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Reducing the Demand of Coolant at the Sidewall of a HighPressure Turbine Cascade by Means of Slot Width Modulation
Institute of Propulsion Technology (Turbine Department)German Aerospace Center (DLR)
Michael Woopen, Axel Dannhauer, Peter-Anton Gieß
ASME Turbo Expo 2012 (Copenhagen)
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The Need for Cooling
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Flow and Heat Transfer Phenomena
I Boundary layer interacts with theleading edge of the blades andseparates into the two legs of theso-called horseshoe vortex
I Passage vortex is mainly driven bya cross flow generated by thepressure gradient within thepassage
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Quantifying Cooling Quality
I Film Cooling Effectiveness: η = Taw−TrT0C−Tr
I Heat Transfer Coefficient: htc = qTw−Tr
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Geometry
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Grid Generation
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TRACE
I Second-order,
I block-structured,
I MPI-parallized,
I finite volume RANS solver
I equipped with k − ω turbulence model
I and γ − ReΘ transition model
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Boundary Conditions – Freestream
Inlet Exit
Total pressure 100 kPaTotal temperature 296 KIsentropic Mach number 0.175 1.00Velocity magnitude 59 m/s 311.6 m/sReynolds number 230 000 850 000Design mass flow 0.33 kg/sTurbulence intensity 1%
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Inflow Conditions
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Turbulent Length Scale
I Estimate lT in the freestream:lT ∼ L/
√Re
I Calculate corresponding eddy
viscosity: lT =√kω =
√32 ·
νTu·Tu
I Assume νT to be constant
I Deduce profile for lT
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Isentropic Mach number Distribution at the End Wall
Simulation Experiment
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Isentropic Mach Number Distribution at Mid-Span
y/t
Tu
-2.2 -2 -1.8 -1.6 -1.4 -1.2 -10
0.02
0.04
0.06
0.08
0.1
SimulationExperiment
x/lax
Mais
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
1.2
SimulationExperiment
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Development of Secondary Flows at the Leading Edge
Simulation Experiment
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Absolute Heat Transfer Coefficient at the End Wall
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Straight Slot – B = 0.7, I = 0.5
Film Cooling Effectiveness Relative Heat Transfer Coefficient
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Contoured Slot
I Optimize the local discharge ofcoolant alongside the cooling slot
I Modulate the slot widthI Avoid back flow
AS =mS
p1/γS
√√√√√√√√√(γ−1)RT0S
2γp
γ−1γ
0S− 1
2p
γ−1γ
S
2
− 14p
2(γ−1)γ
S
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Contoured Slot – Film Cooling Effectiveness
aS/lax = 0.025, B = 0.9, I = 0.8 aS/lax = 0.0125, B = 1.9, I = 3.3
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Contoured Slot – Relative Heat Transfer Coefficient
aS/lax = 0.025, B = 0.9, I = 0.8 aS/lax = 0.0125, B = 1.9, I = 3.3
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Line-Up of Pitchwise Averaged Values
Film Cooling Effectiveness Relative Heat Transfer Coefficient
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Conclusion
I Several film cooling configurations (slot) were investigatedI The modulated slot width shows an advanced distribution of coolant
I Critical areas like the nose region were successfully cooledI Less supplementing cooling holes are necessary
I Configuration may be further optimized by adjusting slot amplitude anddistance
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Thank you!Any questions?
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Number of Grid Points
Block Topology Axial Pitchwise Spanwise
Inner boundary layer O 211 35 151Outer boundary layer C 195 7 151Front passage H 63 27 151Rear passage G 53 26 151Wake H 27 29 151Inlet H 169 45 151Exit H 27 55 151Slot H 49 45 61Plenum H 155 45 61Tube H 41 41 15
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Slot Configurations
∆xs0/lax as/lax φ mc/m ρc/ρ ρcuc/ρu ρcu2c/ρu2
Slot # 1 0.0475 0.0 0.0 0.0059 1.099 0.715 0.465Slot # 2 0.0349 0.025 0.33 0.0059 1.108 0.951 0.816Slot # 3 0.0161 0.0125 0.33 0.0059 1.12 1.908 3.25
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Measurement Planes
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Straight Slot – Streamwise Vorticity
No Cooling Straight Slot
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Contoured Slot – Streamwise Vorticity
No Cooling aS/lax = 0.025
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Contoured Slot – Streamwise Vorticity
No Cooling aS/lax = 0.0125