Research on the influence of needle roughness of Pelton turbine on flow characteristics

The needle in the jetting mechanism of Pelton turbine may be uneven on the surface of the needle due to the knife marks in the cutting process or the erosion of the sediment in the water flow, resulting in the surface roughness of the needle, which affects the flow at the wall. In order to study the influence of the surface roughness of the needle on the jet flow characteristics, the jet flow characteristics and sediment characteristics of the jetting mechanism under different roughnesses were analyzed in this paper. The results show that the flow characteristics of the smooth wall and the rough wall are obviously contrasted. With the increase of the needle roughness, the jet velocity of the jetting mechanism gradually decreases, the turbulent kinetic energy of the needle surface gradually increases, the shear stress on the needle surface gradually increases, the wear amount gradually increases, the wear area increases, and the efficiency of the jet mechanism with a 1mm roughness wall decreases by about 22.3% compared with the smooth wall.


Introduction
The impact turbine nozzle has good jet performance, but in the actual processing process, the wall inevitably appears uneven knife marks, forming the staggered peak and valley phenomenon, that is, the processed surface roughness [1].The impact turbine is mostly used in high head areas, and the water flow often contains quartz sand with high hardness.Due to the impact of the sediment in the water flow, the wall of the spray needle will also wear, resulting in the increase of the wall roughness, thus affecting the jet characteristics of the nozzle.The influence of jet needle roughness on jet flow characteristics is studied for the manufacture of jet mechanism and the improvement of turbine efficiency.
The research on mechanical surface roughness at home and abroad mainly focuses on water pump, wind turbine blade, cylindrical winding flow and so on.Due to the attachment of mechanical surface dust or the erosion of the sediment in the water flow, many scholars at home and abroad have studied the influence of roughness on mechanical properties.Li Jinqiong [2] et al. studied the unsteady characteristics of centrifugal pump inlet reflux with different roughness.They analyzed that the roughness has certain resistance reduction and can reduce the strength of reflux vortex.The properties and mechanical characteristics of the axial flow pump section with 0.1mm to 0.5mm roughness were studied by Li Long [3] et al.Khalfallah,M.G. [4] et al. studied the influence of dust on the performance of the wind turbine, and pointed out that the wind turbine blade will produce surface roughness in the manufacturing process.Koch,C.C et al [5] experimentally studied the boundary layer characteristics caused by the surface scaling of axial flow compressor.Liu C et al [6] studied the influence of gate surface roughness on the flow of the boundary layer at different Reynolds numbers.Some scholars have also studied the cavitation characteristics through the roughness of the water turbine components [7].Zhang Jinlan [8] studied the effect of the roughness of the runner blade surface on the efficiency and cavitation.Some scholars have also studied the sediment erosion through different roughness.Qiao Zhiwei [9] establishes a three-dimensional model based on fluent software, and uses the SSTk   turbulence model to simulate the force characteristics and erosion of the cylinder with different sand content and different roughness.Previous studies mainly focused on machinery such as pumps and fan blades, but lack of research on turbine related components.The actual engineering shows that the quality of the jet is reduced due to the wear of the jet mechanism, resulting in the efficiency loss of the unit of 2%~5% According to the study [10], the particles with small diameter have strong flow behavior, which is easy to cause the head wear of the spray needle, thus forming a rough surface.Therefore, it is of great significance to study the influence of the roughness on the sediment characteristics.
The study of roughness is also closely related to the geometric parameters such as the height, density, and spacing ratio of the rough element.Mei Fanmin [11] et al. studied the interaction effects of geometric parameters such as roughness element height, density, height to spacing ratio, porosity and direction ratio on aerodynamic roughness by using wind tunnel experiments.Kim et al [12] studied the EHL analysis of surfaces with pure longitudinal roughness, pure transverse roughness, and isotropic roughness.Tan Dekun et al. [13] conducted digital analog analysis of rough element of different shapes, and discussed the influence of reynolds number, rough element height, rough element spacing and other factors on flow rate, pressure drop and flow resistance.The results show that the roughness significantly changes the flow.Compared with several rough elements, the rectangular rough element has the greatest influence, the second circle and the smallest triangle.Therefore, it is very important to determine the appropriate rough element for the study of roughness.In this paper, the circular rough element can be used, and the equivalent sand grain size model is adopted.
In this paper, the jet mechanism of impact turbine is modeling by UG, and the jet of injection mechanism under different roughness is calculated and analyzed based on FLUENT, so as to provide a reference for the mechanical manufacturing of impact turbine.The k   turbulence model is the best known and most widely used two-equation vortex viscosity pattern.The k   turbulence model is a two-equation vortex viscosity mode of incompressible / compressible turbulence integrated into the wall.The turbulent transport equation can be expressed as the turbulent energy transport equation and the energy dissipation transport equation [14]: In the formula:   is the vortex viscosity, ij S is the average velocity strain rate tensor, and k is the turbulent kinetic energy,the right end represents the generation term dissipation term and wall term respectively.

The VOF multiphase flow model
The jet at the nozzle outlet is a two-phase flow of water and air.In this paper, water and air are regarded as continuous phases, and the VOF multiphase flow model can be well tracked to the free liquid level of the jet.Its governing equation [14] is as follows:   In formula:the subscripts 1 and 2 represent the gas and water phase respectively;  the physical density,  represents the volume fraction; and v  represents the average velocity.

Equivalent sand particle size model
The equivalent sand particle size model is used to set the wall roughness.The equivalent sand particle size model is a layer of closely arranged equal diameter ball placed in a smooth plane to simulate the undulating wall, as shown in Figure 1 [15].
In formula: p u is the velocity of the point P near the wall; p y is the distance from the point P to the wall; w  is the wall shear stress; the shear speed; E is the constant related to the roughness of the wall,For the smooth wall surface The DPM model is suitable for discrete phase calculations with a particle volume fraction less than 10%.In the governing equation, in addition to the equilibrium of the particles, the force attached to the surrounding fluid and the force due by the pressure gradient of the fluid should be considered.The governing equation is as follows [17]: In formula: The wear model can monitor the wear of the sediment particles on the wall surface.Using the Generic wear model, the reflection of particles on the geometric wall depends on the properties of the particles and the solid surface.The surface reflection value of sand particles on carbon steel is selected.The impact angle function adopts linear segment function; the wall recovery coefficient adopts polynomial function; the particle diameter function and velocity index function are set to constant [18].

Grid division and grid-independence verification
In this paper, UG modeling of CJC601-L-45/2X3.5 impact turbine jet mechanism is performed.ICEM CFD is used for structural mesh division.In order to ensure the accuracy of the calculation, the grid-independent verification is conducted, and six different grid division schemes are adopted, and the results are shown in the figure below.In order to ensure the accuracy and efficiency of the calculation, the grid is necessary to verify the grid independence.Digital calculation of the six grid division schemes based on the FLUENT platform, and the results are shown in Figure 3.It can be seen that with the increase of the number of grids, the jet speed of the jet mechanism is increasing.But when the number of grids is increased after 2.631,000, the speed increase does not exceed 0.78%, while the calculation amount is greatly increased.Therefore, in order to ensure the calculation accuracy while saving the calculation amount, the fourth grid division scheme is selected, and the number of grids is 2.631 million.

Computational method 4.1 Boundary conditions
The water flow inlet is set as the pressure inlet, which is 463564Pa.The jet area is set as the cylindrical air domain, the air domain inlet is set as the pressure inlet, and the relative pressure is 0Pa.The sediment density is 2650 kg/m 3 , the sediment inlet mass flow rate is 0.3083kg/s, the sediment concentration is 1% of the continuous phase, and the sediment diameter is 0.05mm.The jet outlet is also the air domain, set to the pressure outlet with a relative pressure of 0Pa.The wall is set as the unsliding wall boundary condition, the standard wall function is used for the flow near the wall area, the average equivalent roughness of new cast iron is 0.3mm, and the rough height of wall sand particles is set to 0,0.05,0.1,0.2,0.3 and 0.5mm respectively.Calculated with uniform roughness simulation, without considering the case of uneven roughness.

Solution settings
In this paper, the two-phase flow, and the time step is set to 0.001s.The SIMPLE method, which is a semi-hidden method for solving the pressure-coupled equation, is also the most widely used algorithm and widely adopted by various commercial CFD software.The discrete format adopts a first-order windward discrete format.When setting the relaxation factor, pressure was set to 0.3 and momentum to 0.2 to ensure convergence.Since the unsteady flow of Fr and We are relatively large, gravity and surface tension on the mainstream characteristics of the small impact, so this paper in the calculation process to ignore the impact of these forces [19].

Results and analysis
In order to study the effect of spray needle roughness on flow characteristics, the spray mechanism with five roughness, i. e. 0.0.05,0.1,0.2,0.3,0.5,1mm, was numerically simulated.Figure 4 shows the cloud diagram of the numerical simulation results of the two-phase flows.

Efficiency analysis of the injection mechanism
According to the numerical results, we know that the region surrounded by the black circle with the center as the dot and the 30mm as the radius is the effective jet area, which can contain the main velocity of the jet, as shown in Figure 5. Therefore, the velocity average value over the region is taken as the jet velocity of the jet mechanism.
Figure 5.The effective jet region.Figure 6 shows the line diagram of the jet velocity of the jet mechanism at different roughness.In the absence of rough condition, the jet velocity is maximum at 29.72m/s, and the jet mechanism efficiency is 98.14%.With the increase of the roughness, the resistance of the water flow gradually increases, and the jet velocity gradually decreases, resulting in the gradually poor efficiency of the jet mechanism.From smooth to rough conditions, the speed changes greatly, and the efficiency decreases by 12.83%.With the increase of roughness, the efficiency is gradually decreasing, but the rate of reduction decreases, the injection mechanism efficiency is only 75.86% at 1mm roughness, which is about 22.3% lower compared with the smooth coarse injection needle wall.It can be seen that the rough jet needle wall surface has a great impact on the jet velocity, which greatly reduces the efficiency of the jet mechanism, and has an important impact on the efficient operation of the impact unit.

Analysis of turbulent kinetic energy on the surface of the injection needle
Turbulent kinetic energy is one of the most common physical variables in turbulence models, which indicates the average characteristics of turbulent kinetic energy and is an important index to describe the development of turbulence.The smaller the turbulent kinetic energy is, the smaller the turbulent divergence in the channel is.Conversely, the larger the turbulent kinetic energy is, the greater the divergence is.  .Influence of wall roughness on the kinetic energy of wall turbulence.Figure 7 shows a cloud map of turbulent kinetic energy on the surface of injection needles with different roughness.It can be seen that the turbulent kinetic energy is mainly reflected in the tip of the needle, and the gradient changes from the tip upward.With the increase of roughness, the turbulent energy at the tip of the needle is increasing, and the turbulent divergence is increasing.Figure 8 shows the change curve of turbulent kinetic energy with wall roughness.In the case of small roughness (before 0.1 mm roughness) , the turbulent kinetic energy decreases gradually.After 0.1 mm, as the roughness increases, the turbulent kinetic energy increases, the turbulence divergence increases, the turbulence dissipation increases, and the loss increases, this is also the cause of the decrease in the efficiency of the injection mechanism.As a whole, the roughness will aggravate the diffusion of turbulence and is not conducive to the stability of the flow field.Therefore, the wall roughness should be paid attention to during manufacture or maintenance.

The shear stress analysis of the injection needle surface
When the corresponding object deforms due to external forces, there is interaction between the parts of the object.The internal force per unit area that resists the action of this external cause and seeks to return an object from its deformed position to its pre-deformed position is called a shear stress.
Figure 9 shows the effect of wall roughness on wall shear stress.When the wall is smooth, the maximum shear stress is 1380.66pa at the tip of the spray needle.After adding roughness to the wall, the maximum shear stress appears on the left side of the tip head and increases with the increase of roughness.It can be seen that only the tip of the nozzle has strong turbulence phenomenon without roughness.However, the turbulent range is larger for the surface with roughness.Figure 10 shows the change curve of wall shear stress with wall roughness.With the increase of the wall roughness, the shear stress increases gradually, but the increasing rate decreases.The increase of the shear stress is due to the shape resistance formed before and after the roughness element, which results in the increase of the flow friction resistance.The liquid layer block at the surface is more obvious, and the flow pattern near the nozzle is turbulent, so the turbulence near the wall is enhanced and the shear stress is increased.

Sediment characteristics of the injection mechanism under the coarse injection needle
Sediment erosion causes the surface of the spray needle to wear and form Surface roughness [20].As shown in Figure 11, the wear of the tip of the nozzle is mainly caused by sediment erosion, whether the wall is rough or not.But with the increase of the roughness, the wear of the surface of the spray needle increases gradually.It can be seen that the roughness will increase the sand wear on the surface of the spray needle, thus making the Surface roughness larger.The damage of the surface of the spray needle is more serious and the rate of damage increases gradually.

Summary
In this paper, three-dimensional numerical simulation was carried out to study the effects of different roughness and different wall surfaces on the flow and sediment characteristics in the injection mechanism.This study provides a reference and theoretical basis for the manufacture of spray needle and the efficient operation of the unit.
(1)The roughness affects the efficiency of the injection mechanism.With the increase of roughness, the jet velocity and efficiency decrease gradually.The efficiency of the injection mechanism is 75.86%under 1 mm roughness.Compared with the smooth spray needle wall, the efficiency decreases about 22.3% .The roughness of the needle wall greatly reduces the efficiency of the injection mechanism, which has an important effect on the efficient operation of the impulse unit.
(2)The roughness affects the flow characteristics of the needle surface.With the increase of the roughness, the turbulence divergence gradually increases, and the flow pattern around the nozzle becomes turbulent.The turbulent phenomenon near the wall increases, the shear stress increases and the turbulent kinetic energy increases, which affects the stability of the flow field and increases the energy loss.Roughness is the main reason for the decrease of efficiency.
(3)Roughness will increase the wear of the spray needle surface.Compared with the no rough wall, the wear of the rough wall is significantly more serious, and with the increase of the roughness, the wear of the spray needle surface is gradually serious, the amount of wear increases, and the wear area increases.
(4)The smaller the Surface roughness parameter, the smoother the surface.But in some non-special requirements of the surface selection of the smaller, the higher the cost of processing, is not practical.Therefore, the choice of Surface roughness should not only meet the functional requirements of the parts surface, but also consider the economical processing

Figure 1 .
Figure 1.The equivalent sand grain model.

; 2 . 4
the constant determined by the test; B  is the roughness function, a segment function of dimensionless roughness height s K  Discrete phase with the wear model

Figure 2 .
Figure 2. Structural grid of the jet mechanism model.In order to ensure the accuracy and efficiency of the calculation, the grid is necessary to verify the grid independence.Digital calculation of the six grid division schemes based on the FLUENT platform, and the results are shown in Figure3.It can be seen that with the increase of the number of grids, the jet speed of the jet mechanism is increasing.But when the number of grids is increased after 2.631,000, the speed increase does not exceed 0.78%, while the calculation amount is greatly increased.Therefore, in order to ensure the calculation accuracy while saving the calculation amount, the fourth grid division scheme is selected, and the number of grids is 2.631 million.

Figure 4 (
a) is the cloud map of water volume fraction, (b) is the velocity cloud map, and the jet shows good symmetry phenomenon.(a)volume fraction (b) velocity

Figure 4 .
Figure 4. Flow cloud diagram of the jet mechanism.

Figure 6 .
Figure 6.Jet velocity of the jet mechanism at different roughness.

Figure 7
Figure 7. Influence of wall roughness on the kinetic energy of wall turbulence.Figure7shows a cloud map of turbulent kinetic energy on the surface of injection needles with different roughness.It can be seen that the turbulent kinetic energy is mainly reflected in the tip

Figure 8 .
Figure 8. Curve of wall turbulent kinetic energy with wall roughness.

Figure 9 .Figure 10 .
Figure 9.Effect of wall roughness on wall shear

Figure 11 .
Figure 11.Cloud map of spray needle wear at different roughness