UNCERTAINTY QUANTIFICATION ANALYSIS OF BACK FACING STEPS FILM COOLING CONFIGURATIONS

This paper compares two back step film-cooling configurations under an uncertainty quantification framework. An important limit of such configurations is their reliability under geometrical variations, which is taken into account in this study. For the back step configurations, a straight and a curved step is used. Detached eddy simulations with k-co turbulence model are performed using OpenFOAM ver. 4.0. The Reynolds number is based on the main stream velocity and film cooling hole diameter, d, and is Re=15,300. The investigated step heights are 0.5d and 0.75d, and the blowing ratios, BR, are 0.5 and 1.0. The straight and the curved steps are found to enhance lateral spreading of coolant flow, resulting in higher film cooling effectiveness compared to the baseline case without the step at comparatively higher BR conditions. The curved step shows better performance than the straight one in particular from BR=1.0 upwards with the step height of 0.5d. At lower BR with lower Hld, and at higher BR with higher Hld, deterministic simulations are not able to identify the best performer. However when the performance of the two configurations is evaluated considering the stochastic variation of step height and the cooling condition, the benefit of the curved step becomes clear. In particular, the curved step shows better mean performance and has a higher probability to achieve a better performance than the other one. The uncertainty in the film cooling effectiveness caused by the uncertainty of the step height and the BR is investigated using Sparse Approximation of Moment-Based Arbitrary polynomial chaos (SAMBA).