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 %. In this paper, we develop a model-based approach for designing oscillations that suppress turbulence in a channel flow. We utilize eddyviscosity-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 secondorder 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.
Bibliographical noteFunding Information:
Financial support from the National Science Foundation under CAREER Award CMMI-06-44793 and from the University of Minnesota Initiative for Renewable Energy and the Environment under Early Career Award RC-0014-11 is gratefully acknowledged. The University of Minnesota Supercomputing Institute is acknowledged for providing computing resources. The authors would also like to thank anonymous referees and the associate editor for their valuable comments.
- drag reduction
- turbulence control
- turbulence modelling