JI Sheng-cheng, OUAHSINE Abdellatif

Université de Technologie de Compiègne. Laboratoire Roberval, UMR CNRS 7337, Centre de recherché Royallieu BP 20529, 60206 Compiègne cedex, France, E-mail: jishengcheng@gmail.com

SMAOUI Hassan

Université de Technologie de Compiègne. Laboratoire Roberval, UMR CNRS 7337, Centre de recherché Royallieu BP 20529, 60206 Compiègne cedex, France

CETMEF, 2, Bd Gambetta, Compiègne, France

SERGENT Philippe

CETMEF, 2, Bd Gambetta, Compiègne, France

JING Guo-qing

School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China

Impacts of ship movement on the sediment transport in shipping channel*

JI Sheng-cheng, OUAHSINE Abdellatif

Université de Technologie de Compiègne. Laboratoire Roberval, UMR CNRS 7337, Centre de recherché Royallieu BP 20529, 60206 Compiègne cedex, France, E-mail: jishengcheng@gmail.com

SMAOUI Hassan

Université de Technologie de Compiègne. Laboratoire Roberval, UMR CNRS 7337, Centre de recherché Royallieu BP 20529, 60206 Compiègne cedex, France

CETMEF, 2, Bd Gambetta, Compiègne, France

SERGENT Philippe

CETMEF, 2, Bd Gambetta, Compiègne, France

JING Guo-qing

School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China

(Received June 21, 2013, Revised April 2, 2014)

The duration of ship-generated waves (wake waves) and accelerated currents can generate significant influences on the sediment transport. A 3-D numerical model is presented to estimate these effects. The hydrodynamic model is the 3-D Reynolds averaged Navier-Stokes (RANS) equations including the standard -kε model while the 3-D convection-diffusion model is for the resuspended sediment transport. This hydro-sedimentary model is firstly validated with the trench experimental results, and then applied to the open channel with a moving ship. The computed results demonstrate that the resuspension generation mainly depends on ship speeds, barge number, and the relative distance away from ship. The acceleration effects of ship on the sediment transport are analyzed as well.

resuspension of sediment, shipping channel, ship acceleration, CFD, volume of fluid (VOF) mehtod

Introduction

Vessels such as towboats and barges are able of generating wake waves, causing drawdown and return currents along riverbanks in narrow inland waterways, and contributing to sediment resuspension and riverbank erosions[1,2]. Thus, the research subjects have been focusing on various parameters, such as vessel velocity, vessel type, water depth, turbulence intensity and secondary eddies, interaction between vegetation and current[3]etc.. Houser[4]found that the vessel-generated wakes (including drawdown and surge waves) have much more effects on sediment resuspension than wind waves and suspended sediment concentration (SSC) increases with increment of turbulent kinetic energy (TKE) of the supercritical pilot-boat wakes. In Ref.[5], they argued that the maximum wave energy decreases with increasing length for the fast ferry. However, their researches focused on the experimental studies in situ or in laboratory and did not include the ship movement influence on the sediment transport. Hence, we intend to carry out 3-D numerical simulation in shipping channel with moving ship in this paper, in particular, considering the ship acceleration influences on sediment transport.

A 1-D numerical model of the sediment resuspension induced by the moving vessel has been developed by Hassan[5]and validated with the experimental results performed by Pham et al.[6]. It could be predicted that two peaks of SSC are generated by two ships moving in series, although the 2-D or 1-D model is unable to predict the sediment transport in transverse section of the channel. A 3-D numerical model has been developed by Ji[7,8]to estimate the vessel effects on the sediment transport. The sediment transport modes were analyzed in Ref.[7] while the propellereffects were summarized in Ref.[8]. In this paper, a 3-D convection-diffusion model for the resuspended sediment is implemented to examine the ship movement effects on sediment transport.

The present paper is structured as follows: the first part deals with the mathematical model. The second part is devoted to the computational procedures. Part three gives the grid sensibility analysis and the validation of the hydro-sedimentary model. Part four is devoted to the numerical results and discussions concerning the relationships between the SSC and the shear stress on the bottom, the SSC and Fr, the shear stress and Fr. The ship acceleration effects are also analyzed at the end of this section. The last part gives conclusion drawn from the above numerical investigations.

1. Numerical model

1.1Hydrodynamic model

The governing equations for mass and momentum conservations are given as

1.2Three-dimensional resuspended sediment transport

The 3-D equations of suspended sediment for each granulometric class are given by

where c is the mean value of SSC, c＇ is the fluctuation of SSC,iu are the velocity components corresponding toix,iu＇ is the fluctuation of fluid velocity, and sw is particle falling velocity[5]. sw reads:

where s=ρs/ρ, ρsis the sediment density, ρ is the fluid density, d50is the median diameter of the sediment, ν is the fluid kinematic viscosity, and g is the acceleration due to gravity.

The velocity components are computed with Eqs.(1)-(2), while the sediment diffusion flux due to correlation between the velocity fluctuations of turbulence and the fluctuations of the SSC is modeled as

εsi, the sediment mixing coefficient, is assumed to be isotropic and proportional to the kinematic viscosity of turbulence νt[10]. Then,

where σc=0.5 is the turbulent Schmidt number. With reference to Ref.[11], σccould vary from 1/8 to 1 for moderately diffusive scalars. Finally σcis defined as 0.5 by calibration with the experimental data from the trench model.

1.3Boundary conditions

The distribution of the SSC in the suspended load layer is controlled by the convection-diffusion Eq.(3), while the bedload transport can be governed by the formulae proposed by Van Rijn. To solve Eq.(3), a near-bed equilibrium concentrationbc is specified by the following equation

β is the calibration coefficient, δ is the saltation thickness, T is the non-dimensional excess shear stress on bottom

where Re*is the grain Reynolds number, θcris the Shields entrainment function, and ? is the Yalin’s (1979) approach. They are defined as follows:

1.4Wall roughness effects in turbulent wall-bounded flows

The wall roughness effects are included via the modified wall function given by

u+and y+are respectively the non-dimensional velocity and non-dimensional distance from the wall to the first centroid node of the cell, κ=0.4 is the von Kármán constant, E=9.793 is an empirical constant, δBdepends on the type and size of the roughness. Thus, for the sand-grain and similar types of uniform roughness elements, δBmay be correlated with nondimensional roughness height, Ks+

1.5Computational procedures

The set of Eq.(1)-Eq.(3) is solved by the finite vo-lume (FV) method with arbitrary hexahedral meshes. Since the values of the variables are stored in thecenters of each cell, a procedure of interpolation, based on a second-order scheme, is then used to assign values to the faces of the control volumes (CV). The variable gradients on each CV face are computed using a multi-dimensional Taylor series expansion with least-squares cell-based approaches. The SIMPLE algorithm was used for the pressure-velocity coupling. For the added scalar quantity c, the first order implicit scheme is used for time discretization and the QUICK scheme for convection terms.

2. Validation of hydro-sedimentary model by the experimental results

A set of experiments were conducted in a channel (30 m long, 0.5 m wide and 0.7 m deep) at the Delft Hydraulics Laboratory (Van Rijn 1980) to study the morphological evolution of the different profiles of the open trenches (see Fig.1). The average velocity of flow is 0.51 m/s and water depth is 0.39 m. The sandy bed consists of fine particles (d50=160μ m).

Fig.1 Trench sketch and locations of profiles

Fig.2 Graphical representations of Grid 1, Grid 2 and Grid 3

Mesh sensibility analysis is performed for different grid types (Grid 1, Grid 2, Grid 3 in Fig.2), which contain 18 737, 36 993 and 72 285 3-D hexahedral elements respectively. The grid spacing of coarser meshes (Δxc,Δyc,Δzc) to grid spacing of finer meshes (Δxf,Δyf,Δzf) is given as

Fig.3 The velocity profiles at the locations 1-4

Fig.4 The SSC profiles at the locations 1-5

We define the ratio of the solution changes over N points in the interesting region

It is found from Fig.3 that velocities agree well with the experimental results while some overestimation of resuspension concentration is observed in the middle of the trench (see Fig.4). It means that the amount of sediment deposition calculated by the model is smaller than that measured in experiment. The slope effect maybe contributes to the overestimation of resuspension concentration. In addition, the concentration caat reference distance δ depends on calibration parameter β since it is adjusted by the experimental results.

Fig.5 Schematic representation of the model and the boundaries

Fig.6 Graphical representation of chipping channel with one ship

3. Simulation of resuspension distribution in restricted channel

Table 1 Geometric parameters of the ship model and waterway

Based on the validated hydro-sedimentary model, the influences on the sediment transport induced by the moving ships are examined. The erosion and deposition are assumed to occur on the horizontal bottom rather than the inclined banks. The schematic representation of the model and boundaries for the hydrosedimentary coupling is shown in Fig.5. The grid system is presented in Fig.6. A total number of 2.1×106hexahedra are adopted for the shipping channel. The associated geometrical dimensions are given in Table 1. In addition, we have performed the grid dependence analysis in the previous researches[15]. Herein, we adopted the optimized grid directly.

Table 2 Values of+y in different computation cases

In Table 2, the values of y+in the vicinity of ship surface are given and found to increase with the increment of the Froude number, which are limited by the maximum value y+=300[15].

3.1The correlations between SSC and the turbulence fluctuation velocities

The instantaneous turbulent fluctuating velocitiesare calculated from TKE which are the solutions of the standard k-ε model. The averaged＇ on each cross section is calculated by

where A is the area of each transections. The resuspension flux qxSSC is calculated by

where S is the transection areas vector, u is the fluid velocity vector, ucis the resuspension flux vector through the transections per unit area, and nxis unit vector perpendicular to transections S.

Fig.7 Average of fluctuating velocities of turbulence u＇ and qxSSC along the x direction

Fig.8 Instantaneous fluctuating velocities of turbulence u＇ in the x direction with one barge and Vb=-0.90 m/s

3.2The spatial distribution of concentration

Figure 8 gives the instantaneous turbulence fluctuating velocities u＇ at lines L1, L2, L3on the symmetry for Vb=-0.90 m/s with one barge. u＇ rea-ches the maximum value u＇=0.08 m/s for the line located at z/ h=-0.975 since the large fluctuating velocities could suspend more sediment. In Fig.9, two peaks of SSC occur. The first peak of SSC is induced by the bow of the ship while the second one is generated by the stern of the ship.

Fig.9 Instantaneous SSC on lines in x direction with one barge and Vb=-0.90 m/s

Fig.10(a) Maximum of SSC vs Fr

Fig.10(b) Maximum of instantaneous shear stressmaxτ vs Fr

3.3Relationships between SSC and Froude number

As was known, the wave height and return current velocities are dependent on the vessel speeds (Vb), the water depth (h) and the blocking coefficient. Herein ship speed Vbis used as the only variable involved in estimating the influence on SSC. The depressions of the water plane on both sides of the ship are caused by the accelerated water velocities and then give rise to the increase of SSC.

Therefore, the maximum SSC and the maximum shear stress increase with the increment of the ship speed (see Fig.10). The maximum SSC increases with the ship forward speeds to maximum when Fr=0.48 (see Fig.10(a)), while the maximum instantaneous shear stresses increase with the ship speeds to maximum when Fr=0.49 (see Fig.10(b)).

Herein, a sediment net discharge (SND) number is defined in order to estimate the ship’s wake effects on the sediment transport. This SND number indicates the ability of resuspending sediment by the accelerated current for each duration of the ships. We therefore integrate the SSC in a whole duration of ship at a given point near the bottom. The SND is defined as

The SND number actually demonstrates the surface area under SSC curve in Fig.9 and Fig.14. In our case, the SND number goes up with increasing the Froude number (see Fig.11).

Fig.11 SND number vs Froude number

3.4The influences of the ship acceleration on the sediment transport

Four cases were examined to investigate the influences of the acceleration of the ship on the sediment transport. Four cases are given in Fig.12. In case 1, an acceleration of a1=-0.173m/s2is given at the beginning of the movement with the velocity Vbincreasing from 0 m/s to -0.8 m/s. In the other three cases, the accelerations a2, a3, a4are equal to -0.50 m/s2, -2.00 m/s2, and -26.7 m/s2respectively. In Case 4, the ship starts with Vb=-0.80 m/s without acceleration. In fact, the acceleration a4is appro-ximate to infinity theoretically. However, the ship arrives at Vb=-0.80 m/s in only one time step Δt= 0.03 s due to the numerical implementation. It means that the acceleration a4=Vb/Δt=-26.7 m/s2. Figure 13 shows that the wave elevations at a fixed point y/ Lp=0.1 away from the sailing line. Two waves appear before the bow in all of the cases except for Case 1.

Fig.12 Accelerations imposed at the start of the ship

Fig.14 The influence of ship acceleration on the sediment transported

Figure 14 indicates the SSC associated to the four cases. For the smaller acceleration1a, the flow near the bottom could be more accelerated due to the viscosity of fluid with reference to the other three cases.

4. Conclusions

A 3-D numerical model based on hydro-sedimentary coupling is presented to search relationships between the sediment transport and ship length, the ship motion state. The grid sensitivity analysis is also performed for the trench model case. Results highlight the relationship between the maximum SSC, the maximum shear stress and the ship’s speed. The computation results show that sediment spreading area mainly depends on the distance away from the moving ship, on the ship’s speeds. Results also demonstrate that the maximum SSC increase with the ship’s Froude number as

Both the variables of the maximum shear stress and the maximum SSC are proportional to the ship speeds. The following relation is given based on the computed results

To estimate the effect of ship’s wakes on the sediment transport, we define the sediment net discharge (SND) number and propose the following formula

Finally, the acceleration effects are analyzed. The ship at the start with smaller acceleration could produce more sediment.

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10.1016/S1001-6058(14)60079-2

* Biography: JI Sheng-cheng (1982-), Male, Ph. D.