Effect of thermal wall condition on the dissimilarity of momentum and heat transfer in pulsating channel flow

Pulsating turbulent channel flows under constant temperature difference (CTD) condition and uniform heat flux heating (UHF) condition are studied by direct numerical simulation (DNS). The main objective of the present study is to clarify how the dissimilarity between momentum transfer and heat transfer appeared in the pulsating flows, in which the dissimilarity may originate from the CTD condition dissimilar to the no-slip condition of the velocity field rather than from the thermo-fluid physics under pulsation. Simulations have been performed for three pulsation frequencies under the friction Reynolds number at steady-state, Re-tau s = 300. Comparing the phase-averaged quantities under CTD and UHF conditions, it is found that the frequency dependence of the temperature oscillations in the near-wall region is almost the same regardless of the thermal boundary condition although the time-averaged temperature profiles are different. As a result, the ratio of Stanton number to friction factor, which works as a barometer of the analogy, changes during the pulsation period at both CTD and UHF conditions. Besides, the oscillation amplitude becomes larger as the pulsation frequency increases. Therefore, it was confirmed that the dissimilarity appears regardless of the thermal boundary condition. In addition, turbulent Prandtl number shows similar cyclic behavior to the ratio of Stanton number to friction factor. Time variations of each component constituting turbulent Prandtl number reveal that increasing dissimilarity at the high frequency is mainly attributed to the amplified oscillation of velocity gradient near the wall, where Reynolds shear stress and turbulent heat flux are kept at around the time-averaged values because the near-wall vortex structures cannot follow the rapid change of flow rate.