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Research Papers

The Delta Phi Method of Evaluating Overall Film Cooling Performance

[+] Author and Article Information
James L. Rutledge

Department of Aeronautics and Astronautics,
Air Force Institute of Technology,
Wright-Patterson Air Force Base, OH 45433
e-mail: james.rutledge@us.af.mil

Marc D. Polanka

Department of Aeronautics and Astronautics,
Air Force Institute of Technology,
Wright-Patterson Air Force Base, OH 45433

David G. Bogard

Department of Mechanical Engineering,
University of Texas at Austin,
Austin, TX 78712

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received December 3, 2015; final manuscript received December 16, 2015; published online February 17, 2016. Editor: Kenneth C. Hall.

J. Turbomach 138(7), 071006 (Feb 17, 2016) (8 pages) Paper No: TURBO-15-1288; doi: 10.1115/1.4032456 History: Received December 03, 2015; Revised December 16, 2015

Film cooling designs are often evaluated experimentally and characterized in terms of their spatial distributions of adiabatic effectiveness, η, which is the nondimensionalized form of the adiabatic wall temperature, Taw. Additionally, film cooling may alter the convective heat transfer coefficient with the possibility of an increase in h that offsets the benefits of reduced Taw. It is therefore necessary to combine these two effects to give some measure of the benefit of film cooling. The most frequently used method is the net heat flux reduction (NHFR), which gives the fractional reduction in heat flux that accompanies film cooling for the hypothetical case of constant wall temperature. NHFR is imperfect in part due to the fact that this assumption does not account for the primary purpose of film cooling—to reduce the metal temperature to an acceptable level. In the present work, we present an alternative method of evaluating film cooling performance that yields the reduction in metal temperature, or in the nondimensional sense, an increase in ϕ that would be predicted with film cooling. This Δϕ approach is then applied using experimentally obtained η and h/h0 values on a simulated turbine blade leading edge region. The delta-phi approach agrees well with the legacy NHFR technique in terms of the binary question of whether the film cooling is beneficial or detrimental, but provides greater insight into the temperature reduction that a film cooling design would provide an actual turbine component. For example, instead of giving an area-averaged NHFR = 0.67 (indicating a 67% reduction in heat flux through film cooling) on the leading edge region with M = 0.5, the Δϕ approach indicates an increase in ϕ of 0.061 (or a 61 K surface temperature decrease with a notional value of T−Tc = 1000 K). Alternatively, the technique may be applied to predict the maximum allowable increase in T against which a film cooling scheme could protect.

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References

Sen, B. , Schmidt, D. L. , and Bogard, D. G. , 1996, “ Film Cooling With Compound Angle Holes: Heat Transfer,” ASME J. Turbomach., 118(4), pp. 800–806. [CrossRef]
Albert, J. E. , Bogard, D. G. , and Cunha, F. , 2004, “ Adiabatic and Overall Effectiveness for a Film Cooled Blade,” ASME Paper No. GT2004-53998.
Williams, R. P. , Dyson, T. E. , Bogard, D. G. , and Bradshaw, S. D. , 2013, “ Sensitivity of the Overall Effectiveness to Film Cooling and Internal Cooling on a Turbine Vane Suction Side,” ASME J. Turbomach., 136(3), p. 031006. [CrossRef]
Esgar, J. , 1971, “ Turbine Cooling—Its Limitations and Its Future,” NASA Lewis Research Center, Cleveland, OH, NASA Report No. NASA-TM-X-66702.
Polanka, M. D. , Anthony, R. J. , Bogard, D. G. , and Reeder, M. F. , “ Determination of Cooling Parameters for a High Speed, True Scale, Metallic Turbine Vane Ring,” ASME Paper No. GT2008-50281.
Dyson, T. E. , Bogard, D. G. , Piggush, J. D. , and Kohli, A. , 2013, “ Overall Effectiveness for a Film Cooled Turbine Blade Leading Edge With Varying Hole Pitch,” ASME J. Turbomach., 135(3), p. 031011. [CrossRef]
Wang, T. , and Zhao, L. , 2011, “ A Revised Equation for Heat Flux Reduction in Film Cooling Studies and Discussion of Its Applications,” ASME Paper No. GT2011-45953.
Han, J. C. , Dutta, S. , and Ekkad, S. V. , 2000, Gas Turbine Heat Transfer and Cooling Technology, Taylor & Francis, New York.
Trimble, S. , 2013, “ The Heat is On,” Flight Int., 184(5420), pp. 22–25.
Rutledge, J. L. , King, P. I. , and Rivir, R. B. , 2012, “ Influence of Film Cooling Unsteadiness on Turbine Blade Leading Edge Heat Flux,” ASME J. Eng. Gas Turbines Power, 134(7), p. 071901. [CrossRef]
Kline, S. J. , and McClintock, F. A. , 1953, “ Describing Uncertainties in Single Sample Experiments,” ASME J. Mech. Eng., 75(1), pp. 3–8.
Mick, W. J. , and Mayle, R. E. , 1988, “ Stagnation Film Cooling and Heat Transfer Including Its Effect Within the Hole Pattern,” ASME J. Turbomach., 110(1), pp. 66–72. [CrossRef]
Dyson, T. E. , McClintic, J. W. , Bogard, D. G. , and Bradshaw, S. D. , 2013, “ Adiabatic and Overall Effectiveness for a Fully Cooled Turbine Vane,” ASME Paper No. GT2013-94928.

Figures

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Fig. 1

Leading edge model and hole configuration

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Fig. 2

Schematic of test facility

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Fig. 10

h/h0 contours, M = 0.5

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Fig. 11

ΔϕM=0.5 − ΔϕM=1 contours

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Fig. 3

Adiabatic effectiveness, η, contours, M = 1.0

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Fig. 4

h/h0 contours, M = 1.0

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Fig. 5

NHFR contours, M = 1.0, ϕ = 0.6

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Fig. 6

NHFR contours, M = 1.0, ϕ = 0.4

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Fig. 7

Δϕ contours, M = 1.0

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Fig. 8

Area-averaged Δϕ

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Fig. 9

Adiabatic effectiveness, η, contours, M = 0.5

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