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air impingement cooling on ribbed blade leading-edge surface
Journal of Environmental Management xxx (2017) 1e10
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Research article
Numerical investigation of mist/air impingement cooling on ribbed blade leading-edge surface Qingfei Bian a, Jin Wang b, Yi-tung Chen c, Qiuwang Wang a, Min Zeng a, * a
Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, China School of Energy and Environmental Engineering, Hebei University of Technology, Tianjin, 300401, China c Department of Mechanicals Engineering, University of Nevada- Las Vegas, Las Vegas, NV, 89154, USA b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 December 2016 Received in revised form 17 April 2017 Accepted 17 May 2017 Available online xxx
The working gas turbine blades are exposed to the environment of high temperature, especially in the leading-edge region. The mist/air two-phase impingement cooling has been adopted to enhance the heat transfer on blade surfaces and investigate the leading-edge cooling effectiveness. An Euler-Lagrange particle tracking method is used to simulate the two-phase impingement cooling on the blade leading-edge. The mesh dependency test has been carried out and the numerical method is validated based on the available experimental data of mist/air cooling with jet impingement on a concave surface. The cooling effectiveness on three target surfaces is investigated, including the smooth and the ribbed surface with convex/concave columnar ribs. The results show that the cooling effectiveness of the mist/ air two-phase flow is better than that of the single-phase flow. When the ribbed surfaces are used, the heat transfer enhancement is significant, the surface cooling effectiveness becomes higher and the convex ribbed surface presents a better performance. With the enhancement of the surface heat transfer, the pressure drop in the impingement zone increases, but the incremental factor of the flow friction is smaller than that of the heat transfer enhancement. © 2017 Elsevier Ltd. All rights reserved.
Presented at the 11th SDEWES conference Lisbon 2016, 4e9 September, 2016, Lisbon, Portugal. Keywords: Blade leading-edge Mist Two-phase flow Impingement cooling Ribbed surface
1. Introduction Gas turbine has been widely used in vehicle and aviation, electricity generation, refrigeration and other aspects. With the increase in the inlet temperature of gas turbine, the efficiency and output power of gas turbine are rising obviously. Now the turbine inlet temperature can be up to 2000 K with advanced technologies (Liao et al., 2014). The extreme operating conditions can shorten pez-Abente et al., the lifespan and reduce efficiency of the blade (Lo 2014). Especially, the blade leading-edge is directly impinged by hot gas and suffers a great thermal load. The frequent replacement of the blades results in massive material wastes and the low efficiency causes more emissions of NOx (Javed et al., 2007). Therefore, the advanced cooling method for protecting the blade leading-edge has received high attentions. Conducting many experimental tests can also cause environmental and economic concerns, such as
* Corresponding author. E-mail addresses: [email protected] (Q. Bian), [email protected] (J. Wang), [email protected] (Y.-t. Chen), [email protected] (Q. Wang), zengmin@ mail.xjtu.edu.cn (M. Zeng).
material waste and air pollution. Many environmental regulations have been made by the government to demand the different industries to follow the stringent requirements to solve those problems. The widely used Computational Fluid Dynamics (CFD) method can provide the design details based on the operating conditions to satisfy those regulations (Mikul ci c et al., 2016; Baleta et al., 2017) and shows great promise in the environmental science field. For example, Wania et al. (2012) simulated an effect of vegetation on atmospheric processes. Kafle et al. (2015) investigated two down-flow wood bark-based biofilters under the actual swine farm conditions. All of their studies obtained good results by using the CFD techniques. Numerical results by using the CFD method are also obtained to predict effects of the cooling technologies on the protection of turbine blades. Now the two most widely used cooling techniques are the film cooling and the composite cooling. Kanani et al. (2009) numerically proved that many factors had important effects on the film cooling effectiveness and film shrouded homogeneity, such as the film holes shape, the holes arrangement and the blowing ratio. Chang et al. (2015) compared film cooling with composite cooling under the same coolant conditions and they found that the
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Please cite this article in press as: Bian, Q., et al., Numerical investigation of mist/air impingement cooling on ribbed blade leading-edge surface, Journal of Environmental Management (2017), http://dx.doi.org/10.1016/j.jenvman.2017.05.052
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Q. Bian et al. / Journal of Environmental Management xxx (2017) 1e10
Nomenclature Ad cp cp,d CD dd fi 0 fi f0 h Hlatref
Surface area of the particle, m2 Specific heat, J/(kg K) Specific heat of the particle, J/(kg K) Drag coefficient Diameter of the particle, m Mass force, m/s2 Volumetric momentum source, kg/(m2 s2) Interaction forces, m/s2 Enthalpy, J/kg Latent heat at reference conditions, J/kg
hd hfg kc М _d m md Dmd md;in md;out p Re Red t Dt
Particle enthalpy, J/kg Latent heat of particle, J/kg Mass transfer coefficient, m/s Volumetric mass source, kg/(m3 s) Mass flow rate of the particles per cell, kg/s Average mass of the particle on cell entry, kg Mass exchange of the particle per cell, kg Mass of the particle on cell entry, kg Mass of the particle on cell exit, kg Pressure, Pa Relative Reynolds number Reynolds number of the particle Time, s Time step, s
composite cooling effectiveness was higher than the film cooling. Nirmalan et al. (1998), Li and Wang (2005) and, Wang and Li (2008) found that the film cooling effectiveness of the steam/mist twophase flow was higher than that of the steam flow only. Nirmalan et al. (1998) experimentally investigated heat transfer of the turbine vane with water-air cooling method. Li and Wang used the CFD technique to study the film cooling, they found that the cooling effectiveness enhanced with mist injection (Li and Wang, 2005) and then investigated the blade cooling using that method under the real turbine operating conditions (Wang and Li, 2008). Jiang et al. also used the numerical method to study the steam/mist film cooling on the heavy-duty gas turbine vane (Jiang et al., 2014) and further explored the film cooling enhancement techniques on the leading-edge surface and downstream surface of turbine blade (Jiang et al., 2015a). Wang et al. added ribs on the cooling passage to enhance the flow disturbance, which showed good cooling protection for the blade (Wang et al., 2015, 2016a). The similar configuration was used to investigate the effect of the inclined flow angle on film cooling (Wang et al., 2016b). The application of composite cooling and multiphase film cooling can greatly improve the cooling effectiveness near the blade leading-edge. With the increase in turbine inlet temperature, the usage of the coolant increases quickly in order to protect the blade. Meanwhile, a large quantity of coolant flowing into turbine results in losses of benefits (Shi et al., 2015a). In addition, the hole configurations would result in complicated flow distributions around the turbine blades, and some challenges emerge to the stability of the working equipment (Jun et al., 2015). Two-phase impingement cooling method has been gradually introduced into protection of the blade leading edge for the characteristics of high cooling efficiency. Shi et al. (2015b) found that the efficiency of the steam/mist impingement cooling was much higher than that of the steam cooling only. Li et al. (2003) proved that the concave surface had a better impingement cooling effect than the flat surface by the slot steam/mist impingement
T Tin Tout Tref Td TR ui, uj, uk ud xi, xj, xk Yi;s Yi;∞
Temperature, K Temperature of the particle on cell entry, K Temperature of the particle on cell exit, K Reference temperature for enthalpy, K Particle temperature, K Radiation temperature, K Velocity, m/s Velocity of the particle, m/s Coordinate directions, m Vapor mass fraction at the surface Vapor mass fraction in the bulk gas
Greek symbols Heat transfer enhancement coefficient Cell volume, m3 Kronecker's delta Dynamic viscosity coefficient, Pa s Density, kg/m3 Density of the particle, kg/m3 Thermal conductivity, W/(m K) Volumetric energy source, W/m3 εd Emissivity s Stefan Boltzmann constant, 5.67 108 W/(m2 K4) D Convection heat transfer enhancement coefficient q Enlargement factor of flow friction Gj Viscous stress tensor, Pa
d dV dij m r rd l F
experiments. Dhanasekaran et al. conducted a two-phase flow impingement simulation on the surface of a 180 bend pipe and compared the results with the experimental data (Dhanasekaran and Wang, 2012), besides, they also numerically investigated the cooling effect of the surface with 45 angled ribs (Dhanasekaran and Wang, 2013). Jiang et al. (2015b) studied the cooling characteristic of the leading-edge surface of turbine blade using air/steam two-phase impingement cooling method and they found that it was a promising method. But how to further enhance impingement cooling efficiency and bring it into commercial application are still unclear. In this study, the air/mist impingement cooling model of the leading-edge is presented and validated. The cooling effectiveness on rough surfaces with convex/concave ribs is then investigated after the smooth leading-edge surfaces are studied and benchmarked. In addition, the pressure drop characteristics of the impingement zone are also obtained to investigate the benefit of the ribbed surface. 2. Numerical model formulation 2.1. Physical and computational domain descriptions Numerical method has been used to study the cooling characteristics of ribbed surfaces and a few assumptions are made to simplify the present model as follows: 1) One blade is included in the computational domain and the periodic boundary condition is used to simulate the annular cascades; 2) The solid zone of the blade only involves the leading edge part and others are neglected; 3) Air/mist mixing zone is ignored and droplets are injected from the inlets of the impingement zone directly; 4) The hot air is used instead of the combustion gas;
Please cite this article in press as: Bian, Q., et al., Numerical investigation of mist/air impingement cooling on ribbed blade leading-edge surface, Journal of Environmental Management (2017), http://dx.doi.org/10.1016/j.jenvman.2017.05.052
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Fig. 1. Geometry and target turbine blade surfaces.
5) The droplet injection is uniform and the diameters of the droplets are of the same value; 6) Radiation effect is neglected. The simplified geometry used in mist/air impingement cooling simulation is illustrated in Fig. 1. There are 5 rows of impingement holes in the computational domain. Each row is arranged with 13 holes. The distance between two neighbor holes is 0.9 mm and the thickness of the impingement cavity is 5 mm. Different target surfaces are shown in Fig. 1(a)-(c), including the smooth, the ribbed convex and the ribbed concave surfaces. All the rows of the columnar ribs are arranged uniformly on the target surfaces. Each row has 26 ribs and the rib has a height of 0.9 mm. Fig. 2 shows the computational meshes for the impingement cooling simulation of turbine blade. Because the ribbed surfaces
have complicated structure with hundreds of ribs, the unstructured meshes are adopted to save computational resources. Boundary layers are generated on the surfaces in the main flow zone and impingement zone and yþ is about 1 in locations of the first cell row from solid wall. Based on the grid dependency test, the optimum case with 3.4 million cells is selected compared to other cases with 1.5 million and 4.5 million cells.
2.2. Governing equations and boundary conditions In order to track the air/mist two-phase flow in the impingement zone exactly, the Euler-Lagrange method is adopted in this study. The Euler method is used to track the continuous phase consisting of air and water steam which comes from the
Fig. 2. The computational meshes for the turbine blade impingement cooling model.
Please cite this article in press as: Bian, Q., et al., Numerical investigation of mist/air impingement cooling on ribbed blade leading-edge surface, Journal of Environmental Management (2017), http://dx.doi.org/10.1016/j.jenvman.2017.05.052
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Q. Bian et al. / Journal of Environmental Management xxx (2017) 1e10
vrh v v þ ruj h ¼ vt vxj vxj
vT l vxj
!
vpui v þ Gj $ui þ rfi $ui vxj vxi
þ fi0 $ui þ F
(6)
2 Tout ZTin Z _d 6 m F¼ cp;d dT md;out cp;d dT md;in 4md;in m d dV Tref
Tref
3
7 md;out Hlatref 5
Fig. 3. The two-phase conjugate process.
vaporization of water droplets. The Lagrange method is applied to track the discrete phase consisting of water droplets only. During the numerical simulations, the additions of source terms in all governing equations are used to realize the conjugate computation between the two phases. The process of two-phase computation in one control volume is shown in Fig. 3. The governing equations of continuous phase are given as follows: Continuity equation
vr v þ ðrui Þ ¼ M vt vxi
(1)
Dmd _d M¼m md dV
(2)
vrui v vp v þ ruj ui ¼ þ G þ rfi þ fid vxj vxi vxj j vt "
fi0
vui vuj 2 vuk þ d vxj vxi 3 vxk ij
where M is mass source, which shows the mass transfer from the water droplets to the continuous phase, Gj is the viscous stress 0 tensor of continuous phase, fi is the source term of momentum equations, including the interaction drag force and other forces between two phases and F is the source term of the energy, which shows the heat transfer between the two phases. For the discrete phase (water droplet), the governing equations are given by:
md
dui ¼ Fdi þ Fpi þ Fvmi þ Fgi þ Fbi þ Fi0 dt
md cp;d
dTd dmd ¼ hd Ad ðT Td Þ hfg þ Ad εd s TR4 Td4 dt dt
(8)
(9)
When the surface temperature of the droplets is higher than the boiling point of the water, the boiling evaporation dominates. The mass conservation equation for the droplets is shown as:
" # pffiffiffiffiffiffiffiffi cp ðT Td Þ dðdd Þ 4l ¼ 1 þ 0:23 Red ln 1 þ dt hfg rd cp dd
(10)
When the surface temperature of the droplets is lower than the boiling point of the water, the natural evaporation dominates. The equation is as follows:
Momentum equation
Gj ¼ m
(7)
(3)
#
" # X 18mCD Re md 0 ¼ ðud uÞ þ f 2 dV 24rd dd Energy equation
(4)
(5)
" # Yi;s Yi;∞ dðmd Þ ¼ Ad kc r ln 1 þ dt 1 Yi;s
(11)
Boundary conditions for the conjugate simulations are listed in Table 1. The water droplets are injected uniformly from the inlets of the impingement zone. The thermal properties vary with temperature. The k-ε Realizable model is chosen to solve the related equations for the turbulent flow. The bounce and break-up models are used when the droplets collide with the target surface. The convection terms in the governing equations are discretized by the second order upwind scheme. All the conjugate simulations are calculated by ANSYS FLUENT 14.0.
Table 1 Boundary conditions. Zone
Boundary conditions
Value
Inlet for the air
Pressure (Pa) Temperature (K) Velocity (m/s) Pressure (Pa) Mass flow (kg/s) Pressure (Pa) Mist concentration Mist diameter (mm)
500000 1200 15 210000 0.003942 0 3%, 5%, 8%, 10%, 15% 5, 10, 15, 50, 100, 150, 200
Outlet for the air Inlet for the impingement Outlet for the impingement Mist parameter
Please cite this article in press as: Bian, Q., et al., Numerical investigation of mist/air impingement cooling on ribbed blade leading-edge surface, Journal of Environmental Management (2017), http://dx.doi.org/10.1016/j.jenvman.2017.05.052
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3. Results and discussion
2.3. Model validation
3.1. Temperature distribution of the leading edge surface
The convective heat transfer coefficient is defined by:
hðxÞ ¼ qðxÞ Tw ðxÞ Tj
(12)
where q(x), Tw(x) and Tj are the surface heat flux, the local surface temperature and the impingement temperature, respectively. The convection heat transfer enhancement coefficient is shown as follows:
D ¼ hmix =hsteam
5
(13)
where hmix, hsteam are the heat transfer coefficients for the mist/ steam two-phase and the single-phase (steam), respectively. The experiment carried out by Li et al. (2003) is used to validate the accuracy of the numerical model. The main experimental part is extracted as the computational domain and it is marked with circles as shown in Fig. 4. The width of the inlet slot is 7.5 mm, the outer radius is 79.5 mm, the thickness of the impingement cavity is 22.5 mm and the length of the simulated section is 100 mm. Given that there is a mixture zone used in the experiments, the inlet passage in the numerical simulations is extended to produce the same boundary condition as experiment. The final computational meshes for the model validation are shown in Fig. 5. For the numerical simulations, the Reynolds number of the inlet flow is 7500 and the heat flux of the outer surface is 7540 W/m2. The average diameter of the droplets is 12 mm and the mass ratio of the discrete phase to the total is 0.5%. The comparisons of concave surface temperature and heat transfer enhancement coefficient between the numerical simulations and the experiments are shown in Fig. 6. For the temperature of the whole surface, the maximum absolute error is 10 K, corresponding to a relative error of 5%. For the heat transfer enhancement coefficient, the absolute and relative error are 0.15 and 8%, respectively. The comparison of the results reveals that the present numerical method is reasonable and acceptable.
Compared with the single-phase (air) flow, the two-phase (air/ mist) flow decreases the average temperature on the leading-edge surface obviously as shown in Fig. 7. The average temperature of the leading-edge surface gradually decreases with the increase in the mist concentration. With increasing the mist diameter, the average temperature on the leading-edge surface decreases initially and then increases. When the mist diameter exceeds 100 mm, the cooling effectiveness of the mist/air flow reduces sharply. Comparing the three target surfaces under the same impingement conditions, it can be found that the case with the ribbed convex surface shows the lowest temperature, the smooth surface has the highest temperature and the case with the ribbed concave surface has the temperature between the ribbed convex surface and the smooth surface. The effects of the mist concentration on the temperature distribution are shown in Fig. 8. For the case with a droplet diameter of 5 mm, the temperature drop of the leading-edge surface is obvious as the mist concentration increases from 3% to 8%. When the mist concentration increases from 10% to 15%, the temperature variation
Fig. 5. The computational meshes for the model validation.
Fig. 4. Mist/steam impingement cooling experiment on concave surface (Li et al., 2003).
Please cite this article in press as: Bian, Q., et al., Numerical investigation of mist/air impingement cooling on ribbed blade leading-edge surface, Journal of Environmental Management (2017), http://dx.doi.org/10.1016/j.jenvman.2017.05.052
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Fig. 6. Comparisons of concave surface temperature and heat transfer enhancement coefficient between the numerical simulations and the experiments.
of the leading-edge surface becomes small, especially under the smooth target surface condition the gradient approaches zero. For the case with a droplet diameter of 50 mm, the temperature drops and slopes under three different target surfaces conditions are almost uniform between adjacent mist concentrations. The temperature drops and slopes for the ribbed target surfaces are larger than that for the smooth surface and the total temperature drop for the droplet diameter of 50 mm is smaller than that for 5 mm. 3.2. Heat transfer coefficient distribution The heat transfer coefficients are strongly influenced by the mist concentrations under all three different surfaces conditions. The heat transfer coefficient of the two-phase flow is much higher than that of the single air flow as shown in Fig. 9. With increasing the mist concentration, the convective heat transfer coefficient increases gradually and the difference between adjacent conditions also increases generally. The tendencies of the heat transfer coefficient for various mist diameters are different from that for the
Fig. 7. The average surface temperature distribution of leading-edge surface under smooth, convex and concave ribs target surface conditions.
Please cite this article in press as: Bian, Q., et al., Numerical investigation of mist/air impingement cooling on ribbed blade leading-edge surface, Journal of Environmental Management (2017), http://dx.doi.org/10.1016/j.jenvman.2017.05.052
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Fig. 8. The average temperature distribution of the leading-edge surface in various mist diameters conditions.
various concentrations. With the increase in the mist diameter, the coefficient increases initially and then decreases and there is a peak at 15 mm. However, the peak is not obvious when the mist concentration is small. Comparing the three different target surfaces under the same impingement conditions, it can be found that the ribbed convex surface has the highest heat transfer coefficient and the smooth surface has the lowest heat transfer coefficient. Heat transfer enhancement coefficient d is defined by:
d ¼ hribbed =hsmooth
(14)
which is the heat transfer coefficient ratio of the ribbed surface to the smooth surface under the same conditions. For all the cases with ribbed surfaces, the enhancement coefficients increase with the increase in the mist concentration and decrease with the increase in the mist diameter as shown in Fig. 10. When the impingement water droplet diameter reaches above 100 mm, the increase in the enhancement coefficient approaches zero. The enhancement coefficient on the ribbed convex surface is mostly higher compared with that on the ribbed concave surfaces. It is proved that the capability of heat transfer for the ribbed convex
Fig. 9. Average heat transfer coefficients on the smooth, ribbed convex and concave surfaces.
Please cite this article in press as: Bian, Q., et al., Numerical investigation of mist/air impingement cooling on ribbed blade leading-edge surface, Journal of Environmental Management (2017), http://dx.doi.org/10.1016/j.jenvman.2017.05.052
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Fig. 10. Enhancement coefficients on the ribbed surfaces in various conditions.
surface is stronger than that for the ribbed concave surface. 3.3. Pressure drop in the multiphase zone The pressure drops of the single-phase flow in the impingement zone are much smaller than that of the two-phase (mist/air) flow under all three different target surfaces conditions as shown in Fig. 11. The pressure drop in the impingement zone increases sharply with increasing the mist concentration. However, when the mist diameter increases, the pressure drop decreases quickly and then the deviation becomes weak. The pressure drops on the ribbed surfaces are larger than that on the smooth surface under the same flow conditions. In addition, the pressure drop on the ribbed concave surface is the largest when the mist concentration is below 5%. With continuously increasing the mist concentration, the pressure drop on the ribbed convex surface increases sharply and then it is higher than that on the concave surface. The enlargement factor of the flow friction q is defined by:
q ¼ DPribbed =DPsmooth
(15)
which is the pressure drop ratio of the ribbed surface to the smooth
Fig. 11. Pressure drops on the smooth, the ribbed convex and concave surfaces.
surface. The frictions of both of the two ribbed surfaces increase as shown in Fig. 12. The friction enlargement factor is 1.04e1.15 for the ribbed concave surface, while the value for the ribbed convex surface is 1.05e1.40. The flow friction of the ribbed convex surface is larger than that of the ribbed concave surface.
Please cite this article in press as: Bian, Q., et al., Numerical investigation of mist/air impingement cooling on ribbed blade leading-edge surface, Journal of Environmental Management (2017), http://dx.doi.org/10.1016/j.jenvman.2017.05.052
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(2) The ribbed concave/convex surfaces show better cooling characteristics, i.e., lower surface temperature and higher heat transfer coefficient. Compared with the smooth-surface case, the case with the convex ribs obtains the best cooling performance. (3) The pressure drops on the ribbed concave/convex surfaces are higher than that on the smooth surface. For the cases with the high droplet concentration, the enlargement factor of the friction of the convex surface can reach 1.4. However, the heat transfer coefficient of the convex surface can reach 1.45. Acknowledgment This work is financially supported by the National Natural Science Foundation of China under the grant No. 51606059. References
Fig. 12. Enlargement factors of the flow friction on the ribbed surfaces.
However, the enhancement coefficient of heat transfer of the ribbed convex surface is larger than that of the ribbed concave surface under the same operating conditions. As shown in Fig. 10, it can be found that the range of the enhancement coefficients on the ribbed convex surface is about 1.1e1.45 and the value for the concave surface is 1.1e1.25 except one point which is 1.35.
4. Conclusions A numerical method has been applied to investigate the impingement cooling characteristics of mist/air flow on the leading-edge. The convex and concave ribs are arranged on the target turbine blade surfaces in order to study the effects of ribbed surfaces on the protection for the blade surface. The Euler-Lagrange method is adopted to track the two phases. The main conclusions can be drawn as follows: (1) Compared with the single-phase flow, the air/mist twophase flow can reduce the average temperature on the leading-edge surface and increase the heat transfer coefficient of the target surface with the penalty of pressure drop increased in the multiphase zone.
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Wang, J., Gu, C.W., Bengt, S., Yang, J., Gu, C., Wang, Q., 2015. Conjugated heat transfer analysis of a film cooling passage with different rib configurations. Int. J. Numer. Methods Heat Fluid Flow 25 (4), 841e860. http://dx.doi.org/10.1108/HFF-042014-0110. n, B., Wu, H., Yang, J., Gu, C., Wang, Q., 2016a. Conjugated heat Wang, J., Sunde transfer analysis of a film cooling passage with turbulator ribs. Heat Transf. Res. 47 (2), 89e103. http://dx.doi.org/10.1615/HeatTransRes.2015010665. Wang, J., Gu, C.W., Bengt, S., Yang, J., Gu, C., Wang, Q., 2016b. Investigations of film cooling and its non-uniform distribution for the conjugate heat transfer passage with a compound inclined angle jet. Numer. Heat. Transf. Part A Appl. 69 (1), 14e30. http://dx.doi.org/10.1080/10407782.2015.1023156.
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Research article
Numerical investigation of mist/air impingement cooling on ribbed blade leading-edge surface Qingfei Bian a, Jin Wang b, Yi-tung Chen c, Qiuwang Wang a, Min Zeng a, * a
Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, China School of Energy and Environmental Engineering, Hebei University of Technology, Tianjin, 300401, China c Department of Mechanicals Engineering, University of Nevada- Las Vegas, Las Vegas, NV, 89154, USA b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 December 2016 Received in revised form 17 April 2017 Accepted 17 May 2017 Available online xxx
The working gas turbine blades are exposed to the environment of high temperature, especially in the leading-edge region. The mist/air two-phase impingement cooling has been adopted to enhance the heat transfer on blade surfaces and investigate the leading-edge cooling effectiveness. An Euler-Lagrange particle tracking method is used to simulate the two-phase impingement cooling on the blade leading-edge. The mesh dependency test has been carried out and the numerical method is validated based on the available experimental data of mist/air cooling with jet impingement on a concave surface. The cooling effectiveness on three target surfaces is investigated, including the smooth and the ribbed surface with convex/concave columnar ribs. The results show that the cooling effectiveness of the mist/ air two-phase flow is better than that of the single-phase flow. When the ribbed surfaces are used, the heat transfer enhancement is significant, the surface cooling effectiveness becomes higher and the convex ribbed surface presents a better performance. With the enhancement of the surface heat transfer, the pressure drop in the impingement zone increases, but the incremental factor of the flow friction is smaller than that of the heat transfer enhancement. © 2017 Elsevier Ltd. All rights reserved.
Presented at the 11th SDEWES conference Lisbon 2016, 4e9 September, 2016, Lisbon, Portugal. Keywords: Blade leading-edge Mist Two-phase flow Impingement cooling Ribbed surface
1. Introduction Gas turbine has been widely used in vehicle and aviation, electricity generation, refrigeration and other aspects. With the increase in the inlet temperature of gas turbine, the efficiency and output power of gas turbine are rising obviously. Now the turbine inlet temperature can be up to 2000 K with advanced technologies (Liao et al., 2014). The extreme operating conditions can shorten pez-Abente et al., the lifespan and reduce efficiency of the blade (Lo 2014). Especially, the blade leading-edge is directly impinged by hot gas and suffers a great thermal load. The frequent replacement of the blades results in massive material wastes and the low efficiency causes more emissions of NOx (Javed et al., 2007). Therefore, the advanced cooling method for protecting the blade leading-edge has received high attentions. Conducting many experimental tests can also cause environmental and economic concerns, such as
* Corresponding author. E-mail addresses: [email protected] (Q. Bian), [email protected] (J. Wang), [email protected] (Y.-t. Chen), [email protected] (Q. Wang), zengmin@ mail.xjtu.edu.cn (M. Zeng).
material waste and air pollution. Many environmental regulations have been made by the government to demand the different industries to follow the stringent requirements to solve those problems. The widely used Computational Fluid Dynamics (CFD) method can provide the design details based on the operating conditions to satisfy those regulations (Mikul ci c et al., 2016; Baleta et al., 2017) and shows great promise in the environmental science field. For example, Wania et al. (2012) simulated an effect of vegetation on atmospheric processes. Kafle et al. (2015) investigated two down-flow wood bark-based biofilters under the actual swine farm conditions. All of their studies obtained good results by using the CFD techniques. Numerical results by using the CFD method are also obtained to predict effects of the cooling technologies on the protection of turbine blades. Now the two most widely used cooling techniques are the film cooling and the composite cooling. Kanani et al. (2009) numerically proved that many factors had important effects on the film cooling effectiveness and film shrouded homogeneity, such as the film holes shape, the holes arrangement and the blowing ratio. Chang et al. (2015) compared film cooling with composite cooling under the same coolant conditions and they found that the
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Please cite this article in press as: Bian, Q., et al., Numerical investigation of mist/air impingement cooling on ribbed blade leading-edge surface, Journal of Environmental Management (2017), http://dx.doi.org/10.1016/j.jenvman.2017.05.052
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Nomenclature Ad cp cp,d CD dd fi 0 fi f0 h Hlatref
Surface area of the particle, m2 Specific heat, J/(kg K) Specific heat of the particle, J/(kg K) Drag coefficient Diameter of the particle, m Mass force, m/s2 Volumetric momentum source, kg/(m2 s2) Interaction forces, m/s2 Enthalpy, J/kg Latent heat at reference conditions, J/kg
hd hfg kc М _d m md Dmd md;in md;out p Re Red t Dt
Particle enthalpy, J/kg Latent heat of particle, J/kg Mass transfer coefficient, m/s Volumetric mass source, kg/(m3 s) Mass flow rate of the particles per cell, kg/s Average mass of the particle on cell entry, kg Mass exchange of the particle per cell, kg Mass of the particle on cell entry, kg Mass of the particle on cell exit, kg Pressure, Pa Relative Reynolds number Reynolds number of the particle Time, s Time step, s
composite cooling effectiveness was higher than the film cooling. Nirmalan et al. (1998), Li and Wang (2005) and, Wang and Li (2008) found that the film cooling effectiveness of the steam/mist twophase flow was higher than that of the steam flow only. Nirmalan et al. (1998) experimentally investigated heat transfer of the turbine vane with water-air cooling method. Li and Wang used the CFD technique to study the film cooling, they found that the cooling effectiveness enhanced with mist injection (Li and Wang, 2005) and then investigated the blade cooling using that method under the real turbine operating conditions (Wang and Li, 2008). Jiang et al. also used the numerical method to study the steam/mist film cooling on the heavy-duty gas turbine vane (Jiang et al., 2014) and further explored the film cooling enhancement techniques on the leading-edge surface and downstream surface of turbine blade (Jiang et al., 2015a). Wang et al. added ribs on the cooling passage to enhance the flow disturbance, which showed good cooling protection for the blade (Wang et al., 2015, 2016a). The similar configuration was used to investigate the effect of the inclined flow angle on film cooling (Wang et al., 2016b). The application of composite cooling and multiphase film cooling can greatly improve the cooling effectiveness near the blade leading-edge. With the increase in turbine inlet temperature, the usage of the coolant increases quickly in order to protect the blade. Meanwhile, a large quantity of coolant flowing into turbine results in losses of benefits (Shi et al., 2015a). In addition, the hole configurations would result in complicated flow distributions around the turbine blades, and some challenges emerge to the stability of the working equipment (Jun et al., 2015). Two-phase impingement cooling method has been gradually introduced into protection of the blade leading edge for the characteristics of high cooling efficiency. Shi et al. (2015b) found that the efficiency of the steam/mist impingement cooling was much higher than that of the steam cooling only. Li et al. (2003) proved that the concave surface had a better impingement cooling effect than the flat surface by the slot steam/mist impingement
T Tin Tout Tref Td TR ui, uj, uk ud xi, xj, xk Yi;s Yi;∞
Temperature, K Temperature of the particle on cell entry, K Temperature of the particle on cell exit, K Reference temperature for enthalpy, K Particle temperature, K Radiation temperature, K Velocity, m/s Velocity of the particle, m/s Coordinate directions, m Vapor mass fraction at the surface Vapor mass fraction in the bulk gas
Greek symbols Heat transfer enhancement coefficient Cell volume, m3 Kronecker's delta Dynamic viscosity coefficient, Pa s Density, kg/m3 Density of the particle, kg/m3 Thermal conductivity, W/(m K) Volumetric energy source, W/m3 εd Emissivity s Stefan Boltzmann constant, 5.67 108 W/(m2 K4) D Convection heat transfer enhancement coefficient q Enlargement factor of flow friction Gj Viscous stress tensor, Pa
d dV dij m r rd l F
experiments. Dhanasekaran et al. conducted a two-phase flow impingement simulation on the surface of a 180 bend pipe and compared the results with the experimental data (Dhanasekaran and Wang, 2012), besides, they also numerically investigated the cooling effect of the surface with 45 angled ribs (Dhanasekaran and Wang, 2013). Jiang et al. (2015b) studied the cooling characteristic of the leading-edge surface of turbine blade using air/steam two-phase impingement cooling method and they found that it was a promising method. But how to further enhance impingement cooling efficiency and bring it into commercial application are still unclear. In this study, the air/mist impingement cooling model of the leading-edge is presented and validated. The cooling effectiveness on rough surfaces with convex/concave ribs is then investigated after the smooth leading-edge surfaces are studied and benchmarked. In addition, the pressure drop characteristics of the impingement zone are also obtained to investigate the benefit of the ribbed surface. 2. Numerical model formulation 2.1. Physical and computational domain descriptions Numerical method has been used to study the cooling characteristics of ribbed surfaces and a few assumptions are made to simplify the present model as follows: 1) One blade is included in the computational domain and the periodic boundary condition is used to simulate the annular cascades; 2) The solid zone of the blade only involves the leading edge part and others are neglected; 3) Air/mist mixing zone is ignored and droplets are injected from the inlets of the impingement zone directly; 4) The hot air is used instead of the combustion gas;
Please cite this article in press as: Bian, Q., et al., Numerical investigation of mist/air impingement cooling on ribbed blade leading-edge surface, Journal of Environmental Management (2017), http://dx.doi.org/10.1016/j.jenvman.2017.05.052
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Fig. 1. Geometry and target turbine blade surfaces.
5) The droplet injection is uniform and the diameters of the droplets are of the same value; 6) Radiation effect is neglected. The simplified geometry used in mist/air impingement cooling simulation is illustrated in Fig. 1. There are 5 rows of impingement holes in the computational domain. Each row is arranged with 13 holes. The distance between two neighbor holes is 0.9 mm and the thickness of the impingement cavity is 5 mm. Different target surfaces are shown in Fig. 1(a)-(c), including the smooth, the ribbed convex and the ribbed concave surfaces. All the rows of the columnar ribs are arranged uniformly on the target surfaces. Each row has 26 ribs and the rib has a height of 0.9 mm. Fig. 2 shows the computational meshes for the impingement cooling simulation of turbine blade. Because the ribbed surfaces
have complicated structure with hundreds of ribs, the unstructured meshes are adopted to save computational resources. Boundary layers are generated on the surfaces in the main flow zone and impingement zone and yþ is about 1 in locations of the first cell row from solid wall. Based on the grid dependency test, the optimum case with 3.4 million cells is selected compared to other cases with 1.5 million and 4.5 million cells.
2.2. Governing equations and boundary conditions In order to track the air/mist two-phase flow in the impingement zone exactly, the Euler-Lagrange method is adopted in this study. The Euler method is used to track the continuous phase consisting of air and water steam which comes from the
Fig. 2. The computational meshes for the turbine blade impingement cooling model.
Please cite this article in press as: Bian, Q., et al., Numerical investigation of mist/air impingement cooling on ribbed blade leading-edge surface, Journal of Environmental Management (2017), http://dx.doi.org/10.1016/j.jenvman.2017.05.052
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vrh v v þ ruj h ¼ vt vxj vxj
vT l vxj
!
vpui v þ Gj $ui þ rfi $ui vxj vxi
þ fi0 $ui þ F
(6)
2 Tout ZTin Z _d 6 m F¼ cp;d dT md;out cp;d dT md;in 4md;in m d dV Tref
Tref
3
7 md;out Hlatref 5
Fig. 3. The two-phase conjugate process.
vaporization of water droplets. The Lagrange method is applied to track the discrete phase consisting of water droplets only. During the numerical simulations, the additions of source terms in all governing equations are used to realize the conjugate computation between the two phases. The process of two-phase computation in one control volume is shown in Fig. 3. The governing equations of continuous phase are given as follows: Continuity equation
vr v þ ðrui Þ ¼ M vt vxi
(1)
Dmd _d M¼m md dV
(2)
vrui v vp v þ ruj ui ¼ þ G þ rfi þ fid vxj vxi vxj j vt "
fi0
vui vuj 2 vuk þ d vxj vxi 3 vxk ij
where M is mass source, which shows the mass transfer from the water droplets to the continuous phase, Gj is the viscous stress 0 tensor of continuous phase, fi is the source term of momentum equations, including the interaction drag force and other forces between two phases and F is the source term of the energy, which shows the heat transfer between the two phases. For the discrete phase (water droplet), the governing equations are given by:
md
dui ¼ Fdi þ Fpi þ Fvmi þ Fgi þ Fbi þ Fi0 dt
md cp;d
dTd dmd ¼ hd Ad ðT Td Þ hfg þ Ad εd s TR4 Td4 dt dt
(8)
(9)
When the surface temperature of the droplets is higher than the boiling point of the water, the boiling evaporation dominates. The mass conservation equation for the droplets is shown as:
" # pffiffiffiffiffiffiffiffi cp ðT Td Þ dðdd Þ 4l ¼ 1 þ 0:23 Red ln 1 þ dt hfg rd cp dd
(10)
When the surface temperature of the droplets is lower than the boiling point of the water, the natural evaporation dominates. The equation is as follows:
Momentum equation
Gj ¼ m
(7)
(3)
#
" # X 18mCD Re md 0 ¼ ðud uÞ þ f 2 dV 24rd dd Energy equation
(4)
(5)
" # Yi;s Yi;∞ dðmd Þ ¼ Ad kc r ln 1 þ dt 1 Yi;s
(11)
Boundary conditions for the conjugate simulations are listed in Table 1. The water droplets are injected uniformly from the inlets of the impingement zone. The thermal properties vary with temperature. The k-ε Realizable model is chosen to solve the related equations for the turbulent flow. The bounce and break-up models are used when the droplets collide with the target surface. The convection terms in the governing equations are discretized by the second order upwind scheme. All the conjugate simulations are calculated by ANSYS FLUENT 14.0.
Table 1 Boundary conditions. Zone
Boundary conditions
Value
Inlet for the air
Pressure (Pa) Temperature (K) Velocity (m/s) Pressure (Pa) Mass flow (kg/s) Pressure (Pa) Mist concentration Mist diameter (mm)
500000 1200 15 210000 0.003942 0 3%, 5%, 8%, 10%, 15% 5, 10, 15, 50, 100, 150, 200
Outlet for the air Inlet for the impingement Outlet for the impingement Mist parameter
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3. Results and discussion
2.3. Model validation
3.1. Temperature distribution of the leading edge surface
The convective heat transfer coefficient is defined by:
hðxÞ ¼ qðxÞ Tw ðxÞ Tj
(12)
where q(x), Tw(x) and Tj are the surface heat flux, the local surface temperature and the impingement temperature, respectively. The convection heat transfer enhancement coefficient is shown as follows:
D ¼ hmix =hsteam
5
(13)
where hmix, hsteam are the heat transfer coefficients for the mist/ steam two-phase and the single-phase (steam), respectively. The experiment carried out by Li et al. (2003) is used to validate the accuracy of the numerical model. The main experimental part is extracted as the computational domain and it is marked with circles as shown in Fig. 4. The width of the inlet slot is 7.5 mm, the outer radius is 79.5 mm, the thickness of the impingement cavity is 22.5 mm and the length of the simulated section is 100 mm. Given that there is a mixture zone used in the experiments, the inlet passage in the numerical simulations is extended to produce the same boundary condition as experiment. The final computational meshes for the model validation are shown in Fig. 5. For the numerical simulations, the Reynolds number of the inlet flow is 7500 and the heat flux of the outer surface is 7540 W/m2. The average diameter of the droplets is 12 mm and the mass ratio of the discrete phase to the total is 0.5%. The comparisons of concave surface temperature and heat transfer enhancement coefficient between the numerical simulations and the experiments are shown in Fig. 6. For the temperature of the whole surface, the maximum absolute error is 10 K, corresponding to a relative error of 5%. For the heat transfer enhancement coefficient, the absolute and relative error are 0.15 and 8%, respectively. The comparison of the results reveals that the present numerical method is reasonable and acceptable.
Compared with the single-phase (air) flow, the two-phase (air/ mist) flow decreases the average temperature on the leading-edge surface obviously as shown in Fig. 7. The average temperature of the leading-edge surface gradually decreases with the increase in the mist concentration. With increasing the mist diameter, the average temperature on the leading-edge surface decreases initially and then increases. When the mist diameter exceeds 100 mm, the cooling effectiveness of the mist/air flow reduces sharply. Comparing the three target surfaces under the same impingement conditions, it can be found that the case with the ribbed convex surface shows the lowest temperature, the smooth surface has the highest temperature and the case with the ribbed concave surface has the temperature between the ribbed convex surface and the smooth surface. The effects of the mist concentration on the temperature distribution are shown in Fig. 8. For the case with a droplet diameter of 5 mm, the temperature drop of the leading-edge surface is obvious as the mist concentration increases from 3% to 8%. When the mist concentration increases from 10% to 15%, the temperature variation
Fig. 5. The computational meshes for the model validation.
Fig. 4. Mist/steam impingement cooling experiment on concave surface (Li et al., 2003).
Please cite this article in press as: Bian, Q., et al., Numerical investigation of mist/air impingement cooling on ribbed blade leading-edge surface, Journal of Environmental Management (2017), http://dx.doi.org/10.1016/j.jenvman.2017.05.052
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Fig. 6. Comparisons of concave surface temperature and heat transfer enhancement coefficient between the numerical simulations and the experiments.
of the leading-edge surface becomes small, especially under the smooth target surface condition the gradient approaches zero. For the case with a droplet diameter of 50 mm, the temperature drops and slopes under three different target surfaces conditions are almost uniform between adjacent mist concentrations. The temperature drops and slopes for the ribbed target surfaces are larger than that for the smooth surface and the total temperature drop for the droplet diameter of 50 mm is smaller than that for 5 mm. 3.2. Heat transfer coefficient distribution The heat transfer coefficients are strongly influenced by the mist concentrations under all three different surfaces conditions. The heat transfer coefficient of the two-phase flow is much higher than that of the single air flow as shown in Fig. 9. With increasing the mist concentration, the convective heat transfer coefficient increases gradually and the difference between adjacent conditions also increases generally. The tendencies of the heat transfer coefficient for various mist diameters are different from that for the
Fig. 7. The average surface temperature distribution of leading-edge surface under smooth, convex and concave ribs target surface conditions.
Please cite this article in press as: Bian, Q., et al., Numerical investigation of mist/air impingement cooling on ribbed blade leading-edge surface, Journal of Environmental Management (2017), http://dx.doi.org/10.1016/j.jenvman.2017.05.052
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Fig. 8. The average temperature distribution of the leading-edge surface in various mist diameters conditions.
various concentrations. With the increase in the mist diameter, the coefficient increases initially and then decreases and there is a peak at 15 mm. However, the peak is not obvious when the mist concentration is small. Comparing the three different target surfaces under the same impingement conditions, it can be found that the ribbed convex surface has the highest heat transfer coefficient and the smooth surface has the lowest heat transfer coefficient. Heat transfer enhancement coefficient d is defined by:
d ¼ hribbed =hsmooth
(14)
which is the heat transfer coefficient ratio of the ribbed surface to the smooth surface under the same conditions. For all the cases with ribbed surfaces, the enhancement coefficients increase with the increase in the mist concentration and decrease with the increase in the mist diameter as shown in Fig. 10. When the impingement water droplet diameter reaches above 100 mm, the increase in the enhancement coefficient approaches zero. The enhancement coefficient on the ribbed convex surface is mostly higher compared with that on the ribbed concave surfaces. It is proved that the capability of heat transfer for the ribbed convex
Fig. 9. Average heat transfer coefficients on the smooth, ribbed convex and concave surfaces.
Please cite this article in press as: Bian, Q., et al., Numerical investigation of mist/air impingement cooling on ribbed blade leading-edge surface, Journal of Environmental Management (2017), http://dx.doi.org/10.1016/j.jenvman.2017.05.052
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Fig. 10. Enhancement coefficients on the ribbed surfaces in various conditions.
surface is stronger than that for the ribbed concave surface. 3.3. Pressure drop in the multiphase zone The pressure drops of the single-phase flow in the impingement zone are much smaller than that of the two-phase (mist/air) flow under all three different target surfaces conditions as shown in Fig. 11. The pressure drop in the impingement zone increases sharply with increasing the mist concentration. However, when the mist diameter increases, the pressure drop decreases quickly and then the deviation becomes weak. The pressure drops on the ribbed surfaces are larger than that on the smooth surface under the same flow conditions. In addition, the pressure drop on the ribbed concave surface is the largest when the mist concentration is below 5%. With continuously increasing the mist concentration, the pressure drop on the ribbed convex surface increases sharply and then it is higher than that on the concave surface. The enlargement factor of the flow friction q is defined by:
q ¼ DPribbed =DPsmooth
(15)
which is the pressure drop ratio of the ribbed surface to the smooth
Fig. 11. Pressure drops on the smooth, the ribbed convex and concave surfaces.
surface. The frictions of both of the two ribbed surfaces increase as shown in Fig. 12. The friction enlargement factor is 1.04e1.15 for the ribbed concave surface, while the value for the ribbed convex surface is 1.05e1.40. The flow friction of the ribbed convex surface is larger than that of the ribbed concave surface.
Please cite this article in press as: Bian, Q., et al., Numerical investigation of mist/air impingement cooling on ribbed blade leading-edge surface, Journal of Environmental Management (2017), http://dx.doi.org/10.1016/j.jenvman.2017.05.052
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(2) The ribbed concave/convex surfaces show better cooling characteristics, i.e., lower surface temperature and higher heat transfer coefficient. Compared with the smooth-surface case, the case with the convex ribs obtains the best cooling performance. (3) The pressure drops on the ribbed concave/convex surfaces are higher than that on the smooth surface. For the cases with the high droplet concentration, the enlargement factor of the friction of the convex surface can reach 1.4. However, the heat transfer coefficient of the convex surface can reach 1.45. Acknowledgment This work is financially supported by the National Natural Science Foundation of China under the grant No. 51606059. References
Fig. 12. Enlargement factors of the flow friction on the ribbed surfaces.
However, the enhancement coefficient of heat transfer of the ribbed convex surface is larger than that of the ribbed concave surface under the same operating conditions. As shown in Fig. 10, it can be found that the range of the enhancement coefficients on the ribbed convex surface is about 1.1e1.45 and the value for the concave surface is 1.1e1.25 except one point which is 1.35.
4. Conclusions A numerical method has been applied to investigate the impingement cooling characteristics of mist/air flow on the leading-edge. The convex and concave ribs are arranged on the target turbine blade surfaces in order to study the effects of ribbed surfaces on the protection for the blade surface. The Euler-Lagrange method is adopted to track the two phases. The main conclusions can be drawn as follows: (1) Compared with the single-phase flow, the air/mist twophase flow can reduce the average temperature on the leading-edge surface and increase the heat transfer coefficient of the target surface with the penalty of pressure drop increased in the multiphase zone.
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Please cite this article in press as: Bian, Q., et al., Numerical investigation of mist/air impingement cooling on ribbed blade leading-edge surface, Journal of Environmental Management (2017), http://dx.doi.org/10.1016/j.jenvman.2017.05.052