Inertial migration in dilute and semidilute suspensions of rigid particles in laminar square duct flow

Abstract

We study the inertial migration of finite-size neutrally buoyant spherical particles in dilute and semi-dilute suspensions in laminar square duct flow. We perform several direct numerical simulations using an immersed boundary method to investigate the effects of the bulk Reynolds number Re b , particle Reynolds number Re p and duct to particle size ratio h/a at different solid volume fractions φ, from very dilute conditions to 20%. We show that the bulk Reynolds number Re b is the key parameter in inertial migration of particles in dilute suspensions. At low solid volume fraction (φ = 0.4%) and low bulk Reynolds number (Re b = 144), particles accumulate at the center of the duct walls. As Re b is increased, the focusing position moves progressively towards the corners of the duct. At higher volume fractions, φ = 5, 10 and 20%, and in wider ducts with Re b = 550, particles are found to migrate away from the duct core towards the walls. In particular, for φ = 5 and 10%, particles accumulate preferentially at the corners. At the highest volume fraction considered, φ = 20%, particles sample all the volume of the duct, with a lower concentration at the duct core.For all cases, we find that particles reside longer times at the corners than at the wall centers. In a duct with lower duct to particle size ratio h/a (i.e. with larger particles), Re b = 144 and φ = 5% we find that particles preferentially accumulate around the corners. Hence, the volume fraction plays a key role in defining the final distribution of particles in semi-dilute suspensions. The presence of particles induces secondary cross-stream motions in the duct cross-section, for all φ. The intensity of these secondary flows depends strongly on particle rotation rate, on the maximum concentration of particles in focusing positions, and on the solid volume fraction. We find that the secondary flow intensity increases with the volume fraction up to φ = 5%. However, beyond φ = 5% excluded volume effects lead to a strong reduction of cross-stream velocities. Inhibiting particles from rotating also results in a substantial reduction of the secondary flow intensity, and in variations of the exact location of the focusing positions.

Suspensions of finite-size neutrally buoyant spheres in turbulent duct flow

“…Two interesting observations are deduced from figure 6: i) particle layers form close to the walls, and ii) for φ = 0.05 and 0.1, the local particle concentration Φ(y, z) is higher close to the duct corners. We have recently reported a similar result for laminar duct flow at Re b = 550 and same duct-to-particle size ratio, h/a = 18, and volume fractions, φ (Kazerooni et al 2017). At those Re b and h/a, particles undergo an inertial migration towards the walls and especially towards the corners, while the duct core is fully depleted of particles.…”

“…Already in the laminar regime, the flow in conduits is altered by the presence of solid particles. Relevant to mixing, particle-induced secondary flows are generated in ducts, otherwise absent in the unladen reference cases as shown by Amini et al (2012); Kazerooni et al (2017). Interesting results are found also in the transition regime from laminar to turbulent flow.…”

“…For more details on the method, the reader is referred to the works of Breugem & Boersma (2005) and Pourquie et al (2009). This approach has already been used in our group (Kazerooni et al 2017) to study the laminar flow of large spheres in a squared duct.…”

“…The code used in the present work has been already validated against several different cases in previous studies (Breugem 2012;Picano et al 2015;Fornari et al 2016c;Kazerooni et al 2017). To further investigate the accuracy of the code, we calculate the friction factor f = 8 Ū * /U b 2 for the reference unladen case with Re b = 5600, and compare it with the value obtained from the empirical correlation by Jones (1976)…”

Finite-sized rigid spheres in turbulent Taylor–Couette flow: effect on the overall drag

“…In addition, the position of the particles (or the particles clusters) is likely to have a large influence on the skin friction. In DNS at low Reynolds numbers, Kazerooni et al (2017) found that the particle distribution is mainly governed by the bulk Reynolds number. In order to study the effects of particles on turbulence it is convenient to use a closed setup where one can relate global and local quantities directly through rigorous mathematical relations.…”