Effect of the spanwise computational domain size on the flow over a two-dimensional bluff body with spanwise periodic perturbations at low Reynolds number

Abstract

To effectively control the flow over a two-dimensional bluff body, three-dimensional perturbations including spanwise-varying shape modifications and surface actuations have been suggested by previous studies. One of the computational issues is how big the spanwise computational domain size (Lz) should be as compared to the wavelength of these spanwise-varying perturbations (λ), to accurately estimate the effect of these perturbations. To investigate this issue, we consider three different two-dimensional bluff bodies with spanwise periodic perturbations: wavy square cylinder, wavy circular cylinder, and spanwise-varying blowing and suction on a circular cylinder at Re = 100. The spanwise length scales of largest vortical structures existing in the wake significantly depend on Lz, and they are larger than λ, reaching 2λ, 3λ, and even bigger than or equal to 12λ for the cases considered. These largest structures are composed of multiple of elementary vortical structures whose length scales are smaller than or equal to Lz. The amounts of drag reduction by periodic perturbations at Lz > λ are smaller than those at Lz = λ, indicating that the computational domain size equal λ overestimates their performances.