On the origin of the centreline velocity overshoot in the entrance region of a turbulent pipe flow

Abstract

The cause for the overshoot phenomenon on the axial centreline velocity in the entrance region of turbulent pipe flows, and for the wall shear stress undershoot is investigated by numerical simulations. The overshoot is linked directly to the turbulent boundary layer. Examination of the boundary layer showed the dependency of the overshoot of the Reynolds stresses and the turbulent kinetic energy. The state of high anisotropy near the wall leads to small scale eddies which create a radial velocity towards the wall and are counteracting the radial velocity triggered by the displacement effect of the tube wall, which even changes the direction of the radial flow at a certain point. The velocity overshoot on the centreline and the wall shear stress undershoot are the result of this radial velocity towards the wall. The flow reaches a state of isotropy far down the pipe when the stream is fully developed and the radial velocity vanishes. The entrance length is therefore much longer than the simple 40 times diameter.