An Experimental Study of Different Stratified Water Intake Structures in a Deep-Water Reservoir

Abstract

For water temperature stratified reservoirs, stratified water intake structures are used to extract surface warm water to reduce the adverse effects of low-temperature discharge on river habitats and agricultural irrigation. A physical simulation method has been explored and used to conduct the comparative experimental study on the efficiency of the three types of intake structures: a traditional stoplog gate intake, a stoplog gate with a horizontal curtain and a vertical curtain upstream of the intake. In order to extend the laboratory results to the prototype, a similarity relationship for water temperature stratification was derived based on the principle of equal density stratification Froude number between the model and the prototype, as well as the functional relationship between water density and temperature. The similarity relationship makes it possible to simulate the same prototype density flow under different laboratory water temperature conditions, and this was confirmed through experiments conducted in several months with different water temperatures. Under constant water flow conditions, a stable target water temperature distribution can be formed in the experimental model through continuous stratified heating and real-time power regulation, to simulate the density flow generated by various intake operation in water temperature stratified reservoir. The relationships between the intake water temperature and the reference water temperature at intake depth in reservoir were analyzed to distinguish the difference of water intake efficiency. The experimental results showed that, the traditional stoplog gate has a relatively lower efficiency in extracting warm water affected by the lower edge expansion of the drag layer into the cold water zone below the intake elevation; by setting horizontal curtain to prevent the cold water from climbing below, it is helpful to improve the water intake efficiency; by setting vertical curtain in the upstream area of the intake, the velocity of warm water in the upper part of the drag layer increases, and the intake efficiency has been significantly improved. The above research provides a scientific approach for mechanism research and mathematical model validation of thermal density flow.

1. Research Background

Stratified flow widely exists in the atmosphere, oceans, rivers and reservoirs. It is mainly influenced by various terrains, flow boundaries and obstacle types, and in turn, it also affects the distribution of mass transfer such as salinity, pollutants, water temperature and dissolved oxygen [1]. The research currently conducted in this field still has great practical significance [2,3]. The essence of stratified flow is density stratification, and other factors concomitantly exist as causal scalars, such as sediment concentration [4], salinity, solute [5] and water temperature [6]. During the operation of large deep reservoirs, temperature stratification occurs at depth, accompanied by water quality stratification such as dissolved oxygen [7], plankton [8], salinity [9], nutrients [10], etc. By operating stratified water intake facilities [11], the vertical stratification structure of factors such as water temperature [12], dissolved oxygen [13] and turbidity [14] in the reservoir area can be adjusted to mitigate adverse effects on downstream crop growth, fish reproduction and river habitat restoration [8,15]. Therefore, the water temperature-stratified flow in reservoirs has always been a research hotspot. The relevant research approaches are divided into mathematical models, physical models and empirical models based on prototype observations. The focus of mathematical model research is the space–time change in density during water intake process. There is a Boussinesq assumption adopted in most models; that is, only the density change is considered in the buoyancy term of the momentum equation, and the medium density of other terms is a constant, and the relationship between density and temperature follows a linear or nonlinear fitting relationship. In this way, there is a slight loss of calculation accuracy, but sufficient efficiency can be ensured [16,17,18]. In terms of physical model research, density-stratified flow caused by salinity and sediment concentration can result in continuous dynamic simulation processes in the laboratory through the water flow circulation system [19,20,21]. However, density-stratified flow caused by water temperature stratification is mostly achieved by external a heating box with a stratified water supply, which forms a static stratified structure in advance. However, in the subsequent experimental process, it is difficult to maintain a constant stratified flow condition [22,23,24]. At the same time, the water temperature stratification simulated in the experiment often does not match the actual engineering, which means that there is a problem of dissimilarity between the two [25]. Some scholars have proposed specialized algorithms or empirical models directly based on exsiting engineering prototype observations as an option to guide the engineering of ecological scheduling [26,27]. In China, the concept of the ecological control of water temperature during the operation of hydraulic engineering has been widely accepted, and some kinds of stratified water intake measures are also included in newly built large deep reservoirs, such as overflow intake with stoplog gate [28], floating shaft intake [29], multi-hole type intake [30], control curtain [31,32], etc. The design and operation of these water intake projects require analysis and prediction using relevant physical and mathematical models in advance. However, the intake water temperature is not only affected by the stratification structure in the reservoir, intake flow, intake elevation, etc., but also by the complex terrain and specific water intake facilities in the vicinity of the water intake [33,34]. Generally, most numerical models, such as EFDC [35], ELCOM [36], DELFT-3D [37], MIKE3 [38] and CE-QUAL-W2 [39], are suitable for the cause analysis and regulation of large-scale water temperature-stratified structures in reservoir areas, but it is difficult to accurately simulate the influence of complex structural conditions at the stratified water intake on the drag velocity and adjacent water temperature distribution. Even if fine-fluid models such as ANSYS [40] and FLOW-3D [41] are used, there are still significant differences between the simulation results and observational data from actual engineering due to issues such as the assumption of density stratification, external heat exchange correction in the basic equations and turbulence model selection [42,43]. The previous physical model can simulate complex water intake structures and has rich measurement tools for stratified flow [44], but the dynamic heat balance is difficult to regulate in experiments and it cannot provide a repeatable and stable target water temperature-stratified flow and measurement time window [24,45]. The experimental results for reservoir temperature stratification and intake water temperature cannot be directly extended to the engineering prototype [46]. To overcome these difficulties, this paper proposes a physical simulation approach for water temperature stratified flow. Firstly, based on the principle of the equal density stratified Froude number and the functional relationship between water temperature and density, the temperature similarity relationship between the model and the prototype stratified flow is derived. It can translate the simulated water temperature distribution and intake temperature directly to the prototype situation, even if the laboratory water temperature is different from the prototype. Secondly, it can convert a prototype water temperature vertical distribution into the model distribution through the similarity relationship, and then, a stable target water temperature stratification and water intake flow field can be synchronously formed in the physical model through continuous multi-layer heating, real-time monitoring and heating power regulation. Third, when the water intake structure changes, the water temperature stratification and flow field structure in the nearby area will change, and once the water intake structure is restored, the water temperature and flow field will also return to their previous state, so that the model test is repeatable. Based on the above ideas, a physical model of water temperature stratification was established, and comparative experimental studies were conducted on the three types of stratified water intake structures that is common in practical engineering, namely traditional stoplog gate, stoplog gate with horizontal curtain and vertical curtain in front of the water intake. By analyzing the relationship between the intake water temperature and the reference water temperature at the intake elevation in the reservoir, the differences in the water intake efficiency among three water intake structures were judged. The above research provides the possibility for quantitative analysis of actual engineering water intake schemes and future theoretical research and mathematical model validation in related fields.

2. Water Temperature Model Design and Test Method

2.1. The Similarity of Water Temperature Stratification Model

To simulate the water temperature stratified flow in the laboratory, the flow conditions and density stratified conditions should be similar to the prototype; that is, the criteria such as the similarity of water flow Froude number (Fr) and density stratification Froude number (Fd) should be met at the same time [25].

The similarity of flow Fr number should meet:

$$\frac{u_p}{\sqrt{g_p{l}_p}}=\frac{u_m}{\sqrt{g_m{l}_m}}$$

(1)

where u is the flow rate; l is the length, which here refers to the water depth; g is the gravitational acceleration. The subscript p represents the prototype value; the subscript m represents the model value.

The similarity of density Fd number should meet:

$$\frac{u_p}{\sqrt{\frac{\Delta {\rho }_p}{{\rho }_p}{g}_p{l}_p}}=\frac{u_m}{\sqrt{\frac{\Delta {\rho }_m}{{\rho }_m}{g}_m{l}_m}}$$

(2)

where $\rho$ is the water density; $\Delta \rho$ is the density difference in water, caused by temperature difference in water.

The similarity criterion of density stratified flow is obtained by combining the above equations:

$$\frac{\Delta {\rho }_p}{{\rho }_p}=\frac{\Delta {\rho }_m}{{\rho }_m}$$

(3)

The relationship between water temperature $T$ and density $\rho$ is as follows:

$$\left\{\begin{array}{l}\rho =F\left(T\right)\\ \Delta \rho =F^{\prime }\left(T\right)\Delta T=f\left(T\right)\Delta T\end{array}\right.$$

(4)

where, $F(T)$ is the water temperature density function; $f(T)$ is the derivative of $F(T)$ to T; $\Delta T$ is the temperature difference in water.

Substituting Equation (4) into Equation (3), the similarity relationship for water temperature of stratified flow is obtained:

$$\frac{f\left(T_p\right)}{F\left(T_p\right)}\Delta T_p=\frac{f\left(T_m\right)}{F\left(T_m\right)}\Delta T_m$$

(5)

Equation (5) contains the water temperature density function and its derivatives. Therefore, it can be rewritten as the following equation:

$$\frac{f\left(T_p\right)}{T_{p}F\left(T_p\right)}\times T_p\times \Delta T_p=\frac{f\left(T_m\right)}{T_{p}F\left(T_m\right)}\times T_p\times \Delta T_m$$

(6)

In Equation (6), both the left and right sides contain a function: $k\left(T\right)=f(T)/(TF(T))$, which is called water temperature expansion coefficient in this paper. According to the water density table and the 1990 International Temperature Scale, the variation law for the expansion coefficient can be analyzed, as shown in Figure 1. It approximately satisfies a constant $k\left(T\right)\approx -0.91\times {10}^{-5}$ between the water temperature of 8~50 °C. Therefore, the similarity criterion of water temperature stratification is simplified as:

$$T_p\times \Delta T_p=T_m\times \Delta T_m$$

(7)

In the experiment, the model water temperature $T_m$ is usually inconsistent with the prototype water temperature $T_p$. Therefore, it is necessary to use Equation (7) to obtain the model water temperature distribution by recursively calculating by layer, from bottom cold water to surface warm water. The depths of each layer in the calculation have geometric similarity to the prototype. When there is a slight change in the test basic water temperature, the target water temperature distribution should also be dynamically adjusted to ensure that its density-stratified flow is similar to the prototype. So, this work is also carried out in real-time during the experimental process of constructing a stable water temperature-stratified flow. According to Equation (7), as the test basic water temperature increases, the vertical distribution gradient of the target water temperature decreases.

2.2. Test Model Layout and Monitoring Method under Transient Water Intake Conditions

The physical model of water temperature stratification is comprehensively designed in terms of water intake shape, water temperature vertical distribution, intake flow rate and temperature difference between surface and bottom according to the layout characteristics and operating conditions of some practical engineering. The specific parameters are shown in

Table 1. Layout characteristics of stoplog gate intake in some domestic hydropower stations.

Hydropower Station	Huang- Deng	Jing- Ping I	Xiluo- Du	Guang- Zhao	Nuozha- Du	Wudong- De	Bahe- Tan	The Model Test
Design flow of single intake diversion (m3/s)	409	350	424	433	390	691	547	690
Design flow per unit width (m2/s)	25.6	23	22.3	35.3	25.7	28.8	27.4	26
Water depth above stoplog gate (m)	23.5–28	21–35	25–35	15–21	28–42	>30	>21	10.5–46.5
Water intake depth (m)	61	101	82	75	76	62	91	75
Average velocity of trash rack section (m/s)	0.42	0.23	0.27	0.47	0.34	0.46	0.30	0.50

. The scale of the model is 1:150, the total length of the model is about 10 m, the width is 0.23 m and the flume height is 1.05 m. From upstream to downstream, the model is divided into water supply section, layered heating section, water temperature monitoring section and water intake section. In the water supply section, we set a perforated plate to adjust the flow ratio entering the upper heating zone and the lower cold-water tunnel, so that the outflow velocity distribution in the layered heating section tends to be uniform. The heat-insulating panels are set up in layers within the heating zone, and the heating rods with adjustable power are installed between panels to change the distribution of outflow water temperature. In the water temperature monitoring section, the front part is used to monitor the natural adjustment of flow and water temperature field in the far upstream of the intake, and set the 1~3# monitoring cross-sections with the water temperature sensors along the depth on the side wall. The latter part is set at the 4~6# monitoring section to observe whether the water temperature near the intake reaches the target value, otherwise the power of the upstream heating rods needs to be adjusted in real-time. The water intake consists of three types of structures, namely a stoplog gate, a stoplog gate with horizontal curtain and an upstream vertical curtain of intake, to compare the efficiency of extracting surface warm water. The above experimental layout is shown in Figure 2. The model design flow is 2.5 L/s, the corresponding prototype unit width flow is 26 m²/s, and the total intake flow is 690 m³/s. The model water intake depth is 0.5 m, and the corresponding prototype is 75 m. The water level and intake flow in the model remain constant during the experiment. The water depth above the stoplog gate or vertical curtain varies between 0.07 and 0.23 m, corresponding to the prototype water depth of 10.5~46.5 m of the intake. The water temperature monitoring section is 6 m long, corresponding to the prototype reservoir length of 900 m.

The water temperature test device is shown in Figure 3, and three types of experimental water intake structures are shown in Figure 4.

A preliminary experiment was conducted with the water temperature model, in which the thermal equilibrium state was first formed and the influence of water intake conditions on the water temperature stratification and intake water temperature was determined. The basic steps of the experiment are as follows: (1) Adjust water level, flow rate and conventional water intake structure to form a stable flow field. (2) Activate the layered heating facility and monitor, in real-time, the changes in water temperature vertical distribution along the model flume. (3) When the water temperature vertical distribution in the model stabilizes, it is considered as the target water temperature distribution for further stratified water intake research. (4) Change the water intake conditions by adding a set of stoplog gates, and measure its impact on the upstream water temperature stratification and downstream intake water temperature. (5) Remove the stoplog gates to restore the original water intake conditions and wait for the water temperature distribution to gradually return to the target water temperature. (6) When the water temperature distribution returns to the target water temperature distribution again, repeat step (4) to study the next stratified water intake conditions.

Figure 5 shows the formation process of water temperature stratification for thermal equilibrium in cross-sections 4#, 5# and 6#, which was observed under conventional intake conditions without stoplog gates. The horizontal axis in the figure represents the vertical distribution of water temperature in the reservoir area, and the vertical axis represents the water intake elevation. The latter’s H = 0 m corresponds to the bottom elevation of the water intake. After the stratified heating is turned on, the water temperature in the flume reaches a stable state about 4 h later, which can be regarded as the target water temperature distribution. Then, the stoplog gates are quickly installed manually, and the changes in water temperature are continuously monitored and recorded. In order to recover the target water temperature distribution as soon as possible after removing the stoplog gates, it is necessary to limit the variation of upstream water temperature distribution. Therfore, each set of stoplog gate tests lasted approximately 120 s.

Figure 6 shows the synchronous change process in upsteam water temperature (UWT) and the intake water temperature (IWT) after placing the stoplog gates with a height of 0.31 m, corresponding to a prototype height of 46.5 m and an intake water depth of 28.5 m. The UWT is the water temperature at different depths (H = 0–66 m) in the C.S.6 section. IWT is the water temperature in the center of the ouflow pipe of the water intake, measured by a single-point water temperature sensor shown in Figure 2. Under the condition of thermal equilibrium, after the stoplog gates are placed on the water intake (t = 25 s), the water temperature of the intake quickly rises to its peak (t = 35 s). At this time, the water temperature distribution in the reservoir area changes very little. With the elapse of time (t > 40), the surface warm water is heavily extracted, and the water temperature of the intake gradually decreases, tending towards a new thermal equilibrium value. Therefore, the peak water temperature of the intake was considered as an evaluation indicator for the operation impact of the stoplog gate. Figure 7 shows the change in water temperature stratification upstream of the intake at the end of the 120 s. It can be seen that the high surface temperature area has been partially eroded. Figure 8 shows the recovery of water temperature distribution in the upstream reservoir area after removing the stoplog gates. About 40 min later, the upstream water temperature distribution returned to the target value, and then the next set of stoplog gates can be placed. The above method can be applied to the quantitative prediction of the operational effectiveness of the stratified intake structure in the actual engineering. At this time, the typical water temperature stratification of each month in the reservoir needs to be simulated in advance, using preparatory tests and repeated debugging.

2.3. Similarity Verification of Water Temperature Stratification Model

A comprehensive experimental study was conducted under the different substrate water temperatures (Tb) using the same operation of stoplog gates and prototype water temperature stratification.

Table 2. Targeted and simulated water temperature stratification.

Elevation (m)	Equivalent Stratification under Different Substrate Water Temperatures (°C)				Laboratory Simulated Water Temperature Stratification (°C)
66.0	19.15	22.33	23.64	25.03	22.10	23.80	24.67
49.5	14.66	18.63	20.17	21.79	18.31	20.39	22.02
33.0	10.91	15.84	17.64	19.47	15.63	17.74	19.46
16.5	8.85	14.50	16.44	18.39	14.43	16.41	18.58
0.0	8.36	14.21	16.19	18.17	14.18	16.12	18.25
−16.5	8.23	14.13	16.12	18.10	14.11	16.04	18.05
−33.0	8.00	14.00	16.00	18.00	13.97	15.93	17.96

shows the equivalent water temperature stratification under different substrate temperatures and the laboratory simulation results. Starting from the prototype water temperature stratification at the substrate temperature of 8 °C, equivalent water temperature stratifications at substrate temperatures of 14–18 °C were calculated according to Equation (7) and used as the target value for laboratory simulation. The appropriate time windows were selected across several months to simulate the target water temperature distribution. After repeated debugging, the simulated water temperature distributions in the experiment were in good agreement with the target distribution, ensuring that the model density-stratified flows are similar to the prototype under different laboratory substrate temperature conditions. The operating test parameters for the stoplog gate are shown in

Table 3. Operation conditions for stoplog gates.

Case	Lab Substrate Water Temperature (°C)	Intake Flow (m3/s)	Height of Stoplog Gates (m)	Water Depth above the Gate (m)
1	14	665	28.5/37.5/46.5/55.5/64.5	46.5/37.5/28.5/19.5/10.5
2	16	665
3	18	665

. The water depth above the intake platform was maintained at 75 m. The adjustable range of the height of the stoplog gate in the water intake is 28.5–64.5 m, with a height interval of 9 m. The corresponding water depth above the gate is 46.5–10.5 m. After the completion of each group of tests, the stoplog gates need to be removed to restore the initial water temperature conditions. This process requires a long period of time to ensure that the initial water temperature distribution of all test groups is consistent with the target distribution. The experimental testing time in this model is controlled at around 120 s, and the water temperature distribution recovery time is approximately 30–120 min, mainly considering the impact of different stoplog gate conditions.

Figure 9, Figure 10 and Figure 11 show the variation in intake water temperature (T_out) with the height of the stoplog gate under the laboratory substrate water temperatures of 14–18 °C. The peak of intake water temperature is related to the height of the stoplog gates and the manual placement process. It should be pointed out that the intake water temperature T_out in the figures is only the laboratory model value which needs to be converted into the prototype value. Between the physical model and prototype stratified flow, Equation (7) should be satisfied everywhere. However, due to the unknown water temperature gradient $\Delta T$ inside the intake tunnel, Equation (7) cannot be directly used to calculate the prototype intake water temperature. Fortunately, the water temperature stratifications in the reservoir area of both the model and prototype are known, and the streamlines in the model drag layer are similar to those in the prototype too. So, the characteristic depth corresponding to the intake water temperature can be interpolated from the vertical distribution of water temperatures near the water intake in the model. The characteristic water temperature corresponding to that depth can be interpolated from the prototype water temperature distribution. The characteristic water temperature is approximately equal to the prototype intake water temperature. Using the above method, the prototype intake temperature data can be obtained as shown in

Table 4. Comparison between experimental and prototype values of intake water temperature under three laboratory substrate temperatures.

Case	Substrate Water Temperature	Intake Water Temperature	Water Depth above the Gate (m)
	(°C)	(°C)	10.5	19.5	28.5	37.5	46.5
1	14	Model	18.95	18.21	17.47	16.83	15.97
		Prototype	15.83	15.21	14.08	13.09	11.81
2	16	Model	20.99	20.12	19.44	18.6	18.07
		Prototype	15.95	15.19	14.25	12.86	12.11
3	18	Model	22.81	22.09	21.76	21.14	20.3
		Prototype	15.70	15.18	14.33	13.25	12.16

. A plot of the data is shown in Figure 12, where the horizontal axis represents the water depth above the stoplog gate and the vertical axis represents the intake water temperature. The test results indicate that, for the same target prototype water temperature distribution, the simulated intake water temperatures obtained under different laboratory water temperature conditions are particularly consistent. Thus, it was proved that the water temperature similarity between prototype and model and its conversion method are satisfactory in accuracy.

3. Effect of Different Stratified Intake Structures on Extracting Surface Warm Water

3.1. Monitoring Method under Constant Water Intake Conditions

Stratified water intake includes three types of structures, namely traditional stoplog gates, stoplog gates with horizontal curtain, and front curtains. The operating conditions of the three structures are the same as shown in Table 3, and the specific installation is shown in Figure 2 and Figure 3. The horizontal curtain in the stoplog gate has a length of 5 cm, corresponding to a prototype of 7.5 m. It is installed on the top of gate to prevent the cold water from climbing below, thus increasing the intake water temperature. The front curtain is installed 85 cm in front of the water intake, which is equivalent to 123 m away in the prototype. It adopts flexible and foldable materials to achieve changes in water intake height.

In a previous verification experiment of water temperature stratification similarity, the method of manually changing the stoplog gate height was adopted under the same initial conditions of water temperature distribution and flow field. The testing time is short, while the recovery time of the target water temperature distribution is long, and it is difficult to avoid the disturbance in the water intake flow field and water temperature distribution caused by manual operation. In a comparative study of different water intake structures, another test method was adopted that keeps the water intake conditions unchanged and only changes the water temperature stratification of the upstream inflow: (1) keep the water level in the reservoir area, the water intake structure and outflow rate unchanged; (2) turn on a layered heating device, form a water temperature distribution at the upstream inflow boundary and monitor the progress of water temperature stratification in the reservoir area and the variation in intake water temperature; (3) select a time period in which the intake water temperature can stabilize and extract data that characterize the relationship between the water temperature distribution in the reservoir area and the intake water temperature; (4) adjust the layered heating power, change the new water temperature stratification at the upstream inflow boundary and repeat the above test.

The comparative experiment simulates a total of five different target water temperature distributions, and the test data and distribution pattern are shown in Figure 13. The control conditions for the water intake flow field are the same as in Table 3. To facilitate the analysis of the water intake characteristics of the three types of structures, this article introduces the concept of a reference water temperature in the reservoir area, which refers to the water temperature value of the reservoir area corresponding to the water intake elevation. By analyzing the relationship between the intake water temperature and the reference water temperature in the reservoir area, the efficiency of extracting surface temperature water is determined.

Figure 14, Figure 15 and Figure 16 show the variation in intake water temperature in the three structures with a top water depth of 10.5 m. The top water depth is the distance from the top of the stoplog gate or curtain to the water surface. From the figures, it can be seen that around 120 s later, the upstream warm water reaches the water intake and the intake water temperature begins to rise, and about 15 min later the intake water temperature reaches a stable state. The data between 1000 and 3000 s are extracted, and then the average value is taken as the water intake temperature. Then a further analysis is conducted on the differences in water intake characteristics of the three structures.

3.2. Experimental Results and Analysis of Different Stratified Intake Structures

The relationship between the inlet water temperature of the three structures under different top water depths and the reference water temperature in the reservoir area was obtained from the experiment, as shown in Figure 17. In the figure, when the point data falls on the red solid line, it means that the intake temperature is equal to the reference water temperature; when the point data falls below the red line, it means that the intake temperature is lower than the reference water temperature. The test results show that: (1) the efficiency of extracting surface warm water using traditional stoplog gates is relatively low, and the intake water temperature is generally lower than the reference water temperature in the reservoir area within the entire top water depth range of 10.5–46.5 m; (2) by setting a horizontal curtain on the top of the stoplog gate, within the top water depth range of 37.5–46.5 m, the intake water temperature reaches or exceeds the reference water temperature in the reservoir area and the temperature rise can reach 0.6 °C; (3) when installing a vertical curtain upstream of the water intake, within the top water depth range of 28.5–46.5 m, the intake water temperature reaches or exceeds the reference water temperature in the reservoir area. The temperature rise value can reach 1.2 °C, and the efficiency of stratified water extraction is significantly improved.

Figure 18 shows the relationship between the intake water temperature in the three structures and the reference water temperature in the reservoir area under the same top water depths. The experimental results show that: (1) The intake water temperature in the stoplog gate with horizontal curtain is slightly higher than that of the traditional stoplog gate, with an increase of 0.3~0.5 °C. The intake water temperature in the front curtain is significantly higher than that of the traditional stoplog gate, with an increase of 1.0~1.5 °C; (2) The top water intake depth also has an impact on water intake efficiency. Taking the front curtain for example, when the top water intake depth is 10.5 m, the intake temperature is about 1 °C lower than the reference water temperature in the reservoir area. When the intake depth is 28.5 m, the intake temperature is basically equivalent to the reference water temperature. When the intake depth reaches 46.5 m, the intake temperature of the front curtain exceeds the reference water temperature by 0.3~1.2 °C; (3) When the top water intake depth is large, the slope of relationship curve between the intake water temperature and reference water temperature increase. The reason for this is that the reference water temperature difference of the five water temperature distribution decreases when the water intake elevation is lower.

4. Discussion

Table 5. Characteristic values of flow field and water temperature in the different intake structures under case5 water temperature stratification and intake flow rate of 26 m²/s per unit width.

Water intake structure	Top water depth (m)	10.5	19.5	28.5	37.5	46.5
Traditional stoplog	Velocity at water intake elevation (m/s)	3.81	2.05	1.40	1.07	0.86
	Surface velocity of water intake section (m/s)	0.39	0.21	0.14	0.11	0.09
	Thickness of drag layer below intake elevation (m)	20.0	17.0	11.5	6.5	4.0
	Intake water temperature (°C)	20.52	20.40	20.31	20.26	20.18
Stoplog with horizontal curtain	Velocity at water intake elevation (m/s)	3.36	1.76	1.18	0.91	0.74
	Surface velocity of water intake section (m/s)	0.59	0.33	0.24	0.17	0.14
	Thickness of drag layer below intake elevation (m)	15.0	12.5	8.5	5.0	3.0
	Intake water temperature (°C)	20.94	20.86	20.82	20.78	20.65
Front curtain	Velocity at water intake elevation (m/s)	2.26	1.28	0.81	0.63	0.53
	Surface velocity of water intake section (m/s)	1.29	0.64	0.41	0.32	0.26
	Thickness of drag layer below intake elevation (m)	11.5	10.0	6.5	4.0	2.5
	Intake water temperature (°C)	21.70	21.66	21.41	21.29	21.16

shows the characteristic values of the flow field and water temperature in different water intake structures under Case5 water temperature stratification and an intake flow rate of 26 m³/s per unit width. The characteristic velocity is measured by the two-dimensional particle image velocimetry system. The thickness of drag layer below the water intake elevation is determined by potassium permanganate (Changyuan Chemical Group Co., Ltd., Chongqing, China) tracer at the upstream of water chute. During the flow process, the solvent turbulent downward diffuses vertically and at the same time, is affected by buoyancy caused by water temperature stratification. The two effects reach equilibrium near the lower boundary of the drag layer, as shown in Figure 19.

The analysis shows that the efficiency of extracting surface warm water with different water intake structures mainly depends on the velocity distribution, vertical position and water temperature distribution in the drag layer. (1) When the top water depth is small, the drag velocity at the water intake elevation is relatively larger, which causes the lower boundary of the drag layer to expand downward and the proportion of cold water extraction to increase due to the enhancement of boundary shear effect; (2) When the front stoplog gate of the intake is too close to the breast wall, the surface drag velocity decreases due to the obstruction of the breast wall, which leads to a decrease in the proportion of surface warm water. However, when the front curtain is used in the upstream reservoir area of the intake, the surface warm water still has a large drag velocity on the curtain section and can finally enter the water intake through vertical mixing, so as to increase the intake water temperature. (3) In the process of water intake, the turbulent stress, viscous force and buoyancy at the upper and lower boundaries of the drag layer reach equilibrium. When the water temperature gradient above the water intake elevation is large, the upper boundary of the drag layer does not reach the water surface. When the water temperature gradient below the water intake elevation is small, the lower boundary of the drag layer can extend to the cold-water area, resulting in the water temperature lower than the reference water temperature in the reservoir area.

In this paper, by adding a horizontal curtain on the top of the traditional stoplog gate to reduce the climb of cold water below the gate top elevation, the efficiency of extracting surface warm water is improved. A waterproof curtain is set up in the upstream reservoir area of the intake to increase the surface velocity of the drag layer, so that the efficiency of extracting surface warm water is significantly increased compared to the improved stoplog gate. It can be seen that the water temperature into stratified intake is not only determined by the top water depth and the temperature stratification condition, but is also directly related to the hydrodynamic characteristics of the drag zone near the intake. With the above foundation, various factors on the drag layer in the water temperature stratified intake and its control methods can be systematically explored.

It should be noted that the intake water temperature is related to the temperature of all water bodies within the drag layer. When the substrate water temperature in the laboratory is inconsistent with the prototype, in order to more accurately convert the intake water temperature from the physical model to the prototype, it is necessary to select a reasonable water temperature distribution section in the model reservoir area, the vertical distribution of water temperature and flow velocity in the drag layer is measured to obtain the comprehensive water temperature through velocity-weighted integration, and then analyze its relationship with the intake water temperature measured in the experiment. To quantitatively conduct systematic research on the above problems, more precise and complex experimental techniques are needed. As a compromise solution, this paper proposes using a characteristic depth corresponding to the intake water temperature to achieve mutual conversion between the prototype and the model. When the water temperature distribution in the drag layer is approximately linear, this method has sufficient accuracy.

5. Conclusions

The regulation of water temperature during the discharge of large stratified reservoirs in hydropower engineering has an important impact on downstream river habitats and agricultural irrigation; therefore, stratified water intake facilities are widely used in China. The actual operation effect of the stratified water intake scheme requires effective quantitative prediction, and this work should have been carried out during the engineering scheme design and optimization stage. The stratified water intake process involves density flow caused by vertical stratification of the water temperature. Currently, some mathematical models are often used for quantitative research, but there is a lack of relevant physical model validation methods, especially when it comes to identifying complex structures of stratified water intake facilities in front of dams. For this reason, a physical model test method for simulating stratified flow of water temperature was proposed, and accordingly, the similarity relationship between the model water temperature distribution and the prototype was derived, based on the principle of equal density stratification Froude numbers between the model and the prototype, as well as the functional relationship between water density and temperature. The model can repeatedly simulate the stratified flow process for the same prototype, even in months with different laboratory water temperatures, and its precision has been experimentally verified. Based on the physical model of water temperature, a comparative study was made on the three common stratified water intake structures, namely, the traditional stoplog gate, a stoplog gate with a horizontal curtain and a curtain in front of the water intake. By analyzing the relationship between the intake water temperature and the reference water temperature in the reservoir area corresponding to the intake depth, the difference in stratified water intake efficiency was judged. The experiments showed that: (1) Under the same water temperature distribution and top water depth, the intake water temperature of a stoplog gate with a horizontal curtain is 0.3~0.5 °C higher than that of traditional stoplog gate, and further, the intake water temperature of the front curtain is 1.0~1.3 °C higher than that of traditional stoplog gate; (2) In the entire top water depth range of 10.5~46.5 m, the intake water temperature of traditional stoplog gate is generally lower than the reference water temperature in the reservoir area. By adding a horizontal curtain on the top, the intake water temperature can exceed the reference water temperature by 0.6 °C in the range of 37.5~46.5 m top water depth. Using the front curtain, the intake water temperature can exceed the reference water temperature by 1.2 °C in the top water depth range of 28.5~46.5 m. The analysis showed that the thickness, vertical position, water temperature and velocity distribution in the drag layer upstream of the intake are the important factors affecting the efficiency of stratified water intake. For the traditional stoplog gate intake, the water intake efficiency is relatively low due to the influence of the lower boundary of the drag layer located in the cold water zone; the water intake efficiency is improved by setting a horizontal curtain to prevent the cold water from climbing below the water intake elevation; the waterproof curtain in the upstream reservoir area of the intake can increase the velocity of surface warm water in the drag layer, and the water intake efficiency is significantly improved. This research provides a new direction for the optimization and improvement of the layout structure of stratified intake, and a scientific method for the mechanism research and mathematical model validation.