Wake interaction between two side-by-side square cylinders in channel flow

The flow around a pair of side-by-side square cylinders placed in a two-dimensional channel is computed using the lattice Boltzmann method. The Reynolds number is Red = dU0/ν = 73 (d is the side of the cylinder, U0 the upstream velocity, and ν the kinematic viscosity of the fluid) while the lateral separations between the cylinders, s∗ ≡ s/d, ranges between 0.5 and 6. Upon varying the cylinder spacing, in-phase, in-antiphase and quasi-periodic regimes are observed, by considering the lift and drag forces on the bodies. The relative coefficients vary substantially (in terms of mean and fluctuation rms values) in the range considered, while the Strouhal number is almost constant and near 0.16. The quasi-periodic regime, characterised by a second frequency much lower than the shedding, is studied in most detail. It is shown that the amplitude of the modulation follows a regular pattern in time that can be reproduced by a system of coupled Landau equations.

► The flow around a pair of side-by-side square cylinders at low Reynolds number is investigated numerically using the lattice Boltzmann method.
► Upon varying the cylinder spacing, in-phase, in-antiphase and quasi-periodic regimes of the wake are observed.
► While the Strouhal number is almost constant and near 0.16, lift and drag on the bodies also vary over different time scales than the fundamental one.
► The quasi-periodic regime, characterised by a second frequency much lower than that of the shedding, displays a regular modulation. This can be modelled by a couple of Landau’s equations.