Two-way interaction between solid particles and homogeneous air turbulence: particle settling rate and turbulence modification measurements

Abstract

This paper describes experiments on small solid particle settling behaviour in stationary homogeneous isotropic air turbulence. We present here a new methodology using a recently developed cruciform apparatus: a large horizontal cylindrical vessel equipped with a pair of counter-rotating fans and perforated plates at each end is used to generate stationary near-isotropic turbulence in the core region between the two perforated plates and a long vertical vessel is used to supply heavy descending particles from its top. This novel experimental design, without the unwanted influences from the injection of particles, the mean flow, and the decay of turbulence, allows direct imaging and velocity measurements of the two-way interaction between heavy particles and homogeneous isotropic turbulence. Consequently, the spatiotemporal responses of both fluid turbulence and particle settling can be determined by high-speed digital particle image velocimetry and accelerometry, together with the wavelet transform analysis for the first time. Hence, experimental information on and thereby understanding of the particle settling rate, preferential accumulation, and turbulence modification due to the presence of the particles is obtained.

We found that the particle settling velocity (${V}_{s})$ is much greater than the terminal velocity (${V}_{t})$ in still fluid for which the value of (${V}_{s}\,{-}\, {V}_{t})$ reaches a maximum of 0.13$u^\prime $ when the Stokes number $\hbox{\it St}\,{ =}\,\tau_{p}/\tau_{k}\,{\approx}\,$1 and ${V}_{t}/u^\prime \,{\approx}\,$0.5 at $\hbox{\it Re}_{\lambda }\,{=}\,$120 and $\hbox{\it Re}_{p} \,{<}\,$1, in good agreement with previous numerical results, where $\tau _{p}$ is the particle's relaxation time, $\tau _{k}$ is the Kolmogorov time scale, $u^\prime$ is the energy-weighted r.m.s. turbulent intensity, and $\hbox{\it Re}_{\lambda}$ and $\hbox{\it Re}_{p}$ are the Reynolds numbers based on the Taylor microscale ($\lambda$) and the mean diameter of particles, respectively. Non-uniform particle concentration fields are observed and most significant when $\hbox{\it St}\,{\approx}\,$1.0, at which the particle clusters accumulate preferentially around the outer perimeter of small intense banana-shaped vortical structures. These clusters can turn and stretch banana-shaped vortical structures toward the gravitational direction and thus significantly increase the mean settling rate especially when $\hbox{\it St}\,{ =}\,1$. From spatiotemporal analysis of the flatness factor, it is found that the characteristic length and time scales of these preferential particle clusters are related to the spacing between the adjacent intense vorticity structures of the order $\lambda$ and the time passage of these clustering structures of the order $\tau _{k}$, respectively. By comparing the average frequency spectra between laden (heavy particle) and unladen (neutral particle) turbulent flows over the measurement field at a fixed $\hbox{\it Re}_{\lambda }\,{=}\,$120, turbulence augmentation is found for most frequencies in the gravitational direction, especially for $\hbox{\it St}\,{\ge}\,$1. In the transverse direction, augmentation occurs only at higher frequencies beyond the Taylor microscale for all values of $\hbox{\it St}$ studied varying from 0.36 to 1.9. The increase in the size of energy spectra (turbulence augmentation) due to the presence of heavy particles is greatest at $\tau_{k}^{ - 1 }$ when $\hbox{\it St}\,{\approx}\,$1.0. Furthermore, the slip velocities between fluid turbulence and heavy particles can stimulate the laden turbulent flow to become more intermittent in the dissipation range. Finally, a simple energy balance model for turbulence modification is given to explain these results and areas for further study identified.