Shape optimization of the spillway approach channel of Baleh Hydropower Project based on numerical simulation

Baleh Hydropower Project has a protruding headland between the spillway inlet and the power intake structure. Based on the results of the model tests, the velocity gradient near the protruding headland under high flow conditions is large and an unstable vortex occurs. To address the unfavorable flow problems of the original spillway approach channel, this paper simulates the original spillway approach channel using a three-dimensional turbulence numerical model and verifies it with the model tests, and provides numerical simulation results for two optimized cases: excavation and backfilling. The calculation results show that both backfilling and excavation optimization cases improve the right side flow pattern, the unstable vortex disappears, and the flow between the approach channel and the spillway inlet is smoother than the original design. Comparing the two optimized cases, the average flow velocity in the upstream section of the approach channel of the excavation case is reduced, but the flow velocity near the right bank of the approach channel close to the spillway gate bay inlet becomes larger, and the average flow velocity of the excavation modified case is more unevenly distributed.


Introduction
Baleh Hydropower Project is located on the Baleh River in Kapit Division, Sarawak Province, Malaysia, about 3km upstream of the junction with Putai River and 95km upstream of the junction with Rajan River.The main civil works consist of water retaining structure (concrete faced rockfill dam), flood discharge structure (spillway, water diversion structure, intake and penstock), ecological water release structure (low-level operation tunnel), etc.The spillway is composed of approach channel section, gate chamber section, discharge chute section, and deflecting flow section.
According to the project situation, the hydraulic model was established, and the hydraulic measurement work has been carried out, as seen in Figure 1.Based on the results of the model test, under certain flow conditions with large flow rate, the headland nose located between the entrance to the spillway approach channel and the power intake structures causes the flow patterns to break and eddy around the nose into the approach channel.Schematic plan of original approach channel outline as seen in Figure 2. The unfavorable flow pattern of the approach channel is shown in Figure 3. Responding to the results of the model test, additional study should be conducted on the original approach channel design and the revised design for optimizing the outline of the right bank.The optimized cases contain backfilling case and excavation case for obtaining a more stable water inflow.One revised case is to backfill the front of the protruding headland between the approach channel inlet and the power intake structure.The other one is to excavate along the right side of the approach channel to the power intake.The schematic plan of revised approach channel outline is shown in Figure 4.With the rapid development of computers, some of the more difficult and complex problems in fluid mechanics can be further solved [1].Numerical simulations are relatively less expensive than model tests, and they have great advantages when multiple solutions and conditions are needed in the study.Bayon,et al. used k-ε turbulent flow model and volume of fluid method to simulate the gas doping and cavitation characteristics of the spillway of Jinping first stage hydropower station [2].It was found that the dopant cavity and the dopant concentration increased with the increase of the slope of the dopant can, and the dopant concentration decreased along the course and stabilized after a certain distance.Jinwei Du, Junxing Wang, et al. used the RNG k-ε turbulent flow model to simulate the hydraulic characteristics of the Yang Sheng Guan step spillway [3], and found that there is a good linear relationship between the energy dissipation rate and the number of steps, and the turbulent kinetic energy and turbulent energy dissipation rate increase gradually in the downstream direction, and finally a uniform slip flow is formed and both reach the maximum.Xin Guo and Hongwei Xie used the RNG kε turbulent flow model combined with the VOF method of free-tracking water surface to perform 3D numerical simulation of the step spillway stage [4], and found that the numerical simulation values agree well with the experimental values, indicating that the VOF method of free-tracking water surface is suitable for the simulation calculation of the step spillway water flow.Therefore, this paper uses the numerical simulation method of turbulent flow to simulate the hydraulic characteristics of the spillway approach channel of Baleh hydropower project.
In the paper, a three-dimensional turbulence numerical model of the spillway approach channel is established, and the original case is firstly simulated and compared with the model test results to verify the rationality of the numerical model, and then the calculation and analysis of the spillway approach channel body shape optimization case is carried out through numerical simulation and compared with the original case to provide strong support for the engineering optimization design.

Turbulence Model
Currently, CFD technology has undergone relatively mature development [5].With CFD tools, the 3-D unconstant flow field for the water flow can be obtained relatively accurately.Among the CFD tools, the k-ε double-equation turbulence model is widely used.The RNG k-ε double-equation turbulence model was proposed by Yakhot and Orzag in 1986, and its basic idea is using the renormalization group theory to correct the k-ε turbulence model.A large number of numerical simulation results show that the RNG k-ε model is more effective in dealing with the flow with a high strain rate and a large degree of flow line bending [6].In the k-ε model, equation k and equation ε are as follows: k equation: Where: Where, k is the turbulent energy, ε is the turbulent dissipation ratio, μ eff is the effective viscosity coefficient, μ is the kinetic viscosity of fluid, μ t is the turbulent motion viscosity, k  and   are the effective Prandtl numbers, G k is the turbulent energy k production caused by the mean velocity gradient, and E ij is the time average strain rate.The model constants used in the RNG k-ε model are as follows: .39, 0  =4.377, and β=0.012.

Establishment of 3-D Model
According to the prototype size, a three-dimensional geometric model of the original spillway approach channel is established, as shown in Figure 5.The three-dimensional model of backfilling approach channel design is shown in Figure 6, and the three-dimensional model of excavation approach channel design is shown in Figure 7.

parameter setting
In this paper, the RNG k-ε turbulent flow model combined with the VOF method is chosen to numerically simulate the hydraulic characteristics of the spillway approach channel of Baleh hydroelectric project.In order to accelerate the calculation and ensure the accuracy of simulation calculation, a block-structured grid is adopted for grid division, and the grid near the overflow surface is encrypted with a grid size of 0.5~3.0 m.The CVFEM method is used to discretize the control equations, which has high numerical accuracy and numerical stability [7]; the PISO method, which has better convergence to transients, is chosen to calculate the coupled pressure and velocity fields [8], and PRESTO! is selected to calculate the pressure equations, and the standard wall function method is used to deal with the flow in the near-wall area.
In setting the boundary conditions, the approach channel's inlet and downstream outlet are set as pressure inlet and outlet according to the upstream and downstream water levels; the boundary above the approach channel is set as pressure inlet, and the pressure value is atmospheric pressure; other boundaries are set as no-slip solid wall boundaries [9].The relative stability solution is calculated by simulating the constant flow field using non-constant flow with a time step of 0.01 s.The flow is considered stable when the ratio of the difference between the inlet and outlet flow rates and the inlet flow rate is less than 0.1%, and the calculation is stopped.
The numerical simulation take the same case to the test, i.e. 1:10000 AEP case and PMF AEP case for two high flow conditions.The flow velocity measuring sections of the upstream approach channel are shown in Figure 8.

Numerical Simulation of Original Approach Channel Design
Figures 9 and 10 show the numerical simulation results of original approach channel design.Table 1 shows the average velocity of section in original approach channel design.As can be seen from the table and figures, the closer the distance is to the gate pier, the greater the velocity is in the upstream approach channel.For the cross section of the same chainage, the flow velocity on the right side of the approach channel is slightly greater than that on the left side.Near the protruding headland between the spillway inlet and the power intake structure, the velocity gradient is large and unstable vortex occurs.The measured value from the CS1-CS4 section average velocity model is close to the numerical simulation calculated value.The numerical simulation results are basically consistent with the physical model test results.

Numerical Simulation for Backfilling Approach Channel Design
Figures 11 and 12 show the numerical simulation results of backfilling approach channel design.Table 2 and 3 show the section flow velocity comparison between the original design and backfilling revised design under high flow conditions.As can be seen from the tables and figures, after the outline of the right bank of the approach channel is backfilled, the average flow velocity in the approach channel is almost same, the flow pattern on the right side is improved, the unstable vortex disappears, and the flow between the approach channel and the spillway inlet is smoother.show the numerical simulation results of excavation approach channel design.Table 4 and 5 show the section flow velocity comparison between the original design and excavation revised design under high flow conditions.As can be seen from the tables and figures, after the outline of the right bank of the approach channel is excavated, the flow pattern on the right side is improved, the unstable vortex disappears, and the flow between the approach channel and the spillway inlet is smoother.
Comparing the backfilling revised case and excavation revised case, the average flow velocity in the upstream section of the approach channel between sections CS1 and CS3 of excavation revised case is decreased, so the flow in sections CS1-CS3 of excavation revised case is smoother than that of backfilling revised case.However, close to the spillway gate bay inlet (section CS4), the flow velocity near the right bank of the approach channel under excavation revised case becomes larger, and the average flow velocity of excavation revised case is more unevenly distributed.

Conclusion
The optimized design of backfilling and excavation of the right bank profile of the spillway approach channel proved to improve its flow regime.This change is valued in the following areas: (1) According to the numerical simulation results of spillway approach channel of original design in 1:10000 AEP flood and PMF, near the protruding headland between the spillway inlet and the power intake structure, the velocity gradient is large and unstable vortex occurs.The numerical simulation results are basically consistent with the physical model test results.
(2) The outline of the right bank of the approach channel is optimized and designed by both backfilling and excavation cases.To the backfilling and excavation cases, the numerical simulation results show that the flow pattern on the right side is improved, the unstable vortex disappears, and the flow between the approach channel and the spillway inlet is smoother than the original design.
(3) Comparing the backfilling revised case and excavation revised case, the average flow velocity in the upstream section of approach channel between section CS1 and CS3 of excavation revised case is decreased, so the flow in section CS1-CS3 of excavation revised case is smoother than that of backfilling revised case.However, close to the spillway gate bay inlet (section CS4), the flow velocity near the right bank of the approach channel under excavation revised case becomes larger, and the average flow velocity of excavation revised case is more unevenly distributed.

Figure 4 .
Figure 4. Schematic Plan of Revised Approach Channel Outline

Figure 8 .
Figure 8. Flow Velocity Measuring Sections of the Approach Channel

Table 1 .
Average Velocity of Section in Original Approach Channel Design (Unit: m/s)

Table 2 .
Section Flow Velocity Comparison between the Original Design and Backfilling Revised Design under 1:10,000 AEP Flood (unit: m/s)

Table 3 .
Section Flow Velocity Comparison between the Original Design and Backfilling Revised Design under PMF (unit: m/s)

Table 4 .
Section Flow Velocity Comparison between the Original Design and Excavation RevisedDesign under 1:10,000 AEP Flood (unit: m/s)

Table 5 .
Section Flow Velocity Comparison between the Original Design and Backfilling Revised Design under PMF (unit: m/s)