How Does The Length of Wall-Based Perturbations Impact Turbulent Pipe Flow Response and Recovery?

This study numerically investigates the impact of wall-based perturbation length on the response and recovery of turbulent pipe flow towards developing an effective passive flow manipulation system. The Reynolds number is 25,000, and length of the wall perturbation, introduced as a pipe-insert, varies between 2D and 12D, where D is the pipe diameter. The wall perturbations are based on Fourier modes that are designed to induce wall-normal gradients of Reynolds stresses, leading to local mixing, near-wall flow deceleration and axial flow acceleration. The turbulent field downstream of each pipe-insert is analyzed and compared, revealing a higher magnitude of Reynolds shear and normal stress for longer perturbations. The rate of transport of Reynolds shear stress follows the same power-law trend for longer inserts, but at higher magnitudes. The increase in perturbation length delays mean flow recovery, while increasing turbulent kinetic energy and localized frictional drag reduction. Thus, there is an optimal length for maximizing frictional drag reduction, while minimizing pressure drop due to wall-based perturbations.