Direct Numerical Simulation of Transition to Turbulence and Turbulence Control in Pipe Flow

Abstract

The subject of this thesis is the transition to turbulence and turbulence control in pipe flow. In pipes turbulence arises despite the linear stability of the laminar flow (subcritical transition) and directly from onset the flow is spatio-temporally complex. Given sufficiently strong perturbations, turbulence appears in localized patches (puffs) at low Reynolds numbers. At high Reynolds number, patches aggressively grow (slugs) and eventually render the flow fully turbulent. The questions of when and how turbulence starts to grow have long challenged scientists and will be discussed in-depth in this thesis. Turbulence causes higher friction drag and consequently higher energy losses than laminar flow. Control strategies that prevent the formation of turbulence and that relaminarise turbulence are desirable for applications. Some of these strategies were developed in the course of this thesis. In order to study the transition to fully turbulent flow, the growth of turbulence in terms of the speed of the laminar-turbulent interfaces (fronts) was measured at a variety of Reynolds numbers with highly resolved direct numerical simulations (DNS). The front speed data were compared to experimental measurements from my colleagues and excellent agreement was obtained. These front speeds can be perfectly described by a one dimensional pipe flow model developed by Dwight Barkley, which was inspired by the strong analogy between pipe flow and excitable media (such as nerve axons). A collective effort of theory, DNS and experiments showed that the transition from localized puffs to expanding fully turbulent flow (slugs) is a transition from excitability to bistability. This transition is continuous and a special role is played by nonlinear advection, which masks the transition point. The nonlinear advection was studied in the DNS and related to the selection of weak or strong downstream fronts. Based on the transition scenario studied in the first part of the thesis, a forcing strategy was developed to achieve an inverse transition from turbulent to laminar flow. A forcing was used that decelerates the flow near the pipe center and accelerates the flow near the pipe wall, modifying the velocity profile into a plug-like one. This modification was found to greatly weaken the turbulence self-sustaining mechanism. In particular it reduces the so-called transient growth (linear streaks amplification) of the flow and is capable of relaminarising turbulence at high Reynolds numbers. A statistical study showed that the minimum transient growth for turbulence to be sustained stays almost constant across a wide range of Reynolds numbers, suggesting that this constant transient growth sets the boundary between excitable and refractory (i.e., unexcitable). By pushing the transient growth below the critical value, pipe flow becomes refractory so that excitation ceases to be sustained and the flow relaminarises. A number of other control strategies have been developed that modify the shear profile. Another method to relaminarise turbulence is to impose partial slip at the pipe wall. The dynamics of turbulence largely depends on the boundary conditions. The effects of this slip boundary condition on the dynamics of pipe flow turbulence were investigated with DNS. The results showed that azimuthal slip intensifies turbulence, whereas streamwise slip suppresses turbulence. The smallest slip length that suffices to relaminarise turbulence was studied up to Reynolds number 20000 and a linear dependence on Reynolds number was found. While the necessary slip length to achieve relaminarisation is too large to be realized in experiments, the same effect could be achieved by other means, for example by accelerating the fluid near the pipe wall.