The effect of pipe-insert thickness on turbulent pipe flow response and recovery is numerically investigated at a Reynolds number of 25, 000. Three perturbation thicknesses are assessed, referred to as Fourier pipe-inserts, \(h=0.05D, 0.1D\), and 0.15D. The relationship between insert thickness and recovery of turbulent kinetic energy and mean axial velocity is assessed to evaluate the impact of perturbation thickness. Increasing the perturbation strength (thickness) enhances flow turbulence due to increased geometric contraction. Excess turbulence is transported away from the wall, following an empirical power law that scales with h. Global parameters, such as skin friction and pressure loss, are analyzed for future design considerations. All cases demonstrate a localized skin-friction reduction that returns to equilibrium at varying distances downstream. The thickest perturbation (\(h=0.15D\)) has the largest skin-friction reduction and exhibits the largest pressure gradient within the pipe-insert, with an overall increase in pressure loss by 3.1%. These results demonstrate that insert thickness is a critical design parameter for Fourier pipe-inserts with significant implications for flow recovery and drag reduction.
