In this paper, a vortex moment map (VMM) method is proposed to predict the pitching moment on a body from the vorticity field. VMM is designed to identify the moment contribution of each given vortex in the flow field. Implementing this VMM approach in starting flows of a NACA0012 airfoil, it is found that, due to the rolling up of leading-edge vortices (LEVs) and trailing-edge vortices (TEVs), the unsteady nose-down moment about the quarter chord is higher than the steady-state value. The time variation of the unsteady moment is closely related to the LEVs and TEVs near the body and the VMM gives an intuitive understanding of how each part of the vorticity field contributes to the pitching moment on the body.

中文翻译：

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非定常不可压缩粘性流的涡矩图

在本文中，提出了一种涡矩图（VMM）方法来从涡量场预测物体上的俯仰力矩。VMM 旨在识别流场中每个给定涡旋的力矩贡献。在 NACA0012 翼型的起始流动中实施这种 VMM 方法，发现由于前缘涡 (LEV) 和后缘涡 (TEV) 的卷起，关于四分之一弦的不稳定机头向下力矩为高于稳态值。非定常力矩的时间变化与物体附近的 LEV 和 TEV 密切相关，VMM 可以直观地了解涡量场的每个部分如何对物体的俯仰力矩做出贡献。