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Distribution characteristics of salt-out particles in steam turbine stage
Energy 192 (2020) 116626
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Distribution characteristics of salt-out particles in steam turbine stage Pengfei Hu*, Lihua Cao, Jingkai Su, Qi Li, Yong Li School of Energy and Power Engineering, Northeast Electric Power University, Jilin, 132012, Jilin Province, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 April 2019 Received in revised form 5 September 2019 Accepted 23 November 2019 Available online 26 November 2019
Exploring the distribution characteristics of salt-out particles on the blade surface is one of the most urgent problems for supercritical steam turbine. To obtain more practical distribution characteristics of salt-out particles in the steam turbine stage, the population balance model is loaded based on Eulerian multiphase model to simulate the real existed microscopic behaviors of salt-out particles such as nucleation, growth, aggregation and breakage. The results show that along the axial direction the number of salt-out particles gradually decreases and a ladder-like distribution is observed both on the stator and rotor blades. For the stator blade, a critical position which is 62.9% of the axial chord length occurs before which the diameter of salt-out particles on the pressure surface is greater than that on the suction surface, while after that the situation is opposite; for the rotor blade, a different critical position which is 81.1% of the axial chord length occurs. Along the axial direction the volume fraction of particles declines in the entrance area, fluctuates in the middle area on the stator blade, and on the pressure surface of rotor blade, a peak position of the volume fraction is consistent with the maximum turbulence intensity and particle diameter. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Steam turbine Salt-out particles Population balance model Distribution characteristics
1. Introduction Steam turbine is one of the most important power generating turbo-machines in thermal power plants. It has been found that, during its actual operation, one of the major causes for the turbine efficiency reduction is the salt deposition on the blade surface. When the steam works inside the steam turbine, the steam pressure undergoes a significant change, it can be reduced from the supercritical value to the negative value. With the reduction of the steam pressure, the salt-dissolved capacity of the steam decreases, so that the salt previously dissolved in the steam precipitates, adheres to the turbine cascade and accumulates on the surface as particles [1]. When salt deposits on the blades, it will increase the roughness of the cascade surface and change the cascade profile, which further affect aerodynamic characteristics of blades, so that the relative efficiency of the turbine will be reduced and the operational efficiency of the turbine will also be lowered [2]. For instance, for a certain turbine, the serious salt deposition on its cascade surface can result in a 20% reduction in the turbine rating, moreover, every additional 0.1 mm thickness of the salt deposition can reduce the turbine stage efficiency by 3%e4% [3]. For a 400
* Corresponding author. E-mail address: [email protected] (P. Hu). https://doi.org/10.1016/j.energy.2019.116626 0360-5442/© 2019 Elsevier Ltd. All rights reserved.
MWsteam turbine, the salt deposition on the cascade surface can decrease the turbine rating by 5% in the first month, and 10% within six months [4]. Meanwhile, the salt deposition on the cascade surface will change the natural frequency of the steam turbine blades and increase the axial thrust. In addition, certain aggressive deposit will have a great impact on the blades’ high temperature resistance and adversely affect the reliability of the steam turbine. In recent years, with the large-scale commercial application of the large-capacity and high-parameter thermal power unit that runs in supercritical value, especially when the large-capacity once-through boilers and ultra-supercritical units are put into operation [5], the cleaning measures like conventional steam-water separation, steam cleaning, etc., would not be able to control the steam quality, because there’s no boiler drum in once-through boilers. Meanwhile, in an ultra-supercritical unit the increase of steam pressure increases the salt solubility in the steam, which further increases the difficulty of desalting from the steam in the boiler. So, the presence of salt in steam is inevitable, and the salt deposition as shown in Fig. 1 from the steam has prominent impacts on the turbine performance [6e8]. Therefore, it is very important to investigate the distribution characteristics of salt-out particles in the steam turbine stage to improve the steam turbine efficiency and reliability. Due to the complicated salt deposition process on the turbine blade surface, compared with traditional gas-solid two-phase flow
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Fig. 1. Deposition images of salt-out particles on cascade surfaces in steam turbine [9].
system, the two-phase flow generated during the salt-out process in the turbine cascade passage comes along with micro-behaviors such as nucleation and growth of salt-out particles [10,11]. Meanwhile, it is difficult for researchers to conduct the experiments such as laboratory experiments or field experiments, since the steam turbine is considered as a high-temperature and high-pressure equipment. Thus, the physical process of salt-out in the steam and the flow mechanism of salt deposition are failed to be understood deeply. In 1936, Straub [12] made a preliminary analysis on causes of deposition in the steam turbine. It was shown that the salt deposition on steam turbine blades is not confined to a certain range of steam temperature and pressure. Moreover, the amount of deposit is not proportional to the salt content in the boiler feed water, even the low-salt-content feed water can significantly reduce the turbine efficiency as the salt deposition increases the roughness of the cascade surface. In 1939, Goerke [13] pointed out that even the steam undergoes strict water treatment and is under the pressure of 6.895e13.79 MPa, the salt deposition on steam turbine blades is still inevitable. During this period, due to the relatively low steam parameters at the inlet of the steam turbine and the weak salt solubility, the soluble sodium salt in water was mainly discussed, while for the insoluble sediments such as copper, iron, magnesium, aluminum, calcium, silicon compounds, they did not attract enough attention due to a small amount. In the late 1950s, the solubility of salt in steam went up as the inlet steam parameters increased, so that more soluble and insoluble salts were brought into the steam turbine with the steam. The soluble salt deposit can be easily washed off by general means of cleaning. However, the insoluble particles in the steam deposit and accumulate continually on the blade surface which cannot be removed thoroughly by means of cleaning like the way of using saturated vapor, resulting in an adverse impact on the steam turbine efficiency. Especially the copper oxide deposition on the turbine blade surface had drawn considerable attention, which came along with the application of one-through boiler and supercritical unit. In the 1960s, Pocock and Stewart [14] first studied the
dissolution of copper oxides in the steam. During 1970e1980s, researchers made their effort to study how to improve the quality of boiler feed water by using methods of chemical reaction and water treatment, so as to relieve the salt deposition problem in the turbine. In addition, they further studied the corrosion of the blades in the wet steam region resulted from the salt deposition on the surface of the cascade [15e17]. Jonas [18] proposed that the precipitation of chemical compounds from the superheated steam, the deposition and evaporation from hot surfaces and the change of concentration in oxides in depositions are the three mechanisms for concentrating impurities in steam turbines. Chemicals precipitate when concentration exceeds solubility in superheated steam. In the 1990s, on-line monitoring technology for salt deposition and the corrosion of steam turbine cascades received considerable attention. Martynova [19] found that copper oxides generally deposit in the high-pressure cylinder of steam turbine, and proposed that after precipitating from superheated steam, the salt particles would solidly adhere to the turbine blade surface. Later, some researchers paid attention to the blade corrosion in the dry-wet phase transition zone (PTZ) in the steam turbine [20e22]. In the 2000s, as indicated by Jonas et al. [9], the mechanism of salt deposition on the surface of the turbine cascade is not very clear, so for salt deposits that can be dissolved in water, the most effective washing means is still the traditional method of wet steam cleaning. It was also pointed out by Jonas et al. [9] that the effect of salt deposition on the steam turbine’s economy depends on the thickness of the salt deposit, the steam pressure as well as the cascade surface roughness, while there’s no analysis on the physical processes of salt deposition. In the 2010s, Brun et al. [23] evaluated the effectiveness of online turbine cleaning with various cleaning agents. Kushwaha [24] studied the impacts of the corrosion caused by salt deposition on the life of steam turbine blades. In addition, with an increasing number of ultra-supercritical power plants put into operation, steam-solid two-phase flow, most notably in steam turbines, gradually becomes an issue of concern to some researchers who take the fossil units as research object [25,26]. Cai et al. [25] studied the particle erosion of steam-solid two-phase
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flow passing through the governing stage nozzle of the steam turbine. As described by Padhy and Saini [26], the erosion of blades results in lower efficiency of steam turbine, shorter maintenance cycle and higher maintenance costs. As can be seen from above mentioned literatures, the salt deposition on the surface of the turbine cascade is unavoidable. Most of above studies in the analysis of the salt deposition on steam turbine blades only focus on several aspects: the chemical water treatment, the salt solubility in the steam, cascade corrosion caused by the salt deposition, and the impact on the operational economy of the turbine. The studies on the steam-solid two-phase flow mainly present numerical simulations for the solid particle erosion (SPE) on the turbine blade. To the best of our knowledge, the distribution characteristics of salt-out particles from the steam in the turbine stage have not been investigated so far. So, it is necessary to explore the distribution characteristics of salt-out particles by considering their micro-behaviors in the steam turbine stage. In this paper, the computational fluid dynamics coupled with the population balance model (CFD-PBM model) are used to study the characteristics of two-phase flow that is the steam carrying salt-out particles. The 3-D simulations based on the CFD-PBM model were performed with CFD package FLUENT [27]. The micro-behaviors like nucleation, growth, aggregation and breakage of the salt-out particles on steam turbine blades are analyzed. Moreover, the number and the average diameter as well as the volume fraction distribution characteristics of the salt-out particles are presented. The research results in this study reveal the distribution characteristics of salt-out particles in the steam turbine stage, and provide a theoretical basis for reducing or preventing from the salts deposition on steam turbine blades.
Fig. 2. Geometrical model.
2. Geometric model and numerical approach 2.1. Geometric model In this paper the second stage of the intermediate pressure cylinder in steam turbine is selected as the computational domain. The basic geometrical parameters are as follows in Table 1. The geometrical model is shown in Fig. 2. Due to the complex structure of flow passage, the multi-block grid generation technique and unstructured tetrahedral mesh are used to meet the computational accuracy. The generated mesh of flow field is shown in Fig. 3. In order to study the grid number effect on calculation accuracy, validation of grid dependency is carried out. We choose the first 1/4 from the 4th period to verify the mesh independence. For cascade passage, five sets of grids are conducted including 180, 320, 440, 570 and 710 thousands cells. The number of particles at the leading edge of the stator blade is chosen as a reference parameter. Simulation results under different grid number conditions are compared with each other and exhibited in Table 2. It can be seen that the effect of total grid number on particle number is negligible after the total grid number reaching to 440 thousand, which means the total grid number should be supposed to exceed 440 thousand. Considering the speed of computation, 440 thousand is selected as the total grid number of the flow passage in this study.
Fig. 3. Grid sketch.
Table 2 Four calculation grids of steam turbine flow passage.
Grids 103 particles number 1016
1
2
3
4
5
180 5.943
320 6.389
440 6.500
570 6.502
710 6.501
2.2. Population balance model In order to describe the distribution of salt-out particles in steam turbine stage, internal and external coordinates, which are referred as the particle state space, must be employed. The internal coordinates of the particles provide quantitative characterization of
Table 1 Geometrical parameters of the second stage of the intermediate pressure cylinder in steam turbine.
Stator Blade Rotor Blade
Pitch diameter/mm
Height/mm
Axial width/mm
Number
Pitch/mm
Flow outlet angle/( )
1259.58 1283.88
152.52 152.58
63.5 76.2
72 56
54.96 72.03
21.67 24.46
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its distinguishing traits other than its location while the external coordinates merely denote the location of the particles in physical space. Thus, a particle is distinguished by its internal and external coordinates. Number density function is commonly used to describe this distribution in the state space. Given the coordinates of the property vector x ¼ ðx1 ; …; xN Þ that specify the state of the entity, the number density function is defined as in Equation (1) [28,29].
nðx1 ; …; xN ; x; tÞdx1 ; …; dxN ¼ nðx; x; tÞdx
v ¼ ½GðLÞnðL; x; tÞ þ BðL; x; tÞ DðL; x; tÞ vL
(2)
(3)
where GðLÞ is the growth rate, and BðL; x; tÞ and DðL; x; tÞ are, respectively, the birth and death rates due to aggregation and breakage. The moments of the particle size distribution are defined as follows: ∞ ð
nðL; x; tÞLk dL
mk ðx; tÞ ¼
(4)
0
A direct way to calculate the quadrature approximation is by means of its definition through the moments: þ∞ ð
nðLÞLk dLz
mk ¼ 0
Nd X
wi Lki
where S is the solubility of salts in steam, Kn and Nn are a numerical constant that are related to the type of salt. The growth behavior mainly exists in the crystallization and deposition process. For the growth process, equation of its growth rate GðLÞ is [33].
bðL; lÞ ¼
2.3. Boundary conditions 2.3.1. Boundary conditions for population balance model Since the actual operation of the steam turbine is very complicated, the following basic assumptions need to be made:
4 3p 1=2 ε1=2 ðL þ lÞ3 3 10 v
(8)
where L and l are particle sizes, ε is the turbulent dissipation rate and n is the kinematic viscosity. Particle breakage functions can be factored into two parts. The breakage kernel aðLÞ, is the rate coefficient for breakage of a particle of size L, and bðLjlÞ defines the probability that a fragment of size l is formed from the breakage of an L-sized particle. Equation for the breakage kernel aðLÞ is [30].
" # tf 1 ε1=2 aðLÞ ¼ pffiffiffiffiffiffi exp 15 n mðε=nÞ1=2
(9)
where tf is the aggregate strength, m is dynamic viscosity. The fragment distribution function is affected by various factors, including the particle properties and breakage mechanisms. The equation is [30].
(5)
The essence of this method is the fact that the abscissas Li and the weights wi can be specified from the lower-order moments. Nd is the order of the quadrature approximation. The first five moments ðk 20; …; 3Þ are of particular interest, since they are related to the total number particle density (m0 ), the total particle length (m1 ), the total particle area (m2 ), and the total particle volume (m3 ).
(7)
The birth and death of particles occur due to aggregation and breakage processes [30]. Aggregation is caused by the particle collision due to the fluid movement and Brownian movement, and when particles are smaller than the Kolmogorov micro-scale the aggregation kernel can be computed as follows [30].
i¼1
1) The condensed nucleus is introduced; 2) The particles are in the ideal spherical shape.
(6)
GðLÞ ¼ Kg ðS 1ÞNg
where Cui D is the Reynolds-average velocity in the ith direction,xi is the spatial coordinate in the ith,Gt is the turbulent diffusivity, zj is the flux in x-space and hðx; tÞ represents the net rate of introduction of new particles into the system [31]. In this work, we consider a number density function defined in terms of particle length (x1 ≡L). The resulting population balance is
vnðL; x; tÞ vnðL; x; tÞ v vnðL; x; tÞ þ Cui D Gt vt vxi vxi vxi
JðLÞ ¼ Kn ðS 1ÞNn
(1)
where x is the position vector of the particle, x is the property vector that specifies the state of the particle, and t is the time. The population balance model is a continuous statement of the number density function. It can be defined as [30].
vnðx; x; tÞ vnðx; x; tÞ v vnðx; x; tÞ þ Cui D Gt vt vxi vxi vxi ! # " v ¼ n x; t zj þ hðx; tÞ vxj
The microscopic behaviors of the nucleation, growth, breakage and aggregation for salt-out particles can be achieved by applying the PBM model settings, and the following are the specific settings. The nucleation behavior is mainly due to the supersaturation of the fluid and precipitation of the solid matter [32]. For the nucleation process, the equation of the nucleation rate JðLÞ is [33].
bðLjlÞ ¼
8 > 1; > > < 1; > > > : 0;
L ¼ L0 1=3 L ¼ l3 L30
(10)
otherwise
where L0 is the size of the primary particle. The nucleation rate and growth rate are associated with the pressure change of dynamic curve by using user-defined functions in this paper. By solving the solubility equation which changes with pressure, the steam supersaturation can be calculated, and the nucleation and growth rates of particles under different pressures can be further solved. For aggregation rate and breakage rate, according to equations (5)e(7), they can be obtained by using userdefined functions. The salt-out layer is mainly generated by transporting salts after nucleation from the steam to the blade surface. In most cases, this process is achieved through diffusion. Thus, the deposition rate can be expressed as
P. Hu et al. / Energy 192 (2020) 116626
#1=2 9 2 = 1 d 1 d d þ ,DC m_ d ¼ d, , þ DC ; 2 kR 4 kR kR
(11)
where d represents mass transfer coefficient which can be obtained by an empirical deposition model [34]. DC is the salt concentration difference between the salt concentration in steam and the saturation concentration of the solution; kR is the surface reaction rate constant [35]. 2.3.2. Boundary conditions for turbulent model The salt-out flow in the turbine is the steam-solid two-phase flow accompanied by phase changes; the Eulerian multiphase model provided by Fluent is used to calculate the salt-out twophase flow field, and the RNG k-ε model is selected as the turbulence model. The pressure inlet boundary condition is set as the total pressure of 2.778 MPa. The pressure outlet boundary condition is set as 2.380 MPa. The time step is 8.9 107. Sodium chloride is used as the simulated salt medium [36] of which the maximum content is 15 mg,kg1 according to the steam quality standard. The status parameters of superheated steam are provided by IAPWS-IF97 database, and the density of the precipitated sodium chloride particles is 2165 kg,m3.
5
time during the aggregation-breakage process are compared with the results performed by Marchisio [38] in Fig. 5. As can be seen from Fig. 5, the trend of m0 with time comprises two stages: at first m0 decreases with time, and then m0 does not change with time. In the first stage, with the increase of time m0 decreases, which means the decrease of m0 caused by aggregation is larger than the increase of m0 caused by breakage behavior, indicating the aggregation phenomenon is significant. In the second stage, with the increase of time, the aggregation effect decreases and the breakage effect increases, until the aggregation and breakage effects reach a dynamic balance, the m0 of sodium chloride particles no longer changes. The simulation results in this study are consistent with the trend of literature results [38], which proves that the model in this study is correct. It is well known that the superheated steam as working fluid in a turbine is characterized by high temperature and high pressure which is difficult to be analyzed using experimental method. So until now, there are few reports on the online measurement data of the salt-out particles on the turbine blades for a power plant. In order to further validate the results of the paper, salt deposition pictures in steam turbine cascades in a power plant are compared with the simulation results of this paper, as shown in Fig. 6. It can be
2.4. Validation of numerical method To validate the reliability of the established model of this study, the changes of overall particle volume m3 with time during the aggregation process and the breakage process are compared with the results performed by Fan [37] in Fig. 4. As can be seen in this figure, the total salt-out particles volume m3 always remains the same with time during the aggregation process (see Fig. 4(a)) and the breakage process (see Fig. 4(b)). The reason is that under the effect of aggregation or breakage, although particles have chance to become into new bigger particles or small particles, which results in a variation of the number density, the total salt-out particles volume will never change with time. So, these comparison results show that the established model of this study is reliable. Since aggregation and breakage are often the last steps of a complex sequence of phenomena, such as nucleation, fast reactions, combustion, and molecular growth, it is necessary to analyze m0 during the aggregation-breakage processes. In order to further verify the correctness of the model, the changes of m0 with
Fig. 5. Comparison of m0 during the aggregation-breakage processes between Ref. [38] and present study.
Fig. 4. Comparison of m3 between Ref. [37] and present study.
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Fig. 6. Deposition distribution of salt-out particles on turbine cascades in a power plant compared with the present results.
seen that the distribution of salt-out particles on the suction surface of the rotor blade shows a ladder-like distribution in a steam turbine, which is consistent with the simulation results of this paper, indicating that the simulation results of this study are credible. 3. Results and discussion 3.1. The number distribution of salt-out particles In order to clearly reflect the distribution characteristics of sodium chloride particles on the blade, based on a 3-D numerical simulation of turbine cascade, the contours of the number of sodium chloride particles on the stator blade and the rotor blade at different times in a same period is shown in Fig. 7. Fig. 7 shows the salt-out particles beat at the point of the leading edge of the stator blade after entering into the fully developed flow passage. According to the Griffin-Irwin theory [39], if the impact energy EI exceeds the critical energy (i.e., the total energy needed to generate a new surface), when the sodium chloride particles collide with the blade, the solid particles will have brittle fractures and break into smaller particles. The impact energy EI of sodium chloride particles is
EI ¼ Ed Ee
(12)
where Ed is the initial energy of sodium chloride particles at the entrance of the flow passage, Ee is the dissipated energy in the process of collision. The critical energy of sodium chloride particles Es in the breakage process is
Es ¼ 2Gs A
(13)
where Gs is the strain energy release rate of the material, A is the area of fracture in the process of breakage. The impact energy when sodium chloride particles collide with the leading edge of the stator blade is calculated and the obtained result is in the range of 1.6 104e2.4 102 J, while the critical energy required for the particle breakage is 1.5 1010 J. It is obvious that the impact energy is greater than the critical energy. The breakage rate reaches a peak value, resulting in frequent collision and nucleation in the secondary nucleation process, which then produces secondary nucleus and the nucleus further grows into new crystal particle, thus forming an area with high number of particles in the leading edge.
The impact energy of the particle hitting the blade surface is equal to the instantaneous kinetic energy of the particle contacting with the blade surface, and it doesn’t change with time. So, the number of particles at the leading edge of stator blade in Fig. 7 does not change with time. It also can be seen in Fig. 7 that the number of particles on the stator blade and rotor blade shows a ladder-like distribution. Fig. 8 shows the change of the number of particles on the suction surface on both stator and rotor blades along axial direction, at different time in a same period. As we can see, the number of particles decreases along the axial direction. Under the influence of turbulent diffusion force, the steam contacts with the blade and the mass transfer behavior between steam and particles on the blade occurs. When the steam passes by the leading edge of the stator blade, the particles are constantly separated out from the steam on the blade surface because of the continued decrease in steam pressure resulting in an increase in supersaturation, but the concentration of sodium chloride in the steam decreases gradually as the particles are separated out continuously. As a result, the number of particles on the surface of blade shows a downtrend. However, the number of particles on the suction surface of stator blade decreases slowly, and it decreases rather quickly on the rotor blade. The first reason is that the degree of the over-saturation of the steam carrying salt in the stator blade flow passage increases due to the decreasing steam pressure, which provides the driving force for the salt-out process of crystal particles. These particles continually separate from the steam and most of them deposit on the surface of the stator blade, which leads to the reduction of the over-saturation of the steam in the rotor blade flow passage as well as the separating rate of particles. The second reason is that in the second stage of the intermediate pressure cylinder in a steam turbine which is the research object in this study, the steam pressure drop upon the stator blade is larger than that upon the rotor blade. As a result, the driving force of crystallization is larger, so that more particles will be separated out, thus the number of particles on the stator blade decreases more slowly than that on the rotor blade.
3.2. The diameter distribution of salt-out particles In the figures of this study, SS and PS represent the suction surface and pressure surface of blades, respectively. Fig. 9 and Fig. 10 show the diameter distribution of the particles on the suction surface and pressure surface of both rotor and stator blades at the height of z ¼ 0.60 m at 1/4 T, 2/4 T, 3/4 T and 4/4 T. At 1/4 T, it can be seen that, for the stator blade, the particle diameters on the
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Fig. 7. Particle number distribution on stator blade and rotor blade at different time.
Fig. 8. The number distribution of particles on the suction surface at different time in a same period.
suction surface and pressure surface increase generally along the axial direction, and then fluctuate in the tail area of the suction surface; the particle diameter on the suction surface of rotor blade has a similar trend as that of stator blade, but the particle diameter on the pressure surface of rotor blade fluctuates remarkably along the axial direction. To explain this phenomenon, the turbulence intensity needs to be introduced. As can be seen in Figs. 9 and 10, all the particle diameters are smaller than 1 mm so Brownian motion induced collisions is the controlling mechanism for the aggregation process. Higher turbulence intensity leads to more intense collisions, causing more particles to aggregate into larger particles with larger diameters. It can be further explained from Figs. 11 and 12. In Figs. 11 and 12, the turbulence intensity near the suction surface and the pressure surface of stator blade increases generally along the axial direction. When the turbulence intensity increases, the contact frequency between particles becomes strong, so the aggregation of particles becomes obvious, causing the increase growth of particles on the stator blade along the axial direction, and
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Fig. 9. The particle diameter distributions on the suction surfaces of stator and rotor blades.
Fig. 10. The particle diameter distributions on the pressure surfaces of stator and rotor blades.
Fig. 11. The turbulence intensity distributions near the suction surfaces of stator and rotor blades.
Fig. 12. The turbulence intensity distributions near the pressure surfaces of stator and rotor blades.
the fluctuation of turbulence intensity causes a corresponding fluctuation of particle diameter near the tail area of the suction surface of stator blade. Fig. 11 displays that the change of the turbulence intensity near the suction surface of rotor blade is the same as that of stator blade, so the particle diameter on suction surface of rotor blade varies similarly as that of stator blade. By comparing Fig. 10 with Fig. 12, we find the turbulence intensity near the pressure surface of rotor blade fluctuates at three different positions x ¼ 0.202 m, 0.207 m, 0.213 m respectively, where the particle diameter on the pressure surface of rotor blade fluctuates correspondingly. As shown in Figs. 9 and 10, the variation of particle diameter is not obvious both on the suction surface and pressure surface of stator blade at the blade height of z ¼ 0.60 m at the time 1/4 T, 2/4 T, 3/4 T and 4/4 T, while near the leading edge of rotor blade it changes dramatically both on the suction surface and pressure surface. This phenomenon can also be explained by the variation of turbulence intensity with time in Figs. 11 and 12. The reason is that the stator is fixed, resulting in small changes of turbulence intensity at different times, while the rotor is moving, resulting in different relative positions of the rotor and stator blades at different times, so that the turbulence intensity near the leading edge of rotor blade changes dramatically at different times, and the particle diameter varies evidently near the leading edge of rotor blade. Fig. 13 shows the particle diameter distribution on the stator blade surface. It can be seen that, in the region of x ¼ 0.14e0.162 m where the axial chord length is less than 62.9% (0:1620:14 0:1750:14 100% ¼ 62:9%), the diameter of the particles on the pressure surface is larger than that on the suction surface, while in the region of x ¼ 0.162e0.175 m where the axial chord length is larger than 62.9% the situation is opposite. The reason can be explained from Fig. 14 which shows the variation of turbulence intensity with the position. In Fig. 14, when the axial chord length is less than 62.9%, although the turbulence intensity near the suction surface is higher than that near the pressure surface, the difference is not significant, so the effect of inertia plays the dominant role. It means that when the steam carrying the salt-out particles enters the flow passage of the stator blade, the particles, especially larger particles, will move towards the pressure surface without changing their direction due to the effect of inertia, so that they have more opportunities to be gathered together, leading to become much larger particles near the pressure surface than that near the suction surface. Compared
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Fig. 13. The particle diameter distribution on the stator blade surface. Fig. 15. The particle diameter distribution on the rotor blade surface.
Fig. 14. The turbulence intensity distribution near the stator blade surface. Fig. 16. The turbulence intensity distribution near the rotor blade surface.
with the chord length less than 62.9%, the turbulence intensity near the suction surface is obviously higher than that near the pressure surface when the axial chord length is larger than 62.9% in Fig. 14, which makes the particles undergo a larger turbulence effect in a larger region near the suction surface and further leads to more intense collisions, causing more particles to aggregate into larger particles. Therefore, when the axial chord length is larger than 62.9%, the particles grow slower near the pressure surface. In Fig. 15, the diameter distribution of particles on the rotor blade has the similar trend as that on the stator blade in Fig. 13. The diameter of particles on the pressure surface increase more quickly than that on the suction surface of rotor blade in the region of x ¼ 0.18e0.21 m where the axial chord length is less than 81.1% 0:210:18 100% ¼ 81:1%). The reason is mainly related to the (0:2170:18 turbulence intensity which can be seen from Fig. 16. In Fig. 16, when the axial chord length is less than 81.1%, the intensity of turbulence near the pressure surface is higher than that near the suction surface of the rotor blade, and the maximum turbulence intensity near the pressure surface is at x ¼ 0.207 m. The aggregation of particles seems more obvious when the turbulence intensity is much higher, resulting in a faster growth of particles on the pressure surface than that on the suction surface. However, when x > 0.210 m, the diameter of particles on the suction surface is greater than that on
the pressure surface of rotor blade. One reason is that under the impact of the pressure gradient of the steam, the secondary flow from pressure surface to suction surface of rotor blade is formed, and then under the influence of the secondary flow, the diameter of the particles on the suction surface is larger than that on the pressure surface near the trailing edge area of rotor blade. The other reason is also related to the turbulence intensity which is the same with the explanation for the particle diameter distribution on the rotor blade in the region of x ¼ 0.18e0.21 m in Fig. 16. 3.3. The volume fraction distribution of salt-out particles 3.3.1. 1 vol fraction of sodium chloride particles along the axis direction As shown in Fig. 17, for the stator blade, the particle volume fraction on the suction surface has a descend trend at the entrance area. This is because the particle volume fraction is determined by both particle number and particle diameter; the particle number on the suction surface of the stator blade plays the dominant role, while the particle diameter increases slowly and shows a less effect on particle volume fraction. The collision nucleation of particles at the leading edge of the blade is so obvious that results in a peak
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P. Hu et al. / Energy 192 (2020) 116626
coincides with the peak value of the turbulence intensity. This is because the particle diameter on the pressure surface plays a major role, and the volume fraction reaches to a peak value when both the turbulence intensity and the particle diameter reach the peak point (x ¼ 0.2075 m). Moreover, the variation of the particle volume fraction with the position in Fig. 18 is consistent with the change of the particle diameter with the position in Fig. 15.
Fig. 17. The volume fraction of sodium chloride from the stator blade.
volume fraction at the entrance. Then the volume fraction drops as the particle number decreases along the axial direction. The volume fraction fluctuates obviously after the turning point (x ¼ 0.155 m), because the turbulence intensity increases quickly at x ¼ 0.155 m, which leads to the growth of particle diameter. Therefore, we can see a fluctuation phenomenon on the volume fraction curve. The particle volume fraction on the suction surface drops dramatically at the trailing edge, because with the decrease of the number of particles on the suction surface of the stator blade, the particle diameter at the trailing edge becomes an influencing factor to the volume fraction and it can be seen from Fig. 13 that the diameter of particles on the suction surface decreases at the trailing edge. It also can be seen in Fig. 17 that the volume fraction of the particles on the suction surface of stator blade does not change with time. From Fig. 17, we can also see that for the stator blade, at the entrance of the pressure surface the particle volume fraction drops dramatically, then fluctuates obviously after the turning point (x ¼ 0.16 m), and gradually increases in the tail area along the axial direction of the stator blade. The reason is the same with that of the suction surface of stator blade. As seen from Fig. 18, the particle volume fraction on the suction surface of the rotor blade decreases along the axial direction, since the particle number decreases along the axial direction. On the pressure surface, the peak position of the particle volume fraction
Fig. 18. The volume fraction of sodium chloride from the rotor blade.
3.3.2. Comparison of volume fraction for sodium chloride at different time Fig. 19 shows the volume fraction of sodium chloride particles at the blade height of z ¼ 0.60 m at 1/4 T, 2/4 T, 3/4 T and 4/4 T respectively. At 1/4 T, the sodium chloride particle clusters with high volume fraction occur which is circled with red in the wake region. At 2/4 T, the high volume fraction area shifts the adjacent stage. At 3/4 T, the high volume fraction area enters into the adjacent stage. At 4/4 T, the high volume fraction area disappears in the second stage of the intermediate pressure cylinder in this study. This is due to the wake at the outlet of the rotor blade. Because there is always a certain thickness of the exit edge of the blade, the two parts steam flow over the suction surface and the pressure surface of each blade cannot immediately join together after leaving the cascade, so the wake area filled with vortex is formed behind the blade outlet. The pressure and velocity of the steam flow in the wake area are greatly different from the pressure and velocity of the main flow. After an interaction between the two parts of steam flow, the steam flow at the back of the cascade gradually becomes homogenized, and then the steam flow velocity after homogenization decreases and becomes lower than the original mainstream velocity and the steam flow kinetic energy decreases. Therefore, the salt-out particles agglomerate in the wake area to form particle clusters with high volume fractions, and then the particle clusters carried by the steam flow enter into the adjacent stage with time under the influence of the mainstream. 4. Conclusions In this paper, the CFD-PBM model has been used to study the two-phase flow of steam carrying salt particles in the second stage of the intermediate pressure cylinder of the steam turbine. Some conclusions are obtained as follows. 1) After entering the flow passage, the steam carrying salt particles will strike the leading edge of the stator blade, resulting in the collision nucleation, and the number of salt particles will reach a peak value at the leading edge of the stator blade and it doesn’t change with time. Along the axial direction, the number of saltout particles gradually decreases and it shows a ladder-like distribution. Furthermore, the number of particles decreases more slowly on the suction surface of the stator blade than that of the rotor blade. 2) Along the axial direction, the particle diameter on the stator blade and the suction surface of rotor blade increases generally, while that on the pressure surface of rotor blade fluctuates remarkably during the whole time. The particle diameter on the stator blade basically does not change over time, but the particle diameter at the leading edge of the rotor blade changes dramatically. For the stator blade, in the region of x ¼ 0.14e0.162 m where the axial chord length is less than 62.9%, the particle diameter on the pressure surface is generally larger than that on the suction surface, while the situation is opposite in the region of x ¼ 0.162e0.175 m where the axial chord length is larger than 62.9%. For the rotor blade, the particle diameter distribution has the similar trend as that on the
P. Hu et al. / Energy 192 (2020) 116626
11
Fig. 19. The volume fraction of sodium chloride in different time.
stator blade and the turning point is at 81.1% of the axial chord length. 3) For the stator blade, the particle volume fraction on the suction surface decreases in the entrance area with evident fluctuations after the turning point (x ¼ 0.155 m), and then drops at the trailing edge, which does not change with time; the particle volume fraction on the pressure surface rapidly decreases in the entrance area, and there is a significant fluctuation after the turning point (x ¼ 0.16 m), and then in the tail area the particle volume fraction gradually increases. For the rotor blade, the particle volume fraction on the suction surface also decreases along the axial direction, while there is a peak value of that on the pressure surface which is consistent with the peak value of the particle diameter and the turbulence intensity (x ¼ 0.2075 m). The particle clusters with high volume fraction exist under the wake effect in the tail area of the rotor blade and then the high volume fraction area shifts to the adjacent stage. Acknowledgments The authors gratefully acknowledge the support from the National Natural Science Foundation of China (No.51906034, No.41702250) and the Science and Technology Research Project of Education Department of Jilin Province of China during the “13th Five-Year Plan” (No. JJKH20190701KJ). References [1] Zhang HB, Wang DM, Zhang HX. Analyses of deposits on high pressure cylinder of steam turbine. Corros Prot 2015;36(5):506e9 [in Chinese]. [2] Salahshoor K, Kordestani M, Khoshro MS. Fault detection and diagnosis of an industrial steam turbine using fusion of SVM (support vector machine) and ANFIS (adaptive neuro-fuzzy inference system) classifiers. Energy 2010;35(12):5472e82.
[3] Zhong WJ. A brief discussion on causes and countermeasures of flow passage scaling. Northeast Electr Power Technol 2005;26(12):46e8 [in Chinese]. [4] Daniels D. Turbine deposits rob megawatts, but you can catch the thief. Power 1999;143(2):83e7. [5] Zhou H, Chen C, Lai J, et al. Affine nonlinear control for an ultra-supercritical coal fired once-through boiler-turbine unit. Energy 2018;153:638e49. [6] McCloskey TH, Dooley RB, McNaughton WP. Turbine steam path damage: theory and practice. EPRI; 1999. AP-108943. t astnýa M, Sejna [7] S M. Condensation of steam with chemical impurity in a turbine cascade. Proc Inst Mech Eng Part A Journal of Power and Energy 2014;228(2):194e205. [8] Povarov OA, Petrova TI, Semenov VN, et al. Turbine steam chemistry and corrosion: electrochemistry in LP turbines. EPRI; 2001. 1006283. [9] Jonas O. Steam turbine efficiency and corrosion: effects of surface finish, deposits, and moisture. EPRI; 2001. 1003997. [10] Shields KJ, Allmon WE. State-of-knowledge on deposition,part 1:parameters influencing deposition in fossil units. EPRI; 2002. 1004194. [11] Shields KJ, Allmon W, Pop M. State-of-knowledge on deposition,part 2: assessment of deposition activity in fossil plant units. EPRI; 2003. 1004930. [12] Straub FG. The cause and prevention of steam turbine blade deposits. University of Illinois Experimental Station Bulletin; 1936. [13] Goerke H. Salt and silica deposits in steam turbines. Elektrizitatswirtschaft 1939;38:614e6. [14] Pocock FJ, Stewart JF. The solubility of copper and its oxides in supercritical steam. J Eng Gas Turbines Power 1963;85(1):83e8. [15] Bussert BW, Curran RM, Gould GC. The effect of water chemistry on the reliability of modern large steam turbines. J. Eng. Power 1979;101(3):477. [16] Lindsay WT. Behavior of impurities in steam turbines. Power Eng 1979;83(5): 68e72. [17] Dussourd JL. A simple one-dimensional model for primary turbine blade erosion prediction. In: ASME international gas turbine conference and exhibit; 1983. p. 1e9. [18] Jonas O. Characterization of steam turbine environment and selection of test environments. In: EPRI workshop on corrosion fatigue of steam turbine blade Materials; 1981. [19] Martynova. Mechanism of early condensate formation in the LP turbine. EPRI; 1993. TR-102101. [20] Jonas O. On-line diagnosis of turbine deposits and first condensate. In: The 55th annual international water conference; 1994. p. 113e21. Pennsylvania. [21] Jonas O. Steam chemistry and its effects on turbine deposits and corrosion. In: The 57th annual international water conference; 1996. p. 210e7. Pennsylvania. 0
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[22] Jonas O, Bursik A, Dooley B, et al. Steam, chemistry, and corrosion in the phase transition zone of steam turbines. EPRI; 1999. TR-108184-V1. [23] Brun K, Grimley TA, Foiles WC, et al. Experimental evaluation of the effectiveness of online water-washing in gas turbine compressors. J Eng Gas Turbines Power 2014;137(4):4e8. [24] Kushwaha AD. Critical review paper of steam turbine blades corrosion and its solutions. Int J Sci Res Eng Technol 2014;3(5). 76-8. [25] Cai LX, Wang SS, Mao JR, 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;82:341e52. [26] Padhy MK, Saini RP. Study of silt erosion mechanism in Pelton turbine buckets. Energy 2012;39(1):286e93. [27] Yao Y, He YJ, Luo ZH, et al. 3D CFD-PBM modeling of the gas-solid flow field in a polydisperse polymerization FBR: the effect of drag model. Adv Powder Technol 2014;25(5):1474e82. [28] Marchisio DL, Pikturna JT, Fox RO, et al. Quadrature method of moments for population-balance equations. AIChE J 2003;49(5):1266e76. [29] Su JW, Gu ZL, Li Y, et al. Solution of population balance equation using quadrature method of moments with an adjustable factor. Chem Eng Sci 2007;62(21):5897e911. [30] Marchisio DL, Vigil RD, Fox RO. Implementation of the quadrature method of moments in CFD codes for aggregation-breakage problems. Chem Eng Sci 2003;58(15):3337e51. [31] Hulburt HM, Katz S. Some problems in particle technology. Chem Eng Sci 1964;19(8):555e74. [32] Ramkrishna D. Population balances: theory and applications to particulate systems in engineering. New York: Academic Press; 2000. [33] Help Navigator. Ansys fluent population balance module manual. New York: Ansys Inc; 2012. release 14.5. [34] Colburn AP. A method of correlating forced convection heat transfer data and a comparison with fluid friction. Trans Am Inst Chem Eng 1933;29:174e210. [35] Helalizadeh A. Mixed salt crystallization fouling. Ph.D thesis. UK: University of Surrey; 2002. [36] Galobardes JF, Van Hare DR, Rogers LB. Solubility of sodium chloride in dry steam. J Chem Eng Data 1981;26(4):363e6. [37] Fan R, Marchisio DL, Fox RO. Application of the direct quadrature method of moments to polydisperse gas-solid fluidized beds. Powder Technol 2004;139(1):7e20. [38] Marchisio DL, Vigil RD, Fox RO. Quadrature method of moments for aggregation-breakage processes. J Colloid Interface Sci 2003;258(2):322e34. [39] Bao RH, Zhang LC, Yao QY, et al. Estimating the peak indentation force of the edge chipping of rocks using single point-attack pick. Rock Mech Rock Eng 2011;44(3):339e47.
DC: the salt concentration difference [ppm] DðL; x; tÞ: death term due to aggregation and breakage[-] Ed: original energy of sodium chloride particles [J] Ee: dissipated energy in the process of collision [J] EI: impact energy [J] Es: energy needed for breakage [J] GðLÞ: molecular growth rate [] Gs: surface free energy per unit area [J] hðx; tÞ: net rate of introduction of new particles into the system [] J(L): nucleation rate [] kR : the surface reaction rate constant [] L: particle size [mm] Li: abscissa (or node) of the quadrature approximation [mm] L0: primary particle size [mm] m_ d : the deposition rate mk(x,t): k th moment of the particle size distribution [] nðL; x; tÞ: particle size distribution function [] Nd: order of the quadrature approximation [] S: solubility of salt in steam [mg,kg1 ] t: time [s] Cui D: Reynolds-average velocity in the ith direction [] wi : weight of the quadrature approximation x: position vector [] xi: i th component of the position vector []
Nomenclature
Abbreviations
a(L): breakage kernel [] A: area of fracture in the process of breakage [m2] bðLjlÞ: daughter distribution function [] BðL; x; tÞ: birth term due to aggregation and breakage []
PBM: population balance model CFD: computational fluid dynamics PS: pressure surface SS: suction surface
Greek Symbols
bðL; lÞ: aggregation kernel [] Gt : turbulent diffusivity[m2$s-1] d: mass transfer coefficient []
ε: turbulent dissipation rate [m2$s-3] l: particle size [mm] m: dynamic viscosity [Pa$s] n: kinematic viscosity [m2$s-1] z: flux inx-space [] x: the property vector [] tf : aggregate strength [N$s3/2 m3] Subscripts g: growth n: nucleation
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Distribution characteristics of salt-out particles in steam turbine stage Pengfei Hu*, Lihua Cao, Jingkai Su, Qi Li, Yong Li School of Energy and Power Engineering, Northeast Electric Power University, Jilin, 132012, Jilin Province, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 April 2019 Received in revised form 5 September 2019 Accepted 23 November 2019 Available online 26 November 2019
Exploring the distribution characteristics of salt-out particles on the blade surface is one of the most urgent problems for supercritical steam turbine. To obtain more practical distribution characteristics of salt-out particles in the steam turbine stage, the population balance model is loaded based on Eulerian multiphase model to simulate the real existed microscopic behaviors of salt-out particles such as nucleation, growth, aggregation and breakage. The results show that along the axial direction the number of salt-out particles gradually decreases and a ladder-like distribution is observed both on the stator and rotor blades. For the stator blade, a critical position which is 62.9% of the axial chord length occurs before which the diameter of salt-out particles on the pressure surface is greater than that on the suction surface, while after that the situation is opposite; for the rotor blade, a different critical position which is 81.1% of the axial chord length occurs. Along the axial direction the volume fraction of particles declines in the entrance area, fluctuates in the middle area on the stator blade, and on the pressure surface of rotor blade, a peak position of the volume fraction is consistent with the maximum turbulence intensity and particle diameter. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Steam turbine Salt-out particles Population balance model Distribution characteristics
1. Introduction Steam turbine is one of the most important power generating turbo-machines in thermal power plants. It has been found that, during its actual operation, one of the major causes for the turbine efficiency reduction is the salt deposition on the blade surface. When the steam works inside the steam turbine, the steam pressure undergoes a significant change, it can be reduced from the supercritical value to the negative value. With the reduction of the steam pressure, the salt-dissolved capacity of the steam decreases, so that the salt previously dissolved in the steam precipitates, adheres to the turbine cascade and accumulates on the surface as particles [1]. When salt deposits on the blades, it will increase the roughness of the cascade surface and change the cascade profile, which further affect aerodynamic characteristics of blades, so that the relative efficiency of the turbine will be reduced and the operational efficiency of the turbine will also be lowered [2]. For instance, for a certain turbine, the serious salt deposition on its cascade surface can result in a 20% reduction in the turbine rating, moreover, every additional 0.1 mm thickness of the salt deposition can reduce the turbine stage efficiency by 3%e4% [3]. For a 400
* Corresponding author. E-mail address: [email protected] (P. Hu). https://doi.org/10.1016/j.energy.2019.116626 0360-5442/© 2019 Elsevier Ltd. All rights reserved.
MWsteam turbine, the salt deposition on the cascade surface can decrease the turbine rating by 5% in the first month, and 10% within six months [4]. Meanwhile, the salt deposition on the cascade surface will change the natural frequency of the steam turbine blades and increase the axial thrust. In addition, certain aggressive deposit will have a great impact on the blades’ high temperature resistance and adversely affect the reliability of the steam turbine. In recent years, with the large-scale commercial application of the large-capacity and high-parameter thermal power unit that runs in supercritical value, especially when the large-capacity once-through boilers and ultra-supercritical units are put into operation [5], the cleaning measures like conventional steam-water separation, steam cleaning, etc., would not be able to control the steam quality, because there’s no boiler drum in once-through boilers. Meanwhile, in an ultra-supercritical unit the increase of steam pressure increases the salt solubility in the steam, which further increases the difficulty of desalting from the steam in the boiler. So, the presence of salt in steam is inevitable, and the salt deposition as shown in Fig. 1 from the steam has prominent impacts on the turbine performance [6e8]. Therefore, it is very important to investigate the distribution characteristics of salt-out particles in the steam turbine stage to improve the steam turbine efficiency and reliability. Due to the complicated salt deposition process on the turbine blade surface, compared with traditional gas-solid two-phase flow
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Fig. 1. Deposition images of salt-out particles on cascade surfaces in steam turbine [9].
system, the two-phase flow generated during the salt-out process in the turbine cascade passage comes along with micro-behaviors such as nucleation and growth of salt-out particles [10,11]. Meanwhile, it is difficult for researchers to conduct the experiments such as laboratory experiments or field experiments, since the steam turbine is considered as a high-temperature and high-pressure equipment. Thus, the physical process of salt-out in the steam and the flow mechanism of salt deposition are failed to be understood deeply. In 1936, Straub [12] made a preliminary analysis on causes of deposition in the steam turbine. It was shown that the salt deposition on steam turbine blades is not confined to a certain range of steam temperature and pressure. Moreover, the amount of deposit is not proportional to the salt content in the boiler feed water, even the low-salt-content feed water can significantly reduce the turbine efficiency as the salt deposition increases the roughness of the cascade surface. In 1939, Goerke [13] pointed out that even the steam undergoes strict water treatment and is under the pressure of 6.895e13.79 MPa, the salt deposition on steam turbine blades is still inevitable. During this period, due to the relatively low steam parameters at the inlet of the steam turbine and the weak salt solubility, the soluble sodium salt in water was mainly discussed, while for the insoluble sediments such as copper, iron, magnesium, aluminum, calcium, silicon compounds, they did not attract enough attention due to a small amount. In the late 1950s, the solubility of salt in steam went up as the inlet steam parameters increased, so that more soluble and insoluble salts were brought into the steam turbine with the steam. The soluble salt deposit can be easily washed off by general means of cleaning. However, the insoluble particles in the steam deposit and accumulate continually on the blade surface which cannot be removed thoroughly by means of cleaning like the way of using saturated vapor, resulting in an adverse impact on the steam turbine efficiency. Especially the copper oxide deposition on the turbine blade surface had drawn considerable attention, which came along with the application of one-through boiler and supercritical unit. In the 1960s, Pocock and Stewart [14] first studied the
dissolution of copper oxides in the steam. During 1970e1980s, researchers made their effort to study how to improve the quality of boiler feed water by using methods of chemical reaction and water treatment, so as to relieve the salt deposition problem in the turbine. In addition, they further studied the corrosion of the blades in the wet steam region resulted from the salt deposition on the surface of the cascade [15e17]. Jonas [18] proposed that the precipitation of chemical compounds from the superheated steam, the deposition and evaporation from hot surfaces and the change of concentration in oxides in depositions are the three mechanisms for concentrating impurities in steam turbines. Chemicals precipitate when concentration exceeds solubility in superheated steam. In the 1990s, on-line monitoring technology for salt deposition and the corrosion of steam turbine cascades received considerable attention. Martynova [19] found that copper oxides generally deposit in the high-pressure cylinder of steam turbine, and proposed that after precipitating from superheated steam, the salt particles would solidly adhere to the turbine blade surface. Later, some researchers paid attention to the blade corrosion in the dry-wet phase transition zone (PTZ) in the steam turbine [20e22]. In the 2000s, as indicated by Jonas et al. [9], the mechanism of salt deposition on the surface of the turbine cascade is not very clear, so for salt deposits that can be dissolved in water, the most effective washing means is still the traditional method of wet steam cleaning. It was also pointed out by Jonas et al. [9] that the effect of salt deposition on the steam turbine’s economy depends on the thickness of the salt deposit, the steam pressure as well as the cascade surface roughness, while there’s no analysis on the physical processes of salt deposition. In the 2010s, Brun et al. [23] evaluated the effectiveness of online turbine cleaning with various cleaning agents. Kushwaha [24] studied the impacts of the corrosion caused by salt deposition on the life of steam turbine blades. In addition, with an increasing number of ultra-supercritical power plants put into operation, steam-solid two-phase flow, most notably in steam turbines, gradually becomes an issue of concern to some researchers who take the fossil units as research object [25,26]. Cai et al. [25] studied the particle erosion of steam-solid two-phase
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flow passing through the governing stage nozzle of the steam turbine. As described by Padhy and Saini [26], the erosion of blades results in lower efficiency of steam turbine, shorter maintenance cycle and higher maintenance costs. As can be seen from above mentioned literatures, the salt deposition on the surface of the turbine cascade is unavoidable. Most of above studies in the analysis of the salt deposition on steam turbine blades only focus on several aspects: the chemical water treatment, the salt solubility in the steam, cascade corrosion caused by the salt deposition, and the impact on the operational economy of the turbine. The studies on the steam-solid two-phase flow mainly present numerical simulations for the solid particle erosion (SPE) on the turbine blade. To the best of our knowledge, the distribution characteristics of salt-out particles from the steam in the turbine stage have not been investigated so far. So, it is necessary to explore the distribution characteristics of salt-out particles by considering their micro-behaviors in the steam turbine stage. In this paper, the computational fluid dynamics coupled with the population balance model (CFD-PBM model) are used to study the characteristics of two-phase flow that is the steam carrying salt-out particles. The 3-D simulations based on the CFD-PBM model were performed with CFD package FLUENT [27]. The micro-behaviors like nucleation, growth, aggregation and breakage of the salt-out particles on steam turbine blades are analyzed. Moreover, the number and the average diameter as well as the volume fraction distribution characteristics of the salt-out particles are presented. The research results in this study reveal the distribution characteristics of salt-out particles in the steam turbine stage, and provide a theoretical basis for reducing or preventing from the salts deposition on steam turbine blades.
Fig. 2. Geometrical model.
2. Geometric model and numerical approach 2.1. Geometric model In this paper the second stage of the intermediate pressure cylinder in steam turbine is selected as the computational domain. The basic geometrical parameters are as follows in Table 1. The geometrical model is shown in Fig. 2. Due to the complex structure of flow passage, the multi-block grid generation technique and unstructured tetrahedral mesh are used to meet the computational accuracy. The generated mesh of flow field is shown in Fig. 3. In order to study the grid number effect on calculation accuracy, validation of grid dependency is carried out. We choose the first 1/4 from the 4th period to verify the mesh independence. For cascade passage, five sets of grids are conducted including 180, 320, 440, 570 and 710 thousands cells. The number of particles at the leading edge of the stator blade is chosen as a reference parameter. Simulation results under different grid number conditions are compared with each other and exhibited in Table 2. It can be seen that the effect of total grid number on particle number is negligible after the total grid number reaching to 440 thousand, which means the total grid number should be supposed to exceed 440 thousand. Considering the speed of computation, 440 thousand is selected as the total grid number of the flow passage in this study.
Fig. 3. Grid sketch.
Table 2 Four calculation grids of steam turbine flow passage.
Grids 103 particles number 1016
1
2
3
4
5
180 5.943
320 6.389
440 6.500
570 6.502
710 6.501
2.2. Population balance model In order to describe the distribution of salt-out particles in steam turbine stage, internal and external coordinates, which are referred as the particle state space, must be employed. The internal coordinates of the particles provide quantitative characterization of
Table 1 Geometrical parameters of the second stage of the intermediate pressure cylinder in steam turbine.
Stator Blade Rotor Blade
Pitch diameter/mm
Height/mm
Axial width/mm
Number
Pitch/mm
Flow outlet angle/( )
1259.58 1283.88
152.52 152.58
63.5 76.2
72 56
54.96 72.03
21.67 24.46
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P. Hu et al. / Energy 192 (2020) 116626
its distinguishing traits other than its location while the external coordinates merely denote the location of the particles in physical space. Thus, a particle is distinguished by its internal and external coordinates. Number density function is commonly used to describe this distribution in the state space. Given the coordinates of the property vector x ¼ ðx1 ; …; xN Þ that specify the state of the entity, the number density function is defined as in Equation (1) [28,29].
nðx1 ; …; xN ; x; tÞdx1 ; …; dxN ¼ nðx; x; tÞdx
v ¼ ½GðLÞnðL; x; tÞ þ BðL; x; tÞ DðL; x; tÞ vL
(2)
(3)
where GðLÞ is the growth rate, and BðL; x; tÞ and DðL; x; tÞ are, respectively, the birth and death rates due to aggregation and breakage. The moments of the particle size distribution are defined as follows: ∞ ð
nðL; x; tÞLk dL
mk ðx; tÞ ¼
(4)
0
A direct way to calculate the quadrature approximation is by means of its definition through the moments: þ∞ ð
nðLÞLk dLz
mk ¼ 0
Nd X
wi Lki
where S is the solubility of salts in steam, Kn and Nn are a numerical constant that are related to the type of salt. The growth behavior mainly exists in the crystallization and deposition process. For the growth process, equation of its growth rate GðLÞ is [33].
bðL; lÞ ¼
2.3. Boundary conditions 2.3.1. Boundary conditions for population balance model Since the actual operation of the steam turbine is very complicated, the following basic assumptions need to be made:
4 3p 1=2 ε1=2 ðL þ lÞ3 3 10 v
(8)
where L and l are particle sizes, ε is the turbulent dissipation rate and n is the kinematic viscosity. Particle breakage functions can be factored into two parts. The breakage kernel aðLÞ, is the rate coefficient for breakage of a particle of size L, and bðLjlÞ defines the probability that a fragment of size l is formed from the breakage of an L-sized particle. Equation for the breakage kernel aðLÞ is [30].
" # tf 1 ε1=2 aðLÞ ¼ pffiffiffiffiffiffi exp 15 n mðε=nÞ1=2
(9)
where tf is the aggregate strength, m is dynamic viscosity. The fragment distribution function is affected by various factors, including the particle properties and breakage mechanisms. The equation is [30].
(5)
The essence of this method is the fact that the abscissas Li and the weights wi can be specified from the lower-order moments. Nd is the order of the quadrature approximation. The first five moments ðk 20; …; 3Þ are of particular interest, since they are related to the total number particle density (m0 ), the total particle length (m1 ), the total particle area (m2 ), and the total particle volume (m3 ).
(7)
The birth and death of particles occur due to aggregation and breakage processes [30]. Aggregation is caused by the particle collision due to the fluid movement and Brownian movement, and when particles are smaller than the Kolmogorov micro-scale the aggregation kernel can be computed as follows [30].
i¼1
1) The condensed nucleus is introduced; 2) The particles are in the ideal spherical shape.
(6)
GðLÞ ¼ Kg ðS 1ÞNg
where Cui D is the Reynolds-average velocity in the ith direction,xi is the spatial coordinate in the ith,Gt is the turbulent diffusivity, zj is the flux in x-space and hðx; tÞ represents the net rate of introduction of new particles into the system [31]. In this work, we consider a number density function defined in terms of particle length (x1 ≡L). The resulting population balance is
vnðL; x; tÞ vnðL; x; tÞ v vnðL; x; tÞ þ Cui D Gt vt vxi vxi vxi
JðLÞ ¼ Kn ðS 1ÞNn
(1)
where x is the position vector of the particle, x is the property vector that specifies the state of the particle, and t is the time. The population balance model is a continuous statement of the number density function. It can be defined as [30].
vnðx; x; tÞ vnðx; x; tÞ v vnðx; x; tÞ þ Cui D Gt vt vxi vxi vxi ! # " v ¼ n x; t zj þ hðx; tÞ vxj
The microscopic behaviors of the nucleation, growth, breakage and aggregation for salt-out particles can be achieved by applying the PBM model settings, and the following are the specific settings. The nucleation behavior is mainly due to the supersaturation of the fluid and precipitation of the solid matter [32]. For the nucleation process, the equation of the nucleation rate JðLÞ is [33].
bðLjlÞ ¼
8 > 1; > > < 1; > > > : 0;
L ¼ L0 1=3 L ¼ l3 L30
(10)
otherwise
where L0 is the size of the primary particle. The nucleation rate and growth rate are associated with the pressure change of dynamic curve by using user-defined functions in this paper. By solving the solubility equation which changes with pressure, the steam supersaturation can be calculated, and the nucleation and growth rates of particles under different pressures can be further solved. For aggregation rate and breakage rate, according to equations (5)e(7), they can be obtained by using userdefined functions. The salt-out layer is mainly generated by transporting salts after nucleation from the steam to the blade surface. In most cases, this process is achieved through diffusion. Thus, the deposition rate can be expressed as
P. Hu et al. / Energy 192 (2020) 116626
#1=2 9 2 = 1 d 1 d d þ ,DC m_ d ¼ d, , þ DC ; 2 kR 4 kR kR
(11)
where d represents mass transfer coefficient which can be obtained by an empirical deposition model [34]. DC is the salt concentration difference between the salt concentration in steam and the saturation concentration of the solution; kR is the surface reaction rate constant [35]. 2.3.2. Boundary conditions for turbulent model The salt-out flow in the turbine is the steam-solid two-phase flow accompanied by phase changes; the Eulerian multiphase model provided by Fluent is used to calculate the salt-out twophase flow field, and the RNG k-ε model is selected as the turbulence model. The pressure inlet boundary condition is set as the total pressure of 2.778 MPa. The pressure outlet boundary condition is set as 2.380 MPa. The time step is 8.9 107. Sodium chloride is used as the simulated salt medium [36] of which the maximum content is 15 mg,kg1 according to the steam quality standard. The status parameters of superheated steam are provided by IAPWS-IF97 database, and the density of the precipitated sodium chloride particles is 2165 kg,m3.
5
time during the aggregation-breakage process are compared with the results performed by Marchisio [38] in Fig. 5. As can be seen from Fig. 5, the trend of m0 with time comprises two stages: at first m0 decreases with time, and then m0 does not change with time. In the first stage, with the increase of time m0 decreases, which means the decrease of m0 caused by aggregation is larger than the increase of m0 caused by breakage behavior, indicating the aggregation phenomenon is significant. In the second stage, with the increase of time, the aggregation effect decreases and the breakage effect increases, until the aggregation and breakage effects reach a dynamic balance, the m0 of sodium chloride particles no longer changes. The simulation results in this study are consistent with the trend of literature results [38], which proves that the model in this study is correct. It is well known that the superheated steam as working fluid in a turbine is characterized by high temperature and high pressure which is difficult to be analyzed using experimental method. So until now, there are few reports on the online measurement data of the salt-out particles on the turbine blades for a power plant. In order to further validate the results of the paper, salt deposition pictures in steam turbine cascades in a power plant are compared with the simulation results of this paper, as shown in Fig. 6. It can be
2.4. Validation of numerical method To validate the reliability of the established model of this study, the changes of overall particle volume m3 with time during the aggregation process and the breakage process are compared with the results performed by Fan [37] in Fig. 4. As can be seen in this figure, the total salt-out particles volume m3 always remains the same with time during the aggregation process (see Fig. 4(a)) and the breakage process (see Fig. 4(b)). The reason is that under the effect of aggregation or breakage, although particles have chance to become into new bigger particles or small particles, which results in a variation of the number density, the total salt-out particles volume will never change with time. So, these comparison results show that the established model of this study is reliable. Since aggregation and breakage are often the last steps of a complex sequence of phenomena, such as nucleation, fast reactions, combustion, and molecular growth, it is necessary to analyze m0 during the aggregation-breakage processes. In order to further verify the correctness of the model, the changes of m0 with
Fig. 5. Comparison of m0 during the aggregation-breakage processes between Ref. [38] and present study.
Fig. 4. Comparison of m3 between Ref. [37] and present study.
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Fig. 6. Deposition distribution of salt-out particles on turbine cascades in a power plant compared with the present results.
seen that the distribution of salt-out particles on the suction surface of the rotor blade shows a ladder-like distribution in a steam turbine, which is consistent with the simulation results of this paper, indicating that the simulation results of this study are credible. 3. Results and discussion 3.1. The number distribution of salt-out particles In order to clearly reflect the distribution characteristics of sodium chloride particles on the blade, based on a 3-D numerical simulation of turbine cascade, the contours of the number of sodium chloride particles on the stator blade and the rotor blade at different times in a same period is shown in Fig. 7. Fig. 7 shows the salt-out particles beat at the point of the leading edge of the stator blade after entering into the fully developed flow passage. According to the Griffin-Irwin theory [39], if the impact energy EI exceeds the critical energy (i.e., the total energy needed to generate a new surface), when the sodium chloride particles collide with the blade, the solid particles will have brittle fractures and break into smaller particles. The impact energy EI of sodium chloride particles is
EI ¼ Ed Ee
(12)
where Ed is the initial energy of sodium chloride particles at the entrance of the flow passage, Ee is the dissipated energy in the process of collision. The critical energy of sodium chloride particles Es in the breakage process is
Es ¼ 2Gs A
(13)
where Gs is the strain energy release rate of the material, A is the area of fracture in the process of breakage. The impact energy when sodium chloride particles collide with the leading edge of the stator blade is calculated and the obtained result is in the range of 1.6 104e2.4 102 J, while the critical energy required for the particle breakage is 1.5 1010 J. It is obvious that the impact energy is greater than the critical energy. The breakage rate reaches a peak value, resulting in frequent collision and nucleation in the secondary nucleation process, which then produces secondary nucleus and the nucleus further grows into new crystal particle, thus forming an area with high number of particles in the leading edge.
The impact energy of the particle hitting the blade surface is equal to the instantaneous kinetic energy of the particle contacting with the blade surface, and it doesn’t change with time. So, the number of particles at the leading edge of stator blade in Fig. 7 does not change with time. It also can be seen in Fig. 7 that the number of particles on the stator blade and rotor blade shows a ladder-like distribution. Fig. 8 shows the change of the number of particles on the suction surface on both stator and rotor blades along axial direction, at different time in a same period. As we can see, the number of particles decreases along the axial direction. Under the influence of turbulent diffusion force, the steam contacts with the blade and the mass transfer behavior between steam and particles on the blade occurs. When the steam passes by the leading edge of the stator blade, the particles are constantly separated out from the steam on the blade surface because of the continued decrease in steam pressure resulting in an increase in supersaturation, but the concentration of sodium chloride in the steam decreases gradually as the particles are separated out continuously. As a result, the number of particles on the surface of blade shows a downtrend. However, the number of particles on the suction surface of stator blade decreases slowly, and it decreases rather quickly on the rotor blade. The first reason is that the degree of the over-saturation of the steam carrying salt in the stator blade flow passage increases due to the decreasing steam pressure, which provides the driving force for the salt-out process of crystal particles. These particles continually separate from the steam and most of them deposit on the surface of the stator blade, which leads to the reduction of the over-saturation of the steam in the rotor blade flow passage as well as the separating rate of particles. The second reason is that in the second stage of the intermediate pressure cylinder in a steam turbine which is the research object in this study, the steam pressure drop upon the stator blade is larger than that upon the rotor blade. As a result, the driving force of crystallization is larger, so that more particles will be separated out, thus the number of particles on the stator blade decreases more slowly than that on the rotor blade.
3.2. The diameter distribution of salt-out particles In the figures of this study, SS and PS represent the suction surface and pressure surface of blades, respectively. Fig. 9 and Fig. 10 show the diameter distribution of the particles on the suction surface and pressure surface of both rotor and stator blades at the height of z ¼ 0.60 m at 1/4 T, 2/4 T, 3/4 T and 4/4 T. At 1/4 T, it can be seen that, for the stator blade, the particle diameters on the
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Fig. 7. Particle number distribution on stator blade and rotor blade at different time.
Fig. 8. The number distribution of particles on the suction surface at different time in a same period.
suction surface and pressure surface increase generally along the axial direction, and then fluctuate in the tail area of the suction surface; the particle diameter on the suction surface of rotor blade has a similar trend as that of stator blade, but the particle diameter on the pressure surface of rotor blade fluctuates remarkably along the axial direction. To explain this phenomenon, the turbulence intensity needs to be introduced. As can be seen in Figs. 9 and 10, all the particle diameters are smaller than 1 mm so Brownian motion induced collisions is the controlling mechanism for the aggregation process. Higher turbulence intensity leads to more intense collisions, causing more particles to aggregate into larger particles with larger diameters. It can be further explained from Figs. 11 and 12. In Figs. 11 and 12, the turbulence intensity near the suction surface and the pressure surface of stator blade increases generally along the axial direction. When the turbulence intensity increases, the contact frequency between particles becomes strong, so the aggregation of particles becomes obvious, causing the increase growth of particles on the stator blade along the axial direction, and
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Fig. 9. The particle diameter distributions on the suction surfaces of stator and rotor blades.
Fig. 10. The particle diameter distributions on the pressure surfaces of stator and rotor blades.
Fig. 11. The turbulence intensity distributions near the suction surfaces of stator and rotor blades.
Fig. 12. The turbulence intensity distributions near the pressure surfaces of stator and rotor blades.
the fluctuation of turbulence intensity causes a corresponding fluctuation of particle diameter near the tail area of the suction surface of stator blade. Fig. 11 displays that the change of the turbulence intensity near the suction surface of rotor blade is the same as that of stator blade, so the particle diameter on suction surface of rotor blade varies similarly as that of stator blade. By comparing Fig. 10 with Fig. 12, we find the turbulence intensity near the pressure surface of rotor blade fluctuates at three different positions x ¼ 0.202 m, 0.207 m, 0.213 m respectively, where the particle diameter on the pressure surface of rotor blade fluctuates correspondingly. As shown in Figs. 9 and 10, the variation of particle diameter is not obvious both on the suction surface and pressure surface of stator blade at the blade height of z ¼ 0.60 m at the time 1/4 T, 2/4 T, 3/4 T and 4/4 T, while near the leading edge of rotor blade it changes dramatically both on the suction surface and pressure surface. This phenomenon can also be explained by the variation of turbulence intensity with time in Figs. 11 and 12. The reason is that the stator is fixed, resulting in small changes of turbulence intensity at different times, while the rotor is moving, resulting in different relative positions of the rotor and stator blades at different times, so that the turbulence intensity near the leading edge of rotor blade changes dramatically at different times, and the particle diameter varies evidently near the leading edge of rotor blade. Fig. 13 shows the particle diameter distribution on the stator blade surface. It can be seen that, in the region of x ¼ 0.14e0.162 m where the axial chord length is less than 62.9% (0:1620:14 0:1750:14 100% ¼ 62:9%), the diameter of the particles on the pressure surface is larger than that on the suction surface, while in the region of x ¼ 0.162e0.175 m where the axial chord length is larger than 62.9% the situation is opposite. The reason can be explained from Fig. 14 which shows the variation of turbulence intensity with the position. In Fig. 14, when the axial chord length is less than 62.9%, although the turbulence intensity near the suction surface is higher than that near the pressure surface, the difference is not significant, so the effect of inertia plays the dominant role. It means that when the steam carrying the salt-out particles enters the flow passage of the stator blade, the particles, especially larger particles, will move towards the pressure surface without changing their direction due to the effect of inertia, so that they have more opportunities to be gathered together, leading to become much larger particles near the pressure surface than that near the suction surface. Compared
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Fig. 13. The particle diameter distribution on the stator blade surface. Fig. 15. The particle diameter distribution on the rotor blade surface.
Fig. 14. The turbulence intensity distribution near the stator blade surface. Fig. 16. The turbulence intensity distribution near the rotor blade surface.
with the chord length less than 62.9%, the turbulence intensity near the suction surface is obviously higher than that near the pressure surface when the axial chord length is larger than 62.9% in Fig. 14, which makes the particles undergo a larger turbulence effect in a larger region near the suction surface and further leads to more intense collisions, causing more particles to aggregate into larger particles. Therefore, when the axial chord length is larger than 62.9%, the particles grow slower near the pressure surface. In Fig. 15, the diameter distribution of particles on the rotor blade has the similar trend as that on the stator blade in Fig. 13. The diameter of particles on the pressure surface increase more quickly than that on the suction surface of rotor blade in the region of x ¼ 0.18e0.21 m where the axial chord length is less than 81.1% 0:210:18 100% ¼ 81:1%). The reason is mainly related to the (0:2170:18 turbulence intensity which can be seen from Fig. 16. In Fig. 16, when the axial chord length is less than 81.1%, the intensity of turbulence near the pressure surface is higher than that near the suction surface of the rotor blade, and the maximum turbulence intensity near the pressure surface is at x ¼ 0.207 m. The aggregation of particles seems more obvious when the turbulence intensity is much higher, resulting in a faster growth of particles on the pressure surface than that on the suction surface. However, when x > 0.210 m, the diameter of particles on the suction surface is greater than that on
the pressure surface of rotor blade. One reason is that under the impact of the pressure gradient of the steam, the secondary flow from pressure surface to suction surface of rotor blade is formed, and then under the influence of the secondary flow, the diameter of the particles on the suction surface is larger than that on the pressure surface near the trailing edge area of rotor blade. The other reason is also related to the turbulence intensity which is the same with the explanation for the particle diameter distribution on the rotor blade in the region of x ¼ 0.18e0.21 m in Fig. 16. 3.3. The volume fraction distribution of salt-out particles 3.3.1. 1 vol fraction of sodium chloride particles along the axis direction As shown in Fig. 17, for the stator blade, the particle volume fraction on the suction surface has a descend trend at the entrance area. This is because the particle volume fraction is determined by both particle number and particle diameter; the particle number on the suction surface of the stator blade plays the dominant role, while the particle diameter increases slowly and shows a less effect on particle volume fraction. The collision nucleation of particles at the leading edge of the blade is so obvious that results in a peak
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coincides with the peak value of the turbulence intensity. This is because the particle diameter on the pressure surface plays a major role, and the volume fraction reaches to a peak value when both the turbulence intensity and the particle diameter reach the peak point (x ¼ 0.2075 m). Moreover, the variation of the particle volume fraction with the position in Fig. 18 is consistent with the change of the particle diameter with the position in Fig. 15.
Fig. 17. The volume fraction of sodium chloride from the stator blade.
volume fraction at the entrance. Then the volume fraction drops as the particle number decreases along the axial direction. The volume fraction fluctuates obviously after the turning point (x ¼ 0.155 m), because the turbulence intensity increases quickly at x ¼ 0.155 m, which leads to the growth of particle diameter. Therefore, we can see a fluctuation phenomenon on the volume fraction curve. The particle volume fraction on the suction surface drops dramatically at the trailing edge, because with the decrease of the number of particles on the suction surface of the stator blade, the particle diameter at the trailing edge becomes an influencing factor to the volume fraction and it can be seen from Fig. 13 that the diameter of particles on the suction surface decreases at the trailing edge. It also can be seen in Fig. 17 that the volume fraction of the particles on the suction surface of stator blade does not change with time. From Fig. 17, we can also see that for the stator blade, at the entrance of the pressure surface the particle volume fraction drops dramatically, then fluctuates obviously after the turning point (x ¼ 0.16 m), and gradually increases in the tail area along the axial direction of the stator blade. The reason is the same with that of the suction surface of stator blade. As seen from Fig. 18, the particle volume fraction on the suction surface of the rotor blade decreases along the axial direction, since the particle number decreases along the axial direction. On the pressure surface, the peak position of the particle volume fraction
Fig. 18. The volume fraction of sodium chloride from the rotor blade.
3.3.2. Comparison of volume fraction for sodium chloride at different time Fig. 19 shows the volume fraction of sodium chloride particles at the blade height of z ¼ 0.60 m at 1/4 T, 2/4 T, 3/4 T and 4/4 T respectively. At 1/4 T, the sodium chloride particle clusters with high volume fraction occur which is circled with red in the wake region. At 2/4 T, the high volume fraction area shifts the adjacent stage. At 3/4 T, the high volume fraction area enters into the adjacent stage. At 4/4 T, the high volume fraction area disappears in the second stage of the intermediate pressure cylinder in this study. This is due to the wake at the outlet of the rotor blade. Because there is always a certain thickness of the exit edge of the blade, the two parts steam flow over the suction surface and the pressure surface of each blade cannot immediately join together after leaving the cascade, so the wake area filled with vortex is formed behind the blade outlet. The pressure and velocity of the steam flow in the wake area are greatly different from the pressure and velocity of the main flow. After an interaction between the two parts of steam flow, the steam flow at the back of the cascade gradually becomes homogenized, and then the steam flow velocity after homogenization decreases and becomes lower than the original mainstream velocity and the steam flow kinetic energy decreases. Therefore, the salt-out particles agglomerate in the wake area to form particle clusters with high volume fractions, and then the particle clusters carried by the steam flow enter into the adjacent stage with time under the influence of the mainstream. 4. Conclusions In this paper, the CFD-PBM model has been used to study the two-phase flow of steam carrying salt particles in the second stage of the intermediate pressure cylinder of the steam turbine. Some conclusions are obtained as follows. 1) After entering the flow passage, the steam carrying salt particles will strike the leading edge of the stator blade, resulting in the collision nucleation, and the number of salt particles will reach a peak value at the leading edge of the stator blade and it doesn’t change with time. Along the axial direction, the number of saltout particles gradually decreases and it shows a ladder-like distribution. Furthermore, the number of particles decreases more slowly on the suction surface of the stator blade than that of the rotor blade. 2) Along the axial direction, the particle diameter on the stator blade and the suction surface of rotor blade increases generally, while that on the pressure surface of rotor blade fluctuates remarkably during the whole time. The particle diameter on the stator blade basically does not change over time, but the particle diameter at the leading edge of the rotor blade changes dramatically. For the stator blade, in the region of x ¼ 0.14e0.162 m where the axial chord length is less than 62.9%, the particle diameter on the pressure surface is generally larger than that on the suction surface, while the situation is opposite in the region of x ¼ 0.162e0.175 m where the axial chord length is larger than 62.9%. For the rotor blade, the particle diameter distribution has the similar trend as that on the
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Fig. 19. The volume fraction of sodium chloride in different time.
stator blade and the turning point is at 81.1% of the axial chord length. 3) For the stator blade, the particle volume fraction on the suction surface decreases in the entrance area with evident fluctuations after the turning point (x ¼ 0.155 m), and then drops at the trailing edge, which does not change with time; the particle volume fraction on the pressure surface rapidly decreases in the entrance area, and there is a significant fluctuation after the turning point (x ¼ 0.16 m), and then in the tail area the particle volume fraction gradually increases. For the rotor blade, the particle volume fraction on the suction surface also decreases along the axial direction, while there is a peak value of that on the pressure surface which is consistent with the peak value of the particle diameter and the turbulence intensity (x ¼ 0.2075 m). The particle clusters with high volume fraction exist under the wake effect in the tail area of the rotor blade and then the high volume fraction area shifts to the adjacent stage. Acknowledgments The authors gratefully acknowledge the support from the National Natural Science Foundation of China (No.51906034, No.41702250) and the Science and Technology Research Project of Education Department of Jilin Province of China during the “13th Five-Year Plan” (No. JJKH20190701KJ). References [1] Zhang HB, Wang DM, Zhang HX. Analyses of deposits on high pressure cylinder of steam turbine. Corros Prot 2015;36(5):506e9 [in Chinese]. [2] Salahshoor K, Kordestani M, Khoshro MS. Fault detection and diagnosis of an industrial steam turbine using fusion of SVM (support vector machine) and ANFIS (adaptive neuro-fuzzy inference system) classifiers. Energy 2010;35(12):5472e82.
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DC: the salt concentration difference [ppm] DðL; x; tÞ: death term due to aggregation and breakage[-] Ed: original energy of sodium chloride particles [J] Ee: dissipated energy in the process of collision [J] EI: impact energy [J] Es: energy needed for breakage [J] GðLÞ: molecular growth rate [] Gs: surface free energy per unit area [J] hðx; tÞ: net rate of introduction of new particles into the system [] J(L): nucleation rate [] kR : the surface reaction rate constant [] L: particle size [mm] Li: abscissa (or node) of the quadrature approximation [mm] L0: primary particle size [mm] m_ d : the deposition rate mk(x,t): k th moment of the particle size distribution [] nðL; x; tÞ: particle size distribution function [] Nd: order of the quadrature approximation [] S: solubility of salt in steam [mg,kg1 ] t: time [s] Cui D: Reynolds-average velocity in the ith direction [] wi : weight of the quadrature approximation x: position vector [] xi: i th component of the position vector []
Nomenclature
Abbreviations
a(L): breakage kernel [] A: area of fracture in the process of breakage [m2] bðLjlÞ: daughter distribution function [] BðL; x; tÞ: birth term due to aggregation and breakage []
PBM: population balance model CFD: computational fluid dynamics PS: pressure surface SS: suction surface
Greek Symbols
bðL; lÞ: aggregation kernel [] Gt : turbulent diffusivity[m2$s-1] d: mass transfer coefficient []
ε: turbulent dissipation rate [m2$s-3] l: particle size [mm] m: dynamic viscosity [Pa$s] n: kinematic viscosity [m2$s-1] z: flux inx-space [] x: the property vector [] tf : aggregate strength [N$s3/2 m3] Subscripts g: growth n: nucleation