论文标题
可分离的形状张量用于空气动力学设计
Separable Shape Tensors for Aerodynamic Design
论文作者
论文摘要
机翼形状设计是工程和制造中的经典问题。在这项工作中，我们使用数据驱动的方法将基于物理学的原则性考虑与现代计算技术相结合。对2D和3D空气动力学形状的现代和传统分析揭示了对特定变形的基于流动的敏感性，可以通过仿射转化（旋转，缩放，剪切，翻译）表示通常表示。我们提出了形状的新颖表现形式，该形状将仿射式变形在submanifold和submanifold上主要是格拉斯曼尼亚人。 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.
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.
