TSINGHUA SCIENCE AND TECHNOLOGY ISSNll1007-0214ll13/17llpp574-579 Volume 15, Number 5, October 2010

Numerical Simulation of Dissolved Oxygen Supersaturation Flow over the Three Gorges Dam Spillway*

LI Ling (李 玲)1,∗∗, QIN Chunli (覃春丽)1, PENG Qidong (彭期冬)2, YAN Zhifeng (晏智锋)1, GAO Qianhong (高千红)3

1. State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China;

2. China Institute of Water Resource and Hydropower Research, Beijing 100038, China; 3. Centre of Water Environmental Monitor of Yangtze River Three Gorges Project, Yichang 443002, China

Abstract: The dissolved oxygen concentration in a flow changes with distance downstream of the spillway

crest and depends on the geometric configuration of the spillway and the hydraulic and operating conditions.

A mathematical model was developed to simulate the turbulent structure of the flow over the spillway of the

Three Gorges Dam at the 145 m reservoir water level to study the aeration characteristics and the gas

transport. The model was calibrated and verified with measured data. The analysis of distribution of the

aeration and the dissolved oxygen showed that the downstream water level, upstream dissolved oxygen

content, and the flow discharge all affect the dissolved oxygen saturation downstream of the sluicing dam.

The simulation provides guidance for controlling the dissolved oxygen supersaturation and environmentally

friendly operation of the Three Gorges Dam.

Key words: environmental hydrodynamics; dissolved oxygen content; spillway; Three Gorges Dam;

water-gas two-phase flow

Introduction

Since the Three Gorges reservoir started to store water in 2003, the strong turbulence in the water flow from the flood discharge has increased the mass transfer from the air to the water jets, which greatly increases the dissolved oxygen (DO) concentrations downstream. According to data provided by the Centre of Water Environmental Monitoring of the Yangtze River Three Gorges Project, the DO concentrations downstream including the Huanglingmiao, Dongyuemiao, and

Nanjinguan sections all exceeded 110% during flood discharges for reservoir water levels ranging from 135 m to 139 m. Then, according to data of the Three Gorge Hydrology Bureau, when the reservoir water level reached 145 m in 2007, the DO content in the down-

stream river exceeded 100% of saturation with some locations downstream at over 120%. With the incr-

easing reservoir water level. The DO supersaturation causes the bubble disease and threatens fish survival[1,2]. Fish can suffer from bubble disease when the DO concentration reaches 105%-110%, and will die in several hours once the DO concentration exceeds 140%. Therefore, the DO supersaturation after completing the Three Gorges Dam must be reduced to protect fish in the Yangtze River. This study focuses on increases in the DO content due to flow over the spill-way of the Three Gorges Dam.

The research concerning DO supersaturation in the

Received: 2009-05-11; revised: 2010-05-20

* Supported by the National Key Basic Research and DevelopmentProgram (973) of China (No. 2006CB403304) and State Key Labo-ratory of Hydroscience and Engineering Program of China (Nos.2008-TC-1 and 2009-TC-2)

** To whom correspondence should be addressed. E-mail:li-ling@tsinghua.edu.cn; Tel: 86-10-62782297

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lower river originated from the 1960s, during which a large number of field surveys and prototype obser-

vations were completed[3-7]. The results showed that the main factors influencing the DO supersaturation included the discharge flow per meter width, depth of downstream plunge pools, and the turbulent intensity of discharge flow. All these studies were for low-water head dams, with little research for high or super-high dams. With the rapid development of computer models, mathematical models have become the main method for analyzing such flows[8-10]. This paper presents a model that simulates the physical processes controlling the DO changes and the distribution of

the DO content for the flow over the spillway. The main goal is to use a physically based model to study the relative importance of various processes that occur in the spillway flow. The predictions are calibrated with measured data. The results provide a better understanding of how each process affects the DO concentration.

1 Mathematical Models 1.1 Water-gas two-phase flow model

The volume of fluid model (VOF) can be used to pre-dict the interface shape between two or more mutually non-penetrating fluids. The model introduces a volume fraction for each phase, and determines the interface location by solving the volume fraction in each control cell.

If the volume fraction of the phase q in a control cell is qα ( 0 1qα ), then

0qα = denotes cells without the phase q fluid;

1qα = denotes cells filled with the phase q fluid;

0 < <1qα denotes that the cell contains an inter-

face between the fluids. The advection-diffusion equation for the volume

fraction is:

0q qi

i

ut xα α∂ ∂

+ =∂ ∂

(1)

11

n

qqα

=

=∑ (2)

The two-dimensional Reynolds averaged turbulent equations with the RNG k-ε turbulence model were used to predict the turbulent flow. The governing

equations are: The continuity equation:

0i

i

ut xρ ρ∂ ∂+ =

∂ ∂ (3)

The momentum equations:

i j ji ii

j i i j i

u u uu up gt x x x x x

ρρμ ρ⎛ ⎞∂ ∂∂ ∂∂ ∂

+ = − + + +⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂ ∂ ∂⎝ ⎠ (4)

The RNG k-ε turbulence model: ( ) ( )i t

i j k j

k u k k Gt x x xρ ρ μμ ρε

σ

⎡ ⎤∂ ∂ ∂ ∂⎛ ⎞+ = + + −⎢ ⎥⎜ ⎟∂ ∂ ∂ ∂⎢ ⎥⎝ ⎠⎣ ⎦ (5)

( ) ( )i t

i j j

ut x x xε

ρε ρ ε μ εμσ

⎡ ⎤∂ ∂ ∂ ∂⎛ ⎞+ = + +⎢ ⎥⎜ ⎟∂ ∂ ∂ ∂⎢ ⎥⎝ ⎠⎣ ⎦

2*

1 2kC G Ck kε εε ερ− (6)

where w w w a(1 )ρ α ρ α ρ= + − , w w w a(1 )μ α μ α μ= + − ,

wρ is the water density, aρ is the gas density, wμ is the water viscosity, and aμ is the gas viscosity. The variables and constants were discussed earlier[11].

1.2 Advection-diffusion equation for the dissolved oxygen

t

t

( )( ) iC

i j j

u CC C St x x x

ρ μρ μ ρσ

⎡ ⎤∂∂ ∂ ∂⎛ ⎞+ = + +⎢ ⎥⎜ ⎟∂ ∂ ∂ ∂⎢ ⎥⎝ ⎠⎣ ⎦ (7)

where C is the dissolved oxygen concentration, CS is the source term, tμ is the turbulent diffusion coeffi-cient of the water and gas mixture, and tσ is the tur-bulent Schmidt number.

Oxygen transport can occur from air bubbles into the water (bubble transfer) and across the air-water surface interface (surface transfer). The source term

CS in Eq. (7) including these transport mechanisms can be written as

L,B B se L,s s s( ) ( )CS K a C C K a C C= − + − (8) where L,BK is the mass transfer coefficient across the air bubble-water interface, L,SK is the mass transfer coefficient across the air-water surface interface, Ba is the specific bubble surface area per unit water vol-ume, Sa is the specific free water surface area per unit water volume, sC is the saturation concentration at local atmospheric pressure, and seC is the effective saturation concentration at the air bubble-water inter-face (taking into account the hydrostatic pressure). Studies have shown a linear correlation between

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oxygen concentration and the pressure in a bubble. An effective saturation concentration was introduced to explain the vertical pressure in a bubble. The effective saturation concentration, Cse in Eq. (9) expresses the increased mass transfer potential between a bubble and the surrounding water due to the hydrostatic pressure[5]. This is a combination of the atmospheric saturation concentration and the increased transport due to the hydrostatic pressure.

effse s

atm

1 dC Cpγ⎛ ⎞= +⎜ ⎟

⎝ ⎠ (9)

where deff is the effective depth, γ is the specific weight of water, and patm is the atmospheric pressure. The ef-fective depth is the average depth of bubbles in a con-trol volume. As the flow moves downstream, the air bubbles rise and the effective depth changes.

The mass transfer rate across the air bubble into the water is characterized by Eq. (10), obtained by modi-fying a relationship for bubbles entrained in a turbulent flow field[12,13].

1/2mL,B 2/3 3/4

b

2 113 (1 0.09 )π

DK PeReR

β⎧ ⎫

= ⋅ −⎨ ⎬+⎩ ⎭

(10)

where bR is the bubble radius, Pe is the Peclet number, b r m2 /Pe R v D= , Re is the Reynolds number,

b t2 2 / 3 /Re R k ν= , rv is the of bubble ascent ve-locity equal to 0.25 m/s, Dm is the molecular diffusion coefficient equal to 2.5×10−9 m2/s, k is the turbulent kinetic energy; tν is the turbulent diffusivity; and β is an unknown coefficient determined from field data.

The mass transfer rate across the water surface is characterized by

( 5/3) (4/3)L,s 0.002 436K u k−= (11)

where u is the water velocity and k is turbulent kinetic energy.

The DO saturation is defined as

DO saturation = s

100%CC

× (12)

2 Numerical Methods and Boundary Conditions

The governing equations were solved using FLUENT with a user defined function to calculate the DO con-centration to predict the DO saturation and the flow characteristics over the spillway. The calculation domains was filled with irregular elements with the

governing equations solved with the control volume method. The diffusion terms in the momentum and turbulence equations were differenced with the second order upwind scheme, with the PISO algorithm for the pressure-velocity coupling.

A two-dimensional model was used to analyze the flow from the Three Gorges Dam to the Huangling-miao section shown in Fig. 1, a distance of about 12 km. The water flows through deep outlets in the dam, with water jets shooting out into the air and into the downstream plunge pool. The jets form scour pits in the plunge pool[14]. The inlet boundary condition is given by the average velocity determined from the known flow rate per unit width. The inlet DO saturation is also given from measured data. The outlet boundary condition is given by the measured water depth in the Huanglingmiao section with the deviation of DO saturation in the direction being zero. The walls are assumed no-slip with the standard wall function.

Fig. 1 River section schematic

The overflow discharge mixes with the water flow from the power station about 900 m below the Three Gorges Dam. The plane two-dimensional model was used to analyze the flow in the mixing section from about 900 m below the Three Gorges Dam to the fore-bay over the Gezhouba Dam. The station is 38 km long, where the flow tends to be steady and little air is dis-solved into the free water surface. The rigid-lid as-sumption is used to calculate the free surface location. The inlet average velocity and DO saturation are given by averaged vertical two-dimensional calculations de-termined from the flow from the power plant and the spillway. The power plants are located on both sides of the spillway. The flow rate and the DO saturation with spillway discharge are known and the DO saturation at the power plant exit is equal to the DO saturation in the reservoir. For the outlet boundary condition since the

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water flows smoothly in the forebay to the Gezhouba Dam, the gradients of the variables are equal to zero at the calculated region outlet.

3 Model Calibration and Verification 3.1 Model calibration

The measured data for 8 July, 2007 was used to cali-brate the mathematical model. The total discharge was 34 115 m3/s and the flood discharge was 18 077 m3/s. The Taipingxi section is 0.5 km upstream of the Three Gorges Dam while the Huanglingmiao section is 12 km downstream. The water level at Taipingxi was 144.14 m and 68.08 m in the Huanglingmiao section. The DO saturation was 80.4% in the Taipingxi section, 110.7% in the Huanglingmiao section, and 105.6% at the forebay of the Gezhouba Dam.

The parameter β in Eq. (10) was determined from the measured data. The simulation results for the DO

saturation were compared with the measured data in the Huanglingmiao section and in the forebay over the Gezhouba Dam. The predicted DO saturations in the Huanglingmiao section were 111.1% and 102.5% in the forebay over the Gezhouba Dam for β=1.8, which both agree well with the observed data. DO saturation at the inlet was set to 80%. Figure 2 shows as the water flows over the spillway, the DO saturation with water jets increases a little to slightly more that at the inlet. As the jets fall into the pool water, the strong turbu-lence between the water and the air rapidly increases the mass transfer which increases the DO saturation from 80% to 180%. The DO saturation decreases gradually as the turbulent intensity decreases and bub-bles disappear. The oxygen will gradually dissipate into the air so the DO saturation will decrease. As shown in Fig. 3, the DO saturation is 160% 900 m be-low the dam, 110% at the Huanglingmiao section, and 100% in the forebay over Gezhouba Dam.

Fig. 2 DO saturations (%) in the flow over the spillway for July 8, 2007

Fig. 3 DO saturation (%) from 900 m below the Three Gorges Dam to the forebay over the Gezhouba Dam for July 8, 2007 (1, Huanglingmiao section; 2, Gezhouba Dam)

3.2 Model verification

The measured data for 14 July, 2006 was used to vali-date the model. The total discharge was 20 138 m3/s, while the flood discharge was 7103 m3/s. The water level at the Taipingxi section was 135.59 m and the DO saturation was 58.9%. The water level at the Huanglingmiao section was 66.37 m and the DO saturation was 95.8%. The DO saturation in the fore-bay over the Gezhouba Dam was 80.0%.

The distribution of the aeration shown in Fig. 4 shows that the water jets injecting the pool water be

Fig. 4 Aeration rates (αa) over the spillway for July 14, 2006

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low the dam increases aeration from the jet entry point downstream to 550 m. The high aeration has resulted in the high DO saturation in Fig. 5. The DO saturation in the scour pit is nearly 160%. In the calmer sections downstream, the aeration rate and the DO saturation

both decrease. The DO saturation at the Huangling-miao section is about 90% as shown in Fig. 6, while the DO saturation in the forebay over the Gezhouba Dam is 80%, both of which agree well with the field data.

Fig. 5 DO saturation (%) in the flow over the spillway for July 14, 2006

Fig. 6 DO saturation (%) from about 900 m below Three Gorges Dam to the forebay over the Gezhouba Dam for July 14, 2006 (1, Huanglingmiao section; 2, Gezhouba Dam)

4 Factors Affecting the DO Saturation

15 cases were analyzed for the 145 m level for the Three Gorges Reservoir to analyze the effect of factors including the flood discharge rate, water level in the lower river, and DO saturation upstream on the DO supersaturation after the spillway.

Figure 7 shows the effect of the water level in the lower river on the DO saturation at the Huanglingmiao

Fig. 7 Effect of the water level in the lower river on the DO saturation at the Huanglingmiao section

section. High water levels downstream increase the DO saturation downstream. Since the higher water levels slow the escape of the large number of bubbles existing in the flow after the spillway into the air, so the air and the water mix more which increases the DO saturation. The higher water level downstream also slows the oxygen exchange between the water and the air, so the saturation decreases relatively slowly.

Figure 8 shows the effect of DO saturation in the flow over the dam on the DO saturation at the Huan-glingmiao section. The increased DO saturation at the spillway increases the DO saturation downstream, but the DO saturation in the flow over the spillway is still much lower than below the dam.

Fig. 8 Effect of DO saturation in the flow over the dam on the DO saturation downstream

Figure 9 shows the effect of the flood discharge rate on the DO saturation at the Huanglingmiao section. A reduced flood discharge directly reduces the DO satu-ration downstream with a linear relationship between the ratio of the flood discharge to the total discharge and the DO content. Therefore, since the power plant operation reduces the flood discharge, it also reduces

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the DO saturation. When the power station is operating, the DO saturation downstream will be reduced by 40%.

Fig. 9 Effect of the flood to total discharge ratio on the DO saturation

5 Conclusions

The DO supersaturation downstream of the Three Gorge Dam increases with increasing reservoir water level and increasing flood discharge rate. The DO saturations downstream of the Three Gorges Dam were analyzed using a water-gas two-phase flow model with the dissolved oxygen advection-diffusion equation, taking into account the gas transport. The models were calibrated and verified with field data. The DO satura-tions at various operating conditions were predicted for the 145 m reservoir water level. The research shows that higher water levels downstream increase the DO saturation downstream, the increasing DO saturation in the flow over the dam increases the DO saturation downstream, and reduced flood discharge rates reduce the DO saturation downstream with a linear relation-ship between the ratio of the flood discharge to the total discharge rate and the DO concentration downstream.

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