A direct numerical simulation of transitional pipe flow is carried out with the help of
a spectral element method and used to investigate the localized regions
of ‘turbulent’
flow that are observed in experiments. Two types of such regions can be distinguished:
the puff and the slug. The puff, which is generally found at low values of the Reynolds
numbers, is simulated for Re = 2200 where the Reynolds number
Re is based on the mean velocity UB
and pipe diameter D. The slug occurs at a higher Reynolds number
and it is simulated for Re = 5000. The computations start with a laminar pipe flow
to which is added a prescribed velocity disturbance at a given axial position and for
a finite time. The disturbance then evolves further into a puff or slug structure.The simulations confirm the experimentally observed fact that for a puff the
velocity near the leading edge changes more gradually than for a slug where an
almost discontinuous change is observed. The positions of the leading and trailing
edges of the puff and slug are computed from the simulations as a function of time.
The propagation velocity of the leading edge is found to be constant and equal
to 1.56UB and 1.69UB for the
puff and slug, respectively. For the trailing edge the
velocity is found to be 0.73UB and
0.52UB, respectively. By rescaling the simulation
results obtained at various times to a fixed length, we define an ensemble average.
This method is used to compute the average characteristics of the puff and slug such
as the spatial distribution of the mean velocity, the turbulent velocity fluctuations and
also the wall shear stress. By computing particle trajectories we have investigated the
entrainment and detrainment of fluid by a puff and slug. We find that the puff detrains
through its trailing edge and entrains through its leading edge. The slug entrains fluid
through its leading and through most of its trailing edge. As a consequence the fluid
inside the puff is constantly exchanged with fluid outside whereas the fluid inside a
slug remains there. These entrainment/detrainment properties which are in agreement
with the measurements of Wygnanski & Champagne (1973) imply that the puff has
the characteristics of a wave phenomenon while the slug can be characterized more
as a material property which travels with the flow.Finally, we have investigated in more detail the velocity field within the puff. In a
coordinate system that travels with the mean velocity we find recirculation regions
both near the trailing and leading edges which agrees at least qualitatively with
experimental data. We also find streamwise vortices, predominantly in the trailing-edge region which have been also observed in experiments and which are believed to
play an important role in the dynamics of the transition process.
Direct numerical simulation of turbulent pipe flow up to a Reynolds number of 61,000
