Viscous-Inviscid Method for Airfoil Analysis and Design for Aviation and Windmills

Abstract

This study examines an advanced viscous-inviscid interactive method developed for the analysis and design of airfoils in two-dimensional subsonic compressible flow (Ma ∞ < 0.4). Inviscid flow is solved with a panel method. The laminar boundary layer is calculated by Thwaites' method. Transition is determined by Michel's relation or the e n method. An integral solution for a turbulent boundary layer is derived from an entrainment equation. Closure conditions are obtained with empirical relations. Singularities near the separation are avoided by inverting the boundary-layer method. Inviscid and viscous flows are coupled with transpiration. The analysis method is used as a "black box" in the design tasks. The geometry of the starting airfoil is perturbed iteratively by transpiration until the pressure distribution converges to a predefined target. This study proposes the necessary degrees of freedom in the target velocity distribution to obtain a closed airfoil. Design cases are included, which support the general applicability and accuracy of the numerical design method.

A two-dimensional iterative panel method and boundary layer model for bio-inspired multi-body wings

“…The discrepancy in the transition point of Pablo and the APM is due to Pablo rounding the stagnation point to the nearest collocation point, therefore causing the velocity profile to be redistributed around the airfoil and causing the boundary layer to reach the transition condition after a shorter distance. XFoil showed transition 2.87% and 6.64% earlier than the APM without wake relaxation as the e n method has been demonstrated to trigger the transition point earlier than other transition criteria [26]. In comparison between the APM with the integrated wake relaxation scheme, the upper and lower surface transition points occur 8% and 12%, respectively, further upstream.…”

“…Currently, there are an array of solvers available for designing airfoils and assessing the flow around the wing profile [14], including finite element Navier-stokes flow solvers [15][16][17][18], conformal mapping [19][20][21], and panel methods [22][23][24][25]. While Navier-Stokes flow solvers enable the effects of viscosity to be taken into consideration around complex geometries, the complex mesh geometries required cause the simulations to be expensive, both financially and in time [26,27]. However, the implementation of potential flow panel methods has become a popular tool for modeling flow in the aerodynamic community.…”