Inverse Design of 2D Airfoils using Conditional Generative Models and Surrogate Log-Likelihoods

This paper shows how to use conditional generative models in 2D airfoil optimization to probabilistically predict good initialization points within the vicinity of the optima given the input boundary conditions, thus warm starting and accelerating further optimization. We accommodate the possibility of multiple optimal designs corresponding to the same input boundary condition and take this inversion ambiguity into account when designing our prediction framework. To this end, we first employ the conditional formulation of our previous work BezierGAN---Conditional BezierGAN (CBGAN)---as a baseline, then introduce its sibling conditional entropic BezierGAN (CEBGAN), which is based on optimal transport regularized with entropy. Compared with CBGAN, CEBGAN overcomes mode collapse plaguing conventional GANs, improves the average lift-drag (C_l/C_d) efficiency of airfoil predictions from 80.8% of the optimal value to 95.8%, and meanwhile accelerates the training process by 30.7%. Furthermore, we investigate the unique ability of CEBGAN to produce a log-likelihood lower bound that may help select generated samples of higher performance (e.g., aerodynamic performance). In addition, we provide insights into the performance differences between these two models with low-dimensional toy problems and visualizations. These results and the probabilistic formulation of this inverse problem justify the extension of our GAN-based inverse design paradigm to other inverse design problems or broader inverse problems.

Airfoil optimization for small horizontal axis wind turbine

In order to take advantage of the low wind speed found in the Colombian territory, a gradient-based optimization process (GBA) of 2 airfoils is carried out, using the Xfoil software to evaluate the interactions. The shapes chosen will be destined for the root and for the middle zone of a blade for a small horizontal axis wind turbine (sHAWT). The blade will be created from the calculation of the chord and pitch angle with the blade element momentum methodology (BEM) and the SHAWT will be tested by CFD software to check its performance. As a preliminary result, a root-bound airfoil has been obtained with a higher performance than the airfoil used as a bases.

Low-speed airfoil optimization using constrained differential evolution

Nowadays, algorithms designed to optimize the shape of an airfoil are being developed by many researchers. In this paper, to achieve an optimum shape configuration, a methodology based on an evolutionary algorithm is proposed. The main objective is to find the optimum shape of a known airfoil that gives the best aerodynamic performance for a fixed lift coefficient. For the airfoil parametrization, the class-shape method is used to develop a well-behaved geometry. The paper underlines the implementation of a constrained differential evolutionary algorithm using the free penalty scheme by varying the coefficients of the shape parametrization function. The aim is to obtain a better aerodynamic performance for a predetermined lift coefficient by imposing a fixed maximum airfoil thickness interval. The method is a general optimization procedure and can be implemented in a wide range of engineering design problems.