Research Papers

The Optimal Distribution of Chordwise Rib Fin Arrays for Blade Tip Cap Underside Cooling

[+] Author and Article Information
Gustavo A. Ledezma

e-mail: ledezma@ge.com

Ronald S. Bunker

e-mail: bunker@research.ge.com
GE Global Research Center,
Niskayuna, NY 12309

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the Journal of Turbomachinery. Manuscript received June 29, 2012; final manuscript received March 5, 2013; published online September 20, 2013. Editor: David Wisler.

J. Turbomach 136(1), 011007 (Sep 20, 2013) (7 pages) Paper No: TURBO-12-1100; doi: 10.1115/1.4024072 History: Received June 29, 2012; Revised March 05, 2013

A fundamental question in the design of fin-augmented heat transfer surfaces is how to determine the optimal spacing between the fins. It has already been demonstrated that considerable heat transfer augmentation in the underside of a high-pressure turbine (HPT) blade tip cap can be achieved using arrays of discrete shaped pins (Bunker, 2008, “The Augmentation of Internal Blade Tip-Cap Cooling by Arrays of Shaped Pins,” ASME J. Turbomach., 130(4), p. 041007). However, it is desirable to predict the maximum heat transfer augmentation that can be achieved by installing the array of fins and the geometric arrangement (fin-to-fin spacing) that has to be used to achieve such augmentation. In this paper chordwise parallel ribs installed on the underside of a blade tip cap are studied. The objective is to maximize the overall thermal conductance between the fin array and the surrounding fluid. The optimization is performed numerically in the range 25,000 < Re < 100,000 and Pr = 0.72. The behavior of the optimal spacing data is explained and correlated analytically using the method of intersecting the two asymptotes: small spacing and large spacing heat transfer (Bejan and Morega, 1994, “The Optimal Spacing of a Stack of Plates Cooled by Turbulent Forced Convection,” Int. J. Heat Mass Trans., 37, pp. 1045–1048).

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Fig. 1

Schematic of the simulated 180-deg turn model: (a) complete model; (b) detail of fluid-solid interface

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Fig. 2

(a) 11-fin fluid mesh; (b) mesh cut with constant X plane showing details of the inflated prism layers near the finned region

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Fig. 3

Smooth tip cap underside test Nusselt number results, Re = 200,000 [5]

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Fig. 4

Smooth tip cap underside CFD, Re = 200,000 and SST model: (a) Nusselt number contours; (b) velocity-colored Q invariant, Nusselt number contours on the tip cap underside and velocity vectors at a midplane, parallel to the cavity rib; (c) 2D streamlines on a constant Y plane parallel to the fins

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Fig. 5

Fin and tip cap dimensions notation

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Fig. 6

Numerical optimization of the spacing S. Constant temperature fins.

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Fig. 7

Numerical optimization of the spacing S. Constant heat flux at the fins base.

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Fig. 8

Effect of the Reynolds number on the optimal fin spacing results

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Fig. 9

Effect of the Reynolds number on the maximum thermal conductance results

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Fig. 10

Finned tip cap underside CFD results Re = 50,000 and SST turbulence model, seven fins: velocity-colored Q invariant, Nusselt number contours, and velocity vectors at a midplane, parallel to the cavity rib

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Fig. 11

2D streamlines on a constant Y plane parallel to the fins. Re = 50,000.

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Fig. 12

Tip cap underside fin array wetted surface temperature for Re = 25,000. Constant heat flux boundary condition (conjugate heat transfer model).

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Fig. 13

Effect of tip cap underside fins on the 180-deg turn pressure drop




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