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Research Papers

# Film Cooling Using Antikidney Vortex Pairs: Effect of Blowing Conditions and Yaw Angle on Cooling and Losses

[+] Author and Article Information
Lars Gräf

e-mail: graef@ifd.mavt.ethz.ch

Leonhard Kleiser

e-mail: kleiser@ifd.mavt.ethz.ch
Institute of Fluid Dynamics,
Department of Mechanical
and Process Engineering,
ETH Zurich, Sonneggstrasse 3,
Zurich 8092, Switzerland

1Corresponding author.

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 May 4, 2013; published online September 20, 2013. Assoc. Editor: Je-Chin Han.

J. Turbomach 136(1), 011008 (Sep 20, 2013) (8 pages) Paper No: TURBO-12-1103; doi: 10.1115/1.4024648 History: Received June 29, 2012; Revised May 04, 2013

## Abstract

A film-cooling configuration generating an antikidney vortex pair is studied. The configuration features cylindrical cooling holes inclined at an angle of $α=35 deg$ and arranged in two spanwise rows with row-wise alternating yaw angles $±β$. Results of several large-eddy simulations are presented with varying blowing conditions and yaw angles. The effects on the achieved cooling and the generated losses are studied. The film-cooling Reynolds number (based on the fully turbulent hot boundary layer along a flat plate and the cooling hole diameter) is 6570 and the Mach number is 0.2. The density as well as mass-flux ratios (DR and M) range from 1 to 2 and the yaw angles from $β=±30 deg$ to $±60 deg$. We identify scaling parameters and explain relevant mechanisms. Moreover, the flow field is subdivided into three regions featuring different physical mechanisms: the single-jet, the jet-interaction, and the diffusion region. A strong antikidney vortex pair occurs for high momentum ratios I. For the highest ratio, I = 2.3, our configuration may provide even better effectiveness than cooling with particular fan-shaped holes.

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## References

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## Figures

Fig. 1

Injection geometry and resulting vortices (from Fig. 1 of Ref. [18]). (a)–(c): Kidney-vortex pair from simple-angle injection; (d)–(f): antikidney-vortex pair; (a), (d): side; (b), (e): downstream; and (c), (f): top view.

Fig. 2

Comparison of experimental results on film-cooling types listed in Table 1. Black: spanwise-averaged effectiveness ⟨η⟩t,z; blue: maximum effectiveness maxz⟨η⟩t (see online version for color).

Fig. 3

Computational domain (Fig. 2 and case 3 of Ref. [18]) and flow regions. : Inflow sponge; : ambient and outflow sponge; : downstream grid stretching; : wall.

Fig. 4

(a), (c): Effectiveness and (b): efficiency for different blowing conditions. Black: spanwise-averaged; blue: maximum or red: minimum effectiveness. For symbols, see Table 2 (see online version for color).

Fig. 5

(—): Temperature isolines (colored patches online) for row-wise different blowing conditions; ( , ): antikidney vortex-pair trajectories and; (– – –): boundary-layer thickness ⟨U⟩t/U∞ = 0.95. (a)–(d): Top view of ⟨η⟩t; (e)–(h): side view of centerline ⟨Θ⟩t|z/d = 0, note the changed aspect ratio; (i)–(x): downstream view of ⟨Θ⟩t|x/d = -1,3,10,20; isolevels: 0.1, 0.2, …1.0 (see online version for color). For symbols, see Table 2.

Fig. 6

Loss coefficients at different blowing conditions. (a) Hot gas and (b) mixture total-pressure loss; (c) discharge loss; (d) mixture entropy generation. Black symbols: cases V2, B1, B2, and R0; gray symbols: cases I1 and I2 for comparison. For symbols, see Table 2.

Fig. 7

Temperature for different yaw angles, analog to Fig. 5. For symbols, see Table 3.

Fig. 8

(a): Effectiveness for different yaw angles, analog to Fig. 4. (b): Comparison of spanwise-averaged effectiveness with experimental cases L7 and L8 (both: α = 30  deg,β = 0  deg,M = 2.0,S/d = 0). L7: Cylindrical holes [31] (L/d = 6, P/d = 3, DR = 1.8); L8: fan-shaped holes [32] (L/d = 5, P/d = 4, DR = 1.7); for further symbols, see Table 3.

Fig. 9

Loss coefficients at different yaw angles. (a): Hot gas total-pressure loss; (b): mixture entropy generation. Black symbols: cases R0, I1, and I2; gray symbols: cases V2, B1, and B2 for comparison. For symbols, see Table 3.

Fig. 10

Effectiveness for different resolutions and domain extents. ▪: Reference experiment L0 DR = 1, M = 1; : fine LES V1 DR = 1, M = 1; □: coarse LES V2 DR = 1, M = 1; (……), ○: coarse LES DR = 2, M = 2.1 R0, R0 with xmax/d = 28, and R0 with ymax/d = 10. Analog to Fig. 4(a); for hatching, see Fig. 3.

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