Vertical distribution of dilute suspensions in turbulent pipe flow

Abstract

Closed‐form expressions are presented for predicting vertical concentration distribution of the dispersed phase in the turbulent core of pipe and channel flow. Experimental data obtained with spherical particles, of mean diameter d50 comparable to the Kolmogorov microscale, are in good agreement with model predictions. The average value of dimensionless lateral particle diffusivity, ζ = ε/Ru*, determined from these data is approximately 0.25, that is, fairly close to previously reported measurements with much coarser particles.

Measurement of particle concentration in horizontal, multiphase pipe flow using acoustic methods: Limiting concentration and the effect of attenuation

“…It is not thought that differences in the flow and particle properties are able to explain to the discrepancy. Although the Reynolds number was lower in this study than in the Karabelas (1977) study (Re 25 000 vs. Re = 32 700; see Table 5), which would be expected to produce a more heterogeneous suspension, the Archimedes number was lower, so that the particles would be expected to be more easily suspended at a given flow rate. …”

“…Legend: d and d50 are particle diameter and 50 th percentile of size distribution; is volume fraction occupied by particles; Re is Reynolds number. Karabelas (1977) derived a model for vertical particle concentration in pipes and channels and found excellent agreement with his own experimental results (plastic spheres in kerosene, oil, and mixtures thereof) and those of Durand (1952) (sand in water). The "two-layer" model of Gillies et al (1991), which was tested against experiments, incorporates a layer of suspended "fines", i.e.…”

“…Lower half of flow shown. Karabelas (1977), who sampled the concentration physically with a pump, are also included in the plot. Although the number of data from Karabelas are limited (three), it is clear that the inversion method described here under-predicts the particle concentration in the region -0.3 < y'/D < 0 (two points) but gives a good prediction in the lowest region (one point).…”

“…Therefore, the results at Re 25 000 and 50 000 can broadly be categorised as bed-forming and non-bed-forming, respectively. As noted earlier, there is a surprising scarcity of comparable concentration-profile data at low concentrations in the literature, and many of the data that are available are either at too high a concentration (Ekambara et al, 2009;Gillies et al, 2004;Karabelas, 1977;Kaushal and Tomita, 2002b), or were gathered in the presence of a thick bed (Matoušek, 2009;Pugh and Wilson, 1999). The reader is also referred to the studies listed in Table 1.…”

“…Such flows occupy the transition between dilute and concentrated flows, at which fluid-particle and inter-particle interactions -both collisional and hydrodynamicbegin to significantly influence the flow characteristics. Despite the industrial relevance of such flows, there is a scarcity of available data at low concentrations, although some exist at higher concentrations (Ekambara et al, 2009;Gillies et al, 2004;Karabelas, 1977;Kaushal and Tomita, 2002b) and in flows with a stationary bed component (Matoušek, 2009;Pugh and Wilson, 1999).…”