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Research Papers

Biot Number Analogy for Design of Experiments in Turbine Cooling

[+] Author and Article Information
Saiprashanth Gomatam Ramachandran

School of Aeronautics and Astronautics,
Purdue University,
West Lafayette, IN 47907-2045
e-mail: prashanthgrs@gmail.com

Tom I-P. Shih

School of Aeronautics and Astronautics,
Purdue University,
West Lafayette, IN 47907-2045
e-mail: tomshih@purdue.edu

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received June 15, 2014; final manuscript received July 4, 2014; published online November 25, 2014. Editor: Ronald Bunker.

J. Turbomach 137(6), 061002 (Jun 01, 2015) (14 pages) Paper No: TURBO-14-1080; doi: 10.1115/1.4028327 History: Received June 15, 2014; Revised July 04, 2014; Online November 25, 2014

Cooling of turbine components that come in contact with the hot gases strongly affects the turbine's efficiency and service life. Designing effective and efficient cooling configurations requires detailed understanding on how geometry and operating conditions affect the way coolant cools the turbine materials. Experimental measurements that can reveal such information are difficult and costly to obtain because gas turbines operate at high temperatures (up to 2000 K), high pressures (30+ bar), and the dimensions of many key features in the cooling configurations are small (millimeters or smaller). This paper presents a method that enables experiments to be conducted at near room temperatures, near atmospheric pressures, and using scaled-up geometries to reveal the temperature and heat-flux distributions within turbine materials as if the experiments were conducted under engine operating conditions. The method is demonstrated by performing conjugate computational fluid dynamics (CFD) analyses on two test problems. Both problems involve a thermal barrier coating (TBC)-coated flat plate exposed to a hot-gas environment on one side and coolant flow on the other. In one problem, the heat transfer on the coolant side is enhanced by inclined ribs. In the other, it is enhanced by an array of pin fins. This conjugate CFD study is based on 3D steady Reynolds-averaged Navier–Stokes (RANS) closed by the shear-stress-transport turbulence model for the fluid phase and the Fourier law for the solid phase. Results obtained show that, of the dimensionless parameters that are important to this problem, it is the Biot number that dominates. This study also shows that for two geometrically similar configurations, if the Biot number distributions on the corresponding hot-gas and coolant sides are nearly matched, then the magnitude and contours of the nondimensional temperature and heat-flux distributions in the material will be nearly the same for the two configurations—even though the operating temperatures and pressures differ considerably. Thus, experimental measurements of temperature and heat-flux distributions within turbine materials that are obtained under “laboratory” conditions could be scaled up to provide meaningful results under “engine” relevant conditions.

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References

Figures

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Fig. 1

1D steady conduction across a flat plate with constant thermal conductivity

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Fig. 2

Schematic of the rib problem studied

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Fig. 3

Geometry of the ribs on two walls of the coolant duct

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Fig. 6

Grid used for the pin–fin test problem

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Fig. 5

Grid used for the rib test problem

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Fig. 4

Schematic of the pin–fin problem studied

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Fig. 7

Biot number on the hot-gas and coolant sides of the TBC-coated plate for cases 1 and 2 (Table 1)

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Fig. 8

Temperature (K) on the hot-gas and coolant sides of the TBC-coated plate for cases 1 and 2 (Table 1)

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Fig. 9

Heat flux (W/m2) on the hot-gas and coolant sides of the TBC-coated plate for cases 1 and 2 (Table 1)

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Fig. 10

Heat-transfer coefficient (W/m 2 K) on the hot-gas and coolant sides of the TBC-coated plate for cases 1 and 2 (Table 1)

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Fig. 11

Biot number (Eqs. (6a) and (6b)) on the hot-gas and coolant sides for cases 1, 3, and 4 (Table 1)

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Fig. 12

Nondimensional temperature (Eq. (7)) on the hot-gas side and coolant sides for cases 1, 3, and 4 (Table 1)

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Fig. 13

Nondimensional temperature (Eq. (7)) across the TBC-coated plate for cases 1 and 3 (Table 1)

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Fig. 14

Projected velocity vectors and streamlines colored by nondimensional temperature in selected planes for cases 1 and 3 (Table 1)

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Fig. 15

Nondimensional heat flux (Eq. (8)) on the hot-gas and coolant sides for cases 1, 3, and 4 (Table 1)

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Fig. 16

Biot number (Eqs. (6a) and (6b)) on the hot-gas and coolant sides of the TBC-coated plate for cases 1 and 2 (Table 2)

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Fig. 17

Nondimensional temperature (Eq. (7)) on the hot-gas and coolant sides of the TBC-coated plate for cases 1 and 2 (Table 2)

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Fig. 18

Nondimensional heat flux (Eq. (8)) at the hot-gas side and the coolant side of the TBC-coated plate for cases 1 and 2 (Table 2)

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Fig. 19

Biot number (Eqs. (6a) and (6b)), nondimensional temperature (Eq. (7)), and nondimensional heat flux (Eq. (8)) for pin fins in the first five rows in cases 1 and 2 (Table 2)

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