Wall shear stress in accelerating pipe flows

This paper presents results from experimental and computational studies on the response of wall shear stress in transient turbulent pipe flow with a ramp-type increases of flow rate. Wall shear stress has been obtained from the measurements of the axial pressure gradient and flow rate for transients with various accelerations. Numerical simulations have been conducted using a low-Reynolds-number k-epsilon turbulence model in conjunction with a finite volume/finite difference discretization scheme. Simulations with turbulent shear stress or turbulent diffusivity artificially frozen were also carried out. The present studies show that the variation of wall shear stress in a rising ramp flow transient follows a pattern of over-shooting, delay and recovery. This is a consequence of the combined effect of the inertia of the fluid and the delay in the response of turbulence. The effect of the former dominates in the early stages of a faster transient and causes overshooting in the response of wall shear stress. The effect of the delayed response of turbulence builds-up with time during a transient and results in an undershooting in the response of wall shear stress. Both effects become smaller as the flow rate increases in the later stages of a rising ramp and wall shear stress then tends to follow the corresponding pseudo-steady variation. The effect of increasing the starting Reynolds number is to reduce the deviation of the wall shear from its corresponding pseudo-steady state value.