On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug

Abstract

Conditionally sampled hot-wire measurements were taken in a pipe at Reynolds numbers corresponding to the onset of turbulence. The pipe was smooth and carefully aligned so that turbulent slugs appeared naturally atRe> 5 × 104. Transition could be initiated at lowerReby introducing disturbances into the inlet. For smooth or only slightly disturbed inlets, transition occurs as a result of instabilities in the boundary layer long before the flow becomes fully developed in the pipe. This type of transition gives rise to turbulent slugs which occupy the entire cross-section of the pipe, and they grow in length as they proceed downstream. The leading and trailing ‘fronts’ of a turbulent slug are clearly defined. A unique relation seems to exist between the velocity of the interface and the velocity of the fluid by which relaminarization of turbulent fluid is prevented. The length of slugs is of the same order of magnitude as the length of the pipe, although the lengths of individual slugs differ at the same flow conditions. The structure of the flow in the interior of a slug is identical to that in a fully developed turbulent pipe flow. Near the interfaces, where the mean motion changes from a laminar to a turbulent state, the velocity profiles develop inflexions. The total turbulent intensity near the interfaces is very high and it may reach 15% of the velocity at the centre of the pipe. A turbulent energy balance was made for the flow near the interfaces. All of the terms contributing to the energy balance must vanish identically somewhere on the interface if that portion of the interface does not entrain non-turbulent fluid. It appears that diffusion which also includes pressure transport is the most likely mechanism by which turbulent energy can be transferred to non-turbulent fluid. The dissipation term at the interface is negligible and increases with increasing turbulent energy towards the interior of the slug.Mixed laminar and turbulent flows were observed far downstream for\[ 2000 < Re < 2700 \]when a large disturbance was introduced into the inlet. The flow in the vicinity of the inlet, however, was turbulent at much lowerRe. The turbulent regions which are convected downstream at a velocity which is slightly smaller than the average velocity in the pipe we shall henceforth call puffs. The leading front of a puff does not have a clearly defined interface and the trailing front is clearly defined only in the vicinity of the centre-line. The length and structure of the puff is independent of the character of the obstruction which created it, provided that the latter is big enough to produce turbulent flow at the inlet. The puff will be discussed in more detail later.

The rise of fully turbulent flow

“…[1][2][3][4][5][6] At slightly higher speeds the situation changes distinctly and the entire flow is turbulent. Neither the origin of the different states encountered during transition, nor their front dynamics, let alone the transformation to full turbulence could be explained to date.…”

“…The functions f (q, u) and g(q, u) capture the known interplay between turbulence (the excited state), and the shear profile. 3,22 Parameter r plays the role of Reynolds number, ζ accounts for the fact that turbulence is advected more slowly than the centreline velocity, D controls the coupling strength of the turbulent field, and sets the timescale ratio between fast excitation of q and slow recovery of u following relaminarisation. The fast scale of q and cubic nonlinearity in f (q, u) are motivated by known upper-and lower-branch exact coherent structures in shear flows.…”

A doubly localized equilibrium solution of plane Couette flow

“…While small periodic 'minimal flow units' are useful microcosms for studying turbulence, turbulence in extended domains generally involves large numbers of interacting flow structures, whose dynamic coupling presumably decreases with their separation. Additionally the transition to turbulence in extended domains occurs through the growth of turbulent spots or puffs, consisting of localized patches of unsteady, complex flow within a background of laminar flow (Wygnanski & Champagne 1973;Tillmark & Alfredsson 1992;Barkley & Tuckerman 2005;Philip & Manneville 2011).…”

Patterned Turbulence in Liquid Metal Flow: Computational Reconstruction of the Hartmann Experiment

“…We see the main feature of the transitional regimes -localized turbulent spots with laminar flow between them. Localized turbulent spots are well known from HD wall-bounded shear flows [22][23][24][25][26][27] and can be considered in the broader context of patterned turbulence. The best known example is pipe flow, where the spots are known since [9].…”

“…Two types of spots have been identified [22][23][24][25][26]: turbulent puffs with nearly constant length and speed existing in low-Re flows with strong perturbations and turbulent slugs at high Re characterized by aggressive length growth leading to a completely turbulent state. A discussion of their fascinating features, including vorticity dynamics, their nature as a chaotic saddle and the random character and sensitivity to initial conditions, can be found in [22][23][24][25][26].…”