Simulations of turbulence over compliant walls

TL;DR

This study uses direct numerical simulations to explore how compliant walls influence turbulence, focusing on Rayleigh wave interactions, vorticity dynamics, and flow statistics in a channel with elastic surfaces.

Contribution

It introduces a coupled Eulerian-Eulerian model to analyze turbulence over viscoelastic walls and reveals how Rayleigh waves affect flow structures and turbulence characteristics.

Findings

Rayleigh wave speed affects vorticity sheet detachment

Surface deformation correlates with pressure fluctuations

Enhanced turbulence intensity without momentum gain

Abstract

Direct numerical simulations of turbulent flow in a channel with one rigid and one viscoelastic wall are performed. An Eulerian-Eulerian model is adopted with a level-set approach to identify the fluid-compliant material interface. Focus is placed on the propagation of Rayleigh waves in the compliant material, whose speed depends on the shear modulus of elasticity and whose dominant wavelength depends on the thickness of the viscoelastic layer. These parameters are selected to ensure coupling between the compliant surface and turbulence. When the phase speed of Rayleigh waves is commensurate with the advection velocity of near-wall pressure fluctuations, sheets of vorticity are lifted up and detached near the critical layer and lead to a local pressure minimum. These events are caused by the inflectional velocity profile near the troughs, and are controlled by the net vorticity flux at the elastic surface. This phenomenon is central to understanding the statistical characteristics of the flow, including the surface deformation-pressure correlation and enhanced stochastic turbulent shear stresses. The pressure work onto the fluid is positive at the surface, which increases the turbulent intensity and wall-normal mixing, without any streamwise momentum gain. Finally, we discuss the influence of three-dimensionality of the surface topography on the generation of streamwise vorticity, secondary motions, and lateral turbulent transport.