Investigation of Flow, Erosion, and Sedimentation Pattern Around Varied Groynes Under Different Hydraulic and Geometric Conditions: a Numerical Study

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Article Investigation of Flow, Erosion, and Sedimentation Pattern around Varied Groynes under Different Hydraulic and Geometric Conditions: A Numerical Study

Liang Choufu 1, Saeed Abbasi 2, Hanif Pourshahbaz 2,* , Poorya Taghvaei 3 and Samkele Tfwala 4

1 College of Transportation and Civil Engineering, Fujian Agriculture and Forestry University, No. 63, Xiyuangong Road, Shangjie, Minhou County, Fuzhou 350002, China; [email protected] 2 Department of Civil Engineering, University of Zanjan, University Blvd., Zanjan 45371-38791, Iran; [email protected] 3 Department of Civil Engineering, Semnan University, Mowlawi Blvd., Semnan 35196-45399, Iran; [email protected] 4 Department of Geography, Environmental Science and Planning, University of Swaziland, Kwaluseni M201, Swaziland; [email protected] * Correspondence: [email protected]; Tel.: +98-9181262301

Received: 16 November 2018; Accepted: 26 January 2019; Published: 30 January 2019

Abstract: Groynes are popular hydraulic structures often used to control the erosion of banks by altering flow and sediment transport. In this paper, the effects of altering groyne orientation and spatial setup (from large to small and vice versa) on flow patterns, bed erosion, and sedimentation are numerically investigated. Studied groynes were parallel to each other, non-submerged, and impermeable. Numerical simulations were conducted in FLOW-3D. A nested mesh configuration combined with Van-Rijn formula on sediment transport yielded more accurate results when comparing numerical results to experiments. Groynes arranged from large to small at an angle of 45◦ decreased the scour depth by up to 55%, and an arrangement from small to large at an angle of 135◦ reduced the scour depth by up to 72%. Additionally, it was observed that simulations with an orientation closer to 90 degrees needed more equilibrium time when compared to other simulations.

Keywords: groynes with non-equal lengths; numerical simulation; erosion; sedimentation; ﬂow pattern

1. Introduction Scouring around hydraulic structures (such as piers, abutments, levee, groynes, etc.) has been one of the most significant problems in their design. Predicting and reducing scour has posed several challenges to engineers in the last decades. In this study, the emphasis is on groynes. These are structures which may be of different shape and length, submerged or non-submerged, deflecting flow current with the purpose of protecting river banks [1]. Several studies have been undertaken on groynes and their influence. For example, Vaghefi, et al. [2] investigated the effect of the shape of groynes on flow pattern. Zaid, et al. [3] looked into groyne materials by studying the effects of stone and wooden groynes in a restored river reach. Uijttewaal [4] tested four types of groynes found among the largest rivers in Europe to determine efficient alternative designs, while considering the physical, economical, and ecological aspects [4]. Other researchers, such as Garde, et al. [5], Melville [6], Saneie [7], Zhang and Nakagawa [8], Ghodsian and Vaghefi [9], Al-Khateeb et al. [10],

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Radan and Vaghefi [11], and Gualtieri [12] have investigated erosion and sedimentation patterns, scour hole depth, and riverbed stress variation around groynes under various conditions. Through simulation experiments, Uijttewaal et al. [13] studied the exchange processes between a river and its groyne fields. To increase their efficiency, groynes are applied in groups instead. Their inter-distance, length, and height affect performance, which influences factors such as shear stress and subsequently alters the channel morphology. Karami et al. [14], Acharya and Duan [15], Koken and Gogus [16], McCoy et al. [17], and Yossef and Vriend [18] are among researchers to study flow characteristics and scour hole in a group of groynes. Limitations of physical models and advancements in computational power has increased the adoption of numerical solutions in solving complex flow dynamics and related phenomena. Ning et al. [19] numerically investigated the effects of time on turbulent flows to simulate the scour depth around a single groyne. Abdulmajid et al. [20] studied hydraulic conditions and velocity distribution around L shaped groynes at a river arc utilizing a numerical model. Vaghefi et al. [21] probed local scouring around T shaped groynes in a 90◦ bend of a channel. Giglou et al. [22] investigated the impacts of various groyne group orientations, lengths, and distances on flow, erosion, and sedimentation patterns. In the present study, the impacts of varying groyne length and orientation angle on scouring depth in groups of parallel groynes (each group having 3 groynes) of non-equal lengths are investigated. An advanced numerical simulation software, FLOW-3D, is used to simulate the problem, and numerical simulations are validated with laboratory experiments.

2. Governing Equations Fluid motion equations include conservation of mass and momentum equations (Equations (2)–(4)), which FLOW-3D solves to calculate ﬂow hydraulics. Besides these, FLOW-3D applies the volume of ﬂuid (VOF) equation to ensure that proper boundary conditions are applied at the free surface (Equation (5)).

∂ρ ∂ ∂ ∂ V + (ρuA ) + R (ρvA ) + (ρwA ) = R (1) F ∂t ∂x x ∂y y ∂z z SOR

2 ∂u 1 ∂u ∂u ∂u Ayv 1 ∂ρ + uAx + vAyR + wAz − ξ = − + Gx + fx (2) ∂t VF ∂x ∂y ∂z xVF ρ ∂x ∂v 1 ∂v ∂v ∂v Ayuv R ∂ρ + uAx + vAyR + wAz − ξ = − + Gy + fy (3) ∂t VF ∂x ∂y ∂z xVF ρ ∂y ∂w 1 ∂w ∂w ∂w 1 ∂ρ + uAx + vAyR + wAz = − + Gz + fz (4) ∂t VF ∂x ∂y ∂z ρ ∂z ∂F V + ∇.(AUF) = 0 (5) F ∂t where VF = open volume ratio to flow, ρ = fluid density, (u, v, w) = velocity components in (x, y, z), RSOR = source function, (Ax,Ay,Az) = fractional areas, (Gx,Gy,Gz) = gravitational force, (fx, fy, fz) = body force per unit mass in (x, y, z) directions, respectively. The final part of Equations (2) to (4) show mass injection in zero velocity. In Equation (5), A = average flow area, U = average velocity in (x, y, z) direction, and F is volume flow function. When the cell is filled with fluid, the value of F is 1, and when it is empty, F is 0. In FLOW 3D, two methods are utilized for simulations; Volume of Fluid (VOF) and Fractional Area Volume Obstacle Representation (FAVOR) methods [23]. As earlier stated, VOF is used to show the performance of fluid in a free surface and FAVOR is utilized to simulate the surfaces and rigid bodies, such as complex geometric boundaries. To analyze sediment transport, Water 2019, 11, 235 3 of 18 suspended load and bed load are evaluated separately. Suspended load is achieved via the calculation of transient Advection-diffusion equation (ADE) (Equation (6)).

∂c ∂c ∂c ∂ ∂c + Ui + Ws = Γ (6) ∂t ∂xi ∂z ∂xi ∂xi

In which c is concentration of the suspended load, U is Reynolds-averaged water velocity, Ws is fall velocity of the sediment, x is general space dimension, z is the vertical direction, and Γ is diffusion coefﬁcient (which is the ratio of turbulent viscosity to turbulent Schmidt number). Based on Gualtieri et al. [24], there are no universally accepted values of the Schmidt number. In near bed cells, the concentration of sediment and bed load are achieved by utilizing van Rijn [25] equations (Equations (7) and (8), respectively):

1.5 d0.3( τ−τc ) τc cbed = 0.015 ∗ (7) ρs−ρw 0.1 g( 2 ) ρwϑ

In which d is sediment particle diameter, τ is bed shear stress, τc is critical shear stress for the motivation of sediment particles based on Shields diagram, ρs and ρw are the sediment particle and water densities, respectively, ϑ is kinematic viscosity of water, and g is gravitational acceleration. Bed load is evaluated using van Rijn equation:

τ−τ 1.5 q ( c ) b = ∗ τc q 0.053 0.1 (8) 1.5 ρs−ρw 0.3 ρs−ρw d g d ( 2 ) ρw ρwϑ

In which qb is the bed load. It should be noted that a correct prediction of sediment transport improves the accuracy of a scour predictive model. For example, Dodaro et al. [26] and Dodaro et al. [27] modiﬁed an available sediment transport equation to improve scour depth prediction.

3. Numerical Simulation and Validation

3.1. Laboratory Experiment Karami, Basser, Ardeshir, and Hosseini [14] constructed a rectangular flume of 14 m length, 1 m width and 1 m depth with poly glass, stabilized with a metal frame, and placed three non-submerged and impermeable groynes of 0.25 m length transverse to flow. They placed the first groyne at 6.16 m from the flume entrance and selected distances twice the length of the groynes. These values were selected based on the recommendations of Zhang [28] and Gisonni et al. [29]. Flow depth was maintained at 0.15 m. The flume was filled with 0.35 m thick uniform sediments having a median size (d50) of 0.91 mm, specific gravity, ss, of 2.65, and geometric standard deviation, σg, of 1.38. At the beginning of each experiment, the laboratory flume was first gradually filled with water to saturate the bed material. Then the sluice gate located at the end of the flume for controlling water level was raised to achieve the desired discharge (Q). Velocity profile and bed profile changes around the groynes were measured using an Acoustic Doppler Velocimetry (ADV) and a Laser Bed Profiler (LBP), respectively. LBP had an accuracy of ±1 mm in width and ±0.1 mm in depth. As the flow pattern has a significant effect on sediment transport, 50 points of velocity measurements were taken at z = 2 cm above the bed for flow characteristics. Details and results of some experiments utilized for validation are showed in 3 Table1, whereby Q is flow discharge (m /s), Y is flow depth (m), U is flow velocity (m/s), U/Ucr is a proportion of flow velocity to critical velocity of Shields, Fr is Froude number, ds1, ds2, and ds3 are maximum scour depth beneath the first, second, and third groynes in meters, respectively, and V represents the eroded sediment volume (m3). Water 2019, 11, 235 4 of 18

Table 1. Speciﬁcations and results of Karami, Basser, Ardeshir, and Hosseini [14] simulation.

3 3 Test Number. Q (m /s) Y (m) U (m/s) U/Ucr Fr ds1 (m) ds2 (m) ds3 (m) V (m ) E1 0.035 0.150 0.233 0.650 0.190 0.156 0.000 0.026 0.0165

3.2. Numerical Setup In this study, the flow field was computed by solving the Reynolds-averaged Navier-Stokes equations using the k − ε turbulent closure model. To initialize the model, water depth was fixed at 0.5 m. At the inlet, constant discharge was set to 0.035 m3/s, while a continuative boundary was applied at the outlet. A continuative boundary condition consists of zero normal derivatives at the boundary for all quantities. The zero-derivative condition is intended to represent a smooth continuation of the flow through a boundary [23]. Wall boundary conditions were applied on the sides, Water 2018, 10, x FOR PEER REVIEW 5 of 20 and on the remaining sides (bottom and top) a symmetry boundary was assigned (Figure1).

Figure 1. (A) Sketch of laboratory experiment and (B) Utilized Boundary conditions of the Figure 1. (A) Sketch of laboratory experiment and (B) Utilized Boundary conditions of the numerical numerical simulation. simulation. Based on preliminary investigations, the length of the channel was considered to be 5 m and the Based on preliminary investigations, the length of the channel was considered to be 5 m and the distance between 3 m to 8 m was simulated numerically. From 3 m to 6.16 m, where the ﬁrst groyne distance between 3 m to 8 m was simulated numerically. From 3 m to 6.16 m, where the first groyne was placed, the fully developed current would be formed, and from 7.18 m to 8 m, the vortices of the was placed, the fully developed current would be formed, and from 7.18 m to 8 m, the vortices of the last groyne would be fully created, making it possible to depict the profile of erosion and sedimentation in the last groyne as well. After initial tests, the nested mesh was found to be the most appropriate simulation for this case. A comparison on scour on the first, second, and third groynes, and the maximum scour depth with experimental data, was made. Two mesh boxes of different size were utilized; closer to the groynes, a finer mesh box was utilized, while farther from the groynes, a coarse mesh box was used (Figure 2). In total, there were 192,000 coarse cells (2.5 cm in all directions) and 1,315,550 fine cells (1.2 cm in all directions). All simulated groynes were within the finer mesh block to fully resolve flow dynamics and enhance accuracy. Sensitivity analysis was carried out on the mesh size (Table 2). In this Table, ds1, ds2, and ds3 are maximum scour depth at the first, second, and third groynes, respectively. A computer with a Core i7-5820K GHz processor and 32GB RAM was used for the simulations.

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Table 2. Mesh size sensitivity analysis. last groyne wouldCoarser be fullyFiner created, makingTotal it possible to depict the profile of erosion and sedimentation Test Numerical Laboratory Computational Mesh Size Mesh Number of inNumber the last groyne as well. After initial tests, theSimulation nested mesh was foundExperi toment be the mostTime appropriate (hour) simulation for(m) this case.Size A (m) comparison Cells on scour on the first, second, and third groynes, and the ds1 ds2 ds3 ds1 ds2 ds3 maximum scour depth with experimental data,(m) was(m) made. (m) Two(m) mesh (m) boxes (m) of different size were utilized;1 closer0.030 to the groynes,0.020 a finer395880 mesh box0.091 was 0.016 utilized, 0.020 while 0.156 farther 0.000 from 0.026 the groynes,71 a coarse mesh2 box was0.025 used (Figure0.0122 ). In total,1507550 there 0.1 were33 192,0000.005 0.023 coarse 0.156 cells 0.000 (2.5 cm0.026 in all directions)146 and 1,315,550 fine cells (1.2 cm in all directions). All simulated groynes were within the finer mesh block to fullySensitivity resolve flow analysis dynamics indicates and better enhance results accuracy. with mesh refinement at a computational cost (Table 2).

FigureFigure 2. 2. SketchSketch of of mesh mesh setup setup..

3.3. DataSensitivity Validation analysis was carried out on the mesh size (Table2). In this Table, d s1, ds2, and ds3 are maximum scour depth at the ﬁrst, second, and third groynes, respectively. A computer with a Core i7-5820KFlow GHz velocity processor was measured and 32GB at RAM 50 points was used in a forhorizontal the simulations. plane of z = 2 cm over the bed and at distances 5.65, 5.95, 6.16, 6.41, and 6.66 m from the channel inlet. As Karami, Basser, Ardeshir, and Hosseini [14] chose k   RNG turbulenceTable 2. Mesh simulation size sensitivity in their analysis. numerical simulation, for comparison between FLOW-3D, SSIIM 2.0, and laboratory experiments results, the k   RNG turbulence Coarser Finer Total Test Computational simulation wasMesh applied Size Mesh in our Size studyNumber. ComparisonNumerical of Simulation simulated absolute Laboratory velocity Experiment in Computational Number Time (hour) Fluid Dynamics(m) (CFD) simulations(m) of and Cells experimental data is shown in Figure 3 and Table 3. ds1 ds2 ds3 ds1 ds2 ds3 (m) (m) (m) (m) (m) (m) Table 3. Comparison of simulated absolute velocity in Computational Fluid Dynamics (CFD) 1 0.030 0.020 395880 0.091 0.016 0.020 0.156 0.000 0.026 71 simulation2 0.025and experimental 0.012 data 1507550. 0.133 0.005 0.023 0.156 0.000 0.026 146 Cross Section FLOW-3D SSIIM 2.0 FLOW-3D SSIIM 2.0 Sensitivity analysis indicates*R better2 results withR2 mesh reﬁnement**RMSE at a computational RMSE cost (Table2). 3.3. DataX Validation= 5.65m 0.776 0.790 0.031 0.022 X = 5.95m 0.960 0.970 0.055 0.019 FlowX = velocity 6.16m was measured0.428 at 50 points in0.157 a horizontal plane0.117 of z = 2 cm over0.078 the bed and at distancesX = 6.41m 5.65, 5.95, 6.16, 6.41,0.819 and 6.66 m from0.858 the channel inlet.0.071 As Karami, Basser,0.066 Ardeshir, and HosseiniX = 6.66m [14]chose k − ε RNG0.897 turbulence simulation0.967 in their numerical0.038 simulation, for0.051 comparison between FLOW-3D,Note: *R SSIIM2 is Coefficient 2.0, andlaboratory of determination experiments and **RMSE results, is Root the k mean− ε RNG square turbulence error. simulation was applied in our study. Comparison of simulated absolute velocity in Computational Fluid Dynamics (CFD) simulations and experimental data is shown in Figure3 and Table3.

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Figure 3. Velocity in horizontal sections; z = 2 cm, x = 5.65, 5.95, 6.16, 6.41, and 6.66m. Figure 3. Velocity in horizontal sections; z = 2 cm, x = 5.65, 5.95, 6.16, 6.41, and 6.66m. Table 3. Comparison of simulated absolute velocity in Computational Fluid Dynamics (CFD) simulationThe differences and experimental between numerical data. and experimental observation may be due to complexities of flow pattern and vortexes, or other factors that are not considered in the turbulence formula. At some Cross Section FLOW-3D SSIIM 2.0 FLOW-3D SSIIM 2.0 cross-sections differences are seen, which would be the result of complexities and high vortex 2 2 intensities. Nonetheless, based on the*R accuracy parametersR **applied RMSE (R2 and RMSE RMSE in Table 3), the numerical results areX =acceptable. 5.65m 0.776 0.790 0.031 0.022 The laboratoryX experiment = 5.95ms of 0.960Karami, Basser, 0.970 Ardeshir 0.055, and Hosseini 0.019 [14], using Chiew [30] X = 6.16m 0.428 0.157 0.117 0.078 criterion, reached theirX =6.41m equilibrium 0.819state in 3000 0.858 minutes. Hence, 0.071 a change 0.066 in bed elevation of less than 1% during 15%X of = 6.66mthe modelling 0.897 time was set 0.967 to be the simulation 0.038 stop 0.051 time criterion. Based on the scouring-timeNote: chart * R 2 ofis Coefﬁcientthe numer ofical determination simulation and ** (Figure RMSE is 4 RootA), meanthe simulation square error. equilibrium was evident, and the modeling time was therefore set to 1350 seconds. TheComparison differences of two between numerical numerical and laboratory and experimental experiments observation was performed may be using due to dimensionless complexities oftime. ﬂow The pattern scouring and process vortexes, chart or in other the experimental factors that work are not of Karami, considered Basser, in the Ardeshir turbulence, and Hosseini formula. At[14] some, Jahangirzadeh cross-sections et al. differences [31], and numerical are seen, simulation which would of this be paper the result is shown of complexities in Figure 4B. and high vortex intensities. Nonetheless, based on the accuracy parameters applied (R2 and RMSE in Table3), the numerical results are acceptable. The laboratory experiments of Karami, Basser, Ardeshir, and Hosseini [14], using Chiew [30] criterion, reached their equilibrium state in 3000 min. Hence, a change in bed elevation of less than 1% during 15% of the modelling time was set to be the simulation stop time criterion. Based on the scouring-time chart of the numerical simulation (Figure4A), the simulation equilibrium was evident, and the modeling time was therefore set to 1350 s. Comparison of two numerical and laboratory experiments was performed using dimensionless time. The scouring process chart in the experimental work of Karami, Basser, Ardeshir, and Hosseini [14], Jahangirzadeh et al. [31], and numerical simulation of this paper is shown in Figure4B. Comparison of the two charts shows good performance of the numerical simulation in simulating the scouring process. The charts further show that more than 85% of scouring occurred within 20% of the scouring time, and until that time, the experiment and numerical results are almost overlapping. Equilibrium scour is reached after 600 s, as shown in Figure4A. Figure 4. Scouring-time chart.

Comparison of the two charts shows good performance of the numerical simulation in simulating the scouring process. The charts further show that more than 85% of scouring occurred within 20% of the scouring time, and until that time, the experiment and numerical results are almost overlapping. Equilibrium scour is reached after 600 seconds, as shown in Figure 4A.

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Figure 3. Velocity in horizontal sections; z = 2 cm, x = 5.65, 5.95, 6.16, 6.41, and 6.66m.

The differences between numerical and experimental observation may be due to complexities of flow pattern and vortexes, or other factors that are not considered in the turbulence formula. At some cross-sections differences are seen, which would be the result of complexities and high vortex intensities. Nonetheless, based on the accuracy parameters applied (R2 and RMSE in Table 3), the numerical results are acceptable. The laboratory experiments of Karami, Basser, Ardeshir, and Hosseini [14], using Chiew [30] criterion, reached their equilibrium state in 3000 minutes. Hence, a change in bed elevation of less than 1% during 15% of the modelling time was set to be the simulation stop time criterion. Based on the scouring-time chart of the numerical simulation (Figure 4A), the simulation equilibrium was evident, and the modeling time was therefore set to 1350 seconds. Comparison of two numerical and laboratory experiments was performed using dimensionless time. The scouring process chart in the experimental work of Karami, Basser, Ardeshir, and Hosseini [14]Water, Jahangirzadeh2019, 11, 235 et al. [31], and numerical simulation of this paper is shown in Figure 4B. 7 of 18

Water 2018, 10, x FOR PEER REVIEW 8 of 20 FigureFigure 4. Scouring 4. Scouring-time-time chart chart..

AfterAfter the the equilibrium equilibrium state state,, the the maximum maximum scour scour in inFLOW FLOW-3D-3D was was slightly slightly underestimated underestimated at at Comparison of the two charts shows good performance of the numerical simulation in 0.1330.133 m mwhen when compared compared to to the the maximum maximum scour ofof 0.1560.156 m m from from the the laboratory laboratory experiments. experiment Thes. The scour simulating the scouring process. The charts further show that more than 85% of scouring occurred scourpattern pattern is shown is shown in Figure in Figure5. 5. within 20% of the scouring time, and until that time, the experiment and numerical results are almost overlapping. Equilibrium scour is reached after 600 seconds, as shown in Figure 4A.

Figure 5. Bed elevation changes from (A) laboratory experiments and (B) FLOW-3D. Figure 5. Bed elevation changes from (A) laboratory experiments and (B) FLOW-3D. Figure6 and Table4 show the maximum scour beneath the ﬁrst, second, and third groyne of 0.133Figure m, 0.0056 and m, Table and 0.0234 show m, the respectively. maximum scour beneath the first, second, and third groyne of 0.133 m, 0.005 m, and 0.023 m, respectively.

Figure 6. Scour beneath (A) first, (B) second, and (C) third groynes.

Table 4. Maximum scour comparison beneath the three groynes between FLOW-3D and experimental results [14].

ds3(m) ds2(m) ds1(m) Experimental 0.026 0.0 0.156 FLOW-3D 0.023 0.005 0.133

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After the equilibrium state, the maximum scour in FLOW-3D was slightly underestimated at 0.133 m when compared to the maximum scour of 0.156 m from the laboratory experiments. The scour pattern is shown in Figure 5.

Figure 5. Bed elevation changes from (A) laboratory experiments and (B) FLOW-3D.

WaterFigure2019 ,611 and, 235 Table 4 show the maximum scour beneath the first, second, and third groyne of 8 of 18 0.133 m, 0.005 m, and 0.023 m, respectively.

FigureFigure 6. Scour 6. Scour beneath beneath (A) first (A), ( ﬁrst,B) second, (B) second, and (C and) third (C) groynes third groynes..

Table 4. Maximum scour comparison beneath the three groynes between FLOW-3D and experimental Table 4. Maximum scour comparison beneath the three groynes between FLOW-3D and experimental results [14]. results [14].

ds3(m)d s3(m)d ds2s2(m)(m) ds1(m)ds1(m) Experimental Experimental0.026 0.0260.0 0.0 0.1560.156 FLOW-3D FLOW-3D0.023 0.0230.005 0.005 0.1330.133 Water 2018, 10, x FOR PEER REVIEW 9 of 20

To monitormonitor bedbed elevationelevation changes,changes, four cross-cross- andand longitudinallongitudinal sectionssections afterafter thethe constrictionconstriction were selected,selected, from which 160 pointspoints were monitored.monitored. In Figure 77,, thethe scourscour depthdepth atat aa cross-cross- andand longitudinal section around the groyne is shownshown forfor bothboth laboratorylaboratory experimentexperiment and thethe numericalnumerical simulation (about 20 points points perper section). section). Three Three statistical parameters were were used for assessment,assessment, 2 including aa coefﬁcientcoefficient ofof determinationdetermination (R(R2)) = 0.91, mean absolute error (MAE)(MAE) == 0.0162 0.0162,, and root mean squared error (RMSE)(RMSE) == 0.0214. Despite the slight differences in bed elevation changes between FLOW-3DFLOW-3D andand thethe experimentalexperimental datadata inin FigureFigure7 7,, statistical statistical parameters parameters suggest suggest satisfactory satisfactory results. results.

Figure 7.7. ExperimentExperiment andand FLOW-3DFLOW-3D scour scour proﬁles, profiles, ( A(A)) cross cross section section at at x = x=6.16m, 6.16 m, (B) longitudinal longitudinal sectionsection at yy=0.35m = 0.35 m..

3.4. Numerical Simulations Description of Groynes with Different Length and Orientations To understand the influence of orientation and length variation, 15 simulations (Table 5) were used, in which three parallel impermeable and non-submerged groynes with distances of 60 cm and 3 cm thickness were located. Groynes in the table were of the same length (30 cm) and were located on the flow route at an angle of 90°. This simulation served as a reference simulation for other cases. All the angles are measured from downstream and vary between 45° and 135° to maintain a constriction ratio of less than 25%. In the second to eigth simulations, the groynes were arranged in the order 20, 30, and 40 cm length from the first to third groyne, respectively. In order to investigate the impacts of groyne arrangement, in simulations 9 to 15, groynes were arranged in the reverse order, with the first groyne being 40 cm and the last 20 cm. These cases are placed at angles (45°, 60°, 75°, 90°, 105°, 120°, and 135°) similar to the previous arrangement. In all the simulations, the simulation setup was similar to that of validation.

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3.4. Numerical Simulations Description of Groynes with Different Length and Orientations To understand the influence of orientation and length variation, 15 simulations (Table5) were used, in which three parallel impermeable and non-submerged groynes with distances of 60 cm and 3 cm thickness were located. Groynes in the table were of the same length (30 cm) and were located on the flow route at an angle of 90◦. This simulation served as a reference simulation for other cases. All the angles are measured from downstream and vary between 45◦ and 135◦ to maintain a constriction ratio of less than 25%. In the second to eigth simulations, the groynes were arranged in the order 20, 30, and 40 cm length from the first to third groyne, respectively. In order to investigate the impacts of groyne arrangement, in simulations 9 to 15, groynes were arranged in the reverse order, with the first groyne being 40 cm and the last 20 cm. These cases are placed at angles (45◦, 60◦, 75◦, 90◦, 105◦, 120◦, and 135◦) similar to the previous arrangement. In all the simulations, the simulation setup was similar to that of validation.

Table 5. Characteristics of the simulations.

Groynes Orientation First Second Third Simulation Simulation Constriction (with Respect to Flow Groyne Groyne Groyne Number. Description Ratio (%) Direction) in (◦) Length (cm) Length (cm) Length (cm) 1 90D.30.30.30 90 30 30 30 30 2 45D.20.30.40 45 20 30 40 28 3 60D.20.30.40 60 20 30 40 35 4 75D.20.30.40 75 20 30 40 37 5 90D.20.30.40 90 20 30 40 40 6 105D.20.30.40 105 20 30 40 37 7 120D.20.30.40 120 20 30 40 35 8 135D.20.30.40 135 20 30 40 28 9 45D.40.30.20 45 40 30 20 28 10 60D.40.30.20 60 40 30 20 35 11 75D.40.30.20 75 40 30 20 37 12 90D.40.30.20 90 40 30 20 40 13 105D.40.30.20 105 40 30 20 37 14 120D.40.30.20 120 40 30 20 35 15 135D.40.30.20 135 40 30 20 28 Note: D is degrees.

4. Results Figure8 shows the scour equilibrium times and the dimensionless scour versus time in simulation 1/15, indicating that more than 50% of erosion occurred in the first 10% of the total simulation time. Simulations 5 and 6 achieved their equilibrium time later when compared to other simulations. Numerical results indicate continued scouring in some simulations after 1350 s, such as in simulation 1, 5, 6, and 12. The simulation scour equilibrium time considered 1350 s because of computational time and the validation part. In other simulations, more than 70% of scour occurred within 19% of the simulation time. In simulations 9/15, about 70% of scour occurred within 10% of the simulation time. It is evident from all the simulations that the equilibrium time is less than that of the reference simulation. In all the groyne arrangement, it is observed that as the angle of the groynes approached 90◦, the equilibrium time increased. Groynes arranged in an ascending order reached an equilibrium state earlier than their counterparts. Scour depth and sedimentation in the first, second, and third groynes are shown in Table6. Based on Table6, Figures9 and 10, the maximum scour depth increased with an increase in angle until 90◦, after which it decreased. Varying the lengths of groynes in an ascending order decreased the scour depth, while a descending order increased the scour depth. Moreover, as was anticipated, the maximum scour depth in simulations 9–15 occurred around the first dike due to the strength of vortices. Scour variation on the second and third groynes are shown in Table6 and Figure 10. Figure 11 shows the variation of the vortex strength, which decreased due to back flows in farther Water 2019, 11, 235 10 of 18 dikes, (2–7 simulations) while the dike angle increased from 45◦ to 135◦. The strength of these vortices isWater a function 2018, 10 of, x FOR flow PEER characteristics REVIEW and shape, and arrangement of the obstacle elements [32,3311 ].of 20

FigureFigure 8. 8.(A1 (A1) Dimensionless) Dimensionless scour scour versusversus time in in the the simulation simulation 2/8 2/8.. (A2 (A2) Scour) Scour depth depth versus versus time time in inthe the simulation simulation 2/8 2/8.. (B1 (B1) ) Dimensionless Dimensionless scour scour versus versus time time in in the the simulation simulation 1/9 1/9.. (B2 (B2) ) Scour Scour depth depth versus time in the simulation 1/9. D is maximum scour depth at each time and Dtotal is maximum scour versus time in the simulation 1/9. D is maximum scour depth at each time and Dtotal is maximum scourdepth depth at the at end the of end the of simulation the simulation time. time.

In other simulations,Table more 6. thanScouring 70% resultsof scour from occurred the simulation within 1/15.19% of the simulation time. In simulations 9/15, about 70% of scour occurred within 10% of the simulation time. It is evident from Maximum Maximum Simulation Simulation all the simulations that the equilibriumMaximum time is Scourless than Depth that (cm) of the referenceScour simulationDeposition. In all the Number. Description groyne arrangement, it is observed that as the angle of the groynes approachedDepth 90°, (cm) the equilibriumDepth (cm) time Sincreased. Groynes arranged First Groyne in an ascending Second Groyne order reached Third Groyne an equilibrium state earlier than their 1counterparts. 90D.30.30.30 Scour depth and 17.2 sedimentation 2.78 in the first, second 4.61, and third 17.2 groynes are 5.80 shown in Table2 6. 45D.20.30.40 5.96 4.27 5.42 5.96 2.19 3 60D.20.30.40 7.00 4.77 6.96 7.00 2.51 4 75D.20.30.40 8.20 4.48 7.51 8.20 2.22 5 90D.20.30.40Table 10.90 6. Scouring results 4.77 from the simulation 6.15 1/15. 10.90 3.00 6 105D.20.30.40 9.70 3.79 6.82 9.70 1.95 Maximum Maximum Simulation7 120D.20.30.40Simulation 7.30 2.68 5.96 7.30 2.96 Maximum Scour Depth (cm) Scour Depth Deposition Number8. 135D.20.30.40Description 4.77 2.08 3.66 4.77 1.67 9 45D.40.30.20 7.70 2.41 2.50(cm) 7.70Depth 2.93(cm) 10 60D.40.30.20 10.20First Second 2.12 Third 2.51 10.20 3.73 S 11 75D.40.30.20 12.40groyne groyne 0.35 groyne 2.37 12.40 5.39 12 90D.40.30.20 15.30 0.10 1.90 15.30 4.53 131 105D.40.30.2090D.30.30.30 12.8017.2 −2.780.10 4.61 2.5617.2 12.805.80 4.23 142 120D.40.30.2045D.20.30.40 11.205.96 4.27 0.00 5.42 1.725.96 11.202.19 4.59 153 135D.40.30.2060D.20.30.40 9.207.00 4.77 0.65 6.96 1.807.00 9.202.51 2.26 4 75D.20.30.40 8.20 4.48 7.51 8.20 2.22 5 90D.20.30.40 10.90 4.77 6.15 10.90 3.00 6 105D.20.30.40 9.70 3.79 6.82 9.70 1.95 7 120D.20.30.40 7.30 2.68 5.96 7.30 2.96 8 135D.20.30.40 4.77 2.08 3.66 4.77 1.67 9 45D.40.30.20 7.70 2.41 2.50 7.70 2.93 10 60D.40.30.20 10.20 2.12 2.51 10.20 3.73 11 75D.40.30.20 12.40 0.35 2.37 12.40 5.39

Water 2018, 10, x FOR PEER REVIEW 12 of 20

12 90D.40.30.20 15.30 0.10 1.90 15.30 4.53 13 105D.40.30.20 12.80 -0.10 2.56 12.80 4.23 14 120D.40.30.20 11.20 0.00 1.72 11.20 4.59 15 135D.40.30.20 9.20 0.65 1.80 9.20 2.26

Based on Table 6, Figure 9, and Figure 10, the maximum scour depth increased with an increase in angle until 90°, after which it decreased. Varying the lengths of groynes in an ascending order decreased the scour depth, while a descending order increased the scour depth. Moreover, as was anticipated, the maximum scour depth in simulations 9–15 occurred around the first dike due to the strength of vortices. Scour variation on the second and third groynes are shown in Table 6 and Figure 10. Figure 11 shows the variation of the vortex strength, which decreased due to back flows in farther Waterdikes,2019 (2, 11–,7 235 simulations) while the dike angle increased from 45° to 135°. The strength of these vortices11 of 18 is a function of flow characteristics and shape, and arrangement of the obstacle elements [32,33].

FigureFigure 9. 9.Maximum Maximum scour scour depthdepth inin thethe groupgroup of groynes, ascending ascending (green (green bars) bars),, and and descending descending arrangementWaterarrangement 2018, 10, x (red FOR (red bars).PEER bars) REVIEW. 13 of 20

FigureFigure 10. Maximum10. Maximum scour scour depth depth under under ((AA)) descendingdescending and and (B ()B ascending) ascending arrangement arrangement..

Generally, at an angle of 120° the strength of vortices is minimal compared to other simulations. In simulations 9–15, the length of vortices is weak and shorter. At 75° and 120° angles, the first vortex is not completely established and in these series of simulations, the small and secondary vortices are presented in an orientation of 135°.

Water 2019, 11, 235 12 of 18 Water 2018, 10, x FOR PEER REVIEW 14 of 20

Figure 11. Vortices around groynes under simulations 1–15. Figure 11. Vortices around groynes under simulations 1–15.

Water 2019, 11, 235 13 of 18 Water 2018, 10, x FOR PEER REVIEW 15 of 20

◦ UnderGenerally, simulations at an angle 2–7, of deposition 120 the strength for all orientations of vortices is almost minimal 2 cm. compared An increment to other of simulations. the groyne ◦ ◦ angleIn simulations from 45° 9–15,to 90° the produced length of a vorticessediment is weakline between and shorter. the groynes, At 75 and which 120 isangles, more obvious the ﬁrst vortexat 90° (isFigure not completely 12). Increasing established the angle and in until these 135° series removes of simulations, this sediment the small line. and Besides secondary the vorticesdeposition are ◦ betweenpresented the in groynes an orientation in all simulations of 135 . , scour increased beneath the groynes at angles from 45° to 90° to a pointUnder where simulations scour holes 2–7, depositionin the groynes for all merged. orientations is almost 2 cm. An increment of the groyne ◦ ◦ ◦ angleAt from an angle 45 to of 90 135°produced these holes a sediment are completely line between separated the groynes, and the whichsediment is more line obviousdisappears. at 90 In ◦ simulations(Figure 12). Increasing9–15, the maximum the angle untildeposition 135 removes is 3.5 cm this, exceeding sediment that line. of Besides simulations the deposition 2–8. Similarly, between in ◦ ◦ Figurethe groynes 13, the in allscour simulations, hole at zone scour 1 is increased greater beneaththan in zone the groynes 2, due atto anglesthe strength from 45 of tovortices 90 to ain point that zonewhere, as scour discussed holes inin theearlier groynes sections. merged.

Figure 12. Scour variation under simulations 1–15. Figure 12. Scour variation under simulations 1–15.

Water 2019, 11, 235 14 of 18

At an angle of 135◦ these holes are completely separated and the sediment line disappears. In simulations 9–15, the maximum deposition is 3.5 cm, exceeding that of simulations 2–8. Similarly, in Figure 13, the scour hole at zone 1 is greater than in zone 2, due to the strength of vortices in that zone,Water 2018 as discussed, 10, x FOR PEER in earlier REVIEW sections. 16 of 20

Figure 13. (A) Erosion zone 1 and 2, and (B) erosion and sedimentation contours in simulation 12. Figure 13. (A) Erosion zone 1 and 2, and (B) erosion and sedimentation contours in simulation 12. 5. Discussion 5. Discussion One of the most important dead zones are groyne fields. Dead zones change the velocity profile in a channelOne of the and most these important changes bring dead profoundzones are effectsgroyne on fields. sedimentation Dead zones and change scour. the The velocity flow structure profile in a channel dead zone and consists these changes of a mixing bring layer, profound a primary effects gyre, on andsedimentation a core region and within scour. this The gyre. flow Astructure smaller gyrein a dead would zone exist consist dependings of a mixing on the layer, aspect a primary ratio of gyre W/L,, and where a core W region and Lwithin are length this gyre. and A distance smaller betweengyre would them, exist respectively depending [ 12 on]. the The aspect above ratio classification of W/L, where is mainly W and for a L classic are length groyne and or distance groyne fields,between which them, have respectively the same length,[12]. The or whereabove aclassification protective groyne is mainly exists for in a the classic groyne groyne field. or Moreover, groyne applyingfields, which different have the groyne same lengths length, or would where yield a protective unique deadgroyne zone exists and in flowthe groyne structure, field. resulting Moreover, in specialapplying patterns different of sedimentationgroyne lengths and would scour. yield Illustration unique isdead provided zone and for velocityflow structure distributions, resulting under in simulationsspecial patterns 1–8 andof sedimentation 9–15, in Figures and 14 scour. and 15 Illustration, respectively. is provided for velocity distributions under simulationsFrom Figures 1–8 and 14 9and–15, 15 in, theFigure cores 14 of theand gyres 15, respectively is shown in. the regions of low velocity (blue colour). Changing the orientation from 45 to 135 degrees increased the dead zone before the first groyne upstream. This is more obvious in simulations 8 and 15, and the increased dead zone decreased the scour in the order of the orientation angle increase. Under simulations 9–15, the dead zone covers the second and third groynes, and the velocities are lower than the main stream. Hence, the scour

Water 2019, 11, 235 15 of 18 becomes smaller as further illustrated by Table6. On the contrary, in simulations 2–8, the mixing layer Waterwould 2018 affect, 10, xthe FOR second PEER REVIEW and third groynes and increase the scour. 17 of 20

FigureFigure 14. VelocitiesVelocities in 1 1–8–8 simulation simulation..

Storage time is another important effect of the dead zone, which could be raised by the groyne fields. Dead zones trap large amounts of sediment, which are released back into the main channel after a period. Since the descending simulations had larger dead zones, they trapped more sediment, subsequently increasing the equilibrium times compared to ascending configurations. Groyne fields with different lengths and orientations have different characteristics compared to classic groyne fields having the same length. One of the main differences between real groynes in the rivers and ideal groynes is that real groynes have 1:3 slopes on their side and nose, whereas ideal groynes are vertical on the side walls [13]. In future studies, the effects of the slopes and the different nose shapes should be investigated. Furthermore, most of the groynes in the rivers are permeable, whereas in this article impermeable groynes were studied. Studying the combined effects of these variables should be sought, i.e., length of groynes, permeability, distance between groynes, orientation, etc.

Water 2019, 11, 235 16 of 18 Water 2018, 10, x FOR PEER REVIEW 18 of 20

Figure 15. Velocities in simulations 1 and 9–15. Figure 15. Velocities in simulations 1 and 9–15. 6. Conclusions From Figures 14 and 15, the core of the gyres is shown in the regions of low velocity (blue colour). In this paper, a new arrangement of impermeable parallel groynes with non-equal lengths is Changing the orientation from 45 to 135 degrees increased the dead zone before the first groyne proposed. The effects of varying the orientation of these groynes and their arrangement on erosion, upstream. This is more obvious in simulations 8 and 15, and the increased dead zone decreased the sedimentation, and ﬂow patterns are discussed. From the numerical assessments, the following scour in the order of the orientation angle increase. Under simulations 9–15, the dead zone covers the conclusions are drawn. second and third groynes, and the velocities are lower than the main stream. Hence, the scour becomes- When smaller groynes as further are arranged illustrated in an ascendingby Table 6. order, On the more contrary, than 50% in ofsimulation scour occurss 2–8, within the mixing 10% of layer thewould simulation affect the time, second while and in third a descending groynes and order, increase more than the scour. 70% of the scour occurred within a Storagesimilar time time. is another important effect of the dead zone, which could be raised by the groyne fields.- Simulations Dead zones with trap an large orientation amounts close of sediment, to 90◦ had which longer are sediment released scour back equilibrium into the main time. channel after a period. Since the descending simulations had larger dead zones, they trapped more sediment, - Simulations with an ascending order have larger vortices after the third groyne than those of subsequently increasing the equilibrium times compared to ascending configurations. descending arrangement. Groyne fields with different lengths and orientations have different characteristics compared to - Under groynes of 135◦ with descending arrangement (ﬁrst groyne: 40 cm; second groyne: 30 cm; classic groyne fields having the same length. One of the main differences between real groynes in the third groyne: 20 cm), some small vortices are produced around the groynes. rivers and ideal groynes is that real groynes have 1:3 slopes on their side and nose, whereas ideal - Maximum deposition height when groynes are arranged in an ascending order is higher than in groynes are vertical on the side walls [13]. In future studies, the effects of the slopes and the different the reverse direction nose shapes should be investigated. Furthermore, most of the groynes in the rivers are permeable, whereas- An in ascending this article arrangement impermeable produces groynes a sediment were stud line,ied. contrary Studying to the a descending combined orientationeffects of these

Water 2019, 11, 235 17 of 18

- Arranging groynes in a descending order could reduce the maximum scour depth by 55%, and ascending arrangement by up to 72%.

Author Contributions: Conceptualization, S.A., and P.T.; analysis, H.P.; review of numerical results and editing, L.C. and S.T. Acknowledgments: The authors appreciate the comments from the anonymous reviewers and assistance from Nafiseh Tofangdar. Conflicts of Interest: The authors declare no conflict of interest.

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