Fundamentals on Equilibrium Concentration Curves for Sedimentation and Diffusion of Particles in Fluids (original) (raw)
2015
Solutions for the equilibrium sediment concentration profiles, defined as the situation in which the settling movement of sediment particles is compensated by turbulent diffusion in channel flows, are presented and compared with the classical Rouse profile. In the Rouse solution, the settling velocity is considered independent of the sediment concentration, a very restrictive situation which leads to unrealistic results for the sediment concentration near the bottom of the flow. In this paper, the use of the mass conservation principle permits to obtain a more realistic solution for the equilibrium profiles. It is shown that it is possible to extend the obtained profiles until the bottom of the flow (which simplifies further calculations). Further, considering the result of the momentum equation (potential flow) around a sphere, a nonlinear approximation between the settling velocity and the volumetric concentration of sediment is obtained. It is discussed that nonlinear effects mus...
Environmental Earth Sciences, 2016
To achieve a complete knowledge about the effect of particle concentration on sediment and turbulent diffusion coefficients in open-channel turbulent flow is a long-standing problem for the community of researchers. The effect of particle concentration is investigated on the sediment and turbulent diffusion coefficients through the inverse of turbulent Schmidt number or b which is defined by the ratio of sediment diffusion coefficient to turbulent diffusion coefficient. It is observed that with increasing particle concentration, the sediment diffusion coefficient decreases more in comparison with the turbulent diffusion coefficient for both dilute and non-dilute sediment-laden flows. The physical characteristics of b observed are expressed mathematically in terms of normalized settling velocity, reference level and reference concentration. The applicability of the mathematical formulae is confirmed by the agreement analysis between experimental data and particle concentration profile computed from the Rouse equations modified through the newly proposed expression of b. Apart from the better agreement between dilute particle concentration data and the developed Rouse equation, the striking observation is that the modified Rouse equation shows reasonable computational accuracy for non-dilute particle concentration data also. Minimum error is obtained from the present model when it is compared with the models proposed by the previous researchers.
Velocity and concentration profiles in uniform sediment-laden flow
Applied Mathematical Modelling, 2006
This paper presents a theoretical model for computing the velocity and sediment concentration profiles in a uniform sediment-laden flow carrying all fine, medium and coarse sediments. The proposed model essentially includes the effect of sediment concentration in total turbulent shear stress and eddy diffusivity in addition to the modified mixing length derived by Umeyama and Gerritsen [J. Hydr. Engng., ASCE, 118 (2) (1992) 229-245] applied to HuntÕs diffusion equation. Numerical solution of coupled differential equations for velocity and sediment concentration is carried out. The theoretical results show quite good agreement with the experimental data.
Arabian Journal of Geosciences, 2020
This paper presents a theoretical model for predicting the vertical distribution of suspended sediment concentrations in openchannel flows. The model developed uses a new sediment diffusivity coefficient obtained by the application of the Itakura and Kishi correction method to the Kerssens sediment diffusivity profile. The new coefficient is calculated using composite operators applied to the Rouse sediment diffusivity profile. The diffusivity profile proposed increases as a parabolic profile from zero at the bottom to a maximum value in the lower part of the flow, and then decreases slowly towards the water surface without reaching zero. The maximal value is calculated at a level between 20 and 30% of the total water depth as explained previously by Coleman. Based on this diffusivity profile, a theoretical formulation for computing sediment concentration is derived analytically, using the well-known convection-diffusion equation. We compare results from the proposed model with experimental measurements and existing theoretical models, obtained by previous researchers, in order to evaluate the applicability of the present model to predict particle concentration profiles in open-channel flows. The computed values of sediment concentrations are in good agreement with the experimental data reported in the literature.
Sediment transport during unsteady settling in an inclined channel
Journal of Fluid Mechanics, 1987
Settling of a dilute, monodisperse suspension between two inclined, narrowly spaced parallel plates is considered. Effects of sediment motion are accounted for. Lubrication theory and a simplified model for the particle motion lead to a system of two coupled nonlinear hyperbolic equations for the evolution of the two interfaces between clear fluid, suspension and sediment. Two problems are solved: batch settling and the filling of a channel that initially contains clear fluid. In the batch-settling case, the sediment has no major qualitative effect on the motion. In the filling problem, however, effects of sediment are important.
On dispersion of settling particles from an elevated source in an open-channel flow
Journal of Computational and Applied Mathematics, 2006
Longitudinal dispersion of suspended particles with settling velocity in a turbulent shear flow over a roughbed surface is investigated numerically when the settling particles are released from an elevated continuous linesource. A combined scheme of central and four-point upwind differences is used to solve the steady turbulent convection-diffusion equation and the alternating direction implicit (ADI) method is adopted for the unsteady equation. It is shown how the mixing of settling particles is influenced by the 'log-wake law' velocity and the corresponding eddy diffusivity when the initial distribution of concentration is regarded as a line-source. The concentration profiles for the steady-state conditions agree well with the existing experimental data and some other numerical results when the settling velocity is zero. The behaviours of iso-concentration lines in the vertical plane for different releasing heights are studied in terms of the relative importance of convection, eddy diffusion and settling velocity.
The drag coefficient and settling velocity of natural sediment particles
Computational Particle Mechanics, 2019
This article reports a study in which drag coefficient is defined more comprehensively. The coefficient is defined as a function of particle nominal diameter, gravitational acceleration, the ambient fluid kinematic viscosity, and the particle shape. This new definition is different from the conventional definitions proposed in the literature based on direct equations as a function of particle Reynolds number. The conventional definitions appear to be a simplification of drag coefficient and thus decreasing the accuracy of the estimations. Instead, the proposed equation in this article indicates that on average the drag coefficient estimation can be improved at least 3.77% compared to the proposed drag coefficient widely used in the literature. The improved drag coefficient was used to derive a more accurate settling velocity equation in which the effect of particle shape is directly incorporated in the settling velocity equation. Both equations were validated using well known datasets and accurate experiments from the literature as well as new experiments conducted for this purpose in the current research. The experiments cover a wide range of particle shape and a variety of specific gravity. The outcomes of the current study contribute to the use of settling velocity in river hydraulic applications proposing a simpler but more accurate procedure.
Mixing at a sediment concentration interface in turbulent open channel flow
Environmental Fluid Mechanics, 2017
In this work we address the role of turbulence on mixing of clear layer of fluid with sediment-laden layer of fluid at a sediment concentration interface. This process can be conceived as the entrainment of sediment-free fluid into the sediment-laden layer, or alternatively, as the transport of sediment into the top sediment-free flow. This process is governed by four parameters-Reynolds number of the flow Re s , non-dimensional settling velocity of the sediment (proxy for sediment size)Ṽ, Richardson number Ri s and Schmidt number Sc. For this work we have performed direct numerical simulations for fixed Reynolds and Schmidt numbers while varying the values of Richardson number and particle settling velocity. In the simple model considered here, the flow's momentum and turbulence pre-exists over the entire layer of fluid, while the sediment is initially confined to a layer close to the bed. Mixing of sediment-free fluid with the sediment-laden layer is associated primarily with upward transport of sediment and buoyancy. There is no simultaneous upward transport of fluid momentum and turbulence into the sediment-free fluid layer, which is already in motion and turbulent. The analysis performed shows that
Investigation and modelling of sedimentation of mixed particles
Powder technology, 1997
A model was developed to predict the relative velocity necessary for the calculation of the settling velocity in fluid-particle sedimentation systems, both binary and polydisperse suspensions. The model obtained was tested against the experimental data obtained from a countercurrent flow system and was found to give an excellent fit. The Reynolds number ranges between 4 and 1300. The model predictions were compared with those of other published models. The model predictions have shown an improvement and do not have the limitations present in the other models.