Vortex statistics of a cylinder wake flow close to the wall based on IB-LBM

Abstract

In this paper, statistical behaviors of vortex in the wake flow of a circular cylinder placed near a plane wall in the two-dimensional (2D) channel are investigated by Immersed Boundary Lattice Boltzmann Method. Although vortices shed from the cylinder periodically, there are very complicated interactions between vortices and the solid wall. The gap ratios [Formula: see text] are considered in three cases [Formula: see text] to study vortex statistic behaviors when flow is in steady state. It can be seen that a single row of coherent structures in the same sign varies to dipole vortex shedding as [Formula: see text] increases. The results of vortex statistics by the conditional analysis, which are based on a new and accurate vortex identification criteria called Liutex, show the algebraic number density [Formula: see text], where [Formula: see text] is vortex area. The relationship between the vortex circulation [Formula: see text] and vortex area [Formula: see text] is [Formula: see text] and the one between the kinetic energy of vortex [Formula: see text] and [Formula: see text] is [Formula: see text] in the range where [Formula: see text]. Moreover, it has been found that vortices contain about 30% of the total energy of the flow which is almost conserved as Re varies by studying the energy ratio [Formula: see text] of all vortices to the entire flow field. The statistic behaviors of energy spectrums show that the spectrums contain an inertial range in which [Formula: see text] not only in the coherent structure field but also in the background field. More features of the vortex structure in the wake flow have been described by the empirical mode decomposition (EMD). There is a linear relationship between the frequency and the mode of the form [Formula: see text] e[Formula: see text] in the semi-log coordinates. The period of each mode [Formula: see text] e[Formula: see text] in the semi-log coordinates. The time-dependent intrinsic correlation (TDIC) shows that there is a strong negative correlation relationship between the pressure and the flow velocity in the complex attachment vortex.