The rapid advancement in aeronautics has led to the emergence of intricate dynamic processes and structures, such as vortices, shock waves, flow separation, and turbulence, resulting from the flow around airfoils. Acquiring a profound understanding of these local structures and unraveling the physical mechanisms underlying flow phenomena represents an essential and challenging issue in the field of flight science. In this research, the longitudinal–transverse force theory (L–T force theory), as proposed by previous researchers, is employed to quantitatively assess contributions of local flow structures to aerodynamic forces. Specifically, the research encompasses an analysis of steady and viscous compressible flow over the Royal Aircraft Establishment (RAE)-2822 airfoil, with free-stream Mach number (M∞) ranging from 0.1 to 2.0. We comprehensively estimate longitudinal forces (L-force) and transverse forces (T-force), along with effects of compressibility on aerodynamic forces. Furthermore, recognizing the necessity for high-precision algorithms in the computation of L–T force theory, this investigation utilizes a sixth-order accuracy algorithm for spatial discretization and differencing. Our analysis reveals that the influence of compressibility and the contributions of L-forces to aerodynamic forces become increasingly significant in high M∞ regimes as shearing processes weaken. Additionally, a new similarity law is established to characterize aerodynamic forces acting on the RAE-2822 airfoil based on a novel moderating factor, ζmo, reduced from local Mach factors in the L–T force theory. This coefficient, ζmo, elucidates the degree to which transverse processes are modulated by longitudinal processes. Various angles of attack α and airfoils have also been analyzed, including National Advisory Committee for Aeronautics (NACA)0012 and NACA0006, by introducing a parameter denoted as κ to further validate the universality of the new similarity laws. The results demonstrate a high degree of accuracy in fitting the aerodynamic coefficients.

中文翻译：

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从纵向横向力理论中的局部马赫因子简化的新相似定律

航空业的快速发展导致了复杂的动态过程和结构的出现，例如由翼型周围的流动引起的涡流、冲击波、流动分离和湍流。深入了解这些局部结构并揭示流动现象背后的物理机制是飞行科学领域的一个重要且具有挑战性的问题。在本研究中，采用先前研究人员提出的纵向横向力理论（L-T力理论）来定量评估局部流动结构对气动力的贡献。具体来说，该研究包括对皇家飞机公司 (RAE)-2822 翼型上的稳定粘性可压缩流进行分析，自由流马赫数 (M∞) 范围为 0.1 至 2.0。我们全面估计纵向力（L 力）和横向力（T 力），以及压缩性对空气动力的影响。此外，认识到 L-T 力理论计算中高精度算法的必要性，本研究采用六阶精度算法进行空间离散和差分。我们的分析表明，随着剪切过程减弱，压缩性的影响以及 L 力对空气动力的贡献在高 M∞ 状态下变得越来越重要。此外，还建立了一个新的相似律来表征作用在 RAE-2822 翼型上的气动力，该法则基于一种新颖的调节因子 zemo，该因子是从 L-T 力理论中的局部马赫因子减少的。该系数 zemo 阐明了横向过程受纵向过程调节的程度。还对各种攻角α和翼型进行了分析，包括国家航空咨询委员会（NACA）0012和NACA0006，通过引入表示为κ的参数来进一步验证新相似定律的普适性。结果表明空气动力学系数的拟合具有很高的准确性。