Abstract
The drift velocity, defined as the velocity of individual phase relative to the water–sediment mixture, is a key variable in two-phase mixture model. In this paper, a relation for the drift velocity in sediment-laden jets, expressed as a power series of the nozzle Stokes number, was derived by using the perturbation approach. It shows that except the gravity and turbulent diffusion, effects of particle inertia, inter-phase interaction, and other forces contained in the first-order particle inertial corrections also play significant roles in sediment-laden jet flows. Based on the relation for the drift velocity, the velocity and concentration distribution were obtained from the similarity solutions for sediment-laden jets. The calculated concentration and velocity profiles agree well with the experimental observations in literature. Furthermore, analysis on the sediment diffusion coefficient shows that the fluid turbulence is not the only driving force for the sediment diffusion in sediment-laden jets; the effect of particle turbulence on the behavior of sediment-laden jets is also significant with the increasing of particle inertia.
Highlights
Turbulent jet, as a common phenomenon found in fluid engineering and a representative topic in fluid mechanics, has attracted considerable attention and received extensive investigation in the past several decades [1, 12, 18, 25, 34]
6.2 Effect of particle inertia on the sediment diffusion Based on the above analysis, it is found that the effect of particle inertia on the concentration distribution is significant; here we further investigate the effect of particle inertia on the sediment diffusion coefficient, a key parameter for sediment diffusion
Comparing Case 1 and Case 2 with the run of B1 and C1, it is found that with the increasing of the nozzle Stokes number, the effect of fluid turbulence decreases, whereas the effect of particle turbulence gradually increases, the percentage of which can reach about 40%. This implies that the fluid turbulence is not the only driving force for sediment diffusion in sediment-laden jets; the effect of particle turbulence as well plays a significant role with increasing particle inertia; (3) it is found that the contribution of the particle turbulence gradually decreases with the increasing value of |r∕ z|, which implies that the farther the sediment particle is away from the centerline, the smaller the effect of particle inertia is
Summary
As a common phenomenon found in fluid engineering and a representative topic in fluid mechanics, has attracted considerable attention and received extensive investigation in the past several decades [1, 12, 18, 25, 34]. Jiang et al [18] argued that this assumption was still approximately valid to extend to the whole jet field This implies that the effects of particle turbulent stress and inter-phase interaction were not considered in his study. Similar problem occurs to sediment-laden jet flows It shows that, with the increasing of the particle size and solid concentration, particle–particle and inter-phase interaction, play significant roles in the flow fields of sediment-laden jet. Considering the similarities of the velocity and concentration profiles in sediment-laden round jets, theoretical expressions for the velocity and concentration distribution were obtained, which can account for the effects on sediment-laden jets due to inter-phase interactions and particle inertia. We hope this study can deepen the understanding of underlying mechanism of sediment-laden jets, and become the basic foundation of practical applications including dredging and deepening of canals, desalting of reservoirs, and sewage purification, etc
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