Of Pipes and Bends

Abstract: This work is concerned with the transition to turbulence of the flow in bent pipes, but it also includes an analysis of large-scale turbulent structures and their use for flow control.The flow in a toroidal pipe is selected as it represents the common asymptotic limit between spatially developing and helical pipes. The study starts with a characterisation of the laminar flow as a function of curvature and the Reynolds number Re, since the so-called Dean number is found to be of little use except for infinitesimally low curvatures. It is found that the flow is modally unstable and undergoes a Hopf bifurcation for any curvature greater than zero. The bifurcation is studied in detail, and an effort to connect this modal instability with the linearly stable straight pipe is also presented.This flow is not only modally unstable, but undergoes subcritical transition at low curvatures. This scenario is found to bear similarities to straight pipes, but also fundamental differences such as weaker turbulent structures and the apparent absence of puff splitting. Toroidal pipe flow is peculiar, in that it is one of the few fluid flows presenting both sub- and supercritical transition to turbulence; the critical point where the two scenarios meet is therefore of utmost interest. It is found that a bifurcation cascade and featureless turbulence actually coexist for a range of curvature and Re, and the attractors of the respective structures have a small but finite basin of attraction.In 90◦ bent pipes at higher Re large-scale flow structures cause an oscilla- tory motion known as swirl-switching. Three-dimensional proper orthogonal decomposition is used to determine the cause of this phenomenon: a wave-like structure which is generated in the bent section, and is possibly a remnant of a low-Re instability.The final part of the thesis has a different objective: to reduce the turbulent frictional drag on the walls of a channel by employing a control strategy independent of Re-dependent turbulent scales, initially proposed by Schoppa & Hussain [Phys. Fluids 10:1049–1051 (1998)]. Results show that the original method only gives rise to transient drag reduction while a revised version is capable of sustained drag reduction of up to 18%. However, the effectiveness of this control decreases rapidly as the Reynolds number is increased, and the only possibility for high-Re applications is to use impractically small actuators.