Two-Dimensional Numerical Study on the Flow Past Two Staggered Cylinders in a Channel

The lattice Boltzmann method (LBM) is employed to simulate flow around two staggered cylinders within a confined channel. The numerical model is validated against existing experimental data by comparing drag coefficients and Strouhal numbers in the single-cylinder configuration. The study systematically investigates the influence of vertical ( $h$) and horizontal ( $l$) spacing between the cylinders, as well as the Reynolds number ( $Re$ = 0.1–160), on the hydrodynamic forces, streamline patterns, and vortex dynamics. Results indicate that reducing the horizontal spacing $l$ suppresses flow separation behind the upstream cylinder, while either excessively small or large vertical spacing $h$ diminishes separation in the downstream cylinder. The onset of periodic vortex shedding is delayed due to inter-cylinder interactions, with the critical Reynolds number increasing to $R{e}_c$ = 71–112, significantly higher than that of a single-cylinder case ( $R{e}_c$ ≈ 69). During the vortex shedding regime, the downstream cylinder exhibits a greater lift force fluctuation compared to the upstream cylinder. At $Re$ = 160, the root-mean-square lift coefficient ( $C_L^{\prime }$) ranges from approximately 0.17 to 0.56 for the downstream cylinder, and from 0.018 to 0.4 for the upstream one. The shedding frequency, characterized by the Strouhal number ( $St$), increases with Reynolds number, reaching $St$ = 0.12–0.18 at $Re$ = 160. Variations in $h$ and $l$ significantly influence $St$, with a decrease in $l$ or an increase in $h$ lowering the shedding frequency—this effect is more pronounced in the horizontal direction.