Effect of Hinge Gap on Aerodynamics of Thin Airfoils Having an Oscillating Flap

Nonsteady load distributions on a thin airfoil in inviscid incompressible flow having an oscillating flap with a narrow hinge gap are investigated. The angle of attack is assumed to be zero in front of the hinge gap. The problem is first attacked numerically through Poisson’s integral equation to compare it with analytical methods derived later. The logarithmic singularity in the kernal function is treated with special care. Secondly the method of matched asympototic expansions is used to analyze the problem. It brings forth simple closed-form expressions. Comparisons of results of the two methods show excellent agreement with each other, when gap width-to-chord ratio is less than 0.1. In the Appendix, a simplified method is presented where no inner solution needs to be considered. It is useful for the gap/chord ratio less than 0.01.