Numerical study of wall shear stress fluctuations and near-wall structures in a square duct at low Reynolds numbers. (15th December 2022) - Agrawal, Rishav; Mishra, Debi Prasad; Poole, Robert J.
Abstract: Direct numerical simulations (DNS) of turbulent flow through a square duct at two different low Reynolds numbers is performed using OpenFOAM to study the instantaneous wall shear stress fluctuations and near-wall structures. We first benchmarked our simulation results against other DNS studies which used higher-order spectral methods, thereby confirming the accuracy of our results. The mean profile of streamwise wall shear stress is well studied in the literature, however its higher order statistics has not been yet explored. There is also a lack of information on the spanwise component of wall shear stress and its higher-order statistics. Here, we provide an extensive study on streamwise and spanwise wall shear stresses, and their higher-order statistics. The intensities of both components of wall shear stress fluctuations are close to zero near the corner, and monotonically increase while moving towards the duct center. This is in contrast with their mean profiles which do not exhibit similar monotonic trends. However, the third-order moment, i.e. skewness of the streamwise wall shear stress again shows a non-monotonic behavior from the corner to the center. The profiles of the mean as well as the higher-order statistics of wall shear stress follow a better scaling between the two Reynolds number studied, when the spanwise location is normalized using inner scaling. Streamwise velocity correlations near the wall show that the flow structures in a square duct are similar to that of a channel flow near the center, whereas there is a cross-talk of the flow structures between the neighboring walls near the corner. An investigation into the effect of corner on the probability of back flow events is made at a Reynolds number lower than previously reported. The probability follows a non-monotonic behavior as we move from the corner towards the center, where it reaches a minimum at around 50 wall units from the corner. Similar to the wall shear stress profiles, the behavior of the near-wall flow structures as well as the spanwise variation of the probability of backflow events also show a qualitatively similar trend for the two Reynolds numbers, when the spanwise location is normalized using inner scaling. Highlights: DNS of turbulent flow through a square duct is performed using OpenFOAM. An extensive study on streamwise and spanwise wall shear stresses is conducted. Intensities of wall shear stress fluctuations increase from corner to center. Cross-talk of the flow structures between the neighboring walls near the corner. Effect of corner on the probability of near-wall back flow events is investigated.