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)

The Need for Cooling

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

Quantifying Cooling Quality

I Film Cooling Effectiveness: η = Taw−TrT0C−Tr

I Heat Transfer Coefficient: htc = qTw−Tr

Geometry

Grid Generation

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

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%

Inflow Conditions

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

Isentropic Mach number Distribution at the End Wall

Simulation Experiment

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

Development of Secondary Flows at the Leading Edge

Simulation Experiment

Absolute Heat Transfer Coefficient at the End Wall

Straight Slot – B = 0.7, I = 0.5

Film Cooling Effectiveness Relative Heat Transfer Coefficient

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

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

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

Line-Up of Pitchwise Averaged Values

Film Cooling Effectiveness Relative Heat Transfer Coefficient

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

Thank you!Any questions?

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

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

Measurement Planes

Straight Slot – Streamwise Vorticity

No Cooling Straight Slot

Contoured Slot – Streamwise Vorticity

No Cooling aS/lax = 0.025

Contoured Slot – Streamwise Vorticity

No Cooling aS/lax = 0.0125