Response of turbulent pipe flow to targeted wall shapes at a range of Reynolds numbers

Abstract

The response and recovery of turbulent pipe flow to three-dimensional perturbed wall changes were examined numerically in a wide range of Reynolds numbers between Re=5×103 and 1.58×105. The perturbations were based on distinct azimuthal Fourier modes corresponding to m = 3, 15, and 3 + 15. The long-lasting response of the flow was examined by characterizing both the mean and turbulent field in the wake of pipe inserts for each Re. The variation of the recovery with increasing Reynolds number revealed an asymptotic behavior for Re≥7.5×104, which scaled with Re4 for both mean velocity and turbulence kinetic energy. Two peaks were observed for the mean velocity along the wake centerline, where the location of peaks followed a power-law trend in the form of Lp/D∝Re4/3, where D is the pipe diameter. A fast decay of turbulence past the wall change further suggested that maximum Reynolds shear stress in the downstream wake decays as (x/D)−1/3 for all Re. The flow also exhibited long-lasting responses that obstructed its relaxation at 20D downstream of the perturbation, even for low Re of 5×103. Overall, the recovery exhibited a second-order response.