li
R.
,
Feng
J.
 &
Wang
L.
2013
Relationships between total dissolved gas and dissolved oxygen in water
.
Fresenius Environmental Bulletin
22
(
11
),
3243
–
3250
.
Google Scholar
 
Murphy
A. P.
,
Lichtwardt
M. A.
 &
Bisgaard
S.
1998
Novel methods for generating and treating air supersaturated water
. In:
Proceedings of the 1998 ASME Fluids Engineering Division Summer Meeting
,
ASME, New York, USA
.
Google Scholar
 
Monk
B. H.
,
Long
C. W.
 &
Dawley
E. M.
1980
Feasibility of siphons for degassing water
.
Transactions of the American Fisheries Society
109
(
6
),
765
–
768
.
Google Scholar
Crossref
Search ADS
 
Ou
Y.
,
Li
R.
,
Tuo
Y.
,
Niu
J.
,
Feng
J.
 &
Pu
X.
2016
The promotion effect of aeration on the dissipation of supersaturated total dissolved gas
.
Ecological Engineering
95
,
245
–
251
.
Google Scholar
Crossref
Search ADS
 
Politano
M. S.
,
Carrica
P. M.
,
Turan
C.
 &
Weber
L.
2007
A multidimensional two-phase flow model for the total dissolved gas downstream of spillways
.
Journal of Hydraulic Research
45
(
2
),
165
–
177
.
Google Scholar
Crossref
Search ADS
 
Politano
M.
,
Haque
M. M.
 &
Weber
L. J.
2008
A numerical study of the temperature dynamics at McNary Dam
.
Ecological Modelling
212
(
3–4
),
408
–
421
.
Google Scholar
 
Politano
M.
,
Carrica
P.
 &
Weber
L.
2009
A multiphase model for the hydrodynamics and total dissolved gas in tailraces
.
International Journal of Multiphase Flow
35
(
11
),
1036
–
1050
.
Google Scholar
Crossref
Search ADS
 
Politano
M.
,
Amado
A. A.
,
Bickford
S.
,
Murauskas
J.
 &
Hay
D.
2012
Evaluation of operational strategies to minimize gas supersaturation downstream of a dam
.
Computers & Fluids
68
,
168
–
185
.
Google Scholar
Crossref
Search ADS
 
Politano
M.
,
Castro
A.
 &
Hadjerioua
B.
2017
Modeling total dissolved gas for optimal operation of multireservoir systems
.
Journal of Hydraulic Engineering
143
(
6
),
04017007
.
Google Scholar
Crossref
Search ADS
 
Qu
L.
,
Li
R.
,
Li
J.
,
Li
K.
 &
Deng
Y.
2011
Field observation of total dissolved gas supersaturation of high-dams
.
Science China Technological Sciences
54
(
1
),
156
–
162
.
Google Scholar
Crossref
Search ADS
 
Tan
D. C.
,
Ni
Z. H.
,
Zheng
Y. H.
,
Li
L. Y.
 &
Li
Y. F.
2006
Gas supersaturation in rivers caused by high dams and their effects on fish
.
Freshwater Fisheries
36
(
3
),
56
–
59
(in Chinese)
.
Google Scholar
 
US Army Corps of Engineers
2005
Technical Analysis of TDG Processes. US Army Corps of Engineers – Northwest Division, Environmental Resources and Fish Planning Offices, Jacksonville, FL, USA
.
Weitkamp
D. E.
 &
Katz
M.
1980
A review of dissolved gas supersaturation literature
.
Transactions of the American Fisheries Society
109
(
6
),
659
–
702
.
Google Scholar
Crossref
Search ADS
 
Zhang
C. R.
,
Dai
H. C.
,
Gao
J. Z.
 &
Ouyang
J. H.
2007
Major scientific and technological problems in the construction and operation of super-large hydropower projects
.
Journal of Hydraulic Engineering
29
(
S1
),
7
–
14
(in Chinese)
.
Google Scholar
 
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