On the design of optimal compliant walls for turbulence control

ABSTRACT

This paper employs the resolvent framework to consider the design of compliant walls for turbulent skin friction reduction. Specifically, the effects of simple spring–damper walls are contrasted with the effects of more complex walls incorporating tension, stiffness and anisotropy. In addition, varying mass ratios are tested to provide insight into differences between aerodynamic and hydrodynamic applications. Despite the differing physical responses, all the walls tested exhibit some important common features. First, the effect of the walls (positive or negative) is the greatest at conditions close to resonance, with sharp transitions in performance across the resonant frequency or phase speed. Second, compliant walls are predicted to have a more pronounced effect on slower moving structures because such structures generally have larger wall-pressure signatures. Third, two-dimensional (spanwise constant) structures are particularly susceptible to further amplification. These features are consistent with many previous experiments and simulations, suggesting that mitigating the rise of such two-dimensional structures is essential to designing performance-improving walls. For instance, it is shown that further amplification of such large-scale two-dimensional structures explains why the optimal anisotropic walls identified in previous direct numerical simulations only led to drag reduction in very small domains. The above observations are used to develop design and methodology guidelines for future research on compliant walls.

KEYWORDS:

• Wall turbulence
• flow control
• compliant surfaces

Acknowledgments

The authors gratefully acknowledge financial support from AFOSR grant FA9550-12-1-0469 (Program Manager: Doug Smith) and AFOSR/EOARD grant FA9550-14-1-0042 (Program Manager: Russ Cummings). The authors also thank Professor Koji Fukagata for generously sharing previous DNS results.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. This paper focuses on turbulent channel flows but the approach can be generalised to pipe and boundary layer flows as well.

2. As per F2008, the search algorithm had not converged but the available computational time had been exhausted.

3. Or more broadly, all types of flow control that can be represented via linear boundary conditions. [16]

Additional information

Funding

The authors gratefully acknowledge financial support from AFOSR [grant number FA9550-12-1-0469] (Program Manager: Doug Smith); AFOSR/EOARD [grant number FA9550-14-1-0042] (Program Manager: Russ Cummings).