# Simulation and control of aerodynamic flows

## Linear and nonlinear optimal control of by-pass transition.

We apply linear and nonlinear optimal control in a transitional boundary layer flow, subjected to free-stream vortical perturbations. The nonlinear control problem is solved using the Lagrangian variational formulation applied in a receding horizon framework. This formulation results in a set of linearized adjoint equations, which are used to obtain iteratively the optimal wall actuation (blowing and suction from a control slot).

## Improvement of aerodynamic performance of airfoils at low Reynolds numbers

In order to improve the aerodynamic performance of aerofoils at low Reynolds numbers, we apply periodic surface morphing of the suction side. We also use Direct Numerical Simulations (DNS) to gain insight and elucidate the interaction of the moving surface with the separating shear layer. The idea was applied to a NACA-4415 aerofoil at Reynolds number Rec=5×104 and 0° angle of attack. At these flow conditions, the boundary layer separates at x/c=0.42, remains laminar until x/c=0.8, and then transitions to turbulence. We found that periodic surface morphing amplifies the Kelvin–Helmholtz instability mechanism, resulting in the formation of strong spanwise coherent structures, that retain their coherence for a large part of the actuation cycle. Following their formation, these structures entrain high momentum fluid into the near-wall flow, leading to almost complete elimination of the recirculation zone. This leads to a three-fold increase in the Lift/Drag ratio. This work was carried out in collaboration with Temasek Labs (National University of Singapore), where a physical model was built and tested in a wind tunnel. The morphing was implemented experimentally using two macro fiber composite (MFC) actuation patches.

## Simulations of transitional flow around wings

We have performed Direct Numerical Simulations (DNS) of the flow field around a NACA 0012 wing at Reynolds number Re=50,000 and angle of attack 5o, with 3 trailing edge shapes (straight, blunt, and serrated). We instigated in detail the interaction of the separating shear layer and the shape of the trailing edge. We discovered a lock-in mechanism between the fundamental frequency of the Kelvin-Helmholtz instability of the separating shear layer and the vortex shedding frequency in the case of the blunt and serrated trailing edges. We performed also resolvent analysis on the time-averaged flow, and used the dominant resolvent modes to reconstruct the velocity spectra in the whole domain using the time signal of one velocity component at a few calibration points. We obtained very good approximation with only one or two calibration points (depending on the flow examined), provided that they are located in energetic regions of the flow that contain sufficient spectral content at the relevant frequencies.