Intermittency in the Transition to Turbulence

Abstract

Abstract.It is commonly known that the intermittent transition from laminar to turbulent flow in pipes occurs because, at intermediate values of a prescribed pressure drop, a purely laminar flow offers too little resistance, but a fully turbulent one offers too much. We propose a phenomenological model of the flow, which is able to explain this in a quantitative way through a hysteretic transition between laminar and turbulent "states," characterized by a disturbance amplitude variable that satisfies a natural type of evolution equation. The form of this equation is motivated by physical observations and derived by an averaging procedure, and we show that it naturally predicts disturbances having the characteristics of slugs and puffs. The model predicts oscillations similar to those which occur in intermittency in pipe flow, but it also predicts that stationary "biphasic" states can occur in sufficiently short pipes.

Co-current stratified gas–liquid downflow—Influence of the liquid flow field on interfacial structure

“…the flow is occasionally laminar or turbulent (e.g. Wygnaski and Champagne, 1973;Nino and Serio, 2000;Fowler and Howell, 2003). The physical character of this flow may be described by an intermittency factor (c), which represents the fraction of time at which there is turbulent flow.…”

Prandtl-Tietjens intermittency in transitional pipe flows

“…The terms on the right hand side are the pressure drop contributions from the laminar (∝ 1 − l/L), turbulent (∝ l/L) and external portions of the pipe, respectively. Previous work that split ∆P tot between a laminar and turbulent contribution also predicted oscillations, but they were unable to show quantitative agreement between model and experiment [15,16]. This highlights the importance of accounting for the external resistance R and accurately A single slug is engendered at t = 0 by a perturbation, which grows to its maximum size when it reaches the end of the pipe at t = T .…”

“…Rotta's insight laid the foundation for studying the patchy, localized turbulence, now believed to originate from special exact solutions of the governing Navier-Stokes equations such as nonlinear traveling waves [4]. Given the view that intermittency is a natural consequence of the governing equations [5], the PT argument appears irrelevant [11,15,16].…”

Modeling Of Pipe Flows And Observation Of Laminar Turbulent Transition In Smooth Pipes

“…Reynolds 4 referred to these laminar-turbulent oscillations as "flashes;" later Prandtl and Tietjens 7 identified structures within the flow that they called "puffs" and "slugs," which are unstable turbulent regions in the flow. The nature of these structures remains a topic of advanced study in the field 8,9 . Figure 9 compares the model to the mass flow rates measured from the rounded-entrance tube.…”