Numerical scour modeling around parallel spur dikes in FLOW-3D

Spur dikes are some structures which are built in the flow path with the aim of changing flow characteristics in order to bed and bank protection in rivers. These sudden changes in properties caused by the existence of spur dikes, produces erosion and sedimentation around them. In this paper, effects of series of parallel spur dikes have been investigated numerically. For this purpose, by using experimental and numerical research results from technical literatures, the numerical model conducted in FLOW-3D commercial software and the data were compared with experimental and SSIIM results. The 10 results showed that Froude number and the ratio of U/Ucr affect the accuracy of the models. As a result, by discharge increasing, FLOW-3D models need to be calibrated again. Also, by using a calibrated FLOW-3D model, calculation accuracy of the scour depth at the bottom of the spur dikes becomes better and the accuracy level in the modeling of the surface morphology improves 7 percent more than SSIIM software in the bottom of the first spur dike, more than 80 percent at the bottom of the second spur dike and approximately 40 percent at the bottom of the last spur dike. 15


Introduction
Spur dikes are known as structures that are built in the flow path and they are extended from adjacent beach to the center of flow with the aim of reducing coastal erosion by diverting the flow path (Kuhnle et al.,2002).Also, these structures will be used for the purpose of aquatic habit (Klingeman et al., 1984) or coast recreation (Chang et al., 2013).Three-dimensional flow patterns will be changed when flumming structures are placed in channel surface through vortex current development.
In many researches, spur dikes are studied individually.Since these structures are mainly built in groups and the flow characteristic would vary in peak and between spur dikes, researchers such as (Chang et al., 2013) and (Karami et al., 2014) investigated the scour depth in groups of spur dikes.Due to the greater interaction between flow and sediment and revealing turbulent flow in group of spur dikes, exact scour depth forecasting needs consideration of flow turbulence in scouring hole (Mendoza, 1993).
Computational fluid dynamic (CFD) is used in numerical models (Acharya et al., 2013) and in recent years various commercial models such as FLOW-3D, SSIIM and Fluent are developed.Modelling of flow and sediment transport around spur dikes needs at least solving two-dimensional hydrodynamics equations and sediment model simultaneously (Duan et al. 2006, Kuhnle et al. 2008).
In this research, three-dimensional flow is used for scour modelling around impermeable parallel series of non-submerged vertical spur dikes.This type of modelling is used in enormous studies such as (An et al., 2015), (Li et al., 2016) and (Shamohamadi et al., 2016) for scour and sediment transport module which is recently added to FLOW-3D.In order to validate numerical simulation, experimental and numerical results presented by (Karami et al., 2014) are compared with FLOW-3D results.
In which d= diameter of sediment particle, τ= bed shear stress, τ c =critical shear stress for sediment particle motion according to Shields diagram, ρ S and ρ W = respectively, water density and sediment particle density, ϑ= Kinematic viscosity of water and g= gravitational acceleration.Where   is indication for bed load sediment particle.

Experimental model
This paper is based on Karami et al (2014)

Description of the numerical model
A numerical model with the characteristics of the mentioned experiments in the previous section was utilized in FLOW-3D.
Units were selected as SI, the temperature in Celsius degree and water is considered as incompressible fluid.Critical Shields number was considered according to 0.91-millimeter diameter, gravitational acceleration equals to 9.807 meters per second squared, sediment particle density 2650 kilogram per cubic meter and Kinematic viscosity 10-6.Using these data and Shields equation, the shields number evaluated equal to 0.033.Richardson-Zaki coefficient controls drag impression on sediment particle settlement when the flow is concentrated.The value 1 of this coefficient was applied equal to 1In order to unify calculation for comparing   In this paper, this angle is considered equal to 30 degrees.Bed load coefficient, controls the bed load transport rate when the speed is faster than critical speed.According to (Van Rijn, 1987) equations, this value should be1.Entrainment coefficient controls scour rate.This empirical coefficient is used with the aim of comparing the rate of deposition and calibration of the model with experimental data.Default value of this coefficient was considered 0.018 according to (Mastbergen et al., 2003) data.This coefficient depreciates in model by zero value.The value of this coefficient was obtained 0.036 by trial and error method according to Table 2 and applied in the models.

Initial and Boundary conditions:
At the inlet of the channel, the boundary is volume flow rate (Figure 2).Here, according to experimental conditions, volume flow rate was used with a constant discharge of 0.035 and 0.046 cubic meters per second and the entrance flow depth was 0.5m from the channel bottom.On the sides (walls) and the bottom of the channel, the boundary conditions was set to be walls.To estimate the effect of the walls on flow, a well-known empirical equation for the standard wall function is used (Olsen, 2009): Where   = bed roughness, =Prandtl constant and equals 0.4 and ℎ=distance from the wall.
Symmetry boundary was used at the upper and inner boundaries as well.Continuative considered at downstream boundary.
All the applied boundary conditions have shown In Figure 2.

Model Dimensions
One of the usual problems that arise in such modeling is scouring at channel entry.If coarse mesh is used due to the rigid layer changes to sediment substrate, the erosion would become so much and could affect the flow which reaches to spur dikes.Even in some cases one can observe that the erosion of this part causes sedimentation in the scour hole near the first dike.To prevent this hazard, the model should start as far from spur dikes as possible at upstream channel.As another solution, sediment with more solid material can be used at the first of channel (With the same grain size but higher critical Shields number).Considering that the changing channel dimensions seem more reasonable and that the length should not be too short and also it should not be too long to minimize computing costs, some models with different length examined.The channel's length was chosen 5 meters.From the beginning of the channel till the first dike, the flow would become fully developed and then the vortices would start.

Mesh Dimensions
Various models were tested in order to choose a suitable mesh.Nested mesh would lead to good modelling of vortices and also it is matches the experimental data.According to the performed sensitivity mesh analysis, (table 3) and comparing the 5 scour around the first spur dike with experimental results, two different mesh sizes were used at close distances to spur dikes.
It should be noted that in presence of nested mesh, the internal and external mesh should not have a large difference in size.
Empirically and in order to reduce errors, it is recommended that the ratio of two meshes set to be about 2.Also, at the intersections of the two meshes, it should be considered that mesh size should have gradual changes.The dimension of the larger mesh is 2.5 centimeters with a count of 192000.. Smaller mesh size is 1.2 centimeters with a count of 1315550.In general, 1507550 mesh elements were utilized to model the channel (Figure 4).

Conclusions
The parameters R 2 , MAE, and RMSE were compared for the results of FLOW-3D and SSIIM to test the data matching with experimental data (Karami et al. 2014), the mentioned parameters have been expressed respectively in equations ( 10), ( 11) and ( 12). (10) Where   are experimental results,   are numerical results and n are number of data.

Comparison of time modeling
Scour time is an important parameter in numerical simulations.After a few initial tests, it was observed that the greatest depth and associated time with scouring depth, around the first spur dike are more critical than others.Afterward, maximum scourdepth dike was taken into account as the balance considerations of erosion in numerical modeling.Equilibrium basis was considered as depth changes that are less than 1 mm in 100 seconds.The results showed that the E1 model in 1350 seconds and E2 model in 1600 seconds reach equilibrium.As seen in Figure 8, the equilibrium time results ofthe numericalmodel were compared with experimental results and for theE1 test, R 2 , 0.95and for theE2 test, R 2 , 0.98 were calculated which demonstrates the consistency of the experimental and numerical data.It should be mentioned that laboratory equilibrium time was considered as depth change which was less than 1 mm at the time of 8 hours by (Chiew, 1992).Figure 8 parameters are, scour time (t), maximum scour depth at the time (t), (dst), equilibrium scour depth (dse), and the time to reach equilibrium depth (T).
Drink.Water Eng.Sci.Discuss., https://doi.org/10.5194/dwes-2017-21 Drinking  with some RNG extensions indicates the most concordance like software SSIIM (Karami et al. 2014) with experimental results.Figure 9 shows the absolute simulated speed comparison between two software, FLOW-3D, and SSIIM and absolute measured speed.From this figure, it can be concluded that the CFD model simulated the flow with sufficient accuracy.Also, quantitative comparisons results showed that FLOW-3D software with R 2 , 0.89 and SSIIM software with R 2 , 0.94, has the capability for hydraulic flow simulation and there is not much difference between them.10 Drink.Water Eng.Sci.Discuss., https://doi.org/10.5194/dwes-2017forjournal Drink.Water Eng.Sci. Discussion started: 8 June 2017 c Author(s) 2017.CC BY 3.0 License.

Figure 1 :
Figure 1: Schematic diagram of flow pattern and scouring around spur dike (Karami et al., 2014) Drink.Water Eng.Sci.Discuss., https://doi.org/10.5194/dwes-2017 this modeling,k − ε turbulence model with the development of Renormalized group (RNG) is utilized.RNG model has been obtained by the development and expansion of standard model Drink.Water Eng.Sci.Discuss., https://doi.org/10.5194/dwes-2017forjournal Drink.Water Eng.Sci. Discussion started: 8 June 2017 c Author(s) 2017.CC BY 3.0 License.based on Renormalized Group (RNG).Suspended sediment particle diffusion, is defined by two coefficients, molecular diffusion and turbulent coefficient.Turbulent diffusion coefficient is reverse of Schmidt number and approximately is equal to 1. Sediment surface roughness is defined by the ratio of bed roughness d 50 .d 50 is calculated at each time step for each sediment cell.The value of this coefficient was evaluated equal to 5.014.Particles angle of repose shows the most rely angle of the bed which is usually between 30 to 40 degrees and is useful to correct the influence of the slope in critical Shields parameter.
review for journal Drink.Water Eng.Sci. Discussion started: 8 June 2017 c Author(s) 2017.CC BY 3.0 License.

Figure 2 :
Figure 2: boundary conditions of FLOW-3D model For initial condition, a fluid region in a sediment box technique was used with two aims, the first sediment should be saturated and second, sediment should not erode suddenly and wash from the channel due to the channel flow.The dimensions of the area that encompasses the entire sediment are 4.8 meters length, 1 meter wide and 35centimeters depth.

Figure 4 :
Figure 4: View of the meshed model in FLOW-3D

Figure 5 :Figure 6 :Figure 7 :
Figure 5: Numerical modeling results of bed deformation in E1 test, Flow direction: Right to left review for journal Drink.Water Eng.Sci. Discussion started: 8 June 2017 c Author(s) 2017.CC BY 3.0 License.

Figure 8 :
Figure 8: Dimensionless graph of equilibrium time of scouring in (a: Left) E1 test and (b: Right) E2 test in FLOW-3D Hydraulic comparisons (SSIIM, Flow3D, Experimental)With the aim of calibration of CFD flow simulation model results, and the experimental results used in this way that the speed of 50 points in Z (level), equal to 2 cm above the bed, measured in theE2 test for properties.These speeds are at the distances 5.56, 59.5, 6.16, 6.41 and 6.66 meters, which are shown in Figure9.The results showed that k-ɛ turbulence model 5 Drink.Water Eng.Sci.Discuss., https://doi.org/10.5194/dwes-2017forjournal Drink.Water Eng.Sci. Discussion started: 8 June 2017 c Author(s) 2017.CC BY 3.0 License.

Governing equations in sediment transport model
Drink.Water Eng.Sci.Discuss., https://doi.org/10.5194/dwes-2017-21  = open volume ratio to flow, = fluid density,(, , )= velocity components in (, , ),   = source function,(  ,   ,   )= fractional areas, (  ,   ,   )= gravitational force,(  ,   ,   )= viscosity acceleration, (  ,   ,   )= , x=general space dimension, z= dimension inthe vertical direction, Ґ= diffusion coefficient.The diffusion coefficient is equal to flow eddy viscosity which is calculated by thek − ε model.This equation describes sediment transport which includes the effect of the turbulence on deceleration sediment particles settlement.This equation is solved by control volume method in FLOW-3D model on every cell except those are close to the bed.In order to calculate concentration and surface adjacent load, four models, namely Van Rijn equation and Nielsen equation, Meyer-Peter & Muller equation are developed.In this article, Van Rijn equation model is used in order to compare FLOW-3D with SSIIM model in both models.In surface cells, sediment concentration and bed load are calculated by (Van Rijn, 1987) equation respectively, which are presented in equations 6 and 7: work and their work is utilized to find how the Flow-3D could model a scouring phenomenon.They constructed a rectangular 14m long flume, with 1m width and 1m depth in the laboratory of the Amirkabir University of Technology.Three non-submerged, impermeable 25cm length spur dikes were perpendicularly installed in channel.The first dike installed at a distance of 6.16 meters from the beginning of the channel and the distance between them selected twice the length.The input current is kept constant at 15 cm depth.They covered the flume with 0.35m thickness uniform sediment (σ g < 1.4), median size (d 50 ) 0.91mm, specific gravity (s s ) 2.65 and standard deviation (σ g ) 1.38.Velocity and surface changes profile around the spur dikes was measured with ADV and LBP respectively.In table1details and results of their experiment has expressed which is used to validate the numerical model where Q= tested discharge in terms of cubic meters per second, Y= flow depth in terms of meter, U= flow velocity in term of meter per second, U/Ucr= flow rate to the critical Shields velocity Ratio, Fr= Froude number, ds1 and ds2 and ds3= scour depth in the first, second and third spur dike, correspondingly and V= volume of eroded sediment in cubic meters.