Shape optimization to suppress the lift oscillation for a stationary cylinder at low Reynolds numbers: A low-cost lift oscillation intensity proxy objective function

Shape optimization can suppress the lift oscillations generated by the fluid flowing over a stationary cylinder at low Reynolds numbers. By constructing the objective function based on linear stability analysis or resolvent analysis, the calculation of unsteady flow fields in traditional schemes can be avoided. However, additional calculations of the eigenvalues of the Jacobian matrix or singular value decomposition of the resolvent operator are still required on the basis of the steady-state base flow, resulting in high computational costs of the objective function and affecting the optimization efficiency. To address this, this study proposes a low-cost proxy objective function for the intensity of lift oscillations. By establishing a mathematical relationship between the average resistance and the integral of positive lift in a single cycle, the drag coefficient in the subcritical Reynolds number regime is used as the objective function. Thus, only the steady laminar solution at subcritical Reynolds numbers and the stress integral on the cylinder surface need to be calculated. The class function/shape function transformation technique is selected as the shape parameterization method, and the Adaptive Design of Experiments algorithm is used to optimize the objective function. The results show that through shape optimization, the vortex shedding intensity can be effectively suppressed in two-dimensional flow, reducing the amplitude of the lift coefficient by more than 59%. At the same time, the flow stability is improved, and lift oscillations are completely eliminated within the Reynolds number range of 47–60.