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Discharge coefficients and aerodynamic losses for cylindrical and cratered film-cooling holes with various coolant crossflow orientations

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Abstract

In addition to cooling performance, the discharge coefficient, and aerodynamic loss should be considered to apply the film-cooling hole to the modern gas turbine blade's cooling design. The present study describes the discharge coefficients and aerodynamic loss characteristics for cylindrical and cratered holes with a numerical method. The shear stress transport turbulence model is firstly validated in comparison with the literature data. The discharge coefficients, total pressure coefficients, mixing pressure coefficients, and hole pressure coefficients are further determined under the coolant channel outlet's static pressure. The flow fields and velocity distributions of three coolant crossflow orientation configurations, including the co-flow orientation, the counter-flow orientation, and the perpendicular-flow orientation, are analyzed and compared. The numerical results show that the cratered hole always yields a higher discharge coefficient than the cylindrical hole, especially under the low-pressure ratio. The discharge coefficient is highly sensitive to the coolant crossflow orientation, mainly caused by the different separation flow at the hole entrance. The perpendicular-flow orientation configuration has the medium value of the discharge coefficient. For aerodynamic loss valuation, the cratered hole has a higher total pressure loss coefficient and pressure loss coefficient in the hole, but lower mixing pressure loss coefficient. The coolant flow orientation also influences these three pressure loss coefficients for the cylindrical hole and cratered hole, which can be explained by analyzing the flow field around the hole exit.

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Abbreviations

C d :

Discharge coefficient

D :

Cylindrical hole diameter (mm)

F 1, F 2 :

Blending functions

G :

Coefficients

h :

Fluctuating enthalpy (J kg−1)

h tot :

Mean total enthalpy (J kg−1)

k :

Turbulent kinetic energy

m c :

Mass flow rate of coolant flowing through the hole (kg s−1)

m m :

Mass flow rate of mainstream flow (kg s−1)

M :

Blowing ratio

DR:

Ratio of coolant-to-mainstream density

P :

Mean pressure (Pa)

P c,out :

Static pressure at the outlet of the coolant channel (Pa)

P f :

Static pressure at the outlet of the mainstream channel (Pa)

P k :

Production rate of turbulence

P m :

Static pressure in the mainstream channel (Pa)

P t,c :

Total pressure in the coolant channel (Pa)

P t,cin :

Total pressure at the cooling hole entrance (Pa)

P t,m :

Total pressure at the outlet of the mainstream channel (Pa)

P t,min :

Total pressure at the inlet of the mainstream channel (Pa)

P t,cout :

Total pressure at the cooling hole exit (Pa)

P t,f :

Total pressure at the outlet of the mainstream channel (Pa)

R :

Gas constant of air (J kg−1 K−1)

S E :

Energy source

S M :

Sum of the body forces

T :

Mean temperature (K)

T t,c :

Total temperature in the coolant channel (K)

u i, u j :

Fluctuating velocity components (m s−1)

U i, U j :

Mean velocity components (m s−1)

v :

Velocity (m s−1)

v m :

Mainstream flow velocity (m s−1)

v cin :

Averaged velocity at the hole normal surface (m s−1)

v X :

Velocity at the X-direction (m s−1)

v Z :

Velocity at the Z-direction (m s−1)

X :

Streamwise direction (mm)

Y :

Lateral direction (mm)

y + :

Yplus

Z :

Vertical direction (mm)

κ :

Ratio of specific heats

ρ :

Density (kg m−3)

ρ m :

Density of the fluid at the mainstream channel inlet (kg m−3)

µ :

Fluid’s dynamic viscosity

µ t :

Turbulent viscosity

ξ p,hole :

Pressure loss coefficient in the hole

ξ p,mix :

Mixing pressure loss coefficient

ξ p,total :

Total pressure loss coefficient

ξ ratio :

Ratio of pressure loss in the hole to total pressure loss

τ :

Molecular stress tensor

ω :

Turbulent frequency

SST:

Shear stress transport

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Acknowledgements

This investigation was supported by the Natural Science Foundation of Tianjin (Grant Number 18JCQNJC07200) and the National Science Foundation of China (Grant Numbers 51776201, 51506150).

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Authors and Affiliations

  1. Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, Tianjin University of Technology, Tianjin, China

    Chao Zhang & Linchao Bai

  2. China National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin, China

    Chao Zhang & Linchao Bai

  3. Advanced Gas Turbine Laboratory, Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing, China

    Jinglun Fu & Yang Yang

  4. University of Chinese Academy of Sciences, Beijing, China

    Jinglun Fu & Yang Yang

  5. Institute for Engineering Thermal Physics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    Artem Khalatov

Authors
  1. Chao Zhang
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  2. Linchao Bai
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  3. Jinglun Fu
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  4. Artem Khalatov
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  5. Yang Yang
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Correspondence to Chao Zhang or Yang Yang.

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Zhang, C., Bai, L., Fu, J. et al. Discharge coefficients and aerodynamic losses for cylindrical and cratered film-cooling holes with various coolant crossflow orientations. J Braz. Soc. Mech. Sci. Eng. 43, 161 (2021). https://doi.org/10.1007/s40430-021-02891-z

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