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Alessandro Testa
This study is aimed to investigate a linear proportional-integral-differential (PID) feedback control using, eventually, an upstream sensor with the purpose of a net power saving in a turbulent channel flow at Reτ=180. Direct numerical simulations are performed analyzing the variation of the net power saving rate respect to the proportional and integral terms, and the streamwise and z-coordinate of the sensor location. Furthermore, selective control, capable of counteracting only sweep or only ejection events, is briefly examined. The resulting complexity of the wall shape is overcome with the use of an immersed boundary method, which makes the mesh generation trivial and done once at the beginning of each simulation.
A net power saving rate is achieved for many different combinations of parameters indicating good effectiveness and stability of the control scheme; moreover, remarkable power saving is obtained under some sets of parameters (≈ 20%). The control profoundly modifies the near-wall flow behavior whereas, on the contrary, it has minimal effect in the outer region; the velocity fluctuations and the Reynolds shear stress, as well as the production of turbulent kinetic energy, are reduced. Besides, an outward shift of turbulence statistics in the controlled flow is observed.