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Research Papers

Large Eddy Simulation of the Laminar Heat Transfer Augmentation on the Pressure Side of a Turbine Vane Under Freestream Turbulence

[+] Author and Article Information
Yousef Kanani

Materials and Aerospace
Engineering Department,
Illinois Institute of Technology Mechanical,
Chicago, IL 60616
e-mail: ykanani@hawk.iit.edu

Sumanta Acharya

Materials and Aerospace
Engineering Department,
Illinois Institute of Technology Mechanical,
Chicago, IL 60616
e-mail: sacharya1@iit.edu

Forrest Ames

Mechanical Engineering Department,
University of North Dakota,
Grand Forks, ND 58202
e-mail: forrest.ames@engr.und.edu

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received September 5, 2018; final manuscript received September 24, 2018; published online January 21, 2019. Editor: Kenneth Hall.

J. Turbomach 141(4), 041004 (Jan 21, 2019) (12 pages) Paper No: TURBO-18-1233; doi: 10.1115/1.4041599 History: Received September 05, 2018; Revised September 24, 2018

Vane pressure side heat transfer is studied numerically using large eddy simulation (LES) on an aft-loaded vane with a large leading edge over a range of turbulence conditions. Numerical simulations are performed in a linear cascade at exit chord Reynolds number of Re = 5.1 × 105 at low (Tu ≈ 0.7%), moderate (Tu ≈ 7.9%), and high (Tu ≈ 12.4%) freestream turbulence with varying length scales as prescribed by the experimental measurements of Varty and Ames (2016, “Experimental Heat Transfer Distributions Over an Aft Loaded Vane With a Large Leading Edge at Very High Turbulence Levels,” ASME Paper No. IMECE2016-67029). Heat transfer predictions on the vane pressure side are in a very good agreement with the experimental measurements and the heat transfer augmentation due to the freestream turbulence is well captured. At Tu ≈ 12.4%, freestream turbulence enhances the Stanton number on the pressure surface without boundary layer transition to turbulence by a maximum of about 50% relative to the low freestream turbulence case. Higher freestream turbulence generates elongated structures and high-velocity streaks wrapped around the leading edge that contain significant energy. Amplification of the velocity streaks is observed further downstream with max rms of 0.3 near the trailing edge but no transition to turbulence or formation of turbulence spots is observed on the pressure side. The heat transfer augmentation at the higher freestream turbulence is primarily due to the initial amplification of the low-frequency velocity perturbations inside the boundary layer that persist along the entire chord of the airfoil. Stanton numbers appear to scale with the streamwise velocity fluctuations inside the boundary layer.

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Figures

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Fig. 1

Computational domain and the computational grid in the xy-plane

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Fig. 2

Time-averaged Stanton number distribution over the vane, Tu = 7.9%

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Fig. 3

Pressure distribution over the surface

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Fig. 4

Contours of the time-averaged velocity at the midspan of the vane for simulation C1

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Fig. 5

Longitudinal and transverse autocorrelation functions, f(r) and g(r) at 0.36 L upstream of the stagnation point at the midspan

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Fig. 6

Power spectral density of velocity fluctuations at 0.36L upstream of stagnation point, simulation C1

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Fig. 7

Evolution of turbulence intensity with distance at the edge of the boundary layer at midspan of the vane

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Fig. 8

The distribution of skin friction over the pressure surface

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Fig. 9

Stanton number distribution over stagnation and pressure surface for different levels of inflow turbulence intensity. C0–C2 are LES predictions, C3 is 2D laminar calculation, see Table 1 for details.

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Fig. 10

(a) Instantaneous streamwise velocity fluctuations at wall distance of d = 0.001L and (b) Stanton number distribution over the pressure surface over the whole span for case C1

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Fig. 11

(a) Instantaneous streamwise velocity fluctuations at wall distance of d = 0.001L and (b) Stanton number distribution over the pressure surface over the whole span for case C2

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Fig. 12

Joint probability density function of (a) the streamwise velocity and temperature fluctuations at d = 0.0004L (d+ ≈ 3.5) and (b) the streamwise velocity fluctuations at d = 0.0004L and surface Stanton number at s/L = −0.284, simulation C2

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Fig. 13

Iso-surfaces of the Q-criterion over the pressure surface for simulation C1 ((a) and (b)) and C2 ((c) and (d)) overlaying instantaneous Stanton number distribution over pressure surface ((a) and (c)) and velocity fluctuations at d = 0.002L ((b) and (d))

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Fig. 14

Time evolution of (a) the spanwise averaged (over ±10% of span) instantaneous velocity at d = 0.008L and (b) surface temperature at various streamwise locations. Line plots are shifted upward for clarity.

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Fig. 15

Power spectral density of the spanwise averaged (over ±10% of span) velocity signal at s/L = −0.57and d = 0.008L

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Fig. 16

The characteristic time scale of the velocity fluctuations. Velocity fluctuations are sampled at wall distance of 0.008L.

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Fig. 17

The characteristic time scale of the surface temperature fluctuations

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Fig. 18

Time-averaged streamwise velocity profiles at the midspan of the vane at s/L = {−0.1, −0.3, −0.6, −0.8}

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Fig. 19

RMS of velocity fluctuations inside the boundary layer for simulation C0 (gray), C1 (gray), and C2 (black) at different stations over the pressure surface

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Fig. 20

Evolution of the rms of velocity fluctuations over the pressure surface

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Fig. 21

Time-averaged nondimensional temperature profiles at the midspan of the vane for simulation (a) C0, (b) C1, and (c) C2

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Fig. 22

Contribution of different heat transfer mechanism across the boundary layer at s/L = −0.3 for simulation (a) C0, (b) C1, and (c) C2

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Fig. 23

Eddy Prandtl number distribution across the boundary layer at s/L = {−0.2, −0.3, −0.6} for simulation C1 and C2

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Fig. 24

Reynolds analogy factor over the pressure surface for simulation C0, C1, and C2

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