Linear Frequency Domain Method for Load Control by Fluidic Actuation

Simulations of periodic fluidic excitations in the context of active flow control are per- formed using a frequency domain solver for the efficient prediction of global air loads. Frequency domain methods have become a viable choice whenever the disturbance of the flow is small and periodic, and can reduce the computational effort substantially in compar- ison to time-accurate unsteady simulations. Although time-accurate unsteady simulations resolve the entire spectrum of the flow, they suffer from a long transient phase and thus require an extensive use of computational resources. The goal is to extend the time- linearized frequency domain method of the DLR TAU-code toward load control by blowing fluidic actuators. This paper presents the set of discretized unsteady equations and as- sociated boundary conditions for both the time accurate and frequency domain method. The applied time-linearized frequency method decouples each harmonic, forming a linear approach, which renders the sequential calculation of the individual harmonics to evaluate the time response of air loads. At first, blowing actuation for a two-dimensional airfoil with a single slot is considered for which constant as well as periodic excitations are used for validation and investigation purposes of air loads between the time-accurate and nonlinear frequency domain method. In addition, a 2-element high-lift wing with a flow separation on the trailing edge flap is simulated that demonstrates the good prediction quality of air load derivatives with the frequency domain method