High-fidelity simulations and data-driven analysis of transitional and turbulent compressible flows over airfoils

Abstract

The study of compressible flows over airfoils is relevant for several applications including aircraft wings, gas and wind turbine blades, rotorcraft, and industrial ventilation systems. This work will combine large eddy simulations (LES) and data-driven analysis to investigate compressibility and pressure gradient effects on boundary layers developing over airfoil profiles. The high-fidelity simulations will be performed using a high-order compact finite difference formulation including a shock capturing scheme and an overset mesh capability. Data-driven techniques such as proper orthogonal decomposition (POD), dynamic modal decomposition (DMD) and Lagrangian techniques will be applied to provide insights of the flow physics including the analysis of organized flow structures and their interactions with unsteady mechanisms such as shock waves and sound waves. Stability analyses will also be conducted using finite difference approximations of the linearized version of the compressible Navier-Stokes equations. Initially, a modal approach will be used to understand the flow stability properties in an infinite time horizon, i.e., following the definition of Lyapunov through the analysis of the eigenvalue spectrum, eigenfunction plots and neutral curves. Since the modal analysis is incapable of capturing non-normal properties of the flow, a non-modal analysis will also be performed. To employ this analysis, it is first necessary to establish an energy norm of the linear operator and then rewrite it into a matrix exponential form, which is solved by a singular value decomposition (SVD). Transient growth, pseudo spectrum and resolvent analysis will be employed to understand the flow behavior, and results will be compared with those obtained by LES.