Reconstructing the fluid flow by tracking of large particles

Abstract

All the methods which estimate the unperturbed uid ow velocity relying on particle suspensions address the same question: How can the uid velocity be computed measuring the particles trajectory and/or their velocities? The tracking of a few large density-mismatched particles is here used to eciently and accurately reconstruct the background uid ow. Approximating the particulate phase space and taking the limit of vanishing Stokes number St → 0, we retrieve the background ow for three test cases: a shear ow near a wall, a rigid-body vortex, and a strained vortex. The major advantages and the potentials of this approach are discussed in the end, highlighting how to overcome the classic shortcomings of experimental measurements faced for near-boundaries particle tracking.

Stokesian motion of a spherical particle near a right corner made by tangentially moving walls

“…Similar approaches have widely been used in the literature to complement the Maxey–Riley equation by dedicated particle–boundary models (Kharlamov, Chára & Vlasák 2008; Yang 2010; Agarwal, Rallabandi & Hilgenfeldt 2018; Davies et al. 2018; Romanò 2019; Romanò et al. 2019 a ; Agarwal et al.…”

Reconstructing the neutrally-buoyant particle flow near a singular corner

“…The aim is to demonstrate that a robust reconstruction of the particulate phase space for the neutrally-buoyant particle is possible, even for singular flows as the one considered in this paper (not yet demonstrated by Ref. [46]). Such a correction for density-mismatch effect can help to better understand the particle dynamics in phase space, as a major source of dissipation can be corrected for.…”

“…Starting from the method originally proposed by Romanò [46] for retrieving the velocity field in the tracer limit, this paper will extend our previous approach by demonstrating that a similar method has potential for targeting a different objective, i.e., predicting the dynamics of neutrally-buoyant finite-size particles. As in Ref.…”

“…[46], we will still rely on the trajectories of a few large density-mismatched inertial particles, but contrary to Ref. [46] we will not take the tracer limit (Stokes number tending to zero). This will allow us to correct for sedimentation and density-mismatch effects, i.e., to reconstruct the dynamics of a neutrally-buoyant particle preserving the dissipative effects due to its finite size and to the corresponding interaction with the boundaries.…”

“…As in Ref. [46], we will still rely on the trajectories of a few large density-mismatched inertial particles, but contrary to Ref. [46] we will not take the tracer limit (Stokes number tending to zero).…”