The role of biot number in turbine-cooling design and analysis
Abstract
Cooling of gas turbines is critical for efficiency and service life. Design of efficient and effective cooling configurations requires detailed understanding on how geometry and operating conditions affect how coolant cools the turbine material. Experiments that can reveal such information are difficult to obtain because gas turbines operate at high temperatures (up to 2,000 K), high pressures (30+ atmospheres), and the dimensions of many key features in the cooling configurations are small (millimeters or smaller). The objective of this study is twofold. The first is to develop a method to enable experiments conducted at near room temperatures and near atmospheric pressures, using large geometries to reveal temperature and heat flux distribution in turbine materials as if the experiments were conducted under realistic turbine operating conditions. The second is to understand flow and heat transfer mechanisms that could create hot spots, where temperature of the turbine material exceeds the maximum allowable. The two objectives of this study were accomplished by performing computational analyses that account for the hot gas and coolant flows and the turbine material for two test problems. Both problems involve a flat plate exposed to a hot gas flow on one side and coolant flow on the other. In one problem, the heat transfer on the coolant side is enhanced by inclined ribs. For the other problem, the heat transfer on coolant side is enhanced by a staggered array of pin fins. This computational study uses 3-D steady RANS closed by the shear-stress-transport turbulence model for the gas phase and the Fourier law for the solid phase. Results obtained from this study 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 cooling configurations, regardless of the operating pressure and hot-gas/ coolant temperatures, if the Biot number distributions on the hot-gas and the coolant sides are nearly the same, then the magnitude and contours of non-dimensional heat flux and temperature will be nearly the same. Thus, experiments obtained under 'laboratory' conditions can be scaled up to provide meaningful results under 'engine' operating conditions. The Biot number was also found to have dominant effects on temperature variations within turbine materials. To study the effects of Biot number on the temperature and heat flux distribution in the turbine material for the two cooling configurations, a wide range of Biot numbers were examined—from 0.2 to 24 if the length scale in the Biot number is based on the thickness of the plate (L) and 0.1 to 12 if based on L/2. When the cooling is enhanced by inclined ribs, results obtained show that, though variations in temperature from the hot-gas to the coolant side of the plate decrease with decreasing Biot number, the variations in temperature in the spanwise direction can actually increase with decreasing Biot number. When the Biot number based on L is between 0.4 and 1, the temperature in the super alloy next to the thermal barrier coating (TBC) can differ by as much as 10 % along the spanwise direction because of the large variations in the local heat-transfer coefficients induced by the ribs in the spanwise direction. When the cooling is enhanced by pin fins, results obtained show that the temperature variation in the super alloy next to the TBC is very small along the spanwise direction for both low and high Biot number cases. Thus, for the pin-fin configuration, analysis based on laterally averaged temperature is reasonable but not in the case of the inclined rib configuration.
Degree
M.S.E.
Advisors
Shih, Purdue University.
Subject Area
Aerospace engineering|Mechanical engineering
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