Velocity and spatial distribution of inertial particles in a turbulent channel flow

Abstract

We present experimental observations of the velocity and spatial distribution of inertial particles dispersed in the turbulent downward flow through a vertical channel at friction Reynolds numbers Re τ = 235 and 335. The working fluid is air laden with size-selected glass micro-spheres, having Stokes numbers St = O(10) and O(100) when based on the Kolmogorov and viscous time scales, respectively. Cases at solid volume fractions φ v = 3×10 −6 and 5×10 −5 are considered. In the more dilute regime, the particle concentration profile shows near-wall and centerline maxima compatible with a turbophoretic drift down the gradient of turbulence intensity; the particles travel at similar speed as the unladen flow except in the near-wall region; and their velocity fluctuations generally follow the unladen flow level over the channel core, exceeding it in the near-wall region. The denser regime presents substantial differences in all measured statistics: the near-wall concentration peak is much more pronounced, while the centerline maximum is absent; the mean particle velocity decreases over the logarithmic and buffer layers; and particle velocity fluctuations and deposition velocities are enhanced. An analysis of the spatial distributions of particle positions and velocities reveals different behaviors in the core and near-wall regions. In the channel core, dense clusters form which are somewhat elongated, tend to be preferentially aligned with the vertical/streamwise direction, and travel faster than the less concentrated particles. In the near-wall region, the particles arrange in highly elongated streaks associated to negative streamwise velocity fluctuations, several channel height in length and spaced by O(100) wall units, supporting the view that these are coupled to fluid low-speed streaks typical of wall turbulence. The particle velocity fields contain a significant component of random uncorrelated motion, more prominent for higher St and in the near-wall region.

Inertial particle velocity and distribution in vertical turbulent channel flow: A numerical and experimental comparison

“…This study is based on comparing two different numerical models (Richter and Sullivan [42] and Capecelatro and Desjardins [6]) to the experiments of Fong et al [14]. Here we describe the two DNS-based models.…”

“…We now turn our attention towards a more detailed validation, which is based on the recent experiments of [14]. The flow configuration of interest is pressure-driven, downwards-oriented channel flow (see [14]). In the simulations, periodic boundary conditions are applied to both phases in the streamwise (x) and spanwise (z) directions.…”

“…In the simulations, periodic boundary conditions are applied to both phases in the streamwise (x) and spanwise (z) directions. In [14] two flow Reynolds numbers are used, and we focus on the Re bulk = 6020 case, where Re bulk = 2hU bulk /ν is based on the bulk velocity U bulk and channel height 2h. This approximately corresponds to Re τ = 227 based on the friction velocity and h. For the experimental density ratio ρ p /ρ f = 2083 and diameter d p = 4.7 × 10 −5 m, this corresponds to a Stokes number of St + = 58.6 based on viscous units and St η = 6.7 based on the Kolmogorov scale at the centerline.…”

“…Furthermore, [4] studied the effect of mass loading and wall roughness for high inertia particles (St + = 2630), which was further numerically investigated by Capecelatro and Desjardins [7] and Vreman [49]. Recently, [14] studied in detail the particle spatial distribution both close to the wall and in the centerline of a vertical channel, along with series of particle statistics at relatively low Reynolds numbers and multiple mass fractions. With moderate Stokes number (St + = 64−130), they found a significant difference (particle distribution and particle fluctuation velocity) between mass loading Φ m = 6 × 10 −3 and Φ m = 0.1.…”

“…Under these circumstances, preferential concentration and turbophoresis are at play, particle/particle and particle/wall collision might take place, and particles may modify fluid momentum. In this context, we leverage the recent experimental data of Fong et al [14] and perform a statistical comparison between DNS simulations from independent numerical codes (considering both two-and four-way coupling), particularly focusing on particle statistics and clustering behaviour. We aim at investigating (i) particle/particle and particle/wall collisions; (ii) the difference between the numerical predictions of a traditional point-force method with a more advanced volume-filtering method; and (iii) the discrepancies between numerical simulations and experimental results in a Reynolds number, Stokes number, and mass fraction regime which can be achieved using DNS.…”