Dynamically Linearized Time-domain Approach for Nonlinear Aeroelastic Theoretical/Computational Model Using Unsteady Aerodynamics

Abstract

Fluid-Thermal-Structure Interaction (FTSI) problems in high-speed applications (supersonic and hypersonic) have been pursued by researchers and engineers since last century, but even with all the knowledge gathered over the years, modeling the structural response for a flight mission is still cumbersome and complex. In this work, a novel Reduced Order Model is developed combining analytical theory and CFD methods to overcome some of the gaps existing in this field, and leveraging the pros of each technique. The study begins with an expansion of the traditional Linear Piston Theory into the full Potential Aerodynamics to model the unsteady coupling between the structure and the flow field in an aeroelastic solver. This more complete theory allows the consideration of non-locality and memory effects intrinsic to the unsteady flow, which become more prominent and relevant for the panel response as the Mach number becomes closer to the transonic domain. However, due to its analytical nature, the Full Potential Flow is still limited in terms of other more complex aerodynamic nonlinearities it can consider, and thus can only provide significant contributions when dealing with a simple geometry and uniform freestream.To overcome this gap, this study focuses on developing the Dynamically Linearized Time-domain Approach, which uses the Indicial Theory to build a linear relationship between the flow perturbation and the structural deformation of the panel. Initially using an inviscid CFD solver (Euler), the ROM is used to capture how the flow field responds to step perturbations on each structural mode of the structure; this information is then used to couple the aerodynamics to the structure for any arbitrary panel deformation. After validating this method for a uniform inviscid flow field, by correlating the results with the analytical theory (Piston Theory and Full Potential Aerodynamics), a more complex aerodynamic configuration was explored. Using the same geometry, different shock impingement angles were added to the system to assess how the ROM would perform when having to define the aerodynamic response around a nonlinear steady state for the flow field. These results presented some insight into the challenges in including this nonlinearity in the aeroelastic solver, as well as validated the capabilities of the method to overcome the "brute-force" numerical aeroelastic solution. The performance of the DLTA was also explored when considering a viscous boundary layer of different thicknesses, expanding on previous studies where the same problem was approached using the "brute-force" coupling between physics. Due to the order reduction of the model, the current study presented results for a wide range of Mach numbers and boundary layer thickness without compromising the time required to run the aeroelastic simulations. As part of the validation process for the DLTA, this thesis presents a correlation study on the AFRL RC-19 wind tunnel configuration as part of the $3^{rd}$ Aeroelastic Prediction Workshop (AePW3). This wind tunnel experiment provides a very complicated and rich aeroelastic system in the high-speed context, where there are nonlinearities both in the structure and the flow field. Two cases were assessed: a no-shock configuration, for which the analytical theories were used to perform the aeroelastic runs (Linear Piston Theory and the Full Potential Aerodynamic); and a $4^\circ$ wedge shock impingement, for which the DLTA was used. For all cases, a reasonable correlation was made with the experimental data, expanding the understanding of the experimental setting and providing insights on the modeling of the flow and panel dynamics.