Anisotropic particles in two-dimensional convective turbulence

Abstract

The orientational dynamics of inertialess anisotropic particles transported by two-dimensional convective turbulent flows display a coexistence of regular and chaotic features. We numerically demonstrate that very elongated particles (rods) align preferentially with the direction of the fluid flow, i.e., horizontally close to the isothermal walls and dominantly vertically in the bulk. This behaviour is due to the the presence of a persistent large scale circulation flow structure, which induces strong shear at wall boundaries and in up/downwelling regions. The near-wall horizontal alignment of rods persists at increasing the Rayleigh number, while the vertical orientation in the bulk is progressively weakened by the corresponding increase of turbulence intensity. Furthermore, we show that very elongated particles are nearly orthogonal to the orientation of the temperature gradient, an alignment independent of the system dimensionality and which becomes exact only in the limit of vanishing Prandtl numbers. Tumbling rates are extremely vigorous adjacent to the walls, where particles roughly perform Jeffery orbits. This implies that the root-mean-square near-wall tumbling rates for spheres are much stronger than for rods, up to O(10) times at Ra 10 9 . In the turbulent bulk the situation reverses and rods tumble slightly faster than isotropic particles, in agreement with earlier observations in two-dimensional turbulence.

Rotation of anisotropic particles in Rayleigh–Bénard turbulence

“…In figure 4( b ) we also show that disk-like particles get strongly aligned with the temperature gradient, , while rod-like particles stay weakly but preferentially orthogonal to it. This feature occurs equally well in the bulk and in near-wall and it is related to a similarity between the orientation equation for the particle and the evolution equation for the gradient of a scalar field advected by the fluid, as first proposed in Calzavarini et al (2020). Indeed, (2.5) can be rewritten in terms of the evolution of an auxiliary non-unit vector, , (Szeri 1993): The limit of a thin disk, , in (3.1 a , b ) leads to an equation that apart from the diffusive term is formally identical to the one of the gradient of a scalar field, , following the advection diffusion equation Similarly the opposite limit of a rod, , as first pointed out by Pumir & Wilkinson (2011), shares an analogous similarity with the vorticity () equation of motion Note that while the former equivalence becomes exact in the limit of , the latter one occurs in the opposite limit .…”

“…In figure 4(b) we also show that disk-like particles get strongly aligned with the temperature gradient, ∇T, while rod-like particles stay weakly but preferentially orthogonal to it. This feature occurs equally well in the bulk and in near-wall and it is related to a similarity between the orientation equation for the particle and the evolution equation for the gradient of a scalar field advected by the fluid, as first proposed in Calzavarini et al (2020). Indeed, (2.5) can be rewritten in terms of the evolution of an auxiliary non-unit vector, q(t), (Szeri 1993):…”

“…The code has been used for the simulation of convection in a closed cavity (Jiang, Calzavarini & Sun 2019), convection with particles (Calzavarini etal. 2020) and HIT flows with inertial particles (Mathai et al 2016 a ; Calzavarini et al 2018).…”

Transport and deposition of dilute microparticles in turbulent thermal convection

“…Here, 'small' means the diameter of the particle is smaller than the Kolmogorov length scale of the turbulence; however, the diameter of the particle should still be much larger than the molecular mean free path such that the effect of Brownian motion can be neglected. In addition, the particles are assumed to be isotropic such that we only consider the motion of the particle and neglect the rotation of the particle 40,41 . Specifically, the particles' motions are described by Newton's second law as…”

Lagrangian dynamics and heat transfer in porous-media convection

“…Transport and mixing processes in porous-media flows have attracted much attention over the years, owing to their importance in a wide range of natural and industrial settings, such as the contaminant transport in the subsurface, the kinetics of chemical reactions, and the transport in biological systems (Seymour et al 2004;Manke et al 2007;Cushman & Tartakovsky 2016;Gu et al 2019;Wu & Liang 2019). Understanding the dynamics of fluid particles in complex flows is also important from the theoretical perspective, since the features of the fluid flow advecting the particles can be inferred from the particle dynamics (Falkovich, Gawedzki & Vergassola 2001;Biferale et al 2004;Toschi & Bodenschatz 2009;Calzavarini, Jiang & Sun 2020;Mathai, Lohse & Sun 2020).…”