Evaluation of the prototype performance of Wanjiazhai Francis turbine with flow pattern analysis

Multiple Francis turbines are installed in Wanjiazhai water conservancy project to generate electricity, and the operating conditions of the units vary greatly. Because the unit head itself is not high, and the parameters such as head, flow and output vary widely, the operation of the unit becomes very complex. Aiming at this problem, this study predicts and analyzes different typical operating conditions during the operation of the unit, and compares them with the field measured results. The analysis of Prototype unit helps us understand the actual flow state inside the unit and observe the possible complex flow phenomenon. Therefore, the distribution of vortices inside the unit is analyzed in depth, and the flow structures inside the volute, stay vane, guide vane, runner and draft tube are compared to serve the safe and stable operation.


Introduction
With the massive use of fossil energy, global carbon dioxide levels have risen, leading to massive glacial melting and rising sea levels, with the risk of inundating land [1][2].There is therefore an urgent need for a green and clean energy source to come in and reduce the consumption of fossil energy [3][4].Pumped storage technology is a new technology for efficient power generation and stable operation [5][6][7].As the core component of pumped storage technology, the hydraulic turbine plays a crucial role.Therefore, it needs to be analyzed and studied for the stable operation of the turbine.
In this paper, we focus on the flow of water in the Wanjiazhai Francis turbine under three typical operating conditions: prohibited operation zone, turbulent operation zone and stable operation zone [8].Numerical simulations based on CFD are carried out for the Wanjiazhai Francis turbine, and the analysis is based on the obtained basin flow lines to reveal the movement of the water body inside the turbine [9][10].Based on the analysis results, problem areas affecting the efficient operation of the turbine can be identified, so that the design can be optimized to improve the stability and efficiency of the turbine.Such CFD-based simulation methods can save time and economic costs and help to solve engineering problems to a certain extent.

Hydro-turbine Parameters
The object of study in this paper is a mixed-flow turbine unit.The fluid medium flows into the turbine from the inlet snail casing, passes through the stay guide vane and the guide vane into the runner and then out of the draft tube.The number of guide and stay vanes is 24, and the number of runner blades is 13.The draft tube is divided into a straight section and a curved elbow section.This paper focuses on the flow field of the turbine under three operating conditions, namely, the guide vane opening of 12 degrees and 50m head.The guide vane opening is 12 degrees at 68m head, and the guide vane opening is 14 degrees at 68m head.mesh-independence check.We have prepared three sets of grids with different number of grid nodes, coarse(N1=7042620), medium(N2=275.3686),fine(N3=1110522).Irrelevance analysis is carried out for the three sets of grid schemes, and the details of the independence check results are shown in figure 3. the refinement factor of medium and coarse is 1.3535, and the CI value is 0.0003%.the refinement factor of fine and medium is 1.3675, and the CI value is 0.039%, which all satisfy the convergence requirements, and all the three sets of grids have a better convergence, but the combined Considering the computational accuracy and the computational time cost, we finally choose the Fine mesh scheme as the final computational scheme, and the total number of nodes is 1110522.In addition, in this study, the wall y+ values of each overflow component are between 10-100, so that it is easier for the application of the wall function.

CFD Setup
With the development of fluid mechanics and numerical simulation techniques, the use of computational fluid dynamics (CFD) to simulate engineering problems as a way of reducing time and money costs has become a very popular approach, so this paper uses the flow field streamlines to evaluate the raw performance of the Wanjiazhai Francis turbine, which requires the following setup.
The fluid medium is chosen to be water at 25°C and the reference pressure is 1Atm.The SST k-w turbulence model is chosen because it can simulate the fluid motion in most engineering problems and has the advantage of fast convergence and high stability.the transport equations for the turbulent kinetic energy k and specific dissipation rate ω as: where ρ is the fluid density, P is the turbulence generation term, μ is the dynamic viscosity, μt is the eddy viscosity coefficient, σ is the model constant, Cω is the coefficient of turbulent dissipation term, F1 is the blending equation, k-ω is the scale of turbulence.
The turbine inlet is set as a pressure inlet boundary condition with a pressure value of 490,000 Pa (50m) and 666,400 Pa (68m).The turbine outlet is set as a pressure outlet boundary condition with a pressure value of -75 Pa and all walls are set as non-slip walls.A multi-reference system model is used, with the rotor set as the rotating reference system and the rest of the components set as the stationary reference system.The runner speed was set to 100 r/min.A general grid interface ( I) model was chosen for the data transfer between the different components.
The minimum iteration of the stabilization calculation is 300 steps and the maximum iteration is 1000 steps.The convergence criterion is that the root mean square residuals of the continuity and motion equations are less than 0.0001.

Experiment-Numerical Simulation Comparison
The results of the numerical simulations are shown in Table 1.Under the active guide vane opening of 12° and 68m head condition, the unit power is 59.666MW, the efficiency is 74.71% and the flow rate is 122.753kg/s.Under the guide vane opening of 24° and 68m head condition, the turbine power is 161.284MW, the efficiency is 91.97% and the flow rate is 264.796kg/s.264.796kg/s.
Comparing the numerical simulation results with the turbine performance operation diagram (see figure 2), it was found that the numerical simulation results were very close to the experimental results, so it was decided to use the CFD numerical simulation results to analyses the flow field of the Wanjiazhai turbine.

Flow Pattern
The three-dimensional basin flow lines of the turbine under three operating conditions are analyzed.In the forbidden operation area, the three-dimensional flow line of the turbine with the movable guide vane opening at 12° and a head of 50m is shown in figure 3. It can be seen from the figure that the water medium flows in uniformly from the worm shell inlet and subsequently enters the stay vane and guide vane around the worm shell flow path, and after entering the runner, the speed of the water is obviously accelerated during the rotation of the runner and subsequently flows out into the draft tube.As can be seen from the Fig. 3, the flow line at the exit of the runner clearly increases in speed and takes on a twisted shape with the direction of rotation of the runner.At the outlet of the draft tube, the presence of a vortex is clearly visible and the intensity of the vortex is not the same at both outlets.68m: head.In the stable operation zone, the three-dimensional flow line of the turbine with a guide vane opening of 24° and head of 68 m is shown in figure 5.The overall flow velocity of the water has slowed down, and during the rotating process of the runner, the velocity of the water is reduced by a factor of about one relative to the operating conditions in the forbidden operation zone.As can be seen from the diagram, there is no significant change in the trend of the flow line at the outlet of the turbine, which still shows a twist with the direction of rotation of the turbine.The flow line at the outlet of the draft tube is apparently relatively uniform and there is basically no vortex.

Conclusions
In this paper, numerical simulations based on CFD were carried out to solve the Wanjiazhai turbine, and by comparing the numerical simulation results with the experimental results, it was verified that the numerical simulation results were reliable.Therefore, the three-dimensional flow lines of the Wanjiazhai turbine are analyzed and the corresponding conclusions are obtained.Firstly, the three-dimensional flow line of the Wanjiazhai turbine in the forbidden operation zone (12°, 50m) is relatively uniform before the runner, then after the runner rotates and accelerates, it gradually distorts in the elbow section of the draft tube bend and forms a large number of vortices in the outlet section, and the intensity of the vortices in the two outlets is not the same.In the turbulent operating zone condition (12°, 68m), the flow velocity at the inlet of the runner increases significantly, approximately doubling, compared to the no-run zone.The flow line then distorts and vortices form at the draft tube outlet, with different vortex intensities at the two outlets.In the steady running zone (24°, 68m) the overall flow velocity slows down compared to the no-run zone, approximately doubling.No significant vortices were formed at the exit of the draft tube, and the flow lines were relatively uniform and stable at both exits.

Figure 1 .
Figure 1.3D model drawing of the turbine set.Figure2illustrates the 3D grid diagram of a Francis turbine.Considering that the number of meshes will have some impact on the computational accuracy and numerical simulation results, we need to perform a

Figure 2
Figure 1.3D model drawing of the turbine set.Figure2illustrates the 3D grid diagram of a Francis turbine.Considering that the number of meshes will have some impact on the computational accuracy and numerical simulation results, we need to perform a

Figure 2 .
Figure 2. Mesh diagram of 3D model of hydraulic turbine unit.

Figure 3 .
Figure 3. Mesh diagram of 3D model of hydraulic turbine unit.

Figure 4 .
Figure 4. turbine operation full characteristics diagram.Table 1. Head, power, efficiency and flow results for different operating conditions.

Figure 5 .
Figure 5. 3D flow diagram of the unit at 12deg-50m operating conditions.12deg:guide blade opening, 50m: head.The three-dimensional flow line of the turbine in the transient operation zone with a guide vane opening of 12° and a head of 68 m is shown in figure 4.During the rotation of the runner, the velocity of the water body increases by approximately double relative to that in the forbidden operation zone operating conditions.As can be seen from the diagram, the flowline trend at the runner outlet does not change significantly and still shows a torsional shape with the direction of runner rotation.At the outlet of the draft tube, the presence of a vortex is clearly visible and the intensity of the vortex increases to a certain extent.

Figure 6 .
Figure 6.3D flow diagram of the unit at 12deg-68m operating conditions.12deg:guide blade opening,68m: head.In the stable operation zone, the three-dimensional flow line of the turbine with a guide vane opening of 24° and head of 68 m is shown in figure5.The overall flow velocity of the water has slowed down, and during the rotating process of the runner, the velocity of the water is reduced by a factor of about one relative to the operating conditions in the forbidden operation zone.As can be seen from the diagram, there is no significant change in the trend of the flow line at the outlet of the turbine, which still shows a twist with the direction of rotation of the turbine.The flow line at the outlet of the draft tube is apparently relatively uniform and there is basically no vortex.

Table 1 .
Head, power, efficiency and flow results for different operating conditions.