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2D shape optimization under proximity constraints by CFD and response surface methodology

机译：通过CFD和响应面方法在接近约束下进行2D形状优化

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In this paper we consider two-dimensional CFD-based shape optimization in the presence of obstacles, which introduce nontrivial proximity constraints to the optimization problem. Built on Gregory's piecewise rational cubic splines, the main contribution of this paper is the introduction of such parametric deformations to a nominal shape that are guaranteed to satisfy the proximity constraints. These deformed shape candidates are then used in the identification of a multivariate polynomial response surface; proximity-constrained shape optimization thus reduces to parametric optimization on this polynomial model, with simple interval bounds on the design variables. We illustrate the proposed approach by carrying out lift and/or drag optimization for the NACA 0012 airfoil containing a rectangular fuel tank: By identifying polynomial response surfaces using a large batch of 1800 design candidates, we conclude that the lift coefficient can be optimized by a linear model, whereas the drag coefficient can be optimized by using a quadratic model. Higher order polynomial models yield no improvement in the optimization.
机译：在本文中，我们考虑在存在障碍物的情况下基于二维CFD的形状优化，这将非平凡的邻近约束引入了优化问题。基于格雷戈里的分段有理三次样条，本文的主要贡献是将这样的参数变形引入名义形状，以保证满足邻近约束。然后将这些变形的形状候选物用于多元多项式响应面的识别。因此，在设计变量上具有简单的区间边界的情况下，接近约束形状优化简化为对该多项式模型的参数优化。我们通过对包含矩形燃料箱的NACA 0012机翼进行升力和/或阻力优化来说明所提出的方法：通过使用大批1800个设计候选来识别多项式响应面，我们得出结论，升力系数可以通过线性模型，而阻力系数可以通过使用二次模型来优化。高阶多项式模型在优化方面没有改善。

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