Acceleration statistics of solid particles in turbulent channel flow

Abstract

Direct numerical simulations (DNS) are used here to study inertial particle acceleration statistics in the near-wall region of a turbulent channel flow. The study is motivated by observations in homogeneous isotropic turbulence (HIT) suggesting that when particle inertia increases, particle acceleration variance decreases due to both particle preferential accumulation and the filtering effect of inertia. In accordance with these studies, the present DNS shows that for increasing inertia, solid particle acceleration probability density functions (PDFs), scaled by the acceleration root-mean-square (RMS), depart from that of the fluid. The tails of these PDFs become narrower. However, in turbulent channel flow, as the Stokes number increases up to 5, the streamwise acceleration RMS in the near-wall region increases, while further increase of the Stokes number is characterized by the streamwise acceleration RMS decrease. In parallel, contrary to calculations in homogeneous isotropic turbulence, the conditional acceleration statistics of the fluid seen by the solid particle show that while the vertical and transverse acceleration RMS components remain close to the unconditional fluid acceleration, the longitudinal RMS component is remarkably higher in the near wall region. This feature is more pronounced as the Stokes number is increased. Additionally, the conditional acceleration PDFs overlap almost perfectly with the unconditional fluid PDFs, normalized by the acceleration RMS. The enhanced longitudinal acceleration variance of the fluid seen by the particles may be due to the spanwise alternation of high-and-low speed streaks. Depending on inertia, particles may respond to those fluid solicitations (experiencing an increase of the longitudinal acceleration RMS) or ignore the wall turbulent structures (presenting in that case a more homogeneous concentration).