Turbulence suppression by streamwise-varying wall rotation in pipe flow

TL;DR

This study uses DNS to explore how streamwise-varying wall rotation can reduce drag and relaminarize turbulent pipe flow by forming an annular boundary layer called SSL, with effects depending on control parameters.

Contribution

It introduces the concept of the Spatial Stokes Layer (SSL) formed by wall rotation and identifies conditions for drag reduction and flow relaminarization in pipe flow.

Findings

SSL thickness influences drag reduction mechanisms.

Relaminarization occurs when SSL is sufficiently thick and velocity amplitude is high.

Turbulence is suppressed by energy absorption from wall-normal stresses.

Abstract

Direct numerical simulations (DNSs) of turbulent pipe flow subjected to streamwise-varying wall rotation are performed. This control method is able to achieve drag reduction and even relaminarize the flow under certain control parameters at low Reynolds number. Two control parameters, which are velocity amplitude and wavelength, are considered. An annular boundary layer, called Spatial Stokes Layer (SSL), is formed by the wall rotation. Based on the thickness of SSL, two types of drag reduction scenarios are identified. When the thickness is low, the SSL acts as a spacer layer, obstructing the impact of fluids against the wall and hence reducing the shear stress. The flow structures in the outer layer are less affected and are stretched in streamwise direction due to the increased velocity gradient. Within the SSL, the turbulence intensity diminishes dramatically. When the thickness is large, a streamwise wavy pattern of near-wall low-speed streaks is formed. The orientation of streaks is found to lag behind the direction of local mean velocity in phase and conform to the direction of local resultant shear stress. The streamwise scale of near-wall flow structures is significantly reduced, resulting in the disruption of downstream development of flow structures and hence leading to the drag reduction. Besides, it is found that it requires both large enough thickness of SSL and velocity amplitude to relaminarize the turbulence. The relaminarization mechanism is that the annular SSL can continuously absorb energy from wall-normal stress due to the rotation effect, thereby the turbulence self-sustaining process could not be maintained. For the relaminarization cases, the laminar state is stable to even extremely large perturbations, which possibly makes laminar state the only fixed point for the whole system.