Optimum Control of Flow around a Circular Cylinder with Non-Uniform Suction
In the present study, numerical investigations were performed to determine the optimum non-uniform suction profiles to control the flow around a circular cylinder in the range of Reynolds numbers 4<𝑅𝑒<200. To investigate how the characteristics of the optimal control and the resulting flow change depending on the optimisation objective, several objectives were explored, namely: minimising the separation angle, total drag, and pressure drag. A variety of suction control implementations were investigated and compared to the performance of uniform suction. It was determined that the optimal non-uniform suction profiles consisted of a distribution with compact support, and a single locus. The location of the optimum suction region and the amount of suction necessary to achieve each objective varied substantially with Reynolds number, but with a predictable relationship. It is also shown that these parameters can alternatively be considered as related to the separation angle of the uncontrolled flow (the initial separation angle). Depending on the objective, the control parameters varied greatly: less suction was necessary to minimise total drag than to eliminate separation. Non-uniform suction profiles were much more efficient at eliminating boundary layer separation, requiring the removal of less than half the volume of fluid as uniform control to achieve the same objective. Total elimination of boundary layer separation did not always result in an improvement in total drag, and in some circumstances increased it. An analysis of the drag components showed that, although the pressure drag was substantially improved by boundary layer suction, the disappearance of the separated region downstream resulted in faster flow over the cylinder and consequently a higher skin friction drag. The drag-optimised flows had characteristics very close to those of a steady cylinder within the unsteady regime. These results show that the balance of drag components must be an important consideration when designing flow control systems and that, when done appropriately, substantial improvement can be seen in the flow characteristics.