Sedimentation Of Heavy Particles In Turbulence

Abstract

Behavior of particles in buoyancy driven turbulent flow at Ra ≈ 10º is investigated experimentally. The volume fraction of the particles is low enough for the inter particle influence to be neglected, the mass loading of particle is low enough that the turbulence as not modified, and the particles Reynolds numbers (Re p ) st are small enough that the wake effect can be neglected. The buoyancy driven turbulent flow is created by maintaining an unstable density difference, using NaCl dissolved in water, across the ends of a long vertical tube. There is no mean flow and the turbulence is axially homogeneous. A method for uniform introduction of the particles was devised. Glass particles (S.G=2.4-2.5) of different diameter ranges (50-400 µm) are introduced into this flow. The sizes of particles considered are less than the Kolmogrov length scale corresponding to the turbulence level. The turbulence intensity level was varied in order to match its characteristic time and velocity scale to those of the particles. The ratio of the timescales, the Stokes number; is in the range (0.01-0.55); Stokes number is defined as a ratio of the viscous relaxation time of the particle and a turbulent time scale, and represents the effect of the particle inertia in the interaction with the turbulence, Stk =τp/τk. Another important non-dimensional parameter is the velocity ratio, the k ratio of the particle settling velocity in still fluid to a characteristic turbulence velocity. The flow field is illuminated by a continuous Argon-ion laser and a PHOTRON high- speed digital camera is used for imaging. The raw images are processed to evaluate particle centers followed by their velocity measurements. The objective of the experiment is to check for the effect of the turbulent flow on the sedimentation rate of the heavy particles. This sedimentation rate is compared with the settling velocity obtained in still water. It is expected that within a certain range of Stokes numbers and velocity ratios the sedimentation rate would be substantially changed, and the spatial concentration distribution of the particles may become patchy implying that turbulence may actually inhibit rather than enhance mixing of particles. By varying the turbulence level and particle mean diameter we achieved a set of values for the particle parameters, namely St k. ≈ 0.01, 0.1, 0.14, 0.55 and velocity ratios[[Wp ] St]]≈ 0.2, .0, 0.5, 2.25 respectively. The w rms velocity ratio [[Wp ] St /wf defined as a ratio between the article terminal velocity [Wp ] St and a suitable flow velocity scale; it is a measure of the residence time of the particle in an eddy, in eddy turnover time units. In this study we have considered the turbulence r.m.s velocity for the flow velocity scale.The particle Reynolds number (Re p)st corresponding to these 4 cases were 0.2, 31.5, 4.0, 31.5. Some preliminary quantitative measurements were made only for the 150-200 µm particles and turbulence level w rms ≈ 4.0 cm/s,corresponding to Stk ≈0.14 [[Wp ] St] = 0.5. A quantitative picture was obtained for the other cases. Streak pictures for these four different groups of particles revealed that Stk and the velocity ratio [[Wp ] St ] were important in influencing the particle- w rms

turbulence interaction not the Stk alone. The r.m.s velocity fluctuations of particles in both the lateral (utp) and vertical direction (wtp) measured were found to be different from those obtained in still-water case.(For equations, pl see the pdf file)