Analysis of energy dissipation in allowable, restricted and prohibited operating areas of wanjiazhai francis turbine

With the “14th Five-Year Plan” and the “two-carbon” policy, the application of renewable energy has seen a substantial increase. As a kind of hydraulic machinery which converts the kinetic energy of water into electric energy, the turbine is widely used in various hydropower stations. However, due to the variability of flow rate, speed and head, how to ensure the efficiency of unit operation is particularly important in complicated working conditions. In this study, the Francis turbine of Wanjiazhai Hydropower Station is taken as the research object. Through the combination of numerical simulation and experiment, the energy consumption under the permitted, restricted and forbidden conditions is analyzed.


Introduction
The form of turbine has axial flow, mixed flow impact, etc [1].As a kind of counter turbine, the Francis turbine has the characteristics of large range of head, small structure size, easy installation and high efficiency.It is widely used to make use of the kinetic energy of the fluid to drive the flow blade to rotate, so as to obtain energy [2].However, there are still some problems in turbine operation under various working conditions, such as load rejection [3], vortex [4], pressure pulsation [5] and cavitation [6].Fu et al. used the dynamic grid technology and the custom function in the business software FLUENT to simulate the load dumping process through numerical simulation, and analyzed the internal flow, and found that the results were in good agreement with the test values [7].Qian et al. analyzed the relationship between the pressure pulsation of the full flow passage and the intake volume under the water-gas twophase flow through the method of combining numerical simulation and experiment, and found that the intake of the main shaft hole could adjust the pressure difference and reduce the amplitude of the low-frequency pressure pulsation of the tail pipe, but the dynamic and static interaction could increase the blade frequency pressure pulsation in front of the runner.Liu et al. explored the causes of vortices between blades and the influence of different hydraulic parameters on vortices between blades through experiments, and found that the main reason for the vortices between blades was the large incidence Angle between the inlet Angle of the leading edge of the flow passage and the blade Angle.

Hydro-turbine Parameters
Fig. 1 shows the turbine unit applied in this study, which mainly includes volute, stay vane, guide vane, runner and draft tube.When the unit is working, the liquid flow enters from the inlet, passes through the volute, the stay vane, the guide vane, and then enters the rotating area -the runner, and finally flows out through the tail pipe.The number of blades on the runner is 13 and the inlet radius is 3.34m and the outside diameter of the runner is 3.04m.

CFD Setup
In this study, the commercial software CFX was used to perform a steady calculation of the watershed in Figure 1.The rotation speed of the runner is 100rev/min, and the relative pressure is one atmosphere.The fluid medium is set to 20℃ water.The inlet boundary is set as the total pressure force value of head conversion.The pressure outlet boundary is given at the outlet boundary position.In order to explore the energy dissipation in allowable, restricted and prohibited operating Areas, three working conditions are respectively adopted in this study: 1) guide vane opening is 12° and the head is 50m.2) Guide vane opening is 12°, the head is 68m.
3) Guide vane opening is 24 degrees and the head is 68m.
Turbulence model adopts SST model.The model has the advantages of high pressure gradient, shear turbulent flow and near-wall separation, and can effectively improve the convergence of the calculation.The heat transfer method is set to total energy.The maximum number of iteration steps is set to 1000, and the convergence criterion is set to root mean square (RMS) residual less than 1×10-5.

Entropy Production Analysis Method
During a flow, the internal energy increases as the potential and kinetic energy of the flow dissipates.The internal energy E can be expressed as： ( ) ( ) ( ) ( ) In the above equation, E is the product of T (temperature) and the sum of the four terms (Energy dissipation coefficient).Where, the four terms of energy dissipation coefficients can be expressed as: In the above equation, x, y, z stands for the three directions of the coordinate axis, and u, v, w stands for the components of the velocity in three directions.For easier analysis, the dimensionless coefficient   is provided.The dimensionless coefficient can be expressed as:  The energy consumption characteristics of turbine units can be analyzed by the dimensionless coefficients above.

Energy Dissipation in Turbine
As shown in Figure 2, blue to red indicates entropy production from low to high.In general, the main position of entropy production is the impeller region and the leafless region between the guide vane and the runner.When the guide vane opening is 12° and the head is 50m, the entropy yield is the highest.When the guide vane opening is unchanged and the head is increased to 68m, the entropy yield is lower than before, which is partly related to the liquid flow velocity passing through this area.When the head is kept at 68m and the guide vane opening is increased to 26°, the operating condition is rated and the entropy production rate is the lowest.As shown in Figure 3，the distribution of entropy production rate of the draft tube presents a certain law.When the guide vane opening is 12° and the head is 50m, the entropy production of the draft pipe is mainly concentrated in the inlet and diffusion section of the draft pipe, and the entropy production rate from the inlet to the diffusion section firstly increases and then decreases gradually, reaching the maximum value in the middle of the diffusion section.When the head increased to 68m, the position of the peak entropy production rate moved downward.When it is in rated working condition, the entropy production rate of the draft pipe is very low and can be basically ignored compared with the previous two.This article studies the energy loss caused by the internal flow of the water turbine at Wanjiazhai Hydropower Station.Entropy production analysis shows the high energy loss positions.In areas with relatively stable operation, the internal flow pattern is also good.The energy loss is relatively small.After the operation stability decreases, there is obvious flow energy loss inside the runner, especially the surface loss of the blade is large, and the loss of the draft tube is aggravated due to the vortex rope.In the prohibited operation area, the flow instability is extremely strong, and the internal loss of runner also rises sharply, accompanied by the increased energy loss of draft tube vortex rope.This study provides scientific reference for the stable operation of the unit.

Figure 2 .
Energy dissipation diagram of vanes and runner.

Figure 3 .
Energy dissipation diagram of draft tube.