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1
Lagrangian Two-Phase Flow Modeling of Scour in Front of Vertical Breakwater
Abbas Yeganeh-Bakhtiary
1,2,*
,
Hamid Houshangi
3
and Soroush Abolfathi
4
1
School of Civil Engineering, Iran University of Science & Technology (IUST), Narmak,
Tehran 16844, Iran, yeganeh@iust.ac.ir
2
Department of Civil and Architectural Engineering, University of Kurdistan Hewler (UKH),
Erbil 44001, Iraq, abbas.yeganeh@ukh.edu.krd
3
Bonyan Institute of Higher Education, Shahinshahr, Isfahan, Iran, houshangi@alumni.iust.ac.ir
4
School of Engineering, University of Warwick, Coventry, CV4 7AL, United Kingdom,
Soroush.Abolfathi@warwick.ac.uk
2
Abstract
A Lagrangian particle-based two-phase flow model is developed to simulate the scouring process
induced by standing wave in front of the trunk section of a vertical breakwater. Given the two-
dimensional nature of the scouring problem at the trunk of vertical wall, the fluid phase is
simulated with two-dimensional Navier–Stokes equations based on Weakly Compressible
Smoothed Particle Hydrodynamics (WCSPH) formulation in conjunction with Sub-Particle Scale
(SPS) turbulence closure model. The sediment phase is simulated using the Discrete Element
Method (DEM). The effects of interparticle and particle-wall collisions are computed by
activating a spring-dashpot system. The WCSPH fluid-phase and DEM sediment-phase are
coupled through a weakly one-way coupling procedure using wave orbital velocity. The
numerical model is successfully validated against experimental data. The maximum scour depth
predicted by WCSPH-DEM model is closely approximate the experimental data. This study, for
the first time, demonstrated an extra recirculating sediment transport mechanism in front of the
vertical breakwater, similar to steady streaming recirculating cells in the fluid phase, which has a
direct impact on the formation of scour hole and maximum scour depth at the breakwater trunk.
The scenario modelling conducted in this study show that by increasing the steady streaming
velocity, the deposition rate and the depth of scour hole were increased.
Keywords: Lagrangian Two-phase flow model, particle-based methods, WCSPH, DEM,
scouring, vertical breakwater.
3
1 Introduction
The significance of scouring in structural stability and functionality of coastal structures,
specifically vertical breakwaters, have led into many experimental [de Best & Bijker, 1971; Xie,
1981; Irie & Nadaoka, 1984; Hughes & Flower, 1991; Sumer & Fredsøe, 2002] and numerical
[Chen, 2007; Gislason et al., 2009 a, b; Yeganeh-Bakhtiary et al., 2010 & 2017; Tahersima et al.,
2011; Hajivalie et al., 2012; Tofani et al., 2014; Dong et al., 2018] investigations to understand
the underlying hydrodynamic deriving mechanisms and scouring pattern. When the incident
wave terrain reaches the vertical breakwater in shore-normal angle of approach, the scour in
front of the trunk section of vertical wall-type breakwater is a two-dimensional process [Sumer
& Fredsøe, 2002]. The interactions between incident waves attacking the structure and reflected
waves from vertical breakwater produce a series of standing waves in front of breakwater’s trunk
section [Lillycrop & Hughes, 1993; Oumeraci, 1994 a & b; Sumer & Fredsøe, 2002]. The key
underlying hydrodynamic mechanism of scouring is the steady streaming field, including bottom
and top recirculating fluid cells at trunk section of vertical breakwater. The sediment particles
behavior is profoundly affected by recirculating fluid cells; in which the fine and coarse
sediments are picked up and transported by the top and bottom recirculating cells, respectively
(Figure 1).
The majority of existing numerical studies, on scouring in front of vertical breakwater, are
based on single-phase process-based models discretized in Eulerian formation. Simulating
scouring processes with Eulerian methods is not a straightforward task, due to the challenges
associated with trace of the fluid-sediment interphase momentum exchange, during the
simulation. Furthermore, the process-based models are not capable of robust calculation of
4
distinctive aspect of sediment transport including, complicated fluid-sediment and particle-wall
interactions, interparticle collisions and the momentum exchanges between the sediment and
fluid.
Lagrangian particle-based flow models are robust numerical techniques, suitable for fluid–
sediment interphase simulations, and capable of precise interphase computation during each time
step [e.g., Potapov et al., 2001; Shao & Lo 2003; Gotoh et al., 2009; Fernandez et al., 2011;
Huang & Nydal, 2012; Zanganeh et al., 2012; Wang et al., 2016; Gotoh & Khayyer, 2018;
Harada et al., 2018 & 2019]. The Lagrangian modelling approaches compute particle movement
for each phase based on their specific physical characteristics and therefore do not require
interphase [Gotoh & Sakai, 1999; Gotoh et al., 2005; Kayyer & Gotoh, 2008; Ataie-Ashtiani &
Mansour-Rezaei, 2009; Zhang et al., 2009; Zheng et al., 2017; Abolfathi et al., 2018; He et al.,
2018; Khayyer et al., 2018; Wang et al., 2019].
This study develops a new Lagrange–Lagrange two-phase flow model to simulate scouring
process, and describes the pertinent hydrodynamics and sediment transport processes in front of
a vertical breakwater under the influence of standing wave conditions. The fluid phase is
simulated by the solution of two-dimensional Navier–Stokes (N-S) equations based on WCSPH
method in conjunction with the SPS turbulence closure model. The sediment phase is simulated
using DEM model to determine the effects of interparticle and particle-wall collisions with
activating a spring-dashpot system. The WCSPH and DEM models were coupled using the wave
orbital velocity through a weakly one-way coupling procedure. The sediment transport process,
scour – deposition pattern, and the momentum exchanges between fluid-sediment interphase are
