New similarity laws reduced from local Mach factors in longitudinal–transverse force theory

Abstract

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.