Pickup rate of non-cohesive sediments in low-velocity flows

Abstract

Erosion of sediments is of crucial significance to morphologic evolution, management of water quality and aquatic ecosystems. However, the prediction of the pickup rate of non-cohesive sediments is a challenging topic because of the complex interaction between the bed and the flow. This study reports the experimental results of the pickup rate of non-cohesive sediments in uniform flows. Six groups of uniform sand with diameters in the range of 0.183 mm to 1.090 mm were tested. The pickup rate was measured near the erosion thresholds. The experimental data, along with the data collected from previous studies, are applied to evaluate existing formulae for the grain-by-grain pickup rate. Those commonly used formulae fail to reproduce measurements well at both the high and low entrainment rate conditions. Efforts are made to revise the formula of Cao (1997) to predict the grain-by-grain pickup rate at both the high and low entrainment rate conditions.

Keywords:

• Boundary condition
• erosion processes
• entrainment rate
• pickup rate
• sediment transport

Acknowledgements

The authors would like to thank Mohamed Ghidaoui, Moez Louati and two anonymous reviewers for their insightful comments and suggestions, which helped improve the quality of the manuscript.

Funding

This work was supported by the Open Research Fund of State Key Laboratory of Estuarine and Coastal Research [SKLEC-KF202003], the Open Research Fund of State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology [LP2020]; The Fundamental Research Funds for the Central Universities, Hohai University [B200202052]; the Open Research Fund of Key Laboratory of Ministry of Education for Coastal Diasater and Protection, Hohai University [201914, 201807]; the National Natural Science Foundation of China [51879096]; the key project of the National Natural Science Foundation of China [41930538]; the Major International (Regional) Joint Research Project of National Natural Science Foundation of China [51920105013]; and the National Science Fund for Distinguished Young Scholars (51425901).

Notation

$A$	=	area contributing to the entrainment of particles per unit bed area (m2)
$A_b$	=	flow area corresponding to the bed (m2)
$A_d$	=	total flow area (m2)
$A_w$	=	flow area corresponding to the wall of the duct (m2)
$c_{nb}$	=	near-bed volumetric sediment concentration (–)
$d$	=	particle diameter (m)
$D$	=	settling or deposition rate (kg m−2 s−1)
$D_h$	=	hydraulic diameter (m)
$D_{\ast }$	=	dimensionless particle diameter (–)
$E$	=	pickup rate (kg m−2 s−1)
$E_{\ast }$	=	dimensionless pickup rate (–)
$E_{\ast ,c}$	=	predicted dimensionless pickup rate (–)
$E_{\ast ,m}$	=	measured dimensionless pickup rate (–)
$f$	=	friction factor (–)
$g$	=	gravitational acceleration (m s−2)
$J_b$	=	hydraulic gradients related to the bed (–)
$J_w$	=	hydraulic gradients related to the wall (–)
$k$	=	permeability of sediment bed (m s−1)
$k_s$	=	roughness height (m)
$k_{s,b}$	=	roughness height of the sediment sample (m)
$k_{s,w}$	=	roughness height of the wall (m)
${l_x}^{+}$	=	non-dimensional longitudinal dimension of the burst (–)
${l_y}^{+}$	=	non-dimensional spanwise dimension of the burst (–)
${L_x}^{+}$	=	non-dimensional longitudinal spacing of the burst (–)
${L_y}^{+}$	=	non-dimensional spanwise spacing of the burst (–)
$n_0$	=	porosity of the bed (–)
$N$	=	number of data points (–)
$N_p$	=	number of sediment particles per unit area of the bed (–)
${\mathsf{R}}_{\mathsf{e}}$	=	Reynold number (–)
$t$	=	time (s)
$T_B$	=	burst period (s)
${T_B}^{\text{ + }}$	=	turbulent burst period normalized with inner variables (–)
$u_{\ast }$	=	shear velocity (m s−1)
$U$	=	average velocity of duct flow (m s−1)
$v_e$	=	bed erosion velocity (m s−1)
$z$	=	piston displacement (m)
$\mathrm{\Delta }$	=	$\left({\rho }_s/\rho \right)-1$ (–)
$\text{θ}$	=	Shields parameter (–)
${\text{θ}}_{\mathrm{c}\mathrm{r}}$	=	critical Shields parameter (–)
${\lambda }_B$	=	average area of turbulent bursts per unit bed area (–)
$\upsilon$	=	kinematic viscosity of water (m2 s)
$\rho$	=	density of water (kg m−3)
${\rho }_d$	=	dry bulk density of sediment (kg m−3)
${\rho }_s$	=	density of sediment particles (kg m−3)
${\tau }_b$	=	bed shear stress (Pa)
${\tau }_{cr}$	=	critical bed shear stress (Pa)
${\tau }_w$	=	wall shear stress (Pa)
${\phi }_s$	=	solid volume fraction (–)
${\chi }_b$	=	wetted perimeter related to the bed (m)
${\chi }_w$	=	wetted perimeter related to the duct wall (m)