CYFFD Parameterization Method for Cylindrical Components of Aircrafts

飞行器圆柱类部件的气动外形参数化方法

¹ School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
² Unmanned System Research Institute, Northwestern Polytechnical University, Xi’an 710072, China

Received: 5 December 2017

Abstract

This paper proposes a parameterization method using cylindrical coordinates based free-form deformation(CYFFD) technique by introducing a coordinate transformation method and a virtual lattice method. The method is suitable for axisymmetric and non-axisymmetric cylindrical applications. CYFFD is able to deform radially and circumferentially and to maintain first order and curvature continuity across frame border. First, the coordinate transformation step helps capture geometrical characteristics of cylindrical objects to conduct radial and circumferential deformation. Due to the need of delicate shape design, FFD lattice need be set up closely around cylinder-like objects and this will cause the boundary of FFD frame to intersect with the objects, which lead to derivative discontinuity at the intersection. The virtual lattice method is introduced to reuse some control points as virtual ones so that first order and curvature continuity can be preserved. A cylinder deformation example compares the capability of CYFFD with that of conventional FFD for radial and circumferential deformation and keeping derivative continuity. An airplane nose example shows the possibility to use CYFFD and NFFD together for complex shape. A nacelle deformation example and fitting example show that CYFFD is valuable for non-axisymmetric cylindrical objects with complex shapes. The optimization example on cylinder nose shape indicates that CYFFD can give good optimization results and it is valuable for parameterizing cylinder-like objects.

摘要

通过增加坐标转换步骤和虚拟框策略，得到适用于圆柱形物体的cylindrical free-form deformation（CYFFD）参数化方法，既可用于轴对称物体，也可以用于非轴对称物体。CYFFD可捕捉圆柱类物体独特的周向和径向变形特点，并能够保证框边界处曲面的导数和曲率连续。首先，通过使用坐标转换方法可在圆柱坐标系下实现沿周向和径向的变形。其次，由于圆柱形物体的精细外形设计需要，需要布置为首尾相连的贴近物面的控制框，这种布置形式会导致在圆柱周向出现框的边界与曲面的相交，难以保持曲面在控制框边界处的导数连续性，因此引入虚拟框方法并选取一些控制点作为虚拟的控制框点，从而保持导数和曲率连续。使用圆柱外形示例对比了CYFFD和传统方法的变形能力、框边界处的曲率连续特性。机身头部参数化示例表明CYFFD可以和传统FFD协同使用从而实现复杂的变形目的。短舱变形示例和外形拟合示例表明CYFFD可以用于复杂非轴对称圆柱曲面。圆柱头部优化算例表明CYFFD用于优化设计能够得到良好的优化结果，将之用于圆柱类外形的参数化和优化设计中具有实用价值。