Turbulent drag reduction through wall-forcing methods

The constraints brought about by environmental and economical issues have been key elements for devising new techniques for skin-friction drag reduction in turbulent flows. Several methodologies have been applied during the last thirty years. These methods can be categorised as active, passive, closed or open-loop. In general, these techniques are mathematically modelled, then tested in experimental settings and numerical simulations. The numerical model for this study was based on the resolution of the full spatio-temporal scales through Direct Numerical Simulation (DNS). With the advent of powerful high-end computing systems endowed with several thousands of processors and relying on distributed memory programming, the performance deadlock due to highly resolved DNS is progressively being overcome. To study in a first principal basis a flow, DNS based on an efficient flow solver called Incompact3d has been relied on more particularly focusing on the development of a large array of flow control techniques. Motivated by extensive discussion in the literature, by experimental evidence and byrecent direct numerical simulations, we study flows over hydrophobic surfaces with shear-dependent slip lengths and we report their drag-reduction properties. The laminar channel-flow and pipe-flow solutions are derived and the effects of hydrophobicity are quantified by the decrease of the streamwise pressure gradient for constant mass flow rate and by the increase of the mass flow rate for constant streamwise pressure gradient. The nonlinear Lyapunov stability analysis is employed on the three-dimensional channel flow with walls featuring shear-dependent slip lengths. The feedback law extracted through the stability analysis is recognized for the first time to coincide with the slip-length model used to represent the hydrophobic surfaces, thereby providing a precise physical interpretation for the feedback law advanced by Balogh et al. (2001). The theoretical framework by K. Fukagata, N. Kasagi, and P. Koumoutsakos is employed to model the drag-reduction effect engendered by the shear-dependent slip-length surfaces and the theoretical drag-reduction values are in very good agreement with our direct numerical simulation data. The turbulent drag reduction is measured as a function of the hydrophobic-surface parameters and is found to be a function of the time- and space-averaged slip length, irrespectively of the local and instantaneous slip behaviour at the wall. For slip parameters and flow conditions that could be realized in the laboratory, the maximum computed turbulent drag reduction is 50% and the drag reduction effect degrades when slip along the spanwise direction is considered. The power spent by the turbulent flow on the hydrophobic walls is computed for the first time and is found to be a non-negligible portion of the power saved through drag reduction, thereby recognizing the hydrophobic surfaces as a passive-absorbing drag-reduction method. The turbulent flow is further investigated through flow visualizations and statistics of the relevant quantities, such as vorticity and strain rates. When rescaled in drag-reduction viscous units, the streamwise vortices over the hydrophobic surface are strongly altered, while the low-speed streaks maintain their characteristic spanwise spacing. We finally show that the reduction of vortex stretching and enstrophy production is primarily caused by the eigenvectors of the strain rate tensor orienting perpendicularly to the vorticity vector. In a second phase, several drag-reduction techniques were implemented and benchmarked. This step was motivated by the drag-reducing potential benefits of combined active-active and active-passive techniques compared to those taken separately. With this objective in mind, three control techniques were selected and categorized as primary and secondary. The primary control method consisted in an array of steady rotating discs or rings embedded at the walls of the channel flow. The secondary methods consisting of opposition control or constant-slip hydrophobic surfaces were used to complement the primary one. It was found that the combination of the the combination of these techniques did not result in the sum of the contributions of each technique taken separately. In addition to these studies and developments within the code, various techniques for analysing the results have been implemented and used which are presenting a novel aspect for the within the flow control area: probabilistic and eigenvalue methods. All these methods are now part of a full-fledge revised version of the code and can be used in parallel. An extensive guide has also been written for future users of the code for flow control problems.