Airfoil shape design is a classical problem in engineering and manufacturing. In this work, we combine principled physics-based considerations for the shape design problem with modern computational techniques using a data-driven approach. Modern and traditional analyses of 2D and 3D aerodynamic shapes reveal a flow-based sensitivity to specific deformations that can be represented generally by affine transformations (rotation, scaling, shearing, translation). We present a novel representation of shapes that decouples affine-style deformations over a submanifold and a product submanifold principally of the Grassmannian. As an analytic generative model, the separable representation, informed by a database of physically relevant airfoils, offers (i) a rich set of novel 2D airfoil deformations not previously captured in the data, (ii) an improved low-dimensional parameter domain for inferential statistics informing design/manufacturing, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal 2D shapes.
翻译:在这项工作中,我们将基于物理原则的物理因素对形状设计问题的考虑与使用数据驱动法的现代计算技术结合起来。对2D和3D空气动力学形状的现代和传统分析显示,对典型的变形具有基于流动的敏感性,这种变形一般可以以纤维变形(旋转、缩放、剪切、翻译)为代表。我们展示了一种新型的形状表示,这种变形会分解一个侧面和一个主要为格拉斯曼尼的产物的变形。作为一种分析性的基因模型,在与物理有关的空气纤维数据库的启发下,可分离的表示方式提供了:(一) 一套丰富的2D新奇的空气纤维变形,以前没有在数据中得到体现;(二) 一个改进的低维参数域,用于预测性统计数据,为设计/制造提供参考,以及(三) 一致的3D刀形表示和对2D型形状序列的扰动。