Effects of Biot Number on Temperature and Heat-Flux Distributions in a TBC-Coated Flat Plate Cooled by Rib-Enhanced Internal Cooling

Abstract

Advanced turbines are designed to operate at near the material’s maximum allowable temperature. Thus, there is very little room for mistakes in the design of cooling strategies. Since the heat-transfer coefficient varies significantly about ribs and pin fins in internal-cooling passages, different parts of the turbine material exposed to the hot gas are cooled at different rates by internal cooling, and this could produce substantial temperature variations within the material, including hot spots. For a given hot-gas temperature and a given coolant temperature, the amount of temperature variation within the material depends on the Biot number. In this study, conjugate heat-transfer analysis were performed to investigate the effects of Biot number on the temperature and heat flux in a TBC-coated flat plate exposed to hot gas on one side and rib-enhanced internal cooling on the other side. The Biot numbers (Bi) examined range from 0.4 to 6 if the length scale in Bi is based on the thickness of the TBC-coated plate (L) and 0.2 to 3 if based on L/2. This computational study uses 3-D steady RANS closed by the realizable k-ε turbulence model for the gas phase (wall functions not used) and the Fourier law for the solid phase. Results obtained show that for two geometrically similar TBC-coated plates exposed to the same hot-gas and coolant temperatures, if Bi is nearly the same, then the magnitude of the temperature will be nearly the same and contours of the temperatures will be nearly geometrically similar. The contours of heat flux, however, will be geometrically similar but have very different magnitudes because the gradients are different. Also, though the variations in temperature from the hot-gas to the coolant side of the TBC-coated plate decrease with decreasing Bi, the variation in temperature in the spanwise direction can actually increase with decreasing Bi. When the Bi based on L is between 0.4 to 1, that temperature variation in the super alloy next to the TBC can differ by as much as 25 K along the spanwise direction because of the large variations in the local heat-transfer coefficients induced by the ribs in the spanwise direction.