Wall friction and heat transfer in turbulent pulsating flow in a square duct

For the first time, a DNS study of pulsating turbulent flows and heat transfer in a square duct is performed. Calculations were carried out at $Re=2200$ in the current-dominance mode for eight values of the oscillation period and three values of the Prandtl number. It was found that the time-mean friction coefficient in the studied pulsating flows has a lower value than in the stationary flow. The difference reaches $-14.7\text{\%}$. The values of the Nusselt numbers are also decreasing, albeit by a smaller amount. The features of secondary flows of Prandtl’s 2nd kind at different phases of the flow oscillations are studied. The profiles of the wall friction stress and heat transfer coefficients and their evolution over time are determined. The time-oscillations of the wall friction are entirely determined by the oscillations of the main flow, being ahead of it in phase by $\pi /4$, which coincides with the behavior of laminar pulsating flows at high frequencies. The oscillations in heat transfer on the wall are determined by oscillations in the intensity of turbulent heat exchange, and the change in the latter occurs almost in phase with a change in the volume-average intensity of the transverse velocity fluctuations.