A vortex lattice MATLAB implementation for linear aerodynamic wing applications

Abstract

SUMMARY. This document is the Master thesis "A Vortex Lattice MATLAB Implementation for Linear Aerodynamics Wing Applications" by Tomas Melin. A user's manual for the developed vortex lattice code "Tornado" is also included. The physical problem addressed was to find the aerodynamic forces acting on an aircraft flying at low subsonic speeds, below the stall limit. The primary research issue was to detect if it would be possible to code a vortex lattice method fast enough for real time application. One of the requirements was that it must be possible to perform computations for most types of wing layouts. The current version of Tornado handles tapered, swept, dihedraled and twisted multi cranked wing configurations with trailing edge control surfaces. The governing equations used to solve the physical problem came from standard vortex lattice theory. The law of Biot-Savart was used to get the flowfield around a finite straight vortex line, one of the basic vortex segments needed for the lattice. These vortices induce a flow field in the air, and their strength was determined by the boundary conditions that no air should flow through the wings. The forces acting on each vortex segment can be determined by employing the Kutta-Jukovski theorem. These forces may then be integrated to yield a composite force in 3 dimensions, which in turn may be used to compute aerodynamic coefficients and stability derivatives. The computational problem is to creating a good system for dealing with the mathematical results. The Tornado code allows many different kinds of computations, which yields good coherence with experimental data. The Tornado code has shown very good coherence with theoretical data, such as Jones' small aspect ratio theory and Prandtl's lifting line. Furthermore, Tornado gives good results when comparing with commercial software and also yield accurate results when comparing to experimental data. However, the computing time for more complex geometry consume solution times in the order of minutes, which is too slow for a real time application, such as a flight simulator. The conclusion is that Tornado may be used for a wide variety of applications, but that the real time vortex lattice method still requires more computing capacity than available in desktop computers. Tomas Melin. KTH, Department of Aeronautics. Page 3 (45) A Vortex Lattice MATLAB Implementation for Linear Aerodynamic Wing Applications.