Turbulent flows around side-by-side cylinders with regular and multiscale arrangements

Direct numerical simulations are performed to investigate turbulent flows behind two different types of cylinder arrays (i.e., one is a widely used regular array and the other is a less studied multiscale array) with the same blockage ratio. Some important characteristics (e.g., mean velocity, turbulence intensity, and pressure drop) of the two flows are evaluated. It is demonstrated that the overall pressure drops in the two cases are almost the same. In the downstream region, the characteristics of the regular flow resemble those of the homogeneous flow, whereas the flow behind the multiscale array exhibits wakelike behavior. For the regular case, the vortex shedding frequencies due to different cylinders are the same since the cylinders involved are virtually identical and the vortex wakes formed by two neighboring cylinders are always in antiphase synchrony. In contrast, the multiscale array can generate wakes with multiple scales of both space and time. To quantitatively evaluate the difference between the features of the coherent structures in the two flows, we adopt the so-called snapshot proper orthogonal decomposition. It is found that immediately behind the regular array, most of the energy is contained in a few of the first modes. In the multiscale case, however, due to cylinders of various sizes, the increase in the energy cumulation is considerably slower than the regular case. This observation is in accord with the suggestion that by using multiscale structures, turbulence with a wider range of scales can be generated. One perhaps interesting and less reported discovery is that in the downstream region for the two cases the profiles of the energy cumulation are somewhat close to each other, although slight deviation can still be identified when normalized by the dominant vortex shedding frequency. This observation seems to tell us that the multiscale flow may not have a long-lasting memory and can eventually forget its multiscale initial conditions. These findings contribute to the understanding of the recently proposed space-scale unfolding mechanism [Phys. Rev. E 86, 046302 (2012) and J. Fluid Mech. 764, 52 (2015)], which outlines a conceptual model for explaining the high mixing efficiency of the multiscale and fractal structures and objects.