Effect of ejection angle and blowing ratio on heat transfer and film cooling effect on a winglet tip

International Journal of Heat and Mass Transfer 125 (2018) 357–374

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Effect of ejection angle and blowing ratio on heat transfer and film cooling effect on a winglet tip Xin Yan a,⇑, Yan Huang a, Kun He b a b

Institute of Turbomachinery, Xi’an Jiaotong University, Xi’an 710049, China MOE Key Laboratory of Thermo-Fluid Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China

a r t i c l e

i n f o

Article history: Received 2 November 2017 Received in revised form 5 April 2018 Accepted 19 April 2018

Keywords: Winglet tip Heat transfer Film cooling Ejection angle Blowing ratio

a b s t r a c t Effects of ejection angle and blowing ratio on heat transfer and film cooling effect on a winglet tip were numerically investigated with the RANS (Reynolds Averaged Navier-Stokes) equations solutions. The total pressure loss in cascade, and heat transfer coefficient and film cooling effectiveness on the winglet tip with both tip and pressure side holes were computed at a range of pitchwise ejection angles and streamwise ejection angles. At three blowing ratios (M = 0.5, 1.0, 2.0), the sensitivity of heat transfer coefficient and film cooling effectiveness distributions on winglet tip to the variation of blowing ratio was also investigated. The results indicate that the heat transfer coefficient and film cooling effectiveness on the winglet tip are much sensitive to the pitchwise and streamwise ejection angles and blowing ratio. A better heat transfer and film cooling effect on the winglet tip can be achieved as the pitchwise ejection angle is less than 30° and streamwise ejection angle is around 120°. The heat transfer and film cooling effect on winglet tip is not sensitive to the pitchwise ejection angle if it is larger than 45°. If vertical ejection direction is chosen for the cooling flow, a small blowing ratio (M = 0.5 in this study) is beneficial for the reduction of disturbance to pass-over leakage. However, in the case of a small pitchwise ejection angle, a medium blowing ratio (M = 1.0 in this study) is profitable to gain a wider coolant coverage on the cavity floor in pitchwise direction. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction In gas turbine engines, clearance between blade tip and casing is required to allow inevitable thermal and rotating expansions of rotor blade [1–4]. However, due to the pressure gradient between tip pressure side and suction side, leakage flow is driven across the tip gap and then interacted with the mainstream, causing pronounced aerodynamic loss [5,6]. Moreover, the over-tip leakage flow makes the rotor tip expose to hot gas on all sides, causing notable thermal load on blade tip. In order to reduce the heat load in tip gap, two main strategies have been developed in the modern gas turbine engines. One such strategy would utilize efficient tip geometry to improve heat transfer characteristic near tip gap, for example, squealer tip, winglet tip, etc. The other strategy is to adopt a proper film cooling arrangement to reduce heat load on the tip. Evidences have shown that the effective film cooling arrangement is critical to protect tip region in high temperature environment [1].

⇑ Corresponding author. E-mail address: [email protected] (X. Yan). https://doi.org/10.1016/j.ijheatmasstransfer.2018.04.097 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.

For the winglet tip, it is believed that it has an effect of reducing leakage flow in tip gap if it is properly designed [7,8]. Up to present, many types of winglet tip have been developed to improve the aerodynamic performance of turbine blade, for example, the pressure side winglet [9], suction side winglet [10], full coverage of winglet [11–13], partial winglet [14], and even the winglet shroud tip [15], etc. The research issues for winglet tip cover the aerodynamic performance [7–19], heat transfer [20–25] and film cooling effect [26,27] in tip region. Beside these, the designs and optimizations of the winglet tip are also under active research in the opening publications [14,15,28,29]. To account for the improvement of winglet tip on aerodynamic performance in turbine blade, Yaras and Sjolander [8] measured the leakage loss in winglet tip. They found that the total pressure loss in cascade with winglet tip could be reduced by 10% compared with the flat tip. However, the experimental and numerical work carried out by Schabowski and Hodson [19] showed that the aerodynamic loss slope of a winglet-squealer tip configuration can be reduced by 22% in contrast to the flat tip. In the rotating test rig, Dey and Camci [16] measured the total pressure loss in a turbine stage with different winglet configurations. Their experiments indicated that, in contrast to the flat tip, the use of pressure-side

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Nomenclature C Cr h M P q T V x y+

blade axial chord length [m] clearance [m] local heat transfer coefficient [W/m2 K] blowing ratio [–] pressure [Pa] local heat flux [W/m2] temperature [K] velocity [m/s] axial direction dimensionless distance from the wall [–]

Greek symbols a streamwise ejection angle [°] b pitchwise ejection angle [°] g adiabatic film cooling effectiveness [–] n total pressure loss coefficient [–] q density [kg/m3]

winglet significantly affects the flow field in tip gap by weakening the leakage vortex. For the cascade with full coverage of winglet tip, Coull et al. [17,21] found that the rotor efficiency could be improved by 0.6% by varying the thickness of winglet compared with the flat tip. By adding a cavity on the winglet tip, the leakage loss can be reduced by about 45%. Cheon and Lee [11] carried out the experiments for a cascade configured with a full coverage of winglet. Their work showed that, if the winglet is designed with a proper value of width-to-pitch ratio, the total pressure loss in the cascade can be reduced by 5.8% compared with the conventional squealer tip. Ledezma et al. [7] compared the aerodynamic performance between the conventional squealer tip, squealer tip without pressure side rim, and squealer tip with pressure-side winglet. They found that the cascade with pressure-side winglet has a close aerodynamic performance with the conventional squealer tip. Zhang et al. [15] performed the aerodynamic optimizations of a cascade with partial winglet shroud tip. Their numerical results revealed that the mass-averaged total pressure loss in the cascade with optimized winglet tip can be reduced by 2.61% compared to the plain tip. Zhong and Zhou [18] carried out the experiments and CFD predictions to investigate the aerodynamic performance of a high-pressure turbine cascade with cavity-winglet tip. Their work indicated that the tip leakage loss in cavity-winglet tip can be reduced by 16.7%, 16.1% and 12.0% compared with the conventional squealer tip at three different gap sizes, respectively. However, the design of winglet tip does not only rely on aerodynamic considerations, heat transfer and film cooling on blade tip are also crucial to the designer. The representative experimental work carried out by Papa et al. [4] indicated that the pressure side winglet has an effect of reducing heat and mass transfer on tip cavity floor. Silva and Tomita [20] numerically investigated the aerodynamic and heat transfer performance in a turbine stage with flat, squealer and winglet tips. It showed that the efficiency of turbine stage with winglet tip can be improved by 0.3% compared to squealer tip. The tip geometry has a pronounced effect on the tip heat transfer coefficient distributions. Zhou et al. [10,18,22,23,26] carried out a series of numerical simulations to investigate the aero-thermal performance in a HP turbine winglet tip. The effects of endwall motion [22], cooling condition [26] and winglet geometries [10,18,23] on the aerodynamic performance and heat transfer in the tip gap were investigated in detail. O’Dowd et al. [24] experimentally and numerically investigated the aero-thermal perfor-

Superscripts area-averaged value

–

Subscripts aw adiabatic wall condition c coolant in inlet condition local local value m main flow t total value w wall 1 inflow condition Abbreviations M million P.S. pressure side S.S. suction side

mance in a transonic blade winglet tip. They found that the aerodynamic loss of the cooled winglet tip is lower than that in un-cooled configuration, and low film cooling effectiveness is occurred at the tip crown and pressure side trailing edge. Joo and Lee’s [12,13] experiments indicated that the discrepancy of heat/mass transfer rate between the cavity floor and winglet top surface decreases rapidly as the gap-to-span ratio increases for the full coverage winglet tip. Yan et al.’s [25,27] numerical studies show that the averaged heat transfer coefficient on the winglet tip without film cooling can be reduced by 15.8% and the total pressure loss in cascade can be reduced by 13.8% compared to the conventional squealer tip. For the cooled winglet tip, the averaged heat transfer coefficient on the winglet tip can be reduced by about 10% compared with the conventional squealer tip. This paper is an extension of the authors’ previous study [25,27], in which the authors have pointed out the heat transfer and film cooling effect on winglet tip are much sensitive to the blowing ratio and ejection angle compared with the conventional squealer tip. Therefore, the overall performance (aerodynamic, heat transfer and film cooling) in the winglet tip gap at a range of ejection angles and blowing ratios are investigated in this study. At first, the numerical methods, which are based on the previous studies [25,27], are described. Then, the effect of ejection angles (pitchwise ejection angle and streamwise ejection angle) variations on the heat transfer and film cooling effectiveness on winglet tip with two hole-arrays is discussed. Finally, by adopting three blowing ratios (low blowing ratio, medium blowing ratio and high blowing ratio), the flow patterns in the tip gap and heat transfer and film cooling effectiveness on the winglet tip with different ejection configurations are investigated. 2. Numerical methods In this paper, the squealer tip with pressure side winglet (P.S. winglet) is selected as the research objective. The geometrical model is the same with the authors’ previous studies [25,27]. The blade profile is taken from the GE-E3 rotor blade (first stage) tip section [30]. The geometrical dimensions of the blade are listed in Table 1. The geometrical dimensions of the winglet tip are shown in Fig. 1. The multi-block structured grids are generated with ANSYS ICEMCFD 11.0 (see Fig. 2). In the computational cases with pitchwise ejection angle b = 15°, the minimum orthogonalities of the

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X. Yan et al. / International Journal of Heat and Mass Transfer 125 (2018) 357–374 Table 1 Geometrical dimensions [32] Parameter

Value

Blade height Axial chord length Pitch Inlet flow angle Gap size Cavity depth Rim thickness Tip hole no. P.S. hole no. Cooling hole diameter

122 mm 86.1 mm 91.5 mm 32° 1.31 mm 5.08 mm 2.29 mm 13 13 1.27 mm

considered to be converged. The detailed validations of the present numerical methods with experimental data can be referred in the authors’ previous work [25,27]. The boundary condition settings in the present numerical simulations are in accordance with the experimental tests [32]. At the blade inlet, total pressure and total temperature are specified to be 126.9 kPa and 340 K, respectively, and the turbulence intensity is set to 9.7% and turbulence length scale is set to 0.015 m. At the blade outlet, static pressure is specified to be 102.7 kPa. For the cooling flow, the inlet total temperature is set to 328 K and turbulence intensity is 5%, and the coolant mass flow rate is set depending on the blowing ratio. In the heat transfer coefficient computations, a constant temperature (340 K) wall boundary is applied on the blade surfaces (including the tip) to comply with the experiments [32]. The other walls, such as the blade shroud and hub, cooling holes, are set to be adiabatic. To compute the adiabatic film cooling effectiveness on the blade tip, all walls are assumed to be adiabatic. The detailed boundary condition settings in CFD predictions are listed in Table 2. In the present study, the bowing ratio M is defined as

M¼

Fig. 1. Geometrical dimensions for winglet tip.

mesh are controlled above 15°. In other cases, the minimum angles are larger than 28°. For all cases, y +< 1 is ensured for all wall adjacent cell rows to resolve the heat transfer and flow boundary layers. The detailed mesh generation and mesh independency analysis have already been described in the authors’ previous research [25,27]. In the present study, the computational grid number for each case is about 12.1 million. In this study, RANS (Reynolds Averaged Navier-Stokes) equations are solved with the commercial CFD software ANSYS CFX11.0. A high resolution scheme is adopted for the spatial discretization [31]. To simulate the turbulence effect, the k-x turbulence model is selected based on the previous validations of different turbulence models [25,27]. As the root mean square residuals for continuity equation, momentum equations and heat transfer equation are at the level 105, and the root mean square residuals for turbulence equations reach 106, the solutions are

_ c =Sc qc V c m ¼ qm V m m_ m =Sm

ð1Þ

where qc and qm are the densities for coolant flow and main flow at inlet boundaries, respectively. V c and V m are the velocities for the _c coolant flow and main flow at inlet boundaries, respectively. m _ m are the mass flow rates for each coolant hole and main flow and m path (one period), respectively. Sc and Sm are the areas for each coolant hole and main flow path (one period) at inlets, respectively. The local heat transfer coefficient h is computed by

h¼

q T w  T m;1

ð2Þ

where q is the local heat flux on the wall. Tw is the wall temperature. T m;1 is the inlet total temperature of the mainstream. The adiabatic film cooling effectiveness g is computed by

g¼

T aw  T m;1 T c;1  T m;1

ð3Þ

where Taw is the temperature on adiabatic wall surface. T m;1 and T c;1 are the inlet total temperatures of the mainstream and coolant, respectively. In this paper, Greitzer et al.’s [33] method was adopted to calculate the total pressure loss n in the cascade with film cooling. To evaluate the mixing effect of coolants and mainstream, a reference stagnation pressure Pt;ref is introduced to take the coolant total pressure into account. Assuming the flow mixes to the uniform conditions at constant area (this cutplane is located downstream the trailing edge by 10 mm) without external forces, n is defined as

n¼

Pt;ref  Pt;local Pt;ref  Ps;local

ð4Þ

Table 2 Boundary settings in CFD predictions. Boundary

Property

Value

Main flow inlet

Total temperature (K) Total pressure (kPa) Turbulence intensity (%) Turbulence length scale (m) Mass flow rate (kg/s) Total temperature (K) Turbulence intensity (%) Static pressure (kPa) Temperature (K) Adiabatic

297 126.9 9.7 0.015 0.000135 (M = 1) 328 5 102.7 340 or adiabatic –

Coolant flow inlet

Fig. 2. Schematic view of computational meshes for winglet tip.

Outlet Blade wall Hub and shroud

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where

Pt;ref ¼

r Xn

_ c  Pc;t;in Þi ðm Xni¼1 _ c Þi _mþ ðm m i¼1

_ m  Pm;t;in þ m

ð5Þ

_ c and m _ m are the mass flow rates for the coolant and mainstream, m respectively. n is the cooling-hole number. P m;t;in and Pc;t;in are the inlet total pressures (mass-flow averaged values) of the mainstream and coolant, respectively.

k γ

β

tip hole

j α

O

P.S. hole i Line L

3. Results and discussion Fig. 3 illustrates the definitions of ejection angles. For the hole O, the base coordinate is defined by i-j-k, where i is tangential to line L and on the cavity floor, and j is perpendicular to line L and also on the tip cavity floor. The angles between the ejection vector ! r and i, j, k are defined by a, b, and c, respectively. To define the ! coolant ejection vector r , two ejection angles a and b are essential. For the baseline case, ejection angles for all holes are set to be (a, b) = (90°, 90°). 3.1. Effect of ejection angle b Firstly, the ejection angles for all tip holes are kept at (a, b) = (90°, 90°), but a is kept at 90° and b is varied from 90° to 15° for the pressure side holes. Fig. 4 illustrates the three-dimensional streamlines in the tip gaps with different b for P.S. holes. It is seen that the tip leakage (green lines)1 directly flows across the winglet tip gap, forming a large scale of leakage vortex near the suction side. For the coolant from pressure side and tip holes, it is quickly blown towards the suction side rim after ejection due to the pressure difference between tip pressure side and suction side. In Fig. 4(f), it is observed that most of the pressure side coolant is attached onto the cavity floor near pressure side, and then flowing out of the cavity through the trailing edge cutback due to the pressure gradient between the leading edge and trailing edge. Since most of the pressure side coolant is deflected towards the trailing edge and accumulated there, the film cooling effect on the cavity floor near trailing edge will be enhanced, correspondingly (see Fig. 5(f)). Fig. 5 shows the heat transfer coefficient and film cooling effectiveness distributions on the winglet tip with a range of b for P.S. cooling holes. For b = 90° in Fig. 5(a), it is observed that low heat transfer areas are occurred on the cavity floor near S.S. rim and P.S. holes. Since the cooling flow is perpendicular to the cavity floor for the case of b = 90°, the cooling film is just attached onto the cavity floor near cooling holes (see the high film cooling effectiveness in Fig. 5(a)), which can also be observed by the cooling trajectories on the cavity floor. As b decreases to 60°, distributions of heat transfer coefficients and film cooling effectiveness on the cavity floor almost exhibit the similar trend with b = 90° case. As b keeps on decreasing to 45°, it is seen that the cooling effect on the rear part of winglet is enhanced. As b of pressure side holes is further decreased, the cooling flow from the pressure side holes provides excellent cooling effect on the whole winglet, especially for the case of b = 15°. It is interesting to note that, as b of the pressure side holes varies, it has little influence on the heat transfer and film cooling effect on cavity floor near suction side, where is mainly cooled by the coolant from tip holes. In general, a better film cooling effect on the cavity floor near pressure side can be achieved as b of P.S. cooling holes decreases below 30°. 1 For interpretation of color in Figs. 4, 6 and 20, the reader is referred to the web version of this article.

Fig. 3. Definitions of ejection direction.

Fig. 6 plots the pitch-averaged heat transfer and film cooling effectiveness on the winglet tip with different ejection angles b for P.S. holes. For the heat transfer coefficient distributions, it is seen that the pitch-averaged heat transfer coefficient increases with the increase of ejection angle b at the area x/C = (0, 0.8). However, at the area x/C = (0.8,1.0), as the ejection angle increases, the averaged heat transfer coefficient on the tip is firstly increased and then decreased. This can be attributed to the interactions between the tip and pressure side coolants at the trailing edge cutback (Label A in Fig. 4). Similar with the heat transfer coefficient distributions, the pitch-averaged film cooling effectiveness distributions on winglet tip for b = 90°, 75°, 60° and 45° are very close. As b decreases further, the pitch-averaged film cooling effectiveness is enhanced, significantly. Fig. 7 compares the pitch-averaged total pressure loss distributions in the cascade (the cutplane is 10 mm downstream the trailing edge) along spanwise direction. It is evident that the pitchaveraged total pressure loss distributions are not sensitive to the variation of ejection angle b for P.S. holes. This indicates that the coolant ejection has little disturbance to the pass-over flow, thus has little influence on the leakage loss in tip gap.  and g  on winglet tip Table 3 summarizes n in cascade, and h with different ejection angles b for P.S holes. It is seen that the pitchwise ejection angle b almost has no influence on the averaged  and total pressure loss in cascade. As b varies between (45°, 90°), h g are slightly affected. However, in the range of b = (15°, 45°), h is  is increased significantly as b decreases. Theredecreased while g fore, for P.S. winglet tip, better coolant coverage on cavity floor can be achieved with a smaller ejection angle b. In this case, more coolant will be attached onto the cavity floor, which in turn enhances  the film cooling effect there. Compared with the case of b = 90°, h  can be increased by 35.6% for b = can be reduced by 5.6% and g  can be reduced by 11.5% and g  can be increased 30°, whereas h by 83.3% for b = 15°. From Fig. 5, it is evident that the variation of b for P.S. holes has little effect on the heat transfer and film cooling effect on cavity floor near suction side. Therefore, to improve the film cooling effect on the cavity floor near suction side, the variation of b for tip holes is further investigated. Fig. 8 illustrates the streamlines in the tip gaps with different b for both tip and P.S. holes. Note the passover flow (green lines) sweeps across the winglet tip gap, and then rolls down to the blade suction side, forming a large scale of leakage vortex there. Underneath the pass-over flow, two portions of film coolant are observed near the cavity floor. Since the coolant

X. Yan et al. / International Journal of Heat and Mass Transfer 125 (2018) 357–374

361

Fig. 4. Streamlines in winglet tip gap with different b for P.S. holes (M = 1).

is injected with a velocity close to main flow at M = 1, the cooling flow has sufficient momentum to overcome the surrounding crossflow as it exits the holes. Therefore, as b = 90°, 75° and 60°, the cooling flow rolls up higher after it ejects from both pressure side and tip holes due to large ejection angles. In these cases, the passover flow is slightly pushed upwards by both pressure side and tip coolant. It is interesting to note that, at M = 1, the pass-over flow and coolant flow are located at different layers in tip gap. As the pitchwise ejection angle b decreases to (45°, 30°, 15°), more coolants are trapped in the cavity without leaking out from the suction side rim (especially in Fig. 8(f)). Due to the resistance of cooling flow from tip holes, most of the pressure side cooling flow is deflected towards the trailing edge, and then flows out of the cavity. The accumulation of coolant in the cavity will enhance the film cooling effect at the corresponding area. Fig. 9 shows the heat transfer coefficient and film cooling effectiveness as a function of pitchwise ejection angle b for both tip and P.S holes. Note the lateral (pitchwise) spreading of coolant on cavity floor is quite small for both tip and pressure side holes at the range of b = (90°, 45°). However, as the pitchwise ejection angle b further decreases (for example, b = 30°, 15°), the coolant jet is able to penetrate further downstream, leading to higher cooling effectiveness on the cavity floor along the ejection direction. With a small pitchwise ejection angle b, the cooling flow is quickly

deflected towards the trailing edge due to the carry-over effect by the tip leakage. Longer coolant trajectories are observed on the cavity floor in lateral direction downstream the cooling holes, especially for the case of b = 15°. It is also interesting to see that coolant from the first tip and pressure side holes is swirled towards the cavity near leading edge due to the entrainment effect by cavity vortex (yellow lines near the leading edge in Fig. 8). Therefore, higher film cooling effectiveness is obtained on the cavity floor near leading edge, especially in small pitchwise ejection angle b. Fig. 10 plots the pitch-averaged heat transfer coefficient and film cooling effectiveness distributions on winglet tip with a range of pitchwise ejection angles b for both tip and pressure side holes. At the area x/C = (0.2, 0.8), the pitch-averaged heat transfer coefficient and film cooling effectiveness are not sensitive to the pitchwise ejection angle b at the range of b = (90°, 30°). But as b further decreases, the pitch-averaged heat transfer coefficient is decreased and film cooling effectiveness is enhanced, significantly. For all cases, note the pitch-averaged heat transfer coefficient and film cooling effectiveness near the leading edge x/C = (0, 0.2) and trailing edge x/C = (0.8,1.0) are sensitive to the pitchwise ejection angle b. Near the leading edge x/C = (0, 0.2), the entrainment effect by the cavity vortex increases with the decrease of pitchwise ejection angle b (see Fig. 9). Near the trailing edge, with the decrease of pitchwise ejection angle b, more coolant is trapped into the cavity

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Fig. 5. h and g on winglet tip with different b for P.S. holes (M = 1).

and then leaking out of the cavity from the trailing edge cutback (see Fig. 8). However, at the area x/C = (0.2, 0.8), the pitchaveraged heat transfer coefficient and film cooling effectiveness are mainly determined by the deflection and attachment of coolant near the cavity floor. Fig. 11 illustrates the averaged total pressure loss distributions along the spanwise direction for a range of pitchwise ejection angles. Similar with Fig. 7, the variations of pitchwise ejection angle b for both tip and pressure side holes almost have no influence on the aerodynamic loss in the cascade. Slight difference is only observed at the leakage vortex core region (95% span) for dif-

ferent pitchwise ejection angles. This can be attributed to the small disturbance of tip and pressure side coolants to the pass-over leakage (see Fig. 8). The heat transfer and film cooling effect on the winglet tip with a range of pitchwise ejection angles b for only P.S. holes and for both tip and P.S. holes are compared in Fig. 12. It is interesting to note that, compared with the variations of pitchwise ejection angle b only for P.S. holes, the variations of b for both tip and P.S. holes slightly improve the film cooling effect and decrease heat transfer on winglet tip in the cases of b = 75° and 60°. However, the heat transfer and film cooling effect on winglet tip are almost identical

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Fig. 6. Pitch-averaged h and g distribution along axial direction for P.S. holes with different b.

Fig. 7. Total pressure loss along the spanwise direction for P.S. holes with different b.

slightly decreased due to the reduced disturbance to the passover flow. Compared with the case of b = 30° only for P.S. holes,  is decreased by 2.3% and g  is increased by 21.8% in the case of h b = 30° for both P.S. and tip holes. Compared to the case of b =  can be decreased by 5.8% and g  can be 15° only for P.S. holes, h increased by 44.2% in the case of b = 15° for both P.S. and tip holes. From the above discussion, it indicates that the coolant coverage on the cavity floor can be significantly enhanced as b  30°. In this case, heat transfer coefficient is decreased and film cooling effect on the winglet tip is improved significantly compared with the vertical ejection. As b varies in the range of (90°, 45°), the heat transfer and film cooling effect on the winglet tip change slightly. The total pressure loss in the cascade is not sensitive to the variation of ejection angle b. Therefore, to decrease heat transfer and improve film cooling effect on winglet tip, b  30° is recommended for the tip and P.S. cooling holes. In this case, the total pressure loss in the cascade can be slightly reduced due to decreased disturbance to the tip leakage flow in small ejection angle case. Additionally, variation of b for pressure side holes has little effect on the heat transfer and film cooling effect on cavity floor near suction side. 3.2. Effect of ejection angle a

for these two hole-arrangements at b = 90° and 45°. With small ejection angles, i.e. b = (30°, 15°), compared with the variations of pitchwise ejection angle b only for P.S. holes, the variations of b for both tip and P.S. holes significantly decrease the heat transfer coefficient and improve the film cooling effective on winglet tip.  and g  on the winglet tip with different pitchwise Table 4 lists n, h ejection angles for both tip and pressure side holes. As pitchwise ejection angle decreases, the total pressure loss in the cascade is

Since the ejection direction is determined by two parameters a and b, in this section the effect of a on heat transfer and film cooling effect on winglet tip will be investigated. From the above discussion, it is seen that the interactions between tip and pressure side coolants are slight (see Figs. 8 and 9). Therefore, to simplify the analysis, only the variation of a for pressure side holes (b is fixed at 30°) will be discussed in this section. For the tip holes, vertical ejection is specified.

Table 3  and g  in winglet tip gap with different b for P.S. holes (a = 90°, M = 1). n, h

n  h

g

b = 90°

b = 75°

b = 60°

b = 45°

b = 30°

b = 15°

0.101 527.6

0.102 528.83

0.102 519.17

0.102 518.62

0.102 498.24

0.102 466.75

0.132

0.130

0.133

0.143

0.179

0.242

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Fig. 8. Streamlines in tip gaps with different b for both tip and P.S. holes (M = 1).

Fig. 13 illustrates the three-dimensional streamlines in tip gap with different a for pressure side holes. It is observed that coolant from the tip holes is directed towards the suction side rim by the pass-over flow, and then it rolls up and mixes with the leakage vortex at the blade suction side. For the pressure side cooling flow, as noticed earlier, the coolant ejection is deflected towards the trailing edge along camberline. As a varies, it is clearly seen that the coverage of coolant on the cavity floor is different. In large streamwise ejection angle a case (For example, Fig. 13(a)), the cooling flow is quickly deflected to the trailing edge induced by the passover flow, thus travels a shorter distance in the pitchwise direction. In small streamwise ejection angle a case (for example, (a, b) = (30°, 30°)), it is also easier for the pressure side cooling flow to turn to trailing edge, and almost all pressure side coolant streamlines are constrained near pressure side. These flow patterns indicate that too large or too small a is not beneficial for coolant coverage on the cavity floor. Fig. 14 shows h and g contours on the winglet tip with different a for pressure side holes. It is evident that the trajectory of the pressure side coolant jets is not oriented along the ejection direction. Instead, due to the pass-over flow and pressure gradient along streamwise direction, the pressure side coolant is quickly deflected towards the trailing edge after ejection. However, the variation of a for the pressure side holes has no influence to the heat transfer and film cooling effect on cavity floor near suction side (no overlap between two high film cooling areas). Corresponding to Fig. 13, it

is seen that too large or too small of a would lead to a narrow film coolant coverage on the cavity floor along pitchwise direction (see  and g  on winglet tip with a range Fig. 14(a) and (h)). Fig. 15 plots h  and g  for of a for pressure side holes. Table 5 lists the values of h  is obtained at a = different a. It is indicated that the maximum g  is obtained at about a = 75°. Since 120°, whereas the minimum h  h is not sensitive at range of a = (60°, 120°), the best ejection angle  on of a can be selected as a = 120°. Compared with a = 90° case, g  is only increased by the winglet tip can be reduced by 12.3% and h only 1% for a = 120° case. In general, compared with the variation of pitchwise ejection angle b, the variation of streamwise ejection angle a has smaller influence on heat transfer and film cooling effect on winglet tip. Fig. 16 shows the pitch-averaged h and g distributions on winglet tip with different a for pressure side holes. It is seen that the pitch-averaged h distributions are not sensitive to the streamwise ejection angle a except at the trailing edge x/C = (0.85, 1.0). This is because the pitch-averaged h at the trailing edge is mainly affected by the accumulation of coolant near the trailing edge. However, for the pitch-averaged g, it is much sensitive to the variation of a, especially at the area x/C = (0.1, 0.8). This can be attributed to different coverage of pressure side coolant on the cavity floor, as indicated in Fig. 14. In accordance with Fig. 14, the distributions of pitch-averaged g for a = 105°, 120° and 135° are almost identical with each other.

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365

Fig. 9. h and g on winglet tip with different b for both tip and pressure side holes (M = 1).

3.3. Effect of blowing ratio Since blowing ratio represents the momentum of coolant ejection into the cavity, interactions between the pass-over leakage and cooling flow would have a pronounced effect on tip heat transfer and film cooling effect. Generally, coolant with higher blowing ratio is easier to overcome resistance of pass-over leakage flow and pressure gradient. However, cooling flow with too high momen-

tum will deteriorate the coolant attachment onto the cavity floor. Therefore, in this section, the effect of blowing ratio on heat transfer and film cooling effect on winglet tip will be discussed. To simplify the study, only two cases are considered. The first one is the ejection angles for all holes are kept at (a, b) = (90°, 90°) to see the effect of blowing ratio on film cooling effect under vertical ejection conditions. The second one is that the ejection angle for the pressure side holes is kept at (a, b) = (120°, 30°) while the tip holes

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1000

0.6 0.5

β=90° β=75° β=60° β=45° β=30° β=15°

800 700

0.4

Pitch averaged η

Pitch averaged h (W•m-2•K-1)

900

600

0.3 0.2 0.1

500 400 300

β=90° β=75° β=60° β=45° β=30° β=15°

0 -0.1

0

0.2

0.4

0.6

0.8

1

-0.2

0

0.2

0.4

x/C

0.6

0.8

1

x/C

(a) pitch-averaged h

(b) pitch-averaged η

Fig. 10. The pitch-averaged h and g along axial direction for both tip and P.S. holes with different b.

Area averaged h (W•m-2•K-1)

600

Relative blade height

0.8

β=90° β=75° β=60° β=45° β=30° β=15°

0.6

0.4

0.4

h η h η

550

P.S. & tip holes P.S. & tip holes only P.S. holes only P.S. holes

0.35

0.3

0.25

500

0.2

Area averaged η

1

450 0.15

0.2 400

0

0

0.2

0.4

0.6

0.8

1

Pitch averaged ξ Fig. 11. Total pressure loss along the spanwise direction for both tip and P.S. holes with different b.

are kept at (a, b) = (90°, 90°) to see how the blowing ratio affects the cooling effect under small ejection angle conditions. Fig. 17 shows the three dimensional streamlines in the tip gap for M = 0, 0.5, 1.0 and 2.0. It is seen that the pressure side cooling flow is deflected to the suction side after ejection. In low blowing ratio case (M = 0.5), most of the pressure side coolant is directed towards the trailing edge, and then rolls up and flow out of the tip gap along the cutback. Due to small blowing ratio (momentum), the pressure side coolant is mainly flowing in the winglet cavity near pressure side. As blowing ratio M increases, more pressure side coolant flows across the tip gap and then leaking out from the suction side rim, and the coolant rolls up higher due to increased momentum of cooling flow, which in turn deteriorates the heat transfer and film cooling effect on the cavity floor. For the coolant from tip holes, it is also seen that the coolant coverage is deteriorated as M increases. At M = 0.5, it is evident that more coolant is attached onto the cavity floor near suction side compared with the other two cases (M = 1 and M = 2). Moreover, in

0

15

30

45

β

60

75

90

0.1 105

 and g  on winglet tip between b variations for only P.S. Fig. 12. Comparisons of h holes and for both tip and P.S. holes.

low blowing ratio case (M = 0.5), a portion of tip coolant is bounced back from the camberline to pressure side, and then accumulated near the trailing edge. Compared with the no film cooling case (M = 0), it indicates that the coolant is restricted in the inner layer by the pass-over flow in low blowing ratio cases. However, as the blowing ratio increases (for example, M = 2), due to the increased momentum of cooling flow, the coolant rises up higher and mixes with the pass-over flow, leading to higher leakage loss in the tip gap and lower film cooling effect on the cavity floor. Fig. 18 shows the heat transfer coefficient and film cooling effectiveness on winglet tip at different blowing ratios. Compared with the no film cooling case, the tip cooling flow reduces the heat transfer coefficient on the cavity floor near suction side at the area around (0, 0.4C) for M = 0.5, and also, heat transfer coefficient on the cavity floor between tip and pressure side holes is reduced at the area (0.4C, 0.8C) due to the bounce-back of tip coolant by the rim (see Fig. 17(b)). For the pressure side holes, it is clearly seen that the coolant is mainly accumulated near the winglet, providing effective film cooling there. As M increases to 1.0, the film cooling effect on the cavity floor is decreased, significantly. Compared to

367

X. Yan et al. / International Journal of Heat and Mass Transfer 125 (2018) 357–374 Table 4  and g  in winglet tip gap with different b for both tip and P.S. holes (a = 90°, M = 1). n, h

n  h

g

b = 90°

b = 75°

b = 60°

b = 45°

b = 30°

b = 15°

0.101 527.6

0.099 538.02

0.099 529.27

0.100 512.508

0.100 486.33

0.098 439.39

0.132

0.118

0.121

0.146

0.218

0.349

Fig. 13. Streamlines in tip gaps with different a for P.S. holes.

the case of M = 0, it is seen that the tip coolant mainly reduces the heat transfer coefficient on the cavity floor near the suction side due to increased momentum of coolant, which is easier to be blown towards the suction side by the pass-over leakage. Similar

phenomenon is also observed for the coolant from the pressure side holes. However, since the momentum of pressure side coolant is increased, the coolant rolls up higher and more coolant is blown from the pressure side to the suction side rim due to the pressure

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Fig. 14. h and g on winglet tip with different a.

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X. Yan et al. / International Journal of Heat and Mass Transfer 125 (2018) 357–374

Area averaged h Area averaged η

540

0.21

530

0.2

520 0.19 510 0.18

500

0.17

490 480

Area averaged η

-2

-1

Area averaged h (W•m •K )

 and g  on winglet tip at difTable 6 lists n in the cascade, and h ferent blowing ratios for vertical ejection cases. Note the averaged total pressure losses n at M = 0, 0.5 and 1.0 are very close. However, at M = 2.0, the total pressure loss in the cascade is increased significantly (5%) due to large disturbance of coolant to the pass-over  and higher g  are leakage. Among three bowing ratios, lower h achieved at the winglet tip for M = 0.5. Compared with no film  can be reduced by 18.5% for M = 0.5 case. However, cooling case, h as M increases to 2.0, the overall performance in the winglet tip gap is significantly deteriorated. As a result, for the winglet tip with vertical ejections (a = 90°, b = 90°), it is better to adopt a low blowing ratio to reduce disturbance of cooling ejection to pass-over leakage, which in turn improves the coolant attachment on the cavity floor. Fig. 19 plots the pitch-averaged h and g along the axial direction. Compared with no film cooling case, coolant with M = 0.5 provides effective cooling effect on the cavity floor. As M increases from 0.5 to 2.0, it is evident that the pitch-averaged h is increased with the increase of blowing ratio M at x/C = (0, 0.8) due to less coolant coverage on the cavity floor. However, at the trailing edge x/C = (0.8, 1.0), the pitch-averaged h is decreased with the increase of M. This is due to less coolant attachment on trailing edge cutback (see Fig. 17(b)). In Fig. 19(b), it is observed that the pitchaveraged g shows the similar distributions on the winglet tip for M = 0.5 and M = 1.0. Slight difference is only observed at the area x/C = (0.6, 1.0) due to different coolant accumulations near the trailing edge (See Fig. 17(b) and (c)). As M increases to 2.0, the pitch-averaged g on the area x/C = (0, 0.8) is deteriorated significantly except on the cutback region x/C = (0.8, 1.0), where the cool-

0.22

550

0

20

40

60

80

100

120

140

160

0.16 180

α (°)  and g  for winglet tip with different a. Fig. 15. h

difference across the tip gap. Due to the sweeping effect of coolant on suction side rim, the heat transfer coefficient on the rim near cavity is reduced, correspondingly. As the blowing ratio M further increases to 2.0, it is evident that the tip and pressure side coolant provides little film cooling effect on the cavity floor because it rolls up higher and most of the coolant is flowing across the tip gap. High film cooling effect is only observed on the cavity floor near trailing edge due to the accumulation and reattachment of coolant in this region.

Table 5  and g  in winglet tip gap with different a for P.S. holes (b = 30°, M = 1). n, h b = 135°

b = 120°

b = 105°

b = 90°

b = 75°

b = 60°

b = 45°

b = 30°

0.100 521.45

0.100 509.95

0.100 503.89

0.100 500.68

0.102 498.24

0.100 497.37

0.100 504.76

0.099 507.56

0.099 513.48

g

0.182

0.198

0.201

0.198

0.179

0.178

0.171

0.170

0.166

850

0.45

800

0.4 α=30° α=45° α=60° α=75° α=90° α=105° α=120° α=135° α=150°

700 650 600 550

0.3 0.25 0.2 0.15

500

0.1

450

0.05

400

0

0.2

0.4

0.6

α=30° α=45° α=60° α=75° α=90° α=105° α=120° α=135° α=150°

0.35

Pitch averaged η

750

-2

-1

Pitch averaged h (W •m •K )

a = 150° n  h

0.8

1

0

0

0.2

0.4

x/C

(a) pitch-averaged h

0.6

x/C

(b) pitch-averaged η

Fig. 16. The pitch-averaged h and g on winglet tip with different a.

0.8

1

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(a) M=0

(b) M=0.5

(c) M=1.0

(d) M=2.0

Fig. 17. Effect of blowing ratio on three dimensional streamlines in winglet tip gaps (a = 90°, b = 90°).

Fig. 18. h and g contours on winglet tip with different blowing ratios (a = 90°, b = 90°).

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The heat transfer coefficient and film cooling effectiveness on the winglet tip with three blowing ratios are illustrated in Fig. 21. With small blowing ratio (M = 0.5), the pressure side coolant only provides effective film cooling on winglet. As the blowing ratio increases to M = 1.0, compared with the case of M = 0.5, the high film cooling effectiveness area is enlarged wider and the thermal load on winglet tip is reduced, significantly. As the blowing ratio increases further to M = 2.0, the film cooling effect is deteriorated near the pressure side cooling holes because the coolant rolls up higher off the cavity floor (see Fig. 20(c)). However, due to the resistance of pass-over flow, the rolled-up pressure side coolant is reattached onto the cavity floor near the tip holes, generating high film cooling effect there. Seriously, the heat transfer coefficient is increased significantly on the cavity floor near pressure side. Table 7 provides the averaged total pressure loss n in the cascade, averaged heat transfer coefficient and film cooling effectiveness on the winglet tip at three blowing ratios. It is evident that, with small ejection angles (a = 120°, b = 30°), the averaged total pressure loss n in cascade is not sensitive to the blowing ratio due to lower disturbance to leakage flow than that of vertical ejec and g  tion case (see Table 6). Among three bowing ratios, the best h

Table 6  and g  (a = 90°, b = 90°). Effect of blowing ratio on n, h

n  h

g

M=0

M = 0.5

M = 1.0

M = 2.0

0.102 622.57

0.102 507.18

0.101 527.60

0.106 594.76

–

0.142

0.132

0.109

ing flow directly flushes the trailing edge cutback surface (see Fig. 17(d).). For the pressure side coolant with small ejection angles (a, b) = (120°, 30°), the streamlines in tip gap at three different blowing ratios are illustrated in Fig. 20. In the case of small blowing ratio M = 0.5, it is seen that the coolant is easier to be pushed towards the trailing edge after ejection than the other cases. The pressure side coolant is mainly flowing in the cavity near pressure side, and almost no coolant travels across the tip gap from the suction rim. As the blowing ratio M increases to 1.0, the pressure side coolant travels wider in the pitchwise direction due to the increased momentum. Several cooling streamlines (cyan lines) flow across the tip gap from the suction side rim. As blowing ratio increases further to M = 2.0, more pressure side coolant is rolling up higher and directly passing over the tip gap.

0.4

1200

M=0 M=0.5 M=1 M=2

1000 900

0.3

Pitch averaged η

Pitch averaged h (W•m-2•K-1)

1100

800 700 600

M=0.5 M=1 M=2

0.2

0.1

500 400 300

0

0.2

0.4

0.6

0.8

1

x/C

0

0

0.2

0.4

0.6

x/C

(b) pitch-averaged η

(a) pitch-averaged h

Fig. 19. Pitch-averaged h and g on winglet tip with different blowing ratios (a = 90°, b = 90°).

(a) M=0.5

(b) M=1.0

(c) M=2.0

Fig. 20. Effect of blowing ratio on three dimensional streamlines in the tip gaps (a = 120°, b = 30°).

0.8

1

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h (W/m2 K)

η

(a) M=0.5

(b) M=1.0

(c) M=2.0 Fig. 21. h and g contours on winglet tip with three blowing ratios (a = 120°, b = 30°).

are achieved at M = 1.0 because coolant spreads wider in the pitch is decreased by 4.6% wise direction. Compared with M = 0.5 case, h  is increased by 28.9% for M = 1.0 case. Compared with M = and g  is decreased by 9.3% and g  is increased by 1.0% for M 2.0 case, h = 1.0 case. Therefore, to provide sufficient film cooling and reduce thermal load on winglet tip in small ejection angle case, it is better

Table 7  and g  (a = 120°, b = 30°). Effect of blowing ratio on n, h M = 0.5

M = 1.0

M = 2.0

n  h

0.100 526.92

0.100 503.89

0.100 550.57

g

0.143

0.201

0.199

0.45 0.4

900

-1

Pitch averaged h (W•m •K )

1000

M=0.5 M=1 M=2

-2

0.35

Pitch averaged η

M=0.5 M=1 M=2

800

700

600

0.3 0.25 0.2 0.15 0.1

500

0.05 400

0

0.2

0.4

0.6

x/C

(a) pitch-averaged h

0.8

1

0

0

0.2

0.4

0.6

x/C

(b) pitch-averaged η

Fig. 22. Pitch-averaged h and g on winglet tip with three blowing ratios (a = 120°, b = 30°).

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X. Yan et al. / International Journal of Heat and Mass Transfer 125 (2018) 357–374

to adopt a medium blowing ratio (M = 1.0) to ensure proper momentum for the cooling flow. Fig. 22 plots the pitch-averaged h and g on winglet tip at three blowing ratios. In Fig. 22(a), it is seen that the pitch-averaged heat transfer coefficient distributions for M = 0.5 and 1.0 are almost identical, which are smaller than that of M = 2.0 case at the area x/C = (0, 0.8). However, at the trailing edge x/C = (0.8, 1.0), the pitch-averaged heat transfer coefficients for M = 0.5 and 1.0 are much higher than for M = 2.0 case. This is mainly due to the coolant reattachment near the trailing edge for M = 2.0, as indicated in Figs. 20 and 21. For M = 1, film cooling effect on winglet tip at x/C = (0.3, 0.7) is higher than the other two blowing ratios. This is mainly attributed to better coolant coverage on the cavity floor near pressure side by the pressure side coolant (see Fig. 21 (b)). As the blowing ratio M increases, the pitch-averaged g is increased significantly at x/C = (0.75, 1.0) due to more coolant accumulation near trailing edge cutback, which can be observed from Fig. 21.

373

cases with small incline angle, the total pressure loss in cascade is less sensitive to the blowing ratio variation than in vertical ejection cases. Conflict of interest We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled ‘‘Effect of Ejection Angle and Blowing Ratio on Heat Transfer and Film Cooling Effect on a Winglet Tip”. Acknowledgements The authors are grateful for the supports by the Natural Science Foundation of China (Grant No. 51306138) for the present work.

4. Conclusions References In this study, the effects of coolant ejection angle and blowing ratio on heat transfer and film cooling effect at a winglet tip are numerically investigated based on the authors’ previous research [25,27]. The major findings are: (1) The two ejection angles, i.e. streamwise ejection angle a and pitchwise ejection angle b (see the definitions in Fig. 3), have pronounced influence on coolant coverage on the cavity floor in winglet tip. Generally speaking, the pitchwise ejection angle b has larger influence on heat transfer and film cooling effect on winglet tip than the streamwise ejection angle a. (2) The pitchwise ejection angle b mainly affects the interactions between the pass-over leakage flow and coolant in the gap radial direction. Large pitchwise ejection angle b may lead to pronounced disturbance to the pass-over leakage flow and affect the total pressure loss in the cascade. The heat transfer coefficient and film cooling effect are not sensitive to the pitchwise ejection angle if b varies between (45°, 90°). If ejection angle b  30°, higher film cooling effectiveness and lower heat transfer coefficient on the winglet tip can be achieved. (3) The streamwise ejection angle a mainly affects the coolant deflection towards the trailing edge, thus influences the coolant attachment on cavity floor in the pitchwise direction. Since the cooling flow is apt to be deflected to streamwise direction, it is better to set a > 90° which ensures wider spread of coolant on the cavity floor along pitchwise direction. In this study, higher film cooling effect and lower heat transfer coefficient can be achieved at about a = 120°. (4) The blowing ratio has a significant effect on the heat transfer and film cooling effect on winglet tip. In the design process, the blowing ratio has to be adjusted to the ejection angles. If the vertical ejection is adopted ((a, b) = (90°, 90°)), it is better to adopt a small blowing ratio (in this study, M = 0.5) to reduce disturbance of coolant to the pass-over leakage flow. If the small inclined ejection angles are selected, for example (a, b) = (120°, 30°), it is better to adopt medium blowing ratio (in this study, M = 1.0) to increase the momentum of coolant ejection, which ensures wider spreading of coolant on cavity floor in pitchwise direction. With the vertical ejection, the averaged total pressure loss is decreased by 5% as blowing ration increases from 0.5 to 2.0. However, in the

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