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Constructal Design of Elliptical Conduits for Cooling of Gas Turbine Blades with External Thermal Barrier Coating

Abstract

Gas turbines (GTs) are thermal machines used to transform the energy released in combustion with a hydrocarbon into mechanical power, in order to drive a machine or generate thrust in aircraft. The critical issue in the GT design are the parts exposed to extreme mechanical and thermal conditions, e.g., the first row of turbine blades. The GT thermal efficiency is limited by the maximum temperature the blade materials can withstand without softening or creeping. Currently, the maximum operating temperature is above the softening point of the blade material thanks to techniques of ceramic coatings of low thermal conductivity, called Thermal Barrier Coating (TBC), and techniques of blade cooling. The internal cooling of blades involves conduits inside them for air that comes from a bleed in an intermediate compressor stage. The air bleeding is around 3 to 5% of the main GT flow. This air and the heat flow that it receives are not used to generate power, so it is necessary to optimize the cooling techniques in order to control the temperature using the least amount of air and minimum heat flux evacuated, for holding the GT overall efficiency high. The present work studies the internal cooling of Elemental Gas Turbine Blade (EGTB) with a fixed thickness of the TBC and the optimization of the conduit shape and position over a cross section in 2D. The optimization is carried out by exhaustive searching method based on the Constructal Theory. The optimization of the position, size, and aspect ratio of EGTBs was done for two types of standard elliptical conduits of different geometries, uniformly distributed. Two different objective functions are analyzed: minimum maximum temperature on the metal and maximum heat evacuation efficiency. The outcome of this work establishes that the use of elliptical conduits of aspect ratio 2:5 leads to improvement in the thermal performance of cooled blades. As compared with circular conduits of the same area, elliptical conduits allow transfer of a greater amount of heat; with a correct design, they enable a lower maximum temperature on the metal. Besides, the constructal designs obtained in this study for the minimum maximum relative temperature \(\tilde{T}_{\rm{max}}\) or maximum heat evacuation efficiency ξ were not identical.

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Abbreviations

A :

area, dm2

D h :

hydraulic diameter

f :

Darcy friction coefficient

H :

elemental blade height, dm

h :

convection coefficient, W/(m2 · K)

H 0 :

vertical semi-axis of the ellipse 0, dm

H 1 :

vertical semi-axis of the ellipse 1, dm

H 2 :

wall thickness of ellipse 1, dm

k :

thermal conductivity coefficient, W/(m·K)

L :

elemental blade width, dm

L 0 :

horizontal semi-axis of the ellipse 0, dm

L 1 :

horizontal semi-axis of ellipse 1, dm

Nu :

Nusselt number

ε :

emissivity

μ :

dynamic viscosity, kg/m·s

ν :

cinematic viscosity, m2/s

ξ :

heat evacuation efficiency

ρ :

density, kg/m3

P :

pressure

Pe :

Peclet number

Pr:

Prandtl number

q :

total heat, W

R :

thermal resistance, m2·K/W

Re:

Reynolds number

S :

heat source, W/m3

T :

temperature, K

V :

velocity, m/s

W :

transversal dimension, dm

x :

abscissa coordinate, dm

y :

ordinates coordinate, dm

σ :

Stefan-Boltzmann constant, W/(K4m2)

ϕ :

material ratio

ϕ 0 :

1/4 ellipse 0 dimensionless area

ϕ 1 :

1/2 ellipse 1 dimensionless area

~:

non dimensional parameter

0:

ellipse 0

1:

ellipse 1

max:

maximum

min:

minimum

References

  1. 1.

    Han, J.C., Dutta, S., and Ekkad, S., Gas Turbine Heat Transfer and Cooling Technology, New York: Taylor and Francis, 2012.

    Google Scholar 

  2. 2.

    Bejan, A. and Lorente, S., Design with Constructal Theory, Wiley, 2008.

    Book  Google Scholar 

  3. 3.

    Rocha, L.A., Bejan, A., and Lorente, S., Constructal Law and the Unifying Principle of Design, New York: Springer-Verlag, 2013.

    Book  Google Scholar 

  4. 4.

    Feng, H., Chen, L., Xie, Z., and Sun, F., Constructal Design for Gas-Turbine Blade Based on Minimization of Maximum Thermal Resistance, Appl. Therm. Engin., 2015, vol. 90, pp. 792–797.

    Article  Google Scholar 

  5. 5.

    Hylton, L.D., Mihelc, M.S., Turner, E.R., Nealy, D.A., and York, R.E., Analytical and Experimental Evaluation of the Heat Transfer Distribution Over the Surfaces of Turbine Vanes, NASA, 1983.

    Google Scholar 

  6. 6.

    Reyhani, M.R., Rezazadeh, M., Alizadeh, M., Fathi, A., and Khaledi, H., Turbine Blade Temperature Calculation and Life Estimation, a Sensitivity Analysis, Propul. Power Res., 2013, pp. 148–171.

    Google Scholar 

  7. 7.

    David R.C., Matthias, O., and Nitin, P.P., Thermal-Barrier Coatings for More Efficient Gas-Turbine Engines, Mat. Res. Soc. Bull., 2012, vol. 37, no. 10, pp. 891–898.

    Article  Google Scholar 

  8. 8.

    Han, J.C., Recent Studies in Turbine Blade Cooling, Int. J. Rotat. Machin., 2004, vol. 10, no. 6, pp. 443–457.

    Google Scholar 

  9. 9.

    Han, J.C. and Wright, L.M., Enhanced Internal Cooling of Turbine Blades and Vanes, Turbine Heat Transfer Laboratory, Department of Mechanical Engineering, University College Station Texas, USA, 2013.

    Google Scholar 

  10. 10.

    Bunker, R.S., Cooling Design Analysis, GE Global Research, One Research Circle and US DOE, New York, 2006.

    Google Scholar 

  11. 11.

    Sundberg, J., Heat Transfer Correlations for Gas Turbine Cooling; http://www.diva-portal.org/smash/get/diva2:21321/FULLTEXT01.pdf//site visited 06/06/16.

  12. 12.

    Al-Luhaibi, A.J., and Tariq, M., Thermal Analysis of Cooling Effect on Gas Turbine Blade, Int. J. Res. Engin. Tech., 2014, pp. 603–610.

    Google Scholar 

  13. 13.

    Iacovides, H. and Raisee, M., Flow and Heat Transfer in Straight Cooling Passages with Inclined Ribs on Opposite Walls: An Experimental and Computational Study, Exp. Therm. Fluid Sci., 2003, pp. 283–294.

    Google Scholar 

  14. 14.

    Ravi Teja, T. and Krishna Chaitanya, S., Case Study on Turbine Blade Internal Cooling, Int. J. Engin. Res. Tech. (IJERT), 2013, vol. 2, no. 3, pp. 1–5.

    Google Scholar 

  15. 15.

    Nasir, H., Turbine Blade Tip Cooling and Heat Transfer, Doctoral Dissertation, Bangladesh University of Engineering and Technology, 2004.

    Google Scholar 

  16. 16.

    Han, J.C. and Srinath, E., Recent Development in Turbine Blade Film Cooling, Int. J. Rotat. Machin., 2001, vol. 7, no. 1, pp. 21–40.

    Article  Google Scholar 

  17. 17.

    Xu, R., Hou, J., Wang, L., Yu, Y., Wei, J., and Li, C., Fluid Flow and Heat Transfer Characteristics in a 180-Deg Round Turned Channel with a Perforated Divider, J. Appl. Math. Phys., 2014, pp. 411–417.

    Google Scholar 

  18. 18.

    Yuri, M., Masada, J., Tsukagoshi, K., Ito, E., and Hada, S., Development of 1600°C-Class High-Efficiency Gas Turbine for Power Generation Applying J-Type Technology, Mitsubishi Heavy Ind. Techn. Rev., 2013, vol. 50, no. 3, pp. 1–10.

    Google Scholar 

  19. 19.

    Ahn, J., Schobeiri, M.T., Han, J.-C., and Moon, H.-K., Effect of Rotation on Leading Edge Region Film Cooling of a Gas Turbine Blade with Three Rows of Film Cooling Holes, Int. J. Heat Mass Transfer, 2007, vol. 50, no. 12, pp. 15–25.

    Article  Google Scholar 

  20. 20.

    Siddique, W., Design of Internal Cooling Passages: Investigation of Thermal Performance of Serpentine Passages, Doctoral Dissertation, Stockholm: Royal Institute of Technology, 2011.

    Google Scholar 

  21. 21.

    Ferlauto, M., An Inverse Method of Designing the Cooling Passages of Turbine Blades Based on the Heat Adjoint Equation, Proc. Inst. Mech. Engin., Part A: J. Power Energy, 2014, vol. 228, no. 3, pp. 328–339.

    MathSciNet  Article  Google Scholar 

  22. 22.

    Alhajeri, M.H., Alhamad Alhajeri, H., Alrajhi, J., Alardhi, M., and Alshaye, S., Numerical Analysis of Fluid Flow in Turbine Blade Cooling Passage, Int. J. Sci. Adv. Tech., 2011, vol. 1, no. 8, pp. 1–10.

    Google Scholar 

  23. 23.

    Schlichting, H., Boundary-Layer Theory, 6th ed., New York: McGraw-Hill, 1979.

    MATH  Google Scholar 

  24. 24.

    Cengel, Y.A., Heat and Mass Transfer, 3rd ed., McGrawHill, 2007.

    Google Scholar 

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Correspondence to C. Bosc, L. A. O. Rocha, F. R. Centeno or F. Gutierrez.

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Bosc, C., Rocha, L.A.O., Centeno, F.R. et al. Constructal Design of Elliptical Conduits for Cooling of Gas Turbine Blades with External Thermal Barrier Coating. J. Engin. Thermophys. 28, 507–528 (2019). https://doi.org/10.1134/S1810232819040064

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