Biot Number Error in Low Temperature Inconel Overall Effectiveness Experiments

To predict the performance of turbine materials at engine conditions, experiments are often performed at lower temperature laboratory conditions. In order to ensure the low-temperature, laboratory results accurately predict the nondimensionalized surface temperature at engine conditions, several non-dimensional parameters must be matched in the experiment, including the Biot number. Matching the Biot number requires that the ratio of the thermal conductivity of the material to the thermal conductivity of the air must be matched between laboratory experiments and engine conditions. With traditional nickel alloys such as Inconel, it is sometimes assumed that the Biot number is matched since Inconel’s thermal conductivity variation with temperature scales relatively closely with that of air. However, the thermal conductivity ratio does not scale perfectly and therefore some Biot number error does indeed exist, with the problem exacerbated at lower testing temperatures. To date, there has been no experimentally verified quantification of the error in the overall effectiveness, ϕ, that might be caused by this Biot number error. Based on published thermal conductivity data, Ti-6Al-4V is predicted to allow for a better Biot number match, thereby better simulating Inconel at engine conditions in a typical low temperature experiment. In this research, we utilized geometrically identical models constructed of Ti-6Al-4V and Inconel 718 to evaluate the error in overall effectiveness that might occur through simply using an actual engine nickel alloy part at experimental conditions. While the Ti-6Al-4V model has a nearly perfectly matched Biot number, the Inconel model’s Biot number was 73% higher than appropriate. The overall effectiveness experiments were conducted at a range of advective capacity ratios and the overall effectiveness distributions were compared. The results demonstrate that ϕ measured in low temperature tests performed on an Inconel turbine component do not suffer markedly from Biot number error. The theoretically more Biot number appropriate Ti-6Al-4V model produced area averaged overall effectiveness values that differed by only 0.01 from its Inconel counterpart, within experimental uncertainty, and would only represent a roughly 10 K error in surface temperature prediction at engine conditions. These results suggest that typical nickel superalloys used in turbine components may be tested at low temperature without the use of a surrogate material to better match Biot number.