An adjoint-based drag reduction technique for unsteady flows

Abstract

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.