A vortex lattice method implementation for low-speed wings

Abstract

The European Federation for Transport and Environment confirm that in 2019, the aviation industry contributed to 4.7% of all European carbon emissions and is expected to consume more than 10% of the carbon emission budget of the Paris agreement by 2050. Small changes in mentality and more attentive decisions and designs can help mitigate the impact humans have been having on the environment. Intelligent aircraft design is one method which could significantly influence the efficiency of an aircraft. This project developed a Vortex Lattice Method (VLM) implementation in Python to enable a time-effective and accurate method of estimating the performance characteristics of an aircraft wing’s design. The process of developing the VLM implementation began with an intensive review of literature where tactics of building potential flow solvers were identified. The theory behind the VLM was then presented and the methodology of how the theory was implemented in Python was discussed. The developed program was tested through a series of validation models; the first three models were generated from NACA’s 44xx series experiment and had the goal of investigating the capabilities of the program when exposed to varying camber, taper ratio, aspect ratio and geometric washout. The models showed that the VLM program developed was able to predict the performance of the aircraft wings and had near identical results to a commercial software, XFLR5. However, the VLM program and XFLR5 decreased in accuracy at angles of attack where flow separation occurs, which was attributed to the tangency flow boundary condition of the VLM formulation that drops with the onset of flow separation in practice. Another two verification models testing the ability of the model to develop 2D aerofoil characteristic curves of the NACA 0012 and NACA 4412 were created. The study compared results obtained from a 2D Computational Fluid Dynamic (CFD) simulation with the results retrieved from the VLM code. It was found that with VLM implementation the 2D coefficient of drag is not estimated, since the VLM formulation solves only for induced drag. Importantly the model performed well when calculating the coefficient of lift, having congruent results to the CFD simulation except at higher angles of attack due to flow separation. The VLM implementation was able to model any quadrilateral based 3D wing geometries and obtained highly satisfactory estimates of their performance characteristics in steady, low-speed flight.