Closed Form Analytical Model for Airflow around 2-Dimensional Composite Airfoil Via Conformal Mapping

TL;DR

This paper develops a closed-form analytical model using conformal mapping to compute airflow and lift characteristics around a 2D airfoil with an additional object, providing precise insights into airflow interactions.

Contribution

It introduces a novel conformal mapping approach for analyzing airflow around two 2D objects, enabling exact calculations of lift and circulation in such configurations.

Findings

Second object reduces lift coefficient by approximately 6.3%.

Closed-form solution allows precise airflow analysis for two-object configurations.

Method applicable to similar 2D aerodynamic problems.

Abstract

This paper presents a method of computing section lift characteristics for a 2-dimensional airfoil with a second 2-dimensional object at a position at or ahead of the leading edge of the airfoil. Since both objects are 2-dimensional, the analysis yields a closed form solution to calculation of the airflow over the airfoil and second object, using conformal mapping of analytically closed form airflow velocity vector past two circular shaped objects in initial complex plane, using a standard air flow model for each object individually. The combined airflow velocity vector is obtained by linear superposition of the velocity vector for the two objects, computed individually. The lift characteristics are obtained from the circulation around the airfoil and second object which is computed from the combined closed form velocity vector and the geometry along the contour integral for circulation. The illustrative example considered in this paper shows that the second object which is essentially a cylinder whose diameter is approximately 9% of the chord length of the airfoil reduces the section lift coefficient by approximately 6:3% from that of the airfoil alone. 1.