Exploring the influence of span-wise boundary conditions on the wake of a thin flat plate using Fourier-Averaged Navier–Stokes equations

The wake of a thin normal flat plate with different end conditions is numerically analyzed at a Reynolds number of 250. Periodic, slip, and no-slip boundary conditions are considered for the spanwise boundaries in order to analyze the effect of spanwise flow constraints using a new technique: Fourier-Averaged Navier–Stokes equations (FANS). The results of cases with periodic and slip end conditions were similar in both mean and unsteady fields. However, no-slip boundary conditions, which could represent the case of experimental setups with end plates, significantly reduce the velocity, drag and lift fluctuations in the flow. FANS analysis confirmed that loss of the nominal two-dimensional behavior due to the no-slip end condition relates to the presence of a spanwise flow coherence at the vortex shedding frequency (mode). Interactions between the rollers and boundary layer induces large-scale spanwise fluctuations that are absent without the end plates. In this way, the boundary layer due to the end plate serves as a flow control mechanism that suppresses fluctuations in the flow and reduces stresses in the center-plane, alongside increasing coherence in the spanwise flow. •Analysis using Fourier-Averaged Navier-Stokes equations and Bispectral Modes.•Spectral signature for different span-wise end conditions for normal flat plate.•Transport term contributions to spectral content.•Identification of 3D effects in Fourier space.