Abstract
In the deposit regime in which a stationary bed of solids appears on the bottom of the pipe, the ratio of the in situ concentration q to the delivered concentration C and the slip velocity are the most important variables govering the mechanism of slurry flow. Many of the empirical and semi-theoretical studies that have produced the correlations for predicting the values of these variables were based upon data on the limited flow conditions. For this reason, serious disagreement among the correlations can be found at comparatively low velocities where the tendency of the particles to settle due to gravitational forces become sufficiently large so that, eventually, the deposit regime may occur.
The objective of this paper is to develop general correlations which contain no empirical constants determined from experimental data in pipes.After analysing the force due to particle-particle interactions in liquidsolid fluidised systems, we obtained the relationship between qand C as follows:
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in which: V=mean velocity of slurry flow;Vt=terminal settling velocity of single particle; Rep=particle Reynolds number;α, β=Swanson's shape factor of particles;n=index of Richardson-Zaki equation for hindered settling of particles.
Also, solving the above equation numerically by the method of bisection, it could be shown that the ratio q/C was plotted against the Froude number V2/[gD (δ-1)], with the ratio d/D as a parameter if the area index κ of the particles should be constant: in which: g=gravitational constant;δ=specific gravity of particles; d, D=diameter of particles and pipe respectively.Therefore, assuming q and C to be defined, slip velocity, i. e., the difference Vw-Vs in mean velocity between liquid phase and solid phase, can be determined by:(Vw-Vs)/V=(q-C)/[q (1-q)]
Finally, we concluded that the correlations derived theoretically would be applicable in the wide range of slurry flow conditions, since the universality of them was verified with data from the published literature.
