Purpose

This study aims to propose an aerodynamic force decomposition which, for the first time, allows for thrust/drag bookkeeping in two-dimensional viscous and unsteady flows. Lamb vector-based far-field methods are used at the scope, and the paper starts with extending recent steady compressible formulas to the unsteady regime.

Design/methodology/approach

Exact vortical force formulas are derived considering inertial or non-inertial frames, viscous or inviscid flows, fixed or moving bodies. Numerical applications to a NACA0012 airfoil oscillating in pure plunging motion are illustrated, considering subsonic and transonic flow regimes. The total force accuracy and sensitivity to the control volume size is first analysed, then the axial force is decomposed and results are compared to the inviscid force (thrust) and to the steady force (drag).

Findings

Two total axial force decompositions in thrust and drag contributions are proposed, providing satisfactory results. An additional force decomposition is also formulated, which is independent of the arbitrary pole appearing in vortical formulas. Numerical inaccuracies encountered in inertial reference frames are eliminated, and the extended formulation also allows obtaining an accurate force prediction in presence of shock waves.

Originality/value

No thrust/drag bookkeeping methodology was actually available for oscillating airfoils in viscous and compressible flows.

中文翻译：

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非定常可压缩流中兰姆矢量积分的空气动力

目的

本研究旨在提出一种空气动力分解，首次允许在二维粘性和非定常流中进行推力/阻力簿记。在此范围内使用基于 Lamb 矢量的远场方法，本文首先将最近的稳态可压缩公式扩展到非稳态状态。

设计/方法论/途径

考虑惯性或非惯性框架、粘性或非粘性流、固定或移动物体，推导出精确的涡旋力公式。考虑到亚音速和跨音速流态，说明了 NACA0012 翼型在纯切入运动中振荡的数值应用。首先分析总力的精度和对控制体积大小的敏感性，然后分解轴向力，并将结果与​​无粘性力（推力）和稳定力（阻力）进行比较。

发现

提出了推力和阻力贡献的两种总轴向力分解，提供了令人满意的结果。还制定了附加的力分解，该分解与涡旋公式中出现的任意极点无关。消除了惯性参考系中遇到的数值误差，并且扩展公式还允许在存在冲击波的情况下获得准确的力预测。

原创性/价值

实际上，没有推力/阻力簿记方法可用于粘性和可压缩流中的振荡翼型。