A transonic, viscous nonlinear frequency domain Vortex Lattice Method for aeroelastic analyses

The Unsteady Vortex Lattice Method has interesting capabilities for nonlinear subsonic aeroelastic analyses. This paper aims to develop an aeroelastic framework based on the UVLM that is suitable for compressible, transonic and viscous unsteady flows. To achieve these modeling capabilities, the UVLM is first extended to the nonlinear frequency domain using the harmonic balance approach. Secondly, sectional corrections are applied from a steady 2D/2.5D database of aerodynamic forces computed with high-fidelity Euler/RANS flow solvers. The angle of attack coupling scheme on the lift force is complemented by a least-square procedure also coupling the pitching moment. Finally, an approximation of the retarded time is implemented in the influence kernel of the harmonic balance formulation of the UVLM to account for unsteady compressibility. The aerodynamic model is verified against time domain high-fidelity solutions with pitching airfoils in 2D and in 3D with a pitching constant chord NACA 0012 swept wing. Thereafter, the HB/LCO approach is applied with the frequency domain UVLM to 2D and 3D aeroelastic problems and compared against high-fidelity solutions. The proposed framework is capable of capturing strong nonlinear Limit Cycle Oscillation behaviors at high Mach numbers, as well as the flutter boundary for a wide range of Mach numbers while maintaining a low computational cost. As a result, the proposed framework could be of interest for preliminary design and Multi-Disciplinary Design (MDO) optimizations in the context of subsonic and transonic aircraft design.