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Research Papers

# Large-Eddy Simulation of Film Cooling in an Adverse Pressure Gradient Flow

[+] Author and Article Information
Martin Konopka

e-mail: m.konopka@aia.rwth-aachen.de

Wolfgang Schröder

Institute of Aerodynamics,
RWTH Aachen University,
52062 Aachen, Germany

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received July 6, 2012; final manuscript received July 25, 2012; published online March 25, 2013. Editor: David Wisler.

J. Turbomach 135(3), 031031 (Mar 25, 2013) (13 pages) Paper No: TURBO-12-1133; doi: 10.1115/1.4007583 History: Received July 06, 2012; Revised July 25, 2012

## Abstract

In order to analyze the interaction of multiple rows of film cooling holes in flows at adverse pressure gradients, large-eddy simulations (LESs) are performed. The considered three-row cooling configuration consists of inclined cooling holes at an angle of 30 deg with a lateral pitch of $p/D=3$ and a streamwise spacing of $l/D=6$. The cooling holes possess a fan-shaped exit geometry with lateral and streamwise expansions. For each cooling row the complete internal flow is computed. Air and $CO2$ are injected in order to investigate the influence of an increased density ratio on the film cooling physics at adverse pressure gradients. The $CO2$ injected at the same blowing rate as air shows a higher magnitude of the Reynolds shear stress component and, thus, an enhanced mixing downstream of the cooling holes. The LES results of the air and $CO2$ configurations are compared to the corresponding particle-image velocimetry (PIV) measurements and show a convincing agreement in terms of the averaged streamwise velocity and streamwise velocity fluctuations. Furthermore, the cooling effectiveness is investigated for a zero and an adverse pressure gradient configuration with a temperature ratio at gas turbine conditions. For the adverse pressure gradient case, reduced temperature levels off the wall are observed. However, the cooling effectiveness shows only minor differences compared to the zero pressure gradient flow. The turbulent Schmidt number at $CO2$ injection shows large variations. Just downstream of the injection it attains low values, whereas high values are detected in the upper mixing zone of the cooling flow and the freestream at each film cooling row.

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## Figures

Fig. 1

Schematic of the multirow film cooling geometry

Fig. 2

Sketch of the shaped film cooling geometry

Fig. 3

Numerical and experimental freestream velocity versus the streamwise distance at case I

Fig. 4

Computational domain

Fig. 5

Pressure coefficient distribution imposed at the upper boundary compared to the measurements at cases I-III

Fig. 6

Turbulent structures visualized by the λ2 criterion with the mapped-on CO2 mass fraction at case II

Fig. 7

Comparison of the mean streamwise velocity profiles and the RMS profiles of the streamwise velocity component of the current computations with the PIV measurements for air injection at case I and CO2 injection at case II. The streamwise velocity profiles are offset by Δu¯/u∞ = 0.4 and the streamwise RMS profiles are offset by Δu'2¯/u∞ = 0.08.

Fig. 8

Definition of the locations to compare the numerically and experimentally determined flow profiles

Fig. 9

Contours of the cooling effectiveness distribution at case II

Fig. 10

Contours of the cooling effectiveness at the wall at case III for air injection

Fig. 11

Comparison of the laterally averaged cooling effectiveness of the adverse pressure gradient cases II and III to the zero pressure gradient case IV and the computation of Renze et al. [11], which corresponds to case IV

Fig. 12

Comparison of the first row centerline (z/D = 0), and second row centerline (z/D = 1.5) cooling effectiveness of the adverse pressure gradient cases II and III, compared to the zero pressure gradient configuration at case IV

Fig. 13

Temperature profiles of cases III and IV at the centerline of the first film cooling hole (z/D = 0)

Fig. 14

Wall normal turbulent heat transport

Fig. 15

Temperature contours at x/D = 26.88 for case III and case IV at the APG and the ZPG

Fig. 16

Reynolds shear stress component profiles at z/D = 1.5

Fig. 17

The CO2 mass fraction (case II) and the dimensionless fluid temperature fluctuation (case III) in the z/D = 0 plane

Fig. 18

Cooling effectiveness and cooling effectiveness fluctuations at CO2 injection (case II)

Fig. 19

Cooling effectiveness and cooling effectiveness fluctuations at air injection (case III)

Fig. 20

Contours of the wall-normal turbulent Schmidt number Sct,y at CO2 injection (case II) in the z/D = 0 and x/D = 2-plane

Fig. 21

Contours of the isotropic turbulent Schmidt number Sct at CO2 injection (case II) in the z/D = 0 and x/D = 2-plane

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