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Research Papers

Cooling Optimization Theory—Part II: Optimum Internal Heat Transfer Coefficient Distribution

[+] Author and Article Information
Benjamin Kirollos, Thomas Povey

Osney Thermofluids Laboratory,
Department of Engineering Science,
University of Oxford,
Osney Mead,
Oxford OX2 0ES, UK
e-mail: ben.kirollos@eng.ox.ac.uk

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 9, 2015; published online March 15, 2016. Editor: Kenneth C. Hall.

J. Turbomach 138(8), 081003 (Mar 15, 2016) (15 pages) Paper No: TURBO-15-1290; doi: 10.1115/1.4032613 History: Received December 03, 2015; Revised December 09, 2015

Gas turbine cooling system design is constrained by a maximum allowable wall temperature (dictated by the material, the life requirements of the component, and a given stress distribution), the desire to minimize coolant mass flow rate (requirement to minimize cycle-efficiency cost), and the requirement to achieve as close to uniform wall temperature as possible (to reduce thermal gradients, and stress). These three design requirements form the basis of an iterative design process. The relationship between the requirements has received little discussion in the literature, despite being of interest from both a theoretical and a practical viewpoint. In Part I, we show analytically that the coolant mass flow rate is minimized when the wall temperature is uniform and equal to the maximum allowable wall temperature. In this paper, we show that designs optimized for uniform wall temperature have a corresponding optimum internal heat transfer coefficient (HTC) distribution. In this paper, analytical expressions for the optimum internal HTC distribution are derived for a number of cooling systems, with and without thermal barrier coating (TBC). Most cooling systems can be modeled as a combination of these representative systems. The optimum internal HTC distribution is evaluated for a number of engine-realistic systems: long plate systems (e.g., combustors, afterburners), the suction-side (SS) of a high pressure nozzle guide vane (HPNGV), and a radial serpentine cooling passage. For some systems, a uniform wall temperature is unachievable; the coolant penalty associated with this temperature nonuniformity is estimated. A framework for predicting the optimum internal HTC for systems with any distribution of external HTC, wall properties, and film effectiveness is outlined.

Copyright © 2016 by Rolls-Royce plc
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References

Figures

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Fig. 1

Internal cooling arrangements for which the optimum internal HTC is derived: (a) Reverse-pass with point inlet RP (p.i.), (b) forward-pass with point inlet FP (p.i.), (c) reverse-pass with distributed inlet RP (d.i.), and (d) forward-pass with distributed inlet FP (d.i.)

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Fig. 2

Long plate cooling systems: (a) Reverse-pass with point inlet RP (p.i.), (b) forward-pass with point inlet FP (p.i.), (c) reverse-pass with distributed inlet RP (d.i.), and (d) forward-pass with distributed inlet FP (d.i.)

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Fig. 3

Optimum internal HTC distributions for long plate systems

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Fig. 4

Midchord SS systems with separate upstream film cooling plenum

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Fig. 5

Optimum internal HTC distributions for midchord SS systems with separate upstream film cooling plenum: unphysical result: (a) Reverse-pass with point inlet RP (p.i.), ε = 0, (b) forward-pass with point inlet FP (p.i.), ε = 0, (c) reverse-pass with distributed inlet RP (d.i.), ε = 0, and (d) forward-pass with distributed inlet FP (d.i.) ε = 0

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Fig. 6

Optimum internal HTC distributions for midchord SS systems with separate upstream film cooling plenum: physical result

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Fig. 7

Midchord SS systems linked to upstream film cooling plenum: (a) Reverse-pass with point inlet RP (p.i.) and (b) forward-pass with point inlet FP (p.i.)

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Fig. 8

Optimum internal HTC distributions for midchord SS systems linked to upstream film cooling plenum

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Fig. 9

TE SS forward-pass cooling system

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Fig. 10

Optimum internal HTC distributions for SS TE; Biot number equal to 0.4

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Fig. 11

Optimum internal HTC distributions for SS TE; Biot number equal to 0.2

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Fig. 12

Simplified three-pass radial serpentine passage

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Fig. 13

Optimum internal HTC distribution for serpentine cooling systems A and B

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Fig. 14

Optimum internal HTC distributions for long plate systems, with and without TBC (TBC Biot number equal to 0.5, metal Biot number equal to 0.4)

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Fig. 15

Differential control volumes for reverse-pass and forward-pass systems with point inlet: (a) Reverse-pass with point inlet RP (p.i.) and (b) forward-pass with point inlet FP (p.i.)

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Fig. 16

Differential control volumes for reverse-pass and forward-pass systems with distributed inlet: (a) Reverse-pass with distribution inlet RP (d.i.) and (b) forward-pass with distribution inlet FP (d.i.)

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