Turbulent flow of finite-size spherical particles in channels with viscous hyper-elastic walls

Abstract

We study single-phase and particulate turbulent channel flows, bounded by two incompressible hyper-elastic walls at bulk Reynolds number 5600. Different wall elasticities are considered with and without a 10% volume fraction of finite-size neutrally-buoyant rigid spherical particles. A fully Eulerian formulation is employed to account for the fluid-structure interaction at the elastic walls interfaces together with a direct-forcing immersed boundary method (IBM) to model the coupling between the fluid and the particles. The elastic walls are assumed to be made of a neo-Hookean material. We report a significant drag increase and an enhancement of the turbulence activity with growing wall elasticity for both single-phase and particulate cases in comparison with the single phase flow over rigid walls. A drag reduction and a turbulence attenuation is obtained for the particulate cases with highly elastic walls, albeit with respect to the single-phase flow of the same wall elasticity; whereas, an opposite effect of the particles is observed on the flow of the less elastic walls. This is explained by investigating the nearwall turbulence of highly elastic walls, where the strong asymmetry in the magnitude of wall-normal velocity fluctuations (favouring the positive v ), is found to push the particles towards the channel centre. The particle layer close to the wall is shown to contribute to the turbulence production by increasing the wall-normal velocity fluctuations, while in the absence of this layer, smaller wall deformation and in turn a turbulence attenuation is observed. We further address the effect of the volume fraction at a moderate wall elasticity, by increasing the particle volume fraction up to 20%. Migration of the particles from the interface region is found to be the cause of a further turbulence attenuation, in comparison to the same volume fraction in the case of rigid walls. However, the particle induced stress compensates for the loss of the Reynolds shear stress, thus, resulting in a higher overall drag for the case with elastic walls. The effect of wall-elasticity on the drag is reported to reduce significantly with increasing volume fraction of particles.

On the fully coupled dynamics of flexible fibres dispersed in modulated turbulence

“…spherical and isotropic particles (Lucci, Ferrante & Elghobashi 2010; Gualtieri et al. 2013; Capecelatro, Desjardins & Fox 2018; Ardekani & Brandt 2019; Ardekani, Rosti & Brandt 2019; Sozza et al. 2020), anisotropic particles and fibres (Andersson, Zhao & Barri 2012; Ardekani et al.…”

“…The modulation of turbulence in non-dilute conditions has been the subject of studies regarding several classes of particulate and multiphase flows, e.g. spherical and isotropic particles (Lucci, Ferrante & Elghobashi 2010;Gualtieri et al 2013;Capecelatro, Desjardins & Fox 2018;Ardekani, Rosti & Brandt 2019;Sozza et al 2020), anisotropic particles and fibres (Andersson, Zhao & Barri 2012;Ardekani et al 2017a;Olivieri et al 2020bOlivieri et al , 2021, as well as droplets or bubbles (Dodd & Ferrante 2016;Freund & Ferrante 2019;Rosti et al 2019;Cannon et al 2021). Overall, when the concentration is large enough, this modulation effect typically causes a substantial departure from the classical phenomenology observed for a purely Newtonian fluid (e.g.…”

Modulation of turbulence by finite-size particles in statistically steady-state homogeneous shear turbulence

“…Based on the thickness of the particle-wall layer, they proposed a relation able to predict the friction Reynolds number as a function of the bulk Reynolds number (Costa et al 2016(Costa et al , 2018. Ardekani, Rosti & Brandt (2019) showed in a numerical experiment that removing the particle-wall layer results in turbulence attenuation with respect to single-phase flow, while the presence of this layer contributes to larger velocity fluctuations close to the wall for lower particle volume fractions.…”

“…2016, 2018). Ardekani, Rosti & Brandt (2019) showed in a numerical experiment that removing the particle–wall layer results in turbulence attenuation with respect to single-phase flow, while the presence of this layer contributes to larger velocity fluctuations close to the wall for lower particle volume fractions.…”

The effect of particle anisotropy on the modulation of turbulent flows

“…The resulting turbulence modulation effects have been the subject of previous studies over different classes of multiphase turbulent flows, i.e. considering isotropic (Lucci, Ferrante & Elghobashi 2010;Gualtieri et al 2013;Uhlmann & Chouippe 2017;Capecelatro, Desjardins & Fox 2018;Ardekani, Rosti & Brandt 2019;Yousefi, Ardekani & Brandt 2020) or anisotropic (Andersson, Zhao & Barri 2012;Olivieri et al 2020b,a;Wang et al 2022) solid particles, as well as droplets or bubbles (Dodd & Ferrante 2016;Freund & Ferrante 2019;Rosti et al 2019;Cannon et al 2021), typically focusing on the alteration of both the bulk flow properties as well as the scale-by-scale energy distribution. In particular, Lucci et al (2010) and Yousefi et al (2020) showed that Taylor-length-scale-sized spheres reduce turbulent kinetic energy at the large scales and enhance its energy content at the small scales.…”