# Three-Dimensional Numerical Study of Free-Flow Sediment Flushing to Increase the Flushing Efficiency: A Case-Study Reservoir in Japan

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## Abstract

**:**

## 1. Introduction

## 2. Study Case Description

#### 2.1. Site Background

^{2}, and the length of the river is 85 km. The bed slope is steep and varies between 1% and 20%. In the catchment area of the Kurobe River, the average rainfall and total sediment yield are 4000 mm and 1.4 × 10

^{6}m

^{3}/year, respectively, which are both among the highest in Japan [32]. Dashidaira dam, with a height of 76.7 m, was constructed in 1985 by Kansai Electric Power Company in the Kurobe River and has a power of 124 MW. The average bed slope of the reservoir is about 2.2% and also the gross and effective storage capacities are 9.01 and 1.66 million m

^{3}, respectively [7,32]. The mean annual sediment load and the ratio of the total storage to the mean annual runoff in the Dashidaira reservoir are 0.62 × 10

^{6}m

^{3}and 0.00674, respectively [33]. The Dashidaira dam is one of the first dams in Japan constructed with sediment-flushing facilities. The first flushing operation in the Dashidaira reservoir was performed 6 years after the dam construction in 1991. Subsequently, the accumulated distorted sediments within 6 years were diffused to the downstream and estuary zone with many negative environmental implications. After that, the flushing operation is performed every year during the first major flood event in the rainy season to reduce negative environmental impacts on the downstream areas of the dam since aquatic animals have been adapted to the perturbation caused by floods. A flood not only provides enough energy to transport the flood-born sediments through the reservoir, but also scour the previously deposited sediments from the reservoir.

#### 2.2. Field Data Organization

^{3}.

## 3. Numerical Model

#### 3.1. Flow Field Modeling

_{i}is the special geometrical scale, ρ is the water density, g is the acceleration due to gravity and z is the water-level elevation.

_{i}) is a function of the Froude number, the flow direction and the location of neighboring cells:

_{p}is the water level elevation in the cell, z

_{i}is the water level elevation in the ith neighbor cell, p

_{p}is the pressure in the cell and p

_{i}is the pressure in the ith neighbor cell.

_{max}is the maximum number of grid cells in the vertical direction, and p is a user-defined parameter for the number of grid cells.

#### 3.2. Sediment Transport Modeling

_{j}is the water velocity, w is the fall velocity of the sediments, c is the sediment concentration over time t and spatial geometries (i.e., x and z), and Γ

_{T}is the turbulent diffusivity. To compute the equilibrium suspended sediment concentration, used as the boundary condition in the cells close to the bed, an empirical formula developed by Van Rijn is used [39]:

_{i}is the diameter of the i-th fraction, ν is the kinematic viscosity, τ is the shear stress, τ

_{c,i}is the critical shear stress for d

_{i}, which was calculated from the Shield’s curve, and ρ

_{w}and ρ

_{s}are the density of the water and sediment, respectively.

_{b,i}is the sediment transport rate for the $i$-th fraction of the bed load per unit width, d

_{50}is the characteristic sediment size (median sediment size), r is the hydraulic radius, and I is the slope of the energy line. The Van Rijn formula has been used to simulate a wide variety of sediment transport issues in both physical model and prototype scales:

## 4. Numerical Simulations

#### 4.1. Model Setup and Calibration

^{3}. The water levels and inflow discharge fluctuations, which were employed as the hydrodynamic boundary conditions in the simulations, are shown in Figure 1c. In addition, a non-uniform bed material size distribution with spatially varying fractions was introduced to the model by using the seven representative sediment sizes shown in Table 1. More specifically, the computational domain was divided into a number of small segments, and each segment had its own non-uniform grain size distribution. Because the wash load, by its definition, is transported without deposition through the reservoir, its effect on the simulation of the flushing process was neglected in the computations.

^{3}m

^{3}), and if it was larger than 75% compared to the measured one, it was considered a model case for further assessment. Then, the final simulated bed topography pattern was compared, both qualitatively and quantitatively, with the measurements. A qualitative assessment was performed to check whether the erosion in area I, where the coarser sediments exist, could be captured, and a quantitative assessment was conducted to measure the deviation of the simulated bed levels from the measured ones. Therefore, Mean Absolute Error (MAE) of the simulated bed levels after the flushing operation was calculated. Table 2 summarizes the results of the TVFS sensitivity analysis for the major selected empirical parameters. Also, variations in the MAE of the simulated bed levels for each case have been calculated. The TVFS increased with increasing the active layer thickness and water content but decreased with increasing the critical angle of repose. When a larger amount of bed materials can be eroded during one time step (i.e., a thicker active layer), a higher volume of erosion from the deposits is expected. A higher water content in the sediment deposits (e.g., 50%), which decreases the submerged density of the bed material, is assumed to lead to greater sediment entrainment. A higher critical angle of repose retains a steeper side bank of the flushing channel after each time step, resulting in further deepening of the channel, which is not an efficient approach for increasing the TVFS in the numerical model. In contrast, the lateral development of the flushing channel (i.e., channel widening), which is favorable for increasing the TVFS, can be achieved using a lower critical angle of repose. The roughness, active layer thickness, water content of the bed material, and critical angle of repose were after the calibration set to 0.5 m, 1 m, 40% and 32 degrees, respectively, because the application of these values can result in a reasonable TVFS and accuracy (i.e., 313.0 × 10

^{3}m

^{3}, and 1.8 m) and can also satisfy the mentioned qualitative criteria.

#### 4.2. Evaluation of the Flow Field and Morphological Bed Changes in the Reservoir

_{i_ms}is the measured or simulated bed level after the flushing operation at each grid node and z

_{i_reference}is the measured or simulated reference bed level at the corresponding node, which is used for comparison purposes to provide information about erosion or deposition over a specific zone of the computational grid. Furthermore, n is the number of grid nodes considered for comparison purposes. Positive and negative values of BCI represent depositional and erosional conditions, respectively. In other words, BCI reveals the average change in the bed level of each target zone and readily indicates the dominant morphological process (i.e., erosion or deposition) in the zone compared to the reference case.

## 5. Discussion

#### 5.1. Hydrodynamic Scenarios and Their Impacts on the Bed Morphology and Flushing Efficiency

#### 5.1.1. Discharge Scenarios

^{3}/s of additional inflow discharge has been added to the original discharges during the free-flow stage of the 2012 flushing operation. With an original TVFS value equals to 313.0 × 10

^{3}m

^{3}in the reference case (i.e., resulting bed topography after simulation of 2012 flushing), the TVFS increased to 356.0 × 10

^{3}in the ADF 75 scenario, 396.1 × 10

^{3}in the ADF 110 scenario, and 425.0 × 10

^{3}m

^{3}in the ADF 170 scenario. The effects of introducing constant additional discharges under various ADF scenarios on the FE and the TVFS are illustrated in Figure 4c. The horizontal axis shows the ratio of average discharge during the free-flow stage using different ADF scenarios (i.e., Q

_{2}) to the average discharge during the free-flow stage when no additional discharge is introduced in the reference case (i.e., Q

_{1}). FE

_{2}and FE

_{1}are the flushing efficiencies when an ADF scenario is employed and when no additional discharge is employed in the reference case, respectively. The TVFS increases when the discharge increases during the free-flow stage. The FE values reached approximately −6.5% when the ADF 60 scenario was used. In this case, the increase in the flushed sediment volume was smaller than the increase in the used water volume according to the FE definition. Under the ADF 75, 90, and 110 scenarios, both the FE and TVFS increased with increasing average discharge during the free-flow stage. Then, the FE variation trended downward until a stable level was reached for the ADF 150 and ADF 170 scenarios. In contrast, the TVFS continued to increase. Under the given conditions, increasing the discharge magnitude during the free-flow condition can increase the TVFS, but this increase is not proportional to the discharge increase that causes the decrease in the FE for some cases. According to the diagram shown in Figure 4c, when the average discharge during the free-flow stage increased by approximately 56% under the ADF 110 scenario, (i.e., Q

_{2}/Q

_{1}= 1.56), the FE increased approximately by 5%. Under these conditions, the total used water volume for the flushing operation increased by approximately 21%. In Table 3 the average bed level changes compared to the reference case using the BCI parameter in the upstream, midstream and downstream areas have been revealed for the ADF 75, ADF 110, and ADF 170 scenarios. As shown in Figure 4c and Table 3, introducing additional discharge increases the erosion in all areas by between 3% and 36% depending on the additional discharge, but the effect in the areas close to the dam (i.e., areas II and III) is more pronounced. Instead of adding a constant discharge to the original discharge values during the free-flow condition in the reference case, another scenario (i.e., the PDF scenario) using the same additional water volume over a shorter duration and in the form of discharge pulses was tested. The PDF scenario was introduced to determine whether changing the characteristics of the additional inflowing water (e.g., the discharge intensity) markedly affects the quantity of flushed sediments and the bed changes in specific zones of the reservoir. The concept of the PDF scenario has been illustrated schematically in Figure 4d. It should be noted that before the flushing operation, area III was mainly covered with fine materials. During the simulation of the flushing operation, eroded coarser materials from area I were deposited in the lower parts of area III due to the reduced bed shear stress. Thus, introducing an additional discharge during the free-flow condition can contribute to flushing the deposited sediments out of this area.

^{3}/s discharge pulse within 8 h in the first half of the free-flow flushing (i.e., P1 110 8) and a second discharge pulse with variable magnitude and duration in the second half (i.e., P2 Q

_{2}t

_{2}) were introduced for further assessments.

^{3}/s of additional inflow during the free-flow stage may result in a further increase in the flushing channel width and depth in the lower part of area II and throughout area III.

#### 5.1.2. Water Level Scenarios

_{2}) to the original one (i.e., ∆h

_{1}) at the beginning of the target limb during the drawdown stage. On the left vertical axis, FE

_{2}represents the flushing efficiency when a WDS scenario is employed, and FE

_{1}represents the flushing efficiency when the original water level of the 2012 flushing operation is applied. All calculated and presented values are relative to the reference case (i.e., the 2012 flushing operation). As shown in Figure 7b, the FE variations are overall directly related to the variations in ∆h

_{2}/∆h

_{1}. However, removing the coarser material from the far upstream area of the reservoir requires a high extra drop in the water level (i.e., a high ∆h

_{2}/∆h

_{1}). Moreover, in some cases, increasing ∆h

_{2}/∆h

_{1}results in lower TVFS and FE values because coarser eroded material moves from upstream areas to downstream areas and is deposited on finer materials in the deeper areas. If the driving forces produced by the extra drop in the water level are not strong enough to remobilize the newly deposited coarser sediments overlying finer sediments, the erosion of finer fractions may be lower, resulting in lower TVFS values and consequently lower FE

_{2}values. Table 3 also shows the average BCI values in the upstream, midstream and downstream areas of the Dashidaira reservoir after the application of the WDS −0.5, WDS −2.5, and WDS −3.5 scenarios. As shown in Table 3, compared to the reference case with the TVFS of 313.0 × 10

^{3}m

^{3}, the TVFS increases slightly when the magnitude of the extra drop in the water level is small (e.g., 0.5 m in the WDS −0.5 scenario). When the extra drop in the water level is larger (e.g., 2.5 m), the TVFS increases but not remarkably. Although the water-level decrease can enhance the relative roughness (i.e., the ratio of the roughness height to the water depth), this increased roughness is not high enough to lead to the erosion of the coarser materials in the upstream areas. Thus, the main effect is limited to the finer materials in the WDS −0.5 and WDS −2.5 scenarios. Due to the larger extra water level drop in the WDS −3.5 scenario, higher bed erosion occurs over the entire reservoir, including the upstream areas covered with coarser materials. In Figure 5, the bed changes in different cross-sections located in areas I, II, and III under the WDS −3.5 scenario are compared to the bed levels in the reference simulations.

#### 5.2. Auxiliary Channel Scenario

^{3}m

^{3}, compared to the 313.0 × 10

^{3}m

^{3}of the reference case. In Figure 9b–d, the final bed levels in different cross-sections of area II are shown after the flushing operation and are compared to the bed levels in the reference case. One can clearly see that the bed levels decreased noticeably along the thalweg of the auxiliary flushing channel and meanwhile the channel widened. Both deepening and widening process of the auxiliary channel contributes in increasing the TVFS and subsequently the flushing efficiency.

## 6. Conclusions

- Both the MPM and Van Rijn formulas yielded satisfactory performances in the simulation of bed changes in specific segments of the reservoir during the flushing operation (e.g., MPM formula in the upper half of the reservoir and Van Rijn formula in the vicinity of the Dam). These sediment transport formulas have been developed empirically to calculate the sediment transport for a given set of sediment sizes and hydrodynamic boundary conditions. However, the bed sediment size distribution, bed roughness, and hydrodynamic boundary conditions change dynamically during the free-flow flushing process. Such significant changes cannot be handled by empirical sediment transport formulas due to their inherent limitations. Nevertheless, the MPM bed load sediment transport formula qualitatively and quantitatively performed better than the Van Rijn formula for the entire reservoir. The MPM formula was able to achieve TVFS values that were more than 75% that of the measured TVFS values. Due to the application of the empirical formulas, the alluvial roughness also could not be estimated appropriately, which further magnifies the mentioned inability of the sediment transport formulas to accurately represent the morphological bed changes.
- For the Dashidaira reservoir, introducing an artificial additional discharge during the free-flow stage is practically feasible since this discharge can be supplied from upstream reservoirs. In addition, because this additional discharge is introduced when the flushing gates are fully opened and the water level is low, this discharge can be passed through the bottom outlets if its value is less than the maximum capacity of the outlets. Additional discharge has two major effects: first, it increases the induced bed shear stress and bed erosion and supplies an additional driving force to transport eroded sediments farther downstream in the reservoir and flush them out from the reservoir; second, it causes the water level to increase in the downstream river channel, which can be beneficial from an environmental point of view because it washes away fine materials from the downstream channel terraces (thereby preventing river channel clogging). However, it was found that introducing the extra discharge in the form of two discharge pulses with a larger discharge pulse in the second half of the free-flow stage more efficiently increases the FE ratio and the bed degradation in the upstream areas covered with coarser materials. The numerical outcomes showed that introducing approximately 21% more water from upstream reservoirs (i.e., an approximately 56% increase in the average free-flow discharge) can enhance the FE by approximately 5−13% compared to the reference case (i.e., the 2012 flushing operation), depending on how this additional discharge is delivered.
- The construction of an auxiliary longitudinal flushing channel in the dead zone area of the Dashidaira reservoir causes a portion of the flushing flow to deviate from the main channel into the auxiliary channel and to enter the main channel again via a confluence downstream of the diversion point. The non-diverted flow continues along its original path along the thalweg of the main flushing channel and the diverted flow towards the auxiliary channel scour the deposited sediments from the targeted dead zone in the reservoir. The flushing processes associated with the auxiliary longitudinal channel result in a flushing channel that is overall longer and wider. Hence, the FE is higher by as much as approximately 9% compared to the reference case.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**(

**a**) Site map of the Kurobe River showing the location of the Dashidaira reservoir [31]; (

**b**) Measured bed topography of the Dashidaira reservoir before the flushing operation in June 2012 and locations of the cross-sections A-L for further assessment of the bed variations in the upstream (i.e., area I), midstream (i.e., area II), and downstream (i.e., area III) portions of the reservoir; (

**c**) Water level and discharge rates during the flushing operation in June 2012; (

**d**) Onsite view of the dead zone area during the 2012 flushing operation (the dead zone area has been shown with ellipse dashed line and arrows show the flow direction).

**Figure 2.**Computational grid (

**a1**) at the beginning of the drawdown stage (t = 10 h) and (

**a2**) during the free-flow condition in the Dashidaira reservoir (t = 32 h); corresponding surface velocity fields: (

**b1**) at the beginning of the drawdown stage (t = 10 h) and (

**b2**) during the free-flow condition (t = 32 h). The illustration on the right in (

**b1**) shows the reverse flow domain and stagnant water zone.

**Figure 3.**(

**a**) Plan view of the measured bed topography after the 2012 flushing operation; Plan view of the simulated bed topography using (

**b**) the MPM formula and (

**c**) the Van Rijn formula.

**Figure 4.**(

**a**) Constant additional discharge rates used for different ADF scenarios in the Dashidaira reservoir. These additional rates are added to the original discharge rates shown in Figure 1c; (

**b**) Modified hydrodynamic boundary conditions for different ADF scenarios in the Dashidaira reservoir; (

**c**) Non-dimensional curves showing the relationships among TVFS, FE, and the water discharge used under different ADF scenarios compared to the reference case; (

**d**) Schematic figure illustrating the PDF scenario with a variable discharge pulse in the second half of the free-flow stage.

**Figure 5.**Measured bed levels before flushing along with the simulated bed levels after flushing in the reference case and under the ADF 110, ADF 170 and WDS −3.5 scenarios at (

**a1**,

**a2**) cross section A-A; (

**b1**,

**b2**) cross section E-E; (

**c1**,

**c2**) cross section F-F; (

**d1**,

**d2**) cross section H-H; (

**e1**,

**e2**) cross section K-K; and (

**f1**,

**f2**) cross-section L-L. Locations of the cross sections can be found in Figure 1b. Mea. and Sim. are abbreviations for Simulated and Measured, respectively.

**Figure 6.**Measured bed levels before flushing and the simulated bed levels after flushing under the ADF 110 and PDF P1 110 8-P2 183.5 6 scenarios at (

**a**) cross section A-A; (

**b**) cross section B-B; (

**c**) cross section C-C; (

**d**) cross section D-D; and (

**e**) cross section E-E. Locations of the sections can be found in Figure 1b.

**Figure 7.**(

**a**) Utilized water levels and discharge rates for different WDS scenarios; (

**b**) Non-dimensional curves showing the relationship among TVFS, FE, and ∆h under different WDS scenarios compared to the reference case.

**Figure 8.**(

**a**) Schematic illustration of the concept of longitudinal auxiliary flushing channel in the dead zone area of the Dashidaira reservoir; The surface velocity field in different stages using an auxiliary flushing channel: (

**b**) before onset of the drawdown stage (i.e., t = 5 h); (

**c**) at the beginning of the drawdown stage (i.e., t = 10 h); (

**d**) at the middle of the drawdown stage (i.e., t = 16 h); and (

**e**) during the free-flow condition (i.e., t = 32 h).

**Figure 9.**(

**a**) Plan view of the final simulated bed levels using an auxiliary flushing channel along the dead zone of area II. Measured bed levels before flushing and simulated ones after flushing in the reference case along with simulated ones using an auxiliary flushing channel, at the location of (

**b**) cross section F-F; (

**c**) cross section G-G; (

**d**) cross section H-H. Location of the cross sections can be found in Figure 1b.

**Table 1.**Average sediment size distribution in the specified cross-sections shown in Figure 1b. Cs. is an abbreviation for Cross-section.

Sediment Size (mm) | Cs. A-A (%) | Cs. B-B (%) | Cs. C-C (%) | Cs. D-D (%) | Cs. E-E (%) | Cs. F-F (%) | Cs. G-G (%) | Cs. H-H (%) | Cs. I-I (%) | Cs. J-J (%) | Cs. K-K (%) | Cs. L-L (%) |
---|---|---|---|---|---|---|---|---|---|---|---|---|

316 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

118.3 | 74 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 40 |

37.4 | 6 | 73 | 75 | 70 | 69 | 4 | 1 | 0 | 0 | 0 | 0 | 30 |

11.8 | 4 | 7 | 6 | 8 | 13 | 14 | 5 | 0 | 0 | 0 | 0 | 16 |

3.7 | 3 | 14 | 11 | 14 | 12 | 25 | 18 | 0 | 0 | 0 | 0 | 3 |

1.2 | 5 | 4 | 1 | 3 | 2 | 23 | 21 | 0 | 6 | 13 | 0 | 1 |

0.37 | 6 | 2 | 7 | 5 | 4 | 35 | 55 | 100 | 94 | 87 | 100 | 10 |

**Table 2.**Sensitivity analysis of the TVFS in reference case with respect to the selected empirical parameters along with variation of the MAE of simulated bed levels for each case.

Parameter | Active Layer Thickness (m) | Water Content of the Bed Material(%) | Critical Angle of Repose (Degree) | ||||||
---|---|---|---|---|---|---|---|---|---|

0.3 | 0.45 | 0.85 | 50 | 43 | 38 | 33 | 34 | 35 | |

TVFS (×10^{−3} m^{3}) | 261.6 | 290.5 | 299.8 | 369.1 | 306.2 | 316.8 | 311.0 | 302.7 | 284.5 |

MAE (m) | 2.17 | 1.73 | 1.95 | 2.25 | 2.10 | 1.75 | 1.98 | 1.54 | 1.98 |

**Table 3.**Average bed level changes in different areas of the reservoir under different ADF, PDF, and WDS scenarios. For ADF and WDS scenarios, the simulated bed levels after 2012 flushing operation were used as the reference case to extract the BCI parameter, whereas for PDF scenario the simulated bed levels under the ADF 110 scenario were used as the reference case.

Scenario | ADF 75 | ADF 110 | ADF 170 | ||||||
---|---|---|---|---|---|---|---|---|---|

Area | I | II | III | I | II | III | I | II | III |

BCI (m) | 0.32 | −0.47 | −0.54 | 0.06 | −0.49 | −0.55 | 0.20 | −0.76 | −0.90 |

TVFS (×10^{−3} m^{3}) | 356.0 | 396.1 | 425.0 | ||||||

Scenario | PDF P1 110 8-P2 137.5 8 | PDF P1 110 8-P2 157 7 | PDF P1 110 8-P2 183.5 6 | ||||||

Area | I | II | III | I | II | III | I | II | III |

BCI (m) | −0.01 | −0.09 | −0.21 | 0.02 | −0.04 | −0.20 | −0.09 | 0.01 | 0.04 |

TVFS (×10^{−3} m^{3}) | 426.2 | 417.3 | 410.9 | ||||||

Scenario | WDS −0.5 | WDS −2.5 | WDS −3.5 | ||||||

Area | I | II | III | I | II | III | I | II | III |

BCI (m) | 0.03 | −0.14 | 0.02 | 0.10 | −0.13 | −0.23 | −0.08 | −0.33 | −0.22 |

TVFS (×10^{−3} m^{3}) | 322.8 | 331.9 | 378.9 |

© 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**

Esmaeili, T.; Sumi, T.; Kantoush, S.A.; Kubota, Y.; Haun, S.; Rüther, N.
Three-Dimensional Numerical Study of Free-Flow Sediment Flushing to Increase the Flushing Efficiency: A Case-Study Reservoir in Japan. *Water* **2017**, *9*, 900.
https://doi.org/10.3390/w9110900

**AMA Style**

Esmaeili T, Sumi T, Kantoush SA, Kubota Y, Haun S, Rüther N.
Three-Dimensional Numerical Study of Free-Flow Sediment Flushing to Increase the Flushing Efficiency: A Case-Study Reservoir in Japan. *Water*. 2017; 9(11):900.
https://doi.org/10.3390/w9110900

**Chicago/Turabian Style**

Esmaeili, Taymaz, Tetsuya Sumi, Sameh A. Kantoush, Yoji Kubota, Stefan Haun, and Nils Rüther.
2017. "Three-Dimensional Numerical Study of Free-Flow Sediment Flushing to Increase the Flushing Efficiency: A Case-Study Reservoir in Japan" *Water* 9, no. 11: 900.
https://doi.org/10.3390/w9110900