Effects of Flow Separation on Aerodynamic Loads in Linearized Thin Airfoil Theory

摘要

A solution, linear in angle of attack, is given for flow about a thin symmetric airfoil, that is, an inclined flat plate, with a semi-infinite separated region. This solution allows one to ascertain explicitly the effect of the development of upper-surface separation on the airfoil lift and pitching moment coefficients. The main drawback is the enforcement of the uniform-pressure boundary condition on the corresponding segments of the real axis, rather than on the actual boundary of the separated region. Physically, this assumes that the separated region is thin. Errors resulting from such an approximation were estimated by a comparison with the Chaplygin-Lavrientiev classical nonlinear solution. The linear solution was also compared with XFOIL results for a NACA 0012 airfoil. XFOIL's prediction of the location of the upper surface separation point was input into the analytic solutions, to obtain the static dependency of lift and pitching moment coefficients on angle of attack. Results from the linear and nonlinear analytic solution and the XFOIL computation were in satisfactory agreement.