Flow separation is the detachment of boundary layer from a surface, which is associated with aerodynamic loss. In this work, the feasibility of controlling flow separation by backward (toward downstream) traveling waves is studied using large-eddy simulations (LES) of traveling waves (1) within an incompressible turbulent channel to investigate the impact of traveling wave parameters such as wave speed and wave steepness, (2) on an inclined plate and suction side of a NACA0018 airfoil at stall angle of attack where the flow is massively separated, and (3) within a compressible wavy turbulent channel. For (3), an LES framework for compressible flow is developed and combined with the curvilinear immersed boundary (CURVIB) method. Both incompressible and compressible frameworks are validated. The incompressible framework is validated for a fully developed turbulent channel, a pitching airfoil, two-dimensional inclined plate, and an NREL PHASE VI wind turbine. The compressible framework is validated by performing simulations for isotropic decay, subsonic and supersonic turbulent channel, and shock diffraction by a cylinder. The results of the simulations of actuated airfoil and plate reveal that low-amplitude backward traveling waves can postpone stall. Moreover, it is found for the first time that traveling waves are more effective than other types of oscillations, e.g., standing waves and pitching motion, in delaying stall because traveling waves can directly increase the axial momentum of the fluid in addition to triggering boundary layer instabilities, which occurs in all type of flow control with periodic excitation. In addition to the axial momentum, the traveling waves increase the lateral velocity of the fluid near the surface, which tends to separate the flow. The scalings of axial force and lateral velocity, which depend on amplitude, wavelength and frequency, were derived analytically using elongated body theory (EBT). Based on the scalings and the results, in contrast to common belief, wave speed (the main parameter for the axial force) is not the only parameter for flow reattachment, and amplitude, wavelength and frequency individually can impact flow separation by triggering instabilities or increasing the lateral velocity.
