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Multi-objective optimization of laidback fan-shaped film cooling hole on Turbine Vane Suction Surface

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Abstract

A CFD-based multi-objective optimization is performed for improving the film cooling performance of the laidback fan-shaped holes on the suction surface of a turbine guide vane under a typical blowing ratio of M = 1.5. Among the main geometric parameters, the inclination angle (α), lateral expansion angle (β) and forward expansion angle (γ) are selected as the design variables, with respective lower and upper bounds of (25°, 55°), (10°, 20°) and (3°, 15°) in turns. Two independent objective functions that are simultaneously optimized are selected as the spatially-averaged adiabatic film cooling effectiveness (ranging from s/d = 0 to s/d = 12) and the discharge coefficient. By using a variant of non-dominated sorting genetic algorithm (NSGA-II) coupled with the RBFNN-based surrogate model, the Pareto front of optimal solutions is obtained, providing a variety of options for seeking the maximum spatially-averaged adiabatic film cooling effectiveness, the maximum discharge coefficient, or the compromise of both aspects. The optimized results show that the optimal geometers of (α, β, γ) are (50.3°, 19.5°, 9.8°), (25°, 18.7°, 11.8°) and (27.3°, 19°, 5.1°) for achieving the most maximum film cooling effectiveness, the most maximum discharge coefficient and the compromise of both aspects, respectively. In general, a large lateral expansion angle of the laidback fan-shaped film-cooling hole is necessary in the shape optimization for all of the optimal options. However, with regard to the other design variables, their selections are very distinct following the optimal option. Further, the influence role of optimal fan-shaped geometry on the film cooling performance is illustrated according to the detailed flow and thermal behaviors.

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Abbreviations

C :

Chord length (m)

C d :

Discharge coefficient

c p :

Static pressure coefficient

C x :

Axial chord length (m)

d :

Film hole diameter (m)

F 1 :

Fitness function of spatially-averaged adiabatic film cooling effectiveness

F 2 :

Fitness function of discharge coefficient

k :

Ratio of specific heats

l 1 :

Length of cylindrical section (m)

l 2 :

Length of lateral expansion section (m)

l 3 :

Length of forward expansion section (m)

M :

Blowing ratio

Ma :

Mach number

P :

Cascade pitch (mm)

P hole :

Hole-to-hole pitch (mm)

p :

Pressure (MPa)

R :

Gas constant

Re :

Reynolds number

s :

Streamwise-direction

T :

Temperature (K)

t :

Film hole height (m)

u :

Velocity (m/s)

x :

Axial-direction

y :

Normal-direction

z :

Spanwise-direction

α :

Inclination angle (°)

β :

Lateral expansion angle (°)

γ :

Forward expansion angle (°)

δ :

Primary flow angle (°)

θ :

Stagger angle (°)

μ :

Dynamic viscosity (N∙s/m2)

ρ :

Density (kg/m3)

η :

Film cooling effectiveness

Θ :

Dimensionless temperature

ψ :

Pressure-drop ratio

ad:

Adiabatic

av:

Spatially-averaged

avs:

Laterally-averaged

aw:

Adiabatic wall

c:

Coolant or secondary flow

ref:

Reference laidback fan-shaped hole

∞:

Primary flow

*:

Total

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Acknowledgements

The authors gratefully acknowledge the financial supports for this project from the National Natural Science Foundation of China (grant No: U1508212, 51706097).

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Authors and Affiliations

  1. College of Energy and Power Engineering, Jiangsu Province Key Laboratory of Aerospace Power System, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Ying Huang, Jing-Zhou Zhang, Chun-Hua Wang & Xing-Dan Zhu

  2. Collaborative Innovation Center of Advanced Aero-Engine, Beijing, 100191, China

    Jing-Zhou Zhang

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  1. Ying Huang
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  2. Jing-Zhou Zhang
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Correspondence to Jing-Zhou Zhang.

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Huang, Y., Zhang, JZ., Wang, CH. et al. Multi-objective optimization of laidback fan-shaped film cooling hole on Turbine Vane Suction Surface. Heat Mass Transfer 55, 1181–1194 (2019). https://doi.org/10.1007/s00231-018-2500-6

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  • DOI: https://doi.org/10.1007/s00231-018-2500-6

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