Effects of concentration-dependent settling velocity on non-equilibrium transport of suspended sediment

Jing, Haixiao; Chen, Guoding; Wang, Wen; Li, Guodong

doi:10.1007/s12665-018-7731-9

Cited by 17 publications

(3 citation statements)

References 26 publications

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“…Long back, it has been proved by Richarson and Zaki [18] that the presence of sediment particles in flow affects the particle settling velocity, and it must be taken into account when dealing flow with high concentration. Recently, Jing et al [19] considered this effect in their two-dimensional concentration equation, but they did not provide any analytical solution to the problem. To tackle a mathematical problem, two approaches can be adopted: (i) numerical and (ii) analytical/semi-analytical.…”

Section: Introductionmentioning

confidence: 99%

Semi-analytical solution for one-dimensional unsteady sediment transport model in open channel with concentration-dependent settling velocity

Mohan¹,

Kumbhakar²,

Ghoshal³

et al. 2020

Phys. Scr.

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This paper aims to solve the one-dimensional unsteady suspended sediment transport equation in open channels through a semi-analytical approach. The presence of a large amount of particles in flow change the settling velocity of a particle, and this phenomenon, commonly known as hindered settling effect, must be taken into account to deal with high concentrated flows. Inclusion of this mechanism makes the governing equation nonlinear, and together with this nonlinear governing equation, a generalized bottom boundary condition is taken in terms of deposition velocity and equilibrium bottom concentration. An explicit series solution is presented using the method of lines based homotopy analysis method, and the convergence of the series solution is gained through a convergence control parameter. The solution is validated by comparing it with the existing solution as well as a numerical one. Apart from that, the solution has also been validated under a steady-state condition with available experimental data. Results are interpreted both graphically and physically. It is found that the hindered settling effect is dominant in the main flow region only, for sediment free inlet for all types of turbulent diffusion coefficients. On the other hand, in the case of uniform sediment concentration at the inlet, hindered settling affects the concentration in the top portion of the channel too for linear and parabolic profiles of turbulent diffusion coefficients.

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Section: Introductionmentioning

confidence: 99%

Semi-analytical solution for one-dimensional unsteady sediment transport model in open channel with concentration-dependent settling velocity

Mohan¹,

Kumbhakar²,

Ghoshal³

et al. 2020

Phys. Scr.

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“…Mason [17] studied the erosion of scour holes caused by free-trajectory jets, and presented formulae for calculating the probable depths of erosion under free jets. Based on experimental results, Jing [18] investigated the non-equilibrium transport of suspended sediment from one equilibrium state to another, and developed a numerical model for flow with suspended sediment by considering the effect of concentrationdependent settling velocity. Khosravi [19] studied the mobility of non-uniform sediment mixtures resulting from dam break flows and how these differ from uniform-sized sediment.…”

Section: Introductionmentioning

confidence: 99%

Experimental Study on Wide-Graded Soil Transport in Unsteady Flow

Zhao

Ma²,

et al. 2023

Processes

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A special study on the interaction mechanism between flow and soil is of great significance for revealing the macro breaching mechanism of barrier dams. To study the scouring characteristics of wide-graded sediment under different flow conditions, flume scour tests were conducted regarding the grading curve of dam material and the discharge process of the Tangjiashan barrier dam. The results show that: (1) The scouring process of narrow-graded or uniform sediments is the formation and movement of the sand wave, while the scouring mode of wide-graded sediment is mainly the formation, expansion, and movement of the scouring pit. (2) Under the condition of weak unsteady flow, the surrounding and shielding effect of coarse particles on fine particles is obvious, and the erosion resistance of the material is strong. However, under the condition of strong unsteady flow, the erosion resistance is weak. (3) The erosion of wide-graded sediment is mainly caused by slope angle collapse at the initial stage, and mainly reflected by traceable erosion at the later stage. Therefore, in the initial stage of erosion, the downstream erosion intensity is high, and the bed surface can easily form a slope inclined downstream. (4) The scouring intensity under the condition of unsteady flow is greater than that under the condition of steady flow. The sediment transport formula based on the condition of steady flow cannot be used to calculate the dam break process directly.

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“…Also, there are analytical solutions of steady two-dimensional suspended sediment transport in [31]. Later Jing et al [32] modifies the research of Liu [33] incorporating the hindered settling effects. They considered the hindered settling effect and proposed a semi-analytical solution for the first time for such non-linear governing partial differential equation.…”

Section: Introductionmentioning

confidence: 99%

Time fractional advection-dispersion model to study transportation of particles with time-memory for unsteady nonequilibrium suspension in open-channel turbulent flows

Ghosh¹,

Kundu²,

Kumar³

2021

Phys. Scr.

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In this study, the effects of time-memory on the mixing and nonequilibrium transportation of particles in an unsteady turbulent flow are investigated. The memory effect of particles is captured through a time-fractional advection-dispersion equation rather than a traditional advection-dispersion equation. The time-fractional derivative is considered in Caputo sense which includes a power-law memory kernel that captures the power-law jumps of particles. The time-fractional model is solved using the Chebyshev collocation method. To make the solution procedure more robust three different kinds of Chebyshev polynomials are considered. The time-fractional derivative is approximated using the finite difference method at small time intervals and numerical solutions are obtained in terms of Chebyshev polynomials. The model solutions are compared with existing experimental data of traditional conditions and satisfactory results are obtained. Apart from this, the effects of time-memory are analyzed for bottom concentration and transient concentration distribution of particles. The results show that for uniform initial conditions, bottom concentration increases with time as the order of fractional derivative decreases. In the case of transient concentration, the value of concentration initially decreases when $T<1$ and thereafter increases throughout the flow depth. The effects of time-memory \textcolor{green}{are} also analyzed under steady flow conditions. Results show that under steady conditions, transient concentration is more sensitive for linear, parabolic, and parabolic-constant models \textcolor{green}{of} sediment diffusivity rather than the constant model.

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Effects of concentration-dependent settling velocity on non-equilibrium transport of suspended sediment

Cited by 17 publications

References 26 publications

Semi-analytical solution for one-dimensional unsteady sediment transport model in open channel with concentration-dependent settling velocity

Semi-analytical solution for one-dimensional unsteady sediment transport model in open channel with concentration-dependent settling velocity

Experimental Study on Wide-Graded Soil Transport in Unsteady Flow

Time fractional advection-dispersion model to study transportation of particles with time-memory for unsteady nonequilibrium suspension in open-channel turbulent flows

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