Hydropower station tailwater channel is often prone to elevated water levels and insufficient energy consumption, which leads to the influence of the output of the unit. To study the intrinsic connection between the water flow state and elevated water level in the tailwater channel, this paper investigates the water flow characteristics inside the tailwater channel of the Mupo Hydropower Station under different heads and verifies the accuracy of numerical calculations by constructing a physical model test platform. The results show that the maximum velocity at the bottom of the fluid domain near the anti-slope section of the tailwater channel decreases with the increase of head, while the velocity at the top of the fluid domain near the anti-slope section of the tailwater channel does not change much with the increase of head; a large vortex is formed in the middle of the upper part of the fluid domain in the anti-slope section of the tailwater channel; and the lower the head, the more obvious the vortex is. The results provide guidance for the design of tailwater channels at hydropower stations.

In some small and medium-sized hydropower stations, often the tailwater channel design is not reasonable, or the unit draft tube port is perpendicular to the river, resulting in the tailwater channel within the water flow state being an extremely turbulent vortex so that the water flow in a short period cannot be smoothed out of the tailwater channel outlet, which triggers the tailwater level elevation, resulting in a significant reduction in unit output. Therefore, the study of the tailwater channel flow state and its vortex generation and development process will help optimize the water flow effect and provide a reference for the development of China's hydropower industry.

At present, scholars have carried out a large number of in-depth studies to explore the causes of internal flow disorders in the draft tube.1,2 Ji et al.3 studied the internal flow in the draft tube with different guide vane openings and heads and concluded that by increasing the guide vane openings, the large invisible vortex on the inlet tapered section of the draft tube is gradually transformed into a tangible vortex rope. Mitruţ et al.4 analyzed the Francis-99 model draft tube dimensionally. Palkin et al.5 also investigated the internal flow of this model at three different incoming velocities and figured that the vortex structure with a strong coherent component corresponds to the core of the spinning-in vortex and that the vortex shape and amplitude change when the bulk velocity varies. In addition, several scholars showed that flow variations in vortices can provoke pressure pulsations6–8 and energy losses9 in the draft tube, and the draft tube structure affects the vortices. For example, Minakov et al.10 have found that the rotation of the rotating vortex core under asymmetric boundary conditions causes pulsations and longitudinal pressure fluctuations and also induces the superposition of the two to increase the pulsations, whereas the vortex structure in the draft tube with altered boundary conditions is almost unchanged and the vortex core reconstruction is maintained. Cuong11 revealed that the vortex rope behavior has a large impact on the local hydraulic losses by comparing the Liutex amplitude distribution and entropy yield changes. Meanwhile, the Liutex method can effectively remove the influence of the wall boundary layer on the visualized vortex structure. Based on the modified SST partially-averaged Navier-Stokes (MSST PANS) model and dynamic mode decomposition (DMD) method, Geng et al.12 simulated the unsteady flow in the draft tube with a bent structure. It was found that the vortex rope in the draft tube interacts strongly with the backflow, resulting in ultra-low frequency pressure oscillation, and the bent structure promotes the interaction and swirl flow in the draft tube.

Therefore, in order to improve the internal flow state of the draft tube and enhance its performance, many scholars have carried out optimization research on the draft tube in terms of algorithm and structure. In the study of algorithm optimization, scholars adopted a genetic algorithm to optimize the runner and draft tube13,14 and believed that the flow channels of the two interact with each other so that the optimized model can improve the efficiency of the turbine. Scholars utilized a multi-objective function to modify and optimize the draft tube components.15,16 The optimized draft tube elbow section has smooth streamlines and enhanced flow stability. Some scholars used the response surface method to optimize the flow channel of the turbine17–19 and assumed that the larger blade inclination angle had an inhibitory effect on the cavitation of the draft tube. In terms of structural optimization, some scholars have added J-shaped grooves to the draft tube and discovered that structure can improve the pulsation and loss of the draft tube.20,21 At the same time, Luo et al.22 also revealed that the J-groove can inhibit the development of eddy current, reduce energy dissipation, and improve the circumferential velocity component. In addition, some scholars have designed the structure at the front end of the draft tube to optimize the overall performance of the turbine. Zhou et al.23 identified that the installation of inclined conical deflectors can destroy the development of vortex rope and enhance the stability of the draft tube. After installing anti-cavitation fins, Kim et al.24 found that the unsteady pressure in the draft tube was significantly reduced under low flow conditions, and the formation of vortex ropes was inhibited. In addition, some scholars have observed that the air supply device has a significant effect on improving the vortex in the draft tube during the research process. For example, Mohammadi et al.25 showed that adding air to the unoptimized draft tube can reduce its internal pressure pulsation. Kim et al.26 discovered that the anti-cavitation fins used for air replenishment suppress the appearance of vortex ropes in the draft tube, while the air flow velocity inhibits the generation of vortex ropes and vortex components. Scholars have developed a single stage adjustable hydraulic turbine guide vane system that improves the flexible operation performance and efficiency of the turbine and suppresses the generation of vortex strips and their pressure pulsation amplitude.27,28

In summary, most research currently focuses on the internal flow state of the draft tube of the set, with few studies analyzing the flow characteristics inside the tailwater channel. Therefore, this paper selects the Mupo Hydropower Station on the main stream of the Fubian River in Xiaojin County, Sichuan Province, as the research object, focusing on analyzing the flow state and vorticity distribution in the tailwater channel of the Mupo Hydropower Station under different heads and then analyzing the smoothness of the water flow in the tailwater channel, thereby revealing the impact of the flow state in the tailwater channel of the hydropower station on the tailwater level.

The SST k-ω model combines the advantages of the k-ω model and the k-ε model, which not only takes into account the turbulent shear stress but also avoids extreme predictions of the eddy viscosity coefficient. Its model expression is
ρkt+ρvikxi=xjv+viσkkxj+Gkβρkω,
(1)
tρω+xjρvjω=xjμ+μiσωωxj+Gωρβω2+Dω.
(2)
Volume fraction equations for the volume of fluid (VOF) model: the interface between the phases can be traced by solving the continuous equation for the volume fraction of one or more phases. The continuity equation for the volume fraction of the q-th phase is
1ρqtαqρq+αqρqvqSαq+mpqmqp=0,
(3)
where ρq is the physical density of the q-th phase; vq is the velocity of the q-th phase; mpq is the mass transfer from the q-th phase to the p-th phase; mqp is the mass transfer from the p-th phase to the q-th phase; and Sαq is the source term, which defaults to zero and can be specified as a constant or a user-defined mass source term.
The basic volume fraction is calculated from the restraint that the sum of the volume fractions of all phases is the sum of the volume fractions of all phases without solving the volume fraction equation:
αq=1.
(4)

Mupo Hydropower Station is selected as the research object. The basic parameters of the unit are shown in Table I. The computational domain is modeled in three dimensions by using UG software; meanwhile, as shown in Fig. 1, it consists of the volute, the stay vanes, the guide vanes, the runner, the draft tube, and the tailwater channel.

TABLE I.

Basic parameters of turbine.

ParameterValue
Turbine model HL(F713)-LJ-140 
Rated head 118 m 
Maximum head 134.6 m 
Rated flow 15.76 m3/s 
Rated revolution 500 rpm 
Runner diameter 1400 mm 
Number of stay vane 16 
Number of guide vane 20 
Number of runner blade 15 
ParameterValue
Turbine model HL(F713)-LJ-140 
Rated head 118 m 
Maximum head 134.6 m 
Rated flow 15.76 m3/s 
Rated revolution 500 rpm 
Runner diameter 1400 mm 
Number of stay vane 16 
Number of guide vane 20 
Number of runner blade 15 
FIG. 1.

Numerical calculation model.

FIG. 1.

Numerical calculation model.

Close modal

Because of the complicated structure and irregular shape of the flow passage components of hydraulic turbines, unstructured meshes are used to divide the calculation domain. At the same time, the paper mainly observes the flow state and vortex distribution in the anti-slope section of the tailwater channel, so the tailwater channel is locally encrypted. The mesh division is shown in Fig. 2. Details of the tailwater channel grid and Y plus are shown in Figs. 3 and 4.

FIG. 2.

The mesh of computational domain.

FIG. 2.

The mesh of computational domain.

Close modal
FIG. 3.

Details of the tailwater channel grid.

FIG. 3.

Details of the tailwater channel grid.

Close modal

The Richardson extrapolation method is used to verify the grid-independence of the computational model, in which the R value represents the ratio between the size of the latter set of grids and the size of the former set of grids, and Ni denotes the total number of grids in the i-th set of grids. Grid Convergence Index (GCI) which was first proposed by Roache (1998) is based on the Richardson Extrapolation and has been used to estimate the discretization error. If the GCI value is less than 5%, it is considered that the error brought by the grids has been negligible and can be ignored after the calculation of the GCI32 value of 0.79%, so the final choice of 8 670 000 is this set of grids as the corresponding calculation data, as shown in Table II (B represents the total pressure of the draft tube).

TABLE II.

GCI grid independence verification.

ParameterSymbolData
Mesh N1,N2,N3 69 000 000, 86 700 000, 105 300 000 
 R21 1.07 
 R32 1.06 
 B1 63 060.35 (Pa) 
 B2 63 125.6 (Pa) 
 B3 63 154.8 (Pa) 
 10.48 
 GCI32 0.79% 
ParameterSymbolData
Mesh N1,N2,N3 69 000 000, 86 700 000, 105 300 000 
 R21 1.07 
 R32 1.06 
 B1 63 060.35 (Pa) 
 B2 63 125.6 (Pa) 
 B3 63 154.8 (Pa) 
 10.48 
 GCI32 0.79% 

In this paper, the eddy current characteristics of the calculation model under different heads are simulated by FLUENT software. The turbulence selected is the SST k-ω model, the multiphase flow selected is the VOF model, the inlet boundary condition is set as the velocity inlet, and the outlet boundary condition is set as the pressure outlet. The average static pressure at the outlet of the tailwater channel is 0, and the volume fraction of the returned air at the outlet is 1. The interface of the runner, the guide vanes, and the tailwater channel is set as a dynamic and static interface; the upper and lower cover plates and the blades of the runner are set as relative non-slip wall surfaces; the other wall surfaces are selected as absolute non-slip wall surfaces; and the convergence accuracy is set to 10−6. The pressure and velocity are solved by the PISO algorithm.

To verify the accuracy of the numerical calculations, a physical model test study is carried out on the simulation calculation domain to compare the numerical calculation results with the test results. Due to the large size of the real model, the test platform is built according to 1:20, as shown in Figs. 5 and 6. In the actual operation process, submersible pumps, outlet regulating valves, and valve manifolds are utilized to control the flow rate to reach the required value of the test. When the flow is stabilized, the flow state inside the tailwater channel is photographed.

FIG. 5.

Test platform.

FIG. 6.

The layout test platform. 1 - Submersible pump, 2 - outlet regulating valve, 3 - suction pipe, 4 - electromagnetic flowmeter, 5 - four-way pipe, 6 - valve manifold, 7 - turbine unit, 8 - plant contour, 9 - sediment storage dam, 10 - spur dike, 11 - tailwater channel anti-slope section.

FIG. 6.

The layout test platform. 1 - Submersible pump, 2 - outlet regulating valve, 3 - suction pipe, 4 - electromagnetic flowmeter, 5 - four-way pipe, 6 - valve manifold, 7 - turbine unit, 8 - plant contour, 9 - sediment storage dam, 10 - spur dike, 11 - tailwater channel anti-slope section.

Close modal

In order to study the flow characteristics and vortex structure distribution inside the tailwater channel in a comprehensive way, this paper slices the part from two angles (xy-plane and zy-plane), namely, transverse and longitudinal, with each section sliced as shown in Fig. 7. Comparing the test taken angle with the simulation divided section, it is obvious that the location where planexy-4 is located is the closest to the test location. Therefore, the results of the three heads obtained from the test are compared with the velocity streamline distribution of the transverse planexy-4 of the numerical simulation, and the results are shown in Fig. 8. Observing the velocity streamline graph of planexy-4, it is easy to obtain that the vortex structure of the tailwater channel at the straight angle of the inlet is obvious and more aggregated, and there is a complete vortex structure in the middle of the flow channel. In comparison, it is found that the vortex structure can be clearly observed at the inlet straight angle of the tailwater channel in the experimental results, but the vortex in the middle of the flow channel may be disturbed by the flow at the bottom of the tailwater channel and is not easy to observe. Overall, the experimental and numerical results are in good agreement, which verifies the accuracy of the numerical simulation.

FIG. 7.

Section diagram of tailwater channel.

FIG. 7.

Section diagram of tailwater channel.

Close modal
FIG. 8.

Comparison between experimental and numerical results.

FIG. 8.

Comparison between experimental and numerical results.

Close modal

The velocity streamlines are analyzed on four transverse sections of the tailwater channel, which are perpendicular to the inlet surface of the tailwater channel and partially intersect the inlet surface. Planexy-1 section passes through the middle of the inlet surface of the tailwater channel, planexy-2 section shares the upper edge line with the inlet surface of the tailwater channel, and planexy-3 section is at a certain distance from the upper edge line of the inlet of the tailwater channel. Due to the slope of the backslope section of the tailwater channel, planexy-4 intercepts a larger range of sections than planexy-1, planexy-2, and planexy-3.

Figure 9 shows the velocity streamlines of the four sections in the transverse direction under different heads. From the overall observation of the four sections of different heads of the velocity streamline, it can be found that the first three sections of the highest speed decreased with the increase of the heads, while the speed of the planexy-4 did not change with the increase of the heads in each section of the high-speed region and vortex region by the division of the position of the distribution of the different influences. Planexy-1 did not generate a complete vortex; meanwhile, there is a large backflow phenomenon on both sides of the tailwater channel port; planexy-2 has obvious vortices on both sides of the tailwater channel port under two low heads; planexy-3 vortex gradually moves to the corners of the tailwater channel port, but the overall stability is not as good as planexy-1 and planexy-2; planexy-4 formed a large vortex in the middle, and the lower the head, the more obvious vortex. From the flow state of each section, it can be seen that the unit in different heads under the tailwater channel anti-slope section of the tailwater dissipation plays a small role; that is, the tailwater outlet flow is not smooth, which is easy to lead to the unit water level elevation, and the output is insufficient.

FIG. 9.

Velocity streamlines in four sections in the transverse direction at different heads.

FIG. 9.

Velocity streamlines in four sections in the transverse direction at different heads.

Close modal
The vorticity describes the rotational properties in the fluid flow, which can be used to measure the rotational strength and direction of the vortex in the fluid. In the velocity field, the size and direction of vorticity determine the rotation speed and direction of the fluid. Based on the velocity streamline distribution on the transverse section of the tailwater channel, the vorticity analysis of the above four sections is carried out. The vorticity expression is
ω=wyvzi+uzwxj+vxuyk.
(5)

Figure 10 shows the vorticity distribution of four transverse sections under different heads. Observing the vorticity distribution of different heads in four sections as a whole, it can be learned that the vorticity is distributed in strips or clusters. Combined with the velocity streamlines under the corresponding section, it is found that the vorticity value is larger in the high-speed region. Observing planexy-1 and planexy-2, it was revealed that the vorticity value reaches its maximum near the inlet of the tailwater channel. This is because the section of fluid that flows into the tailwater channel increases sharply, the velocity gradient changes drastically, and the velocity only has a maximum near the inlet. Planexy-3 has vorticity changes at two right-angle corners of the inlet side. The vorticity value decreases with the increase of the heads, and the vorticity range increases with the increase of the heads. According to the vorticity distribution observation of transverse planexy-4, it is observed that the vorticity change is mainly concentrated in the tailwater channel near the river wall. Because the flow is unstable after the water flow comes out of the anti-slope section, the energy is not completely dissipated, resulting in the impact of the water flow on the outlet wall of the tailwater channel, which further indicates that the energy dissipation effect of the tailwater channel of the hydropower station cannot meet the production needs.

FIG. 10.

Distribution of vorticity in four transverse sections at different heads.

FIG. 10.

Distribution of vorticity in four transverse sections at different heads.

Close modal

To analyze the velocity distribution of different sections in the longitudinal direction of the tailwater channel, this paper divides it into ten sections along the longitudinal direction and divides the sections in the longitudinal direction into two main categories. Among them, the first category is the first five sections, in which the movement of fluid in space is transverse, representing the movement of fluid from the bend to the outlet. Meanwhile, the second category is the last five sections, where the movement in space is longitudinal, which can be expressed as the movement of fluid spreading from the inlet to the two sides.

Figure 11 shows the velocity streamlines of the first five sections in the longitudinal section under various heads. It can be found that the high-speed region is concentrated in the rectangular region near the upper part of the fluid domain of the tailwater channel, and the low-speed region is concentrated in the triangular region near the lower part of the fluid domain of the tailwater channel, showing extremely pronounced vortex structures in each section. To investigate the effect of the heads on the velocity distribution, it is easy to know that the head and fluid velocity are positively correlated. It is found that the core location of the vortex in planezy-4 and planezy-5 gradually moves to the outer wall of the tailwater channel with the increase of the heads.

FIG. 11.

Velocity streamlines in the first five sections of the longitudinal section at different heads.

FIG. 11.

Velocity streamlines in the first five sections of the longitudinal section at different heads.

Close modal

From Fig. 11, it can also be observed that on planezy-1 to 3, vortices of basically the same size exist in the triangular region at the lower part of the fluid domain of the tailwater channel, and vortices of basically the same size exist in the rectangular region in the upper part of the fluid domain of the tailwater channel, which indicates that the flow pattern in each longitudinal section of the tailwater channel outlet section is basically the same, while the stability of the flow in the triangular low-speed region of planezy-4 and planezy-5 is obviously deteriorated, which indicates that this area is greatly affected by the flow state of the draft tube, while the rectangular region in these two cross sections is less affected. Overall, in the tailwater channel outlet section, the flow velocity is larger, but because the flow is more turbulent, the energy loss is greater.

Figure 12 illustrates the velocity streamlines of the last five sections on the longitudinal section under different heads. From Fig. 12 and combined with Fig. 11, it can be seen that there is a vortex all the time from planezy-1 to planezy-7 on the side of the upper surface of the tailwater channel, which indicates that the anti-slope section does not ensure the smooth flow of the water at the outlet of the tailwater channel, that is, it cannot play the role of good energy dissipation. At the same time, from planezy-6 to planezy-10 can be detected in the anti-slope section of the longitudinal section of the flow stability is poor, and the closer to the middle of the stability is worse, indicating that the unit draft tube port of the water into the anti-slope section of the flow is not smooth.

FIG. 12.

Velocity streamlines in the last five sections of the longitudinal section at different heads.

FIG. 12.

Velocity streamlines in the last five sections of the longitudinal section at different heads.

Close modal

Figure 13 shows the distribution of vorticity at different heads in the longitudinal section of the tailwater channel. It can be found that the region with the most obvious vorticity change is located at the junction of the triangular region and the rectangular region, where the vorticity is distributed in a strip shape and the central vorticity value is the largest. Exploring the influence of heads on vorticity distribution, it can be perceived that the maximum vorticity of planezy-3, planezy-4, and planezy-5 increases with the increase of heads, and the maximum vorticity range gradually decreases.

FIG. 13.

Distribution of vorticity at different heads in the longitudinal section of a tailwater channel. (a) The first five sections of the longitudinal section. (b) The last five sections of the longitudinal section.

FIG. 13.

Distribution of vorticity at different heads in the longitudinal section of a tailwater channel. (a) The first five sections of the longitudinal section. (b) The last five sections of the longitudinal section.

Close modal

Combined with Fig. 11, it can be seen that the central vorticity of the vortex is small, and the vorticity at the junction of the high-speed zone and the low-speed zone is large, indicating that the slip between the high-speed zone and the low-speed zone is large. Meanwhile, it further indicates that most of the water flow in the lower part of the tailwater channel has remained at the bottom of the tailwater channel in a vortex state, and only the upper water flow flows out from the outlet of the tailwater channel. From the vorticity distribution under different heads at five sections behind the tailwater channel, it can be seen that the water flow in the anti-slope section of the tailwater channel gradually flows from the anti-slope section of the tailwater channel to the outlet section of the tailwater channel in the form of vortices.

In summary, it is known that the flow condition in the tailwater channel of Mupo Hydropower Station is poor, and the water flow in the tailwater channel must circulate in the form of a continuous vortex in the anti-slope section of the tailwater channel many times before it can flow out of the tailwater channel, which will greatly increase the height of the tailwater and lead to the reduction of the unit output. It can also be seen that the change of heads has little effect on the distribution of eddy current in the tailwater channel.

  1. The maximum velocity at the bottom of the fluid domain near the anti-slope section of the tailwater channel decreases with increasing head, while the velocity at the upper part of the fluid domain near the anti-slope section of the tailwater channel does not change much with increasing head. At the bottom of the fluid domain near the anti-slope section of the tailwater channel, no complete vortex was formed.

  2. There is a large backflow phenomenon on both sides of the draft tube. However, the higher the vortex on both sides of the draft tube port, the more obvious it is, while gradually moving to the corners of both sides of the draft tube port. In the middle of the upper part of the tailwater channel anti-slope section of the fluid domain, a larger vortex is formed, and the lower the head, the more obvious the vortex is.

  3. The flow condition in the tailwater channel of Mupo Hydropower Station is poor, and the water in the tailwater channel has to circulate in the form of a continuous vortex many times in the anti-slope section of the tailwater channel to flow out of the tailwater channel, which will greatly increase the height of the tailwater and lead to a reduction in the output of the unit. Therefore, the shape of the tailwater channel must be redesigned so that the anti-slope section can play a better role in energy dissipation and ensure that the tailwater can flow smoothly out of the tailwater channel outlet.

This research was funded by the Central Leading Place Scientific and Technological Development Funds for Surface Project (Grant No. 2021ZYD0038) and the Major Science and Technology Project of Sichuan Province (Grant No. 22JBGS0009).

The authors have no conflicts to disclose.

Yulin Xue: Methodology (equal); Software (equal). Yanlin Lu: Conceptualization (equal); Investigation (equal). Bangjie Meng: Writing – review & editing (equal). Liersha Wu: Supervision (equal). Hongjuan Li: Validation (equal). Xunyun Ye: Writing – original draft (equal).

The data that support the findings of this study are available within the article.

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