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Research Papers

# A Film-Cooling Correlation for Shaped Holes on a Flat-Plate Surface

[+] Author and Article Information
Will F. Colban

Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94551

Karen A. Thole

Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, PA 16802

David Bogard

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

J. Turbomach 133(1), 011002 (Sep 07, 2010) (11 pages) doi:10.1115/1.4002064 History: Received August 28, 2008; Revised June 04, 2010; Published September 07, 2010; Online September 07, 2010

## Abstract

A common method of optimizing coolant performance in gas turbine engines is through the use of shaped film-cooling holes. Despite widespread use of shaped holes, existing correlations for predicting performance are limited to narrow ranges of parameters. This study extends the prediction capability for shaped holes through the development of a physics-based empirical correlation for predicting laterally averaged film-cooling effectiveness on a flat-plate downstream of a row of shaped film-cooling holes. Existing data were used to determine the physical relationship between film-cooling effectiveness and several parameters, including blowing ratio, hole coverage ratio, area ratio, and hole spacing. Those relationships were then incorporated into the skeleton form of an empirical correlation, using results from the literature to determine coefficients for the correlation. Predictions from the current correlation, as well as existing shaped-hole correlations and a cylindrical hole correlation, were compared with the existing experimental data. Results show that the current physics-based correlation yields a significant improvement in predictive capability, by expanding the valid parameter range and improving agreement with experimental data. Particularly significant is the inclusion of higher blowing ratio conditions (up to $M=2.5$) into the current correlation, whereas the existing correlations worked adequately only at lower blowing ratios $(M≈0.5)$.

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## Figures

Figure 1

Effect of blowing ratio on η for shaped holes (AR=3.9,P/D=6.5,t/P=0.48)(12)

Figure 2

Illustration of shaped-hole geometrical parameters

Figure 3

Effect of L/D ratio on η for shaped holes (M=1.5,AR=3.5,P/D=6.0,t/P=0.49)(8)

Figure 4

Effect of area ratio on η for shaped holes (P/D=6.0,t/P=0.43)(8)

Figure 5

Effect of hole spacing on η for shaped holes (M=1.5,AR=4.2)(8)

Figure 6

Correlation predictions versus low blowing ratio data from Gritsch (8)(M=0.5,AR=3.5,P/D=6.0,t/P=0.49)

Figure 7

Correlation predictions versus high blowing ratio data from Gritsch (8)(M=2.5,AR=3.5,P/D=6.0,t/P=0.49)

Figure 8

R2 values versus blowing ratio for each data set (Eq. 19). The shaded region indicates the correlation limit for the parameter M.

Figure 9

R2 values versus coverage ratio for each data set (Eq. 19). The shaded region indicates the correlation limit for the parameter t/P.

Figure 10

R2 values versus the parameter AR/(M⋅P/D) for each data set (Eq. 19). The shaded regions indicate the correlation limits for the parameter AR/(M⋅P/D).

Figure 11

R2 values versus the parameter AR/(M⋅P/D) for each data set (Eq. 20(2)). The shaded regions indicate the correlation limits for the parameter AR/(M⋅P/D).

Figure 12

R2 values versus the parameter AR/(M⋅P/D) for each data set (Eq. 21(2)). The shaded regions indicate the correlation limits for the parameter AR/(M⋅P/D).

Figure 13

R2 values versus the parameter AR/(M⋅P/D) for each data set (Eq. 22(2)). The shaded regions indicate the correlation limits for the parameter AR/(M⋅P/D).

Figure 14

R2 values versus the parameter AR/(M⋅P/D) for each data set (Eq. 23(2)). The shaded regions indicate the correlation limits for the parameter AR/(M⋅P/D).

Figure 15

R2 values versus the parameter AR/(M⋅P/D) for each data set (cylindrical hole correlation (6)). The shaded regions indicate the correlation limits for the parameter AR/(M⋅P/D).

Figure 16

Comparison of current correlation predictions (Eq. 19) with experimental data for a range of blowing ratios (AR=3.9,P/D=6.5,t/P=0.48)

Figure 17

Comparison of current correlation predictions (Eq. 19) with experimental data for a range of coverage ratios (M=1.5)

Figure 18

Comparison of current correlation predictions (Eq. 19) with experimental data for a range of area ratios (M=1.5,P/D=6.0,t/P=0.43)

Figure 19

Comparison of current correlation predictions (Eq. 19) with experimental data for a range of hole spacings (M=1.5,AR=4.2)

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