Effect of different blade number and thickness on performance of micro-turbine

At present, due to its special operating environment and operating conditions, there are few relevant theoretical studies and numerical simulation studies on micro-turbines. Therefore, the use of simulation technology to explore the internal flow law of micro-turbines is of great significance for the design optimization guidance of micro-turbines. The research method of this paper is through CFD software, using SST k-ω algorithm model. This paper studies the efficiency and output of micro-turbine with 8 blade numbers of 13,15,17,19,21,23,25 and 28, as well as the efficiency and output of micro-turbine with thickness of 12mm, 12.5mm, 13mm, 13.5mm and 14mm. The internal flow field characteristics, the pressure pulsation characteristics of impeller region and tip clearance region and the power loss distribution diagram are studied and analyzed. The results show that the maximum efficiency is 22.42% when the number of blades is 15, and 23.92% when the thickness is 10.5mm.


CFD simulation of hydraulic turbine
With the development of computer technology in recent years, more and more numerical simulation technology has been applied in the research field of hydraulic turbines, which are mainly divided into large hydraulic turbines, small hydraulic turbines and micro hydraulic turbines [1].
In terms of large water turbines, in 1997, Geppert [2] et al., based on the assumption of free jet flow, solved the governing equation using finite difference scheme, and used CFD simulation to study the influence of different openings and different water heads on the free jet flow of impact turbines, Then E.Parkinson [3][4][5] et al. carried out numerical simulation research on various jet interference situations inside the impact turbine, and used numerical simulation technology to explore the flow process inside the impact turbine.Faping Zheng [6]et al. used the numerical simulation software CFX to analyze the injection needle and nozzle runner in the impact turbine, and analyzed the velocity and pressure distribution in the internal flow field as well as the internal loss to guide the optimization and modification of the nozzle runner.G.M. Morgunov [7]analyzed the causes and reduction methods of large-scale fluctuations in the flow channel pressure of large turbines, and proposed innovative and experimentally verified solutions to smooth the low frequency fluctuations of turbine branch pipe flow.Starting from the momentum theorem, Wentong Zhou and Xiaoquan Zhou [8][9][10]built the basic principle model of the impact turbine, rigorously derived the basic equation and numerical solution of the impact turbine model, established the general equation of the internal kinetic energy of water and the direction of water discharge of the impact turbine, and summarized and sorted out the basic laws followed by the impact turbine.
With regard to small turbines, Fei Zhu [11] et al. used CFD to conduct three-dimensional unsteady flow simulation on the designed turbine model to guide the design of small Francis turbines in cooling towers.Yuan Zheng [12] et al. designed and developed a new type of environmentally friendly small turbine that could replace the motor in the cooling tower with CFD software as an auxiliary tool, studied the influence of turbine runner size, blade number and nozzle shape on turbine performance, and guided the optimization design of the turbine.Based on the traditional design method of turbine flow parts, Manhuan Chen [13] et al. studied the law of water flow movement in turbine through numerical simulation, and compared it with the experimental value, successfully developed a high-performance HLN type energy-saving turbine.Mario Luis Chew Hernandez [14] et al. proposed the development of a multi-criterion design framework for small hydraulic turbine networks.The framework is suitable for some of the rivers available for turbine installation are polluted and there are several towns in the area with different needs for electricity.Chung Kyun Kim [15] et al. conducted a finite element analysis on the contact characteristics of the mechanical seal face of a small hydraulic turbine.
Yuzhu Lu [16] from Huazhong Agricultural University reported the design of a micro-turbine and the performance experiment of a prototype to meet the electricity demand of farmers in mountainous areas and the needs of agricultural products processing.He Liu [17] et al. proposed an electric energy conversion technology based on micro-turbine, which was applied to the power supply of equipment in the intelligent stratified water injection process of oil Wells, and used computational fluid dynamics software to conduct numerical simulation of the micro-turbine model to guide the structural optimization design of micro-turbine.The CFD simulation data of the micro-turbine for residential power generation, such as Alvear Perez Libia Cenith [18], are run three times against three operating points to obtain the output pressure, the descent of the turbine and the hydraulic power to be utilized by the device.
It can be seen from the above that the CFD numerical model of large hydraulic turbines mainly applies to the design optimization of large pump tension or various adverse flow analysis, and the current technology is relatively mature and has many achievements.The CFD numerical simulation of small turbine is mainly used in small and medium-sized power stations or distributed energy, and the research results are more and more, and the technology is becoming mature.Due to its special application scenarios and operating conditions, there are few research results related to CFD numerical simulation of micro-turbines.Therefore, it is of great significance to study the internal flow law of micro-turbines by numerical simulation for turbine optimization guidance and design.

Portable electronic devices and power generation
With the continuous progress of science and technology, portable electronic products have gradually entered people's lives, especially in recent years, the progress of microprocessor technology has improved power efficiency, and effectively reduced power consumption requirements, accelerating the development of mobile phones, laptops and other electronic product.At present, the operation of these devices is mainly met by the battery, however, the need to charge the problem of these electronic products caused a significant limit to the operation time or service life of these electronic products, although these electronic products are basically adopted low power design, and equipped with high performance batteries, but in some cases, the battery life is still insufficient.Generally speaking, for users living in areas with stable and developed power grids, when the power of these electronic devices is exhausted, it is only necessary to connect it to the grid to charge; However, for soldiers marching in the field or users traveling in remote areas, it is difficult to connect to the power grid in time when the power is exhausted, and it is often necessary to carry batteries for replacement or carry bulky charging equipment such as solar chargers for power supply, which greatly increases the burden on the human body and is quite inconvenient [19][20].
Therefore, because of its small size and easy to carry, the micro turbine has a potential application in portable electronic equipment and power generation, so it is necessary to study the performance of the micro turbine.

Introduction of micro-turbine and establishment of fluid domain
The micro-turbine is mainly composed of an impeller, a shell, a stator, a rotor and a top cover, as shown in Figure 1, in which, the impeller is equipped with annular permanent magnet, equivalent to the rotor, the stator is wrapped with a coil, when the impeller rotates, it will drive the annular permanent magnet installed in the inside to rotate around the stator wrapped with a coil, cutting the magnetic inductance line to generate electricity.The initial parameters of the micro-turbine are shown in Table 1.
Table1.Structure and operating parameters of micro-turbine.

Structure and operation parameters
Outer Considering that the stator and rotor are basically assembled inside the impeller, and the gap between them is extremely narrow, and the impact on the jet impact blade is relatively small, in order to simplify the fluid domain, the gap inside the stator and rotor is ignored, and the void inside the impeller is replaced by a solid, so as to simplify the calculation.The simplified fluid domain model of the micro-turbine is used, as shown in Figure 2   As shown in Figure 2, the fluid domain of the micro-turbine is the calculation domain of the numerical simulation in this paper.Since the impeller is rotating, the fluid domain of the impeller is rotating fluid domain, and the rest is stationary fluid domain.In addition, in order to prevent backflow from affecting the calculation in the outlet fluid domain, the fluid domain of the outlet pipe is extended by 5 times the original length.

The partitioning of the computational domain grid
In this paper, the Fluent Meshing module of commercial software Ansys is used to mesh the computing domain.Since the components of the micro-turbine used in this paper are basically regular three-dimensional bodies, the mesh division of each region adopts polyhedron and hexahedron mixed mesh, and the mesh density of the focus area, namely the impeller region, is improved to improve the calculation accuracy.The grid of the completed calculation domain is shown in Figure 3 below.The number of grids is 290W, the maximum skewness is 0.54, and the values of y + in the near-wall area are all less than 10.

Hydrodynamic governing equations and turbulence models
In the micro-turbine designed in this paper, the movement of fluid ignores heat exchange and energy dissipation, so the only governing equations used in the numerical simulation of micro-turbine are the mass conservation equation and the momentum conservation equation.
(1) Mass conservation equation In equation ( 1), ρ is the density of the fluid, t is the time, and u, v, and w are the components of the velocity vector in the x, y, and z directions, respectively.The above equation gives the mass conservation equation of the transient three-dimensional compressible fluid.For the steady state incompressible fluid, the density ρ is constant.
(2) Momentum conservation equation Where, is the stress tensor, is the momentum of the additional source term.Through the mass conservation equation and the momentum conservation equation, the pressure field and the velocity field of the fluid can be solved, and the flow of the fluid can be analyzed.
The SST k-ω model is used in the calculation.The advantage of this model is that it can accurately all aspects of turbulence, the generation, propagation and dissipation of turbulence, etc., and has great advantages in predicting the flow around and swirl in the near avoidance zone.It is widely used in the unsteady flow simulation of rotary hydraulic mechanical pumps and hydraulic turbines.The expression is as follows: Where: k is turbulent kinetic energy; ε is the turbulent dissipation rate; v t Is turbulent viscosity.The formula is as follows: WhereF 1 and F 2 are mixed functions.

Calculated setup
The SST k-ω model is used in the calculation.The discrete scheme adopts the second-order upwind scheme, the algorithm adopts the SIMPLE algorithm, and the transient calculation is adopted.The model can be expressed as: Set the inlet water pipe section as velocity-inlet, outlet water pipe's outlet interface as free outflow, impeller boundary as wall boundary and rotate along with impeller one piece.The interface between the impeller fluid domain and the surrounding tip clearance fluid domain is set as the interface boundary, and the other peripheral boundaries are set as the wall boundary.The operating point is selected as speed n=1050 r/min and the inlet flow rate v= 8.4m /s.

Verification of calculation scheme
Because the output of the impeller of the micro-turbine is in the order of milliwatt, more high-precision instruments are needed for accurate measurement.At the same time, due to the influence of the size and structure of the micro-turbine itself, it is difficult to directly measure the output of the micro-turbine through experiments.Therefore, the three-phase power of the micro-motor is measured in this experiment, and the output of the turbine is equal to the product of the three-phase power and the electromagnetic conversion efficiency (the friction resistance factor existing in the rotation of the impeller is also included in the electromagnetic conversion efficiency), and in general, when the flow rate is not very large, the electromagnetic conversion efficiency can be basically considered to be a fixed value: Where, C is the electromagnetic conversion efficiency, is the experimentally measured three-phase power, unit W, P turbine is the output of the simulated turbine, expressed in W. The experimental data are shown in Table 1, and the results are shown in Figure 4.As can be seen from the figure, under each flow, the ratio of three-phase power to turbine output is basically about 83%, and the error is within 10%.Considering that the fluid domain is simplified to a certain extent during calculation, and the influence of friction during operation of the device is ignored, this error is acceptable.Although the electromagnetic conversion efficiency of the micro-motor used in this paper is unknown, it can be seen from the comparison results that the ratio between the calculated value and the real value obtained through numerical simulation is basically unchanged.Moreover, the focus of this paper is to compare the output and efficiency of the micro-turbine under different working conditions, so the purpose of optimization can be achieved by qualitative comparison of the output and efficiency of different working conditions.

Influence of different blade number on performance of micro-turbine
In order to study the effects of different blade numbers on the performance of micro-turbines, three-dimensional micro-turbine models with different blade numbers were established and three-dimensional transient numerical simulation of the internal flow field of micro-turbines with different blade numbers was carried out under the condition that other structural and operating parameters were unchanged and the computational boundary conditions were set the same.The flow characteristics and changes of flow field in micro-turbine with different number of blades are obtained.Due to the influence of impeller diameter, excessive number of blades will cause the flow channel between blades to be too narrow and the jet cannot impact the blades, so the maximum number of blades is 28.In this paper, 8 models with different blade numbers are selected, namely Z=13,15,17, 19, 21, 23, 25, 28, and the influence of different blade numbers on the performance of micro-turbine is analyzed.

Analysis of efficiency and output
Figure 5 shows the efficiency and output diagram of micro-turbine with different number of blades.Among them, the output of the turbine is defined as： = • (7) Where, M is the total torque of the impeller, unitN • m, ωis the rotational speed of the impeller, unit rad s.Turbine efficiency is defined as: Where, 1 、 1 are the total pressure of the entrance and exit sections respectively, Q is the water flow through the micro-turbine.
As can be seen from Figure 5, with the increase of the number of blades, the turbine efficiency basically increases first and then decreases, and the turbine output also basically increases first and then decreases, except that there is a small rebound at 28 blades.When the number of blades increases from 13 to 28, the highest efficiency is found when the number of blades is 15, and the efficiency is 25.32%,When the number of blades is 25, the lowest efficiency is 22.42%, and the difference between the maximum efficiency and the minimum efficiency is 2.9%.The variation trend of turbine output is almost the same as that of efficiency, and the maximum output point is 1.106W when it appears on 17 blades.This indicates that within a certain range, the increase in the number of blades can increase the work capacity and efficiency of the impeller and make full use of the energy of the water jet.However, when the number of blades is increased too much, the flow channel between the blades will be too narrow, and the efficiency of water jet utilization is not high, and the output will be reduced.Therefore, when the number of blades is 15, the efficiency of the turbine reaches the maximum, and when the number of blades is greater than 15 blades, the efficiency of the turbine will gradually decrease, and the range of change is also large, indicating that the number of blades has a significant impact on the efficiency.

Quantization of contour
In order to more intuitively react the size of the parameter, the cloud map scale is dimensionless.The rule of dimensionlessness is: The calculated speed is divided by 8.36m/s; the calculated pressure is divided by 0.5•1000kg/m 3 •8.36 2 m/s; the calculated turbulent kinetic energy is divided by 8.36m/s 2 .

Velocity field and turbulence analysis
Since the entire fluid domain is symmetrical about the central section of the impeller, the central section of the fluid domain of the impeller is selected to output the central section of different blade numbers.In order to more intuitively respond to the size of the parameters, the cloud map scale is dimensionless, as shown in Figure 6.As can be seen from Figure 6, with the increase of the number of blades, the high-speed region area in the inner region of the impeller fluid domain gradually increases, and the high-speed region in the impeller fluid domain is close to the left boundary.This is because with the increase of the number of blades, the number of blades impacted by the water flow per unit time also increases, so the high-speed region of the impeller fluid domain becomes larger and larger.At the same time, it can be seen that the velocity distribution area at the outlet when the number of blades is 13 is much larger than that at the outlet when the number of blades is 28.This is because with a small number of blades, fewer blades are in contact per unit time.Therefore, the velocity distribution area at the outlet when the number of blades is 13 is significantly larger than that of other blades.At the same time, the turbulence distribution inside different blades was compared, as shown in Figure 7.In order to more directly show the influence of different blade numbers on the turbulence intensity inside the micro-turbine, the regional energy dissipation inside the micro-turbine is analyzed.The turbulent kinetic energy cloud image of the internal flow field of the micro-turbine with different blade numbers is shown in Figure 7.As can be seen from Figure 7, in the blade region impacted by jet and its tail region, the internal turbulence intensity is larger, while the turbulent kinetic energy in other regions is smaller.The turbulent kinetic energy of the surrounding area increases and then decreases when the jet impacts the blade.With the increase of the number of blades, the turbulence intensity inside the micro-turbine is uneven and does not show obvious regularity.However, it can be obviously seen that the internal turbulence intensity when the number of blades is 17 and 21 is smaller than that when the number of blades is 25 and 28, resulting in the lowest efficiency and output of the turbine when the number of blades is 25 and 28.

Pressure pulsation in the internal area
In this section, the pressure pulsation in each region of the micro-turbine under different blade numbers is studied, and the change of pressure pulsation amplitude under different blade numbers is explored, which is used as a reference for improving the operation stability of the micro-turbine.According to the operation characteristics of the micro-turbine, the internal region is divided into impeller region and tip clearance region, each region is set with 4 monitoring points, a total of 8 monitoring points, as shown in Figure 8 below.In Figure 8, a1、a2、a3、a4are the monitoring points in the tip clearance region, and b1、b2、b3、 b4 are the monitoring points in the impeller region.After the calculation the pressure data of these monitoring points are exported, and the curve in the pressure time domain diagram is performed by fast Fourier transform in Origin software.The maximum and minimum pressure pulsation frequency domain of the corresponding working conditions are obtained as shown in figure 8and figure 9.The maximum pulsation amplitude of the main frequency of the monitoring point b1 in the impeller region occurs when the number of blades is 13 and the minimum is 28; the maximum pulsation amplitude of the main frequency of the tip clearance region a1 occurs when the number of blades is 13 and the minimum is 28, as shown in figure.9 and 10.

Internal loss analysis
The essence of the work of the micro-turbine is to convert the pressure energy and kinetic energy of the liquid into the mechanical energy of the impeller, and then convert the mechanical energy into electrical energy through the micro-motor.In order to better understand the internal energy conversion characteristics and rules of micro-turbine, figure.11 shows the turbine output, internal total loss and outlet loss power of micro-turbine under different blade numbers.Among them, the outlet loss power is defined as the total pressure of the outlet section multiplied by its corresponding flow rate, and the internal total loss is defined as the total loss of all other internal flow field areas excluding the outlet loss power, which is obtained from the total input power minus the turbine output and the outlet loss power, and the total input power is defined as the product of the total pressure of the inlet section and the total water flow rate.It can be seen from Figure 11 that the losses are mainly concentrated in the internal losses.Since the inlet pipe is short and smooth, the losses in the inlet and outlet are small, so the internal losses are mainly concentrated in the losses in the impeller area.As can be seen from the figure, the internal losses gradually increase as the number of blades increases.This is because with the increase of the number of blades, various friction losses, impact losses and other losses increase, resulting in the sum of internal losses is increasing.

Analysis of efficiency and output
This paper also explores the influence of the upper and lower thickness of the micro-turbine on its performance.The schematic diagram is shown in Figure 12.The performance of the micro-turbine with thickness of 10.5mm, 12mm, 12.5mm, 13mm ,13.5mm and 14mm is explored, and its efficiency diagram is shown in Figure 12.With the increase of the thickness, the output of the micro-turbine hardly changes, but the efficiency of the micro-turbine increases slightly first and then decreases.The highest efficiency occurs when the thickness of the micro-turbine is 12mm, which is 23.9%; the lowest efficiency occurs when the thickness is 14mm, which is 22.67%; the difference between the highest and the lowest is 1.23%.The central section velocity and turbulence intensity contour images of micro-turbines with different thicknesses have little change, so they are not listed below.

Pressure pulsation in the internal area
The frequency domain diagram of maximum and minimum pressure pulsation under corresponding working conditions is shown in figure .13 and 14 below.Among them, the maximum pulsation amplitude of the main frequency of the monitoring point a1 in the impeller region appears when the thickness of the micro-turbine is 12.5mm and the minimum is 13.5mm; the maximum pulsation amplitude of the main frequency b1 in the tip clearance region appears when the thickness of the micro-turbine is 14 and the minimum is 12.5mm.

Internal loss analysis
Figure .15 shows the turbine output, total internal loss and outlet loss of the micro-turbine at different thicknesses.It can be seen from the figure that the internal loss of the micro-turbine at thicknesses of 12.5mm, 13mm, 13.5mm and 14mm is significantly greater than that at thicknesses of 10.5 and 12.This results in a micro turbine with a thickness of 10.5 and 12 when the efficiency is greater than the remaining four.

Conclusion
(1) The efficiency and output of micro-turbines with different blade numbers are studied.The turbine efficiency basically increases first and then decreases, and the turbine output also basically increases first and then decreases, and it is concluded that the highest efficiency occurs when the number of blades is 15, and the maximum efficiency is 22.42%.(2) With the increase of the number of blades, the high-speed area in the inner region of the fluid domain of the impeller gradually increases, and the high-speed area in the fluid domain of the impeller is near the left boundary.The velocity distribution area at the outlet when the number of blades is 13 is larger than that at the outlet when the number of blades is 28, and the internal turbulence intensity is stronger when the number of blades is 25 and 28, resulting in low efficiency.
(3) The maximum pulsation amplitude of the main frequency a1 in the tip clearance region appears at the number of blades 13 and the thickness is 12.5mm, and the minimum pulsation amplitude is 28 when the thickness is 13.5mm.The maximum pulsation amplitude of the main frequency of the monitoring point b1 in the impeller region appears at the number of blades 13 and the thickness is 14mm, and the minimum pulsation amplitude is 28 when the thickness is 12.5mm.(4) The internal loss distribution of micro-turbine with different blade number and thickness is studied.With the increase of blade number, the internal loss increases gradually.The thickness of 10.5mm and 12mm is low internal loss, so the efficiency is high.(5) The performance of micro-turbine under different thicknesses is studied.The output of micro-turbine hardly changes, but the efficiency of micro-turbine increases slightly first.It is concluded that the highest efficiency occurs when the thickness of micro-turbine is 12mm, which is 23.9%, and the lowest efficiency occurs when the thickness is 14mm. below.

Figure 4 .
Figure 4. Comparison diagram of three-phase power and turbine output ratio.

Figure 5 .
Figure 5. Efficiency and output of micro-turbine with different number of blades.

Figure 8 .
Figure 8. Diagram of pressure monitoring points.

Figure 9 .
Figure 9.The maximum pulsation amplitude and minimum pulsation amplitude of the main frequency a1.

Figure 10 .
Figure 10.The maximum pulsation amplitude and minimum pulsation amplitude of the main frequency b1.

Figure 11 .
Figure 11.Output and loss of micro-turbine under different blade number.

Figure 12 .
Figure 12.Efficiency and output of micro-turbine with different thickness.

Figure 13 .
Figure 13.The maximum pulsation amplitude and minimum pulsation amplitude of the main frequency a1.

Figure 14 .
Figure 14.The maximum pulsation amplitude and minimum pulsation amplitude of the main frequency b1.

Figure 15 .
Figure 15.Output and loss of micro-turbine under different thickness.

Table 2 .
Experimental data table.