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Research on characteristics of solid particle erosion in governing stage of a 600 MW supercritical steam turbine
Accepted Manuscript Research Paper Research on Characteristics of Solid Particle Erosion in Governing Stage of a 600MW Supercritical Steam Turbine Zhongbin Zhang, Fang Li, Lihua Cao, Pengfei Hu, Yong Li PII: DOI: Reference:
S1359-4311(16)31746-X http://dx.doi.org/10.1016/j.applthermaleng.2017.02.103 ATE 9984
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
19 September 2016 25 February 2017 25 February 2017
Please cite this article as: Z. Zhang, F. Li, L. Cao, P. Hu, Y. Li, Research on Characteristics of Solid Particle Erosion in Governing Stage of a 600MW Supercritical Steam Turbine, Applied Thermal Engineering (2017), doi: http:// dx.doi.org/10.1016/j.applthermaleng.2017.02.103
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Research on Characteristics of Solid Particle Erosion in Governing Stage of a 600MW Supercritical Steam Turbine Zhongbin ZHANG, Fang LI, Lihua CAO, Pengfei HU, Yong LI (School of Energy and Power Engineering, Northeast Electric Power University, Jilin 132012, Jilin Province, China)
Abstract：Solid particle erosion (SPE) of governing stage has been proved to be great threat to steam turbine performance. Based on Eulerian-Lagrangian method and Finnie rebound model, the urgent SPE problem of high-parameter steam turbine is studied and the characteristics of SPE in governing stage of a 600MW supercritical steam turbine were simulated and analyzed under different particle sizes and rotation speeds in this paper. Results show that the eroded area on nozzle is mainly at the mid-rear part of the pressure surface and is distributed along the radial direction from root to tip. The erosion on rotor blade appears on the leading edge, the mid-rear part of the pressure surface and the suction surface near to the leading edge. Additionally, the eroded area on rotor blade has an obviously upward trend, the radial migration of eroded area increases with the increase of rotation speed and the radial migration quantity is about 7% of blade height at 3000 rpm. The maximum erosion rate density on the rotor blade is 1.9 times of the rate on nozzle. Besides, the critical size of particle is different in nozzle and rotor blade. Key words：steam turbine; governing stage; solid particle erosion(SPE); rotation speed Introduction Solid particle erosion (SPE) is one of the major problems in supercritical and ultra-supercritical unit. Scales flaking away from the inner wall of boiler super-heater and main steam pipe are carried to steam turbine by main steam, which causes SPE in the flow passage, especially in the nozzles and the rotor blades of governing stage. SPE can result in lower efficiency of steam turbine, shorter repair cycle and higher maintenance cost [1]. Therefore, reducing SPE can enhance the economy, efficiency and reliability of unit. Several articles have discussed the effect factors of SPE by means of analysis and simulation. Finnie [2] put forward the influence of particle velocity and impact angle of brittle material, which is quite different from that of ductile material. For ductile materials, the impact angle leading to maximum erosion can be predicted. Hamed.[3] et al. showed clearly that the turbomachinery erosion is influenced by many factors such as the ingested particle characteristics, flow passage, blade geometry, operating conditions and blade material. Alfonso [4] et al. numerically investigated the
influence of the parameters such as particle velocity, impact angle and particle distribution. The particle trajectories and the streamline of steam for basic running were shown but there is no deep discussion on the difference between them in governing stage. Cai [5,6] et al. also analyzed the influence of opening conditions, particle size distribution in the inlet of nozzle and axial clearance between vanes and rotating blades based on SPE characteristics and rebound characteristics of steam turbine blade materials. Their results indicate that the erosion damage of the first reheat stage nozzles in high parameter steam turbines is mainly caused by the particle impact on suction surface. Li [7] et al. analyzed the effect of particle parameters on the erosion rate of nozzle and rotor blade surfaces in unsteady condition and resulted that the erosion rate of the vane blade is sensitive to the fluctuation of the potential flow field. Hamed [8] et al. indicated that both erosion rate and surface roughness increase with the particle impact velocities and impact angles for blade and coating material erosion by experiment. Azimian [9] et al. proved that with
the increase of rotation speed, the higher the impact velocity is, the higher the erosion rate density will be. Furthermore, they also noted that the erosion rate density changes with the change of rotation speed. However, the change of the migration quantity wasn’t mentioned. Brun [10] et al. developed a mixed Computational Fluid Dynamics-Empirical software tool, making the kinematic and impacting behavior of solid particulates in the near-filed of turbomachinery blades and impellers surfaces can be analyzed by probabilistic method. However, Oka [11] et al. found that the impact velocity does not affect the dependence of erosion behavior on the impact angle for the metallic materials. In addition, the influence of SPE on efficiency of unit has been reported analytically and experimentally. Wang [12] et al. stated that the weight-loss of the nozzle can be reduced by about 40-50 percent and the nozzle efficiency is increased by 0.4-0.5 percent through improving the end-wall contouring of nozzle. Khaimov [13] et al. studied the first stages of IPC(intermediate-pressure cylinders) of T-250/300-240 turbines and found that the blades experienced intense erosion wear due to products of decomposition of the oxide film deposited on the superheater conduit of the boiler, which decreases the efficiency of operation and reduces the service life of blade. There are several ways to improve SPE by using ceramic coating and modified design. Tabakoff [14] et al. designed a high temperature erosion test facility to provide erosion data in the range of operating temperatures experienced in compressors and turbines and he found that the material of high density and fine grained ceramic coating with good adhesion to the substrate could significantly improve erosion. Dai [15] et al. researched the anti-erosion of the tip endwall contouring, the aft-loaded nozzle and a straight endwall nozzle. They conducted that the severely
eroded area and the maximum erosion rate of the tip endwall contouring nozzle are reduced by about 30 and 40 respectively. By changing the particle trajectories and impact angle, the solid particle erosion rate in main steam bypass valve was reduced by 51[16, 17]. The main goal of this paper is to analyze the SPE problem under various particle sizes and rotation speeds by three-dimensional numeral simulation in the governing stage of a 600MW supercritical steam turbine. The difference between particle trajectories and streamline of steam are compared in nozzle and rotor blade. The maximum erosion rate density and the eroded area on nozzle and rotor blade are also given. Furthermore, the radial migration quantity of eroded area on the pressure surface of rotor blade caused by the change of rotation speed is investigated quantitatively. The research results in this paper reveal the erosion characteristics of SPE in steam turbine governing stage. It provides a theoretical basis for preventing and reducing SPE of high-parameter steam turbine. 1 Mesh Sketch and Boundary Conditions 1.1 Mesh Sketch A physical model of the governing stage of a 600MW supercritical steam turbine is established. Tab.1 displays the geometric parameters of the governing stage. The geometrical model and grid sketch of the governing stage flow passage are shown in Fig.1. In order to determine the grid number effects on calculation accuracy, validation of grid dependency is carried out. For cascade passage, five sets of grids of 190, 410, 640, 730 and 960 thousands cells are conducted. Tab.2 illustrates the effects of grid number on the CFD results using the maximum erosion rate density as reference parameters and it is found that the total grid number has little effect on the maximum erosion rate density when the total grid number reaches to 640 thousands. These data mean that the total grid 2
Tab.1 Geometrical parameters of governing stage blades Project
Nozzle
Pitch diameter
Unit
96
81
27.31
29.7
mm
Number of blade Blade height
Rotor
1 068.71
1 077.90
mm
Pitch of cascade
32.46
41.81
mm
Axial length
63.81
63.5
mm
（a）Geometrical model
b Grid sketch Fig.1 Geometrical model and grid sketch of governing stage flow passage Tab.2 Relations between erosion rate density and grid number Scheme
Total number
the maximum erosion rate density /kg/(m2 s)
1
190000
2.043e-004
2
410000
1.661e-003
3
640000
1.727e-003
4
730000
1.742e-003
5
960000
1.739e-003
1.2 Boundary Conditions Numerical simulations are performed by ANSYS-CFX software. The working medium is superheated vapor whose status parameters are provided by the IAPWS-IF97. The total temperature T0, the total pressure P0 and the flow angle at the inlet of governing stage are 839 K, 23.63MPa and 0, respectively. The static pressure P2 at the outlet of governing stage is 16.804MPa. The
periodic boundary condition is used on the boundaries of the model. The adiabatic and non-slip boundary conditions are applied on the blade surface. The areas near the wall are processed by the scalable wall-function method. To obtain well boundary layer, the boundary layer mesh refinement technology is used and the dimensionless distance from the wall（y+）is ensured below 30 as the turbulence model requirement. The frozen rotor model produces a steady state solution to the multiple frame of reference problems and takes some account of the interaction between the two frames. Therefore, it is applied at the interface between nozzle and rotor in this simulation. 1.3 Validation of turbulence model To simulate the compressible viscous flow in the governing stage of steam turbine, the time-averaging continuity equation, Navier-Stokes equation and energy equation are solved by the control volume method. In order to find the best turbulence model to predict the erosion of governing stage, three different models including the RNG k- model with a scalable wall function, the SST model with an automatic near wall treatment approach and the standard k- model with a scalable wall function are provided by ANSYS-CFX to model the dilute-phase steam-particle movement and results are shown in Fig. 2. 1.0 0.8 0.6 0.4
Cps
number should not be less than 640 thousands. Considering the computing speed, the total grid number of the flow passage is identified as 640 thousands in this paper.
EXP. RNG k-ε model SST model k-ε model
0.2 0.0 -0.2 -0.4 0.0
0.2
0.4
0.6
0.8
1.0
y/B
(a) Static pressure distribution
3
1.0
ζp 0.8
EXP. RNG k-ε model SST model k-ε model
hr
0.6
0.4
0.0 0.06
0.08
0.10
0.12
0.14
p02,t p2
(3)
Here, p02,t is the mass average value of P02, t,
0.2
0.04
p02,t p2,t
0.16
ξp
(b) Variation of ζp with hr Fig.2 Comparison of the numerical simulation and experiment
Fig. 2(a) displays the comparison of the numerical simulations and experiment in the static pressure distributions of the governing stage cascade. The static pressure coefficient Cps can be defined as P P2 Cps s (1) P02,t P2 Here Ps is the surface static pressure of the cascade at the mid-span, P2 is the final static pressure at the nozzle exit, P02,t is the stagnation pressure at the nozzle inlet. The transverse axis y/B is the relative axial chord length. It can be seen that the simulation results are highly consistent with the experimental result and the average error of Cps is less than 2%. However, the results are unable to determine which the best model is because the curves of three different models completely overlap. Fig.2(b) further displays the comparison of numerical simulations and the experiment in the variation of ζ p along the radial direction of the governing stage. hr is the relative height of the cascade and it is defined as (r rh ) hr (2) H Here, r is the distance from an eroded site to the rotation centre of the rotor and rh is the radius of the nozzle’s hub. The transverse axis ζp is the total pressure loss coefficient which is defined as
and P2,t is the stagnation pressure at the nozzle exit. It can be seen that the RNG k- model is the closest to the experimental data and the average error of ζp is less than 3 %. Besides, the RNG k- model has the best performance in the simulation of flow with high strain rates, swirl and separation [19], and is also validated by other literatures [16-18]. Therefore, the RNG k- model is used to closure the Navier-Stokes equation in this paper.
2 Computing Method of Erosion Behavior 2.1 Particle motion equation On account of dilute-phase steam-particle movement, one-way coupled dispersed particles model is selected. The solid particle transport model is used to model the behavior of solid particle, which is only valid for quite low volume fractions. This model is based on the Lagrangian tracking model [16] to characterize the flow behavior of particles. Particle track behavior at a wall boundary is calculated by Finnie rebound model [2]. The motion equation [20] of particle is: dup 18 CD Re (4) u up dt p d p 2 24 Here the drag force coefficient CD is given by the following equation: CD
b Re 24 (1 b1 Reb2 ) 3 Re b4 Re
b1 exp(2.3288-6.4581 2.448 2 )
b2 0.0964 0.5565 b3 exp(4.905 13.8944 18.4222 2 10.2599 3 )
b4 exp(1.4681 12.2584 20.7322 2 15.8855 3 )
4
Where u and up are the steam velocity and
Here 1 1 2 tan( ) 3 cos 3 (6) f ( ) 2 sin(2 ) 3sin tan ( ) 1 3
the particle velocity, respectively, m/s, dp is the particle diameter, m, μ is the fluid dynamic viscosity, N s/m2, ρp is the density of particles, kg/m3, Re is Reynolds numbers, is particle shape factor.
angle function,
Tab.3 Diameter distribution of solid particles Size range (m)
Average diameter (m)
Mass flow (kg/s)
5-10
7.5
0.00024
12-20
15
0.00248
20-30
25
0.00646
30-50
40
0.02332
50-100
75
0.06751
is the impact angle in
radians between the approaching particle track and the wall.
The main compositions of oxide particles are Fe3O4 and Fe2O3. The corresponding densities are 5180 kg/m3 and 5240 kg/m3, respectively. The Mohs hardness of particles is about 5.5[21]. Since the density of Fe3O4 and Fe2O3 has little difference, the density of Fe3O4 is used in the simulation to simplify the calculation. According to analysis result of the sample of drain in boiler and superheater in the power plant, the size of oxide particles is usually less than 100 μm [22]. Particles size distribution of oxide scales are shown in Tab.3 [15] . To shorten the calculating time, the average diameters 7.5μm、15μm、25μm、 40μm、75μm are used to replace the scope of particle size. 2.2 Computing Method of Erosion Rate Erosion rate is influenced by many factors. On one side, the velocity of particle and impact angel with blade as well as a variety of physical properties can influence the erosion rate. On the other side, the profile, rigidity, ductility, residual stress and corrosion resistance of blade also affect the erosion rate [23] . The erosion in the governing stage is thought as the accumulation of all particles with different diameter. Therefore, the formulas associated with the erosion model [15] are used to calculate the erosion rate.
E 2.12 10-13 up3.16 f ( )
Where the E is the erosion rate of a single particle, f ( ) is the dimensionless impact
(5)
Fig.3 Relationship between erosion rate and impact angle
[1]
Fig.3 shows the relationship between erosion rate and impact angle of particles. It can be observed that the erosion rate reaches the peak when the impact angle is about 25. In order to reduce the erosion caused by particles, the impact angle range from 20° to 35° should be avoided. The total amount of erosion on the blade is calculated by the follow equation
me E N p mp
(7)
Where N p is the mass flow rate of particle, kg/s, and mp is the mass of a single particle, kg. Furthermore，several basic assumptions are made for this simulation: ⅰ Geometry change caused by the removal of blade surface by solid particles is neglected and the roughness is constant. ⅱ Collisions among particles are neglected. ⅲ Breakage of particles are not considered in the simulation.
3 Results and Analysis 5
3.1 SPE on Nozzle The trajectories of three kinds of particles 7.5μm, 25μm and 75μm in the nozzle are shown in Fig.4. We can see that, the eroded area of three different diameters particles focuses on the leading edge and the pressure surface. However, the suction surface is not eroded obviously. By comparison to the trajectories in nozzle, it is not difficult to find that the trajectories of 7.5μm particles are almost the same as steam flow direction and about 50 of the particles escape from the nozzle flow passage without impacting the blade surface. With the increase of particle size, the particle trajectories tend to straight line. Therefore, the critical size is defined as the maximum size of particles whose trajectories are the same as steam flow direction. When the particle size is over the critical size, the particle trajectories tend to straight line. Otherwise, the particle trajectories are almost the same as steam flow direction. In five kinds of particles (7.5μm, 15μm, 25μm, 40μm and 75μm), the trajectories of 25μm particles almost tends to straight line. Thus, the critical size of particle
in the nozzle is in the range of 15-25μm. Besides, the eroded area moves forward with the increase of particle size.
7.5μm
25μm
and the maximum impact velocity of 75μm is at 0.88 axial chord length. In addition, with the increase of the particle size, the impact velocity declines gradually. Since the small particles have small inertia force itself, they are easily carried by steam. On the contrary, the large particles have large inertia force itself and are not interfered easily by external factors.
Fig.5 Impact velocity of particles on nozzle pressure surface
Fig.6 displays the impact angle of particles on the nozzle pressure surface. The shaded area means the angle range of the maximum erosion rate. We can see that the impact angle of the 7.5μm particles is near the 5°, which is far away from the angle range of the maximum erosion rate. However, the impact angle of 75μm particles at pressure surface mid-real part is between 20-27° which is in the angle range of the maximum erosion rate. As shown in Fig.6, the impact angle increases with the increase of particle size. Large size particles have a large impact angle because the trajectories of large particles tend to straight line.
75μm
Fig.4 Radial projection of solid particle trajectory in nozzle
The impact velocity of particles on the nozzle pressure surface along the axial direction can be obtained from Fig.5. We can find that with the impact position moves forward along axial distance, the impact velocity increases. The maximum impact velocity of 7.5μm and 25μm particles appears on the trailing edge of nozzle pressure surface
Fig.6 Impact angle of particles on nozzle pressure surface
The eroded scope and the erosion 6
degree of nozzle at the rotation speed 3000 rpm are shown in Fig.7. It can be seen that the eroded scope is consistent with the trajectories of particles showed in Fig.4. Most of the erosion appears on the mid-rear part of the pressure surface and the erosion degree of the leading edge is comparatively slight. However, there is little effect of erosion on the nozzle suction surface. The movement of solid particles in the flow passage is influenced by its inertia, the steam pressure gradient and the steam carryover. Part of the solid particles impact on the leading edge directly, resulting the erosion on the leading edge but the erosion degree is slight because the particle velocity at the inlet of the passage is low. Small particles have small inertia and are easily carried to the nozzle flow passage by main steam. The trajectories of small particles in the nozzle are almost the same as main steam flow direction, leading to the impact position on the latter of the nozzle pressure surface. Therefore, the eroded area is at the mid-rear part of the pressure surface. With the increase of particles size, the inertia force increases. At the same time, the moving directions of these large particles are hard to be changed by the main steam. As a result, the trajectories of large particles tend to straight line. The impact position on the nozzle pressure surface moves forward and the eroded scope of the large particles on the nozzle pressure surface moves forward too. As the pressure drop at the mid-rear part of the pressure surface is relatively large, the particles velocity accelerate quickly in this area and the erosion on the mid-rear part of the nozzle pressure surface is more serious than that on other eroded area. SPE can destroy the integrity of the trailing edge and decrease the efficiency of the governing stage. Thus the mid-rear part of the pressure surface is
eroded easily on the nozzle. The maximum erosion rate density of 7.5μm particles on the nozzle is 3.930e-006 kg/ (m2 s) while the maximum erosion rate density of 75μm particles is 6.755e-004 kg/ (m2 s). The maximum erosion rate density of 75μm particles is 179 times of 7.5μm particles. Therefore, the large particles play a major role on the nozzle erosion. After impacting on the nozzle pressure surface, the rebound angle of particles is very small and the particles rarely rebound to the nozzle suction surface. As a result, the erosion rarely appears on the nozzle suction surface. As illustrated in Fig.7, since the nozzle blades do not rotate, the eroded area on the nozzle pressure surface is not skewed along the radial direction. Therefore, the erosion distributes uniformly from blade root to tip.
7.5μm
25μm
7
75μm Fig.7 SPE on nozzle blade
3.2 SPE on Rotor The trajectories of the three different diameter particles in the governing stage rotor blade at the rotation speed 3000 rpm are shown in Fig.8. As can be seen in Fig.8(a), the trajectories of 7.5μm particles in the rotor flow passage are almost the same as steam flow direction. The impact points focus on the leading edge and the pressure surface closing to the trailing edge. Some of the particles entering into the rotor flow passage with main steam do not collide with the rotor surface and directly flow to the next stage with the main steam. Only the trajectories of 75μm particles tend to straight line in the five kinds of particles (7.5μm, 15μm, 25μm, 40μm and 75μm). Therefore, the critical size of particle
in the rotor blade is in the range of 50-75μm.The erosion points of 75μm particles focus on the leading edge, the suction surface near to the leading edge and the pressure surface. Compare the trajectories of three different diameters in the rotor flow passage, we can see that the erosion points move forward with the increase of particle size.
7.5μm
25μm
75μm
Fig.8 Radial projection of solid particle trajectory in rotor flow passage
The impact velocity of particles on the rotor blade pressure surface can be obtained
from Fig.9. It can be seen that the velocity of 7.5μm particles is the largest in all the different size particles and the maximum impact velocity can reach to 322m/s, which appears on the trailing edge of pressure surface. The maximum impact velocity of 25μm particles is 277m/s, which appears on the mid-rear part of pressure surface. The impact velocity of 7.5μm particles and 25μm particles all have an obvious rising trend as the impact position moves forward in axial direction. The impact velocity distribution of 75μm particles are somewhat different with 7.5μm and 25μm along the rotor axial distance because the 75μm particles have the secondary impact with the rotor pressure surface, which can be seen obviously from Fig.8. The impact velocity in the rotor flow passage of three different diameter particles (7.5μm, 25μm and 75μm) presents a downward trend with the increase of particle size.
Fig.9 Impact velocity of particles on rotor blade pressure surface
Fig.10 shows the impact angle of particles on rotor blade pressure surface. The shaded area means the angle range of the maximum erosion rate. From Fig.10, we can see that the larger the solid particle size is, the greater the impact angle will be. The impact angle of the 7.5μm particles is near the 15° which is far away from the angle range of the maximum erosion rate. The impact angle of the 25μm particles is in the range of 17.5-20° and a few particles’ impact angle is a little greater than 20°. However, most of the impact angle of the 75μm particles is in the range of
8
20-35° which is in the angle range of the maximum erosion rate. The trajectories of small particles are almost the same as main steam direction so the impact angle of particles on the rotor pressure surface is small correspondently. The inertia increases with the increase of particle size, which leads to the trajectory tending to straight line and the impact angle increases too.
Fig.10 Impact angle of particles on rotor blade pressure surface
The eroded scope and the erosion degree of rotor blade at the rotation speed 3000 rpm are shown in Fig.11. As we can see that the eroded scope of rotor appears on the leading edge, the suction surface close to the leading edge and the pressure surface. Most of the erosion appears on the pressure surface and has a wide distribution along the axial direction. When solid particles flow out from the nozzle with the main steam, some of these particles impact directly on the leading edge of rotor blade and the suction surface of rotor blade close to the leading edge resulting in the erosion in the two areas. But the erosion degree is comparatively slighter than that of trailing edge since their impact velocity is smaller than that on the trailing edge. The solid particles at the mid-rear part of rotor flow passage accelerate quickly as the rotor blade has a certain degree of reaction, making the erosion at the mid-rear part more serious. At the same time, SPE can destroy the blade integrity because the trailing edge is thin. Just like the erosion on nozzle, the erosion on rotor blade of different size particles is different too. The erosion made by small particles focuses
on the trailing edge of the pressure surface. The impact points move forward with the increase of the particle size. Compared to the erosion made by small particles, the erosion made by large particles has a wider distribution along the axial direction. At the rotation speed 3000 rpm, the eroded area on the pressure surface has obvious upward trend because of centrifugal force and the radial migration quantity is about 7% of blade height, resulting in the erosion on the blade tip more serious than that on root. Moreover, different size particles have different erosion rate density on the rotor blade, as we can see from Fig.11. The maximum erosion rate density of 7.5μm particles is 1.453e-005 kg/ (m2 s) while the maximum erosion rate density of 75μm particles is 1.332e-003 kg/ (m2 s). As a result, the maximum erosion rate density of 75μm particles is 90 times of 7.5μm particles. Compared to nozzle, the maximum erosion rate density on rotor blade is 1.9 times of the rate on nozzle. Consequently, the erosion degree on the rotor blade is more serious than that on nozzle. As we all know, stage efficiency is one of the important indexes of steam turbine performance evaluation. SPE can destroy the integrity of nozzle and rotor blade, which is proved in Fig.7 and Fig.11. Thereby, the efficiency of governing stage will decrease. The eroded area appears on part of the blade surface, not on the whole blade surface, so the roughness is increased on the local scope. In addition, the size, shape and location of notch made by SPE also have an important influence on stage efficiency. Kawagishi [24] et al. investigated an eroded nozzle and the result showed a 3~6 percent decrease in efficiency compared to the non-erosion nozzle. Due to the complexity of decline of stage efficiency made by SPE, this problem is not analyzed quantitatively in this paper and will be studied 9
in detail in future research.
increase of particle size. In addition, there is almost no difference with the results in literature [5] on maximum impact angle of 7.5μm, 15μm in this paper. Moreover, the maximum error of maximum impact angle is 5.5 for 25μm particles. Based on the above analysis, the simulation results in this paper are believable.
7.5μm
(a) nozzle
(b) rotor blade
Fig.12 SPE morphology of governing stage in a supercritical steam turbine [19] 30
25μm
results of this paper results of ref [5]
Impact angle/(°)
25 20 15 10 5 0 0
10
20
4 Validation of SPE In order to verify the reliability of the simulation results in this paper, Fig.11 shows the solid particle erosion morphology of governing stage in a typical supercritical steam turbine. As we have seen from the preceding discussion, most of the erosion appears on the mid-rear part of the pressure surface. The result is consistent with the erosion occurring on actual operation in Fig.12. Fig.13 shows the maximum impact angle with the change of particle diameter on nozzle pressure surface. By comparison to the results in literature [5], it is verified that the impact angle gradually increases with the
40
50
60
70
80
dp/μm
75μm Fig.11 SPE on rotor blade
30
Fig.13 Maximum impact angle along with the change of particle diameter on nozzle pressure surface
5 Conclusion The comprehensive numerical simulation on SPE in the governing stage of a supercritical steam turbine is performed in this paper. The erosion characteristics of SPE on nozzle and rotor blade are studied under different particle sizes and rotation speeds. The conclusions of this study are summarized as follows: (1) In the flow passage of governing stage, the trajectories of small particles are almost the same as steam flow direction. With the increase of particle size, the particle 10
trajectories tend to straight line. The critical size of particles in the nozzle is in the range of 15-25μm while the critical size of particles in the rotor blade is in the range of 50-75μm. (2) The erosion rate density on the nozzle is smaller than that on the rotor blade. The maximum erosion rate density on the rotor blade is 1.9 times of the rate on nozzle. SPE can destroy the integrity of the trailing edge of nozzle and rotor blade. (3) The eroded area is concentrated mainly on the mid-rear part of the nozzle pressure surface and is distributed is along the radial direction from root to tip without any skew. However, the eroded area of rotor blade appears on the leading edge, the suction surface close to the leading edge and the pressure surface and has an obvious upward trend. The radial migration quantity is about 7% of blade height at 3000 rpm. (4) With the increase of particle size, the impact velocity on the nozzle and rotor blade pressure surface presents a downward trend simultaneously. However, the impact angle shows an opposite trend. The larger the solid particle size is, the greater the impact angle will be. Acknowledgement This work was supported by National Natural Science Foundation of China (NSFC) (No. 51376041 and No. 51576036). Nomenclature B axial chord length mm steam velocity, m/s u particle velocity, m/s up dp Re E
f( )
particle diameter, m relative Reynolds numbers erosion rate of a single particle dimensionless impacting angle function
Np
particle number flow rate kg/s
Greek symbols μ fluid dynamic viscosity N s/m2 particle shape factor density of particles, kg/m3 impact angle° Abbreviations SPE solid particle erosion CFD computational fluid dynamics IPC intermediate-pressure cylinders Reference [1] W.J. Sumner, J.H. Vogan, R.J. Lindinger. ρp
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13
Highlights 1 Radial projection of solid particle trajectory in nozzle are presented 2 The distribution of SPE on nozzle and rotor blade are analyzed
3 the radial migration quantity of SPE on rotor blade are taken into considerations
S1359-4311(16)31746-X http://dx.doi.org/10.1016/j.applthermaleng.2017.02.103 ATE 9984
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
19 September 2016 25 February 2017 25 February 2017
Please cite this article as: Z. Zhang, F. Li, L. Cao, P. Hu, Y. Li, Research on Characteristics of Solid Particle Erosion in Governing Stage of a 600MW Supercritical Steam Turbine, Applied Thermal Engineering (2017), doi: http:// dx.doi.org/10.1016/j.applthermaleng.2017.02.103
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Research on Characteristics of Solid Particle Erosion in Governing Stage of a 600MW Supercritical Steam Turbine Zhongbin ZHANG, Fang LI, Lihua CAO, Pengfei HU, Yong LI (School of Energy and Power Engineering, Northeast Electric Power University, Jilin 132012, Jilin Province, China)
Abstract：Solid particle erosion (SPE) of governing stage has been proved to be great threat to steam turbine performance. Based on Eulerian-Lagrangian method and Finnie rebound model, the urgent SPE problem of high-parameter steam turbine is studied and the characteristics of SPE in governing stage of a 600MW supercritical steam turbine were simulated and analyzed under different particle sizes and rotation speeds in this paper. Results show that the eroded area on nozzle is mainly at the mid-rear part of the pressure surface and is distributed along the radial direction from root to tip. The erosion on rotor blade appears on the leading edge, the mid-rear part of the pressure surface and the suction surface near to the leading edge. Additionally, the eroded area on rotor blade has an obviously upward trend, the radial migration of eroded area increases with the increase of rotation speed and the radial migration quantity is about 7% of blade height at 3000 rpm. The maximum erosion rate density on the rotor blade is 1.9 times of the rate on nozzle. Besides, the critical size of particle is different in nozzle and rotor blade. Key words：steam turbine; governing stage; solid particle erosion(SPE); rotation speed Introduction Solid particle erosion (SPE) is one of the major problems in supercritical and ultra-supercritical unit. Scales flaking away from the inner wall of boiler super-heater and main steam pipe are carried to steam turbine by main steam, which causes SPE in the flow passage, especially in the nozzles and the rotor blades of governing stage. SPE can result in lower efficiency of steam turbine, shorter repair cycle and higher maintenance cost [1]. Therefore, reducing SPE can enhance the economy, efficiency and reliability of unit. Several articles have discussed the effect factors of SPE by means of analysis and simulation. Finnie [2] put forward the influence of particle velocity and impact angle of brittle material, which is quite different from that of ductile material. For ductile materials, the impact angle leading to maximum erosion can be predicted. Hamed.[3] et al. showed clearly that the turbomachinery erosion is influenced by many factors such as the ingested particle characteristics, flow passage, blade geometry, operating conditions and blade material. Alfonso [4] et al. numerically investigated the
influence of the parameters such as particle velocity, impact angle and particle distribution. The particle trajectories and the streamline of steam for basic running were shown but there is no deep discussion on the difference between them in governing stage. Cai [5,6] et al. also analyzed the influence of opening conditions, particle size distribution in the inlet of nozzle and axial clearance between vanes and rotating blades based on SPE characteristics and rebound characteristics of steam turbine blade materials. Their results indicate that the erosion damage of the first reheat stage nozzles in high parameter steam turbines is mainly caused by the particle impact on suction surface. Li [7] et al. analyzed the effect of particle parameters on the erosion rate of nozzle and rotor blade surfaces in unsteady condition and resulted that the erosion rate of the vane blade is sensitive to the fluctuation of the potential flow field. Hamed [8] et al. indicated that both erosion rate and surface roughness increase with the particle impact velocities and impact angles for blade and coating material erosion by experiment. Azimian [9] et al. proved that with
the increase of rotation speed, the higher the impact velocity is, the higher the erosion rate density will be. Furthermore, they also noted that the erosion rate density changes with the change of rotation speed. However, the change of the migration quantity wasn’t mentioned. Brun [10] et al. developed a mixed Computational Fluid Dynamics-Empirical software tool, making the kinematic and impacting behavior of solid particulates in the near-filed of turbomachinery blades and impellers surfaces can be analyzed by probabilistic method. However, Oka [11] et al. found that the impact velocity does not affect the dependence of erosion behavior on the impact angle for the metallic materials. In addition, the influence of SPE on efficiency of unit has been reported analytically and experimentally. Wang [12] et al. stated that the weight-loss of the nozzle can be reduced by about 40-50 percent and the nozzle efficiency is increased by 0.4-0.5 percent through improving the end-wall contouring of nozzle. Khaimov [13] et al. studied the first stages of IPC(intermediate-pressure cylinders) of T-250/300-240 turbines and found that the blades experienced intense erosion wear due to products of decomposition of the oxide film deposited on the superheater conduit of the boiler, which decreases the efficiency of operation and reduces the service life of blade. There are several ways to improve SPE by using ceramic coating and modified design. Tabakoff [14] et al. designed a high temperature erosion test facility to provide erosion data in the range of operating temperatures experienced in compressors and turbines and he found that the material of high density and fine grained ceramic coating with good adhesion to the substrate could significantly improve erosion. Dai [15] et al. researched the anti-erosion of the tip endwall contouring, the aft-loaded nozzle and a straight endwall nozzle. They conducted that the severely
eroded area and the maximum erosion rate of the tip endwall contouring nozzle are reduced by about 30 and 40 respectively. By changing the particle trajectories and impact angle, the solid particle erosion rate in main steam bypass valve was reduced by 51[16, 17]. The main goal of this paper is to analyze the SPE problem under various particle sizes and rotation speeds by three-dimensional numeral simulation in the governing stage of a 600MW supercritical steam turbine. The difference between particle trajectories and streamline of steam are compared in nozzle and rotor blade. The maximum erosion rate density and the eroded area on nozzle and rotor blade are also given. Furthermore, the radial migration quantity of eroded area on the pressure surface of rotor blade caused by the change of rotation speed is investigated quantitatively. The research results in this paper reveal the erosion characteristics of SPE in steam turbine governing stage. It provides a theoretical basis for preventing and reducing SPE of high-parameter steam turbine. 1 Mesh Sketch and Boundary Conditions 1.1 Mesh Sketch A physical model of the governing stage of a 600MW supercritical steam turbine is established. Tab.1 displays the geometric parameters of the governing stage. The geometrical model and grid sketch of the governing stage flow passage are shown in Fig.1. In order to determine the grid number effects on calculation accuracy, validation of grid dependency is carried out. For cascade passage, five sets of grids of 190, 410, 640, 730 and 960 thousands cells are conducted. Tab.2 illustrates the effects of grid number on the CFD results using the maximum erosion rate density as reference parameters and it is found that the total grid number has little effect on the maximum erosion rate density when the total grid number reaches to 640 thousands. These data mean that the total grid 2
Tab.1 Geometrical parameters of governing stage blades Project
Nozzle
Pitch diameter
Unit
96
81
27.31
29.7
mm
Number of blade Blade height
Rotor
1 068.71
1 077.90
mm
Pitch of cascade
32.46
41.81
mm
Axial length
63.81
63.5
mm
（a）Geometrical model
b Grid sketch Fig.1 Geometrical model and grid sketch of governing stage flow passage Tab.2 Relations between erosion rate density and grid number Scheme
Total number
the maximum erosion rate density /kg/(m2 s)
1
190000
2.043e-004
2
410000
1.661e-003
3
640000
1.727e-003
4
730000
1.742e-003
5
960000
1.739e-003
1.2 Boundary Conditions Numerical simulations are performed by ANSYS-CFX software. The working medium is superheated vapor whose status parameters are provided by the IAPWS-IF97. The total temperature T0, the total pressure P0 and the flow angle at the inlet of governing stage are 839 K, 23.63MPa and 0, respectively. The static pressure P2 at the outlet of governing stage is 16.804MPa. The
periodic boundary condition is used on the boundaries of the model. The adiabatic and non-slip boundary conditions are applied on the blade surface. The areas near the wall are processed by the scalable wall-function method. To obtain well boundary layer, the boundary layer mesh refinement technology is used and the dimensionless distance from the wall（y+）is ensured below 30 as the turbulence model requirement. The frozen rotor model produces a steady state solution to the multiple frame of reference problems and takes some account of the interaction between the two frames. Therefore, it is applied at the interface between nozzle and rotor in this simulation. 1.3 Validation of turbulence model To simulate the compressible viscous flow in the governing stage of steam turbine, the time-averaging continuity equation, Navier-Stokes equation and energy equation are solved by the control volume method. In order to find the best turbulence model to predict the erosion of governing stage, three different models including the RNG k- model with a scalable wall function, the SST model with an automatic near wall treatment approach and the standard k- model with a scalable wall function are provided by ANSYS-CFX to model the dilute-phase steam-particle movement and results are shown in Fig. 2. 1.0 0.8 0.6 0.4
Cps
number should not be less than 640 thousands. Considering the computing speed, the total grid number of the flow passage is identified as 640 thousands in this paper.
EXP. RNG k-ε model SST model k-ε model
0.2 0.0 -0.2 -0.4 0.0
0.2
0.4
0.6
0.8
1.0
y/B
(a) Static pressure distribution
3
1.0
ζp 0.8
EXP. RNG k-ε model SST model k-ε model
hr
0.6
0.4
0.0 0.06
0.08
0.10
0.12
0.14
p02,t p2
(3)
Here, p02,t is the mass average value of P02, t,
0.2
0.04
p02,t p2,t
0.16
ξp
(b) Variation of ζp with hr Fig.2 Comparison of the numerical simulation and experiment
Fig. 2(a) displays the comparison of the numerical simulations and experiment in the static pressure distributions of the governing stage cascade. The static pressure coefficient Cps can be defined as P P2 Cps s (1) P02,t P2 Here Ps is the surface static pressure of the cascade at the mid-span, P2 is the final static pressure at the nozzle exit, P02,t is the stagnation pressure at the nozzle inlet. The transverse axis y/B is the relative axial chord length. It can be seen that the simulation results are highly consistent with the experimental result and the average error of Cps is less than 2%. However, the results are unable to determine which the best model is because the curves of three different models completely overlap. Fig.2(b) further displays the comparison of numerical simulations and the experiment in the variation of ζ p along the radial direction of the governing stage. hr is the relative height of the cascade and it is defined as (r rh ) hr (2) H Here, r is the distance from an eroded site to the rotation centre of the rotor and rh is the radius of the nozzle’s hub. The transverse axis ζp is the total pressure loss coefficient which is defined as
and P2,t is the stagnation pressure at the nozzle exit. It can be seen that the RNG k- model is the closest to the experimental data and the average error of ζp is less than 3 %. Besides, the RNG k- model has the best performance in the simulation of flow with high strain rates, swirl and separation [19], and is also validated by other literatures [16-18]. Therefore, the RNG k- model is used to closure the Navier-Stokes equation in this paper.
2 Computing Method of Erosion Behavior 2.1 Particle motion equation On account of dilute-phase steam-particle movement, one-way coupled dispersed particles model is selected. The solid particle transport model is used to model the behavior of solid particle, which is only valid for quite low volume fractions. This model is based on the Lagrangian tracking model [16] to characterize the flow behavior of particles. Particle track behavior at a wall boundary is calculated by Finnie rebound model [2]. The motion equation [20] of particle is: dup 18 CD Re (4) u up dt p d p 2 24 Here the drag force coefficient CD is given by the following equation: CD
b Re 24 (1 b1 Reb2 ) 3 Re b4 Re
b1 exp(2.3288-6.4581 2.448 2 )
b2 0.0964 0.5565 b3 exp(4.905 13.8944 18.4222 2 10.2599 3 )
b4 exp(1.4681 12.2584 20.7322 2 15.8855 3 )
4
Where u and up are the steam velocity and
Here 1 1 2 tan( ) 3 cos 3 (6) f ( ) 2 sin(2 ) 3sin tan ( ) 1 3
the particle velocity, respectively, m/s, dp is the particle diameter, m, μ is the fluid dynamic viscosity, N s/m2, ρp is the density of particles, kg/m3, Re is Reynolds numbers, is particle shape factor.
angle function,
Tab.3 Diameter distribution of solid particles Size range (m)
Average diameter (m)
Mass flow (kg/s)
5-10
7.5
0.00024
12-20
15
0.00248
20-30
25
0.00646
30-50
40
0.02332
50-100
75
0.06751
is the impact angle in
radians between the approaching particle track and the wall.
The main compositions of oxide particles are Fe3O4 and Fe2O3. The corresponding densities are 5180 kg/m3 and 5240 kg/m3, respectively. The Mohs hardness of particles is about 5.5[21]. Since the density of Fe3O4 and Fe2O3 has little difference, the density of Fe3O4 is used in the simulation to simplify the calculation. According to analysis result of the sample of drain in boiler and superheater in the power plant, the size of oxide particles is usually less than 100 μm [22]. Particles size distribution of oxide scales are shown in Tab.3 [15] . To shorten the calculating time, the average diameters 7.5μm、15μm、25μm、 40μm、75μm are used to replace the scope of particle size. 2.2 Computing Method of Erosion Rate Erosion rate is influenced by many factors. On one side, the velocity of particle and impact angel with blade as well as a variety of physical properties can influence the erosion rate. On the other side, the profile, rigidity, ductility, residual stress and corrosion resistance of blade also affect the erosion rate [23] . The erosion in the governing stage is thought as the accumulation of all particles with different diameter. Therefore, the formulas associated with the erosion model [15] are used to calculate the erosion rate.
E 2.12 10-13 up3.16 f ( )
Where the E is the erosion rate of a single particle, f ( ) is the dimensionless impact
(5)
Fig.3 Relationship between erosion rate and impact angle
[1]
Fig.3 shows the relationship between erosion rate and impact angle of particles. It can be observed that the erosion rate reaches the peak when the impact angle is about 25. In order to reduce the erosion caused by particles, the impact angle range from 20° to 35° should be avoided. The total amount of erosion on the blade is calculated by the follow equation
me E N p mp
(7)
Where N p is the mass flow rate of particle, kg/s, and mp is the mass of a single particle, kg. Furthermore，several basic assumptions are made for this simulation: ⅰ Geometry change caused by the removal of blade surface by solid particles is neglected and the roughness is constant. ⅱ Collisions among particles are neglected. ⅲ Breakage of particles are not considered in the simulation.
3 Results and Analysis 5
3.1 SPE on Nozzle The trajectories of three kinds of particles 7.5μm, 25μm and 75μm in the nozzle are shown in Fig.4. We can see that, the eroded area of three different diameters particles focuses on the leading edge and the pressure surface. However, the suction surface is not eroded obviously. By comparison to the trajectories in nozzle, it is not difficult to find that the trajectories of 7.5μm particles are almost the same as steam flow direction and about 50 of the particles escape from the nozzle flow passage without impacting the blade surface. With the increase of particle size, the particle trajectories tend to straight line. Therefore, the critical size is defined as the maximum size of particles whose trajectories are the same as steam flow direction. When the particle size is over the critical size, the particle trajectories tend to straight line. Otherwise, the particle trajectories are almost the same as steam flow direction. In five kinds of particles (7.5μm, 15μm, 25μm, 40μm and 75μm), the trajectories of 25μm particles almost tends to straight line. Thus, the critical size of particle
in the nozzle is in the range of 15-25μm. Besides, the eroded area moves forward with the increase of particle size.
7.5μm
25μm
and the maximum impact velocity of 75μm is at 0.88 axial chord length. In addition, with the increase of the particle size, the impact velocity declines gradually. Since the small particles have small inertia force itself, they are easily carried by steam. On the contrary, the large particles have large inertia force itself and are not interfered easily by external factors.
Fig.5 Impact velocity of particles on nozzle pressure surface
Fig.6 displays the impact angle of particles on the nozzle pressure surface. The shaded area means the angle range of the maximum erosion rate. We can see that the impact angle of the 7.5μm particles is near the 5°, which is far away from the angle range of the maximum erosion rate. However, the impact angle of 75μm particles at pressure surface mid-real part is between 20-27° which is in the angle range of the maximum erosion rate. As shown in Fig.6, the impact angle increases with the increase of particle size. Large size particles have a large impact angle because the trajectories of large particles tend to straight line.
75μm
Fig.4 Radial projection of solid particle trajectory in nozzle
The impact velocity of particles on the nozzle pressure surface along the axial direction can be obtained from Fig.5. We can find that with the impact position moves forward along axial distance, the impact velocity increases. The maximum impact velocity of 7.5μm and 25μm particles appears on the trailing edge of nozzle pressure surface
Fig.6 Impact angle of particles on nozzle pressure surface
The eroded scope and the erosion 6
degree of nozzle at the rotation speed 3000 rpm are shown in Fig.7. It can be seen that the eroded scope is consistent with the trajectories of particles showed in Fig.4. Most of the erosion appears on the mid-rear part of the pressure surface and the erosion degree of the leading edge is comparatively slight. However, there is little effect of erosion on the nozzle suction surface. The movement of solid particles in the flow passage is influenced by its inertia, the steam pressure gradient and the steam carryover. Part of the solid particles impact on the leading edge directly, resulting the erosion on the leading edge but the erosion degree is slight because the particle velocity at the inlet of the passage is low. Small particles have small inertia and are easily carried to the nozzle flow passage by main steam. The trajectories of small particles in the nozzle are almost the same as main steam flow direction, leading to the impact position on the latter of the nozzle pressure surface. Therefore, the eroded area is at the mid-rear part of the pressure surface. With the increase of particles size, the inertia force increases. At the same time, the moving directions of these large particles are hard to be changed by the main steam. As a result, the trajectories of large particles tend to straight line. The impact position on the nozzle pressure surface moves forward and the eroded scope of the large particles on the nozzle pressure surface moves forward too. As the pressure drop at the mid-rear part of the pressure surface is relatively large, the particles velocity accelerate quickly in this area and the erosion on the mid-rear part of the nozzle pressure surface is more serious than that on other eroded area. SPE can destroy the integrity of the trailing edge and decrease the efficiency of the governing stage. Thus the mid-rear part of the pressure surface is
eroded easily on the nozzle. The maximum erosion rate density of 7.5μm particles on the nozzle is 3.930e-006 kg/ (m2 s) while the maximum erosion rate density of 75μm particles is 6.755e-004 kg/ (m2 s). The maximum erosion rate density of 75μm particles is 179 times of 7.5μm particles. Therefore, the large particles play a major role on the nozzle erosion. After impacting on the nozzle pressure surface, the rebound angle of particles is very small and the particles rarely rebound to the nozzle suction surface. As a result, the erosion rarely appears on the nozzle suction surface. As illustrated in Fig.7, since the nozzle blades do not rotate, the eroded area on the nozzle pressure surface is not skewed along the radial direction. Therefore, the erosion distributes uniformly from blade root to tip.
7.5μm
25μm
7
75μm Fig.7 SPE on nozzle blade
3.2 SPE on Rotor The trajectories of the three different diameter particles in the governing stage rotor blade at the rotation speed 3000 rpm are shown in Fig.8. As can be seen in Fig.8(a), the trajectories of 7.5μm particles in the rotor flow passage are almost the same as steam flow direction. The impact points focus on the leading edge and the pressure surface closing to the trailing edge. Some of the particles entering into the rotor flow passage with main steam do not collide with the rotor surface and directly flow to the next stage with the main steam. Only the trajectories of 75μm particles tend to straight line in the five kinds of particles (7.5μm, 15μm, 25μm, 40μm and 75μm). Therefore, the critical size of particle
in the rotor blade is in the range of 50-75μm.The erosion points of 75μm particles focus on the leading edge, the suction surface near to the leading edge and the pressure surface. Compare the trajectories of three different diameters in the rotor flow passage, we can see that the erosion points move forward with the increase of particle size.
7.5μm
25μm
75μm
Fig.8 Radial projection of solid particle trajectory in rotor flow passage
The impact velocity of particles on the rotor blade pressure surface can be obtained
from Fig.9. It can be seen that the velocity of 7.5μm particles is the largest in all the different size particles and the maximum impact velocity can reach to 322m/s, which appears on the trailing edge of pressure surface. The maximum impact velocity of 25μm particles is 277m/s, which appears on the mid-rear part of pressure surface. The impact velocity of 7.5μm particles and 25μm particles all have an obvious rising trend as the impact position moves forward in axial direction. The impact velocity distribution of 75μm particles are somewhat different with 7.5μm and 25μm along the rotor axial distance because the 75μm particles have the secondary impact with the rotor pressure surface, which can be seen obviously from Fig.8. The impact velocity in the rotor flow passage of three different diameter particles (7.5μm, 25μm and 75μm) presents a downward trend with the increase of particle size.
Fig.9 Impact velocity of particles on rotor blade pressure surface
Fig.10 shows the impact angle of particles on rotor blade pressure surface. The shaded area means the angle range of the maximum erosion rate. From Fig.10, we can see that the larger the solid particle size is, the greater the impact angle will be. The impact angle of the 7.5μm particles is near the 15° which is far away from the angle range of the maximum erosion rate. The impact angle of the 25μm particles is in the range of 17.5-20° and a few particles’ impact angle is a little greater than 20°. However, most of the impact angle of the 75μm particles is in the range of
8
20-35° which is in the angle range of the maximum erosion rate. The trajectories of small particles are almost the same as main steam direction so the impact angle of particles on the rotor pressure surface is small correspondently. The inertia increases with the increase of particle size, which leads to the trajectory tending to straight line and the impact angle increases too.
Fig.10 Impact angle of particles on rotor blade pressure surface
The eroded scope and the erosion degree of rotor blade at the rotation speed 3000 rpm are shown in Fig.11. As we can see that the eroded scope of rotor appears on the leading edge, the suction surface close to the leading edge and the pressure surface. Most of the erosion appears on the pressure surface and has a wide distribution along the axial direction. When solid particles flow out from the nozzle with the main steam, some of these particles impact directly on the leading edge of rotor blade and the suction surface of rotor blade close to the leading edge resulting in the erosion in the two areas. But the erosion degree is comparatively slighter than that of trailing edge since their impact velocity is smaller than that on the trailing edge. The solid particles at the mid-rear part of rotor flow passage accelerate quickly as the rotor blade has a certain degree of reaction, making the erosion at the mid-rear part more serious. At the same time, SPE can destroy the blade integrity because the trailing edge is thin. Just like the erosion on nozzle, the erosion on rotor blade of different size particles is different too. The erosion made by small particles focuses
on the trailing edge of the pressure surface. The impact points move forward with the increase of the particle size. Compared to the erosion made by small particles, the erosion made by large particles has a wider distribution along the axial direction. At the rotation speed 3000 rpm, the eroded area on the pressure surface has obvious upward trend because of centrifugal force and the radial migration quantity is about 7% of blade height, resulting in the erosion on the blade tip more serious than that on root. Moreover, different size particles have different erosion rate density on the rotor blade, as we can see from Fig.11. The maximum erosion rate density of 7.5μm particles is 1.453e-005 kg/ (m2 s) while the maximum erosion rate density of 75μm particles is 1.332e-003 kg/ (m2 s). As a result, the maximum erosion rate density of 75μm particles is 90 times of 7.5μm particles. Compared to nozzle, the maximum erosion rate density on rotor blade is 1.9 times of the rate on nozzle. Consequently, the erosion degree on the rotor blade is more serious than that on nozzle. As we all know, stage efficiency is one of the important indexes of steam turbine performance evaluation. SPE can destroy the integrity of nozzle and rotor blade, which is proved in Fig.7 and Fig.11. Thereby, the efficiency of governing stage will decrease. The eroded area appears on part of the blade surface, not on the whole blade surface, so the roughness is increased on the local scope. In addition, the size, shape and location of notch made by SPE also have an important influence on stage efficiency. Kawagishi [24] et al. investigated an eroded nozzle and the result showed a 3~6 percent decrease in efficiency compared to the non-erosion nozzle. Due to the complexity of decline of stage efficiency made by SPE, this problem is not analyzed quantitatively in this paper and will be studied 9
in detail in future research.
increase of particle size. In addition, there is almost no difference with the results in literature [5] on maximum impact angle of 7.5μm, 15μm in this paper. Moreover, the maximum error of maximum impact angle is 5.5 for 25μm particles. Based on the above analysis, the simulation results in this paper are believable.
7.5μm
(a) nozzle
(b) rotor blade
Fig.12 SPE morphology of governing stage in a supercritical steam turbine [19] 30
25μm
results of this paper results of ref [5]
Impact angle/(°)
25 20 15 10 5 0 0
10
20
4 Validation of SPE In order to verify the reliability of the simulation results in this paper, Fig.11 shows the solid particle erosion morphology of governing stage in a typical supercritical steam turbine. As we have seen from the preceding discussion, most of the erosion appears on the mid-rear part of the pressure surface. The result is consistent with the erosion occurring on actual operation in Fig.12. Fig.13 shows the maximum impact angle with the change of particle diameter on nozzle pressure surface. By comparison to the results in literature [5], it is verified that the impact angle gradually increases with the
40
50
60
70
80
dp/μm
75μm Fig.11 SPE on rotor blade
30
Fig.13 Maximum impact angle along with the change of particle diameter on nozzle pressure surface
5 Conclusion The comprehensive numerical simulation on SPE in the governing stage of a supercritical steam turbine is performed in this paper. The erosion characteristics of SPE on nozzle and rotor blade are studied under different particle sizes and rotation speeds. The conclusions of this study are summarized as follows: (1) In the flow passage of governing stage, the trajectories of small particles are almost the same as steam flow direction. With the increase of particle size, the particle 10
trajectories tend to straight line. The critical size of particles in the nozzle is in the range of 15-25μm while the critical size of particles in the rotor blade is in the range of 50-75μm. (2) The erosion rate density on the nozzle is smaller than that on the rotor blade. The maximum erosion rate density on the rotor blade is 1.9 times of the rate on nozzle. SPE can destroy the integrity of the trailing edge of nozzle and rotor blade. (3) The eroded area is concentrated mainly on the mid-rear part of the nozzle pressure surface and is distributed is along the radial direction from root to tip without any skew. However, the eroded area of rotor blade appears on the leading edge, the suction surface close to the leading edge and the pressure surface and has an obvious upward trend. The radial migration quantity is about 7% of blade height at 3000 rpm. (4) With the increase of particle size, the impact velocity on the nozzle and rotor blade pressure surface presents a downward trend simultaneously. However, the impact angle shows an opposite trend. The larger the solid particle size is, the greater the impact angle will be. Acknowledgement This work was supported by National Natural Science Foundation of China (NSFC) (No. 51376041 and No. 51576036). Nomenclature B axial chord length mm steam velocity, m/s u particle velocity, m/s up dp Re E
f( )
particle diameter, m relative Reynolds numbers erosion rate of a single particle dimensionless impacting angle function
Np
particle number flow rate kg/s
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13
Highlights 1 Radial projection of solid particle trajectory in nozzle are presented 2 The distribution of SPE on nozzle and rotor blade are analyzed
3 the radial migration quantity of SPE on rotor blade are taken into considerations