Aerothermal characteristics of transonic over-tip leakage flow for different tip geometries with cooling injection
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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.
KeywordsAerodynamic Heat transfer Over-tip leakage flow Cooling injection Tip geometries
Counter-rotating vortex pair
Heat transfer coefficient
Tip leakage vortex
Nondimensional total temperature
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. . 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  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 . Ameri  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.  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.  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 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 k–ω model (SST k–ω), 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
Part of boundary conditions
Inlet total pressure P0,in (kPa)
Inlet total temperature T0,in (K)
Inlet flow angle (°)
Coolant total pressure P0,c (kPa)
Coolant total temperature T0,c (K)
Outlet static pressure Pexit (kPa)
Wall temperature Tw (K)
2.2 Grid independence study
Grid details of 3D computational domains
Grid number (million)
Grid points within tip gap
Grid points within cavity height
Average y+ on tip surfaces
Average HTC (W/m2 K)
2.3 Turbulence model validation
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 k–ω 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 k–ω 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
3.2 Effect of cooling injection on transonic OTL flow
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.
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
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. .
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.
The aerothermal characteristics of transonic OTL flow with the cooling injection for different blade tip geometries are numerically investigated. The simulations using SST k–ω 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.
The authors gratefully acknowledge the support of China Scholarship Council, Chinese National Science Foundation (51506120, 51376127) and the Aeronautical Scientific Funding.
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