Numerical and Experimental Study on the Shutdown Transition Process of a Large Axial Flow Pump System Focusing on the Influence of Gate Control

Abstract

Large axial flow pump systems (LAPS) are widely used in coastal pump stations. In the actual operation of a LAPS, various accidents often occur during shutdown due to the unreasonable control of stop flow measures such as the gate. In this paper, based on the secondary development of Flowmaster numerical software, a numerical simulation study was conducted on the shutdown process of a LAPS with different gate control laws. It was found that the MBV of the shutdown process was greater if the gate was closed more slowly after the unit was powered off. When a 30 s shutdown scheme was used, the MBV during shutdown was 1.63Q_r. When a 60s long shutdown scheme was used, the MBV during shutdown was 1.67Q_r, an increase of 2.45%. When the 150s long shutdown scheme was used, the MVV during the stopping process reached 1.68Q_r, which is an increase of 3.07%. The shutdown method of closing the gate in advance can significantly improve the violent fluctuations of the KCPs of a LAPS during the shutdown transition and will effectively reduce the backflow and the reverse speed of the pump during the shutdown process. Taking the total gate closing time of 120 s as an example, when the 25% gate was closed in advance, the MBV and MRS during the shutdown process were reduced by 14.31% and 1.93%. When the shutdown scenario of preclosing 100% of the gates was adopted, the MBV and MRS during shutdown were reduced by 96.31% and 100%.

1. Introduction

In recent years, the axial flow pump in water jet propulsion systems and coastal pump stations has gradually played an increasingly important role [1,2,3]. At present, coastal pump stations basically use a large axial flow pump system (LAPS). Researchers at home and abroad have conducted many studies on LAPS [4,5,6,7,8,9,10], focusing on improving the energy characteristics of LAPS to improve their operational efficiency. At present, all types of LAPS have basically achieved efficient operation, and the stability and reliability of the operation of LAPS have become a key issues limiting the further development of LAPS [11,12].

LAPS have a high daily operating flow. According to the actual operating experience of a LAPS site, the water carrying a huge inertia will have a large impact on the pump body in the shutdown process. The impeller speed, flow rate, head, impeller torque, and other characteristic parameters will change drastically. Various accidents often occur during the shutdown process of LAPS in China [13,14], resulting in huge economic losses. At the same time, it should be pointed out that compared with centrifugal pump stations and mixed flow pump stations, the problems associated with the shutdown transition process of LAPS have their particularity. Mainly of them lie in LAPS for short pipeline and pump coupling systems; the pipeline is mostly reinforced concrete pouring. Wave propagation and pipe elasticity are not the main factors to be considered in the pump shutdown process of LAPS. The key problem facing the shutdown process of LAPS is not eliminating the abnormal water hammer pressure in the system but rather to reduce the violent fluctuations of the characteristic parameters of the pump unit during the shutdown process, as well as to reduce the backflow time and the backflow and maximum runaway speeds (RS) of the pump [15,16,17,18,19].

At present, domestic and foreign scholars have conducted many studies on the shutdown process of hydraulic machinery and their system [20,21,22,23,24,25,26]. For pumped storage hydropower stations and centrifugal pumping stations, many valuable results have been accumulated on their shutdown characteristics. Zhou D. Q. [27] et al. investigated the transient characteristics of pumped storage hydropower stations during power failure using a 3D numerical simulation based on the SP-VOF hybrid model. The results demonstrate that the 3D SP-VOF hybrid model can effectively reveal the transient processes of pumped storage hydropower stations. Zhongjie Li [28] used STAR-CCM 3D numerical simulation technology to study the transient and flow characteristics of a prototype pump turbine during the shutdown process. It was found that both the flow rate and the runner torque decreased with the closing of the guide vane, and the rotational speed decreased with the increase in the negative torque on the runner. This provides a basis for the further study of the flow field inside a pump turbine.

The research on the shutdown process of LAPS started late, and the related research results are very limited. From only the research results available on the downtime process of LAPS, there are two main research tools for the downtime process of LAPS. One is to establish a mathematical model through theoretical derivation and to carry out a one-dimensional calculation of a simple, single case. For example, Yuming Sun [29] et al. established a mathematical model of the pump power-off transition process by theoretical derivation and checked the reverse speed and discharge flow of the pump under the runaway condition. Jing Song [30] established a mathematical model of a LAPS pump shutdown transition process based on rigid water hammer theory and analyzed the runaway speed and maximum backflow of the pump during the shutdown at different heads. The other is the CFD method, which has developed rapidly in recent years, to simulate the 3D model numerically [31,32]. For example, Yuefei Liu [33] et al. carried out a three-dimensional numerical simulation of the shutdown process of a LAPS with a vacuum damage valve and studied the evolution of the internal gas–liquid two-phase flow during the shutdown process. Zhifeng Wu [34] et al. used the CFD method to study the runaway transition process using a LAPS and analyzed the changes in the relevant parameters of the unit with the runaway during the runaway process. From the application of these two methods in the LAPS shutdown process, the theoretical derivation method is very cumbersome, and more assumptions and simplifications are made in the calculation process. The CFD method is very time consuming, and a single example will result in a huge computational cost; therefore, it is difficult to compare and discuss a large number of different schemes. At the same time, it is difficult to achieve convergence if the CFD calculations involve multiple dynamic boundaries, such as overflow holes, flap gates, and gates. At present, most of LAPS adopt a gate cut-off [35,36,37,38,39]. An improper control strategy for the gate during the shutdown will lead to backflow and pump runaway, which will seriously affect the safety of the unit. However, there is almost no research on the shutdown process of a LAPS with a gate cut-off. In order to obtain a scientific control strategy for the gate during the shutdown process, it is necessary to compare the LAPS shutdown process under different gate control strategies. Considering that the theoretical derivation method and CFD method have great defects in obtaining a large number of different stopping process trajectory schemes, it is necessary to propose a new simulation strategy for the LAPS shutdown process.

The main objective of the research work in this paper was to understand, in detail, the variation law of the key characteristic parameters during the LAPS shutdown with different gate control schemes and to seek the optimal gate control strategy during the LAPS shutdown with gate disconnection. On the basis of this, the damage to the unit caused by large fluctuations of the KCPs during the shutdown can be reduced, and the safety of the LAPS shutdown process can be improved.

2. Simulation Method and Experimental Platform

2.1. Physical Model

This paper selected a LAPS in China as the research object. As shown in Figure 1, its main components were the inlet channel, axial flow pump, elbow, and outlet channel. At the same time, the system was equipped with safety aids, including rapid-drop gates, flap valve, and overflow holes. The parameters of the LAPS are shown in

Table 1. Characteristic parameters of a large axial flow pump station system.

Geometric Parameter	Value	Hydraulic Parameter	Value
Impeller diameter, D	1.86 m	Design flow rate, Qr	12.79 m3·s−1
Moment of inertia of pump, Jp	425.80 kg·m2	Design net head, Hr	4.55 m
Moment of inertia of motor, Jm	3350 kg·m2	Maximum net head, Hm	5.35 m
Relative elevation of overflow hole, H	5.9 m	Rated speed, nr	214.3 r·min−1
Flap valve area, S	3.5 m2	Rated power, Pr	735.38 kW
Maximum motor power, Pm	1000 kW	Rated torque, Nr	32771.25 N·m

. Considering that a LAPS has the highest risk when it stops at the maximum net head, a study of the shutdown process was carried out in this paper with the maximum net head as the calculation boundary.

2.2. Simulation Strategy

In the one-dimensional simulation process of the LAPS, if the pipeline characteristics (i.e., pressure drop curves) and pump characteristics (i.e., performance curve) can be accurately provided, the simulation accuracy will be significantly improved. After the secondary development of the Flomaster software, it was possible to create custom equivalent flow resistance components and store the flow resistance coefficients (i.e., pressure drop curves) of the components, as well as the pump performance curves. Therefore, the simulation strategy of this paper first needed to obtain the characteristics of the flow channel and the characteristics of the pump and store them in the Flomaster database. In this paper, the inlet and outlet channels of the LAPS were modeled in three dimensions, and the hydraulic loss coefficients of the inlet and outlet channels under different flow conditions were numerically calculated using the CFD method to obtain the flow channel characteristic curves (i.e., pressure drop curves). At the same time, the pump model was processed, and the performance curve of the pump was obtained by the method of the model experiment. Then, the third step of the simulation strategy in this paper was to store the flow channel characteristic curve and the pump performance curve into the Flomaster database. After the storage, the custom created flow resistance elements (i.e., inlet and outlet channels) could call the flow channel characteristic curve, and the pump element could call the pump performance curve. Finally, the LAPS was modeled in one dimension based on the Flomaster software, and the LAPS shutdown process was simulated. Figure 2 shows a block diagram of the numerical strategy for this numerical calculation.

2.3. Numerical Models and Method

Before developing a one-dimensional simulation based on Flomaster, the CFD method (based on ANSYS CFX software, ANSYS, America) was used to obtain the hydraulic loss coefficients of the inlet and outlet channels under different flow conditions. CFD uses the RANG method for time-averaging of the N-S equation. Discretization of the control equations adopts a finite volume method. The SIMPLEC algorithm was used to calculate the velocity and pressure coupling. The CFD used the SST turbulence model based on the RANG method. When setting the boundary conditions, the inlet boundary condition used the velocity inlet, and the outlet boundary condition used the free outflow. The solid wall surfaces were all non-slip wall surfaces. Both the inlet and outlet channels adopted a structured grid, with a grid number for the inlet channel of 108 w and a grid number for the outlet channel of 96 w.

Flowmaster simplifies the complex fluid network into a series of piping components. The components are connected to each other by nodes. Flowmaster controls the flow ability of the components through continuous and momentum equations. The direction of the flow from the element to the node is specified as positive.

The simplified equation for solving the fluid network is as follows [40]:

$$\overline{\mathrm{v}}\frac{\partial \mathrm{h}}{\partial \mathrm{x}}+\frac{\partial \mathrm{h}}{\partial \mathrm{t}}-\overline{\mathrm{v}}\sin \mathsf{\alpha }+\frac{{\mathrm{a}}^2}{\mathrm{g}}\frac{\partial \overline{\mathrm{v}}}{\mathrm{x}}=0$$

(1)

$$\mathrm{g}\frac{\partial \mathrm{h}}{\partial \mathrm{x}}+\overline{\mathrm{v}}\frac{\partial \overline{\mathrm{v}}}{\partial \mathrm{x}}+\frac{\partial \overline{\mathrm{v}}}{\partial \mathrm{t}}+\frac{\mathrm{f}\overline{\mathrm{v}}\left|\overline{\mathrm{v}}\right|}{2\mathrm{D}}=0$$

(2)

where h is the head along the way; the pipes represents the sum of the pressure energy and potential energy, and in the free surface reservoir, it is expressed as the water level; $\overline{\mathrm{v}}$ is the average velocity of the fluid on the cross-section; g is the acceleration of the gravity; f is the friction factor; α is the angle between the centerline of the pipe and the horizontal line; D is the diameter of the pipe; and a is the wave velocity.

The whole fluid network is composed of a series of pipeline elements, and all piping components are dominated by the pressure–flow relationship. Therefore, when using a Flowmaster simulation, firstly, a linear equation set of the fluid network should be established based on the pressure–flow relationship to obtain the characteristic parameters of each component in the steady state; then, the characteristic line method should be used to calculate the transient process.

After the fluid medium flows through the component, the pressure difference and fluid flow rate relationship is [41]:

$$\Delta \mathrm{P}=\mathsf{\mu }\frac{\mathsf{\rho }{\overline{\mathrm{v}}}^2}{2}$$

(3)

where ∆P is the pressure difference; µ is the pressure loss coefficient; ρ is the density of flow; and $\overline{\mathrm{v}}$ is the average velocity of the fluid.

During the simulation calculation, it is necessary to establish the functional relationship between the mass flow and pressure difference. In a fluid network, the flow rate is proportional to the flow rate and inversely proportional to the cross-sectional area; that is [41]:

$$\overline{\mathrm{v}}=\frac{\mathrm{m}}{\mathsf{\rho }\mathrm{A}}$$

(4)

where m is the mass flow rate; A is the cross-sectional area (between the two nodes, the pipe cross-sectional area is constant); and ρ is the density of flow.

According to Equations (3) and (4) [41]:

$$\Delta \mathrm{P}=\mathsf{\mu }\frac{\mathrm{m}\left|\mathrm{m}\right|}{2\mathsf{\rho }{\mathrm{A}}^2}$$

(5)

where ∆P is the pressure difference; m is the mass flow rate; µ is the pressure loss coefficient; ρ is the density of flow; and A is the cross-sectional area (between the two nodes, the pipe cross-sectional area is constant).

It is further obtained that [41]:

$$\mathrm{m}=\frac{2\mathsf{\rho }{\mathrm{A}}^2}{\mathsf{\mu }\left|\mathrm{m}\right|}\Delta \mathrm{P}$$

(6)

where ∆P is the pressure difference; m is the mass flow rate; µ is the pressure loss coefficient; ρ is the density of flow; and A is the cross-sectional area (between the two nodes, the pipe cross-sectional area is constant).

In a fluid network, taking a pipe as an example, assume that the pipe inlet is node 1, the mass flow is m₁, the pressure is P₁, the pipe outlet is node 2, the mass flow is m₂, and the pressure is P₂; substituted into Formulas (5) and (6), we can obtain the node 1 and node 2 pressure difference and the mass flow rate of the linear system of equations as [42]:

$$\left\{\begin{array}{l}{\mathrm{m}}_1=\frac{2\mathsf{\rho }{\mathrm{A}}^2}{\mathsf{\mu }\left|{\mathrm{m}}_1\right|}\left({\mathrm{P}}_2-{\mathrm{P}}_1\right)\\ {\mathrm{m}}_2=\frac{2\mathsf{\rho }{\mathrm{A}}^2}{\mathsf{\mu }\left|{\mathrm{m}}_2\right|}\left({\mathrm{P}}_1-{\mathrm{P}}_2\right)\end{array}\right.$$

(7)

where µ is the pressure loss coefficient; ρ is the density of flow; and A is the cross-sectional area (between the two nodes, the pipe cross-sectional area is constant).

It is further obtained that [42]:

$$\left\{\begin{array}{l}{\mathrm{m}}_1=-\frac{2\mathsf{\rho }{\mathrm{A}}^2}{\mathsf{\mu }\left|{\mathrm{m}}_1\right|}{\mathrm{P}}_1+\frac{2\mathsf{\rho }{\mathrm{A}}^2}{\mathsf{\mu }\left|{\mathrm{m}}_1\right|}{\mathrm{P}}_2\\ {\mathrm{m}}_2=\frac{2\mathsf{\rho }{\mathrm{A}}^2}{\mathsf{\mu }\left|{\mathrm{m}}_2\right|}{\mathrm{P}}_1-\frac{2\mathsf{\rho }{\mathrm{A}}^2}{\mathsf{\mu }\left|{\mathrm{m}}_1\right|}{\mathrm{P}}_2\end{array}\right.$$

(8)

where µ is the pressure loss coefficient; ρ is the density of flow; and A is the cross-sectional area (between the two nodes, the pipe cross-sectional area is constant).

It is also known from continuity that m₁ = m₂ and, thus, the system of linear equations is [42]:

$$\left\{\begin{array}{l}{\mathrm{m}}_1={\mathrm{A}}_1{\mathrm{P}}_1+{\mathrm{A}}_2{\mathrm{P}}_2+{\mathrm{B}}_1\\ {\mathrm{m}}_2={\mathrm{A}}_3{\mathrm{P}}_1+{\mathrm{A}}_4{\mathrm{P}}_2+{\mathrm{B}}_2\end{array}\right.$$

(9)

where ${\mathrm{A}}_1=-\frac{2\mathsf{\rho }{\mathrm{A}}^2}{\mathsf{\mu }\left|{\mathrm{m}}_1\right|}$, ${\mathrm{A}}_2=\frac{2\mathsf{\rho }{\mathrm{A}}^2}{\mathsf{\mu }\left|{\mathrm{m}}_1\right|}=-{\mathrm{A}}_1$, ${\mathrm{A}}_3=\frac{2\mathsf{\rho }{\mathrm{A}}^2}{\mathsf{\mu }\left|{\mathrm{m}}_2\right|}=-{\mathrm{A}}_1$, ${\mathrm{A}}_4=\frac{2\mathsf{\rho }{\mathrm{A}}^2}{\mathsf{\mu }\left|{\mathrm{m}}_2\right|}={\mathrm{A}}_1$, and ${\mathrm{B}}_1={\mathrm{B}}_2=0$.

For any one node, n, in the fluid network, it should satisfy [42]:

$${\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{m}}_{\mathrm{i}}}={\mathrm{Q}}_{\mathrm{n}}$$

(10)

where m_i is the flow rate of node i into node n, ${\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{N}}}$ is the sum of all N nodes that have traffic input to node n, and Q_n is the total flow of the input node, n.

The system of the total linear equations of the fluid network can be established by associating all of the nodes accordingly.

2.4. Experimental Platform

The experimental test in this paper was conducted on a high-precision hydraulic machinery test bench at the Key Laboratory of Hydraulic Power Engineering in Jiangsu Province. The test bench was a closed cycle system with a combined uncertainty of ±0.39%. The test rig used a differential pressure transmitter to measure the head. The model was EJA 110 A, the measuring range was 0–200 kPa, and the calibration accuracy was ±0.1%. The flow rate was measured by an electromagnetic flowmeter, model E-mag type, range DN400 mm, with a calibration accuracy of ±0.20%. The torque was measured by speed and torque sensors. The model was ZJ, the range was within 200 N·m, and the calibration accuracy was ±0.15%. Figure 3 shows a schematic diagram of the high-precision hydro-mechanical test bench. Figure 4 shows a physical diagram of the pump hydraulic model. Figure 5 shows a physical diagram of the pump performance test.

3. Simulation Model’s Construction and Validation

3.1. Simulation Model’s Construction

This paper builds a simulation model based on Flowmaster software. Figure 6 shows a schematic diagram of the LAPS simulation model.

Table 2. Simulation component name.

Serial Number	Real Physical Model	Components of Simulation Model	Transient Simulation Implementation Method
1	Inlet channel	Flow resistance components and rigid pipes	-
2	Pump	Axial flow pump	Pump speed controller
3	Outlet channel	Flow resistance components and rigid pipes	-
4	Overflow hole	Rigid pipes and check valve	-
5	Rapid-drop gate	Sluice	Gate controller
6	Flap valve	Clapper	-

shows the names of the components representing the LAPS components. The component 1 pipe length was taken from the centerline length of the model’s inlet pipe, which was 10.62 m. The inlet channel from the inlet to the outlet uniformly took 25 sections and the weighted average of 25 sections for the diameter of the pipe for component 1, which was 2.82 m. The component 2 pipe length was taken from the centerline length of the model’s outlet pipe, which was 23.87 m. The outlet channel from the inlet to the outlet uniformly took 25 sections and the weighted average of 25 sections for the diameter of the pipe for component 2, which was 2.87 m. After the independence test of the calculation time step, 0.0025 s was selected as the time step of the transient calculation, and the total calculation time was 250 s.

3.2. Simulation Model’s Validation

In order to verify the feasibility of the numerical strategy and the accuracy of the simulation results, a LAPS was constructed for this paper. The model experiment text chart is shown in Figure 7.

Figure 8 shows a comparison of the experimental results and simulation results. From Figure 8a, it can be seen that the change trend of the energy characteristic curve obtained by the numerical simulation and experiment was basically the same, and the head and shaft power obtained by the numerical simulation and experiment under different flow conditions were relatively close. From Figure 8b, it can be seen that the change trend of the runaway speed obtained by the numerical simulation and experiment with the upstream and downstream water level difference was exactly the same, and the runaway speed obtained by the numerical simulation and experiment under the upstream and downstream water level difference was basically the same.

It can be seen from Figure 9a that as the difference in the water levels between the upstream and downstream increased, the error of the runaway speed obtained by the numerical simulation gradually decreased. When the upstream and downstream water level difference was greater than 5 m, the error of the numerical simulation was less than 2%. In general, the error of the runaway speed obtained by the numerical simulation did not exceed 6.3% under the different flow conditions. It can be seen from Figure 9b that when 11 m³·s⁻¹ < Q < 12 m³·s⁻¹, the error of the head between the numerical simulation and experiment was small. When 12 m³·s⁻¹ < Q < 13 m³·s⁻¹, the error of the shaft power obtained by the numerical simulation and experiment was small. In general, under the different flow conditions, the error of the head and shaft power obtained by the numerical simulation was less than 6.5%.

4. Results and Discussion

4.1. The Effect of an Uncontrolled Gate on the Shutdown Transition Process of the LAPS

In order to explore the characteristics of the LAPS power-off transition process when the gate is out of control (GOOC), in this section, the LAPS power-off transition process simulation for five different upstream and downstream water level differences was conducted. The five different upstream and downstream water level differences were 1.35, 2.35, 3.35, 4.35, and 5.35 m. Of which, 5.35 m was the maximum net head of the LAPS. It should be noted that all analyses of the LAPS’s parameters in Section 4 were in the dimensionless form (i.e., the parameters were divided by the design parameters of the LAPS).

Figure 10 shows the variation of the flow and head with time after that the LAPS was powered off when the GOOC. The following conclusions can be drawn from Figure 10. First, after the power failure of the LAPS, if the gates could not be closed due to the GOOC, the flow of the LAPS rapidly reduced. Over a short period of time, the LAPS experienced the phenomenon of the backflow of water, and the backflow after gradually increasing to a certain value tended to stabilize. Secondly, when the GOOC, the speed of the pump decreased rapidly after the LAPS was powered off. Due to the impact of the backflow water in the LAPS on the impeller, the impeller began to reverse after falling to a speed of zero. Meanwhile, the reverse rotation speed gradually increased and stabilized after increasing to a certain value. Thirdly, when the GOOC and the LAPS were powered off, the overall variation of the flow and rotational speeds under a different net head was basically the same. However, the specific values of the falling speed and the speed and flow rate after stabilization were different.

Figure 11 shows the maximum backflow value (MBV) and RS of the LAPS after a power failure when the GOOC. The following conclusions can be drawn from Figure 11. First, as the net head increased, the MBV of the LAPS after a power failure also gradually increased. At the same time, the speed of the backflow of water in the pump gradually accelerated; there was a 1.35 m net head under the power failure, the MBV in the LAPS was 0.78Q_r, and the length of time required to reach the MBV was 88.20 s. There was a 5.35 m net head under the power failure, and the MBV in the LAPS was 1.68Q_r, and the length of time required to reach the MBV was 35.40 s. Second, the variation pattern of the RS and the MBV was basically the same. With an increasing net head, the RS of the pump increased gradually after the LAPS was powered off. At the same time, the speed of the pump from the forward to the reverse state gradually accelerated, and there was a 1.35 m net head power failure, the RS of the LAPS was 0.63n_r, and the length of time required for the pump to reach the runaway state was 84.63 s. There was a 5.35 m net head power failure, the RS of the LAPS was 1.45n_r, and the length of time required for the pump to reach the runaway state was 37.83 s.

Figure 12 shows the variation of the key characteristic parameters (KCPs) with time after the power failure of the LAPS at a net head of 5.35 m when the GOOC. It can be seen from Figure 13 that in the case of the GOOC, after the power failure of the LAPS, with the rapid backflow of water and pump reversal, the shaft power of the LAPS, impeller torque, and other parameters also changed rapidly. The impeller torque and shaft power had a short climb after a rapid decline, followed by a rapid decline. When the LAPS reached a stable runaway state, the impeller torque and shaft power of the LAPS gradually approached zero and remained stable.

4.2. Influence of the Gate Closing Speed on the LAPS Shutdown Transient Process

From Section 4.1, it can be seen that the power failure at a 5.35 m maximum net head was the most unfavorable situation for the LAPS power-off transition process. This section took the maximum net head of 5.35 m as the calculation boundary. According to the design code of the LAPS, five different lengths of the total time of gate closing (TTGC) were designed, which were 30, 60, 90, 120, and 150 s, respectively (the corresponding gate closing speeds were 5.00, 2.50, 1.67, 1.25, and 1.00 m/min). Exploring the impact of the gate closing speed on the LAPS shutdown transition process, it should be noted that the moment when the gates started to close in this section was synchronized with the power failure of the unit.

Figure 13 shows the variation of the flow rate and rotational speed with time at different gate closing speeds. Figure 14 shows the flow at the flap valve and the overflow hole at the different gate closing speeds. The following conclusions can be drawn from Figure 13 and Figure 14. First, no matter what closing speed the gate took, the flow rate at the flap valve and overflow hole was zero during the shutdown process. This shows that after the unit was powered off, if the gate was closed synchronously, the flap valve and the overflow hole did not play a role in the shutdown process and did not affect the shutdown characteristics of the LAPS. This shows that after the power failure of the unit, if the gate was closed synchronously, neither the flap valve nor the overflow hole played any role in the shutdown process, and this did not affect the LAPS’s stopping characteristics. Second, the slower the gate closed, the longer the LAPS continued to flow backwards and the longer the pump reversed the length of time. Third, the trend of the pump speed and the trend of the backflow were very similar at the different gate closing speeds. This shows that the backflow in the LAPS was the dominant factor in the pump reversal.

Figure 15 shows the MBV of the LAPS and the MRS of the pump at different gate closing speeds. The following conclusions can be drawn from Figure 15. First, the slower the gate closed, the larger the MBV of the water in the LAPS, but it eventually stabilized. The MBV of the LAPS was 1.63Q_r when the 30 s duration shutdown scheme was adopted. The MBV of the LAPS was 1.67Q_r when the 60 s duration shutdown scheme was adopted. The MBV of the LAPS was 1.68Q_r when the 150 s duration shutdown scheme was adopted. Second, at the beginning of the gradual decrease in the gate closing speed, the length of time taken for the water flow to plummet to the MBV increased significantly. With the further slowing down of the gate closing speed, the length of time taken for the water to reach the MBV tended to stabilize. When the 30 s duration closing scheme was adopted, the length of time to reach the MBV was 18.48 s. The length of time increased to 24.5 s when the 60 s duration closing scheme was adopted. The length of time increased to 30.8 s when the 150 s duration closing scheme was adopted. Third, at different gate closing speeds, the change trend of the MRS of the pump was very similar to that of the MBV. This shows that the MRS that the pump could reach was closely related to the MBV in the LAPS. When the 30 s duration closing scheme was adopted, the MRS of the pump was 1.40n_r, and it was 0.05n_r away from the RS of the pump. When the 150 s duration closing scheme was adopted, the MRS of the pump was 1.45n_r; it was the same as the RS of the pump. It should be noted that the conclusions of the correlation between the gate closure speed and MBV obtained in this section were consistent with those of Song and Zhou et al. [27,30].

4.3. The Effect of Closing the Rapid-Drop Gate Early on the Shutdown Transition Process of the LAPS

According to the LAPS’s design specifications, the closing speed of the rapid-drop gate of the LAPS was required to be less than 5 m/min. It can be found from Section 4.2 that if the gate closed synchronously with the motor, water backflow inevitably occurred inside the LAPS, and the impact of the backflow of the water during the shutdown process of the LAPS posed a great threat to the safety of the pump blades.

In order to determine the measures to reduce the extent of the water backflow during the shutdown process, the total gate closing times of 60 s and 120 s were used as an example to study the effect of closing the gate in advance by different degrees on the transition process of the power failure of the LAPS in this section (gate closing in advance of the unit power failure; that is, the LAPS started to close the gate under normal operation), including preclosing 25%, 50%, 75%, and 100% of the gates.

Figure 16 shows the variation of the flow rate and rotational speed with time when the different gate closing schemes were adopted (TTGC: 60s). Figure 17 shows the flow rate and the flow rate at the overflow hole at the different gate closing schemes in advance (TTGC: 60 s). The following conclusions can be drawn from Figure 16 and Figure 17. First, because the gate closed ahead of the unit power failure, when the LAPS was operating normally, the gate began to gradually close. This also allowed the flap valve and the overflow hole to start working during the shutdown process and to take on the role of shunting. This effectively reduced the surge in the head and power caused by the closing of the gate during the normal operation of the LAPS. In this process, the flap valve undertook the main diversionary role, and the overflow hole had a weaker diversion capacity. When taking a preclosing of 75% of the gate, the maximum diversion flow at the clapper gate was 0.12Q_r, and the maximum diversion flow at the overflow hole was 0Q_r. When taking a preclosing of 100% of the gate, the maximum diversion flow at the clapper gate was 0.61Q_r, and the maximum diversion flow at the overflow hole was 0.20Q_r. Second, compared with the shutdown method of synchronizing the gate with the unit power failure, the shutdown method of closing the gate in advance could effectively reduce the MBV of the system and the duration of the backflow. At the same time, it also effectively reduced the MRS and duration of the pump reversal.

Figure 18 shows the statistics of the KCPs of the LAPS when the different gate advance closing schemes were adopted (TTGC: 60 s). The following conclusions can be drawn from Figure 18.

First, the MRS of the pump was influenced by the preclosing of the gate very similarly to the MBV influenced by the preclosing of the gate. The higher the degree of preclosing of the gate, the smaller the MBV and the MRS of the pump during the LAPS shutdown process. Moreover, as the degree of the gate preclosing gradually increased, the tendency of the MBV and the MRS of the pump during shutdown decreased faster.

Second, when the shutdown scheme of preclosing 25% of the gate was adopted, the MBV in the LAPS was 1.64Q_r, and the length of time required to reach the MBV was 20.58 s. Compared to the shutdown scenario where the gate closure was synchronized with the unit power failure, the MBV and the length of time required to reach the MBV were reduced by 14.31% and 0.80%. When the shutdown scheme of preclosing 100% of the gate was adopted, the MBV in the LAPS was 0.06Q_r, and the length of time required to reach the MBV was 2.55 s. The MBV was reduced by 96.31%, and the length of time required to reach the MBV was reduced by 89.59%.

Third, when the shutdown scheme of preclosing 25% of the gate was adopted, the MRS in the LAPS was 1.41n_r, and the length of time required to reach the MRS was 21.95 s. Compared to a shutdown scenario where the gate closure was synchronized with the unit power failure, the MRS and the length of time required to reach the MRS were reduced by 1.93% and 14.76%. When the shutdown scheme of preclosing of the gate by 100% was adopted, the MRS of the pump was 0 and the MRS was reduced by 100%.

Fourth, when the shutdown plan of an early gate closure was adopted, the water flow at the outlet of the LAPS was squeezed, causing a surge in the head and power of the LAPS in normal operation. As the degree of the gate preclosing gradually increased, the head and shaft power of the LAPS also gradually increased, and the trend of increasing the head and shaft power of the LAPS also gradually accelerated. When the shutdown scenario with a 25% gate preclosing was adopted, the maximum head and maximum power were 1.21H_r and 1.06P_r, an increase of 0.1% and 0.05%, respectively. When the shutdown scenario with a 100% gate preclosing was adopted, the maximum head and maximum power were 1.33H_r and 1.11Pr, an increase of 10.36% and 5.05%, respectively.

Figure 19 shows a comparison of the changes in the KPCs of the LAPS when the gate was closed synchronously or in advance (TTGC: 60 s). The following conclusions can be drawn from Figure 19. First, if the pump shutdown method of the gate closure synchronized with the unit power failure was adopted, the KCPs of the LAPS showed more dramatic fluctuations during the shutdown transition. As the pump lost power after the power failure, and the gate was still in the process of a slow descent, the water flow from the upstream reservoir backed up from the gate into the LAPS. This caused the LAPS flow to drop rapidly to the MBV, and the pump, therefore, was in reverse rotation. The characteristic parameters such as the power and impeller torque were affected by the impact of the backflow, showing a trend of a fluctuating decline first and then rebound. When the gate was completely closed, the backflow in the system was cut off, and the characteristic parameters of the LAPS were forced to move closer to the 0 value. Second, if the pump stop method of preclosing 100% of the gate was adopted, the water backflow and pump reversals during the shutdown were completely eliminated. This obviously improved the phenomenon of the severe fluctuation of the KCPs of the LAPS during the shutdown transition process. As the LAPS was in normal operation when the gate began to slowly close, the water flow at the outlet of the LAPS was squeezed, and the flow rate of the LAPS gradually decreased. This also caused a surge in the head and shaft power of the LAPS. At this time, the flap valve and overflow hole began to work, and the drop in the LAPS flow rate, head, and shaft power surge did not appear to cause serious deterioration. When t = 60 s, the unit was in a power failure, and the gate was completely closed. At this time, the backflow in the system was completely cut off, the KCPs of the LAPS dropped rapidly to zero, and the unit was not affected by the impact of the backflow.

In order to further verify the effectiveness of the shutdown method of closing of the gate in advance at different gate closing speeds, the power-off transition process of the LAPS when the TTGC was 120 s was further simulated. Figure 20 shows the variation law of the flow rate and speed with time when the different gate advance closing schemes were adopted (TTGC: 120 s). Figure 21 shows the flow at the flap valve and the overflow hole when the different gate advance closing schemes were adopted (TTGC: 120 s). Figure 22 shows the statistics of the KCPs of the LAPS when the different gate advance closing schemes were adopted (TTGC: 120 s). The following conclusions can be drawn.

First, when the total length of time of the fast gate closing was adjusted to 120 s, the flow rate, rotational speed, and other parameters that changed in the process of closing the rapid-drop gate in advance were basically the same as when the TTGC was 60 s. This shows that under the different gate closing speeds, the effects of closing the gate in advance on the transient process of the LAPS were similar.

Second, when the shutdown scheme of preclosing 25% of the gate was adopted, the MBV in the LAPS was 1.66Q_r, and the time required to reach the MBV was 25.3 s. Compared with the shutdown scheme of the gate closing synchronized with the unit power failure, the MBV and the length of time required to reach the MBV were reduced by 0.80% and 14.31%. When the shutdown scheme of preclosing 100% of the gate was adopted, the MBV in the LAPS was 0.06Q_r, and the time required to reach the MBV was 2.55 s. Compared with the shutdown scheme of the gate closing synchronized with the unit power failure, the MBV was reduced by 96.30%, and the length of time required to reach the MBV was reduced by 91.36%.

Third, when the shutdown scheme of preclosing 25% of the gate was adopted, the MRS in the LAPS was 1.44nr, and the length of time required to reach the MRS was 26.7 s. Compared with the shutdown scheme of the gate closing synchronized with the unit power failure, the MRS and the length of time required to reach the MRS were reduced by 0.82% and 13.59%. When the shutdown scheme of closing the gate 100% in advance was adopted, the MRS of the pump was 0, and the MRS was reduced by 100%.

Forth, the maximum head and maximum power of the LAPS during the shutdown process were 1.21H_r and 1.06P_r, an increase of 0.11% and 0.05%, respectively, when the shutdown scheme of preclosing 25% of the gate was adopted. When the shutdown scheme of preclosing 100% of the gate was adopted, the maximum head and maximum power were 1.34H_r and 1.11P_r, which are increases of 10.65% and 5.19% respectively.

Figure 23 shows a comparison of the KCPs of the LAPS with synchronous or premature gate closing (TTGC: 120 s). The following conclusions can be drawn from Figure 23. First, when the total time of the fast gate closing was adjusted to 120 s, if the pump stopping scheme of the synchronous closing of the gate and motor was adopted, the change of each KCP of the LAPS was similar to that when the TTGC was 60 s. There was a serious backflow of water, and the pump was in a reverse rotation for a long time. Second, adopting the stopping method of closing 100% of the gate in advance was still effective when the TTGC was 120 s, which completely eliminated the backflow of water and pump reversal during the shutdown process and significantly improved the phenomenon of the dramatic fluctuations in the KCPs of the LAPS during the shutdown transition process. However, it was similar to the case when the TTGC was 60 that the head and shaft power of the LAPS increased to a certain extent.

5. Conclusions

• After the power failure of the unit, if the gate could not be closed due to the GGOC, with the increase in the net head, the MBV and the RS of the LAPS after the power failure gradually increased. The backflow rate of the water and the length of time required for the pump to reach the runaway state gradually decreased. When the LAPS was in a power failure at the maximum net head of 5.35 m, the MBV in the LAPS was 1.68Q_r, and the length of time required for the water flow to reach the MBV was 44.08 s. The RS of the LAPS was 1.45Q_r, and the length of time required for the pump to reach the runaway state was 37.83 s.
• After the power failure of the unit, if the gate was closed simultaneously, the flap valve and overflow hole would not work during the shutdown process. The slower the gate closed, the larger the MBV of the LAPS and the MRS of the LAPS, eventually stabilizing. At the same time, the slower the gate closed, the longer the water stayed backed up, and the longer the pump reversed. When a 30 s shutdown scheme was adopted, the MBV during the shutdown process was 1.63Q_r. When the 60 s long shutdown scheme was adopted, the MBV during the shutdown process was 1.67Q_r, an increase of 2.45%. When the 150 s long closing scheme was adopted, the MBV during the shutdown process reached 1.68Q_r, an increase of 3.07%.
• The shutdown method of closing the gate in advance could significantly improve the violent fluctuation of the KCPs of the LAPS during the shutdown transition and effectively reduced the backflow flow and the reverse speed of the pump during the shutdown process. Taking the total gate closing time of 120 s as an example, when the 25% gate was closed in advance, the MBV and MRS during the shutdown process were reduced by 14.31% and 1.93%. The MBV and MRS were reduced by 96.31% and 100% during the shutdown process when the 100% gate was closed in advance.
• The early closing of the gate will lead to a reduction in the over-flow capacity at the gate, causing a surge in the head and shaft power of the LAPS. If the shutdown method of closing the gate in advance is to be adopted to improve the quality of the shutdown transition process of the LAPS, and the LAPS should be required to be equipped with a flap valve and an overflow hole. If the LAPS is not equipped with flap valves and overflow holes, it can be very dangerous to take the shutdown method of an early gate closure. This can easily cause the motor power to overload or the LAPS to fall into the saddle area of the flow during operation.

In this paper, a scientific control strategy between the unit power outage and the gate closing law was taken, and it revealed the variation law of the KCPs during the LAPS shutdown process under different gate opening and closing laws. The conclusion of the correlation between the gate closing speed and MBV is consistent with the conclusion of Song and Zhou et al. [27,30]. In the future research, more three-dimensional flow analyses will be carried out on the LAPS shutdown process with a gate cutoff based on three-dimensional numerical simulations to reveal the hydraulic transient flow characteristics.