Direct numerical simulations (DNS) and experiments are carried out to study fully developed turbulent pipe flow at Reynolds number Rec ≈ 7000 based on centreline velocity and pipe diameter. The agreement between numerical and experimental results is excellent for the lower-order statistics (mean flow and turbulence intensities) and reasonably good for the higher-order statistics (skewness and flatness factors). To investigate the differences between fully developed turbulent flow in an axisymmetric pipe and a plane channel geometry, the present DNS results are compared to those obtained from a channel flow simulation. Beside the mean flow properties and turbulence statistics up to fourth order, the energy budgets of the Reynolds-stress components are computed and compared. The present results show that the mean velocity profile in the pipe fails to conform to the accepted law of the wall, in contrast to the channel flow. This confirms earlier observations reported in the literature. The statistics on fluctuating velocities, including the energy budgets of the Reynolds stresses, appear to be less affected by the axisymmetric pipe geometry. Only the skewness factor of the normal-to-the-wall velocity fluctuations differs in the pipe flow compared to the channel flow. The energy budgets illustrate that the normal-to-the-wall velocity fluctuations in the pipe are altered owing to a different ‘impingement’ or ‘splatting’ mechanism close to the curved wall.

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The data base of an extensive DNS of turbulent flow in a pipe (Eggels et al. J. Fluid Mech. 268 (1994) 175) at Re = 7000, based on the pipe diameter and the centerline velocity or Ref = 360 based on the friction velocity u~, has been used to study some of the alignments discovered recently in quasi-isotropic and shear turbulent flows and attracted considerable attention. These are the alignments between the velocity u and vorticity vectors to, between the vorticity to and the eigenvectors of the rate of strain tensor sij, and between to and the vortex stretching vector Wi = toj sij. Comparison of these alignments strongly indicates that the quasi-two-dimensional (QTD) state of turbulent pipe flow in regions of strong alignment between to and the intermediate eigenvector ,~int of the rate of strain tensor sij is qualitatevly different from purely two-dimensional one. This is manifested in stronger alignments between to and W in these regions as well as in larger enstrophy generation ((.OiWjSij) =-(o)iWi) and large (W2), which are identically zero for a purely two-dimensional flow.The same is true of regions with concentrated vorticity, most of which are embedded into the regions with strong alignment between to and ~[int.

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