Model-based design of transverse wall oscillations for turbulent drag reduction

• Published in: Journal of fluid mechanics 2012-09, Vol.707, p.205-240
• Main Authors: Moarref, Rashad, Jovanović, Mihailo R.
• Format: Article
• Language: English
• Subjects: Boundary layer; Channel flow; Computational fluid dynamics; Computer simulation; Exact sciences and technology; Flow control; Flows in ducts, channels, nozzles, and conduits; Fluid dynamics; Fluid flow; Fluid mechanics; Fundamental areas of phenomenology (including applications); Mathematical models; Oscillations; Physics; Reynolds number; Simulation; Turbulence; Turbulence control; Turbulence simulation and modeling; Turbulent flow; Turbulent flows, convection, and heat transfer; Viscosity; Walls
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2012.272

Over the last two decades, both experiments and simulations have demonstrated that transverse wall oscillations with properly selected amplitude and frequency can reduce turbulent drag by as much as $40\hspace{0.167em} \% $ . In this paper, we develop a model-based approach for designing oscillations that suppress turbulence in a channel flow. We utilize eddy-viscosity-enhanced linearization of the turbulent flow with control in conjunction with turbulence modelling to determine skin-friction drag in a simulation-free manner. The Boussinesq eddy viscosity hypothesis is used to quantify the effect of fluctuations on the mean velocity in flow subject to control. In contrast to the traditional approach that relies on numerical simulations, we determine the turbulent viscosity from the second-order statistics of the linearized model driven by white-in-time stochastic forcing. The spatial power spectrum of the forcing is selected to ensure that the linearized model for uncontrolled flow reproduces the turbulent energy spectrum. The resulting correction to the turbulent mean velocity induced by small-amplitude wall movements is then used to identify the optimal frequency of drag-reducing oscillations. In addition, the control net efficiency and the turbulent flow structures that we obtain agree well with the results of numerical simulations and experiments. This demonstrates the predictive power of our model-based approach to controlling turbulent flows and is expected to pave the way for successful flow control at higher Reynolds numbers than currently possible.