Energy 188 (2019) 116094
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Influence of aerodynamic characteristics optimization of exhaust passage on heat transfer of condenser in steam turbine Lihua Cao a, *, Longge Li a, Enfu Dong b, Heyong Si a, Zhe Ning c, Miao Liu b a
School of Energy and Power Engineering, Northeast Electric Power University, Jilin, 132012, Jilin Province, China State Grid Liaoning Electric Power Supply CO.,LTD, Shenyang, 110004, Liaoning Province, China c XI’AN Thermal Power Research Institute CO.,LTD, Xian, 710054, Shanxi Province, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 2 March 2019 Received in revised form 25 June 2019 Accepted 8 September 2019 Available online xxx
In the previous research, static pressure recovery coefficient (SPRC) and total pressure loss coefficient (TPLC) were used to evaluate the aerodynamic characteristics of exhaust passage of steam turbine. In this paper, the heat transfer performances of condenser are used to evaluate the aerodynamic characteristics of exhaust passage. The aerodynamic characteristics of exhaust passage are optimized through installing guide devices considering the influence of the whole last stage. The computational fluid dynamics software is applied to numerically solve NeS equation and k-ε equation in three dimensions. Then the flow field and the heat transfer performances of condenser were simulated, which using porous medium model and UDF condensation program. The results show that the heat transfer performances of condenser are improved obviously after the flow field of exhaust passage is optimized. The heat transfer coefficient of condenser increases by about 37.5% and the vacuum (VAC) increases by about 0.9 kPa. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Steam turbine Exhaust passage Aerodynamic characteristics Condenser Heat transfer performance
1. Introduction Exhaust passage is an important component in steam turbine whose function is to transform the residual velocity energy of exhaust steam into pressure energy to improve efficiency of the unit and to guide the exhaust steam into the condenser [1]. However, the flow field in the exhaust passage is affected by the extraction pipelines, low-pressure (LP) heater, boiler feed pump turbine (BFPT) and support frame etc., which further influence the performance of condenser and the economy of steam turbine. So far, the aerodynamic characteristics of exhaust passage have been studied mainly by the method of numerical simulation. Wang et al. [2] optimized the exhaust hood by Kriging surrogate model to maximize the static pressure recovery coefficient. Using the streamline curvature method, Gan et al. [3] optimized the geometric structure of the diffuser to improve the aerodynamic characteristics of exhaust hood. Wang et al. [4] applied the cubic Bessel curve to optimize the diffuser geometry, and confirmed that the aerodynamic characteristics of the optimized exhaust hood was improved through the comparison of aerodynamic characteristics experiments. Gribin et al. [5] determined the optimal axial distance
* Corresponding author. E-mail address:
[email protected] (L. Cao). https://doi.org/10.1016/j.energy.2019.116094 0360-5442/© 2019 Elsevier Ltd. All rights reserved.
of exhaust hood, by which the total energy loss decrease by 30%. And Cao et al. [6] found that the total pressure loss coefficient of exhaust passage increased with the tilt angle of flow guide from 30 to 40 . Moreover, the flow field of last stage is another important factors that influence the aerodynamic characteristics of exhaust passage [7]. Stastný [8] found that the inlet swirl is a main factor affecting the flow separation in the diffuser by numerical simulation and full-scale experimental study. Musch [9] optimized the geometry of diffuser coupling the last stage. However, the effect of single passage of the last stage on the aerodynamic characteristics of diffuser was merely considered in these studies. The flow field at the inlet of exhaust passage is not uniformly distributed in the circumferential direction, so it is necessary to study the aerodynamic characteristics of exhaust passage coupled with the whole last stage. Fu et al. [10] showed that the characteristics of exhaust hood was greatly affected by the inlet pressure distribution and the inlet flow angle. Therefore, in his paper [11], the aerodynamic characteristics of exhaust hood coupling the last stage is studied by changing the geometric shape of the diffuser. Cao et al. [12] indicated that various factors such as the last stage, extraction pipelines and BFPT, as well as the interaction between them should be taken into account to research the aerodynamic characteristics of exhaust passage. Ris et al. [13] proposed that the aerodynamic performance
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was improved by installing a diversion device in the exhaust passage, but the effect of multiple factors were ignored. Burton [14] pointed that the flow field at the inlet of exhaust passage is nonuniform caused by the tip jet, and the performance of diffuser is influenced by the outlet pressure gradient. Burton [15] found the asymmetric exhaust flow field using the simulation calculation without considering the interaction between the exhaust hood and the condenser throat. From previous research, we can know that it is very necessary to study the exhaust passage coupled with the whole last stage. Meanwhile, most researchers used the TPLC and SPRC to evaluate the aerodynamic characteristics of exhaust passage, but its influence on condenser have not been given. The condenser is an important device whose heat transfer performance has great significance to the economy of power plant [16]. It is composed of the tube side and the shell side. Hu et al. [17] gave some recommendations for different closure correlations considering the influence of fluid flow on the tube side. Mirzabeygi [18] proposed a three-dimensional numerical model to analyze the fluid flow and heat transfer of condenser, and the numerical calculation results were consistent with the experimental data. Zeng et al. [19] made a numerical analysis of the flow field and the heat transfer performance of a condenser using the porous medium blewski [20] described the condensing steam flow model. Wro model with droplet size distribution for condenser. Many scholars studied the flow of working fluid and heat exchange in the condenser by numerical simulation with the inlet boundary condition of the uniform velocity field. However, the distribution of inlet velocity at the condenser is non-uniform in practice. In order to study the influence of inlet flow field on heat transfer performance of condenser, it is necessary to conduct combined simulation by coupling the whole last stage, the exhaust passage with the condenser. Therefore, in this paper, the aerodynamic characteristics of exhaust passage is optimized by installing guide devices, and the influences of the whole last stage, extraction pipes and BFPT are considered. The outlet parameters at the condenser throat are taken as the inlet boundary condition of condenser. The heat transfer performances and the VAC of condenser are analyzed based on porous medium model and UDF condensation program. The TTD and the VAC are first used as the visual indexes to evaluate the improvement effect of aerodynamic characteristics of exhaust passage. 2. Computational method 2.1. Physical model of exhaust passage The physical model is established based on the exhaust hood and condenser throat of a 600 MW supercritical steam turbine equipped with double back pressure condenser. The bottom area and the height of exhaust hood is 3772 mm 6642 mm and 7074 mm, respectively. The bottom area and the height of condenser throat is 3772 mm 10920 mm and 4622 mm, respectively. The influence of the whole last stage, extraction pipelines, diffuser, BFPT and LP heater are considered in the model, as shown in Fig. 1.
Fig. 1. Computational model of the exhaust passage.
symmetrical, the steam chamber on one side is selected for simulation calculation whose structure and calculation grid are shown in Fig. 2. 2.3. Grid generation The structured grids of last stage are generated by Turbo-grid software. Unstructured grids are generated by ICEM software to study the exhaust passage and condenser. The grid independence verification is shown in Table 1. It is shown that when the grid number of the last stage, the exhaust passage and the condenser reaches to 7.6 million, 4 million and 45000 respectively, the calculation results are almost unchanged with the high accuracy. Therefore, the proper grid number is determined in the numerical simulation. 2.4. Numerical model It is difficult to generate grids of high quality as there are a large number of cooling water pipes with small diameter in the condenser. Therefore, the porous media model is used to simulate the tube bundle area of condenser [21]. The cooling water pipes that are regularly arranged in the condenser are considered as the solid skeleton of the porous medium, and the interstices between the pipes are considered as pores. The physical quantity on the calculation node of the porous medium model refers to the average value of the control volume including the calculation node. The liquid phase action is presented in the distributed resistance relations and the corresponding governing equation is unified in the
2.2. Physical model of condenser The tube bundles of high and low pressure are arranged symmetrically in the condenser. The extraction ports and air cooling areas in each tube bundle area are separated by diaphragm plate, so that each tube bundle area are divided into 14 relatively independent steam chambers. Because the overall structure of condenser is
Fig. 2. Structure and grid diagram of condenser.
L. Cao et al. / Energy 188 (2019) 116094 Table 1 Grid independent verification. Number/( 104) Last stage/Exhaust passage/Condenser
Uniformity coefficient/% Exhaust passage/Condenser
2 322/310/3.3 2 368/360/3.9 2 380/400/4.5 2 432/430/4.8 2 466/470/5.3
61.47/62.3 69.53/68.77 72.61/73.86 72.60/73.84 72.61/73.86
3
calculated by the Quasi-three dimensional method. The solid wall is assumed to be adiabatic and non-permeable without distributed mass sink. The outlet velocity flow field at the throat is taken as the inlet boundary condition of condenser. The boundary condition of the air exhaust port is set to “pressure outlet ". The calculation flow chart of exhaust passage and condenser is shown in Fig. 3. 3. Aerodynamic characteristics analysis of exhaust passage 3.1. Exhaust passage flow field before optimization
rectangular coordinate system, as shown in equation (1):
v v v vf v vf ðbrufÞ þ ðbrvfÞ ¼ Sf þ þ bGf bGf vx vy vx vx vy vy
(1)
when f is treated as uv, the air mass percentage density q and 1, equation (1) represents the momentum equation, air concentration equation and continuity equation in the coordinate direction, respectively. Gf and Sf are generalized diffusion coefficients and generalized source terms, which depends on f, as shown in Table 2. In Table 2, m is the molecular viscosity coefficient of the mixture with the 106e105 order of magnitude. mt is the turbulent viscosity of the mixture with the 104e103 order of magnitude. Sct is Schmidt number of turbulence, and its value is between 0.9 and 1.0 according to experience. Q is the distributed mass sink. Fx and Fy are the components of distribution resistance of the mixture at the x and y directions, respectively. 2.5. Calculation method and boundary conditions In order to increase computation speed, the condenser and the exhaust passage coupling with whole last stage are separately calculated and then coupled. The computational fluid dynamics software CFX is applied to solve NeS equation and k-ε equation in the exhaust passage [1]. The near wall region is managed by the scalable wall function. The convection term is adopted in the highorder upwind precision format and the convergence criterion of numerical residual is lower than 1 104. The “steam3vl” equilibrium wet steam model in the IAPWS-IF97 working medium library is selected. The parameters of inlet and outlet boundary are determined depending on the turbine heat acceptance (THA) operation condition. The frozen-rotor model is adopted for the interface. The boundary condition at the last stage inlet is set to “Mass - flow - inlet”. The outlet boundary condition of the condenser throat is set to “outflow”. The specific inlet boundary condition of the last stage and BFPT are shown in Table 3. The improved k-ε turbulence model is used for the calculation of heat transfer performances in condenser [22]. For accurate calculation result, the resistance of tube bundles and vapor-liquid two phases in this turbulence model is considered. The calculation method of steam condensation comes from literature [23]. Numerical calculation of the control macro and parameters of steam condensation is shown in Table 4. By the UDF condensation program, the heat transfer and flow characteristics of condenser are Table 2 Physical meaning of Gf and Sf f
Gf
Sf
u
m þ mt
v
m þ mt
1 q
m þ mt ðm þ mt Þ=Sct
v p Qu þ bFx vx v b p Q v þ bFy vy Q Ma b
The flow field of exhaust passage coupling the whole last stage is simulated numerically. The velocity streamline is shown in Fig. 4. The inlet velocity distribution of steam in the exhaust passage is non-uniform. A small part of steam flows through the blade tip clearance with the tangential velocity component of the outlet stator blade and forms leakage flow. As the main steam is affected by the leakage flow, the outlet velocity distribution of last stage blade is non-uniform. The exhaust steam of BFPT is influenced by the upstream flow field, which makes the steam flow skewing to the LP heater side. The outlet of condenser throat is the interface plane connecting the upstream exhaust passage and the downstream condenser. The heat transfer performance of condenser is directly affected by the outlet velocity distribution of condenser throat and the VAC is indirectly affected. It can be seen from Fig. 5 that the distribution of outlet velocity is non-uniform, and the velocity peak zone (greater than 90 m/s) appears near the wall. The velocity valley zone (less than 30 m/s) is around the center of flow field. Therefore, increasing the valley velocity and decreasing the peak velocity will improve the velocity field and the aerodynamic characteristics of exhaust passage will be improved too. 3.2. Installing guide devices in exhaust passage The outlet flow field is more uniform by installing guide devices in the condenser throat. The devices guide the exhaust steam from the high velocity region to the low velocity region. The number, position, size and installation angle are adjusted through 57 numerical tests based on quadratic regression orthogonal design [12]. Combining with orthogonal experiment and considering the influence factors such as the flow field of last stage, the exhaust steam of BFPT and the steam extraction pipelines, the optimal installation scheme of the guide devices is determined, as shown in Fig. 6. The vertex coordinate positions of each guide device are shown in Table 5. 3.3. Analysis of exhaust passage with guiding devices The distribution of outlet velocity at the condenser throat before and after optimization is presented in Fig. 7. As can be seen from Fig. 7, the low velocity zones on both sides of the exhaust steam of BFPT become smaller after optimization. The velocity zones below 20 m/s almost disappears while the velocity zone larger than 40 m/ s is obviously enlarged. The high velocity zone near the wall is narrowed and the average velocity at the condenser throat outlet is obviously increased. At the same time, the central high velocity zone narrows and the velocity decreases. The flow field distribution at the exhaust passage is much more uniform. 3.4. Analysis of aerodynamic characteristics under different operating conditions Fig. 8 shows the change of performance indicators of exhaust passage under different conditions. Under the 50%-100%THA
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Table 3 Last stage and BFPT exhaust steam parameters of THA condition. Parameters
Condition
Total temperature /K
Wetness fraction
Mass flow rate /(kg/s)
inlet of last stage
100%THA 75%THA 50%THA 100%THA 75%THA 50%THA
335.05 329.75 322.95 309.03 309.03 309.03
0.054 0.041 0.033 0.046 0.030 0.014
67.783 25 2 53.218 47 2 38.171 18 2 11.215 69 6.046 53 2.816 25
inlet of BFPT
9 8 2 9 1 4
Table 4 UDF for steam condensation. Physical quantities
Control macro(parameter)
Initializes velocity Initialize temperature difference Superposition of condensate volume Air density/viscosity Vapor density/viscosity Air mass dispersion rate Condensation rate Distribution resistance of source term Condensation of source term
DEFINE_PROFILE(inlet_y_velocity, thread,position) DEFINE_INIT(dt_init, d) DEFINE_ADJUST(q_adjust,d) DEFINE_PROPERTY(air_density/viscosity,c,t) DEFINE_PROPERTY(steam_density/viscosity,c,t) DEFINE_DIFFUSIVITY(air_diff,c,t,i) DEFINE_SOURCE(mass_source,c,t,dS,eqn) DEFINE_SOURCE(velcity_u/v_source1,c,t,dS,eqn) DEFINE_SOURCE(velcity_u/v_source2,c,t,dS,eqn)
Establish exhaust Passage model (coupling last stage)
Simulate calculation by CFX
Design four factors and two levels orthogona experiment
Get information about optimal guide devices, such as position, size, etc
Output throat velocity field of before and after optimization
Establish porous medium model for condenser
Load UDF condensation program to simulate flow flied of condenser
Analyze heat transfer performances of condenser
Fig. 3. Calculus flow-chart.
condition, the TPLC and SPRC increase after installing guide devices, but the increase amplitude of TPLC is less than that of SPRC. After installing guide devices, the TPLC increases by 2.04% and 2.22% at 50% and 100%THA condition, respectively. The SPRC increases by 16.19% and 6.78%, respectively.
steam chambers in the condenser. Only three inlet velocities are given, for example 1, 7 and 14. As seen from Fig. 9, after optimization, the flow field distribution at the inlet of condenser is more uniform. 4.2. Heat transfer performances of condenser
4. Calculation results and analysis of condenser 4.1. Inlet velocity of condenser The outlet velocity at the throat before and after optimization is taken as the inlet boundary condition of condenser. There are 14
Combined with Fig. 9, it is found that the velocity distribution of mixture at the inlet of each steam chamber is unevenly distributed and varies largely. As a result, the mixture contacts with the heat exchange surface insufficiently and the heat transfer in some parts of the steam chamber is poor. With the cooling water flows through
L. Cao et al. / Energy 188 (2019) 116094
5
Fig. 6. Exhaust passage equipped with guiding devices.
Table 5 Vertex coordinate positions of guiding devices.
Plate 1 Fig. 4. Three dimensional velocity streamline in exhaust passage. Plate 2
Plate 3
Plate 4
Plate 5
Fig. 5. Outlet velocity distribution of condenser throat.
every steam chamber, the temperature of the cooling water rises. Therefore, the heat transfer of each steam chamber is reduced in turn. Because the first steam chamber is close to the cooling water inlet, the cooling water temperature is the lowest and the thermal resistance of the tube bundle is high, which reduces the heat transfer capacity. After optimization, the distribution of the inlet steam velocity of each steam chamber is uniform and the steam fully contacts with the tube bundle surface, then the thermal
No.
X/mm
Y/mm
Z/mm
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
6500 6500 7970 7970 6710 6710 8170 8170 6000 6000 7470 7470 6200 6200 7670 7670 5200 5200 6670 6670
860 1190 1500 1160 2530 2350 2800 2970 3000 3000 3330 3330 3800 3230 3230 3570 1140 800 490 860
2140 1200 1300 2240 3590 2610 2500 3490 2370 1360 1350 2350 2550 3410 3410 2470 2060 3000 2900 1970
resistance reduces and the heat transfer coefficient is significantly increased. So the heat transfer coefficient on the outside side of the tube bundle zone is the largest. However, with the mixture flowing and condensing, the air concentration increases in the steam chamber and the heat transfer coefficient decreases gradually from the outside to the inside which reaches to the minimum in the air cooling zone. After optimization, the average heat transfer coefficient increases from 2792 W =ðm2 $ CÞ to 3839 W =ðm2 $ CÞ which improves the cooling effect of condenser. The flow rate of non-condensed gas in each steam chamber before and after optimization is shown in Fig. 10. It can be seen from Fig. 10 that under a certain flow rate and temperature of cooling water, the condensation volume of each steam chamber increases after optimization, and the steam volume in the mixture at the extraction port greatly decreases. When the power consumption of
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L. Cao et al. / Energy 188 (2019) 116094
a) Throat outlet velocity before optimization
b) Throat outlet velocity after optimization
Fig. 7. Velocity contour of throat outlet before and after optimization.
100
80
90
Original Optimal
Original Optimal
8 80 70
60
60 6
50
50
40
40 4
30
30
20
20 2
10
10
0
SPRC / %
70
0 50%
75%
Original Optimal
0.07
Non-condensed gas /kg/s
90
TPLC / %
0.08
10 100
0.06 0.05 0.04 0.03 0.02
100%
Load
2
4
8
10
12
14
Fig. 10. Flow rate of non-condensed gas of each steam chamber before and after optimization.
120 Original 1st steam chamber Original 7st steam chamber Original 14st steam chamber
100
Velocity / (m/s)
6
Steam chamber No.
Fig. 8. Aerodynamic performance indicators under different conditions.
dt ¼
80
Dt kAc
e4187Dw 1
(2)
The condenser pressure is usually lower less than the local atmospheric pressure, and the difference between them is VAC. The condenser pressure can be obtained from the following formula:
60
pc ¼ 9:81
40
Optimal 1st steam chamber Optimal 7st steam chamber
20
Optimal 14st steam chamber
-4
-3
-2
-1
0
1
2
3
4
Z axis / m Fig. 9. Inlet velocity of condenser before and after optimization.
the air extractor is constant, the pressure at the condenser inlet decreases, which improves the VAC and the operation economy of steam turbine.
ts þ 100 7:46 57:66
(3)
The total heat transfer area of condenser is 20560.5 m2, the flow rate of cooling water is 61690.68 t/h. According the TTD formula (2), the TTD before and after optimization is 4.571 Cand 2.263 C, respectively. Thus, the TTD reduces 2.308 C. The local atmospheric pressure is 98.6 kPa. Based on the temperature rise of cooling water and TTD before and after optimization, and according to formula (3), the VAC before and after optimization is 94.34 kPa and 95.24 kPa, respectively. The VAC increases by 0.9 kPa. The results indicate that the TTD and VAC can be used as visual index to evaluate the aerodynamic characteristics optimization of exhaust passage. 4.4. Performance analysis under different operating conditions
4.3. Terminal temperature difference and vacuum The formula for calculating the condenser terminal temperature difference (TTD) is:
The condenser performance mentioned above is analyzed at rated operating condition of steam turbine. It is necessary to study the condenser performance under different operating conditions
L. Cao et al. / Energy 188 (2019) 116094
96.0
10
Temperature / C
8
94.17
94.96 94.28
7 6
6.54 5.41
5
4.92
Original TTD Optimal TTD Original VAC Optimal VAC
94.5 94.0 93.5 93.0 92.5
3.59
3
14
95.0 94.34
4.57
4
16
95.5
92.0 91.5 91.0
2
2.26
Condenser pressure /kPa
94.74
95.24
VAC / kPa
9
90.5
50%
75%
Before installing guide devices
12
After installing guide devices
10 8 6 4 2
90.0
1
7
100%
0
Load
5
10
15
20
25
30
35
40
Inlet temperature of cooling water /
Fig. 11. Performance parameters of condenser under different loads.
Fig. 12. Results of thermal test before and after installing guide devices.
and to comprehensively analyze the influence of installing guide devices. The TTD and VAC at 50%, 75% and 100% THA condition before and after optimization are shown in Fig. 11. It can be seen from Fig. 11 that the TTD and VAC have been significantly improved after installing guide devices under different loads. The TTD reduces by 1.62e2.31 C and the VAC increases by 0.6e0.9 kPa. The aerodynamic characteristics of the exhaust passage can be improved through installing guide devices under 50%-100%THA condition. However, when the load rate is below 45%, the flow field of last stage is more complex, which can severely affect the aerodynamic characteristics of exhaust passage of steam turbine. Therefore, the aerodynamic characteristics of exhaust passage under the small volume flow condition should be further studied in the future. 4.5. Thermal test verification Based on our research, the optimized exhaust passage has already been applied in a 300 MW steam turbine. In order to verify the simulation results, thermal test of condenser in a 300 MW steam turbine have been carried out before and after installing guide device. Results of thermal test at different inlet temperature of cooling water are shown in Fig. 12. It can be seen from Fig. 12 that the condenser pressure decreases by about 0.83e1.44 kPa after installing guide device, so the VAC increases by about 0.83e1.44 kPa after installing guide device. In this paper, the VAC increases by 0.6e0.9 kPa according the simulation results. An agreement of simulation results and practical applications shows that the simulation results are reliable. Even if the 600 MW steam turbine with guide devices in the exhaust passage has not been applied in practice yet, the optimization results will provide the theoretical basis for the actual transformation of 600 MW units. 5. Conclusion The aerodynamic characteristics optimization of exhaust passage has an important influence on the heat transfer performances of condenser under different loads. At the 100% THA condition, after installing guide devices, the TPLC increases by 2.22% and the SPRC increases 6.78%. At the same time, the heat transfer coefficient, TTD and non-condensable gas in condenser are greatly improved through optimizing the aerodynamic characteristics of exhaust passage under different operating conditions. Under 50%-100%THA condition, the TTD reduces by 1.62e2.31 C, and the VAC increases
by 0.6e0.9 kPa. So, the TTD and the VAC can also be used as indexes to evaluate the aerodynamic characteristics optimization of exhaust passage. Acknowledgement The authors would like to thank for the financial support of the National Key R&D Plan (2017YFB0902100). Nomenclature u v
b r f G S
m Sct Q Dt Ac DW pc ts x,y,z
velocities of steam at x direction [m/s] velocities of air at y direction[m/s] volume porosity of porous media densityof mixture [kg/m3] any variable generalized diffusion coefficient generalized source term dynamicviscosity [N$s/m2] Schmidt number distributed mass sink temperature rise of cooling water[ C] heat transfer area [m2] cooling water flow rate [t/h] condenser pressure [Pa] condensation temperature of condenser [ C] Cartesian coordinates
Abbreviations SPRC static pressure recovery coefficient TPLC total pressure loss coefficient VAC condenser vacuum LP low-pressure BFPT boiler feed pump turbine TTD terminal temperature difference THA turbine heat acceptance References [1] Veerabathraswamy K, Senthil Kumar A. Effective boundary conditions and turbulence modeling for the analysis of steam turbine exhaust hood. Appl Therm Eng 2016;103:773e80. [2] Wang H, Zhu X, Du Z. Aerodynamic optimization for low pressure turbine exhaust hood using Kriging surrogate model. Int Commun Heat Mass Transf
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