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Research Papers

Determination of Time Resolved Heat Transfer Coefficient and Adiabatic Effectiveness Waveforms With Unsteady Film

[+] Author and Article Information
James L. Rutledge

Air Force Institute of Technology
e-mail: James.rutledge@us.af.mil

Jonathan F. McCall

U.S. Air Force
e-mail: jonathan.mccall@us.af.mil

Alternative situations can be imagined in which t and/or tc depend on time. The impact remains the same, though, in that taw is a function of time. The time dependent values t(t) and tc(t) would then be used in the nondimensionalization of taw(t) to determine η(t).

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the Journal of Turbomachinery. Manuscript received July 2, 2012; final manuscript received July 24, 2012; published online November 5, 2012. Editor: David Wisler.

J. Turbomach 135(2), 021021 (Nov 05, 2012) (9 pages) Paper No: TURBO-12-1115; doi: 10.1115/1.4007545 History: Received July 02, 2012; Revised July 24, 2012

Traditional hot gas path film cooling characterization involves the use of wind tunnel models to measure the spatial adiabatic effectiveness (η) and heat transfer coefficient (h) distributions. Periodic unsteadiness in the flow, however, causes fluctuations in both η and h. In this paper we present a novel inverse heat transfer methodology that may be used to approximate the η(t) and h(t) waveforms. The technique is a modification of the traditional transient heat transfer technique that, with steady flow conditions only, allows the determination of η and h from a single experiment by measuring the surface temperature history as the material changes temperature after sudden immersion in the flow. However, unlike the traditional transient technique, this new algorithm contains no assumption of steadiness in the formulation of the governing differential equations for heat transfer into a semi-infinite slab. The technique was tested by devising arbitrary waveforms for η and h at a point on a film cooled surface and running a computational simulation of an actual experimental model experiencing those flow conditions. The surface temperature history was corrupted with random noise to simulate actual surface temperature measurements and then fed into an algorithm developed here that successfully and consistently approximated the η(t) and h(t) waveforms.

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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, pp. 800–806. [CrossRef]
Rutledge, J. L., King, P. I., and Rivir, R., 2010, “Time Averaged Net Heat Flux Reduction for Unsteady Film Cooling,” ASME J. Eng. Gas Turb. Power, 132(12), p. 121901. [CrossRef]
Vedula, R. P., and Metzger, D. E., 1991, “A Method for the Simultaneous Determination of Local Effectiveness and Heat Transfer Distributions in Three Temperature Convective Situations,” ASME Paper No. 91-GT-345.
Ekkad, S. V., Ou, S., and Rivir, R. B., 2004, “A Transient Infrared Thermography Method for Simultaneous Film Cooling Effectiveness and Heat Transfer Coefficient Measurements From a Single Test,” ASME J. Turbomach., 126, pp. 597–603. [CrossRef]
Incropera, F., and DeWitt, D., 1996, Fundamentals of Heat and Mass Transfer, 4th ed., John Wiley & Sons, New York.
Özisik, M. N., and Orlande, H. R. B., 2000, Inverse Heat Transfer, Taylor & Francis, New York.
Savitzky, A., and Golay, M. J. E., 1964, “Smoothing and Differentiation of Data by Simplified Least Squares Procedures,” Anal. Chem., 36, pp. 1627–1639. [CrossRef]
Anderson, JohnD., 1995, Computational Fluid Dynamics—The Basics with Applications, McGraw-Hill, New York.
Carslaw, H. S., and Jaeger, J. C., 1986, Conduction of Heat in Solids, 2nd ed., Oxford University Press, New York, NY.
Kreith, F., 1998, The CRC Handbook of Mechanical Engineering, CRC Press, Boca Raton, FL.
Rutledge, J. L., 2009, “Pulsed Film Cooling on a Turbine Blade Leading Edge,” Ph.D. dissertation, Department of Aeronautics and Astronautics, Air Force Institute of Technology, Wright-Patterson AFB, OH.

Figures

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Fig. 1

Flow chart showing steps to conduct experiment and reduce data in accordance with IFSAW algorithm

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Fig. 2

Validation procedure flow chart

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Fig. 3

Temperature error (K) in numerical simulation of experiment as compared with analytical solution for steady h and η

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Fig. 4

Surface temperature over first 0.5 s of simulated experiment with h=100+50 sin(2π·10t) and η=0.4+0.3 sin(2π·10t)

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Fig. 5

Actual surface temperature, simulated noisy measured data with 0.1 K uncertainty, and filtered data

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Fig. 6

Surface heat flux determined by IFSAW algorithm compared to actual heat flux

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Fig. 7

η(t) waveform determined with 20 s simulated experiment with h=100+50sin(2π·10t) and η=0.4+0.3sin(2π·10t)

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Fig. 8

h(t) waveform determined with 20 s simulated experiment with h=100+50sin(2π·10t) and η=0.4+0.3sin(2π·10t)

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Fig. 9

η(t) waveform determined with 20 s simulated experiment with waveforms given by Eqs. (34) and (35)

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Fig. 10

h(t) waveform determined with 20 s simulated experiment with waveforms given by Eqs. (34) and (35)

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Fig. 11

η(t) waveform determined with 20 s simulated experiment with waveforms given by Eqs. (36) and (37)

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Fig. 12

h(t) waveform determined with 20 s simulated experiment with waveforms given by Eqs. (36) and (37)

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