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Efficient numerical computation and experimental study of temporally long equilibrium scour development around abutment

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Abstract

For the abutment bed scour to reach its equilibrium state, a long flow time is needed. Hence, the employment of usual strategy of simulating such scouring event using the 3D numerical model is very time consuming and less practical. In order to develop an applicable model to consider temporally long abutment scouring process, this study modifies the common approach of 2D shallow water equations (SWEs) model to account for the sediment transport and turbulence, and provides a realistic approach to simulate the long scouring process to reach the full scour equilibrium. Due to the high demand of the 2D SWEs numerical scheme performance to simulate the abutment bed scouring, a recently proposed surface gradient upwind method (SGUM) was also used to improve the simulation of the numerical source terms. The abutment scour experiments of this study were conducted using the facility of Hydraulics Laboratory at Nanyang Technological University, Singapore to compare with the presented 2D SGUM–SWEs model. Fifteen experiments were conducted with their scouring flow durations vary from 46 to 546 h. The comparison shows that the 2D SGUM–SWEs model gives good representation to the experimental results with the practical advantage.

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Abbreviations

c :

Wave celerity

C :

Flux averaged volumetric sediment concentration

\(C_{\mathrm{E}}\) :

Equilibrium sediment concentration

\(C_{\mathrm{FL}}\) :

Courant number

\(d_d\) :

Sediment median diameter

\(d_\mathrm{f}\) :

Flow depth in floodplain

\(d_\mathrm{m}\) :

Flow depth in main channel

\(d_\mathrm{s}\) :

Scour depth

\(d_\mathrm{sc}\) :

Sediment deposition rate

\(d_\mathrm{se}\) :

Equilibrium scouring depth

\(e_\mathrm{sc}\) :

Sediment erosion rate

g :

Gravitational acceleration

h :

Water depth

i :

Space step

k :

Flow energy

L :

Abutment length

\(l_\mathrm{A}\) :

Dimensionless adaptation length scale

m :

Last time space

n :

Manning’s friction coefficient

N :

Time step

Q :

Resultant velocity

\(Q_\mathrm{fm}\) :

Discharge from magnetic flow metre

\(Q_\mathrm{vel}\) :

Discharge obtained from integration of ADV point-measured velocities

s :

wave speed

\(S_\mathrm{f}\) :

Friction/energy slope of flow

\(S_\mathrm{o}\) :

Bed slope

\(s_\mathrm{s}\) :

Sediment specific density

t :

Time domain

\(t_\mathrm{actual}\) :

Actual scouring time run for an experiment

\(t_\mathrm{e}\) :

Equilibrium scouring time

u :

Depth averaged flow velocity in streamwise direction

\(U_\mathrm{f}\) :

Flow velocity at flood plain

\(U_{\mathrm{m}}\) :

Flow velocity at main channel

\(u_\mathrm{s}\) :

Shear velocity

v :

Depth averaged flow velocity in lateral direction

\(w_\mathrm{V}\) :

Sediment fall velocity

x :

Spatial-longitudinal domain

y :

Spatial-transverse domain

\(z_\mathrm{b}\) :

Mobile bed elevation

\(\nabla \) :

Gradient operator

\(\varepsilon \) :

Flow energy dissipation

\(\lambda \) :

Sediment bed porosity

\(\nu _\mathrm{t}\) :

Depth averaged turbulent viscosity

\(\varOmega \) :

Computational cell area

\(\phi \) :

Flow geopotential

\(\Pi \) :

Slope limiter

\(\rho _\mathrm{s}\) :

Density of sediment

\(\rho _\mathrm{w}\) :

Density of water

\(\sigma _\mathrm{g}\) :

Geometric standard deviation of sediment size

L:

Left region

R:

Right region

*:

Star region

ADV:

Acoustic Doppler velocimeter

FV:

Finite volume

HLLC:

Harten Lax van Leer-contact

MUSCL:

Monotonic upwind scheme for conservative laws

NS:

Navier Stokes

SCC:

Sediment transport continuity-concentration

SGUM:

Surface gradient upwind method

SWEs:

Shallow water equations

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Acknowledgments

The authors would like to thank Dr. Joko Nugroho for providing his Ph.D. experimental data (under the supervision of the second author Dr. Siow Yong Lim).

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Authors and Affiliations

  1. University of Southampton Malaysia Campus, No. 3, Persiaran Canselor 1, Kota Ilmu, EduCity @ Iskandar, 79200 , Nusajaya, Johor, Malaysia

    Jaan Hui Pu

  2. School of Civil and Environmental Engineering, Nanyang Technological University, Singapore, 639798, Singapore

    Siow Yong Lim

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  1. Jaan Hui Pu
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Correspondence to Jaan Hui Pu.

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Pu, J.H., Lim, S.Y. Efficient numerical computation and experimental study of temporally long equilibrium scour development around abutment. Environ Fluid Mech 14, 69–86 (2014). https://doi.org/10.1007/s10652-013-9286-3

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