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Research Papers

Unsteady Effects on the Experimental Determination of Overall Effectiveness

[+] Author and Article Information
James L. Rutledge

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

William P. Baker

Air Force Institute of Technology,
Wright-Patterson Air Force Base,
Air Force Base, OH 45433

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received August 15, 2018; final manuscript received August 18, 2018; published online October 15, 2018. Editor: Kenneth Hall.This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J. Turbomach 140(12), 121005 (Oct 15, 2018) (10 pages) Paper No: TURBO-18-1203; doi: 10.1115/1.4041233 History: Received August 15, 2018; Revised August 18, 2018

An increasingly common experimental method allows determination of the overall effectiveness of a film cooled turbine component. This method requires the Biot number of the experimental model to match that of the engine component such that the nondimensional surface temperature, ϕ, is matched to that of the engine component. The matched Biot number requirement effectively places a requirement on the thermal conductivity of the model and the traditional implementation places no requirement on the model's density or specific heat. However, such is not the case if such a model is exposed to unsteadiness in the flow such as with film cooling unsteadiness. In this paper, we develop an additional nondimensional parameter that must also be theoretically matched to conduct overall effectiveness experiments with unsteady film cooling. Since finding suitable materials with an acceptable combination of thermodynamic properties for a typical low temperature experiment can be difficult, simulations were conducted to determine the impact of imperfectly matched parameters achievable with common materials. Because the disparity between the diffusion and the unsteadiness time scales can hinder numerical simulation, a novel analytical solution to the heat equation with relevant unsteady Robin type boundary conditions is developed. Particular solutions are examined to determine the sensitivity of the temperature response of a turbine blade (or a model of one) to its material properties and the form of the unsteady variation in the convection parameters. It is shown that it is possible to obtain useful experimental results even with imperfectly matched parameters.

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References

Williams, R. P. , Dyson, T. E. , Bogard, D. G. , and Bradshaw, S. D. , 2014, “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]
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Rutledge, J. L. , Polanka, M. D. , and Greiner, N. J. , 2017, “Computational Fluid Dynamics Evaluations of Film Cooling Flow Scaling Between Engine and Experimental Conditions,” ASME J. Turbomach., 139(2), p. 021004. [CrossRef]
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Rutledge, J. L. , King, P. I. , and Rivir, R. , 2010, “Time Averaged Net Heat Flux Reduction for Unsteady Film Cooling,” ASME J. Eng. Gas Turbines Power, 132(12), p. 121601. [CrossRef]
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Rutledge, J. L. , and Polanka, M. D. , 2015, “Waveforms of Time-Resolved Film Cooling Parameters on a Leading Edge Model,” J. Propul. Power, 31(1), pp. 253–264. [CrossRef]
Rutledge, J. L. , Rathsack, T. C. , Van Voorhis, M. , and Polanka, M. D. , 2016, “Film Cooling Parameter Waveforms on a Film Cooled Turbine Blade Leading Edge With Oscillating Stagnation Line,” ASME J. Turbomach., 138(7), p. 071005. [CrossRef]
DuPont, 2015, “DuPont Corian Performance Properties,” E.I. du Pont de Nemours and Company, Wilmington, DE.
Stewart, W. R. , and Dyson, T. E. , 2017, “Conjugate Heat Transfer Scaling for Inconel 718,” ASME Paper No. GT2017-64873.
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]

Figures

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Fig. 2

Nondimensional surface temperature response of an Inconel component at engine conditions with unsteadiness in η at various amplitudes

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Fig. 1

Nondimensional surface temperature response of a Corian model with unsteadiness in η and h at a very low frequency of 0.01 Hz

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Fig. 3

Nondimensional surface temperature response of an Inconel component at engine conditions with unsteadiness in η in phase with h and hamp = 0.8 hmean

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Fig. 4

Nondimensional surface temperature response of an Inconel component at engine conditions with unsteadiness in η at various phases with h and hamp = 0.8 hmean. The inset shows detail of differences between ψ = 5π/4 and 3π/2.

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Fig. 5

Nondimensional surface temperature response of an Inconel component at engine conditions with different boundary condition oscillation frequencies

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Fig. 6

Nondimensional temperature within the Inconel component for the f = 1 Hz case

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Fig. 9

Time-resolved ϕ values for several experimental conditions described in Table 1, but with phase shift ψ = π

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Fig. 10

Time-resolved ϕ values for several experimental conditions described in Table 1, but with phase shift ψ = π, ηmean = 0.3, and ηamp = 0.2

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Fig. 11

Time-resolved ϕ values for a hypothetical material like Corian and conditions and in Table 1, but with different densities

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Fig. 7

Time-resolved ϕ values for several experimental conditions described in Table 1

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Fig. 8

Time-resolved ϕ values; detail of Fig. 7

Tables

Errata

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