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Numerical simulation on impingement and film composite cooling of blade leading edge model for gas turbine
Applied Thermal Engineering xxx (2014) 1e12
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Numerical simulation on impingement and film composite cooling of blade leading edge model for gas turbine Zhao Liu, Lv Ye, Changyee Wang, Zhenping Feng* Institute of Turbomachinery, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, PR China
h i g h l i g h t s The performances of different turbulence model are validated. Effects of blowing ratio and spanwise angle on composite cooling are investigated. Spanwise angle is more effective to improve film cooling than impingement cooling. Proper blowing ratio and lower spanwise angle is suitable for cooling design.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 January 2014 Received in revised form 28 April 2014 Accepted 7 May 2014 Available online xxx
In this paper numerical simulation is performed to simulate the impingement and film composite cooling on blade leading edge region. The relative performances of turbulence models are compared with available experimental data, and the results show that SST keu model is the best one based on simulation accuracy. Then the SST keu model is adopted for the simulation. The grid independence study is also carried out by using the Richardson extrapolation method. A single array of circle jets and three rows of film holes are arranged to investigate the impingement and film composite cooling. Five different blowing ratios and five different film hole spanwise angles are studied in detail. The results indicate that the heat transfer coefficient on the internal surface of turbine blade leading edge increases with the blowing ratio, and slightly changes with film hole spanwise angle. And the external film cooling effectiveness distribution would vary rapidly with the blowing ratio and the film hole spanwise angle. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Blade leading edge Impingement cooling Film cooling Composite cooling
1. Introduction In order to enhance the turbine efficiency and power, modern gas turbine systems are required to operate at higher and higher temperature, and thus turbine components are suffering an increasing heat loads. As a result, turbine inlet temperature has already been far beyond the material acceptable level. It is worth to mention that the leading edge area of gas turbine blade will have a higher heat flows as it is upwind to high temperature inflows. A series of cooling technologies such as impingement cooling, film cooling and other forced convection heat transfer methods have been applied to the turbine blade leading edge, among which impingement cooling is one of the most effective internal cooling methods but its arrangement would weaken the blade structure strength [1], and also film cooling is the only method for external
* Corresponding author. Tel.: þ86 29 82663195; fax: þ86 29 82668704. E-mail address: [email protected] (Z. Feng).
cooling. Thus impingement and film composite cooling are used extensively in gas turbine blades in recent years. Two decades ago, experiment was the only way to obtain detailed and reliable heat transfer information about the turbulent, 3-dimensional flows in the complex impinging cooling flows. The early investigation on concave surface impingement cooling has been summarized by Chupp et al. [2], Metzger et al. [3,4], and then Bunker and Metzger [5] continued their works in 1990 to suit the need of turbine cooling design. The cooling performance are influenced by many parameters, such as, Reynolds number [2,3,5,6], jet spacing [2,4,6], the distance between jet exit and target surface [2,5,6], target surface shape [4,5], jet nozzle shape [7], rotation [8], jet direction [9] and so on. The first numerical investigation was conducted by Kayansayan and Küçüka [10], and then many works compared the numerical results with experimental data [10e19]. Further studies on the influence factors were continued, such as wall roughness [11], horseshoe ribs [12], cross flow and exit flow schemes [13], curvature target surface [18], and the arrangement of jet nozzle [19]. And some of them deduced dimensionless correlations between the
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Nomenclature B C D H h I L M Nu P q r* Re S V T Y yþ
width of equivalent slot jet used in Ref. [5] [mm] hole spacing of each row [mm] diameter [mm] jet from target surface [mm] heat transfer coefficient [W/(m2 K)] turbulent intensity length of flat portion [mm] average blowing ratio Nusselt number pressure [Pa] heat flux [W/m2] ratio of curvature radius to of semi-cylindrical airfoil radius used in Ref. [5] Reynolds number streamwise coordinate [mm] velocity [m/s] temperature [K] transverse coordinates from wall (m) non-dimensional distance, ¼Yut/n
r a b g l ut
n
density [kg/m3] angle of the second row of film holes from the stagnation line [ ] angle of film holes from the surface in spanwise [ ] attack angle of main flow [ ] thermal conductivity of fluid [W/(m K)] shear velocity [m/s] kinematic viscosity [m2/s]
subscripts av average aw adiabatic wall c coolant f film hole i inlet ip impingement hole sp spanwise average w wall o outlet x, y, z the direction of the vector ∞ mainstream 1,2 film hole number
Greek symbols h cooling effectiveness
average or the maximum Nusselt number and the influence parameters [15,19]. Concern on film cooling, most work focus on the effect of film hole exit shape and geometry [20e22], effect of film cooling combined with inclined ribs [23] and so forth. All papers cited above are about the investigation on new shape film holes, or the effect of jet parameters on impingement cooling without film coolant extraction. The addition of film cooling is expected to affect the heat transfer in the internal region of the impingement cooling since it changes the flow path of the coolant and reduces the cross flow. Only few of pervious work focused on impingement/film composite cooling. The first work was done by Hollworth and Dagan in 1980 [24], and also Ekkad et al. [25] investigated impingement cooling with film coolant extraction on a plate. Then Metzger and Bunker [26] experimentally studied impingement cooling of concave surface through lines of circular air jets with and without film coolant extraction. Taslim et al. [27,28], and Taslim and Khanicheh [29] investigated heat transfer of impingement cooling on concave surface with film holes under the influence of roughness target wall, jet nozzle geometry, showerhead and gill film holes. Mouzon et al. [30], Ravelli et al. [31], Maikell et al. [32] and Mathew et al. [33] investigated the effect of internal impingement on film cooling of blade leading edge model. Obviously, the previous work focused on the influence of film extraction on impingement cooling or the effect of flow condition on external film cooling. But almost no attentions were paid to the effects of film hole geometries on the internal heat transfer and the external film cooling effectiveness. In this study, the flow structure and heat transfer of the impingement and film composite cooling on turbine leading edge model are studied, and the effects of blowing ratio and spanwise angle of film holes are investigated. 2. Physical and mathematical model 2.1. Geometrical details This numerical study adopted the blade leading edge model which was used in the experimental study of Maikell et al. [32] and
the computational study of Mathew et al. [33]. Fig. 1 shows the leading edge model geometry structure. The film cooling configuration included three rows of holes positioned staggered along the stagnation line and at ±25 from the stagnation line, the impingement jets were directed to impact the internal surface in each stagnation film hole. The geometrical dimensions of different jet configurations are listed in Table 1. 2.2. Numerical method 2.2.1. Boundary conditions and solution procedure The boundary conditions are matched with those in Ref. [32]. As shown in Fig.1(b), periodic and symmetry conditions were applied to minimize the computational effort. The mainstream inlet air total temperature is 300 K; the velocity is 15 m/s and the inlet turbulent intensity I is 5%, and its definition can be found in Equation (1). The coolant inlet total temperature is 200 K, and the inlet turbulent intensity is 5% as well. The average static pressure at the outlet is 0.106 MPa. The impingement target wall temperature is 235 K, other walls are adiabatic and nonslip. The fluid is nitrogen (ideal gas). The convergence of simulation is achieved when the root mean square residuals of the momentum equations, mass equation, energy equation and turbulent equations are lower than 105 and remain steady.
I¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Vx2 þ Vy2 þ Vz2 Vav
(1)
2.2.2. Mesh procedure The numerical simulations are performed by using a commercial CFD software CFX11.0. The solutions are obtained by solving the steady compressible Reynolds averaged NaviereStokes equations, in which the finite control volume method is applied to discretize these equations, and a second order form with high
Please cite this article in press as: Z. Liu, et al., Numerical simulation on impingement and film composite cooling of blade leading edge model for gas turbine, Applied Thermal Engineering (2014), http://dx.doi.org/10.1016/j.applthermaleng.2014.05.060
Z. Liu et al. / Applied Thermal Engineering xxx (2014) 1e12
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Fig. 2. Computational mesh (cross section).
Fig. 1. Schematic of the model and boundary condition. Fig. 3. Comparison of numerical results with available experimental data.
Table 1 Geometric detail of jet configurations. Dimension
Values
C (mm) Df (mm) Di (mm) Dip (mm) Do (mm) L (mm) a ( ) b ( )
24.20 3.18 25.40 5.00 50.80 10.90 25.00 20.00
Table 2 Average Nusselt number on impingement target surface. Node number (million)
Impingement cooling
Film cooling
Average Nu
Relative error
Average h
Relative error
0.91 1.59 2.03 3.16 Extrapolation
10.59 10.14 10.02 10.00 9.94
6.52% 2.01% 0.80% 0.60% e
0.1484 0.1500 0.1509 0.1512 0.1521
2.43% 1.38% 0.79% 0.59% e
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Table 3 Mass flow rate and average blowing ratio through each film hole in different M. M
m1 (%)
M1av
m2 (%)
M2av
1.0 1.5 2.0 2.5 3.5
22.53 23.67 24.11 24.34 24.68
0.6777 1.068 1.450 1.830 2.598
77.47 76.33 75.89 75.66 75.32
1.164 1.722 2.283 2.845 3.964
resolution correction is used to discretize the convection term in this paper. The overall accuracy of the calculation is of the second order. The software Gambit 2.3.16 is adopted to generate the unstructured grids for the calculation domains. The mesh includes tetrahedral elements in the main flow passage and prism elements in the near wall regions, the jet nozzle, film hole and the grid nodes in and around its downstream are also refined. The low-Reynolds
number keu turbulence model would require at least yþ < 2. In this investigation, for standard keu turbulence model and SST keu turbulence model, the wall grid yþ is less than 1.0; more than 15 cells are put into the boundary layer; and the total grid nodes number is about 2.03 million. But for standard keε model and RNG keε model, the wall grid yþ is in the range between 20 and 100, and the total grid nodes number is about 1.91 million. The ratio of cell size increases by about 30% outward from the walls in all cases. Fig. 2 shows the grid generation result. The grid size definition for the identical parts of other cases is the same. As a result, the total grid node is changed with the geometry of the jet nozzle and the film holes. 2.2.3. Comparisons with available experimental data In order to validate the ability of the different turbulence models to represent flow and heat transfer of the present work, first calculation of an experimental case investigated by Bunker and
Fig. 4. Streamlines and contours of velocity magnitude on horizontal cross-sections at the center of film hole No.1 and No.2 in different M.
Fig. 5. Relative velocity magnitude on tangential section of film hole No.1 outlet in different M.
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Z. Liu et al. / Applied Thermal Engineering xxx (2014) 1e12
Metzger [5] is adopted as model verification for impingement cooling in this paper. Detailed geometry can be found in Ref. [5]. The case with H/B ¼ 24, r* ¼ 1.0, Re ¼ 6750 and C/Dip ¼ 4.67 is considered as a comparison. Calculations are carried out with three turbulence models, the RNG keε model, the standard keu model and the SST keu model. Fig. 3(a) shows the comparison between the predicted and the available measured results including the spanwise area weighted average Nusselt number along the target plate, and the model validation results by Kumar et al. [16]. The results demonstrated that the SST keu model is the best one based on the simulation accuracy, and the maximum relative error is 13.58%. For a constant temperature surface, the local heat transfer coefficient can be expressed as
h¼
qw Tw Tc
5
(2)
and the value of h can be normalized in the form of local Nusselt number as
Nu ¼
hDf qw $Df ¼ l ðTw Tc Þl
(3)
Then, a calculation of an experimental case investigated by Maikell et al. [32] is adopted as model verification for film cooling in the impingement and film composite cooling. Geometry is provided in Fig. 1. The case with blowing ratio M ¼ 1.0 is considered as a
Fig. 6. Relative velocity magnitude on tangential section of film hole No.2 outlet in different M.
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Z. Liu et al. / Applied Thermal Engineering xxx (2014) 1e12
h¼
T∞ Taw T∞ Tc
(4)
Fig. 3(b) shows the comparison of the predicted spanwise averaged film cooling effectiveness with the available measured results along the leading edge model. The results demonstrated that the SST keu model is the best, and its mean relative error is 5.85%. Since the relative error predicted by the SST keu model are the minimum one among the models both in the impingement cooling case and in the film cooling with impingement case, all the following results reported are based on SST keu model.
Fig. 7. Sketch of tangential section of film hole No.2 outlet.
comparison. Calculations are carried out with four turbulence models, the standard keε model, the RNG keε model, the standard keu model and the SST keu model. For an adiabatic surface, the local film cooling effectiveness can be expressed as
2.2.4. Grid independence analysis Four different meshes with the grid node number of 0.91 million, 1.59 million, 2.03 million and 3.16 million were used to validate the grid independence. The mesh refinement has been synchronously imposed on every mesh in three coordinate directions. The SST keu turbulence model is employed, the wall yþ is less than 1.0 and more than 15 cells were put into the boundary layer in all of the cases. The case with M ¼ 1.0 is adopted for grid independence test.
Fig. 8. Nu contours of the target surface in different M.
Please cite this article in press as: Z. Liu, et al., Numerical simulation on impingement and film composite cooling of blade leading edge model for gas turbine, Applied Thermal Engineering (2014), http://dx.doi.org/10.1016/j.applthermaleng.2014.05.060
Z. Liu et al. / Applied Thermal Engineering xxx (2014) 1e12
The area weighted average Nusselt numbers on the leading edge internal surface and the area weighted average film cooling effectiveness on the leading edge external surface obtained through the different meshes are demonstrated in Table 2. The extrapolation value was calculated by means of the Richardson extrapolation method [34] with the results of 2.03 million nodes and 3.16 million nodes. A second order format with high resolution correction is applied to discretize the convection term in this paper. Therefore, based on the Roache's investigation, the average Nusselt number from the Richardson extrapolation has a fourth order accuracy. Provided that these Nusselt number and cooling effectiveness are baseline solution, we can conclude that when the grid node number is larger than 2.03 million, the increasing node number has little effect on the value of error. In order to balance the calculation accuracy and the simulation time, about 2.03 million nodes were employed in the present numerical study with geometry showed in Table 1, and the same grid size definition was generated for the identical parts of other cases. 3. Results and discussions The blowing ratio and film hole structure have a significant effect on the flow pattern of the film cooling, and would affect the
7
flow of the internal impingement cooling, so they are critical to the flow and heat transfer of the impingement and film composite cooling. In order to study these effects, numerical simulations are carried out at five different M (blowing ratio): 1.0, 1.5, 2.0, 2.5, 3.5; and five different b (Angle of film holes from the surface in spanwise, the definition of b is showed in Fig. 1): 20 , 30 , 40 , 50 and 70 . For a convenient analysis, it is suggested that the film hole positioned along the stagnation line will be numbered No.1, and the other numbered No.2. 3.1. Effect of blowing ratio In order to investigate the effects of M on the impingement and film composite cooling of turbine leading edge, a numerical simulation was performed under the conditions of five different M, 1.0, 1.5, 2.0, 2.5, and 3.5 at b ¼ 20 , g ¼ 0.0 . And a detailed analysis was made for the calculation of four M: 1.5, 2.0, 2.5, and 3.5. Table 3 indicates the percent of mass flow rate and average blowing ratio of film hole No.1 and film hole No.2 in different M. It can be observed that the mass flow rate and average blowing ratio of film hole No.2 are consistently above those of film hole No.1. It is possibly because of the farther location of film hole No.1 than that
Fig. 9. Film cooling effectiveness contours in different M.
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Z. Liu et al. / Applied Thermal Engineering xxx (2014) 1e12
increases; more coolant will jet into the main stream and the low velocity area in downstream just below the film hole reduces. 3.1.2. Heat transfer Fig. 8 shows the Nusselt number contours of the internal impingement target surface in different M. The Nu at the sharp corner of the film hole inlet side and on the jet stagnation region is the largest, since the flow boundary is the thinnest and the turbulence intensity is the largest in these regions. And the Nu at the
Fig. 10. Spanwise averaged film cooling effectiveness in different M.
of film hole No.2, the effect of the crossflow caused by neighbor impinging jets, and the suppression of the main stream. With the increase of blowing ratio, the relative mass flow ratio in film hole No.1 increases slightly, while the relative flow ratio in film hole No.2 reduces. This may be caused by the variation of the flow resistance of the two film holes. 3.1.1. Flow fields Fig. 4 shows the streamlines and contours of velocity magnitude on horizontal cross-sections at the center of film holes No.1 (right one of each figure) and No.2 (left one of each figure) in different M. There are two typical vortexes of impingement on both sides of the impingement in the cross-section. This vortex makes both sides of the stagnation region be scoured by the coolant jet. And a smallscale vortex generates at the corner of film hole No.2. There is an ejection from the target surface at the middle on horizontal crosssections at the center of film hole No.1, which is caused by the encounter of the crossflow of adjacent impinging jets. With the increase of M, the jet velocity, the range and strength of the typical vortex of impingement, and the eject velocity at the confluence increase. Fig. 5 presents the velocity magnitude on tangential section of film hole No.1 outlet in different M. The left side is the upside of the film hole. From these figures, it can be seen that the velocity in the upside of film hole No.1 is larger, while in the downside is lower. And the velocity increases with the increase of M. Fig. 6 presents the velocity magnitude on tangential section of film hole No.2 outlet in different M. The bottom side is the downstream of the main flow, and the left side is the upside of the film hole, as shown in Fig. 7. From these figures, it can be found that the velocity in down-left side of film hole No.2 is larger, while the opposite is lower. This may be caused by the sharp corner at the film hole inlet and the impact of the main stream. With the increase of M, the maximum velocity in the down-left side of film hole No.2 Table 4 Mass flow rate and average blowing ratio through each film hole in different b.
b
m1(%)
M1av
m2(%)
M2av
20 30 40 50 70
22.53 22.51 22.40 22.14 21.19
0.6777 0.6770 0.6737 0.6659 0.6372
77.47 77.49 77.60 77.86 78.81
1.164 1.165 1.167 1.171 1.185
Fig. 11. Streamlines and contours of velocity magnitude on horizontal cross-sections at the center of film hole No.1 and No.2 in different b.
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confluence of the crossflows where a second injection occurred is also larger than the others. But low Nu regions appear on both sides, because of the ejection from the target wall on both sides of the confluence, and the deceleration of the coolant before the ejection. And the Nu at the both sides of the target surface which are scoured by the typical vortex of impingement is also larger, while the Nu at the corner of target surface and impingement surface is the lowest. With the increase of M, since the impingement velocity increases, both the maximal Nu and the high Nu region area on the target surface become larger. Fig. 9 shows the film cooling effectiveness contours of the leading edge surface in different M, with the results in two periods and on the symmetric surface. The high cooling effectiveness area around the film hole caused by cooling jet is clearly shown in Fig. 9. At b ¼ 20 , the spanwise component of the coolant film momentum is larger than the radial component, and with the suppression of the main flow, the coolant film will flow along the leading edge wall, so there is a large high h region on the leading edge. But there is a low cooling effectiveness region at part of the neighbor cooling holes in the same row, since the coolant film could not cover this area. And for the better wall attachment performance, the coolant from film hole No.1 could form more effective cooling film, and lead a larger range of high film cooling effective area than that of coolant from hole No.2. With the increase of M, the area of the highest h decreases, especially for the highest h region of film hole No.1, which reduces quickly and becomes far away from film hole. This is because the coolant film's momentum increases with M, and that will weaken
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the suppression of the main stream, and more coolant flowing into the mainstream, mixing with the mainstream instead of flow along the wall. Since the total coolant increases with M, the relative high h region increases, particularly the relative high h region covered by film hole No.1. Fig. 10 indicates the spanwise averaged film cooling effectiveness of the leading edge in different M. It can be found that the hsp (spanwise averaged film cooling effectiveness) increases with M in the front of film hole No.2 (0.5 S/Df 3), and there is a best value of M in the region behind film hole No.2 (S/Df 4). That is because with the increase of M, the coolant flow from film hole No.1 and its spanwise component momentum increases; the region covered by the coolant from film hole No.1 increases; and the high h area will make a transition between adjacent film hole though the peak value of h reduces. But behind film hole No.2, the high h area also increases with M when M 2.5, but most coolant from film hole No.2 will jet into the main stream while M is too large (M > 2.5), so the hsp increases first and then decreases. And the hsp will decrease rapidly in the range 4 S/Df 12 when M ¼ 3.5. One reason for this could be that the large momentum of coolant impinges to the main flow, the detachment of the cooling film from the surface lead a worse film cover in this area, as shown in Fig. 9. 3.2. Effect of spanwise angle In order to investigate the effects of spanwise angle of film hole (angle b) on the impingement and film composite cooling of turbine leading edge, a detailed analysis was performed under the
Fig. 12. Relative velocity magnitude on tangential section of film hole No.2 outlet in different b.
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conditions of five different b, that is 20 , 30 , 40 , 50 , and 70 at M ¼ 1. Also a detailed analysis was made for the calculation of four b: 30 , 40 , 50 , and 70 . Table 4 presents the percent of mass flow rate and average blowing ratio of film hole No.1 and film hole No.2 in different b. It can be observed that the mass flow rate and average blowing ratio of film hole No.2 are consistently above those of film hole No.1. That is the same with the above cases. The mass flow rate of the two rows of film holes slightly varies with b. It can be concluded that the angle b has low impact on the mass flow distribution of the two rows of film holes. 3.2.1. Flow fields Fig. 11 shows the streamlines and contours of velocity magnitude on horizontal cross-sections at the center of film hole No.1 and No.2. With the increase of b, the range of the typical vortex of impingement increases; the typical vortex core on hole No.1 section move to impingement surface; and the film hole inlet velocity on horizontal cross-section increases. Fig. 12 presents the velocity magnitude on tangential section of film hole No.2 outlet in different b, in which the bottom side is the downstream of the main flow, and the left side is the upside of the film hole, as shown in Fig.7. From these figures, it can be found that
with the increase of b, the maximum velocity in the down-left side of film hole No.2 increases; the low velocity region area caused by the interaction of film coolant and main flow decreases; the distance of film coolant impinging to main flow extends; and its position moves to the left.
3.2.2. Heat transfer Fig. 13 shows the Nusselt number contours of the internal impingement target surface in different b. With the increase of b, since the typical vortex core on hole No.1 section moves to the impingement surface, and the film hole inlet velocity on horizontal cross-section increases, Nu at the film holes inlet corner increases, and low Nu region area increases. Fig. 14 shows the film cooling effectiveness contours of the leading edge surface in different b, with the results in two periods and on the symmetric surface. With the increase of b, spanwise component of the coolant film momentum decreases, and the radial component increases, that leads to weaker suppression of the main flow and worse wall attachment performance of the coolant. Therefore, the area uncovered by the coolant film increases, and the maximum h and the high h region area decreases with the increase in b.
Fig. 13. Nu contours of the target surface in different b.
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Fig. 14. Film cooling effectiveness contours in different b.
Fig. 15 indicates the spanwise averaged film cooling effectiveness of the leading edge in different b. It can be found that the hsp reduces with the increase of b for S/Df < 8, especially when b ¼ 70 . While b ¼ 70 , most of the coolant jet into the mainstream and only few of them flow close to the wall. The reattachment of the coolant on the leading edge surface caused by the suppression of the main flow results in a lower peak value of hsp near S/Df ¼ 13. 4. Conclusions In this paper we proposed a numerical study on the impingement and film composite cooling of turbine blade leading edge model, the blowing ratio and the film hole spanwise angle are considered to enhance the heat transfer. Based on the numerical simulation results, it can be concluded that the SST keu model is the best for the numerical study of the impingement and film composite cooling in view of its simulation accuracy. With the increases of the blowing ratio, the Nusselt numbers on the internal target wall increases monotonously, but there is a best value for the cooling effectiveness on the external leading surface. With the increase of b, the Nu on the internal target surface hardly changes, but h on the leading edge external surface decreases rapidly. Proper blowing ratio (2.5 in this study), and lower spanwise angle is desirable to improve the performance of impingement cooling on the turbine leading edge.
Fig. 15. Spanwise averaged film cooling effectiveness in different b.
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Acknowledgements This work is financially supported by National Natural Science Foundation of China (Grant No. 51336007) and China Postdoctoral Science Foundation (Grant No. 2013M542345). References [1] J.C. Han, S. Dutta, S.V. Ekkad, Gas Turbine Heat Transfer and Cooling Technology, Taylor & Francis, New York, 2000. [2] R.E. Chupp, H.E. Helms, P.W. McFadden, T.R. Brown, Evaluation of internal heat transfer coefficients for impingement cooled turbine airfoils, J. Aircr. 6 (1969) 203e208. [3] D.E. Metzger, T. Yamashita, C.W. Jenkins, Impingement cooling of concave surface with lines of circular air jets, ASME J. Eng. Power 91 (1969) 149e158. [4] D.E. Metzger, R.T. Baltzer, C.W. Jenkins, Impingement cooling performance in gas turbine airfoils including effects of leading edge sharpness, ASME J. Eng. Power 94 (1972) 219e225. [5] R.S. Bunker, D.E. Metzger, Local heat transfer in internally cooled turbine airfoil leading edge regions: part I e impingement cooling without film coolant extraction, ASME J. Turbomach. 112 (1990) 451e458. [6] M. Choi, H.S. Yoo, G. Yang, J.S. Lee, D.K. Sohn, Measurements of impinging jet flow and heat transfer on a semi-circular concave surface, Int. J. Heat Mass Transfer 43 (2000) 1811e1822. [7] G. Yang, M. Choi, J.S. Lee, An experimental study of slot jet impingement cooling on concave surface: effects of nozzle configuration and curvature, Int. J. Heat Mass Transfer 42 (1999) 2199e2209. [8] H. Wei, D. Chiang, H.L. Li, Jet impingement and forced convection cooling experimental study in rotating turbine blades, in: Proceedings of the ASME Turbo Expo, 2009. GT2009-59795. [9] S.K. Hong, D.H. Lee, H.H. Cho, Effect of jet direction on heat/mass transfer of rotating impingement jet, Appl. Therm. Eng. 29 (2009) 2914e2920. [10] N. Kayansayan, S. Küçüka, Impingement cooling of a semi-cylindrical concave channel by confined slot-air-jet, Exp. Therm. Fluid Sci. 25 (2001) 383e396. [11] M.E. Taslim, L. Setayeshgar, S.D. Spring, An experimental evaluation of advanced leading edge impingement cooling concepts, ASME J. Turbomach. 123 (2001) 147e153. [12] M.E. Taslim, K. Bakhtari, H. Liu, Experimental and numerical investigation of impingement on a rib- roughened leading edge wall, ASME J. Turbomach. 125 (2003) 682e691. [13] M.E. Taslim, D. Bethka, Experimental and numerical impingement heat transfer in an airfoil leading-edge cooling channel with cross-flow, ASME J. Turbomach. 131 (2009) 011e021. [14] N. Souris, H. Liakos, M. Founti, Impinging jet cooling on concave surfaces, AICHE J. 50 (2004) 1672e1683. [15] M. Frageau, F. Saeed, I. Paraschivoiu, Numerical heat transfer correlation for array of hot-air jets impinging on 3-dimensional concave surface, J. Aircr. 42 (2005) 665e670. [16] B.V.N.R. Kumar, B.V.S.S.S. Prasad, Computational flow and heat transfer of a row of circular jets impinging on a concave surface, Heat Mass Transfer 4 (2008) 667e678.
[17] M.A.R. Sharif, K.K. Mothe, Parametric study of turbulent slot-jet impingement heat transfer from concave cylindrical surfaces, Int. J. Therm. Sci. 49 (2010) 428e442. [18] Z. Liu, Z.P. Feng, L.M. Song, Numerical study of flow and heat transfer of impingement cooling on model of turbine blade leading edge, in: ASME Turbo Expo, 2010. GT2010-23711. [19] Z. Liu, Z.P. Feng, Numerical simulation on the effect of jet nozzle position on impingement cooling of gas turbine blade leading edge, Int. J. Heat Mass Transfer 54 (2011) 4949e4959. [20] M.G. Ghorab, Film cooling effectiveness and heat transfer analysis of a hybrid scheme with different outlet configurations, Appl. Therm. Eng. 63 (2014) 200e217. [21] C.S. Yang, C.L. Lin, C. Gau, Film cooling performance and heat transfer over an inclined film-cooled surface at different convergent angles with respect to highly turbulent mainstream, Appl. Therm. Eng. 29 (2009) 167e177. [22] Y. Zheng, I. Hassan, Experimental flow field investigations of a film cooling hole featuring an orifice, Appl. Therm. Eng. 62 (2014) 766e776. [23] X. Liu, Z. Tao, S. Ding, G. Xu, Experimental investigation of heat transfer characteristics in a variable cross-sectioned two-pass channel with combined film cooling holes and inclined ribs, Appl. Therm. Eng. 50 (2013) 1186e1193. [24] B.R. Hollworth, L. Dagan, Arrays of impingement jets with spent fluid removal through vent holes on the target surface, part I: average heat transfer, J. Eng. Power 102 (1980) 994e999. [25] S.V. Ekkad, Y. Huang, J.C. Han, Impingement heat transfer on a target plate with film holes, J. Thermophys. Heat Transfer 13 (1999) 522e528. [26] D.E. Metzger, R.S. Bunker, Local heat transfer in internally cooled turbine airfoil leading edge regions: part II e impingement cooling with film coolant extraction, ASME J. Turbomach. 112 (1990) 459e466. [27] M.E. Taslim, Y. Pan, S.D. Spring, An experimental study of impingement on roughened airfoil leading-edge walls with film holes, ASME J. Turbomach. 123 (2001) 766e773. [28] M.E. Taslim, Y. Pan, K. Bakhtari, Experimental racetrack shaped jet impingement on roughened leading edge wall with film holes, in: ASME Turbo Expo, 2002. GT2002-30477. [29] M.E. Taslim, A. Khanicheh, Experimental and numerical study of impingement on an airfoil leading edge with and without showerhead and gill film holes, ASME J. Turbomach. 128 (2006) 310e320. [30] B.D. Mouzon, E.J. Terrel, J.E. Albert, D.G. Bogard, Net heat flux reduction and overall effectiveness for a turbine blade leading edge, in: ASME Turbo Expo, 2005. GT2005-69002. [31] S. Ravelli, L. Dobrowolski, D.G. Bogard, Evaluating the effects of internal impingement cooling on a film cooled turbine blade leading edge, in: ASME Turbo Expo, 2010. GT2010-23002. [32] J. Maikell, D.B. Bogard, J. Piggush, A. Kohli, Experimental simulation of a film cooled turbine blade leading edge including thermal barrier coating effects, ASME J. Turbomach. 133 (2011). No. 011014. [33] S. Mathew, S. Ravelli, D.G. Bogard, Evaluation of CFD predictions using thermal field measurements on a simulated film cooled turbine blade leading edge, ASME J. Turbomach. 135 (2013). No. 011021. [34] P.J. Roache, Perspective: a method for uniform reporting of grid refinement studies, J. Fluids Eng. 116 (1994) 405e413.
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Numerical simulation on impingement and film composite cooling of blade leading edge model for gas turbine Zhao Liu, Lv Ye, Changyee Wang, Zhenping Feng* Institute of Turbomachinery, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, PR China
h i g h l i g h t s The performances of different turbulence model are validated. Effects of blowing ratio and spanwise angle on composite cooling are investigated. Spanwise angle is more effective to improve film cooling than impingement cooling. Proper blowing ratio and lower spanwise angle is suitable for cooling design.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 January 2014 Received in revised form 28 April 2014 Accepted 7 May 2014 Available online xxx
In this paper numerical simulation is performed to simulate the impingement and film composite cooling on blade leading edge region. The relative performances of turbulence models are compared with available experimental data, and the results show that SST keu model is the best one based on simulation accuracy. Then the SST keu model is adopted for the simulation. The grid independence study is also carried out by using the Richardson extrapolation method. A single array of circle jets and three rows of film holes are arranged to investigate the impingement and film composite cooling. Five different blowing ratios and five different film hole spanwise angles are studied in detail. The results indicate that the heat transfer coefficient on the internal surface of turbine blade leading edge increases with the blowing ratio, and slightly changes with film hole spanwise angle. And the external film cooling effectiveness distribution would vary rapidly with the blowing ratio and the film hole spanwise angle. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Blade leading edge Impingement cooling Film cooling Composite cooling
1. Introduction In order to enhance the turbine efficiency and power, modern gas turbine systems are required to operate at higher and higher temperature, and thus turbine components are suffering an increasing heat loads. As a result, turbine inlet temperature has already been far beyond the material acceptable level. It is worth to mention that the leading edge area of gas turbine blade will have a higher heat flows as it is upwind to high temperature inflows. A series of cooling technologies such as impingement cooling, film cooling and other forced convection heat transfer methods have been applied to the turbine blade leading edge, among which impingement cooling is one of the most effective internal cooling methods but its arrangement would weaken the blade structure strength [1], and also film cooling is the only method for external
* Corresponding author. Tel.: þ86 29 82663195; fax: þ86 29 82668704. E-mail address: [email protected] (Z. Feng).
cooling. Thus impingement and film composite cooling are used extensively in gas turbine blades in recent years. Two decades ago, experiment was the only way to obtain detailed and reliable heat transfer information about the turbulent, 3-dimensional flows in the complex impinging cooling flows. The early investigation on concave surface impingement cooling has been summarized by Chupp et al. [2], Metzger et al. [3,4], and then Bunker and Metzger [5] continued their works in 1990 to suit the need of turbine cooling design. The cooling performance are influenced by many parameters, such as, Reynolds number [2,3,5,6], jet spacing [2,4,6], the distance between jet exit and target surface [2,5,6], target surface shape [4,5], jet nozzle shape [7], rotation [8], jet direction [9] and so on. The first numerical investigation was conducted by Kayansayan and Küçüka [10], and then many works compared the numerical results with experimental data [10e19]. Further studies on the influence factors were continued, such as wall roughness [11], horseshoe ribs [12], cross flow and exit flow schemes [13], curvature target surface [18], and the arrangement of jet nozzle [19]. And some of them deduced dimensionless correlations between the
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Please cite this article in press as: Z. Liu, et al., Numerical simulation on impingement and film composite cooling of blade leading edge model for gas turbine, Applied Thermal Engineering (2014), http://dx.doi.org/10.1016/j.applthermaleng.2014.05.060
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Z. Liu et al. / Applied Thermal Engineering xxx (2014) 1e12
Nomenclature B C D H h I L M Nu P q r* Re S V T Y yþ
width of equivalent slot jet used in Ref. [5] [mm] hole spacing of each row [mm] diameter [mm] jet from target surface [mm] heat transfer coefficient [W/(m2 K)] turbulent intensity length of flat portion [mm] average blowing ratio Nusselt number pressure [Pa] heat flux [W/m2] ratio of curvature radius to of semi-cylindrical airfoil radius used in Ref. [5] Reynolds number streamwise coordinate [mm] velocity [m/s] temperature [K] transverse coordinates from wall (m) non-dimensional distance, ¼Yut/n
r a b g l ut
n
density [kg/m3] angle of the second row of film holes from the stagnation line [ ] angle of film holes from the surface in spanwise [ ] attack angle of main flow [ ] thermal conductivity of fluid [W/(m K)] shear velocity [m/s] kinematic viscosity [m2/s]
subscripts av average aw adiabatic wall c coolant f film hole i inlet ip impingement hole sp spanwise average w wall o outlet x, y, z the direction of the vector ∞ mainstream 1,2 film hole number
Greek symbols h cooling effectiveness
average or the maximum Nusselt number and the influence parameters [15,19]. Concern on film cooling, most work focus on the effect of film hole exit shape and geometry [20e22], effect of film cooling combined with inclined ribs [23] and so forth. All papers cited above are about the investigation on new shape film holes, or the effect of jet parameters on impingement cooling without film coolant extraction. The addition of film cooling is expected to affect the heat transfer in the internal region of the impingement cooling since it changes the flow path of the coolant and reduces the cross flow. Only few of pervious work focused on impingement/film composite cooling. The first work was done by Hollworth and Dagan in 1980 [24], and also Ekkad et al. [25] investigated impingement cooling with film coolant extraction on a plate. Then Metzger and Bunker [26] experimentally studied impingement cooling of concave surface through lines of circular air jets with and without film coolant extraction. Taslim et al. [27,28], and Taslim and Khanicheh [29] investigated heat transfer of impingement cooling on concave surface with film holes under the influence of roughness target wall, jet nozzle geometry, showerhead and gill film holes. Mouzon et al. [30], Ravelli et al. [31], Maikell et al. [32] and Mathew et al. [33] investigated the effect of internal impingement on film cooling of blade leading edge model. Obviously, the previous work focused on the influence of film extraction on impingement cooling or the effect of flow condition on external film cooling. But almost no attentions were paid to the effects of film hole geometries on the internal heat transfer and the external film cooling effectiveness. In this study, the flow structure and heat transfer of the impingement and film composite cooling on turbine leading edge model are studied, and the effects of blowing ratio and spanwise angle of film holes are investigated. 2. Physical and mathematical model 2.1. Geometrical details This numerical study adopted the blade leading edge model which was used in the experimental study of Maikell et al. [32] and
the computational study of Mathew et al. [33]. Fig. 1 shows the leading edge model geometry structure. The film cooling configuration included three rows of holes positioned staggered along the stagnation line and at ±25 from the stagnation line, the impingement jets were directed to impact the internal surface in each stagnation film hole. The geometrical dimensions of different jet configurations are listed in Table 1. 2.2. Numerical method 2.2.1. Boundary conditions and solution procedure The boundary conditions are matched with those in Ref. [32]. As shown in Fig.1(b), periodic and symmetry conditions were applied to minimize the computational effort. The mainstream inlet air total temperature is 300 K; the velocity is 15 m/s and the inlet turbulent intensity I is 5%, and its definition can be found in Equation (1). The coolant inlet total temperature is 200 K, and the inlet turbulent intensity is 5% as well. The average static pressure at the outlet is 0.106 MPa. The impingement target wall temperature is 235 K, other walls are adiabatic and nonslip. The fluid is nitrogen (ideal gas). The convergence of simulation is achieved when the root mean square residuals of the momentum equations, mass equation, energy equation and turbulent equations are lower than 105 and remain steady.
I¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Vx2 þ Vy2 þ Vz2 Vav
(1)
2.2.2. Mesh procedure The numerical simulations are performed by using a commercial CFD software CFX11.0. The solutions are obtained by solving the steady compressible Reynolds averaged NaviereStokes equations, in which the finite control volume method is applied to discretize these equations, and a second order form with high
Please cite this article in press as: Z. Liu, et al., Numerical simulation on impingement and film composite cooling of blade leading edge model for gas turbine, Applied Thermal Engineering (2014), http://dx.doi.org/10.1016/j.applthermaleng.2014.05.060
Z. Liu et al. / Applied Thermal Engineering xxx (2014) 1e12
3
Fig. 2. Computational mesh (cross section).
Fig. 1. Schematic of the model and boundary condition. Fig. 3. Comparison of numerical results with available experimental data.
Table 1 Geometric detail of jet configurations. Dimension
Values
C (mm) Df (mm) Di (mm) Dip (mm) Do (mm) L (mm) a ( ) b ( )
24.20 3.18 25.40 5.00 50.80 10.90 25.00 20.00
Table 2 Average Nusselt number on impingement target surface. Node number (million)
Impingement cooling
Film cooling
Average Nu
Relative error
Average h
Relative error
0.91 1.59 2.03 3.16 Extrapolation
10.59 10.14 10.02 10.00 9.94
6.52% 2.01% 0.80% 0.60% e
0.1484 0.1500 0.1509 0.1512 0.1521
2.43% 1.38% 0.79% 0.59% e
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Z. Liu et al. / Applied Thermal Engineering xxx (2014) 1e12
Table 3 Mass flow rate and average blowing ratio through each film hole in different M. M
m1 (%)
M1av
m2 (%)
M2av
1.0 1.5 2.0 2.5 3.5
22.53 23.67 24.11 24.34 24.68
0.6777 1.068 1.450 1.830 2.598
77.47 76.33 75.89 75.66 75.32
1.164 1.722 2.283 2.845 3.964
resolution correction is used to discretize the convection term in this paper. The overall accuracy of the calculation is of the second order. The software Gambit 2.3.16 is adopted to generate the unstructured grids for the calculation domains. The mesh includes tetrahedral elements in the main flow passage and prism elements in the near wall regions, the jet nozzle, film hole and the grid nodes in and around its downstream are also refined. The low-Reynolds
number keu turbulence model would require at least yþ < 2. In this investigation, for standard keu turbulence model and SST keu turbulence model, the wall grid yþ is less than 1.0; more than 15 cells are put into the boundary layer; and the total grid nodes number is about 2.03 million. But for standard keε model and RNG keε model, the wall grid yþ is in the range between 20 and 100, and the total grid nodes number is about 1.91 million. The ratio of cell size increases by about 30% outward from the walls in all cases. Fig. 2 shows the grid generation result. The grid size definition for the identical parts of other cases is the same. As a result, the total grid node is changed with the geometry of the jet nozzle and the film holes. 2.2.3. Comparisons with available experimental data In order to validate the ability of the different turbulence models to represent flow and heat transfer of the present work, first calculation of an experimental case investigated by Bunker and
Fig. 4. Streamlines and contours of velocity magnitude on horizontal cross-sections at the center of film hole No.1 and No.2 in different M.
Fig. 5. Relative velocity magnitude on tangential section of film hole No.1 outlet in different M.
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Z. Liu et al. / Applied Thermal Engineering xxx (2014) 1e12
Metzger [5] is adopted as model verification for impingement cooling in this paper. Detailed geometry can be found in Ref. [5]. The case with H/B ¼ 24, r* ¼ 1.0, Re ¼ 6750 and C/Dip ¼ 4.67 is considered as a comparison. Calculations are carried out with three turbulence models, the RNG keε model, the standard keu model and the SST keu model. Fig. 3(a) shows the comparison between the predicted and the available measured results including the spanwise area weighted average Nusselt number along the target plate, and the model validation results by Kumar et al. [16]. The results demonstrated that the SST keu model is the best one based on the simulation accuracy, and the maximum relative error is 13.58%. For a constant temperature surface, the local heat transfer coefficient can be expressed as
h¼
qw Tw Tc
5
(2)
and the value of h can be normalized in the form of local Nusselt number as
Nu ¼
hDf qw $Df ¼ l ðTw Tc Þl
(3)
Then, a calculation of an experimental case investigated by Maikell et al. [32] is adopted as model verification for film cooling in the impingement and film composite cooling. Geometry is provided in Fig. 1. The case with blowing ratio M ¼ 1.0 is considered as a
Fig. 6. Relative velocity magnitude on tangential section of film hole No.2 outlet in different M.
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Z. Liu et al. / Applied Thermal Engineering xxx (2014) 1e12
h¼
T∞ Taw T∞ Tc
(4)
Fig. 3(b) shows the comparison of the predicted spanwise averaged film cooling effectiveness with the available measured results along the leading edge model. The results demonstrated that the SST keu model is the best, and its mean relative error is 5.85%. Since the relative error predicted by the SST keu model are the minimum one among the models both in the impingement cooling case and in the film cooling with impingement case, all the following results reported are based on SST keu model.
Fig. 7. Sketch of tangential section of film hole No.2 outlet.
comparison. Calculations are carried out with four turbulence models, the standard keε model, the RNG keε model, the standard keu model and the SST keu model. For an adiabatic surface, the local film cooling effectiveness can be expressed as
2.2.4. Grid independence analysis Four different meshes with the grid node number of 0.91 million, 1.59 million, 2.03 million and 3.16 million were used to validate the grid independence. The mesh refinement has been synchronously imposed on every mesh in three coordinate directions. The SST keu turbulence model is employed, the wall yþ is less than 1.0 and more than 15 cells were put into the boundary layer in all of the cases. The case with M ¼ 1.0 is adopted for grid independence test.
Fig. 8. Nu contours of the target surface in different M.
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Z. Liu et al. / Applied Thermal Engineering xxx (2014) 1e12
The area weighted average Nusselt numbers on the leading edge internal surface and the area weighted average film cooling effectiveness on the leading edge external surface obtained through the different meshes are demonstrated in Table 2. The extrapolation value was calculated by means of the Richardson extrapolation method [34] with the results of 2.03 million nodes and 3.16 million nodes. A second order format with high resolution correction is applied to discretize the convection term in this paper. Therefore, based on the Roache's investigation, the average Nusselt number from the Richardson extrapolation has a fourth order accuracy. Provided that these Nusselt number and cooling effectiveness are baseline solution, we can conclude that when the grid node number is larger than 2.03 million, the increasing node number has little effect on the value of error. In order to balance the calculation accuracy and the simulation time, about 2.03 million nodes were employed in the present numerical study with geometry showed in Table 1, and the same grid size definition was generated for the identical parts of other cases. 3. Results and discussions The blowing ratio and film hole structure have a significant effect on the flow pattern of the film cooling, and would affect the
7
flow of the internal impingement cooling, so they are critical to the flow and heat transfer of the impingement and film composite cooling. In order to study these effects, numerical simulations are carried out at five different M (blowing ratio): 1.0, 1.5, 2.0, 2.5, 3.5; and five different b (Angle of film holes from the surface in spanwise, the definition of b is showed in Fig. 1): 20 , 30 , 40 , 50 and 70 . For a convenient analysis, it is suggested that the film hole positioned along the stagnation line will be numbered No.1, and the other numbered No.2. 3.1. Effect of blowing ratio In order to investigate the effects of M on the impingement and film composite cooling of turbine leading edge, a numerical simulation was performed under the conditions of five different M, 1.0, 1.5, 2.0, 2.5, and 3.5 at b ¼ 20 , g ¼ 0.0 . And a detailed analysis was made for the calculation of four M: 1.5, 2.0, 2.5, and 3.5. Table 3 indicates the percent of mass flow rate and average blowing ratio of film hole No.1 and film hole No.2 in different M. It can be observed that the mass flow rate and average blowing ratio of film hole No.2 are consistently above those of film hole No.1. It is possibly because of the farther location of film hole No.1 than that
Fig. 9. Film cooling effectiveness contours in different M.
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Z. Liu et al. / Applied Thermal Engineering xxx (2014) 1e12
increases; more coolant will jet into the main stream and the low velocity area in downstream just below the film hole reduces. 3.1.2. Heat transfer Fig. 8 shows the Nusselt number contours of the internal impingement target surface in different M. The Nu at the sharp corner of the film hole inlet side and on the jet stagnation region is the largest, since the flow boundary is the thinnest and the turbulence intensity is the largest in these regions. And the Nu at the
Fig. 10. Spanwise averaged film cooling effectiveness in different M.
of film hole No.2, the effect of the crossflow caused by neighbor impinging jets, and the suppression of the main stream. With the increase of blowing ratio, the relative mass flow ratio in film hole No.1 increases slightly, while the relative flow ratio in film hole No.2 reduces. This may be caused by the variation of the flow resistance of the two film holes. 3.1.1. Flow fields Fig. 4 shows the streamlines and contours of velocity magnitude on horizontal cross-sections at the center of film holes No.1 (right one of each figure) and No.2 (left one of each figure) in different M. There are two typical vortexes of impingement on both sides of the impingement in the cross-section. This vortex makes both sides of the stagnation region be scoured by the coolant jet. And a smallscale vortex generates at the corner of film hole No.2. There is an ejection from the target surface at the middle on horizontal crosssections at the center of film hole No.1, which is caused by the encounter of the crossflow of adjacent impinging jets. With the increase of M, the jet velocity, the range and strength of the typical vortex of impingement, and the eject velocity at the confluence increase. Fig. 5 presents the velocity magnitude on tangential section of film hole No.1 outlet in different M. The left side is the upside of the film hole. From these figures, it can be seen that the velocity in the upside of film hole No.1 is larger, while in the downside is lower. And the velocity increases with the increase of M. Fig. 6 presents the velocity magnitude on tangential section of film hole No.2 outlet in different M. The bottom side is the downstream of the main flow, and the left side is the upside of the film hole, as shown in Fig. 7. From these figures, it can be found that the velocity in down-left side of film hole No.2 is larger, while the opposite is lower. This may be caused by the sharp corner at the film hole inlet and the impact of the main stream. With the increase of M, the maximum velocity in the down-left side of film hole No.2 Table 4 Mass flow rate and average blowing ratio through each film hole in different b.
b
m1(%)
M1av
m2(%)
M2av
20 30 40 50 70
22.53 22.51 22.40 22.14 21.19
0.6777 0.6770 0.6737 0.6659 0.6372
77.47 77.49 77.60 77.86 78.81
1.164 1.165 1.167 1.171 1.185
Fig. 11. Streamlines and contours of velocity magnitude on horizontal cross-sections at the center of film hole No.1 and No.2 in different b.
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Z. Liu et al. / Applied Thermal Engineering xxx (2014) 1e12
confluence of the crossflows where a second injection occurred is also larger than the others. But low Nu regions appear on both sides, because of the ejection from the target wall on both sides of the confluence, and the deceleration of the coolant before the ejection. And the Nu at the both sides of the target surface which are scoured by the typical vortex of impingement is also larger, while the Nu at the corner of target surface and impingement surface is the lowest. With the increase of M, since the impingement velocity increases, both the maximal Nu and the high Nu region area on the target surface become larger. Fig. 9 shows the film cooling effectiveness contours of the leading edge surface in different M, with the results in two periods and on the symmetric surface. The high cooling effectiveness area around the film hole caused by cooling jet is clearly shown in Fig. 9. At b ¼ 20 , the spanwise component of the coolant film momentum is larger than the radial component, and with the suppression of the main flow, the coolant film will flow along the leading edge wall, so there is a large high h region on the leading edge. But there is a low cooling effectiveness region at part of the neighbor cooling holes in the same row, since the coolant film could not cover this area. And for the better wall attachment performance, the coolant from film hole No.1 could form more effective cooling film, and lead a larger range of high film cooling effective area than that of coolant from hole No.2. With the increase of M, the area of the highest h decreases, especially for the highest h region of film hole No.1, which reduces quickly and becomes far away from film hole. This is because the coolant film's momentum increases with M, and that will weaken
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the suppression of the main stream, and more coolant flowing into the mainstream, mixing with the mainstream instead of flow along the wall. Since the total coolant increases with M, the relative high h region increases, particularly the relative high h region covered by film hole No.1. Fig. 10 indicates the spanwise averaged film cooling effectiveness of the leading edge in different M. It can be found that the hsp (spanwise averaged film cooling effectiveness) increases with M in the front of film hole No.2 (0.5 S/Df 3), and there is a best value of M in the region behind film hole No.2 (S/Df 4). That is because with the increase of M, the coolant flow from film hole No.1 and its spanwise component momentum increases; the region covered by the coolant from film hole No.1 increases; and the high h area will make a transition between adjacent film hole though the peak value of h reduces. But behind film hole No.2, the high h area also increases with M when M 2.5, but most coolant from film hole No.2 will jet into the main stream while M is too large (M > 2.5), so the hsp increases first and then decreases. And the hsp will decrease rapidly in the range 4 S/Df 12 when M ¼ 3.5. One reason for this could be that the large momentum of coolant impinges to the main flow, the detachment of the cooling film from the surface lead a worse film cover in this area, as shown in Fig. 9. 3.2. Effect of spanwise angle In order to investigate the effects of spanwise angle of film hole (angle b) on the impingement and film composite cooling of turbine leading edge, a detailed analysis was performed under the
Fig. 12. Relative velocity magnitude on tangential section of film hole No.2 outlet in different b.
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conditions of five different b, that is 20 , 30 , 40 , 50 , and 70 at M ¼ 1. Also a detailed analysis was made for the calculation of four b: 30 , 40 , 50 , and 70 . Table 4 presents the percent of mass flow rate and average blowing ratio of film hole No.1 and film hole No.2 in different b. It can be observed that the mass flow rate and average blowing ratio of film hole No.2 are consistently above those of film hole No.1. That is the same with the above cases. The mass flow rate of the two rows of film holes slightly varies with b. It can be concluded that the angle b has low impact on the mass flow distribution of the two rows of film holes. 3.2.1. Flow fields Fig. 11 shows the streamlines and contours of velocity magnitude on horizontal cross-sections at the center of film hole No.1 and No.2. With the increase of b, the range of the typical vortex of impingement increases; the typical vortex core on hole No.1 section move to impingement surface; and the film hole inlet velocity on horizontal cross-section increases. Fig. 12 presents the velocity magnitude on tangential section of film hole No.2 outlet in different b, in which the bottom side is the downstream of the main flow, and the left side is the upside of the film hole, as shown in Fig.7. From these figures, it can be found that
with the increase of b, the maximum velocity in the down-left side of film hole No.2 increases; the low velocity region area caused by the interaction of film coolant and main flow decreases; the distance of film coolant impinging to main flow extends; and its position moves to the left.
3.2.2. Heat transfer Fig. 13 shows the Nusselt number contours of the internal impingement target surface in different b. With the increase of b, since the typical vortex core on hole No.1 section moves to the impingement surface, and the film hole inlet velocity on horizontal cross-section increases, Nu at the film holes inlet corner increases, and low Nu region area increases. Fig. 14 shows the film cooling effectiveness contours of the leading edge surface in different b, with the results in two periods and on the symmetric surface. With the increase of b, spanwise component of the coolant film momentum decreases, and the radial component increases, that leads to weaker suppression of the main flow and worse wall attachment performance of the coolant. Therefore, the area uncovered by the coolant film increases, and the maximum h and the high h region area decreases with the increase in b.
Fig. 13. Nu contours of the target surface in different b.
Please cite this article in press as: Z. Liu, et al., Numerical simulation on impingement and film composite cooling of blade leading edge model for gas turbine, Applied Thermal Engineering (2014), http://dx.doi.org/10.1016/j.applthermaleng.2014.05.060
Z. Liu et al. / Applied Thermal Engineering xxx (2014) 1e12
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Fig. 14. Film cooling effectiveness contours in different b.
Fig. 15 indicates the spanwise averaged film cooling effectiveness of the leading edge in different b. It can be found that the hsp reduces with the increase of b for S/Df < 8, especially when b ¼ 70 . While b ¼ 70 , most of the coolant jet into the mainstream and only few of them flow close to the wall. The reattachment of the coolant on the leading edge surface caused by the suppression of the main flow results in a lower peak value of hsp near S/Df ¼ 13. 4. Conclusions In this paper we proposed a numerical study on the impingement and film composite cooling of turbine blade leading edge model, the blowing ratio and the film hole spanwise angle are considered to enhance the heat transfer. Based on the numerical simulation results, it can be concluded that the SST keu model is the best for the numerical study of the impingement and film composite cooling in view of its simulation accuracy. With the increases of the blowing ratio, the Nusselt numbers on the internal target wall increases monotonously, but there is a best value for the cooling effectiveness on the external leading surface. With the increase of b, the Nu on the internal target surface hardly changes, but h on the leading edge external surface decreases rapidly. Proper blowing ratio (2.5 in this study), and lower spanwise angle is desirable to improve the performance of impingement cooling on the turbine leading edge.
Fig. 15. Spanwise averaged film cooling effectiveness in different b.
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Please cite this article in press as: Z. Liu, et al., Numerical simulation on impingement and film composite cooling of blade leading edge model for gas turbine, Applied Thermal Engineering (2014), http://dx.doi.org/10.1016/j.applthermaleng.2014.05.060