Assessing the influence of design variables on serpentine duct intake performance using surrogate-based sensitivity analysis

Real-world engineering designs and computational models often incorporate uncertainties introduced by approximations and simplifications. Hence, uncertainty quantification (UQ) and global sensitivity analysis (GSA) are essential tools. UQ assesses the propagation of input uncertainties on quantities of interest (QoIs), whereas GSA decomposes the QoI variance to identify the contributions of individual input variables. Despite extensive studies on diffusing serpentine ducts (s-ducts) in the field of aerospace, the application of GSA has been largely neglected. Existing studies have often employed parameterization techniques that conflate cross-sectional shape and area, making them unsuitable for GSA. This study overcomes this limitation by presenting a novel framework for performing GSA on an s-duct, aligning with the National Aeronautics and Space Administration (NASA) 2030 vision of UQ-enabled multidisciplinary optimization. The s-duct geometry is parameterized using two design variables: eccentricity, which adjusts the cross-sectional shape, and a control point on a cubic Bezier curve, which modifies the centerline. These variables are treated as random with uniform distributions. Using OpenFOAM, we conduct simulations and compute QoIs on a fully automated grid. Surrogate models are constructed using generalized polynomial chaos expansion, and Sobol indices are calculated to quantify each variable's contribution to the QoI variance. The results reveal that the control point contributes nearly 70% to the variance in circumferential distortion and pressure recovery, while eccentricity accounts for 68% of the variance in radial distortion. The proposed framework lays the foundation for future UQ-enabled s-duct optimization.