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

By Rashad Moarref, M. Jovanovi'c. Journal of Fluid Mechanics, 2012

134 citations recorded by the source corpus.

Abstract 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.

Subfields: Computational Mechanics, Global and Planetary Change, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/61063fd1e1e6e84f819a553abdc2a381ea89c4c4

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Citations in the corpus

Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis (2017, methodology): “…been shown to be reasonable in some flows and is frequently used for the construction of low-order models (Farrell & Ioannou, 1993, 1996, 2001), including resolvent-based models (Jovanović & Bamieh, 2001; Bagheri et al., 2009; Sipp et al., 2010; Moarref & Jovanović, 2012; Dergham et al., 2013).”
Colour of turbulence (2016, methodology): “This model was also used to study the optimal response to initial conditions and body forcing fluctuations in turbulent channel (Hwang & Cossu 2010b) and Couette flows (Hwang & Cossu 2010a), and served as the basis for model-based control design in turbulent channel flow (Moarref & Jovanović 2012).”
Conditions for validity of mean flow stability analysis (2016, unknown): “Non-modal analysis with turbulent mean flows has been introduced by Butler & Farrell (1993), Chernyshenko & Baig (2005), Del Álamo & Jimenez (2006), Cossu, Pujals & Depardon (2009), Pujals et al. (2009) and Moarref & Jovanović (2012).”