Improved delayed detached-eddy simulation and proper orthogonal decomposition analysis of turbulent wake behind a wall-mounted square cylinder

Abstract

The turbulent flow past a wall-mounted square cylinder with an aspect ratio of 4 was investigated with the aid of Spalart–Allmaras improved delayed detached-eddy simulation and proper orthogonal decomposition (POD) analysis. The Reynolds number was equal to 12 000 (based on the free-stream velocity and obstacle width). The boundary layer thickness was ∼0.18 of the obstacle height. This study focused on analyzing the vortical structure of the wake and vortex shedding process along the obstacle height. A quantitative comparison of the first- and second-order flow statistics with the available experimental and direct numerical simulation data was used to validate the numerical results. The numerical model coupled with the vortex method of generating the turbulent inflow conditions could successfully reproduce the flow field around and behind the obstacle with commendable accuracy. The flow structure and vortex shedding characteristics near the wake formation region were discussed in detail using time-averaged and instantaneous flow parameters obtained from the simulation. Dipole type mean streamwise vortices and half-loop hairpin instantaneous vortices with energetic motions were identified. A coherent shedding structure was reported along the obstacle using two-point correlations. Two types of vortex shedding intervals were identified, namely, low amplitude fluctuations (LAFs) and high amplitude fluctuations (HAFs) [P. Sattari et al., Exp. Fluids 52, 1149–1167 (2012)]. The HAFs’ interval exhibits von Kármán-like behavior with a phase difference of ∼180°, while the LAFs’ interval shows less periodic behavior. It was observed that the effect of the LAFs’ interval tends to weaken the alternating shedding along the obstacle height. The POD analysis of the wake showed that for the elevations between 0.25 and 0.5 of the obstacle height, the first two POD modes represent the alternating shedding and contribute to 66.6%–57.6% of the total turbulent kinetic energy. However, at the free end of the obstacle, the first two modes have a symmetrical shedding nature and share 36.5% of the kinetic energy, while the rest of the energy is distributed between the alternating and the random shedding processes. A simple low-order model based on the vortex-shedding phase angle and the spectrum of the time coefficients obtained from POD was developed to predict the wake dynamics at the range of elevations where the alternating shedding is dominated.