Content area
Purpose
Multi-level intake structures are used to take the surface water of reservoirs. The changed boundary conditions will certainly make the water hammer phenomenon more complicated. This paper aims to find out the influence and law of the water hammer pressure after setting the stop log gates.
Design/methodology/approachThe authors use the computational fluid dynamics method with the adaptive grid technology to stimulate the water hammer phenomenon of the multi-level intake hydropower station. In the analysis, we set several different heights of stop log gates and two representative times in the starting up and shutdown processes to reflect the impact of multi-level intake structures.
FindingsThe authors find that the setting of the stop log gates will reduce the pressure during the normal operation and will increase the period and amplitude of the water hammer wave, but will not necessarily increase the maximum water hammer pressure during the shutdown process. The relationship between the height of the stop log gates and the amplitude of the water hammer wave is affected by the shutdown time. After setting stop log gates, the depression depth and wave height of the water level in front of the dam increase when the load changes.
Originality/valueThe authors study in this paper the water pressure of the multi-level intake hydropower station that has never been studied before and obtain some laws.
1. Introduction
Many kinds of accidents, such as accidental operation of gate valves, accidental powering off of pumping stations and the abrupt change of water level in an intake sump and starting up of a water pump unit and quick starting up and shutdown of a water turbine unit of a hydropower station (Ammar and Al-Zahrani, 2015; Asli et al., 2012) will cause a drastic change of velocity and the fluctuation of the liquid pressure in the pipeline. In engineering, this alternately increased and decreased pressure is called water hammer pressure (Wang, 1980; Wu, 2003), which acts like a hammer on the pipe walls, valves or other pipeline components. The process of water hammer phenomenon from generation to attenuation is a very typical and important unsteady transition process. Because of the change of electrical load and working conditions, hydropower stations need to stop and start the units in time, or adjust the guide vane opening. And any one of these transition processes will cause water hammer phenomenon in the pipelines (Afshar and Rohani, 2008). The maximum pressure of water hammer can be up to several dozen times of the normal operating pressure, which may cause the overpressure rupture of the pipeline and the damage of equipment (Geng et al., 2017; Ghodhbani and Taïeb, 2017; Zeng et al., 2013).
Every year, the huge loss of pipe rupture caused by water hammer in the world is inestimable. Therefore, it is necessary to analyze the water hammer phenomenon to estimate the maximum increase and decrease of water hammer pressure in the pipe and the attenuation of the water hammer phenomenon, which will provide the basis for the strength design of the pipeline and verify the rationality of the pipeline arrangement (Ghidaoui et al., 2005; Riasi and Tazraei, 2017).
There are three methods of water hammer calculation and analysis: analytical method, graphical method and numerical method. The analytic method can only solve the simplified basic equations, and it is only suitable for the simple pipe without head loss. The process of the graphic method is complicated and tedious. The numerical method can deal with the boundary conditions well, the calculation speed is fast and the result is more accurate. So, the numerical method of water hammer calculation has gradually replaced the traditional analytical method and graphical method. Numerical methods now include: method of characteristics, method of finite element, method of finite difference, etc. (Zhao and Ghidaoui, 2004; Tijsseling et al., 2008). The method of characteristics is one of the most mature methods in the numerical methods. However, the method of characteristics did not find wide applications because of the limitations such as the poor numerical stability, the complicated solution schemes and the fixed grids. And the method of characteristics is a one-dimensional calculation method which is unable to realize the visualization of the flow field and cannot solve the multi-feature interpolation problem and the error of non-integral term very well (Zheng et al., 2000; Guo et al., 2014; Saemi et al., 2017). With the development of mathematical models and numerical methods for fluid flows, the computational fluid dynamics (CFD) is widely used to simulate some hydraulic transients (Zhang and Cheng, 2012). Huaping Liu and Fu Chen used the dynamic grid technology to simulate the flows of four kinds of valves in the pipeline (Liu et al., 2008). This numerical simulation method breaks the limitations of previous static research and simulates the flow condition, and the valve body force more realistically during the dynamic valve on-off processes (Wu et al., 2007).
The construction of reservoir has formed a huge stagnant water area. The solar radiation and the physicochemical properties of the water make the water environment completely different from the original natural river. The original flowing water with uniform water temperature is transformed into a large volume of water which is relative static or flowing slowly. And it forms a unique water temperature field. Because of the submerged depth of the water intake, the location of the water intake is low. Most of the water entering the pipe is the deep water in the reservoir. Taking the deep water from the reservoir will bring many adverse effects to the downstream agriculture and other ecological environment (Zheng et al., 2017). To meet the ecological development requirements of downstream river, the discharged water must have enough temperature and oxygen content. At home and abroad, a kind of intake can take water from different elevations which is called multi-level intake. Using top log gate is one way of this kind of intake often used (Gao et al., 2013). This kind of intake uses the spare trash rack to set up stop log gates. According to the change of the reservoir water level, it can realize taking water on multi-level by adjusting the height of the stop log gates.
The multi-level intake of one hydropower station is a dam intake, and there are no pressure relief measures such as a surge tank. The front edge and wetted cross-section are smaller than the bank tower intake. The setting of the stop log gates in front of the intake changes the boundary conditions in the traditional calculation of water hammer, and it will inevitably lead to the more complicated water hammer phenomenon. Therefore, it is necessary to calculate the water hammer of this kind of hydropower station. However, the water hammer research on multi-level intake hydropower stations is rare at this moment. To the best of our knowledge, it is the first attempt to stimulate this type of water hammer. In this work, we use the CFD calculation software to simulate the water hammer phenomenon of a multi-level intake hydropower station in the on-off processes. The CFD calculation software is based on the finite element method of three-dimensional, compressible and unsteady N-S equations. And it can achieve the visualization of the flow field for further analysis. The calculation uses the 2-D standard k−ε model and considers the compressibility of water to stimulate the complex flow field and the water hammer phenomenon. An adaptive grid technology is used to deal with the grid deformation that caused by the complex flow field. This technology can automatically divide the grid based on the calculation results of the variable during the calculation process, and automatically determine the mesh density of each part. This technology can not only save computing resources, but also improve the accuracy of calculation. In this paper, the numerical simulations are used to study the characteristics of water hammer in multi-level intake hydropower station. We find the relationship between the height of the stop log gates and the water hammer wave by using different shutdown times and different stop log gates height.
2. Study objects and boundary conditions
The intake structure shown in Figure 1 is our research object. The bottom elevation of the intake is 418 m, the bottom elevation of the trash rack is 415 m, the elevation of the dam crest is 465 m, the diameter of the penstock is 8.7 m. The bottom elevation of the bell mouth is 416 m, and the top elevation is 432.95 m.
The maximum elevation of the stop log gates is 443.00 m. The total height of the stop log gates is 28 m. It is divided into 10 sections with the height of 2.8 m for each one. Figure 2 is the 3d model of 1 stop log gate, and Figure 3 is the 3d model of 10 stop log gates. The stop log gates are the same width as the trash rack.
2.1 Calculation model
We chose a single intake as the simulation object to build the two-dimensional models. In the models, the cross-section which is 145 m away from intake is selected as the inflow boundary and the cross-section of the end of the penstock is the outflow boundary. The upstream water level for operation is normal storage level 458 m and the bottom elevation of the reservoir is 400 m.The bottom elevation of stop log gates is 415 m and the elevation of the center point at the end of the penstock is 366.6 m. The elements of each model are three-node triangular elements. In this paper, we build 11 calculation models to simulate the 11 working conditions of setting 0 ∼ 10 stop log gates in front of the intake.
Figure 4 is the calculation model with 10 stop log gates which has a total of 23768 elements. Figure 5 is the calculation model with 0 stop log gate which has a total of 26308 elements.
2.1.1 Boundary Conditions.
The Inflow boundary is uniform flow. The uniform flow condition is based on the assumption that the fluid is consistent along the boundary.
The outflow boundary is according to the average flow velocity of the penstock and the velocity at normal operation is 7.27 m/s.
The water surface is free surface. Other boundaries are no-slip walls.
3. Water hammer calculation for 8S shutdown scheme
The switch time recommended by the turbine manufacturer is 8 s. The opening degree of the turbine changes in a straight line
3.1 Starting up process
The calculation of the starting up process includes starting up process and normal operation process. 0 ∼ 8 s is the starting up process, and 8s ∼ 14 s is the normal operation. The flow velocity at the end of the penstock is increased from 0 to 7.27 m/s by linear change in 8 s during the starting up process.
Node 70 is the center point at the end of the penstock (the position of node 70 is shown in Figure 6). The elevation of node 70 is 366.6 m and its static water pressure is a water head of 91.4 m. Figure 7 shows the pressure fluctuations of node 70 in the starting up process (including 11 working conditions).
The flow velocity in the penstock before the starting up is 0. At the beginning of the starting up process, the flow velocity at the end of the penstock suddenly increases, and the water in the pipe keeps static because of the inertia. The increased velocity causes the pressure at the end of the penstock begin to decrease. The negative pressure wave generated by the continuously increasing flow velocity travels up to the upstream. When the pressure wave reaches the reservoir, the reservoir reflects the pressure wave into the positive pressure wave. The positive pressure wave travels back to the end of the penstock, and when it reaches the end of the pipe the pressure there starts to increase. According to this rule the water hammer wave travels back and forth in the penstock, and the pressure at the end of the penstock fluctuates up and down. So, the pressure of node 70 starts to fluctuate greatly after the startup, and it shows a decreasing trend. Because of the effect of the friction, the water hammer wave is gradually attenuated, and the fluctuation of the pressure lasts about 6s. The pressure of node 70 in all working conditions has done 2.5 to 2.7 periodic fluctuations in 1s, which is low frequency oscillation.
As shown in Figure 7 and Table I, the minimum pressure of each working condition occurs at the end of the first phase. Because of the stop log gates in front of the water intake, the propagation distance of the water hammer wave increases, and the period becomes longer. The stop log gates have the reflection increasing effect on the water hammer wave (increasing the wave amplitude of the water hammer wave). The higher the height of the stop log gates, the larger the wave amplitude, the smaller the minimum pressure during the starting up process. Table I shows that the minimum pressure generated during the starting up process is 75 per cent ∼ 78 per cent of the net head.
Figure 8 shows the relationship between the height of the stop log gates and the minimum pressure at node 70 which is similar to the linear relationship.
When the starting up process is completed, the units enter into the normal operation stage. The flow velocity at the end of the penstock stops increasing, while the water in the pipe is still accelerating because of the inertia. So, the water at the end of the pipe is compressed by the water upstream which is still accelerating. This compression causes a local increase of the pressure at the end of the penstock. A chain reaction then takes place along the penstock with each stationary element of water which compressed by the upstream water. So that the pressure at the end of the penstock continues to rise. When the pressure wave reaches the reservoir, the reservoir reflects the pressure wave into the negative pressure wave. The water hammer wave travels back and forth in the penstock, and the pressure at the end of the pipe fluctuates up and down. As shown in Figure 9, the pressure of node 70 increases after the units enter the normal operation stage. The amplitude of fluctuation gradually decreases because of the friction, and the fluctuation lasts about 4s. The higher the height of the stop log gates, the lower the pressure of the normal operation. The pressure fluctuation is smaller than it in the starting up, and the fluctuation duration is short. The pressure of node 70 of in working conditions is 89.4 per cent ∼ 94.4 per cent of the net head.
Figures 10 and 11 respectively show the pressure cloud diagram at 8 s and 14 s of setting 10 and 0 stop log gate. The 8 s is the end of the starting up, and the 14 s is the normal operation. In Figure 8, it can be seen that the downstream pressure of the stop log gates is significantly less than the upstream pressure during the starting up and normal operation.
Figures 12 and 13 respectively show the velocity cloud diagram at 8 s and 14 s of setting 10 and 0 stop log gate. The intake without stop log gate takes water directly from the reservoir. The flow velocity of the middle area in reservoir is large, while the velocity of the surface and the bottom part is small. When the intake uses the stop log gates, the water flow from the reservoir needs to bypass the stop log gates to enter the penstock. Compared with the condition of setting 0 stop log gate, the reservoir surface flow velocity increases in the condition of setting 10 stop log gates, and the mainstream is relatively concentrated. The velocity gradient increases along the direction of flow and the velocity distribution is more uneven.
3.2 Shutdown process
The initial condition of the shutdown process is normal operation. 0 ∼ 8 s is the shutdown process, and 8 ∼ 14 s is the after-shutdown process. The flow velocity at the end of the penstock changes from 7.27 m/s to 0 by linear change in 8 s during the shutdown process.
At the beginning of the shutdown, the flow velocity at the end of the penstock suddenly decreases, and the water in the penstock is still flowing to the end of the penstock at the original velocity because of the inertia. The water at the end of the penstock is then compressed by the upstream water which is still flowing. This compression causes a local increase in the pressure of the water. A chain reaction then takes place along the pipe with each stationary element of water compressed by the flowing water upstream. So that the pressure at the end of the penstock continues to rise. When the pressure wave reaches the reservoir, the pressure in front of the intake is less than the pressure in the penstock. To keep balance, the water starts to flow out of the penstock into the reservoir. An unloading pressure wave now travels back along the pipe towards the end of the penstock. The pressure at the end of the penstock starts to decrease after the negative pressure wave reflected from the upstream arrives at the end of the penstock. The positive pressure wave generated by the continuously decreasing flow velocity continues to travel to the upstream. According to this rule, the water hammer wave travels back and forth in the penstock, and the pressure at the end of the penstock fluctuates up and down. Because of the effect of the friction, the water hammer wave attenuates gradually.
We can see from Figure 14 that the pressure of node 70 suddenly increases and starts to fluctuate greatly at the beginning of shutdown, and it shows an increasing trend. The amplitude of pressure fluctuation gradually decreases because of the friction, and the fluctuation of the pressure lasts about 6 s.
Table II shows the maximum pressure value and the maximum pressure occurrence time of node 70 during the shutdown process. It can be seen from the table that the maximum pressure of setting 0-3 stop log gates occurs at the end of the first phase, which is called first phase water hammer. However, the maximum pressure of setting 10-4 stop log gates occurs at the last moment of the shutdown process, which is called limited water hammer. This is because the reflection of the water hammer wave increases with the increase of the height of the gates. The maximum pressure generated during the shutdown process of all working conditions is 116.43-117.35 per cent of the net head.
Figure 15 is the maximum pressure of node 70 in each working condition during the shutdown process. We can see that the maximum pressure of setting 9 stop log gates generated during the shutdown process is the largest, and the maximum pressure of setting 4 stop log gates is the smallest. This is because the stop log gates decrease the pressure of normal operation. If the shutdown time is not especially short and the height of the stop log gates is not too high, the increase of the water hammer pressure in the shutdown process is not enough to offset the decrease that generated in the normal operation. So that, the maximum water hammer pressure will be less than that without the stop log gates. In this shutdown scheme, the increase of the water hammer pressure of setting 1-5 stop log gates is not enough to offset the decrease of the pressure that generated in normal operation. In addition, the maximum water hammer pressure value of setting 1-5 stop log gates is less than that setting 0 stop log gates.
The maximum pressure fluctuation amplitude is the pressure of the first phase minus the pressure of normal operation. Figure 16 shows that in the shutdown process the higher the height of the stop log gates is, the higher the pressure fluctuation amplitude is. The height of the 0-4 stop log gates is so low that only cover just a small part in front of the intake. In addition, the stop log gates cannot completely reflect the water hammer wave, so that the increment rate of the water hammer wave is small. The height of the 5-7 stop log gates exceeds the centerline of the intake. The covering part by the stop log gates is significantly increased in front of the intake, and the reflection effect of the stop log gates increases. Therefore, the increment rate of the water hammer wave increases, and the change rate is approximately linear. The height of the 7 stop log gates is a critical height. Because the height of the 7 stop log gates exceeds the top of the bell mouth, and the reflection effect of the water hammer wave is reached the maximum stage. After this critical height, the increase of the height of the stop log gates will not increase pressure fluctuation amplitude as before. Therefore, the change rate with 8-10 stop log gates gradually decreases.
Figures 17 and 18, respectively, show the pressure cloud diagram at the first phase and the end of the shutdown process of setting 10 stop log gates and 0 stop log gate.
After the shutdown process ended, the flow velocity at the end of the penstock is 0. Figure 19 shows that the pressure at node 70 drops and fluctuates greatly after the shutdown ended. The fluctuation amplitude gradually decreases, and the fluctuation lasts about 5 s. The higher the height of the stop log gates, the larger the amplitude of the fluctuation and the longer the period. At last, the pressure at node 70 of all working conditions is around 102.5 per cent of net head.
In Figure 20, we can see that after the shutdown ended, the relationship between the maximum pressure fluctuation amplitude and the height of the gates is not as complicated as the shutdown process.
4. Water hammer calculation for 1 second shutdown scheme
Reduce the shutdown time to 1 s to simulate a sudden shutdown situation. The initial condition of the calculation is normal operation. The flow velocity at the end of the penstock is changed from 7.27 m/s to 0 by linear change in 1 s. 0-1 s is shutdown process, and 1-14 s is after-shutdown process.
We can see from Figure 21 that the characteristics of pressure fluctuation are similar to that of the 8 s shutdown scheme, but the amplitude is much larger.
Table III shows the maximum pressure value and the occurrence time of node 70 in the shutdown process. Figure 21 and Table III show that the maximum pressure generated during the shutdown process occurs at the end of the first phase. Therefore, the water hammer is the first phase water hammer. The maximum pressure generated during the shutdown process is 274.13 per cent ∼ 285.14 per cent of the net head.
Table III and Figure 22 show that the water hammer pressure and pressure fluctuation amplitude increase with the height of the stop log gates, and the curve is similar to the straight line.
Figures 23 and 24, respectively, show the pressure cloud diagram at the first phase and the end of the shutdown process of setting 10 stop log gates and 0 stop log gate.
We can see from Figure 25 that the characteristics of pressure fluctuation are similar to that of the 8 s shutdown scheme, but the amplitude is much larger.
We can see from Figure 26 that the change rate of the amplitude after the shutdown ended is much larger than that in the shutdown process.
5. Water surface fluctuation caused by load mutation
The sudden load change will cause the fluctuation of water level in front of the dam. We select the point A (the position of point A is shown in Figure 27) to observe the fluctuation of water surface during the shutdown process.
5.1 Shutdown time is 8 seconds
It is shown in Figure 28 that the wave height of point A is negative because of the water diversion in the normal operation. The higher the height of the stop log gates is, the larger the water surface depression is. The wave height of point A gradually increases as the flow decreases after the beginning of the shutdown. In addition, the higher the height of the stop log gates is, the faster the change is. After the shutdown finished, the wave height continues to increase to the maximum value then gradually decreases. In all conditions, the maximum wave height of point A of setting 9 stop log gates is 3.08 m which is the largest, and the maximum wave height of point A of setting 1 stop log gate is 3.42 m which is the smallest. The maximum wave height of all working conditions occurs at about 9 s.
5.2 Shutdown time is 1
Figure 29 shows that the wave height value of point A increases from negative to positive rapidly, because of the shutdown time is short. In addition, the higher the height of the stop log gates is, the more water in the penstock cannot be diffused rapidly into the reservoir. Therefore, the wave height of point A increases extremely fast, and the working condition of setting 10 stop log gates has already reached the maximum wave height value for 4.05 m at 2.02 s. The wave height of setting 10, 9, 8 and 7 stop log gates of these four working conditions gradually reduces after the rapid increase, then gradually increases, and the higher the height of the stop log gates, the greater the fluctuation. In the rest of the working conditions, the wave height of point A increases rapidly, the increasing speed decreases after the shutdown process ends, but it still increases until reaches the maximum wave height. The maximum wave height of point A of settings 10 stop log gates is 4.05 m which is the largest, and occurs earliest. In the remaining working conditions, the maximum wave height of point A all occurs at about 9 s, and the maximum wave height of settings 1 stop log gate is 3.32 m which is the smallest.
5.3 Comparison of two shutdown schemes
Figure 30 shows that the maximum wave height of the 1 s shutdown scheme is larger than that of the 8 s shutdown scheme. With the height of the stop log gates increasing, the maximum wave height difference between the two schemes also increases. In the two shutdown schemes, the wave height of setting 10 stop log gates is the largest, and the wave height of setting 1 stop log gate is the smallest.
It is shown in Figure 31 that the higher the height of the stop log gates is, the higher the wave height difference is. When the 10 stop log gates are set, the maximum wave height generated by the 1 s shutdown scheme is increased by 0.826 m compared with the 8 s shutdown scheme. In addition, the maximum wave height of setting 0 stop log gate is increased by 0.272 m.
Tables IV and V are, respectively, the maximum wave height and occurrence time of each working condition in the two shutdown schemes. It is shown in the tables that the shorter time of the shutdown scheme causes the higher wave height, and the longer the shutdown time is, the earlier the maximum wave height occurs. In the 8 s shutdown scheme, the maximum wave height occurs at 1 s ∼ 2 s after the shutdown process ended, but in the 1 s shutdown scheme, the maximum wave height occurs at 5 s ∼ 6 s after the shutdown process ended.
Figures 32 and 33 are the schematic diagram of the maximum wave height of the two working conditions of setting 0 and 10 stop log gates in the two shutdown schemes.
6. Conclusions
The CFD method with the FEM model is proposed to simulate the water hammer phenomenon of a multi-level intake hydropower station in this paper. The processes of starting up, normal operation, shutdown and after-shutdown are calculated respectively. The shutdown time adopts 8 and 1 s, and the two shutdown schemes calculate 11 working conditions of setting 0-10 stop log gates.
We find that setting the stop log gates will reduce the pressure during the starting up process and the normal operation, and will increase the period and amplitude of the water hammer wave, but will not necessarily increase the maximum water hammer pressure during the shutdown process. This is because the stop log gates can reduce the pressure of normal operation. If the shutdown time is not especially short and the height of the stop log gates is not so high, the increase of the water hammer pressure caused by the stop log gates in the shutdown process is not enough to offset the decrease in the normal operation, and the maximum water hammer pressure will be less than that without the stop log gate.
We also find the relationship between the height of the stop log gates and the amplitude of the water hammer wave. When the shutdown time is 1 s, the relationship between the height of the stop log gates and the amplitude of the water hammer is approximately linearly increased, and the changing rate after shutdown ended is greater than that during the shutdown. When the shutdown time is 8 s, the relationship between these two is increased in curve. Because of the different shielding area before the intake, the changing rate of the curve is larger in the middle.
The sudden load change will cause the fluctuation of water level in front of the dam. After setting up the stop log gates, the water level before dam should decrease and increase if the load mutates. The shorter the shutdown time and the higher the stop log gates, the higher the wave height and the greater the fluctuation of the water surface.
Finally, we suggest avoiding a sudden shutdown situation in the actual operation. If the height of the stop log gates is higher, the flow velocity should be greater and the water head should be bigger. It is hoped that the optimal arrangement of the stop gate can be obtained by combining the simulation results of water temperature.
This project is supported by the National Key Research and Development Plan (Grant No. 2016YFC0401601).
The figure of the multi-level intake structure
3D model of 1 stop log gate
3D model of 10 stop log gates
The calculation model with 10 stop log gates
The calculation model with 0 stop log gate
The position diagram of node 70
The pressure fluctuations of node 70 in the starting up process
The minimum pressure of node 70 in each working condition during the starting up process
The pressure fluctuations of node 70 in the normal operation process
The pressure cloud diagrams of setting 10 stop log gates (Pa)
The pressure cloud diagrams of setting 0 stop log gate (Pa)
The velocity cloud diagrams of setting 10 stop log gates (m/s)
The velocity cloud diagrams of setting 0 stop log gate (m/s); (a)
The pressure fluctuations of node 70 in the shutdown process
The maximum pressure of node 70 in each working condition during the shutdown process
The relationship between the height of the stop log gates and the amplitude of the water hammer wave of node 70 during the shutdown process
The pressure cloud diagrams of setting 10 stop log gates (Pa)
The pressure cloud diagrams of setting 0 stop log gate (Pa)
The pressure fluctuations of node 70 after the shutdown process ended
The relationship between the height of the stop log gates and the amplitude of the water hammer wave of node 70 during the shutdown process and after the shutdown ended
The pressure fluctuations of node 70 in the shutdown process
The maximum pressure of node 70 in each working condition during the shutdown process
The pressure cloud diagrams of setting 10 stop log gates (Pa)
The pressure cloud diagrams of setting 0 stop log gate (Pa)
The fluctuations of node 70 after the shutdown ended
The relationship between the height of the stop log gates and the amplitude of the water hammer wave of node 70 in the shutdown process and after the shutdown ended
The position diagram of point A
The wave height changes of point A in the shutdown process
The wave height changes of point A in the shutdown process
The maximum wave height of water surface in the shutdown process of each working condition
The maximum wave height difference between the two shutdown schemes
The schematic diagram of the maximum wave height of the two working conditions in the 1 s shutdown scheme
The schematic diagram of the maximum wave height of the two working conditions in the 8 s shutdown scheme
The minimum pressure value of node 70 and the occurrence time in the starting up process
| The no. of stop log gates | Minimum water head |
Minimum pressure occurrence time |
Percentage of net head |
|---|---|---|---|
| 10 | 68.90 | 0.2 | 75.38 |
| 9 | 69.14 | 0.195 | 75.65 |
| 8 | 69.42 | 0.195 | 75.95 |
| 7 | 69.69 | 0.19 | 76.25 |
| 6 | 69.97 | 0.19 | 76.55 |
| 5 | 70.20 | 0.185 | 76.80 |
| 4 | 70.42 | 0.185 | 77.05 |
| 3 | 70.60 | 0.18 | 77.25 |
| 2 | 70.74 | 0.18 | 77.40 |
| 1 | 70.84 | 0.18 | 77.51 |
| 0 | 70.89 | 0.18 | 77.56 |
The maximum pressure value and the occurrence time of node 70 in the shutdown process
| The no. of stop log gates | Water head before shutdown(m) | Maximum water head(m) | Maximum pressure occurrence time(s) | Percentage of net head |
|---|---|---|---|---|
| 10 | 81.81 | 107.21 | 8 | 117.30 |
| 9 | 82.40 | 107.25 | 8 | 117.35 |
| 8 | 82.84 | 107.08 | 8 | 117.16 |
| 7 | 83.54 | 106.93 | 8 | 116.99 |
| 6 | 84.32 | 106.90 | 8 | 116.96 |
| 5 | 84.88 | 106.75 | 8 | 116.79 |
| 4 | 85.36 | 106.41 | 8 | 116.43 |
| 3 | 85.75 | 106.49 | 0.18 | 116.51 |
| 2 | 85.98 | 106.63 | 0.18 | 116.66 |
| 1 | 86.08 | 106.68 | 0.18 | 116.72 |
| 0 | 86.29 | 106.86 | 0.18 | 116.92 |
The maximum pressure value and the occurrence time at node 70 in the shutdown process
| The no. of stop log gates | Water head before shutdown |
Maximum water head |
Maximum pressure occurrence time |
Percentage of net head |
|---|---|---|---|---|
| 10 | 81.81 | 260.62 | 0.195 | 285.14 |
| 9 | 82.40 | 259.83 | 0.195 | 284.28 |
| 8 | 82.84 | 258.50 | 0.195 | 282.82 |
| 7 | 83.54 | 257.39 | 0.19 | 281.61 |
| 6 | 84.32 | 255.99 | 0.185 | 280.07 |
| 5 | 84.88 | 254.63 | 0.185 | 278.59 |
| 4 | 85.36 | 253.27 | 0.185 | 277.10 |
| 3 | 85.75 | 252.23 | 0.18 | 275.96 |
| 2 | 85.98 | 251.41 | 0.18 | 275.07 |
| 1 | 86.08 | 250.78 | 0.18 | 274.37 |
| 0 | 86.29 | 250.56 | 0.18 | 274.13 |
The maximum wave height and occurrence time of each working condition in the 8 s shutdown scheme
| The no. of stop log gates | The maximum wave height |
Occurrence time |
|---|---|---|
| 10 | 4.571 | 8.93 |
| 9 | 4.301 | 9.445 |
| 8 | 4.208 | 9.46 |
| 7 | 4.098 | 9.545 |
| 6 | 4.031 | 9.505 |
| 5 | 3.947 | 9.59 |
| 4 | 3.724 | 9.85 |
| 3 | 3.731 | 9.685 |
| 2 | 3.736 | 9.895 |
| 1 | 3.563 | 9.945 |
| 0 | 3.635 | 9.925 |
The maximum wave height and occurrence time of each working condition in the 1 s shutdown scheme
| The no. of stop log gates | The maximum wave height |
Occurrence time |
|---|---|---|
| 10 | 5.397 | 6.645 |
| 9 | 5.064 | 6.84 |
| 8 | 4.803 | 6.96 |
| 7 | 4.61 | 7.13 |
| 5 | 4.304 | 7.095 |
| 4 | 4.106 | 7.245 |
| 3 | 4.058 | 7.285 |
| 2 | 4.009 | 7.44 |
| 1 | 3.857 | 7.325 |
| 0 | 3.907 | 7.345 |
© Emerald Publishing Limited 2019