Flow through an elbow: A direct numerical simulation investigating turbulent flow quantities

Turbulent flow in a sharp $90°$ elbow in a square duct was numerically investigated by performing a direct numerical simulation (DNS) and the results were compared to experimental and Reynolds Averaged Navier–Stokes (RANS) data. This is the first part of an effort to expand the understanding of particle transport in complex geometries. The paper is divided into two parts: a validation of the flow, and then a discussion of additional flow quantities that are important for modeling particles but were not measured experimentally. In the validation section the DNS results were compared to experimental and RANS data at a Reynolds number of $11,500$. Profiles of the mean and root-mean-square (RMS) fluctuating velocities were compared at various points along the elbow's midplane. Upstream of the bend, the predicted mean and RMS velocities from the RANS and DNS simulations compared well with the experiment, differing only slightly near the walls. Downstream of the bend the DNS and the experimental results were virtually identical, varying by no more than $2\%$. However, the RANS results deviated, showing a more extended region of flow re-circulation, causing the mean and RMS velocities to differ by as much as $40\%$. After the validation, one of the additional quantities was the secondary flow structures in the plane perpendicular to the mean flow direction. The RANS and DNS showed similar results upstream of the bend, exhibiting in-plane vortices of the second-kind. Downstream, the vortical flows of the first-kind were observed with a magnitude of about $40\%$ of the mean flow and differed by about $5\%$ between the DNS and the RANS. Eulerian time scales at different locations upstream and downstream of the elbow were also evaluated. The upstream Eulerian time scales showed trends similar to channel flow data, with maximum time scales near the wall. The downstream time scales were qualitatively different showing non monotonic behavior across the channel and values that were significantly different than a channel flow.