Advancements in Vortex Lattice Method for Improved Low-order Supersonic Aerodynamics

This research presents advancements to the Vortex Lattice Method (VLM), which transforms it into a more robust and efficient tool for supersonic aerodynamic analysis and the preliminary conceptual design of next-generation aircrafts. This thesis enhances the Vortex Lattice Method (VLM) for supersonic analysis through three contributions. First, an unsteady VLM (UVLM) with adaptive time-stepping is implemented and validated, achieving approximately 82% agreement with conventional CFD while being about 24× faster. Second, a hybrid supersonic extension is developed by coupling VLM with Taylor–Maccoll shock modelling (TMHM) to account for Mach cone and shock-cone physics. This approach yields lift and drag predictions with 90–95% accuracy across configurations including delta and highly swept wings. Third, a compressibility correction using a multiphase Lattice Boltzmann Method (LBM) is integrated, showing 92% agreement with k–ω SST RANS reference solutions, while retaining the low computational cost of VLM. These improvements were implemented using MATLAB subroutines developed within the Tornado framework to enhance the prediction of aerodynamic characteristics under complex flow conditions. End-to-end case studies on the SCALOS configuration and the Concorde wing demonstrate that the framework bridges the gap between conventional low-order tools and highfidelity CFD: cases requiring >68 h with URANS were completed in 15 h with the hybrid UVLM framework. These findings highlight the viability of combining VLM, Mach-cone modelling, and LBM corrections as a rapid preliminary-design methodology for supersonic aerodynamics. The advances made provide a strong foundation for future developments in aerodynamic modelling, contributing to reduced development costs and improved performance in the design of next-generation supersonic vehicles.