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, wing shape optimization, and many other range of applications. 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. Research studies on airfoil have been conducted ever since to decrease drag and increase lift, introducing new techniques like the suction and blowing flow control, thickness optimization, and serrated trailing edges. These techniques have several economic and environmental benefits which serve in increasing airfoil efficiency and thus decreasing the fuel consumption and CO~2~ emissions. Currently adopted advanced mathematical models that are used to predict airfoil performance, though are essential tools in the advancement of aviation industry, require large computational cost in order to optimize the design of such applications. As a primary step, this paper aims to build an approximate model of an airfoil, termed also a surrogate model, for the sake of reducing the simulations computational cost. The approximate model is based on creating a simplified reduced-order algebraic model which will be suitable then to perform aerodynamic design optimization for airfoil performance rather than solving the highly non-linear set of continuity and momentum equations. Various approaches such as Kriging, neural networks, polynomials, and Gaussian processes exist to construct the surrogate models. In this work, the non-intrusive polynomial chaos expansion (NIPC) technique was employed on a NACA2412 airfoil. The main objective of this work is then to investigate the performance of the NIPC model with different orders on solution outcomes. Before accomplishing this step, a sequential methodology was adopted. First, a full 2D CFD model of the NACA2412 airfoil was developed using the finite volume method. The pressure based method was used with the SIMPLE algorithm adopted to resolve the pressure-velocity coupling in the continuity and momentum equations. An experimental setup of the NACA2412 airfoil was then prepared and the variations of lift and drag coefficients under different angle of attacks and Reynolds’s numbers were reported. The experimental data were then used to validate the numerical results generated by the 2D CFD simulations. A good agreement was achieved between the numerical and experimental results. Finally, the theory of the surrogate model was discussed and implemented using Matlab. The construction of the surrogate model was done by first defining the random variables which were limited to Reynolds number and the airfoil angle of attack. Then, the solution vector, whose components are the coefficient of lift values for all the possible combinations of Reynolds number and angle of attack, was generated. By doing so, each data set that is represented by a Reynolds number and angle of attack value {Re, AoA} was linked to one value in the solution vector {CL}.  The multivariate Hermite polynomials, which is the product of univariate ones, were finally obtained. A pre-conditioning pseudo-inverse technique was used on Hermite matrix A with the least square method adopted to approximate the solution. The surrogate model coefficients were then generated by the product of the inverse of A and the solution vector. In order to validate the surrogate model, its performance was initially verified with CFD results. Analysis was also performed to investigate the effect of polynomial order on the solution accuracy. Results showed that for a fixed number of data sets, increasing the order of the polynomial could deteriorate the solution accuracy. At a certain order k, the analytical solution starts diverging mainly at the extremities of angle of attack at -60 and 60.


Performance Assessment of a Naca-2412 Surrogate Model Using Non-Intrusive Polynomial Chaos Method

Division / Sponsors: 
Heat Transfer Division (HTD), Fluids Engineering Division (FED)

Heat Transfer Summer Conference
Paper Proceedings: https://asmedigitalcollection.asme.org/HT/HT2020/volume/83709

18th International Conference on Nanochannels, Microchannels, and Minichannels
Paper Proceedings: https://asmedigitalcollection.asme.org/ICNMM/ICNMM2020/volume/83693

Fluids Engineering Division Summer Meeting
Paper Proceedings: https://asmedigitalcollection.asme.org/FEDSM/FEDSM2020/volume/83716

HT-ICNMM2020 - Virtual Conference, SHTC - Virtual Conference, FEDSM2020 - Virtual Conference

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