Contrôle optimal par simulation aux grandes échelles d'un écoulement turbulent

Abstract : Two control strategies were successively implemented to reduce the drag and the turbulent kinetic energy of a plane channel flow in turbulent regime (Re[tau]=180). Wall transpiration (unsteady blowing/suction) with zero net mass flux is used as the control. The main objective was to prove that a large eddy simulation (LES) could be relevant as a reduced-order model of the Navier-Stokes equations and thus strongly reduce the numerical costs. A heuristic approach known as opposition control was initially employed. The results show that the energetic efficiency is maximum for a position of the detection plane different from that which corresponds to the maximum of drag reduction. In addition, our results confirm that the drag reduction decreases with the increase of the Reynolds number. Then, an optimal control procedure was used by considering different cost functional (drag, terminal turbulent kinetic energy, mean turbulent kinetic energy). At Re[tau] =100, control managed to fully relaminarize the flow (drag reduction of about 50%) by considering as cost functional the terminal kinetic energy. For this same cost functional, an important drag reduction of about 55% is still obtained at Re[tau] =180 but without reaching the relaminarization. Our results show that to minimize the flow drag, it is more effective to consider the kinetic energy as cost functional than directly the drag. Lastly, it is essential for the convergence of the minimization that the optimality system is solved on a sufficiently long time horizon
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Ali El Shrif. Contrôle optimal par simulation aux grandes échelles d'un écoulement turbulent. Autre. Institut National Polytechnique de Lorraine, 2008. Français. ⟨NNT : 2008INPL035N⟩. ⟨tel-01753040⟩

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