Shear flow experiments: Characterizing the onset of turbulence as a phase transition

Abstract

In this cumulative thesis the onset of turbulence in shear flows with a linearly stable laminar flow is investigated experimentally. The experiments are performed in a pipe and a Taylor-Couette setup, both with large system sizes. A high-precision Taylor-Couette experiment has been designed and three important main results have been obtained in the course of this study. The first main result gives the solution to a question from the 19th century by one of the pioneers of fluid dynamics, Osborne Reynolds. He asked at what critical Reynolds number Re_c pipe flow turns persistently turbulent. My experiments show it is at Re_c = 2040 ± 10. The pressure driven pipe flow experiment had a length of more than 3300 pipe diameters and water was used as working fluid. Turbulence was induced in a controlled manner and its development detected downstream with pressure sensors. Large statistical ensembles were performed. The second main result is to identify the mechanism that determine this transition between laminar flow and sustained turbulence. It is shown that purely temporal aspects like the Ruelle-Takens scenario or the statistical decay of turbulent patches are not sufficient to characterize it. Instead the spatial proliferation of turbulence, which is also a statistical process, has to be taken into account. The competition of the decay and the spreading of turbulence define Re_c. The larger picture emerging from these observations is that the onset of turbulence in pipe flow can be characterized as a non-equilibrium phase transition. The third main result is that the phase transition is of second order. In contrast to the previous observation, this result was obtained in a flow between two concentric counter-rotating cylinders (Taylor-Couette flow). In the selected parameter regime the dynamics resembles that of pipe flow, but with the advantage that the time scales are much shorter. Therefore it was possible to investigate the phase transition in more detail by analyzing the scaling of the mean turbulent fraction depending on Re. A system size 12 times larger than previous Couette experiments combined with a high accuracy and long observation times allowed it to measure substantially closer to the critical point than previously. The continuity of the transition could be identified for the first time, thereby contradicting interpretations from experiments in literature, but supported by models of pipe flow and recent numerical simulations of Couette flow. A radius ratio of η = 0.98 and an aspect ratio of about 260 were used and the working fluid, silicone oil, was seeded with Al-tracers for visualization. The flow was monitored with a high speed camera from which the mean turbulent fraction was obtained by image processing. Another accomplishment of this thesis is the construction of the Taylor-Couette experiment that was used for the aforementioned investigation. Besides its large system size and high accuracy this setup offers a wide regime of parameters. The radius ratio can be easily changed from extremes of a thin inner cylinder (radius ratio η = 0.03) to almost identical radii (η = 0.98), the aspect ratio can be dynamically varied during measurements and the rotation rates of the cylinders allow studies in the transitional as well as in the turbulent regime. By independently rotating the top and bottom lid the boundary condition can be adjusted to minimize endwall effects. The sophisticated bearing system is combined with several cooling circuits to provide a high precision during long-time measurements. Excellent optical access and index matching allow for optical measurement techniques.