Scaling Properties of Turbulent Pipe Flow at Low Reynolds Number

Direct numerical simulation of an equilibrium turbulentpipeflow at a Reynoldsnumber of 2500, based on bulk velocity and pipe diameter, has been carried out with a grid of about 7.4×10^5 points and a fully resolved wall layer. The simulation fills the existing gap in the availability of accurate turbulence data in the lowReynoldsnumber range, so that the sensitivity of the main statistical quantities to the Reynoldsnumber effects could be completed. The systematic dependence of the turbulent stress tensor components upon Re in the near wall region, when the normalization is based upon the wall shear stress and kinematic viscosity, is confirmed. Normalization based on the Kolmogorov velocity and length scales as suggested by Antonia and Kim [1] in the context of plane channel flow, proves effective also for pipeflow at lower Re. The high values attained by the fourth-order moments of the radial and azimuthal velocities are shown to be of truly physical nature and to be related with rare and energetic events characterizing the whole wall layer. Vorticity dynamics analysis suggests that the origin of the high flatness factors is associated with the interaction of counter-rotating streamwise vortices with the wall. Analysis of the transport equations of the turbulent kinetic energy shows that the production, turbulent dissipation and viscous diffusion rates, the leading terms of the budget, increase considerably with Re for y+<20.