Turbulent pipe flow in the presence of centerline velocity overshoot and wall-shear undershoot

The existence and characteristics of an overshoot phenomenon in the axial velocity distribution that occurs at the centerline of a turbulent pipe flow is investigated and documented by means of numerical simulation. A complementary phenomenon is also encountered in which the axial variation of the wall shear stress experiences an undershoot. These occurrences are not restricted to the case of a uniform velocity profile at the pipe inlet. The magnitude of the inlet turbulence intensity was found to play a major role in the downstream development of the flow. In particular, the magnitude of the overshoot showed a dependence on the value of the inlet turbulence intensity; the higher the intensity value, the lower the magnitude of the overshoot. Evidence was presented that enabled the attribution of the velocity peak and the wall shear undershoot to an initial tendency for the flow to laminarize. In particular, the presence of the velocity peak was related to different patterns of radial flow. When a peak was present, there was a radial inflow of fluid toward the centerline of the pipe followed downstream by a radial outflow from the centerline to the wall. The suppression of the velocity peak was accomplished by a very high value of the turbulence intensity at the inlet which neutralized the tendency towards laminarization. Other evidence of the laminarization tendency was obtained by examining the magnitude of the turbulence viscosity.