Receptivity-orientated drag reduction of twin cylinders by steady leading-edge suction control based on adjoint method

Abstract

This study investigates the drag reduction of two tandem square cylinders under steady suction control at Reynolds numbers 50–200. The position where the suction flow should be placed is determined by using a receptivity analysis based on the adjoint method, and we investigate how control affects the fluid force and flow structures. High-order dynamic mode decomposition (HODMD) is applied to analyze the dynamic coherence modes and uncover the underlying control mechanism. The adjoint modes show that the regions of maximum receptivity to momentum forcing are localized on each side of the up-cylinder (UC) near the leading edge (LE). Thus, the suction flow is placed on the LE. The drag can be significantly reduced at wide gap distances, especially for the co-shedding regime. Under suction flow control, the separation is suppressed near the LE, and the gap vortices are no longer fed by the vorticity generated by the separated shear layer; they only result from the trailing-edge separation, which weakens and shrinks. Subsequently, the interaction between the gap flow and the down-cylinder (DC) is weakened, which reduces the drag and lift forces. The decrease in drag exceeds 66.4% for the UC and reaches 81.6% for the DC. The fluctuating reduction in the lift for the UC (DC) exceeds 59.0% (75.7%). HODMD results show that, as the suction flow velocity increases, the LE suction flow modifies the local time-averaged modes rather than the global mode energy. Conversely, the dynamic mode energy decreases significantly, whereas the mode shape remains unchanged except for a phase shift.