Abstract

Computational Fluid Dynamics (CFD) models have been regarded as inevitable tools in the design of various aerodynamics applications like formula 1 cars, wind turbines, airfoil design, and many others. Such models rely on applying advanced numerical methods to solve the set of Navier-Stokes equations and other auxiliary models to quantify the aerodynamics performance, such as lift and drag in airfoil applications. However, currently adopted advanced mathematical models that are used to predict airfoil performance, though are essential tools in the advancement of aviation industry, incur large computational costs. As a primary step, an approximate model of an airfoil is built for the sake of reducing computational cost while preserving accuracy. The approximate model is based on creating a simplified algebraic model which is suitable then to perform aerodynamic design optimization rather than solving the highly non-linear set of continuity and momentum equations. In this work, the non-intrusive polynomial chaos expansion (NIPC) technique is employed on a NACA-2412 airfoil. The main objective of this research is to investigate the performance of the NIPC model with different orders on solution accuracy. A methodology is designed by first developing a full CFD model of the NACA-2412 airfoil. An experimental setup of the airfoil was then prepared with the variations of lift and drag coefficients under different operative conditions were reported. The experimental data were used to validate the numerical results generated by the CFD simulations. The surrogate model was then constructed via the NIPC technique. The performance of the surrogate model was then benchmarked with CFD results under different flow and operating conditions. Analysis was also performed to investigate the effect of polynomial order on the solution accuracy. Results showed that for a given data set size, increasing the order of the polynomial would deteriorate the solution accuracy. At a certain order k, the analytical solution starts diverging especially for values of angle of attack close to −60 and 60°.

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