# 3D CFD Modeling of Local Scouring, Bed Armoring and Sediment Deposition

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Laboratory Experiments

#### 2.1. Experimental Setup and Measurement Procedure

_{avg}is the water depth at the outlet, v

_{avg}is the averaged flow velocity, Fr is the Froude number, Re is the Reynolds number, τ

_{avg}is the averaged bed shear stress, estimated as described later on and S

_{bed}is the bed slope. The variables show that the flow was subcritical (Fr < 1) and turbulent (Re > 40,000) in every case.

_{50}points. The following formula describes this relation between the AbN and VbW d

_{50}values, which is specific to this study:

_{50,VbW}and d

_{50,AbN}are the d

_{50}values according to the volume-by-number and area-by-number GSD, respectively. This formula allowed us to compare the experimental and numerical results (the latter will indicate volumetric information).

_{m}= 8.7 mm, and d

_{50}= 5.2 mm, determined from the VbW GSD.

#### 2.2. Assessment of Laboratory Experiments

_{50}values are indicated by circles on the plots.

_{50}values could be assessed—the larger and lighter the circle, the coarser the bed material, also shown in Figure 3.

_{50}indicates bed material coarsening in the erosion zone, which refers to the bed armoring process. The initial d

_{50}= 5.2 mm increased remarkably up to 21 mm until the end of the last run.

_{50}distribution; Figure 3 shows, that due to the persisting selective erosion process and the higher erosion capability of the flow, the finer fractions are entrained during the last model run, resulting in an increasing d

_{50}along the entire study domain. The areal distribution of the d

_{50}sizes also indicates that the bed material in the recirculation zone became finer than in the main stream. Indeed, the eroded finer fractions from the scour are trapped in the zone.

## 3. Numerical Modeling

#### 3.1. Applied Numerical Model

_{s}is the Nikuradze roughness.

_{x}, U

_{y}, P and ε have zero gradient boundary conditions, whereas U

_{z}is set to a certain value and k is equal to zero.

_{1}is a constant (C

_{1}~ 0.20) and ρ is the water density [23].

#### 3.2. Model Setup

#### 3.3. 3D Flow Model Validation

#### 3.4. Implementation of Combined Bedload Transport Models

## 4. Results and Discussion

_{1}= 58 L/s, Q

_{2}= 72 L/s and Q

_{3}= 100 L/s. Numerical simulations were performed applying the (i) van Rijn bedload transport formula; (ii) Wilcock and Crowe bedload transport formula and (iii) the combined approach. The measured bed geometry after reaching equilibrium conditions at Q

_{1}= 58 L/s indicates the formation of a scour hole at the tip of the groin with a depth of 0.03 m (Figure 9).

_{50}values (circles in Figure 10) indicates an overall coarsening of the bed material after the first run.

_{50}increases to 12 mm, whereas in the upstream section and in the recirculation zone, the d

_{50}is around the initial diameter. The numerical simulations using the van Rijn formula show unrealistic local coarsening around the groin, enhancing the limitation of this approach when inhomogeneous bed material is present (Figure 10-i). The Wilcock and Crowe formula shows the similar behavior of the d

_{50}pattern along the flume with respect to the measured ones. The selective erosion of the finer particles, i.e., the coarsening in the main stream is well reproduced; however, the coarsest grain size in the scour hole indicates larger grains in the simulations (Figure 10-ii). It has to be noted that the measured (image-based) analysis represents an averaged d

_{50}for a ~0.1 m × 0.1 m size square, whereas the numerical model results belong to the given grid points. The application of the combined formula leads to a very similar pattern of d

_{50}than in the previous model variant. The selective erosion in this case, however, appears along the whole downstream section where the van Rijn model is activated with higher weight in the bedload transport model.

_{50}distribution of the Wilcock and Crowe model also indicates that the eroded particles were deposited immediately after the erosion zone (Figure 12-ii). Nevertheless, the combined model seems to result in less stable particles in the main stream and so indicates higher d

_{50}values downstream of x = 3.5 m (Figure 12-ii). Thus, the combined model barely calculates deposition in the main stream (Figure 11-iii). The combined model overall shows better agreement with the measurements.

_{50}distribution calculated by the Wilcock and Crowe model refers to the resuspension of the fine particles, which indicates the disappearance of fine materials along the downstream half of the flume.

_{50}distribution of the bed material suggests the applicability of the Wilcock and Crowe model. The calculated distribution not only reproduces the spatial patterns but also shows an acceptable quantitative match (Figure 14-ii).

_{50}distribution fields (Figure 14-ii,iii), the d

_{50}distribution calculated by the combined approach has the same precision as the Wilcock and Crowe formula. However, there is no measured point between x = 1.5–3 m, where the deposition dune stopped moving forward during the combined approach calculation. Figure 14-iii indicates some coarsening (x > 1.5 m, green spots, d

_{50}> 0.01 m) around this region. A possible reason for this phenomenon can be the above detailed incorrect effect of the constant active layer. Accordingly, the lower part of the deposition is taken into account by the numerical model as being coarser than it is. Thus, a more stable deposition is assumed, leading to the stoppage of the dune.

_{90}= 0.021 m isolines, which bound the regions where the Wilcock and Crowe formula is applied. The off-line areas show the regions where the van Rijn model calculates the sediment transport.

_{90}= 0.021 m isoline, the bed material is coarser and the Wilcock and Crowe formula is activated. In this zone, the transport capacity of the flow is higher ($\tau \gtrsim 1.5N/{m}^{2}$), but the estimated higher stability of the grains leads to a resistant bed formation. Thus, the combined application of the two formulas with the above presented conditions (Equations (4) and (5)) results in the described equlibrium bed formation. The formed dune ridge of the deposition zone (red spot in Figure 15) designates the places where the morphological conditions ($\tau \sim 1.5N/{m}^{2},{d}_{90}\text{}=\text{}0.021\text{}\mathrm{m}$) do not result in any substantial sediment transport according to both formula.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Parker, G. Transport of Gravel and Sediment Mixtures. In Sedimentation Engineering: Processes, Measurements, Modeling, and Practice; García, M., Ed.; ASCE: Reston, VA, USA, 2008; pp. 165–251. [Google Scholar]
- Meyer-Peter, E.; Müller, R. Formulas for Bed-Load Transport. In Proceedings of the Second Congress IAHR, Stockholm, Sweden, 7–9 June 1948.
- Einstein, H.A. The Bed-Load Function for Sediment Transportation in Open Channel Flows; Technical Bulletin; U.S. Department of Agriculture: Washington, DC, USA, 1950; p. 71.
- Ashida, K.; Michiue, M. Study on hydraulic resistance and bedload transport rate in alluvial streams. Trans. Jpn. Soc. Civ. Eng.
**1972**, 206, 59–69. [Google Scholar] [CrossRef] - Parker, G.; Klingeman, P.C.; Mclean, D.G. Bedload and Size Distribution in Paved Gravel-Bed Streams. J. Hydraul. Div.
**1982**, 108, 544–571. [Google Scholar] - Parker, G. Surface-Based Bedload Transport Relation for Gravel Rivers. J. Hydraul. Res.
**1990**, 28, 417–436. [Google Scholar] [CrossRef] - Wilcock, P.R.; Kenworthy, S.T. A two-fraction model for the transport of sand/gravel mixtures. Water Resour. Res.
**2002**, 38, 1194–1205. [Google Scholar] [CrossRef] - Wilcock, P.R.; Crowe, J.C. Surface-based transport model for mixed-size sediment. J. Hydraul. Eng.
**2003**, 129, 120–128. [Google Scholar] [CrossRef] - Wu, W.; Wang, S.S.Y.; Jia, Y. Nonuniform sediment transport in alluvial rivers. J. Hydraul. Res.
**2000**, 38, 427–434. [Google Scholar] [CrossRef] - Powell, D.M.; Reid, I.; Laronne, J.B. Evolution of bed load grain size distribution with increasing flow strength and the effect of flow duration on the caliber of bed load sediment yield in ephemeral gravel bed rivers. Water Resour. Res.
**2001**, 37, 1463–1474. [Google Scholar] [CrossRef] - Yang, C.T.; Wan, S. Comparison of Selected Bed-Material Load Formulas. J. Hydraul. Res.
**1991**, 117, 973–989. [Google Scholar] [CrossRef] - Van Rijn, L.C. Sediment Transport, Part I, Bed Load Transport. J. Hydraul. Eng.
**1984**, 110, 1431–1456. [Google Scholar] [CrossRef] - Fernandez Luque, R. Erosion and Transport of Bed-load Sediment. Bachelor’s Thesis, Delft Technical University, Delft, The Netherlands, 1974. [Google Scholar]
- Fernandez Luque, R.; van Beek, R. Erosion and Transport of Bed-load Sediment. J. Hydraul. Res.
**1976**, 14, 127–144. [Google Scholar] [CrossRef] - Guy, H.P.; Simons, D.B.; Richardson, E.V. Summary of Alluvial Channel Data from Flume Experiments, 1956–1961; Geological Survey Professional Paper; USGS: Washington, DC, USA, 1966; 104p.
- Stein, R.A. Laboratory Studies of Total Load and Apparent Bed Load. J. Geophys. Res.
**1965**, 70, 1831–1842. [Google Scholar] [CrossRef] - Delft Hydraulics Laboratory. Verification of Flume Tests and Accuracy of Flow Parameters; Note R 657-VI; Delft Hydraulics Laboratory: Delft, The Netherlands, 1979. [Google Scholar]
- Wilcock, P.R.; Kenworthy, S.T.; Crowe, J.C. Experimental study of the transport of mixed sand and gravel. Water Resour. Res.
**2001**, 37, 3349–3358. [Google Scholar] [CrossRef] - Török, G.T.; Baranya, S.; Rüther, N.; Spiller, S. Laboratory analysis of armor layer development in a local scour around a groin. In Proceedings of the International Conference on Fluvial Hydraulics River Flow, Lausanne EPFL, Lausanne, Switzerland, 3–5 September 2014.
- Detert, M.; Weitbrecht, V. User guide to gravelometric image analysis by BASEGRAIN. In Advances in Science and Research; Fukuoka, S., Nakagawa, H., Sumi, T., Zhang, H., Eds.; Taylor & Francis Group: London, UK, 2013. [Google Scholar]
- Strom, K.B.; Kuhns, R.D.; Lucas, H.J. Comparison of Automated Image-Based Grain Sizing to Standard Pebble-Count Methods. J. Hydraul. Eng.
**2010**, 136, 461–473. [Google Scholar] [CrossRef] - Cea, L.; Puertas, J.; Pena, L. Velocity measurements on highly turbulent free surface flow using ADV. Exp. Fluids
**2007**, 42, 333–348. [Google Scholar] [CrossRef] - Kim, S.C.; Friedrichs, C.T.; Maa, J.P.Y.; Wright, L.D. Estimating bottom stress in tidal boundary layer from Acoustic Doppler velocimeter data. J. Hydraul. Eng.
**2000**, 126, 399–406. [Google Scholar] [CrossRef] - Biron, P.M.; Robson, C.; Lapointe, M.F.; Gaskin, S.J. Comparing different methods of bed shear stress estimates in simple and complex flow fields. Earth Surf. Process. Landf.
**2004**, 29, 1403–1415. [Google Scholar] [CrossRef] - Soulsby, R.L.; Dyer, K.R. The form of the near-bed velocity profile in a tidally accelerating flow. J. Geophys. Res. Oceans
**1981**, 86, 8067–8074. [Google Scholar] [CrossRef] - Török, G.T.; Baranya, S.; Rüther, N. Three-dimensional numerical modeling of non-uniform sediment transport and bed armoring process. In Proceedings of the 18th Congress of the Asia & Pacific Division of the IAHR 2012, Jeju, Korea, 19–23 August 2012. Paper 0816.
- Fischer-Antze, T.; Rüther, N.; Olsen, N.R.B.; Gutknecht, D. 3D modeling of non-uniform sediment transport in a channel bend with unsteady flow. J. Hydraul. Res.
**2009**, 47, 670–675. [Google Scholar] [CrossRef] - Gaeuman, D.; Andrews, E.D.; Krause, A.; Smith, W. Predicting fractional bed load transport rates: Application of the Wilcock-Crowe equations to a regulated gravel bed river. Water Resour. Res.
**2009**, 45, W06409. [Google Scholar] [CrossRef] - Janssen, S.R. A Part of Transport: Testing Sediment Models under Partial Transport Conditions. Master’s Thesis, University of Twente, Enschede, The Netherlands, 2010. [Google Scholar]
- Rüther, N.; Olsen, N.R.B. Modelling free-forming meander evolution in a laboratory channel using three-dimensional computational fluid dynamics. Geomorphology
**2007**, 89, 308–319. [Google Scholar] [CrossRef] - Rüther, N.; Olsen, N.R.B. 3D modeling of transient bed deformation in a sine-generated laboratory channel with two different width to depth ratios. In Proceedings of the International Conference on Fluvial Hydraulics, Lisbon, Portugal, 6–8 September 2006.
- Rüther, N.; Olsen, N.R.B. Three-dimensional modeling of sediment transport in a narrow 90° channel bend. J. Hydraul. Eng.
**2005**, 131, 917–920. [Google Scholar] [CrossRef] - Olsen, N.R.B.; Melaaen, M.C. Three-dimensional calculation of scour around cylinders. J. Hydraul. Eng.
**1993**, 119, 1048–1054. [Google Scholar] [CrossRef] - Bihs, H.; Olsen, N.R.B. Numerical Modeling of Abutment Scour with the Focus on the Incipient Motion on Sloping Beds. J. Hydraul. Eng.
**2011**, 137, 1287–1292. [Google Scholar] [CrossRef] - Zinke, P.; Olsen, N.R.B.; Bogen, J. Three-dimensional numerical modelling of levee depositions in a Scandinavian freshwater delta. Geomorphology
**2011**, 129, 320–333. [Google Scholar] [CrossRef] - Olsen, N.R.B. A Three-Dimensional Numerical Model for Simulation of Sediment Movements in Water Intakes with Moving Option; User’s Manual 2002; Department of Hydraulic and Environmental Engineering, The Norwegian University of Science and Technology: Trondheim, Norway, 2002. [Google Scholar]
- Pope, S.B. Turbulent Flows; Cambridge University Press: Cambridge, UK, 2000. [Google Scholar]
- Patankar, S.V. Numerical Heat Transfer and Fluid Flow; McGraw-Hill Book Company: New York, NY, USA, 1980. [Google Scholar]
- Schlichting, H. Boundary Layer Theory; McGraw-Hill: New York, NY, USA, 1979. [Google Scholar]
- Parker, G.; Paola, C.; Leclair, S. Probabilistic Exner Sediment Continuity Equation for Mixtures with No Active Layer. J. Hydraul. Eng.
**2000**, 126, 818–826. [Google Scholar] [CrossRef] - Villaret, C.; Van, L.A.; Huybrechts, N.; Van Pham Bang, D.; Boucher, O. Consolidation effects on morphodynamics modelling: Application to the Gironde estuary. La Houille Blanch.
**2010**, 6, 15–24. [Google Scholar] [CrossRef] - Van Rijn, L.C. Equivalent roughness of alluvial bed. J. Hydraul. Eng.
**1982**, 108, 1215–1218. [Google Scholar] - Koken, M.; Constantinescu, G. An investigation of the flow and scour mechanisms around isolated spur dikes in a shallow open channel: 2. Conditions corresponding to the final stages of the erosion and deposition process. Water Resour. Res.
**2008**, 44, W08407. [Google Scholar] [CrossRef] - Catalano, P.; Wang, M.; Iaccarino, G.; Moin, P. Numerical simulation of the flow around a circular cylinder at high Reynolds numbers. Int. J. Heat Fluid Flow
**2003**, 24, 463–469. [Google Scholar] [CrossRef] - Roulund, R.; Sumer, B.M.; Fredsøe, J.; Michelsen, J. Numerical and experimental investigation of flow and scour around a circular pile. J. Fluid Mech.
**2005**, 534, 351–401. [Google Scholar] [CrossRef] - Baranya, S.; Olsen, N.R.B.; Stoesser, T.; Sturm, T. Three-dimensional RANS modeling of flow around circular piers using nested grids. Eng. Appl. Comput. Fluid Mech.
**2012**, 6, 648–662. [Google Scholar] [CrossRef] - Baranya, S.; Józsa, J. Investigation of flow around a groin with a 3D numerical model, II. In Proceedings of the Ph.D. CivilExpo Symposium, Budapest, Hungary, 29–31 January 2004; pp. 12–19.
- Shields, A.F. Application of Similarity Principles and Turbulence Research to Bed-Load Movement; California Institute of Technology: Pasadena, CA, USA, 1936; Volume 26, pp. 5–24. [Google Scholar]
- Parker, G.; Dhamotharan, S.; Stefan, H. Model experiments on mobile, paved gravel bed streams. Water Resour. Res.
**1982**, 18, 1395–1408. [Google Scholar] [CrossRef] - Jaeggi, M.N.R. Effect of Engineering Solutions on Sediment Transport. In Dynamics of Gravel-Bed Rivers; Billi, P., Hey, R.D., Thorne, C.R., Tacconi, P., Eds.; John Wiley & Sons Ltd.: Hoboken, NJ, USA, 1992. [Google Scholar]
- Ramooz, R.; Rennie, C.D. Laboratory measurement of bedload with an ADCP. In Bedload-Surrogate Monitoring Technologies; U.S. Geological Survey Scientific Investigations Report 2010-5091; Gray, J.R., Laronne, J.B., Marr, J.D.G., Eds.; USGS: Reston, VA, USA, 2010. [Google Scholar]
- Muste, M.; Baranya, S.; Tsubaki, R.; Kim, D.; Ho, H.; Tsai, H.; Law, D. Acoustic mapping velocimetry. Water Resour. Res.
**2016**, 52, 4132–4150. [Google Scholar] [CrossRef] - Visconti, F.; Stefanon, L.; Camporeale, C.; Susin, F.; Ridolfi, L.; Lanzoni, S. Bed evolution measurement with flowing water in morphodynamics experiments. Earth Surf. Process. Landf.
**2012**, 37, 818–827. [Google Scholar] [CrossRef]

**Figure 1.**The interpretation of the local coordinate system [19].

**Figure 2.**The initial area-by-number (purple) and volume-by-number (green) grain-size distribution of the bed material.

**Figure 3.**Contour plots: bed changes distribution after each experiment. Circles: local VbW d

_{50}(volume-by-weight) values of the bed surface (size and tone indicate size).

**Figure 4.**The bed change time series in the deposition zone (red line and dots) and in the scour hole (blue line and dots). The discharge time series is also visualized by the black solid line.

**Figure 6.**Calculated bed shear stress distribution by the numerical 3D model. Above: ${k}_{s}=3.0{d}_{90}$; below: ${k}_{s}=0.84{d}_{90}$ . Circles refer to the estimated shear values from the ADV (Acoustic Doppler Velocimeter) measurements.

**Figure 8.**Calculated and measured v

_{hozitontal}(first column), v

_{x}(second column) and v

_{y}(third column) vertical velocity profiles in the three equilibrium states. Three diagrams in a row belong to one vertical component, whose position can be identified by the letters (A, B, C…F) in Figure 7. The y axes show the water depth, while the x axes indicate the horizontal, longitudinal and the transversal velocity values. The model calculation was carried out using ${k}_{s}=0.84{d}_{90}$.

**Figure 9.**Measured and simulated equilibrium bed levels at Q = 58 L/s (top: measured, i: vR; ii: Wilcock and Crowe formula; iii: combined approach).

**Figure 10.**Measured (circles) and calculated (i: vR; ii: Wilcock and Crowe formula; iii: combined approach) d

_{50}distribution at Q = 58 L/s.

**Figure 11.**Measured and simulated equilibrium bed levels at Q = 72 L/s. (top: measured; ii: Wilcock and Crowe formula; iii: combined approach).

**Figure 12.**Measured (circles) and calculated (ii: Wilcock and Crowe formula; iii: combined approach) d

_{50}distribution at Q = 72 L/s.

**Figure 13.**Measured and simulated equilibrium bed levels at Q = 100 L/s. (top: measured; ii: Wilcock and Crowe formula; iii: combined approach).

**Figure 14.**Measured (circles) and calculated (ii: Wilcock and Crowe formula; iii: combined approach) d

_{50}distribution at Q = 100 L/s.

**Figure 15.**Equilibrium bed levels and d

_{90}= 0.021 m isolines (dotted lines) at Q = 58 L/s, resulting from the combined approach.

**Figure 16.**Equilibrium bed shear stress distribution and d

_{90}= 0.021 m isolines (dotted lines) at Q = 58 L/s, resulting from the combined approach.

Q, L/s | h_{out}, m | v_{avg}, m/s | Fr, - | Re, - | τ_{avg}, N/m^{2} | S_{bed}, - |
---|---|---|---|---|---|---|

58 | 0.137 | 0.42 | 0.15 | 45,500 | 1.9 | 0.0027 |

72 | 0.143 | 0.50 | 0.21 | 56,000 | 3.4 | 0.0027 |

100 | 0.175 | 0.57 | 0.25 | 74,100 | 3.7 | 0.0027 |

_{avg}: water depth at the outlet, v

_{avg}: averaged flow velocity, Fr: Froude number, Re: Reynolds number, τ

_{avg}: averaged bed shear stress, S

_{bed}: bed slope.

**Table 2.**The V

_{m}/V

_{c}values, where V

_{m}is the calculated and V

_{c}is the measured volume of the deposition form. W&C: Wilcock and Crowe.

Flow discharge, L/s | Sediment Transport Model | ||
---|---|---|---|

Van Rijn | W&C | Combined | |

58 | 40.62 | 6.47 | 6.38 |

72 | - | 2.12 | 1.10 |

100 | - | 0.48 | 0.54 |

**Table 3.**The V

_{Sh}/V

_{tot}values, where V

_{Sh}is the volume of the shifted and V

_{tot}is the total volume of the total deposition amount.

Measured | Sediment Transport Model | |
---|---|---|

W&C | Combined | |

0.39 | 0.09 | 0.54 |

© 2017 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Török, G.T.; Baranya, S.; Rüther, N.
3D CFD Modeling of Local Scouring, Bed Armoring and Sediment Deposition. *Water* **2017**, *9*, 56.
https://doi.org/10.3390/w9010056

**AMA Style**

Török GT, Baranya S, Rüther N.
3D CFD Modeling of Local Scouring, Bed Armoring and Sediment Deposition. *Water*. 2017; 9(1):56.
https://doi.org/10.3390/w9010056

**Chicago/Turabian Style**

Török, Gergely T., Sándor Baranya, and Nils Rüther.
2017. "3D CFD Modeling of Local Scouring, Bed Armoring and Sediment Deposition" *Water* 9, no. 1: 56.
https://doi.org/10.3390/w9010056