Analysis for circumferential velocity distribution of the vortex core model in plateau region and its roll-up effect behind wings with elliptic lift distribution

Abstract

An analysis is carried out for the vortex core structure particularly on circumferential velocity in plateau region and its roll-up effects on the downwash behind wings of elliptic circulation distribution. Widely used analytical models of Betz, Rankine and Lamb are generally not in acceptable agreement with experimental data of the maximum circumferential velocity, due to the fact that rotational energy and integral invariants are not satisfied. Thus, an attempt is made to satisfy them by applying, modifying and matching the conical flow model solution, because the variation of flow properties along free stream direction is very small compared to radial direction. The results indicate the existence of so called the overshoot region of circulation in the inner core. The analysis of the effect of plateau region downstream of wing related to the downwash velocity shows that if AR/C$_L$ is greater than 9.107, the effect of plateau region on wing is negligible.