A framework based on a continuous adjoint-based analysis of steady and unsteady flows to predict and control the drag force due to surface morphing is presented. By establishing a relation between perturbations in the body shape and in the boundary condition on a certain geometry, we derive an analytical expression of the sensitivity to changes in the geometry of the body and its relation to the sensitivity to the perturbation of the boundary conditions. The methodology is evaluated on the incompressible flow around a cylinder for steady and unsteady flows. A reduction of the drag coefficient was obtained and investigated by several surface deformations, conducted in the direction of the sensitivity vector field obtained by solving the derived adjoint problem. In unsteady flows, the sensitivity field is computed by integrating the unsteady adjoint problem backward in time from the unsteady flow solution. Two different types of deformations based on the calculated sensitivity were applied: time-averaged deformation and time-dependent. Attempting the latter, a deformation at each time step, did not yield the same satisfactory results as the time-averaged in terms of expected drag reduction. We provide a theoretical reasoning for the difference between both methodologies, together with an insight into the physics of the sensitivity vector field distribution relating it to the drag force sources.
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Sorbonne Univ, Inst Jean Le Rond dAlembert, CNRS, F-75005 Paris, France
Sorbonne Univ, Inst Sci Calcul & Donnees ISCD, F-75005 Paris, FranceSorbonne Univ, Inst Jean Le Rond dAlembert, CNRS, F-75005 Paris, France
Costanzo, S.
Sayadi, T.
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Sorbonne Univ, Inst Jean Le Rond dAlembert, CNRS, F-75005 Paris, FranceSorbonne Univ, Inst Jean Le Rond dAlembert, CNRS, F-75005 Paris, France
Sayadi, T.
de Pando, M. Fosas
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Univ Cadiz, Dept Mech Engn & Ind Design, Cadiz, SpainSorbonne Univ, Inst Jean Le Rond dAlembert, CNRS, F-75005 Paris, France
de Pando, M. Fosas
Schmid, P. J.
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KAUST, Dept Mech Engn, Thuwal 23955, Saudi ArabiaSorbonne Univ, Inst Jean Le Rond dAlembert, CNRS, F-75005 Paris, France
Schmid, P. J.
Frey, P.
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机构:Sorbonne Univ, Inst Jean Le Rond dAlembert, CNRS, F-75005 Paris, France
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Sorbonne Université, CNRS, Institut Jean Le Rond d'Alembert, Paris,F-75005, France
Sorbonne Université, Institut des Sciences du Calcul et des Données, ISCD, Paris,F-75005, FranceSorbonne Université, CNRS, Institut Jean Le Rond d'Alembert, Paris,F-75005, France
Costanzo, S.
Sayadi, T.
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Sorbonne Université, CNRS, Institut Jean Le Rond d'Alembert, Paris,F-75005, FranceSorbonne Université, CNRS, Institut Jean Le Rond d'Alembert, Paris,F-75005, France
Sayadi, T.
Fosas de Pando, M.
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Department of Mechanical Engineering and Industrial Design, Universidad de Cádiz, Cadiz, SpainSorbonne Université, CNRS, Institut Jean Le Rond d'Alembert, Paris,F-75005, France
Fosas de Pando, M.
Schmid, P.J.
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Department of Mechanical Engineering, KAUST, Thuwal,23955, Saudi ArabiaSorbonne Université, CNRS, Institut Jean Le Rond d'Alembert, Paris,F-75005, France
Schmid, P.J.
Frey, P.
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h-index: 0
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Sorbonne Université, Institut des Sciences du Calcul et des Données, ISCD, Paris,F-75005, FranceSorbonne Université, CNRS, Institut Jean Le Rond d'Alembert, Paris,F-75005, France