Extension of the 1D Unsteady Friction Model for Rapidly Accelerating and Decelerating Turbulent Pipe Flows

Abstract

This work aims to examine the flow dynamics that contribute to the transient wall shear stress τw(t) of accelerating and decelerating turbulent pipe flows, using a series of direct numerical simulations (DNSs) of accelerating and decelerating flows between two fully turbulent states. Results show that accelerating and decelerating pipe flows exhibit different time dependence, especially in their turbulence response. It is observed that decelerating flows respond earlier than accelerating flows; however, they also require more extensive periods in which to relax towards their final turbulent state than accelerating flows. An identity that decomposes τw(t) into its dynamic contributions was used to determine the dominant flow dynamics involved within the different stages experienced by these flows. It is revealed that one of the existing 1D unsteady friction models accurately predicts one of the components of the dynamic decomposition of τw. Nonetheless, it is noted that the 1D model does not capture the transient response of the laminar and turbulent contributions. Consequently, the identity mentioned above was utilized as a framework to develop a hybrid model that improves the current 1D unsteady friction approaches.