On the design of optimal compliant walls for turbulence control

TL;DR

This paper uses a theoretical framework to analyze the design of compliant walls for turbulence control, highlighting the importance of resonance effects, structure susceptibility, and anisotropy in reducing skin friction.

Contribution

It provides a systematic analysis of compliant wall designs, comparing simple and complex configurations, and offers guidelines for optimizing turbulence control based on physical and resonance considerations.

Findings

Walls are most effective near resonance conditions.

Compliant walls impact slower-moving turbulent structures more.

Two-dimensional structures are highly susceptible to amplification.

Abstract

This paper employs the theoretical framework developed by Luhar et al. (J. Fluid Mech., 768, 415-441) 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 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 by Fukagata et al. via DNS (J. Turb., 9, 1-17) 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.