Abstract
The flow of an incompressible fluid in a straight circular pipe driven by a pressure gradient is a canonical shear flow undergoing subcritical transition. It is well established that at transitional Reynolds numbers 1760 ≲ Re ≲ 2700 (based on the mean axial flow speed U¯ and pipe diameter D), flow in the pipe becomes spatially intermittent with irregular alternation of laminar flow and the turbulent coherent structures commonly referred to as puffs and slugs. In the present study, we describe quasi-equilibrium turbulent puffs at 2000 ⩽ Re⩽ 2200 by solving unsteady Navier-Stokes equations with periodic velocity along the pipe for very long times up to 8×104D/U¯. We present results with both constant mass flux and constant pressure gradient driving. We show that one can obtain different values of mean pressure gradient for different initial conditions, i.e., that multiple numerical Navier-Stokes solutions exist at a given Re. These solutions have an extensive statistically stationary stage and describe localized puffs surrounded by laminar flow or clusters of interacting puffs. A detailed pattern of entrainment of fluid at the laminar turbulent interfaces is provided by computing trajectories of fluid tracers. Specific backstreaming regions are exposed for both the trailing and leading fronts of the puff.
Published Version
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