On divergence, curl, and helicity of the inertial particle velocity in a 4-way coupled channel flow

Inertial particle data from three-dimensional direct numerical simulations of dilute, four-way coupled particle-laden turbulent channel flow at Re_τ ≈ 230 are analyzed. Delaunay tessellation is applied to the particle positions considering a range of mass loading (10\%-300\%) and particle inertia (St⁺ ≈ 1-60). Using finite-time measures, we then quantify the divergence and rotation of the particle velocity and determine likewise the particle flow helicity (Oujia et al. J. Fluid Mech., 2020; Oujia et al. TSFP-12, 2022). Statistical analyses of divergence, curl, and helicity are performed, along with their dependence on the wall distance, to assess the influence of the flow anisotropy. The probability distribution functions (PDFs) of the divergence and curl show that the particle inertia affects the tails of the PDFs, which implies extreme events. Joint PDFs of the divergence and the Delaunay volume further clarifies if the divergence is most prominent in the cluster regions or in the void regions. The PDFs of the inertial particle vorticity are compared to those of the fluid vorticity and they are found to deviate from a Laplace distribution. Finally, PDFs of the particle flow helicity show that swirling motion has the tendency to be suppressed for sufficiently large particle inertia. The relationship with sweep and ejection motion of the particles will be discussed.