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

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 en 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. Nomenclature c = chord length cd = drag coefficient CE = entrainment coefficient C f = skin-friction coefficient based on edge velocit