Numerical studies on flows with secondary motion

Abstract: This work is concerned with the study of flow stability and turbulence control - two old but still open problems of fluid mechanics. The topics are distinct and are (currently) approached from different directions and with different strategies. This thesis reflects this diversity in subject with a difference in geometry and, consequently, flow structure: the first problem is approached in the study of the flow in a toroidal pipe, the second one in an attempt to reduce the drag in a turbulent channel flow.The flow in a toroidal pipe is chosen as it represents the common asymptotic limit between spatially developing and helical pipes. Furthermore, the torus represents the smallest departure from the canonical straight pipe flow, at least for small curvatures. The interest in this geometry is twofold: it allows us to isolate the effect of the curvature on the flow and to approach straight as well as helical pipes. The analysis features a characterisation of the steady solution as a function of curvature and the Reynolds number. The problem of forcing fluid in the pipe is addressed, and the so-called Dean number is shown to be of little use, except for infinitesimally low curvatures. It is found that the flow is modally unstable and undergoes a Hopf bifurcation that leads to a limit cycle. The bifurcation and the corresponding eigenmodes are studied in detail, providing a complete picture of the instability.The second part of the thesis approaches fluid mechanics from a different perspective: the Reynolds number is too high for a deterministic description and the flow is analysed with statistical tools. The objective is to reduce the friction exerted by a turbulent flow on the walls of a channel, and the idea is to employ a control strategy independent of the small, and Reynolds number-dependent, turbulent scales. The method of choice was proposed by Schoppa & Hussain [Phys. Fluids 10:1049-1051 (1998)] and consists in the imposition of streamwise invariant, large-scale vortices. The vortices are re-implemented as a volume force, validated and analysed. Results show that the original method only gave rise to transient drag reduction while the forcing version is capable of sustained drag reduction of up to 18%. An analysis of the method, though, reveals that its effectiveness decreases rapidly as the Reynolds number is increased.