Advertisement

Aerospace Systems

, Volume 2, Issue 2, pp 189–196 | Cite as

Aerothermal characteristics of transonic over-tip leakage flow for different tip geometries with cooling injection

  • Mingxing Tang
  • Shaopeng LuEmail author
  • Yunkai Liu
  • Jinfang Teng
Original Paper
  • 73 Downloads

Abstract

In turbomachinery, the effect of cooling injection on the over-tip leakage (OTL) flow has been the focus. In the present work, the flow and heat transfer on the blade tip surfaces of two typical different tip structures including a flat tip and a squealer tip are investigated. The grid independence verification and turbulence model validation (including Shear Stress Transport k–ω model and Spalart–Allmaras model) are conducted. Numerical results are compared with the existing experimental results. It is found that there exists the shock wave near the corner of the pressure side, and a striped high-pressure coefficient region appears on the tip surface near the pressure side. The cooling injection could alter the range of high striped pressure coefficient region. The tip leakage vortex (TLV) was formed by the blending between the OTL flow and mainstream, causing a large aerodynamic penalty. In comparison, the flat tip shows a greater loss near the casing and the tip surface than the squealer tip. An interesting observation is that the coolant ejecting from the cooling jet hole bifurcates and then forms a counter-rotating vortex pair (CRVP) for both the flat tip and the squealer tip, which greatly changes the flow structures and heat transfer characteristics within the tip region. The branches of the CRVP cause the thermal stripes on the surfaces of blade tip and the suction side rim. The present results reveal the cooling injection has a strong effect on OTL flow and enlighten the design and optimization of blade tips.

Keywords

Aerodynamic Heat transfer Over-tip leakage flow Cooling injection Tip geometries 

Abbreviations

Cp

Pressure coefficient

CRVP

Counter-rotating vortex pair

EXP

Experiment

HPT

High-pressure turbine

HTC

Heat transfer coefficient

mʺ

Mass flux

OTL

Over-tip leakage

P

Pressure

PS

Pressure side

SS

Suction side

TLV

Tip leakage vortex

V

Velocity, vortex

θ

Nondimensional total temperature

Subscripts

c

Coolant

exit

Mainstream outlet

in

Mainstream inlet

0

Total

1 Introduction

In modern gas turbines, a continuous increase in turbine inlet temperature has improved the turbine thermal efficiency. Meanwhile, the large thermal load caused by such high temperature makes the turbine tips one of the most susceptible parts. There exists a clearance between turbine blade tip and the casing, and the gas driven by the pressure difference crosses the tip surface and forms the over-tip leakage flow. The resulting leakage flow loss is an important part of the stage losses in high-pressure turbine (HPT). As a result, comprehensive research on heat transfer and aerodynamics over the blade tip regions has been more and more significant for investigators nowadays.

Many numerical simulations have been carried out to study the aerothermal characteristics. The effects of tip clearance heights and casing recess on stage efficiency and heat exchange for different squealer tip geometries were investigated by Ameri et al. [1]. It was found that the heat transfer on the pressure side (PS) was decreased when the recessed casing was introduced. A marked reduction of thermal load could be observed on the blade tip regions. Ameri and Bunker [2] conducted a numerical study of the heat transfer performances on turbine blade tip surfaces for a large-power generation turbine and the computational results were compared with the experimental results reported by Bunker [3]. Ameri [4] compared the results of a mean-camber line strip tip with a sharp edge tip, and it was found that a sharp edge tip works better in reducing the tip leakage loss and the tip heat transfer. Considering three different tip geometries of baseline flat tip, cavity tip and suction side (SS) squealer tip, Krishnababu et al. [5] numerically studied the effects of diverse tip geometries on aerothermal characteristics in unshrouded axial flow turbines. Their results revealed that the leakage mass flow and the heat transfer on tip regions increased as the tip gap heights increased. Krishnababu and Newton et al. [6, 7] also examined the effects of relative casing motion and coolant injection on the aerodynamics and heat exchange of the OTL flow. Yang et al. [8, 9] performed the similar studies as well. Their conclusions showed that although the heat transfer coefficient (HTC) decreased as the cavity depth increased, the shallow cavity is the more effective configuration to decrease the large thermal load. In addition, the GE-E3 blade with two different tip geometries, flat tip and squealer tip, were used by Yang et al. [10, 11] to study the flow and heat transfer, and distributions of HTC were in satisfactory agreement with the experimental results reported by Azad et al. [12, 13].

Lots of experiments have been performed to investigate the aerodynamic and heat transfer characteristics on the blade tip areas. With the transient liquid technique, a two-dimensional model of first stage gas turbine rotor blade was studied by Azad et al. [12, 13]. The detailed static pressure distributions and HTC on flat and squealer tip surfaces were measured, and the effects of the tip gap size are considered as well. Using the same research technique and blade models, Kwak and Han [14, 15] discussed the effects of blowing ratio and tip gap sizes as the coolant injection was introduced. Their results showed that the overall film-cooling effectiveness increased with increasing blowing, and the overall heat exchange enhanced with increasing tip gap size. Kwak et al. [16] further studied the effects of the positions of squealer rims, and it was found that the suction side squealer tip provided the lowest HTC on the blade tip and near tip regions compared to the other layouts. To assess the overall film-cooling benefit of the pressure side blowing, Christophel et al. [17, 18] measured the adiabatic effectiveness levels and the HTC.

The typical characteristics of a subsonic tip flow and a transonic tip flow are shown in Fig. 1. Zhang et al. [20] reported that the shock wave structure in transonic OTL flow greatly influenced the heat transfer on tip surface. The contours of the multiple reflected shock wave structure were clearly visible. Some researchers such as Couch et al. [21] and Wheeler et al. [22, 23] investigated the effects of tip coolant injection on transonic OTL loss. Similarly, Ma et al. [24, 25] numerically and experimentally studied the transonic squealer tip with the cooling injection. It was observed that dominant driving flow structure was a counter-rotating vortex pair (CRVP) caused by the bifurcation of coolant impinging on the casing. Such CRVP was responsible for the emergence of high thermal stripes on the tip regions.
Fig. 1

Schematics of subsonic and transonic tip flow structure [19]

The present numerical study focuses on the flow and heat transfer on the blade tip regions with two different tip geometries including a flat tip and a squealer tip. The strong interactions between OTL flow and cooling injection has been discussed. A part of the computational results was compared with the experimental results of Ma et al. [24, 25].

2 Numerical methods

The commercially available CFD solver, ANSYS-CFX, was employed in present numerical calculations. By solving the steady Reynolds-averaged Navier–Stokes (RANS) equations, the computational results are obtained. Two different turbulence models, the Spalart–Allmaras (SA) model and the Shear Stress Transport kω model (SST kω), are selected to verify the grid dependence and compare the experimental results. All high-quality structured meshes are generated using ICEM software.

2.1 Computational model and mesh

The blade model with cooling jet holes is presented in Fig. 2a. This model shares the same blade profile in Ma [25], but the cooling jet holes differs. The tip clearance height and the cooling hole diameter share the same size of 0.675 mm. Five cooling holes are located along the camber lines and the distance between two adjacent holes equals 5 times of the hole diameter. As is shown in Fig. 2b, four diverse tip geometries, including cooled/uncooled flat and cooled/uncooled squealer tips, are chosen to implement current research.
Fig. 2

Geometric model and four different blade tips

As shown in Fig. 3, the computational domain is a single-channel fluid domain with translational periodic boundaries and the structured mesh is clearly visible.
Fig. 3

Computational domain and meshes

The total pressure and total temperature boundary conditions are specified to the inlet and cooling holes, and the outlet is set to be the static pressure boundary. The hub is specified as a symmetric boundary. All walls are set as the no-slip isothermal boundary conditions. Some specific boundary conditions are listed in Table 1.
Table 1

Part of boundary conditions

Inlet total pressure P0,in (kPa)

180

Inlet total temperature T0,in (K)

300

Inlet flow angle (°)

45.3

Coolant total pressure P0,c (kPa)

198

Coolant total temperature T0,c (K)

150

Outlet static pressure Pexit (kPa)

101

Wall temperature Tw (K)

280/290

2.2 Grid independence study

Table 2 lists the detailed characteristics of the computational grids used in grid independence study. Increasing the grid nodes within the tip clearance and cavity heights, the total grid elements, as shown in Table 2, have changed from 3.65 × 106 to 5.74 × 106. The average y+ value over the tip regions is around 0.8 for all cases.
Table 2

Grid details of 3D computational domains

Grid number (million)

 

3.65

4.70

5.74

6.97

Grid points within tip gap

SA/SST

20

30

40

50

Grid points within cavity height

SA/SST

30

40

50

60

Average y+ on tip surfaces

SA

0.7687

0.7782

0.8190

0.8273

SST

0.8096

0.8070

0.8047

0.8039

Average HTC (W/m2 K)

SA

1156.8

1125.3

1113.2

1110.9

SST

1135.7

1148.9

1154.0

1157.4

Figure 4 shows the relative HTC difference between different grid sizes. In comparison, the local HTC difference between 5.74 × 106 and 6.79 × 106 elements is less than 1.5% for the most of the tip surface. Besides, when the number of grid elements increases from 3.65 × 106 to 5.74 × 106, the change of average HTC on the tip surface is relatively large. However, such a change becomes pretty slight as the total grid elements further grow into 6.97 × 106. In other words, the influence of introducing more grid elements will be negligible. Consequently, the number of 5.74 × 106 elements is selected for the present research.
Fig. 4

Relative HTC difference among the different grid quantities a 3.65 and 4.70 million, b 4.70 and 5.74 million, c 5.74 and 6.97 million

2.3 Turbulence model validation

Based on the experimental results (Ma et al. [25]), the HTC distributions of numerical simulations with SST k–ω model and SA model are shown in Fig. 5. By contrast, the difference in the distribution of HTC on the blade tip surface is pretty evident.
Fig. 5

Comparison of HTC on the tip surfaces between numerical results (SST kω model and SA model) and experimental results

As shown in Fig. 5, the overall HTC distributions for SST k–ω model and SA model are in good agreement with the experimental results, especially for the low-HTC regions on the cavity floor close to the pressure side and the high-HTC regions near the leading edge. Comparing the range of high-HTC regions on the cavity floor and the rim surfaces, it is obvious that the SST kω model shows a better prediction on the high-HTC regions than the SA model. Similar results were reported by Ma et al. [32, 33]. It means the SST kω model is more suitable and accurate than SA model in simulating the near wall flow in the present study.

3 Results and discussions

3.1 Effects of shock wave structure and pressure coefficient

The nondimensional pressure coefficient Cp is employed to describe the distributions of the relative pressure. The definition of Cp is

$$ C_{\text{p}} = \frac{{P_{{ 0 , {\text{in}}}} - P}}{{P_{{ 0 , {\text{in}}}} - P_{\text{exit}} }}, $$
(1)
where the P0,in is the total pressure of the inlet fluid, P is the local static pressure, and the Pexit is the static pressure of the fluids at the exit.
To better elaborate the aerodynamic performance within the tip gap, the contours of Y component of density gradient distributions on three cut-planes and Cp on the uncooled flat tip are presented in Fig. 6. The shock waves within the tip gap are evidently visible on those cut-planes. The reflected shock wave (the oblique shock wave) appears near the pressure side edge. A normal shock wave is generated along the border of the high striped Cp region. Note that the range of shock wave in plane 1 is smaller than that in plane 2. This is because most of the area of plane 1, namely, the downstream of the high striped Cp border, is in subsonic state. It is observed that the pressure load increases when the shock waves hitting the tip surface. Similar conclusions were reported by Zhang et al. [20].
Fig. 6

Contours of Y component of density gradient (kg/m4) distributions on three cut-planes and the pressure coefficient over the flat tip

The results of pressure coefficients on the tip surfaces of four different tip geometries are plotted in Fig. 7. The averaged pressure coefficient of flat tip surfaces, both for uncooled and cooled cases, is higher than that of squealer tip surfaces. In other words, the introduction of groove for squealer tips decreases the pressure load over the blade tip surfaces. The frontal parts for given cases stand a low Cp region, and the minimum Cp for squealer tips occurs inside the region B. It means a less pressure difference to drive the fluid across the tip gap. It is seen that the Cp shows a striped distribution in region A, and its border is consistent with the profile of low-HTC stripe (marked B) in Fig. 12a. The flow in this region is transonic and the reflected shock wave captured through density gradient is shown in Fig. 6. Compared with the uncooled flat tip, the size of the high Cp region for cooled flat tip shrinks with the introduction of cooling holes. The values of Cp in region C of suction side, for the uncooled and cooled squealer tips, are bigger than those on the rim surfaces of the pressure side. The reason for such a difference is that flow separation zone on the rim surface of suction side is larger than that on the rim surface in the pressure side.
Fig. 7

Distributions of pressure coefficient on different blade tip surfaces: a uncooled flat tip, b uncooled squealer tip, c cooled flat tip, d cooled squealer tip

3.2 Effect of cooling injection on transonic OTL flow

Figure 8 shows the OTL flow patterns over the flat and squealer tip surfaces, and the stagnation pressure ratio contours on three cut-planes are presented as well. For the flat tip in Fig. 8a, the flow separates as it enters the tip gap and then reattaches. Driven by the big pressure difference, the OTL flow goes to the suction side and blends with the mainstream, forming the tip leakage vortex (TLV). It is observed that the considerable aerodynamic penalty was caused by such TLV. The local stagnation pressure ratio in TLV core region is even below 50%. The Mach number in region D is relatively higher than other parts of the flat tip and the flow is in transonic condition. This region is consistent with the high Cp region where the shock waves occurred.
Fig. 8

Stagnation pressure ratio (P0/P0,in) along three cut-planes and the OTL flow streamlines over the tip surfaces

For the squealer tip in Fig. 8b, the flow separation still exists at the entrance of the pressure side, but no flow attachment happens on the surface of the pressure side rim. A part of the flow goes into the groove and then forms the vortices. The Mach number of these flow is small. Note that the similar TLV and the resulting aerodynamic penalty could be observed for the squealer tip as well. However, the flat tip apparently shows a smaller stagnation pressure ratio near the casing and the tip surface than the squealer tip.

Figure 9 shows the nondimensional averaged mass flux distributions of the OTL flow along the suction side edge. Compared to the flat tip, it is evident that the squealer tip reduces the OTL mass flux, especially in the frontal part. When the cooling injection is introduced, a slight increase of OTL mass flux is observed in the frontal part. Then, a zigzag line could be vividly found in the mid-chord (x/Cx = 30−60%) region. This is mainly due to the discrete layout of the cooling holes. From the region of x/Cx > 60%, there is no big difference of OTL mass flux for all cases. However, a considerable reduction of OTL mass flux exists near the region of x/Cx = 80%.
Fig. 9

Nondimensional averaged OTL mass flux distribution along the suction side edge

Figure 10 shows the flow structure of the cooling injection for the cooled squealer tip. Driven by the upstream OTL flow and the casing, the coolant bifurcates in Fig. 10a, c, and the counter-rotating vortex pair (CRVP) is formed since these two branches rotate in opposite directions. Starting from the leading edge, it is observed that the diffusion range of coolant ejecting from cooling holes is getting smaller around every cooling hole, while the local Mach number is becoming bigger and bigger.
Fig. 10

Flow structure of cooling injection

To better explore the interaction between coolant and OTL flow, the nondimensional total temperature θ is defined to describe such interaction in Fig. 10b, d. The expression of θ is

$$ \theta = \frac{{T_{{ 0 , {\text{in}}}} - T_{0} }}{{T_{{ 0 , {\text{in}}}} - T_{\text{c}} }}, $$
(2)
where T0,in is the total temperature of inlet flow, T0 is the local total temperature, and Tc is the temperature of the coolant. The larger the θ is, the more dominant the coolant is. For both the cooled flat tip and the cooled squealer tip, we could clearly observe the distributions of θ on corresponding planes (plane M and plane N). These two planes are perpendicular to the camber line and cross over the center of the cooling holes. Note that the θ is relatively large when the coolant was injected from the cooling holes, and the profiles of high θ regions vividly illustrate the position of coolant core. The coolant core locally blocks the upstream OTL flow and forces fluids to bypass the coolant core.
Figure 11 shows the overall OTL flow structures on blade tip surfaces for cooled flat and squealer cases. The streamlines of the coolant (cold) and the upstream fluid (hot) are in blue and red, respectively. Compared to the flat tip, a wider diffusion range of coolant is found for the cooling hole in the same position for the squealer tip. As shown by the white dotted lines, a portion of upstream fluid goes to the bottom of the coolant and intensifies the heat exchange on the tip surface. But the other part flows to the middle of the two branches of the CRVPs. This part is lifted and it makes the heat transfer on the tip surface weakened. It causes the existence of the thermal stripes on the cooled tip surfaces in Fig. 12. Similar to the uncooled squealer tip, the fluid flows to the groove and the vortices are formed as the fluid hits the suction side rim in the frontal part of the blade tip.
Fig. 11

Overall OTL flow streamlines for cooled flat and squealer cases

Fig. 12

Comparison of HTC on different tip geometries: a uncooled flat tip, b uncooled squealer tip, c cooled flat tip, d cooled squealer tip

3.3 Heat transfer coefficients on different tip geometries

Figure 12 compares the HTC on the tip surfaces of the four tip geometries, and the uncooled/cooled cases for flat and squealer tips are investigated. For all given cases, it is observed that an evident ridge of high HTC appears near the leading edge (marked A). The flow separates and then reattaches in region A. Similar to the region A, a striped high-HTC region is displayed along the edge near the pressure side. For the flat tips (including uncooled and cooled cases), the stripe of low HTC is found in region B. The profile of the striped low-HTC region in Fig. 11a is in good accordance with the border of the normal shock wave in Fig. 6.

It is found that the HTC distributions over the tip surfaces change greatly with the introduction of cooling injection. Compared to the uncooled flat tip in Fig. 12a, the area of the low-HTC stripe (region B) shrinks in Fig. 12c. In addition, the striped high-HTC region is clearly visible in region C. Moreover, the value of HTC on the left side of the high-HTC stripe is larger than that on the right side. This is because the right branch of CRVP is more dominant than the right branch on the tip surface. A similar analysis was carried through by Ma et al. [25].

For the cooled squealer tip in Fig. 12d, the high-HTC regions can be observed on both sides of the camber line (marked D) except for the region around the first cooling hole. Note that a series of thermal stripes appear on the suction side rim (region E). These thermal stripes are mainly caused by the asymmetrical branches of the CRVP. It indicates that the cooling injection strongly influences the heat transfer over the tip surfaces.

4 Conclusions

The aerothermal characteristics of transonic OTL flow with the cooling injection for different blade tip geometries are numerically investigated. The simulations using SST kω model were observed to be in good agreement with the experimental result, especially for the low-HTC regions on the cavity floor close to the pressure side and the high-HTC regions near the leading edge.

For the flat tip, the reflected shock wave (the oblique shock wave) appears near the pressure side corner. There exists a high striped Cp region on the tip surfaces near the pressure side. In addition, a normal shock wave is produced along the border of this region. It is found that the introduction of cooling injection reduces the range of the high striped Cp region. For the uncooled and cooled squealer tips, a larger flow separation zone makes the values of Cp on the surfaces of the suction side rim bigger than those on the surfaces of the pressure side rim.

Driven by the big pressure difference, the OTL flow goes to the suction side and blends with the mainstream, forming the tip leakage vortex. In addition, a considerable aerodynamic penalty was caused by such TLV for both the flat tip and squealer tip. However, the flat tip apparently shows a smaller stagnation pressure ratio near the casing and the tip surface than the squealer tip.

The coolant first hits the casing and then bifurcates into two branches, forming the counter-rotating vortex pair (CRVP). The coolant core, described by the nondimensional total temperature, locally blocks the upstream OTL flow and forces fluids to bypass the coolant core.

Another interesting observation is that the cooling injection greatly changes the heat transfer on the blade tip surfaces, especially for the area around the cooling holes and the downstream of such holes. In addition, the branches of the CRVP cause the thermal stripes. It illustrates the cooling injection has a strong effect on heat transfer on the tip surfaces.

Notes

Acknowledgements

The authors gratefully acknowledge the support of China Scholarship Council, Chinese National Science Foundation (51506120, 51376127) and the Aeronautical Scientific Funding.

References

  1. 1.
    Ameri AA, Steinthorsson E, Rigby DL (1999) Effects of tip clearance and casing recess on heat transfer and stage efficiency in axial turbines. ASME J Turbomach 121:683–693CrossRefGoogle Scholar
  2. 2.
    Ameri AA, Bunker RS (1999) Heat transfer and flow on the first stage blade tip of a power generation gas turbine: part II: simulation results. ASME J Turbomach 122:272–277CrossRefGoogle Scholar
  3. 3.
    Bunker RS, Bailey JC, Ameri AA (1999) Heat transfer and flow on the first stage blade tip of a power generation gas turbine—part I: experimental results. In: ASME paper no. 99-GT-169Google Scholar
  4. 4.
    Ameri AA (2001) Heat transfer and flow on the blade tip of a gas turbine equipped with a mean-camber line strip. ASME J Turbomach 123(4):704–708CrossRefGoogle Scholar
  5. 5.
    Krishnababu SK, Newton PJ, Dawes WN, Lock GD, Hodson HP, Hannis J (2007) Aerothermal investigations of tip leakage flow in axial flow turbines—part I: effect of tip geometry and tip clearance gap. AMSE J Turbomach 131(1):727–738Google Scholar
  6. 6.
    Krishnababu SK, Hodson HP, Dawes WN, Lock GD, Hannis J, Whitney C (2007) Aerothermal investigations of tip leakage flow in axial flow turbines—part II: effects of relative casing motion. In: ASME paper no. GT2007-27957Google Scholar
  7. 7.
    Newton P, Lock GD, Krishnababu S, Hodson H, Dawes W, Hannis J, Whitney C (2009) Aero-thermal investigation of tip leakage flow in axial flow turbines—part iii: tip cooling. ASME J Turbomach 131(1):011008CrossRefGoogle Scholar
  8. 8.
    Yang H, Chen HC, Han JC (2006) Turbine rotor with various tip configurations flow and heat transfer prediction. J Thermophys Heat Transfer 20(1):80–91CrossRefGoogle Scholar
  9. 9.
    Yang H, Chen HC, Han JC (2013) Flow and heat transfer prediction on turbine rotor blade with various tip configurations. J Thermo-phys Heat Transfer 20(1):80–91CrossRefGoogle Scholar
  10. 10.
    Yang H, Acharya S, Ekkad SV, Prakash C, Bunker R (2002) Flow and heat transfer predictions for a flat-tip turbine blade. In: ASME paper GT-2002-30190Google Scholar
  11. 11.
    Yang, H, Acharya, S, Ekkad, S. V, Prakash, C, Bunker, R (2002) Numerical simulation of flow and heat transfer past a turbine blade with a squealer-tip. In: ASME paper GT-2002-30193Google Scholar
  12. 12.
    Azad GMS, Han JC, Teng S, Boyle R (2000) Heat transfer and pressure distributions on a gas turbine blade tip. ASME J Turbomach 122(4):717–724CrossRefGoogle Scholar
  13. 13.
    Azad GMS, Han JC, Boyle R (2000) Heat transfer and pressure distributions on the squealer tip of a gas turbine blade. AMSE J Turbomach 122(4):725–732CrossRefGoogle Scholar
  14. 14.
    Kwak JS, Han JC (2002) Heat transfer coefficient and film cooling effectiveness on a gas turbine blade tip. ASME paper no. 2002-GT-30194Google Scholar
  15. 15.
    Kwak JS, Han JC (2002) Heat transfer coefficient and film cooling effectiveness on the squealer tip of a gas turbine blade. In: ASME paper no. 2002-GT-30555Google Scholar
  16. 16.
    Kwak JS, Ahn J, Han JC, Lee CP, Boyle R, Gaugler R (2003) Heat transfer coefficients on the squealer tip and near tip regions of a gas turbine blade with single squealer or double squealer). In: ASME paper GT2003-38907Google Scholar
  17. 17.
    Christophel JR, Thole KA (2005) Cooling the tip of a turbine blade using pressure side holes—part I: adiabatic effectiveness measurements. ASME J Turbomach 127(2):270–277CrossRefGoogle Scholar
  18. 18.
    Christophel JR, Thole KA, Cunha FJ (2005) Cooling the tip of a turbine blade using pressure side holes—part II: heat transfer measurements. ASME J Turbomach 127(2):278–286CrossRefGoogle Scholar
  19. 19.
    Wheeler APS, Atkins NR, He L (2011) Turbine blade tip heat transfer in low speed and high-speed flows. ASME J Turbomach 133(4):041025-1–041025-9CrossRefGoogle Scholar
  20. 20.
    Zhang Q, He L, Wheeler A, Ligrani P, Cheong B (2011) Over-tip shock wave structure and its impact on turbine blade tip heat transfer. ASME J Turbomach 133(4):041001CrossRefGoogle Scholar
  21. 21.
    Couch E, Christophel J, Hohlfeld E, Thole KA, Cunha FJ (2005) Comparison of measurements and predictions for blowing from a turbine blade tip. AIAA J Propul Power 21(2):335–343CrossRefGoogle Scholar
  22. 22.
    Wheeler AP, Saleh Z (2013) Effect of cooling injection on transonic tip flows. AIAA J Propul Power 29(6):1374–1381CrossRefGoogle Scholar
  23. 23.
    Wheeler AP, Atkins NR, He L (2011) Turbine blade tip heat transfer in low speed and high-speed flows. ASME J Turbomach 133(4):041025CrossRefGoogle Scholar
  24. 24.
    Ma H, Zhang Q, He L, Wang Z, Wang L (2016) Cooling injection effect on a transonic squealer tip—part I: experimental heat transfer results and CFD validation. In: ASME paper no. GT2016-57579Google Scholar
  25. 25.
    Ma H, Zhang Q, He L, Wang Z, Wang L (2016) Cooling injection effect on a transonic squealer tip—part II: analysis of aerothermal interaction physics. J Eng Gas Turbines Power 139(5):052507CrossRefGoogle Scholar

Copyright information

© Shanghai Jiao Tong University 2019

Authors and Affiliations

  1. 1.School of Aeronautics and AstronauticsShanghai Jiao Tong UniversityShanghaiChina

Personalised recommendations