The influence of nozzle chamber structure and partial-arc admission on the erosion characteristics of solid particles in the control stage of a supercritical steam turbine

Energy xxx (2015) 1e12

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The influence of nozzle chamber structure and partial-arc admission on the erosion characteristics of solid particles in the control stage of a supercritical steam turbine Liu-xi Cai a, Shun-sen Wang a, Jing-ru Mao b, *, Juan Di a, Zhen-ping Feng a a b

Institute of Turbomachinery, Xi'an Jiaotong University, Xi'an 710049, PR China State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an 710049, PR China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 30 September 2014 Received in revised form 11 January 2015 Accepted 14 January 2015 Available online xxx

Reducing solid particle erosion of blades is one of the most urgent problems for supercritical steam turbine power generation technology. Based on the erosion rate models and the particle rebound models of blade materials obtained through accelerated erosion test under high temperature, systematic numerical simulations of the complex steam-particle flow in high pressure inlet flow channel and governing stage cascade of a supercritical steam turbine with four control valves was performed in this paper. The influence the typical nozzle chamber structure and partial-arc admission on the erosion characteristics of control stage blades was first investigated. Results show that erosion condition of nozzles in the same nozzle segment vary greatly along circumferential direction, while erosion damage to the leading edge of different circumferential rotating blades is uniform. Compared with four-valve opening condition, erosion weight-loss of the whole nozzle segment increases by 14% and 25% under three-valve opening condition and two-valve opening condition, respectively. Besides, under the partialarc admission conditions, some large particles coming from the steam admission nozzle segment will collide back and forth between vanes and rotating blades in the downstream nozzle segment without steam admission, thus causing certain erosion to the trailing edge of nozzle suction side. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Supercritical steam turbine Solid particle erosion Numerical simulation Nozzle chamber Partial-arc admission Erosion weight-loss

1. Introduction SPE (solid particle erosion) problems of steam turbine components, such as nozzles and the rotor blades, especially in the governing stage, have been a problem of concern to power company for many years. It is generally agreed that erosion damage is caused by the high hardness iron oxide particles exfoliated from the inner wall of the boiler and steam pipeline. These particles entrained in the high pressure steam flow, causing serious erosion to steam path and turbine components. As described in publication [1], erosion of blades results in lower efficiency of steam turbine, shorter repair cycle and higher maintenance costs. In literature [2], systematic numerical simulations had been carried out to investigate SPE on the performance of first stage nozzles, which indicated that the change of nozzle surface roughness would reduce the nozzle efficiency by 2%, while the change of nozzle profile would decrease the

* Corresponding author. Tel.: þ86 29 82667808; fax: þ86 29 82668704. E-mail address: [email protected] (J.-r. Mao).

efficiency by 1.1%. Based on the field investigation in a power plant, Khaimov et al. [3] pointed out that, the unit efficiency decreased by 0.35% under the rated load and decreased by as much as 2.16% in the part load operation due to the oxide particle erosion. With the development of ultra-supercritical technology, although the heat rate of units and the cost of electricity decreased in some extent based on the thermodynamic analysis and design optimization of an ultra-supercritical steam turbine in literature [4], the economic advantage would be heavily discounted by SPE. Therefore, reducing SPE of control stage blades to maintain the efficiency and security operation of units has been one of the key issues for experts and scholars around the world. Hamed et al. [5] observed that particles would directly impacted stator PS (pressure surface) when entering the cascade passage, and the erosion conditions become worsen along the flow direction. With numerical simulation method, Campos-Amezcua et al. [6] found that the erosion rate increased with the increase of solid particle flow, and deceased with the increase of particle size. According to Mazur Z et al. [7], a step on the PS near nozzle trailing edge could change the particle impact angle and impact position, and results in 50% reduction of nozzle erosion rate.

http://dx.doi.org/10.1016/j.energy.2015.01.044 0360-5442/© 2015 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Cai L-x, et al., The influence of nozzle chamber structure and partial-arc admission on the erosion characteristics of solid particles in the control stage of a supercritical steam turbine, Energy (2015), http://dx.doi.org/10.1016/ j.energy.2015.01.044

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Li YF et al. [8] stated that the erosion rate of nozzle is sensitive to fluctuations in the flow field, and not entirely dependent on the solid particle size. Literature [9] systematically discussed the effect of the oxide particle size on the erosion of control stage nozzles, and considered that small particles would impact the trailing edge of nozzle PS with high impingement velocity and small angle, while particles with large size would rebound back and forth in the nozzle passage, which caused great destruction to the coating of SS (suction surface). Besides, Dai LP et al. [10] who had performed systematic numerical simulations to the anti-erosion performance of control stage nozzles with different geometry profile believed that nozzles with end-wall contouring could effectively reduce the local erosion rate and erosion area by 40% and 30%, respectively. With the employment of experimental and numerical simulations, Wang SS et al. [11] pointed out that the weight-loss of nozzle could be reduced by 50% and nozzle efficiency was improved by 0.4%~0.5% by improving the end-wall contouring of nozzle. What's more, based on the systematic research on SPE, Wang et al. [12] further proposed that the impact intensity of particles on nozzle trailing edge could be reduced through the optimization of nozzle profile and cascade structure characteristic parameter G, where G ¼ (B2  t)/B(B2 is circumferential width of blade, t is the pitch of cascade and B is the axial width of blade). Numerical simulation results about the full circle control stage nozzles in a subcritical steam turbine with six control valves in publication [13] revealed that particles were concentrated to erosion a small number of nozzles or the local area of one nozzle because of the upstream pipelines, which greatly accelerated the erosion damage of nozzle segment. From the above works, it is can be seen that most of the above studies only performed numerical simulation to the erosion conditions of a single control stage nozzle passage. Although a annulus of control stage nozzles had been simulated in literature [13], the results could not fully reveal the real erosion conditions of governing stage blades in supercritical steam turbine because the control stage rotor blades were not considered. Fig. 1 shows the particle erosion morphology of control stage blades in a typical supercritical steam turbine with four control valves. It can be seen that erosion condition of nozzles in the same nozzle segment vary greatly along the circumferential direction (the length of erosion notches in some nozzle cascades has amounted to 20% of the chord length, yet some nozzle cascades still remained intact), but erosion condition of the corresponding rotor blades in different circumferential location is very similar, which is rarely mentioned in the present studies. Moreover, as more supercritical units are used to undertake peak regulation task, it is unavoidable that these units will operate under different load conditions alternately. Therefore, it is particularly necessary to explore the motion behavior of oxide

particles in control stage cascade under partial-arc admission conditions. In this paper, systematic high temperature erosion tests about the supercritical steam turbine blade materials are conducted based on the high temperature high speed accelerated erosion test rig, the erosion rate models and particle rebound models of blade materials under the simulated operating conditions of the steam turbine in power plant are then established. With the employment of these models, comprehensive numerical simulation on the gasparticle flow in the high pressure nozzle chamber and control stage cascade of a supercritical steam turbine with four control valves is performed in this paper using three-dimensional numerical simulation method. The influence of this typical nozzle chamber structure and partial-arc admission on the erosion characteristics of control stage blades is detailedly investigated. The research results in this paper reveal and perfect the blade erosion mechanism of oxide particle in steam turbine governing stage, providing a theoretical basis for preventing and reducing SPE of control stage cascade. 2. High temperature high speed accelerated erosion tests 2.1. Introduction of high temperature high speed accelerated erosion test system Fig. 2 shows the high temperature and high speed accelerated erosion test system, which can be used to model material erosion behavior under a wide range of conditions: test temperature 20  Ce700  C, particle impingement angles 12 ~90 , particle impingement velocity 0e420 m/s. The test system consists of three parts: particle feeding system, high temperature gas system and erosion testing system. The basic working principle of the facility is stated as follows. First, the compressed air with the flow mass of 10 Nm3/min is heated in the combustor producing the required high-temperature gas. Then, the high-temperature gas flow is divided into two pipelines. Gases in one pipeline directly flow into the test chamber to heat the specimen and establish the high temperature erosion environment. Gases in the other pipeline enter the pneumatic nozzle for accelerating solid particles. Solid particles from the screw feeder are carried directly into the acceleration nozzle throat by the secondary air. After the acceleration by high temperature flue gas, a uniform gasesolid mixture meeting the test requirements of temperature and velocity is produced in the nozzle and followed by impinging the test target at an incidence angle b in the test chamber. Erosion rate of the target can be obtained by measuring the cumulative mass of the particle involved in the erosion and the target mass before and after the erosion.

Fig. 1. Erosion morphology of control stage blades in a supercritical steam turbine: (a) Erosion of control stage nozzle; (b) Erosion of control stage rotating blades.

Please cite this article in press as: Cai L-x, et al., The influence of nozzle chamber structure and partial-arc admission on the erosion characteristics of solid particles in the control stage of a supercritical steam turbine, Energy (2015), http://dx.doi.org/10.1016/ j.energy.2015.01.044

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Fig. 2. Schematic diagram of test system for high-temperature SPE.

In this test, iron oxide particles with the Sauter diameter of 42 mm are selected as erodent. The size distribution which are measured by Malvern 26040L particle size analyzer is very close to that of oxide scales sampled in power plant, as shown in Table 1 dp is the particle diameter, Cum.m1 and Cum.m2 are cumulative particle size distributions of the sampled oxide scales in a power plant and test erodent, respectively. The PIV (particle velocity imaging) system is employed to measure particle velocity field. A region of interest, covering incident particles and rebounded particles, is illuminated by the light sheet from the laser system. The CCD (charge coupled device) camera for PIV is positioned perpendicular to the laser sheet. Systematic test results from Wang et al. [14] show that the measurement uncertainty of particle velocity at the acceleration nozzle exit is less than 1.5%, and the dispersion of the impingement angle is less than 1. Besides, the Rosemount pressure transmitters which have a measuring accuracy of 0.075% are chosen to measure the airflow pressure. The target surface temperature is measured by RST-800 infrared thermometer. The mass of specimen before and after the erosion test are measured by BS224S precision electronic balance, whose measurement accuracy is 0.1 mg. These high precision testing instruments and methods ensure the reliability of the experimental results. According to the actual operating parameters of steam turbine in power plant, three particle impingement velocities (150 m/s, 250 m/s and 350 m/s) and seven kinds of particle impingement angles (12 , 18 , 24 , 30 , 45 , 60 , 75 and 90 ) are selected in the test. The erosion environment temperature is in the range of 500  Ce600  C. 2.2. Erosion rate models and particle rebound models of blade materials According to the analysis results in literature [15], a general relationship among the material erosion rate εm, particle Table 1 Size distribution of particles sampled in the power plant and used in the test. dp/mm

Cum.m1/%

Cum.m2/%

0e10 10e30 30e50 50e70 70e90 90e110 110e130 130e150

0.3 14 48.1 76.5 90.2 95.4 100 100

0.7 13.7 48.8 78.4 92.9 97.3 99.8 100

impingement velocity V, impingement angle b and material temperature T can be expressed as follows:

εm ¼ KT ðTÞQ ðbÞV nðbÞ

(1)

Each blade material needs to determine its own temperature function KT(T), impingement Angle function Q(b) and velocity index function n(b). On the basis of lots of high temperature erosion test results, key parameters of blade material erosion rate expressions are obtained through the least squares fitting method. For the martensitic heat-resistant stainless steel 2Cr10MoVNbN, which is commonly used as supercritical steam turbine blade material, functions of the key parameters of the erosion rate can be expressed as follows:

KT ðTÞ ¼ 1:4047 þ 0:0027872T

(2)

Q ðBÞ ¼ 0:0036201 þ 2:5843b  4:8462b2 þ 3:2331b3  0:74413b4

nðbÞ ¼ 2:6101  0:55477b þ 0:77315b2  0:18053b3

(3)

(4)

At the moment of impingement, the rebound velocity of the particle is lower than the incident velocity due to energy transfer. Energy is dissipated as heat, noise and target material deformation. This impingement signature is usually described by the normal velocity restitution coefficient eN and tangential velocity restitution coefficient eT, which has been found to be mainly depend on the incidence angle for a given particle-target material combination based on systematic tests results in literature [16]. In this study, the particle rebound models under high temperature and high pressure environment are established based on the PIV results of the process about oxide particles impinging the target surface. The statistical test results about the particle incidence velocity, rebound velocity and the incidence angle are fitted through least square fitting method, as is shown in the formulas (5) and (6).

eT ðbÞ ¼

V2T ðbÞ ¼ 0:9888  3:6566b þ 11:0451b2  11:0394b3 V1T þ 3:4972b4 (5)

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eN ðbÞ ¼

V2N ðbÞ ¼ 0:9922  4:5272b þ 10:3146b2  9:1787b3 V1N þ 2:7013b4 (6)

Where b is the particle incidence angle, and is measured by radians. VN1 and VT1 are the particle incident velocity, while VN2 and VT2 are the particle rebound velocity. The fitting error of erosion rate model and particle rebound model can be seen in the Appendix. These experimental results will be put into the CFD( computational fluid dynamics) code by a User Fortran subroutine to predict the particle trajectories in cascade channels and erosion weightloss distribution of blade materials. 3. Geometric modal and numerical approach 3.1. Geometric model Of all stages in a steam turbine, the inlet temperature and pressure in control stage are the highest, and so is the steam velocity in cascade. The flow area which is not symmetric changes with the variation of operation load under partial-arc admission condition, so the accurate flow characteristics of control stage cascade can only be obtained based on a full-cycle model. Fig. 3 shows a typical inlet channel structure model of high pressure cylinder in a supercritical steam turbine with 4 control valves. TV1 and TV2 in the figure represent the main stop valve 1 and the main stop valve 2. GV1, GV2, GV3, and GV4 are four control valves. It can be seen that each nozzle chamber is connected to corresponding outlets of control valves via a complicated 3D pipeline composed of two to five elbows and a plurality of straight pipes, and the length of the connection parts is far greater than the scale of the nozzle chamber plus control valves. The unit employs a sequential valve start-up mode in the power plant. When impulse the rotor, the GV3 and GV4 control valves are opened simultaneously, while the GV1 and GV2 control valves are then opened in order as the load increases. Along the rotational direction of a rotor, four nozzle segments and nozzle chambers are named A, B, C and D in turn, as shown in Fig. 4,which is corresponding to the four high pressure control valve. Each nozzle segment includes fifteen nozzle channels, and there are in total sixty channels, named as SA1~SA15, SB1~SB15, SC1~SC15 and SD1~SD15, respectively. Between each two nozzle segments, one nozzle passage is blocked, as displayed in Fig. 4.

Fig. 4. Nozzle chamber structure and control stage cascade a supercritical steam turbine.

3.2. Numerical approach In this study, the following time-averaged continuity equation, NaviereStokes (NeS) equation, and energy equation are solved by using a fully implicit discretization of the equations and a coupled solver to simulate the three-dimensional steady compressible viscous flow in cascade.


 v ruj ¼0 vxj " !# " !#
 v rui uj vuj vp v vui vuj 2 v ¼ þ þ ðm þ mt Þ  ðm þ mt Þ vxi vxj 3 vxi vxj vxi vxj vxj !
  v ruj h v vT v
¼ l þ u t þ SE vxj vxj vxj vxj j ij (7)

Fig. 3. Inlet flow channel of a supercritical steam turbine with four control valves.

Where h is the fluid total enthalpy, l is fluid heat transfer coefficient. v(ujtij)/vxj represents the part of energy conversion from mechanical energy to heat due to the effect of viscosity, which is called dissipation function. SE is the inner heat source of fluid. Because of the better performance in the simulation of flow with high strain rates, swirl, and separation, therefore, in this article, the renormalization group k-ε turbulent model is selected to estimate the turbulence viscosity mt in the NeS equation. For the flow with high Reynolds number, mt can be expressed asmt¼rCmk2/ε, whereCm¼0.0845. The transport equations of k and ε can refer to the literature [17]. A scalable wall function is used to solve the near wall region. In addition, in order to model the compressible flow in the blade cascade, the velocity profile of the law-of-the-wall is transformed using a so-called ‘Van Driest transformation’ [18]. For multiphase flows, it can be important to correctly set the buoyancy reference density. For a flow containing a continuous phase and a dilute dispersed phase in this study, the buoyancy reference density

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should be set to that of the continuous phase. This is because the pressure gradient is nearly hydrostatic, so the reference density of the continuous phase cancels out buoyancy and pressure gradients in the momentum equation. Due to the complex structure topology of inlet channel and cascade, the computational domain is divided into several subdomains. Although the structured mesh generation method can reduce the number of grid, the NC (nozzle chamber) is dispersed through unstructured tetrahedral mesh for the strong threedimensional structure and lower steam velocity, while other subregions are dispersed through structured grid, to improve the accuracy of numerical simulation as much as possible. The grid number of each sub-region are listed as follows: the grid number of control valves and steam pipeline is about 5,000,000, and the grid number of four high-pressure nozzle chambers about 2,400,000. The annulus of control stage cascade model is dispersed through 9,000,000 HeI type multi-block structured grids. So the total grid number of the entire model is 16,400,000. Checking of the grid quality shows that the minimum orthogonal angle is greater than 30 , the maximum aspect ratio and expansion ratio are less than 300 and 3, respectively. The boundary layer mesh refinement technology was used to ensure that the dimensionless distance from the wall (yþ) is below 100 under various operating conditions. The status parameters for steam are provided by IAPWS-IF97 database. The cascade passage mesh is displayed in Fig. 5. One-way coupled dispersed particle model can be used to simulate the dilute particle phase of the steam-particle flow in a steam turbine. The particle motion equation can be written as [5]:


 ! g rp  r dup 18m CD Re ðu  VÞ þ ¼ þ FR dt rp rp d2p 24

(8)

The terms on the right-hand side represent the aerodynamic, gravitational, and forces acting on the particle due to the reference frame rotation. The particle drag coefficient CD can be expressed as the following formula [19]:

CD ¼

 24  b Re 1 þ b1 Reb2 þ 3 Re b4 þ Re

(9)

The particle Reynolds numbers Re, which is based on the slip velocity and particle diameter, is defined as:

Re ¼

rdp ðV  uÞ m

(10)

b1, b2, b3 and b4 all are the functions of particle shape factor 4 (4 ¼ A/ S, here, A is the surface area of spherical particle which has the same volume as actual particle, S is the surface area of actual particle). Erosion rate models and particle rebound models established in this paper are used to simulate the interaction between particles

5

and blade surface. The above erosion computation methods has been validated by Dai et al. [10] and Chen et al. [20], both of which show that the simulation results are in good agreement with test data. 3.3. Boundary conditions Referring to the operation parameters of control stage in a supercritical 800 MW unit, the boundary conditions are set as follows: The total pressure P0, the total temperature T0 at the inlet of control valve and the static pressure P2 at the rotor outlet are set in the simulation. The initial parameters under different operating conditions are exhibited in Table 2, which is obtained from the operating and design parameters of the investigated units in power plant. The design value of steam admission attack angle is 0 . The turbulence intensity, which is defined as the ratio of the root mean square value of velocity fluctuations to the time-average value of velocity, is set to 5%. A no slip flow condition is set at all solid walls. The equivalent sand diameter D, which is set to 1.8 mm in publication [21], is employed to characterize the surface roughness of valve seat, valve disc and a new cascade before erosion. For other steam pipelines, D is set to 300 mm according to roughness of the cast pipe wall. The General Connection interface mode is a powerful way to connect regions together, which can be used to apply a frame change condition, pitch change condition, fully transient sliding interfaces condition and connect non-matching grids. So it is applied at the interface between stators and rotors in this simulation. The frozen rotor model, which produces a steady state solution to the multiple frame of reference problems and takes some account of the interaction between the two frames, is most useful when the circumferential variation of the flow is large relative to the component pitch. Therefore, it is chosen for the frame change model. According to the investigation results in power plant provided by literature [2,3], the size of oxide particles was usually smaller than 150 mm, the long-term research accumulations and field investigations from the authors also confirmed this conclusion. In view of the measured results of particle size distribution of oxide scales shown in Table 1, totally 7 kinds of mono-sized particles are selected in the inlet of cascade, which include 10 mm, 20 mm, 40 mm, 60 mm, 80 mm, 100 mm and 120 mm. According to the mesh scale of computational domain, together with the consideration of computational efficiency and precision, 2000 seeding locations for each size of particle were selected at the inlet of each control valve. Here we should note that, 2000 is not the real number of particles, but the refined degree of particle distribution in the space. The particle concentration in the inlet of each control valve is set to 1  10-3mg particles in per kilogram steam and a zero slip velocity for particles is chosen in the inlet of four control valves. Since the

Table 2 Geometric parameters and steam parameters of control stage cascade.

Fig. 5. Grid systems of typical control stage cascade channel.

Parameters

Stator

Rotor

Number of blades Pitch Chord length Blade width Blade height Pitch diameter P0 T0 P2 under 4 vavle open P2 under 3 vavle open P2 under 2 vavle open

60 54 mm 105 mm 70 mm 37 mm 1100 mm 23.54 MPa 813 K 16.7 MPa 15.7 MPa 10.8 MPa

60 57.60 mm 97.63 mm 96.14 mm 40 mm 1100 mm

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Fig. 6. Streamline in the nozzle chamber and governing stage cascade under four-valve opening condition.

flaky shape of the oxide particles, particle shape factor 4 is set to simulate particles motion behavior in cascade channel. In this paper, shape factors of particle are set in the range of 0.4e0.8 according to the particle size to approximate the erosion morphology, which will affect the drag force calculated in ANSYS-CFX. Furthermore, during the simulation, collisions between particles, fragmentation of particles and geometry modifications caused by the removal of wall by solid particles have not been considered. To record the motion parameters (number of particles impinging on the surface, particle impinging velocity and particles direction relative to surface) of all representative particles passing through the computational domain grids, very large amount of calculation is needed due to a large number of grid for the model.

4. Results and discussion 4.1. Influence of nozzle chamber structure on the flow field and particle erosion characteristic of governing stage cascade From Figs. 3 and 4, we can see that the inlet channel structure of the supercritical steam turbine high pressure cylinder is very complex, resulting in extremely complex steam flow in the nozzle chamber and control stage cascade. Fig. 6 displays the three dimensional streamline in the nozzle chamber and governing stage cascade under four-valve opening condition. It can be seen that after entering the nozzle chamber through control valves, most of the steam medium will flow into the nozzle channel to accelerated directly, while a small amount of steam medium will impact the wall at two ends of nozzle chamber to produce a strong vortex flow, following by flowing into the corresponding nozzle passage. Fig. 7 shows the contour of steam flow pressure distribution, temperature distribution and the velocity vector at the mid-span of control stage cascade under four-valve opening condition. As we can see, the flow field is very uniform and exhibits a good flow periodicity in each arc segment under the condition of four-valve opening. The steam medium is accelerated gradually in the nozzle passage, and flows into the rotor passage through axial clearance to push the rotor to do work. Only in the blockage between each two nozzle segments, a large amount of low energy fluid is found in the corresponding rotor blade passage. Besides, the minimum value of steam flow pressure and temperature, as well as dramatic parameter change is observed in cascade passage at the end of each nozzle segment, which indicates a complex flow condition.

From the above analysis, although the complicated nozzle chamber structure leads to complex steam flow in it, the steam flow is relatively uniform after flowing into the blade passage. However, whether flaky oxide scales mixed in steam have the same flow pattern with the steam medium? Fig. 8 presents the trajectory of oxide particle in the high-pressure nozzle chamber and cascade passage under the condition of four-valve opening. It can be seen that trajectories of small size particles are close to the airflow direction because of the small inertial force, producing relatively uniform distribution of particles in different circumferential cascades. With the increase of particle size, particles gradually gather in the bottom of nozzle chamber near the horizontal split of turbine casing under the increasing inertia force, and then enter the corresponding nozzle passage. The uneven distribution of particles in different circumferential cascade channel is enhanced greatly. Careful observation also find that, along the direction of rotor rotation, particles in the last several nozzle passages (near the cascade of SA15, SB15, SC15 and SD15) of each nozzle segment, especially in the nozzle passages (near the cascade of SB15 and SD15) where particles are prone to concentrate will be impinged by the high-speed rotating blade when flow out of the vane passage. After that, these particles will impact the PS of downstream rotating blade and enter into the next stage cascade eventually, as shown in Fig. 9. This is different from erosion mechanism of particles in the first reheat stage cascade in intermediate-pressure cylinder. Due to the relatively lower density of steam flow in the first reheat stage, particles with large size obtain huge energy after impacting the rotating blade leading edge, overcoming the resistance of steam flow in axial clearance between stator and rotor, which will cause serious erosion on the suction side of the adjacent stator trailing edge. Furthermore, the phenomenon of particle migration is also observed in the clearance between stators and rotating blades from Fig. 9, which shows that some particles will impact the leading edge of different rotor blades in sequence and then flow into the downstream rotor blade passage under the drive of steam flow force and inertia force. The impingement on rotor blade leading edge by oxide particles and the particle migration phenomenon in different cascade have not been found in other circumference cascade passages of nozzle segments. Therefore, it is difficult to fully reveal the erosion mechanism of control stage nozzles and rotating blades just through simple simulation to one single cascade passage. In order to further explore the effect of nozzle chamber structure on the erosion distribution of the control stage cascade, relative surface coordinates (sr, hr) are defined. Here sr ¼ s/s0 and hr ¼ rrh/H，where s0 is the total arc length from the leading edge to the trailing edge along the PS or SS of a blade, s is the arc length from the leading edge to a particle eroded site, r is the distance from an eroded site to the rotational center of the rotor, rh is the radius of hub and H is the height of blade. For facilitating statistics, the PS and the SS of blades are segmented evenly into ten intervals based on segmental arc length, as shown in Fig. 10. At each interval, the accumulated weight-loss of blade within 10,000 h can be calculated according to the following formula: 10000 Z

i=10 Z

HZ0 ðsr Þ

Es ðiÞ ¼

eðsr ; hr Þdzr dsr dt; 0

ði1Þ=10

i ¼ 1; 2/10

(11)

0

Where H0 (sr) is the variation of blade height along sr, e(sr,hr) is the erosion rate density on the blade surface. Investigations on large number of eroded nozzles showed that the erosion-induced damage to nozzles centered at the region near trailing edge. Moreover, it is noted that the erosion has expanded to the region of sr ¼ 0.7

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Fig. 7. Steam parameters distribution at the mid-span of control stage cascade under four-valve opening condition: (a) Steam pressure; (b) Steam temperature; (c) Steam velocity vector.

based on the mapping of the most severe damaged nozzle in Fig. 1(a). One of the main reasons for being easily damaged in nozzle trailing edge is the thinner thickness of the region than other areas of the nozzle, but the great erosion intensity in trailing edge is the decisive factor for its broken. So the parameter E is defined to characterize the erosion weight-loss in the region of sr ¼ 0.7e1.0 within 10,000 h in this paper:

0 10000 Z1:0 HZðsr Þ Z

eðsr ; hr Þdzr dsr dt

E¼ 0

0:7

(12)

0

Fig. 11 shows the erosion weight-loss of nozzle PS trailing edge in each cascade of nozzle segment D under the condition of fourvalve opening. As can be seen, erosion weight-loss of 15 nozzle cascade (SD1~SD15) in different circumferential position presents a great difference. Along the direction of rotor rotation, the most severe damaged nozzle, which is labeled as SD15, is located at the

Fig. 8. Particle trajectories in nozzle chamber and control stage cascade under fourvalve opening condition: (a) dp ¼ 10 mm; (b) dp ¼ 120 mm.

Fig. 9. Erosion to rotor blade leading edge and particle migration phenomenon in the clearance (dp ¼ 40 mm).

Fig. 10. The profile of nozzle and the definition of sr and hr.

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4.2. Influence of partial-arc admission on the aerodynamic performance and particle erosion characteristic of control stage cascade

Fig. 11. Erosion weight-loss of nozzle PS trailing edge in each cascade of nozzle segment D.

bottom of nozzle segment D. The maximum erosion weight-loss of SD15 can reach up to 3.9 g/10000 h, while the erosion weight-loss of SD5 nozzle pressure side in the same nozzle segment is only 0.16 g/10000 h, which is very consistent with the erosion damage distribution along circumferential direction showed in Fig. 1(a). It is not difficult to find based on careful analysis that, due to the intake direction and the special structure of nozzle chamber, particles are concentrated to erode a small number of nozzles near horizontal split of turbine casing under the action of inertia force, which is account for the great difference of nozzle erosion damage along circumferential direction in a same nozzle segment. Although the particle impact on rotating blade leading edge occurs only in several cascades at the ends of nozzle segment, the erosion of rotor blade by particles is uniformly shared by 60 different rotating blades because of the high-speed rotation of rotor. Therefore, erosion notch of blade leading edge is found on different circumferential locations of rotating blade, and the erosion degree is less severe than stationary nozzles, as shown in Fig. 1(b). In addition to the erosion on moving blade leading edge, particles with small and medium size mixed in the steam flow will impinge the midstream of blade PS in the rotating blade passage. But this type of erosion can be ignored since relatively lower impinging velocity and thick thickness of blade material. The above simulation results on the erosion conditions of control stage nozzles and rotating blades further verify the reliability of the numerical simulation method used in this paper.

When power output from a steam turbine generator needs to be adjusted to meet the requirements of different loads, this is commonly realized by admitting flow only in one arc or several segmental arcs of turbine annulus, i.e. partial-arc admission. Partial-arc admission in control stage leads to dramatic change of aerodynamic parameters along the circumferential direction. And the motion behavior of oxide particles mixed in steam flow will also change correspondingly. Therefore it is necessary to investigate the aerodynamic performance and particle erosion characteristics of governing stage cascade under different admission conditions. For this purpose, in addition to four-valve opening condition, threevalve opening and two-valve opening working conditions are also calculated in this paper according to the actual operation state of steam turbine in power plant to perform a detailed analysis of the effect of partial-arc admission on the aerodynamic performance and erosion damage characteristics of control stage cascade. Fig. 12 shows the three dimensional streamline in the nozzle chamber and governing stage cascade under three-valve opening condition and two-valve opening condition, respectively. As can be seen, the streamline is relatively uniform in the cascade of steam admission nozzle segment, which indicates a smooth flow along the flow path. While disordered streamline and a great deal of irregular flow are found in the cascade of nozzle segment without steam admission. Steam flow back into nozzle chamber from the axial clearance between stators and rotors, producing a large amount of vortex. Fig. 13 displays the contour of steam pressure distribution and the velocity vectors at the mid-span of control stage cascade under three-valve opening condition. As we can see, because of the evenly steam intake of nozzle segments A, C and D, the pressure field and velocity field along the flow direction as well as in different cascade channel along circumferential direction has a good consistency. However, owing to no high parameter steam entering from control valve of GV2, the steam pressure of nozzle segment B is sizable to the outlet pressure of rotor, which is obviously lower than the pressure of steam admission nozzle segments. As also can be seen in Fig. 13, steam is accelerated in the nozzle passage and reach to a high velocity in the axial clearance between stators and rotors. The maximum steam velocity is found in the cascade located at end of each steam intake nozzle segments. Besides, certain amount of steam in the nozzle segments with steam admission flow into the arc segment without steam admission, producing a large number of vortex and leading to the mixing of high pressure steam and low

Fig. 12. Streamline in the nozzle chamber and governing stage cascade under partial-arc admission conditions: (a)Three-valve opening condition; (b)Two-valve opening condition.

Please cite this article in press as: Cai L-x, et al., The influence of nozzle chamber structure and partial-arc admission on the erosion characteristics of solid particles in the control stage of a supercritical steam turbine, Energy (2015), http://dx.doi.org/10.1016/ j.energy.2015.01.044

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Fig. 13. Steam parameters distribution at the mid-span of control stage cascade under three-valve opening condition: (a) Steam pressure; (b) Steam velocity vector.

pressure steam. Compared to four-valve opening condition, the steam enthalpy drop in nozzle channel under partial-arc admission conditions increases, resulting in a substantial increase of steam flow velocity. Meanwhile, the leaving velocity is difficult to be effectively utilized by the next stage due to the extremely uneven distribution of flow along circumferential direction. Consequently, the stage efficiency is far lower than that under the condition of four-valve opening. Under partial-arc admission conditions, the trajectories of particles in cascade channel of each steam admission nozzle segment are similar as that under the condition of four-valve opening. While in the arc segment without steam admission, some particles with large size（dp  100 mm）that flow through the nozzle passage located at the end of the steam admission nozzle segment (such as the cascade of SD15, where particles are prone to concentrate) will impact the leading edge of rotor blade, after which colliding back and forth between vanes and rotating blades in the downstream nozzle segment without steam admission, thus causing certain erosion to the trailing edge of nozzle suction side, as is presented in Fig. 14. A small amount of particles between 40 mm and 80 mm in the

Fig. 14. Colliding of particles between stators and rotating blades in the nozzle segment without steam admission (dp ¼ 120 mm).

same cascade of SD15 will flow into the axial clearance and impinge the SS trailing edge of some nozzles in the downstream nozzle segment without steam admission after impacting the leading edge of rotor blade. Thanks to the limited amount of these particles, the erosion of the nozzle suction side is not severe. In addition, the erosion on nozzle PS of cascades in steam admission arc segments increase significantly since the greater enthalpy drop of nozzle passage under partial-arc admission condition comparing to the condition of four-valve opening. Statistical results show that, compared with four-valve opening condition, the whole erosion weight-loss of all cascades in nozzle segment D increased by 14% under three-valve opening condition, and increased by 25% under two-valve opening condition. Fig. 15 shows the erosion weight-loss distribution on PS of the most severe damaged cascade SD15 among nozzle segment D under three different admission conditions. As can be seen, the erosion distribution of nozzle PS along the flow direction remains unchanged under the three intake conditions. The maximum erosion weight-loss occurs in the vicinity of the trailing edge on nozzle PS. The erosion weight-loss on the trailing edge of SD15 cascade pressure side increases by 20% when the operating condition of unit changes from four-valve opening to three-valve opening, and increases by 35% when the operating condition of unit changes from four-valve opening to two-valve opening.

Fig. 15. Distribution of Es along sr under different intake conditions.

Please cite this article in press as: Cai L-x, et al., The influence of nozzle chamber structure and partial-arc admission on the erosion characteristics of solid particles in the control stage of a supercritical steam turbine, Energy (2015), http://dx.doi.org/10.1016/ j.energy.2015.01.044

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Fig. 16. Impingement parameters on the PS of SD15 cascade.

Fig. 16 further displays the impingement parameters on nozzle PS of SD15 cascade under three kinds of load. As we can see, the impingement velocity on pressure side trailing edge increases by about 15.2% when the operating condition of unit changes from four-valve opening to two-valve opening, while the impingement angle on the nozzle PS is almost unchanged. Based on the above analysis, efficiency of governing stage will decrease significantly and the oxide particle erosion of cascade will deteriorate rapidly when the supercritical steam turbine operates under the partial-arc admission conditions.

5. Conclusions Systematic high temperature accelerated erosion tests of the supercritical steam turbine blade materials have been conducted based on the high temperature high speed accelerated erosion test facility, the erosion rate models and the particle rebound models of blade materials are then established. Based on these models, the influence of the typical nozzle chamber structure and partial-arc admission on the aerodynamic performance and erosion characteristics of governing stage cascade in a supercritical steam turbine was first simulated and analyzed in this paper using threedimensional numerical simulation method. The main conclusions are as follows: Oxide particles are prone to concentrate in the nozzle passage near horizontal split of turbine casing due to the intake direction and the complex structure of nozzle chamber. Erosion condition of nozzles in the same nozzle segment vary greatly along the circumferential direction, and erosion weight-loss of the most severe damaged nozzle is about 24 times that of the slightest eroded nozzle, which greatly shortens the service life of the nozzle segments. Along the direction of rotor rotation, particles in the last several nozzle passages of each nozzle segment, especially in the nozzle channels where particles are prone to concentrate will be impinged by the high-speed rotating blade when flow out of the vane passage, after which impacting the PS of downstream rotor blade and entering into the next stage cascade eventually. Meanwhile, the phenomenon of particle migration is observed in the clearance between stators and rotating blades, which shows that some particles would impact the leading edge of different rotor blades in sequence and then flow into the downstream rotor blade channel. Since the impingement velocity on the leading edge of rotor blades is lower than that on the trailing edge of nozzle PS, and the erosion is uniformly shared by sixty different rotating blades, therefore, erosion damage of blade leading edge is uniformly

distributed along the circumferential direction of different rotating blades, and the erosion degree is less severe than the trailing edge of stationary nozzles. Under partial-arc admission conditions, not only the efficiency of governing stage will decrease significantly, but also the oxide particle erosion of cascade will deteriorate rapidly because of the greater enthalpy drop and particle impingement velocity. Compared with the four-valve opening conditions, erosion weightloss of the whole nozzle segment increases by 14% and 25% under three-valve opening condition and two-valve opening condition, respectively. Correspondingly, erosion weight-loss of the most severe damaged cascade SD15 increases by 20% and 35%. Besides, some oxide particles in the nozzle passage located at the end of the steam admission nozzle segment would impact the leading edge of rotor blade, after which colliding back and forth between vanes and rotating blades in the downstream nozzle segment without steam admission, thus causing certain erosion to the trailing edge of nozzle suction side. Therefore, for the safe and high-efficiency operation of supercritical steam turbine, the running frequency and time for partial-arc admission operation conditions should be minimized. Considering only one kind of typical high pressure nozzle chamber that commonly used in the current high-parameter units is studied in this paper, in order to get a better understanding of the effect of nozzle chamber structure, the erosion problem of other high pressure nozzle chambers and segments, such as nozzle chamber with six control valves structure, will be investigated comparatively in the future work. The results of this study reveal and perfect the blade erosion mechanism of oxide particle in steam turbine control stage and provide a theoretical basis for preventing and alleviating SPE in control stage. Acknowledgment The authors would like to thank for the financial support of Research Fund for the Doctoral Program of Higher Education of China (No. 20120201120065) and National Natural Science Foundation of China (NSFC) (No. 50476051). Appendix

Nomenclature A surface area of spherical particle which has the same volume as actual particle [mm2] B axial width of blade [mm] B2 circumferential width of blade [mm] CD particle drag coefficient, defined by Equation (9) [-] E accumulated erosion weigh loss on sr ¼ 0.7e1.0 of blade surface, defined by Equation (8) [g/10000h] Es accumulated weight-loss in each interval of sr, defined by Equation (7) [g/10000h] H height of blade [mm] H0 the variation of nozzle height along sr [-] P0 total pressure at the inlet of control valve[Pa] P2 static pressure at the rotor outlet [Pa] Re particle Reynolds numbers, defined by Equation (10) [-] S surface area of actual particle [mm2] T surface temperature of the target [K] T0 total temperature at the inlet of control valve[K] V particle impingement velocity [m/s] VN1 normal incidence velocity [m/s] VN2 normal rebound velocity [m/s] VT1 tangential incidence velocity [m/s]

Please cite this article in press as: Cai L-x, et al., The influence of nozzle chamber structure and partial-arc admission on the erosion characteristics of solid particles in the control stage of a supercritical steam turbine, Energy (2015), http://dx.doi.org/10.1016/ j.energy.2015.01.044

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VT2 dp e eN eT hr i r rh s s0 sr t u

tangential rebound velocity [m/s] particle diameter [mm] erosion rate density on blade surface [kg/m2s] normal velocity restitution coefficients [-] tangential velocity restitution coefficients [-] defined as hr ¼ r-rh/H [-] ¼ 1,2 … 10, indices for each interval of sr along the pressure surface or suction surface distance from an eroded point to the rotation center of the rotor [mm] hub radius [mm] arc length along the pressure or suction surface of blade from leading edge to the erosion point [mm] total arc length along the pressure or suction surface of blade from leading edge to trailing edge [mm] defined as sr ¼ s/s0 [-] pitch of cascade [mm] steam velocity [m/s]

Greek Symbols b particle incidence angle [ ] D equivalent sand diameter [mm]

εm

m r rp 4

11

mass erosion rate [mg/g] molecular dynamic viscosity[kg/ms] steam density [kg/m3] density of particles[kg/m3] defined as 4 ¼ A/S, particle shape factor [-]

Subscripts p particle phase N normal direction T tangential direction

Abbreviations SPE solid particle erosion PIV particle image velocimetry CCD charge coupled device PS pressure surface SS suction surface NC nozzle chamber Fitting curve of erosion rate model and particle rebound model

Fig. S1. Erosion rate model and the error of fitting (V ¼ 350 m/s, T ¼ 566  C).

Fig. S2. Particle rebound model and the error of fitting. (a) Tangential velocity restitution coefficient, (b)Normal velocity restitution coefficient.

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References [1] Padhy MK, Saini RP. Study of silt erosion mechanism in pelton turbine buckets. Energy 2012;39(1):286e93. [2] Wang SS, Mao JR, Liu GW, Feng ZP. Performance deterioration of the governing stage nozzle caused by solid particle erosion in the steam turbine. Proc Institution Mech Eng Part A J Power Energy 2010;224(2):279e92. [3] Khaimov VA, Kachuriner YY, Voropaev YA. Erosion wear caused by coarse particles in the flow-through part of the medium-pressure stage of T-250/ 300-240 turbines. Power Technol Eng 2004;38(5):279e84. [4] Li Y, Zhou L, Xu G, Fang YX, Zhao SF, Yang YP. Thermodynamic analysis and optimization of a double reheat system in an ultra-supercritical power plant. Energy 2014;74:202e14. [5] Hamed AA, Tabakoff W, Richard BR, Kaushik D, Puneet A. Turbine blade surface deterioration by erosion. J Turbomach 2005;127(3):445e52. [6] Campos-Amezcua A, Gallegos-Munoz A, Alejandro Romero C, Mazur-Czerwiec Z, Campos-Amezcua R. Numerical investigation of the solid particle erosion rate in a steam turbine nozzle. Appl Therm Eng 2007;27(14e15):394e403. [7] Mazur Z, Campos-Amezcua R, Campos-Amezcua A. Shape modification of an axial flow turbine nozzle to reduce erosion. Int J Numer Method H 2009;19(2): 242e58. [8] Li Y, Yan P, Han W. Unsteady numerical simulation of steam-solid two-phase flow in the governing stage of a steam turbine. J Therm Sci 2009;18(4):313e20. [9] Cai L, Wang S, Zhang L, Mao J, Zhang JJ, Xu YT. Influence of oxide particle size on the erosion of the control stage nozzle in a supercritical steam turbine. In: ASME Turbo Expo 2013: turbine technical conference and exposition. San Antonio, Texas, USA; 2013. [10] Dai L, Yu M, Dai Y. Nozzle passage aerodynamic design to reduce solid particle erosion of a supercritical steam turbine control stage. Wear 2007;262(1e2): 104e11.

[11] Wang S, Mao J, Liu G, Feng Z. Reduction of solid-particle erosion on the control-stage nozzle of a steam turbine through improved end-wall contouring. Proc Institution Mech Eng Part C J Mech Eng Sci 2010;224(10). 219e210. [12] Wang S, Cai L, Mao J, Zhang J, Xu Y. Mechanisms of steam turbine blade particle erosion and crucial parameters for minimizing blade erosion. Proc Institution Mech Eng Part A J Power Energy 2013;227(5):546e56. [13] Wang SS, Mao JR, Cai LX, Zhang JJ, Xu YT. Influence of the inlet channel flow of a steam turbine on solid particle erosion of the control stage nozzles. Proc Institution Mech Eng Part A J Power Energy 2012;226(5):636e49. [14] Wang S, Mao J, Liu G. Uncertainty of the PIV testing results for gas flow field caused by tracer particles and seeding method. In: Proc.. Of the 5th Int. symp. On measurement techniques for multiphase flows. Macau: AIP Publishing; 2007. p. 148e55. [15] Misra A, Finnie I. A review of the abrasive wear of metals. J Eng Mater Technol 1982;104(2):94e101. [16] Grant G, Tabakoff W. Erosion Prediction in turbomachinery resulting from environmental solid particles. J Aircr 1975;12(5):471e8. [17] Speziale CG, Thangam S. Analysis of an RNG based turbulence model for separated flows. Int J Eng Sci 1992;30(10):1379e84. [18] Huang PG, Bradshaw P, Coakley TJ. Skin friction and velocity profile family for compressible turbulent boundary layers. AIAA J 1993;31(9):1600e4. [19] Haider A, Levenspiel O. Drag coefficient and terminal velocity of spherical and nonspherical particles. Powder Technol 1989;58:63e70. [20] Chen X, McLaury BS, Shirazi SA. Numerical and experimental investigation of the relative erosion severity between plugged tees and elbows in dilute gas/ solid two-phase flow. Wear 2006;261(7e8):715e29. [21] Hamed A, Tabakoff WC, Wenglarz RV. Erosion and deposition in turbomachinery. J Propul Power 2006;22(2):350e60.

Please cite this article in press as: Cai L-x, et al., The influence of nozzle chamber structure and partial-arc admission on the erosion characteristics of solid particles in the control stage of a supercritical steam turbine, Energy (2015), http://dx.doi.org/10.1016/ j.energy.2015.01.044