Effects of operational and geometrical uncertainties on heat transfer and pressure drop of ribbed passages

In this paper uncertainty quantification of turbulent flow and heat transfer through ribbed channels of gas turbine blades is presented and discussed. The uncertainty quantification method is first validated using the Ishigami function and then applied to turbulent flow and heat transfer through a ribbed pipe. Combination of four operational and geometrical uncertain variables (Re, Pr, P/h and D/h) are considered. Results for local Nusselt number, average Nusselt number and non-dimensional pressure drop using a polynomial chaos expansion of order 3 are presented and discussed. Uncertainty quantification results for the local Nusselt number showed that the regions located on top and immediately after the rib are more sensitive to the uncertain input variables. To tackle the curse of dimensionality, the sparse polynomial chaos expansion is further employed in this study. Results for quantities of interest showed that the sparse polynomial chaos method reduces the computational cost by at least 50% in comparison to the full polynomial chaos expansion method. Furthermore, results show that the sparse PCE works better for the non-dimensional pressure drop than the average Nusselt number. Results of sensitivity analysis for non-dimensional pressure-drop showed that, in agreement with the empirical correlations, this quantity is independent of Reynolds number. Also, results of sensitivity analysis for local Nusselt number showed that generally the major variability of Nusselt number is due to the blockage ratio.