Adjoint-Based Optimal Control on Flows with Multiple Moving Cylinders in Tandem

In this work, an adjoint-based approach is developed and implemented to optimize the hydrodynamic force on multiple moving solid bodies in laminar incoming flow for the first time. Two-dimensional (2D) moving cylinders arranged in tandem formation are studied in the present paper, and the hydrodynamic force in the streamwise direction, including drag and thrust on the trailing cylinders, is optimized by controlling the solid motion. Dual-cylinder and triple-cylinder systems are investigated. It is found that for the dual-cylinder case, the drag can be reduced by 47.1% primarily by controlling the oscillation of the trailing cylinder. For triple-cylinder case, a drag-to-thrust conversion, with 215% enhancement in thrust, has been achieved for the third cylinder by controlling the amplitude of oscillating and pitching motion for both trailing cylinders. Further analysis on vortex structures indicates that the trailing cylinder tends to avoid the direct impingement of vortices from the leading cylinders. In this way, the trailing cylinder is able to make use of more coherent vortex structures in the near-solid area when the flow is optimized, which might contribute to the huge hydrodynamic benefit including much lower drag or even drag-to-thrust conversion. The results achieved in this work may shed some light on understanding the mechanism of hydrodynamic benefits brought by the interactions between flows and solid bodies.