非定常薄翼理论再探：近似解析解与黏性流中的自相似Wagner效应

中文摘要 AI 辅助

本文从黏性流视角推导了具有一般非定常运动的薄翼非定常升力的近似解析解，其中尾迹涡片强度以显式卷积型表达式给出，作为Wagner积分方程的近似解。为验证该解析解，将其应用于Wagner和Theodorsen问题，分别得到Wagner函数和Theodorsen函数的显式积分形式作为退化情形。进一步，将该解析解应用于广义Wagner问题中具有有限时间尺度的起动流，揭示了重新归一化的环量升力系数的自相似性，以及其在有限时间域内与重新归一化的Wagner函数的等价性。更重要的是，在低雷诺数下起动平板翼型的流动数值模拟中，即使流动存在中等程度分离，也发现了自相似Wagner效应。该自相似性体现了雷诺数不变性。

英文摘要

An approximate analytical solution for the unsteady lift of a thin airfoil with a general unsteady motion is derived from a viscous-flow perspective, where the wake vortex-sheet strength is given in an explicit convolution-type expression as an approximate solution of the Wagner integral equation. For validation, this analytical solution is applied to the Wagner and Theodorsen problems, giving the explicit integral forms of the Wagner and Theodorsen functions as the reduced cases. Further, this analytical solution is applied to the starting flow with a finite timescale in the generalized Wagner problem, revealing the self-similarity of the re-normalized circulatory lift coefficient and its equivalence to the re-normalized Wagner function in a finite time domain. More importantly, the self-similar Wagner effect is found in numerical simulation of the flow over a starting flat-plate airfoil at low Reynolds numbers even when the flow is moderately separated. This self-similarity represents the Reynolds-number-invariance.

发表机构

• Western Michigan University（西密歇根大学）

机构由 AI 辅助整理，请以论文原文为准。