Mohammad Nazari-Sharabian, Aliasghar Nazari-Sharabian, Moses Karakouzian, Mehrdad Karami
Abstract
Scour is defined as the erosive action of flowing water, as well as the excavating and carrying away materials from beds and banks of streams, and from the vicinity of bridge foundations, which is one of the main causes of river bridge failures. In the present study, implementing a numerical approach, and using the FLOW-3D model that works based on the finite volume method (FVM), the applicability of using sacrificial piles in different configurations in front of a bridge pier as countermeasures against scouring is investigated. In this regard, the numerical model was calibrated based on an experimental study on scouring around an unprotected circular river bridge pier. In simulations, the bridge pier and sacrificial piles were circular, and the riverbed was sandy. In all scenarios, the flow rate was constant and equal to 45 L/s. Furthermore, one to five sacrificial piles were placed in front of the pier in different locations for each scenario. Implementation of the sacrificial piles proved to be effective in substantially reducing the scour depths. The results showed that although scouring occurred in the entire area around the pier, the maximum and minimum scour depths were observed on the sides (using three sacrificial piles located upstream, at three and five times the pier diameter) and in the back (using five sacrificial piles located upstream, at four, six, and eight times the pier diameter) of the pier. Moreover, among scenarios where single piles were installed in front of the pier, installing them at a distance of five times the pier diameter was more effective in reducing scour depths. For other scenarios, in which three piles and five piles were installed, distances of six and four times the pier diameter for the three piles scenario, and four, six, and eight times the pier diameter for the five piles scenario were most effective.
Keywords
Scouring; River Bridges; Sacrificial Piles; Finite Volume Method (FVM); FLOW-3D.
References
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Mohammad Raze Raeisi Dehkordi1*, Amir Hossein Yeganeh Mazhar1 , Farzaneh Kheradzare2 1– PhD. Student in the Department of Construction and Water Management, Science and Research Unit, Islamic Azad University, Tehran, Iran 2– M.Sc. Graduate Water resource management, Department of Civil Engineering and Mechanics, Ghiaseddin Jamshid Kashani University, Qazvin, Iran
One of the key issues in river engineering is analyzing the flow properties at the intersection of natural rivers and canals. The flow of the side channel moves away from the intersection of the two channels as a result of the exchange of input force from the side channel with the main flow after coming into contact with it. One of the most evident properties of the flow in these sections is the development of a revolving region with low pressure and even negative pressure close to the inner wall of the side channel. One advantage of the whirling flow in this low-pressure region is that it gives the flow enough space to sediment, but it also increases flow speed near the channel’s bottom and outside wall by lowering the intersectional area of the flow. One of the most crucial considerations in the design of these intersections is minimizing sedimentation in the rotating region and scouring in the area above the shear plane.
Materials and methods:
The channel (flume) created in the laboratory based on Weber et al., (2001) model, was employed in the current investigation to confirm the validity and examine other study objectives. The main channel is 21. 95 meters long, while the side channel, which is at a 90-degree angle to the main channel, is 3. 66 meters long. The total downstream discharge is approximately 0. 17 m3/s, with the upstream velocities of the main channel being 0. 166 m/s and the side channel being 0. 5 m/s. In both channels, the flow depth and width are 0. 91 meters and 0. 296 meters, respectively. In this study, 6 various models’ angles of intersection between the main and side channels, inlet flow velocity, intersectional area, and side channel length have been examined. Models 2 and 3 have intersection angles of 60 and 30 degrees, respectively, and share the rest of their attributes with the fundamental model, or model number 1. Model 1 is the same as Weber’s experimental model. The length of the side channel in model 4 is different from model 1. The only difference between model 6 and the basic model is the side channel intake speed.
Results and Discussion
Analyzing the intersection angle The angle between the main channel and the side channel is investigated in this section of the findings. Models 1, 2, and 3 are assessed using the intersection angles of 90, 60, and 30 degrees, respectively. In some studies, the impact of the intersection angle has been examined, but in this study, three-dimensional investigation in transverse and longitudinal sections as well as the plan of the intersection is discussed, as can be observed from the literature review. Considering three models with intersection angles of 90, 60, and 30 degrees, the kinetic energy contours at the channel’s middle height can be obtained for each model. The channel with a 30-degree intersection angle (model 3) has the maximum kinetic energy in the flow. The channel with a 60-degree intersection has the minimum kinetic energy. As a result of the maximum deviation of the flow in the main channel caused by the flow of the side channel, the channel with a 90-degree intersection also has the maximum kinetic energy near the wall in front of the side channel.
Examining the side channel length In model 1, the side channel is 3. 66 meters long, whereas in model 4, it is 5. 52 meters long. This study aims to determine how changing the side channel’s length affects the flow pattern where two channels intersect. The kinetic energy contours were obtained for two states of the channel length, which are known to extend the lateral channel, increase the energy of the flow after the intersection, and shorten the length of the high-kinetic energy zone. When compared to model 1 with a shorter length of the side channel, the width of the flow separation zone is reduced by approximately 20%, which results in less flow sedimentation. Figure 12 illustrates the rotating zones in the flow separation area. The flow separation region’s length is essentially unchanged. Studying the intersection of the lateral channel After determining the lateral channel’s length, its width and, consequently, its intersectional area should be evaluated.
This section compares model 1 width of 0. 91 meters to model 5 width of 1. 40 meters. One of the most recent topics related to the intersection of the main and side channels is examining the intersection of the side channel. In model 5, the side channel’s flow rate has also increased due to an increase in the width or intersection of the channel. The flow rate through the intersection and the momentum of the flow from the side channel and the main channel increase when the side channel flow rate rises. The findings indicate that when flow width and side channel flow rise, energy increases after the inlet.
Investigating the value of inlet speed in the side channel Unlike the preceding sections, which were all concerned with the channel geometry, the inlet velocity in the side channel is one of the hydraulic parameters of the flow. In this section, models 1 and 6 with inlet velocities of the side channel of 0. 5 and 0. 75 m/s are evaluated. According to the modeling, the flow is somewhat horst before and immediately on the intersection of the flow level, but it undergoes a substantial prolapse just after the intersection. Model 6 has a larger volume and height of flow, but a smaller and softer prolapse after the intersection.
Conclusion
Some hydraulic and geometric properties of the intersection of channels have been examined using Flow-3D software. The RNG turbulence model was used for three-dimensional modeling. Some of the results are listed below. The flow is uniform upstream of the main and minor channels and only slightly becomes horst at the intersection. The analysis of the lengthening of the side channel revealed a 20% reduction in the separation zone’s width and a considerable reduction in the kinetic energy at the intersection. The input flow rate of this channel to the intersection increases with the speed and width of the side channel, which accounts for the local drop in the width of the main channel flow.
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•Landslide travel distance is considered for the first time in a predictive equation.
•Predictive equation derived from databases using 3D physical and numerical modeling.
•The equation was successfully tested on the 2018 Anak Krakatau tsunami event.
•The developed equation using three-dimensional data exhibits a 91 % fitting quality.
Abstract
Landslide tsunamis, responsible for thousands of deaths and significant damage in recent years, necessitate the allocation of sufficient time and resources for studying these extreme natural hazards. This study offers a step change in the field by conducting a large number of three-dimensional numerical experiments, validated by physical tests, to develop a predictive equation for the maximum initial amplitude of tsunamis generated by subaerial landslides. We first conducted a few 3D physical experiments in a wave basin which were then applied for the validation of a 3D numerical model based on the Flow3D-HYDRO package. Consequently, we delivered 100 simulations using the validated model by varying parameters such as landslide volume, water depth, slope angle and travel distance. This large database was subsequently employed to develop a predictive equation for the maximum initial tsunami amplitude. For the first time, we considered travel distance as an independent parameter for developing the predictive equation, which can significantly improve the predication accuracy. The predictive equation was tested for the case of the 2018 Anak Krakatau subaerial landslide tsunami and produced satisfactory results.
The Anak Krakatau landslide tsunami on 22nd December 2018 was a stark reminder of the dangers posed by subaerial landslide tsunamis (Ren et al., 2020; Mulia et al. 2020a; Borrero et al., 2020; Heidarzadeh et al., 2020; Grilli et al., 2021). The collapse of the volcano’s southwest side into the ocean triggered a tsunami that struck the Sunda Strait, leading to approximately 450 fatalities (Syamsidik et al., 2020; Mulia et al., 2020b) (Fig. 1). As shown in Fig. 1, landslide tsunamis (both submarine and subaerial) have been responsible for thousands of deaths and significant damage to coastal communities worldwide. These incidents underscored the critical need for advanced research into landslide-generated waves to aid in hazard prediction and mitigation. This is further emphasized by recent events such as the 28th of November 2020 landslide tsunami in the southern coast mountains of British Columbia (Canada), where an 18 million m3 rockslide generated a massive tsunami, with over 100 m wave run-up, causing significant environmental and infrastructural damage (Geertsema et al., 2022).
Physical modelling and numerical simulation are crucial tools in the study of landslide-induced waves due to their ability to replicate and analyse the complex dynamics of landslide events (Kim et al., 2020). In two-dimensional (2D) modelling, the discrepancy between dimensions can lead to an artificial overestimation of wave amplification (e.g., Heller and Spinneken, 2015). This limitation is overcome with 3D modelling, which enables the scaled-down representation of landslide-generated waves while avoiding the simplifications inherent in 2D approaches (Erosi et al., 2019). Another advantage of 3D modelling in studying landslide-generated waves is its ability to accurately depict the complex dynamics of wave propagation, including lateral and radial spreading from the slide impact zone, a feature unattainable with 2D models (Heller and Spinneken, 2015).
Physical experiments in tsunami research, as presented by authors such as Romano et al. (2020), McFall and Fritz (2016), and Heller and Spinneken (2015), have supported 3D modelling works through validation and calibration of the numerical models to capture the complexities of wave generation and propagation. Numerical modelling has increasingly complemented experimental approach in tsunami research due to the latter’s time and resource-intensive nature, particularly for 3D models (Li et al., 2019; Kim et al., 2021). Various numerical approaches have been employed, from Eulerian and Lagrangian frameworks to depth-averaged and Navier–Stokes models, enhancing our understanding of tsunami dynamics (Si et al., 2018; Grilli et al., 2019; Heidarzadeh et al., 2017, 2020; Iorio et al., 2021; Zhang et al., 2021; Kirby et al., 2022; Wang et al., 2021, 2022; Hu et al., 2022). The sophisticated numerical techniques, including the Particle Finite Element Method and the Immersed Boundary Method, have also shown promising results in modelling highly dynamic landslide scenarios (Mulligan et al., 2020; Chen et al., 2020). Among these methods and techniques, FLOW-3D HYDRO stands out in simulating landslide-generated tsunami waves due to its sophisticated technical features such as offering Tru Volume of Fluid (VOF) method for precise free surface tracking (e.g., Sabeti and Heidarzadeh 2022a). TruVOF distinguishes itself through a split Lagrangian approach, adeptly reducing cumulative volume errors in wave simulations by dynamically updating cell volume fractions and areas with each time step. Its intelligent adaptation of time step size ensures precise capture of evolving free surfaces, offering unparalleled accuracy in modelling complex fluid interfaces and behaviour (Flow Science, 2023).
Predictive equations play a crucial role in assessing the potential hazards associated with landslide-generated tsunami waves due to their ability to provide risk assessment and warnings. These equations can offer swift and reasonable evaluations of potential tsunami impacts in the absence of detailed numerical simulations, which can be time-consuming and expensive to produce. Among multiple factors and parameters within a landslide tsunami generation, the initial maximum wave amplitude (Fig. 1) stands out due to its critical role. While it is most likely that the initial wave generated by a landslide will have the highest amplitude, it is crucial to clarify that the term “initial maximum wave amplitude” refers to the highest amplitude within the first set of impulse waves. This parameter is essential in determining the tsunami’s impact severity, with higher amplitudes signalling a greater destructive potential (Sabeti and Heidarzadeh 2022a). Additionally, it plays a significant role in tsunami modelling, aiding in the prediction of wave propagation and the assessment of potential impacts.
In this study, we initially validate the FLOW-3D HYDRO model through a series of physical experiments conducted in a 3D wave tank at University of Bath (UK). Upon confirmation of the model’s accuracy, we use it to systematically vary parameters namely landslide volume, water depth, slope angle, and travel distance, creating an extensive database. Alongside this, we perform a sensitivity analysis on these variables to discern their impacts on the initial maximum wave amplitude. The generated database was consequently applied to derive a non-dimensional predictive equation aimed at estimating the initial maximum wave amplitude in real-world landslide tsunami events.
Two innovations of this study are: (i) The predictive equation of this study is based on a large number of 3D experiments whereas most of the previous equations were based on 2D results, and (ii) For the first time, the travel distance is included in the predictive equation as an independent parameter. To evaluate the performance of our predictive equation, we applied it to a previous real-world subaerial landslide tsunami, i.e., the Anak Krakatau 2018 event. Furthermore, we compare the performance of our predictive equation with other existing equations.
2. Data and methods
The methodology applied in this research is a combination of physical and numerical modelling. Limited physical modelling was performed in a 3D wave basin at the University of Bath (UK) to provide data for calibration and validation of the numerical model. After calibration and validation, the numerical model was employed to model a large number of landslide tsunami scenarios which allowed us to develop a database for deriving a predictive equation.
2.1. Physical experiments
To validate our numerical model, we conducted a series of physical experiments including two sets in a 3D wave basin at University of Bath, measuring 2.50 m in length (WL), 2.60 m in width (WW), and 0.60 m in height (WH) (Fig. 2a). Conducting two distinct sets of experiments (Table 1), each with different setups (travel distance, location, and water depth), provided a robust framework for validation of the numerical model. For wave measurement, we employed a twin wire wave gauge from HR Wallingford (https://equipit.hrwallingford.com). In these experiments, we used a concrete prism solid block, the dimensions of which are outlined in Table 2. In our experiments, we employed a concrete prism solid block with a density of 2600 kg/m3, chosen for its similarity to the natural density of landslides, akin to those observed with the 2018 Anak Krakatau tsunami, where the landslide composition is predominantly solid rather than granular. The block’s form has also been endorsed in prior studies (Watts, 1998; Najafi-Jilani and Ataie-Ashtiani, 2008) as a suitable surrogate for modelling landslide-induced waves. A key aspect of our methodology was addressing scale effects, following the guidelines proposed by Heller et al. (2008) as it is described in Table 1. To enhance the reliability and accuracy of our experimental data, we conducted each physical experiment three times which revealed all three experimental waveforms were identical. This repetition was aimed at minimizing potential errors and inconsistencies in laboratory measurements.
Table 1. The locations and other information of the laboratory setups for making landslide-generated waves in the physical wave basin. This table details the specific parameters for each setup, including slope range (α), slide volume (V), kinematic viscosity (ν), water depth (h), travel distance (D), surface tension coefficient of water (σ), Reynolds number (R), Weber number (W), and the precise coordinates of the wave gauges (WG).
The acceptable ranges for avoiding scale effects are based on the study by Heller et al. (2008).⁎⁎
The Reynolds number (R) is given by g0.5h1.5/ν, with ν denoting the kinematic viscosity. The Weber number (W) is W = ρgh2/σ, where σ represents surface tension coefficient and ρ = 1000kg/m3 is the density of water. In our experiments, conducted at a water temperature of approximately 20 °C, the kinematic viscosity (ν) and the surface tension coefficient of water (σ) are 1.01 × 10−6 m²/s and 0.073 N/m, respectively (Kestin et al., 1978).
Table 2. Specifications of the solid block used in physical experiments for generating subaerial landslides in the laboratory.
Solid-block attributes
Property metrics
Geometric shape
Slide width (bs)
0.26 m
Slide length (ls)
0.20 m
Slide thickness (s)
0.10 m
Slide volume (V)
2.60 × 10−3 m3
Specific gravity, (γs)
2.60
Slide weight (ms)
6.86 kg
2.2. Numerical simulations applying FLOW-3D hydro
The detailed theoretical framework encompassing the governing equations, the computational methodologies employed, and the specific techniques used for tracking the water surface in these simulations are thoroughly detailed in the study by Sabeti et al. (2024). Here, we briefly explain some of the numerical details. We defined a uniform mesh for our flow domain, carefully crafted with a fine spatial resolution of 0.005 m (i.e., grid size). The dimensions of the numerical model directly matched those of our wave basin used in the physical experiment, being 2.60 m wide, 0.60 m deep, and 2.50 m long (Fig. 2). This design ensures comprehensive coverage of the study area. The output intervals of the numerical model are set at 0.02 s. This timing is consistent with the sampling rates of wave gauges used in laboratory settings. The friction coefficient in the FLOW-3D HYDRO is designated as 0.45. This value corresponds to the Coulombic friction measurements obtained in the laboratory, ensuring that the simulation accurately reflects real-world physical interactions.
In order to simulate the landslide motion, we applied coupled motion objects in FLOW-3D-HYDRO where the dynamics are predominantly driven by gravity and surface friction. This methodology stands in contrast to other models that necessitate explicit inputs of force and torque. This approach ensures that the simulation more accurately reflects the natural movement of landslides, which is heavily reliant on gravitational force and the interaction between sliding surfaces. The stability of the numerical simulations is governed by the Courant Number criterion (Courant et al., 1928), which dictates the maximum time step (Δt) for a given mesh size (Δx) and flow speed (U). According to Courant et al. (1928), this number is required to stay below one to ensure stability of numerical simulations. In our simulations, the Courant number is always maintained below one.
In alignment with the parameters of physical experiments, we set the fluid within the mesh to water, characterized by a density of 1000 kg/m³ at a temperature of 20 °C. Furthermore, we defined the top, front, and back surfaces of the mesh as symmetry planes. The remaining surfaces are designated as wall types, incorporating no-slip conditions to accurately simulate the interaction between the fluid and the boundaries. In terms of selection of an appropriate turbulence model, we selected the k–ω model that showed a better performance than other turbulence methods (e.g., Renormalization-Group) in a previous study (Sabeti et al., 2024). The simulations are conducted using a PC Intel® Core™ i7-10510U CPU with a frequency of 1.80 GHz, and a 16 GB RAM. On this PC, completion of a 3-s simulation required approximately 12.5 h.
2.3. Validation
The FLOW-3D HYDRO numerical model was validated using the two physical experiments (Fig. 3) outlined in Table 1. The level of agreement between observations (Oi) and simulations (Si) is examined using the following equation:(1)�=|��−����|×100where ε represents the mismatch error, Oi denotes the observed laboratory values, and Si represents the simulated values from the FLOW-3D HYDRO model. The results of this validation process revealed that our model could replicate the waves generated in the physical experiments with a reasonable degree of mismatch (ε): 14 % for Lab 1 and 8 % for Lab 2 experiments, respectively (Fig. 3). These values indicate that while the model is not perfect, it provides a sufficiently close approximation of the real-world phenomena.
In terms of mesh efficiency, we varied the mesh size to study sensitivity of the numerical results to mesh size. First, by halving the mesh size and then by doubling it, we repeated the modelling by keeping other parameters unchanged. This analysis guided that a mesh size of ∆x = 0.005 m is the most effective for the setup of this study. The total number of computational cells applying mesh size of 0.005 m is 9.269 × 106.
2.4. The dataset
The validated numerical model was employed to conduct 100 simulations, incorporating variations in four key landslide parameters namely water depth, slope angle, slide volume, and travel distance. This methodical approach was essential for a thorough sensitivity analysis of these variables, and for the creation of a detailed database to develop a predictive equation for maximum initial tsunami amplitude. Within the model, 15 distinct slide volumes were established, ranging from 0.10 × 10−3 m3 to 6.25 × 10−3 m3 (Table 3). The slope angle varied between 35° and 55°, and water depth ranged from 0.24 m to 0.27 m. The travel distance of the landslides was varied, spanning from 0.04 m to 0.07 m. Detailed configurations of each simulation, along with the maximum initial wave amplitudes and dominant wave periods are provided in Table 4.
Table 3. Geometrical information of the 15 solid blocks used in numerical modelling for generating landslide tsunamis. Parameters are: ls, slide length; bs, slide width; s, slide thickness; γs, specific gravity; and V, slide volume.
Solid block
ls (m)
bs (m)
s (m)
V (m3)
γs
Block-1
0.310
0.260
0.155
6.25 × 10−3
2.60
Block-2
0.300
0.260
0.150
5.85 × 10−3
2.60
Block-3
0.280
0.260
0.140
5.10 × 10−3
2.60
Block-4
0.260
0.260
0.130
4.39 × 10−3
2.60
Block-5
0.240
0.260
0.120
3.74 × 10−3
2.60
Block-6
0.220
0.260
0.110
3.15 × 10−3
2.60
Block-7
0.200
0.260
0.100
2.60 × 10−3
2.60
Block-8
0.180
0.260
0.090
2.11 × 10−3
2.60
Block-9
0.160
0.260
0.080
1.66 × 10−3
2.60
Block-10
0.140
0.260
0.070
1.27 × 10−3
2.60
Block-11
0.120
0.260
0.060
0.93 × 10−3
2.60
Block-12
0.100
0.260
0.050
0.65 × 10−3
2.60
Block-13
0.080
0.260
0.040
0.41 × 10−3
2.60
Block-14
0.060
0.260
0.030
0.23 × 10−3
2.60
Block-15
0.040
0.260
0.020
0.10 × 10−3
2.60
Table 4. The numerical simulation for the 100 tests performed in this study for subaerial solid-block landslide-generated waves. Parameters are aM, maximum wave amplitude; α, slope angle; h, water depth; D, travel distance; and T, dominant wave period. The location of the wave gauge is X=1.030 m, Y=1.210 m, and Z=0.050 m. The properties of various solid blocks are presented in Table 3.
Test-
Block No
α (°)
h (m)
D (m)
T(s)
aM (m)
1
Block-7
45
0.246
0.029
0.510
0.0153
2
Block-7
45
0.246
0.030
0.505
0.0154
3
Block-7
45
0.246
0.031
0.505
0.0156
4
Block-7
45
0.246
0.032
0.505
0.0158
5
Block-7
45
0.246
0.033
0.505
0.0159
6
Block-7
45
0.246
0.034
0.505
0.0160
7
Block-7
45
0.246
0.035
0.505
0.0162
8
Block-7
45
0.246
0.036
0.505
0.0166
9
Block-7
45
0.246
0.037
0.505
0.0167
10
Block-7
45
0.246
0.038
0.505
0.0172
11
Block-7
45
0.246
0.039
0.505
0.0178
12
Block-7
45
0.246
0.040
0.505
0.0179
13
Block-7
45
0.246
0.041
0.505
0.0181
14
Block-7
45
0.246
0.042
0.505
0.0183
15
Block-7
45
0.246
0.043
0.505
0.0190
16
Block-7
45
0.246
0.044
0.505
0.0197
17
Block-7
45
0.246
0.045
0.505
0.0199
18
Block-7
45
0.246
0.046
0.505
0.0201
19
Block-7
45
0.246
0.047
0.505
0.0191
20
Block-7
45
0.246
0.048
0.505
0.0217
21
Block-7
45
0.246
0.049
0.505
0.0220
22
Block-7
45
0.246
0.050
0.505
0.0226
23
Block-7
45
0.246
0.051
0.505
0.0236
24
Block-7
45
0.246
0.052
0.505
0.0239
25
Block-7
45
0.246
0.053
0.510
0.0240
26
Block-7
45
0.246
0.054
0.505
0.0241
27
Block-7
45
0.246
0.055
0.505
0.0246
28
Block-7
45
0.246
0.056
0.505
0.0247
29
Block-7
45
0.246
0.057
0.505
0.0248
30
Block-7
45
0.246
0.058
0.505
0.0249
31
Block-7
45
0.246
0.059
0.505
0.0251
32
Block-7
45
0.246
0.060
0.505
0.0257
33
Block-1
45
0.246
0.045
0.505
0.0319
34
Block-2
45
0.246
0.045
0.505
0.0294
35
Block-3
45
0.246
0.045
0.505
0.0282
36
Block-4
45
0.246
0.045
0.505
0.0262
37
Block-5
45
0.246
0.045
0.505
0.0243
38
Block-6
45
0.246
0.045
0.505
0.0223
39
Block-7
45
0.246
0.045
0.505
0.0196
40
Block-8
45
0.246
0.045
0.505
0.0197
41
Block-9
45
0.246
0.045
0.505
0.0198
42
Block-10
45
0.246
0.045
0.505
0.0184
43
Block-11
45
0.246
0.045
0.505
0.0173
44
Block-12
45
0.246
0.045
0.505
0.0165
45
Block-13
45
0.246
0.045
0.404
0.0153
46
Block-14
45
0.246
0.045
0.404
0.0124
47
Block-15
45
0.246
0.045
0.505
0.0066
48
Block-7
45
0.202
0.045
0.404
0.0220
49
Block-7
45
0.204
0.045
0.404
0.0219
50
Block-7
45
0.206
0.045
0.404
0.0218
51
Block-7
45
0.208
0.045
0.404
0.0217
52
Block-7
45
0.210
0.045
0.404
0.0216
53
Block-7
45
0.212
0.045
0.404
0.0215
54
Block-7
45
0.214
0.045
0.505
0.0214
55
Block-7
45
0.216
0.045
0.505
0.0214
56
Block-7
45
0.218
0.045
0.505
0.0213
57
Block-7
45
0.220
0.045
0.505
0.0212
58
Block-7
45
0.222
0.045
0.505
0.0211
59
Block-7
45
0.224
0.045
0.505
0.0208
60
Block-7
45
0.226
0.045
0.505
0.0203
61
Block-7
45
0.228
0.045
0.505
0.0202
62
Block-7
45
0.230
0.045
0.505
0.0201
63
Block-7
45
0.232
0.045
0.505
0.0201
64
Block-7
45
0.234
0.045
0.505
0.0200
65
Block-7
45
0.236
0.045
0.505
0.0199
66
Block-7
45
0.238
0.045
0.404
0.0196
67
Block-7
45
0.240
0.045
0.404
0.0194
68
Block-7
45
0.242
0.045
0.404
0.0193
69
Block-7
45
0.244
0.045
0.404
0.0192
70
Block-7
45
0.246
0.045
0.505
0.0190
71
Block-7
45
0.248
0.045
0.505
0.0189
72
Block-7
45
0.250
0.045
0.505
0.0187
73
Block-7
45
0.252
0.045
0.505
0.0187
74
Block-7
45
0.254
0.045
0.505
0.0186
75
Block-7
45
0.256
0.045
0.505
0.0184
76
Block-7
45
0.258
0.045
0.505
0.0182
77
Block-7
45
0.259
0.045
0.505
0.0183
78
Block-7
45
0.260
0.045
0.505
0.0191
79
Block-7
45
0.261
0.045
0.505
0.0192
80
Block-7
45
0.262
0.045
0.505
0.0194
81
Block-7
45
0.263
0.045
0.505
0.0195
82
Block-7
45
0.264
0.045
0.505
0.0195
83
Block-7
45
0.265
0.045
0.505
0.0197
84
Block-7
45
0.266
0.045
0.505
0.0197
85
Block-7
45
0.267
0.045
0.505
0.0198
86
Block-7
45
0.270
0.045
0.505
0.0199
87
Block-7
30
0.246
0.045
0.505
0.0101
88
Block-7
35
0.246
0.045
0.505
0.0107
89
Block-7
36
0.246
0.045
0.505
0.0111
90
Block-7
37
0.246
0.045
0.505
0.0116
91
Block-7
38
0.246
0.045
0.505
0.0117
92
Block-7
39
0.246
0.045
0.505
0.0119
93
Block-7
40
0.246
0.045
0.505
0.0121
94
Block-7
41
0.246
0.045
0.505
0.0127
95
Block-7
42
0.246
0.045
0.404
0.0154
96
Block-7
43
0.246
0.045
0.404
0.0157
97
Block-7
44
0.246
0.045
0.404
0.0162
98
Block-7
45
0.246
0.045
0.505
0.0197
99
Block-7
50
0.246
0.045
0.505
0.0221
100
Block-7
55
0.246
0.045
0.505
0.0233
In all these 100 simulations, the wave gauge was consistently positioned at coordinates X=1.09 m, Y=1.21 m, and Z=0.05 m. The dominant wave period for each simulation was determined using the Fast Fourier Transform (FFT) function in MATLAB (MathWorks, 2023). Furthermore, the classification of wave types was carried out using a wave categorization graph according to Sorensen (2010), as shown in Fig. 4a. The results indicate that the majority of the simulated waves are on the border between intermediate and deep-water waves, and they are categorized as Stokes waves (Fig. 4a). Four sample waveforms from our 100 numerical experiments are provided in Fig. 4b.
The dataset in Table 4 was used to derive a new predictive equation that incorporates travel distance for the first time to estimate the initial maximum tsunami amplitude. In developing this equation, a genetic algorithm optimization technique was implemented using MATLAB (MathWorks 2023). This advanced approach entailed the use of genetic algorithms (GAs), an evolutionary algorithm type inspired by natural selection processes (MathWorks, 2023). This technique is iterative, involving selection, crossover, and mutation processes to evolve solutions over several generations. The goal was to identify the optimal coefficients and powers for each landslide parameter in the predictive equation, ensuring a robust and reliable model for estimating maximum wave amplitudes. Genetic Algorithms excel at optimizing complex models by navigating through extensive combinations of coefficients and exponents. GAs effectively identify highly suitable solutions for the non-linear and complex relationships between inputs (e.g., slide volume, slope angle, travel distance, water depth) and the output (i.e., maximum initial wave amplitude, aM). MATLAB’s computational environment enhances this process, providing robust tools for GA to adapt and evolve solutions iteratively, ensuring the precision of the predictive model (Onnen et al., 1997). This approach leverages MATLAB’s capabilities to fine-tune parameters dynamically, achieving an optimal equation that accurately estimates aM. It is important to highlight that the nondimensionalized version of this dataset is employed to develop a predictive equation which enables the equation to reproduce the maximum initial wave amplitude (aM) for various subaerial landslide cases, independent of their dimensional differences (e.g., Heler and Hager 2014; Heller and Spinneken 2015; Sabeti and Heidarzadeh 2022b). For this nondimensionalization, we employed the water depth (h) to nondimensionalize the slide volume (V/h3) and travel distance (D/h). The slide thickness (s) was applied to nondimensionalize the water depth (h/s).
2.5. Landslide velocity
In discussing the critical role of landslide velocity for simulating landslide-generated waves, we focus on the mechanisms of landslide motion and the techniques used to record landslide velocity in our simulations (Fig. 5). Also, we examine how these methods were applied in two distinct scenarios: Lab 1 and Lab 2 (see Table 1 for their details). Regarding the process of landslide movement, a slide starts from a stationary state, gaining momentum under the influence of gravity and this acceleration continues until the landslide collides with water, leading to a significant reduction in its speed before eventually coming to a stop (Fig. 5) (e.g., Panizzo et al. 2005).
To measure the landslide’s velocity in our simulations, we attached a probe at the centre of the slide, which supplied a time series of the velocity data. The slide’s velocity (vs) peaks at the moment it enters the water (Fig. 5), a point referred to as the impact time (tImp). Following this initial impact, the slides continue their underwater movement, eventually coming to a complete halt (tStop). Given the results in Fig. 5, it can be seen that Lab 1, with its longer travel distance (0.070 m), exhibits a higher peak velocity of 1.89 m/s. This increase in velocity is attributed to the extended travel distance allowing more time for the slide to accelerate under gravity. Whereas Lab 2, featuring a shorter travel distance (0.045 m), records a lower peak velocity of 1.78 m/s. This difference underscores how travel distance significantly influences the dynamics of landslide motion. After reaching the peak, both profiles show a sharp decrease in velocity, marking the transition to submarine motion until the slides come to a complete stop (tStop). There are noticeable differences observable in Fig. 5 between the Lab-1 and Lab-2 simulations, including the peaks at 0.3 s . These variations might stem from the placement of the wave gauge, which differs slightly in each scenario, as well as the water depth’s minor discrepancies and, the travel distance.
2.6. Effect of air entrainment
In this section we examine whether it is required to consider air entrainment for our modelling or not as the FLOW-3D HYDRO package is capable of modelling air entrainment. The process of air entrainment in water during a landslide tsunami and its subsequent transport involve two key components: the quantification of air entrainment at the water surface, and the simulation of the air’s transport within the fluid (Hirt, 2003). FLOW-3D HYDRO employs the air entrainment model to compute the volume of air entrained at the water’s surface utilizing three approaches: a constant density model, a variable density model accounting for bulking, and a buoyancy model that adds the Drift-FLUX mechanism to variable density conditions (Flow Science, 2023). The calculation of the entrainment rate is based on the following equation:(2)�������=������[2(��−�����−2�/���)]1/2where parameters are: Vair, volume of air; Cair, entrainment rate coefficient; As, surface area of fluid; ρ, fluid density; k, turbulent kinetic energy; gn, gravity normal to surface; Lt, turbulent length scale; and σ, surface tension coefficient. The value of k is directly computed from the Reynolds-averaged Navier-Stokes (RANS) (k–w) calculations in our model.
In this study, we selected the variable density + Drift-FLUX model, which effectively captures the dynamics of phase separation and automatically activates the constant density and variable density models. This method simplifies the air-water mixture, treating it as a single, homogeneous fluid within each computational cell. For the phase volume fractions f1and f2, the velocities are expressed in terms of the mixture and relative velocities, denoted as u and ur, respectively, as follows:(3)��1��+�.(�1�)=��1��+�.(�1�)−�.(�1�2��)=0(4)��2��+�.(�2�)=��2��+�.(�2�)−�.(�1�2��)=0
The outcomes from this simulation are displayed in Fig. 6, which indicates that the influence of air entrainment on the generated wave amplitude is approximately 2 %. A value of 0.02 for the entrained air volume fraction means that, in the simulated fluid, approximately 2 % of the volume is composed of entrained air. In other words, for every unit volume of the fluid-air mixture at that location, 2 % is air and the remaining 98 % is water. The configuration of Test-17 (Table 4) was employed for this simulation. While the effect of air entrainment is anticipated to be more significant in models of granular landslide-generated waves (Fritz, 2002), in our simulations we opted not to incorporate this module due to its negligible impact on the results.
3. Results
In this section, we begin by presenting a sequence of our 3D simulations capturing different time steps to illustrate the generation process of landslide-generated waves. Subsequently, we derive a new predictive equation to estimate the maximum initial wave amplitude of landslide-generated waves and assess its performance.
3.1. Wave generation and propagation
To demonstrate the wave generation process in our simulation, we reference Test-17 from Table 4, where we employed Block-7 (Tables 3, 4). In this configuration, the slope angle was set to 45°, with a water depth of 0.246 m and a travel distance at 0.045 m (Fig. 7). At 0.220 s, the initial impact of the moving slide on the water is depicted, marking the onset of the wave generation process (Fig. 7a). Disturbances are localized to the immediate area of impact, with the rest of the water surface remaining undisturbed. At this time, a maximum water particle velocity of 1.0 m/s – 1.2 m/s is seen around the impact zone (Fig. 7d). Moving to 0.320 s, the development of the wave becomes apparent as energy transfer from the landslide to the water creates outwardly radiating waves with maximum water particle velocity of up to around 1.6 m/s – 1.8 m/s (Fig. 7b, e). By the time 0.670 s, the wave has fully developed and is propagating away from the impact point exhibiting maximum water particle velocity of up to 2.0 m/s – 2.1 m/s. Concentric wave fronts are visible, moving outwards in all directions, with a colour gradient signifying the highest wave amplitude near the point of landslide entry, diminishing with distance (Fig. 7c, f).
3.2. Influence of landslide parameters on tsunami amplitude
In this section, we investigate the effects of various landslide parameters namely slide volume (V), water depth (h), slipe angle (α) and travel distance (D) on the maximum initial wave amplitude (aM). Fig. 8 presents the outcome of these analyses. According to Fig. 8, the slide volume, slope angle, and travel distance exhibit a direct relationship with the wave amplitude, meaning that as these parameters increase, so does the amplitude. Conversely, water depth is inversely related to the maximum initial wave amplitude, suggesting that the deeper the water depth, the smaller the maximum wave amplitude will be (Fig. 8b).
Fig. 8a highlights the pronounced impact of slide volume on the aM, demonstrating a direct correlation between the two variables. For instance, in the range of slide volumes we modelled (Fig. 8a), The smallest slide volume tested, measuring 0.10 × 10−3 m3, generated a low initial wave amplitude (aM= 0.0066 m) (Table 4). In contrast, the largest volume tested, 6.25 × 10−3 m3, resulted in a significantly higher initial wave amplitude (aM= 0.0319 m) (Table 4). The extremities of these results emphasize the slide volume’s paramount impact on wave amplitude, further elucidated by their positions as the smallest and largest aM values across all conducted tests (Table 4). This is corroborated by findings from the literature (e.g., Murty, 2003), which align with the observed trend in our simulations.
The slope angle’s influence on aM was smooth. A steady increase of wave amplitude was observed as the slope angle increased (Fig. 8c). In examining travel distance, an anomaly was identified. At a travel distance of 0.047 m, there was an unexpected dip in aM, which deviates from the general increasing trend associated with longer travel distances. This singular instance could potentially be attributed to a numerical error. Beyond this point, the expected pattern of increasing aM with longer travel distances resumes, suggesting that the anomaly at 0.047 m is an outlier in an otherwise consistent trend, and thus this single data point was overlooked while deriving the predictive equation. Regarding the inverse relationship between water depth and wave amplitude, our result (Fig. 8b) is consistent with previous reports by Fritz et al. (2003), (2004), and Watts et al. (2005).
The insights from Fig. 8 informed the architecture of the predictive equation in the next Section, with slide volume, travel distance, and slope angle being multiplicatively linked to wave amplitude underscoring their direct correlations with wave amplitude. Conversely, water depth is incorporated as a divisor, representing its inverse relationship with wave amplitude. This structure encapsulates the dynamics between the landslide parameters and their influence on the maximum initial wave amplitude as discussed in more detail in the next Section.
3.3. Predictive equation
Building on our sensitivity analysis of landslide parameters, as detailed in Section 3.2, and utilizing our nondimensional dataset, we have derived a new predictive equation as follows:(5)��/ℎ=0.015(tan�)0.10(�ℎ3)0.90(�ℎ)0.10(ℎ�)−0.11where, V is sliding volume, h is water depth, α is slope angle, and s is landslide thickness. It is important to note that this equation is valid only for subaerial solid-block landslide tsunamis as all our experiments were for this type of waves. The performance of this equation in predicting simulation data is demonstrated by the satisfactory alignment of data points around a 45° line, indicating its accuracy and reliability with regard to the experimental dataset (Fig. 9). The quality of fit between the dataset and Eq. (5) is 91 % indicating that Eq. (5) represents the dataset very well. Table 5 presents Eq. (5) alongside four other similar equations previously published. Two significant distinctions between our Eq. (5) and these others are: (i) Eq. (5) is derived from 3D experiments, whereas the other four equations are based on 2D experiments. (ii) Unlike the other equations, our Eq. (5) incorporates travel distance as an independent parameter.
Table 5. Performance comparison among our newly-developed equation and existing equations for estimating the maximum initial amplitude (aM) of the 2018 Anak Krakatau subaerial landslide tsunami. Parameters: aM, initial maximum wave amplitude; h, water depth; vs, landslide velocity; V, slide volume; bs, slide width; ls, slide length; s, slide thickness; α, slope angle; and ����, volume of the final immersed landslide. We considered ����= V as the slide volume.
Geometrical and kinematic parameters of the 2018 Anak Krakatau subaerial landslide based on Heidarzadeh et al. (2020), Grilli et al. (2019) and Grilli et al. (2021): V=2.11 × 107 m3, h= 50 m; s= 114 m; α= 45°; ls=1250 m; bs= 2700 m; vs=44.9 m/s; D= 2500 m; aM= 100 m −150 m.⁎⁎
aM= An average value of aM = 134 m is considered in this study.⁎⁎⁎
The equation of Bolin et al. (2014) is based on the reformatted one reported by Lindstrøm (2016).⁎⁎⁎⁎
Error is calculated using Eq. (1), where the calculated aM is assumed as the simulated value.
Additionally, we evaluated the performance of this equation using the real-world data from the 2018 Anak Krakatau subaerial landslide tsunami. Based on previous studies (Heidarzadeh et al., 2020; Grilli et al., 2019, 2021), we were able to provide a list of parameters for the subaerial landslide and associated tsunami for the 2018 Anak Krakatau event (see footnote of Table 5). We note that the data of the 2018 Anak Krakatau event was not used while deriving Eq. (5). The results indicate that Eq. (5) predicts the initial amplitude of the 2018 Anak Krakatau tsunami as being 130 m indicating an error of 2.9 % compared to the reported average amplitude of 134 m for this event. This performance indicates an improvement compared to the previous equation reported by Sabeti and Heidarzadeh (2022a) (Table 5). In contrast, the equations from Robbe-Saule et al. (2021) and Bolin et al. (2014) demonstrate higher discrepancies of 4200 % and 77 %, respectively (Table 5). Although Noda’s (1970) equation reproduces the tsunami amplitude of 134 m accurately (Table 5), it is crucial to consider its limitations, notably not accounting for parameters such as slope angle and travel distance.
It is essential to recognize that both travel distance and slope angle significantly affect wave amplitude. In our model, captured in Eq. (5), we integrate the slope angle (α) through the tangent function, i.e., tan α. This choice diverges from traditional physical interpretations that often employ the cosine or sine function (e.g., Heller and Hager, 2014; Watts et al., 2003). We opted for the tangent function because it more effectively reflects the direct impact of slope steepness on wave generation, yielding superior estimations compared to conventional methods.
The significance of this study lies in its application of both physical and numerical 3D experiments and the derivation of a predictive equation based on 3D results. Prior research, e.g. Heller et al. (2016), has reported notable discrepancies between 2D and 3D wave amplitudes, highlighting the important role of 3D experiments. It is worth noting that the suitability of applying an equation derived from either 2D or 3D data depends on the specific geometry and characteristics inherent in the problem being addressed. For instance, in the case of a long, narrow dam reservoir, an equation derived from 2D data would likely be more suitable. In such contexts, the primary dynamics of interest such as flow patterns and potential wave propagation are predominantly two-dimensional, occurring along the length and depth of the reservoir. This simplification to 2D for narrow dam reservoirs allows for more accurate modelling of these dynamics.
This study specifically investigates waves initiated by landslides, focusing on those characterized as solid blocks instead of granular flows, with slope angles confined to a range of 25° to 60°. We acknowledge the additional complexities encountered in real-world scenarios, such as dynamic density and velocity of landslides, which could affect the estimations. The developed equation in this study is specifically designed to predict the maximum initial amplitude of tsunamis for the aforementioned specified ranges and types of landslides.
4. Conclusions
Both physical and numerical experiments were undertaken in a 3D wave basin to study solid-block landslide-generated waves and to formulate a predictive equation for their maximum initial wave amplitude. At the beginning, two physical experiments were performed to validate and calibrate a 3D numerical model, which was subsequently utilized to generate 100 experiments by varying different landslide parameters. The generated database was then used to derive a predictive equation for the maximum initial wave amplitude of landslide tsunamis. The main features and outcomes are:
•The predictive equation of this study is exclusively derived from 3D data and exhibits a fitting quality of 91 % when applied to the database.
•For the first time, landslide travel distance was considered in the predictive equation. This inclusion provides more accuracy and flexibility for applying the equation.
•To further evaluate the performance of the predictive equation, it was applied to a real-world subaerial landslide tsunami (i.e., the 2018 Anak Krakatau event) and delivered satisfactory performance.
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Funding
RS is supported by the Leverhulme Trust Grant No. RPG-2022-306. MH is funded by open funding of State Key Lab of Hydraulics and Mountain River Engineering, Sichuan University, grant number SKHL2101. We acknowledge University of Bath Institutional Open Access Fund. MH is also funded by the Great Britain Sasakawa Foundation grant no. 6217 (awarded in 2023).
Acknowledgements
Authors are sincerely grateful to the laboratory technician team, particularly Mr William Bazeley, at the Faculty of Engineering, University of Bath for their support during the laboratory physical modelling of this research. We appreciate the valuable insights provided by Mr. Brian Fox (Senior CFD Engineer at Flow Science, Inc.) regarding air entrainment modelling in FLOW-3D HYDRO. We acknowledge University of Bath Institutional Open Access Fund.
Data availability
All data used in this study are given in the body of the article.
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Gonzalo Duró, Mariano De Dios, Alfredo López, Sergio O. Liscia
ABSTRACT
This study presents comparisons between the results of a commercial CFD code and physical model measurements. The case study is a hydro-combined power station operating in spillway mode for a given scenario. Two turbulence models and two scales are implemented to identify the capabilities and limitations of each approach and to determine the selection criteria for CFD modeling for this kind of structure. The main flow characteristics are considered for analysis, but the focus is on a fluctuating frequency phenomenon for accurate quantitative comparisons. Acceptable representations of the general hydraulic functioning are found in all approaches, according to physical modeling. The k-ε RNG, and LES models give good representation of the discharge flow, mean water depths, and mean pressures for engineering purposes. The k-ε RNG is not able to characterize fluctuating phenomena at a model scale but does at a prototype scale. The LES is capable of identifying the dominant frequency at both prototype and model scales. A prototype-scale approach is recommended for the numerical modeling to obtain a better representation of fluctuating pressures for both turbulence models, with the complement of physical modeling for the ultimate design of the hydraulic structures.
본 연구에서는 상용 CFD 코드 결과와 물리적 모델 측정 결과를 비교합니다. 사례 연구는 주어진 시나리오에 대해 배수로 모드에서 작동하는 수력 복합 발전소입니다.
각 접근 방식의 기능과 한계를 식별하고 이러한 종류의 구조에 대한 CFD 모델링의 선택 기준을 결정하기 위해 두 개의 난류 모델과 두 개의 스케일이 구현되었습니다. 주요 흐름 특성을 고려하여 분석하지만 정확한 정량적 비교를 위해 변동하는 주파수 현상에 중점을 둡니다.
일반적인 수리학적 기능에 대한 허용 가능한 표현은 물리적 모델링에 따라 모든 접근 방식에서 발견됩니다. k-ε RNG 및 LES 모델은 엔지니어링 목적을 위한 배출 유량, 평균 수심 및 평균 압력을 잘 표현합니다.
k-ε RNG는 모델 규모에서는 변동 현상을 특성화할 수 없지만 프로토타입 규모에서는 특성을 파악합니다. LES는 프로토타입과 모델 규모 모두에서 주요 주파수를 식별할 수 있습니다.
수력학적 구조의 궁극적인 설계를 위한 물리적 모델링을 보완하여 두 난류 모델에 대한 변동하는 압력을 더 잘 표현하기 위해 수치 모델링에 프로토타입 규모 접근 방식이 권장됩니다.
ADRIAN R. J. (2007). “Hairpin vortex organization in wall turbulence.” Phys. Fluids 19(4), 041301. DEWALS B., ARCHAMBEAU P., RULOT F., PIROTTON M. and ERPICUM S. (2013). “Physical and Numerical Modelling in Low-Head Structures Design.” Proc. International Workshop on Hydraulic Design of Low-Head Structures, Aachen, Germany, Bundesanstalt für Wasserbau Publ., D.B. BUNG and S. PAGLIARA Editors, pp.11-30. GRENANDER, U. (1959). Probability and Statistics: The Harald Cramér Volume. Wiley. HIRT, C. W. and NICHOLS B. D. (1981). “Volume of fluid (VOF) method for the dynamics of free boundaries.” Journal of Computational Physics 39(1): 201-225. JOHNSON M. C. and SAVAGE B. M. (2006). “Physical and numerical comparison of flow over ogee spillway in the presence of tailwater.” J. Hydraulic Eng. 132(12): 1353–1357. KHAN L.A., WICKLEIN E.A., RASHID M., EBNER L.L. and RICHARDS N.A. (2004). “Computational fluid dynamics modeling of turbine intake hydraulics at a hydropower plant.” Journal of Hydraulic Research, 42:1, 61-69 LAROCQUE L.A., IMRAN J. and CHAUDHRY M. (2013). “3D numerical simulation of partial breach dam-break flow using the LES and k–ϵ turbulence models.” Jl of Hydraulic Research, 51:2, 145-157 LI S., LAI Y., WEBER L., MATOS SILVA J. and PATEL V.C. (2004). “Validation of a threedimensional numerical model for water-pump intakes.” Journal of Hydraulic Research, 42:3, 282-292 NOVAK P., GUINOT V., JEFFREY A. and REEVE D.E. (2010). “Hydraulic modelling – An introduction.” Spon Press, London and New York, ISBN 978-0-419-25010-4, 616 pp.
Weirs are essential structures used to manage excess water flow from behind dams to downstream areas. Enhancing discharge efficiency often involves extending the effective length of Piano Key Weirs (PKW) in dams or regulating flow within irrigation and drainage networks. This study employed both numerical and laboratory investigations to assess the impact of different base nose shapes installed beneath the outlet keys and varying Input to output key width ratios (Wi/Wo) on discharges ranging from 5 to 80 liters per second. Furthermore, the study aimed to achieve research objectives and compare the performance of Piano Key Weirs with Ogee Weir. For numerical simulation, the optimal number of cells for meshing was determined, and an appropriate turbulence model was selected. The results indicated that the numerical model accurately simulated the laboratory sample with a high degree of precision. Moreover, the numerical model closely approximated PKW for all parameters Q, H, and Cd compared to the laboratory sample. The findings revealed that in laboratory models with a maximum discharge area of 80 liters per second, the weir with Wi/Wo=1.2 and a flow head value of 285 mm exhibited the lowest value, whereas the weir with Wi/Wo=0.71 and a flow head value of 305 mm showed the highest, attributed to the higher discharge in the input-output ratio. Additionally, as the ratio of flow head to weir height H/P increased, the discharge coefficient Cd decreased. Comparing the flow conditions in weirs with different base nose shapes, it was observed that the weir with a spindle nose shape (PKW1.2S) outperformed the PKW with a flat (PKW1.2), semi-cylindrical (PKW1.2CL) and triangular base nose (PKW1.2TR). The results emphasized that models featuring semi-cylindrical and flat noses exhibited notable flow deviation and abrupt disruption upon impact with the nose. However, this effect was significantly reduced in models equipped with triangular and spindle-shaped noses. Also, the coefficient of discharge in PKW1.2S and PKW1.2TR weirs, compared to the PKW1.20 weir, increased by 27% and 20%, respectively.
웨어는 댐 뒤에서 하류 지역으로의 과도한 물 흐름을 관리하는 데 사용되는 필수 구조물입니다. 배출 효율을 높이는 데에는 댐의 피아노 키 위어(PKW) 유효 길이를 연장하거나 관개 및 배수 네트워크 내 흐름을 조절하는 것이 포함됩니다.
이 연구에서는 콘센트 키 아래에 설치된 다양한 베이스 노즈 모양과 초당 5~80리터 범위의 배출에 대한 다양한 입력 대 출력 키 너비 비율(Wi/Wo)의 영향을 평가하기 위해 수치 및 실험실 조사를 모두 사용했습니다. 또한 본 연구에서는 연구 목적을 달성하고 Piano Key Weir와 Ogee Weir의 성능을 비교하는 것을 목표로 했습니다.
수치 시뮬레이션을 위해 메시 생성을 위한 최적의 셀 수를 결정하고 적절한 난류 모델을 선택했습니다. 결과는 수치 모델이 높은 정밀도로 실험실 샘플을 정확하게 시뮬레이션했음을 나타냅니다. 더욱이, 수치 모델은 실험실 샘플과 비교하여 모든 매개변수 Q, H 및 Cd에 대해 PKW에 매우 근접했습니다.
연구 결과, 최대 배출 면적이 초당 80리터인 실험실 모델에서는 Wi/Wo=1.2, 플로우 헤드 값이 285mm인 웨어가 가장 낮은 값을 나타냈고, Wi/Wo=0.71 및 a인 웨어는 가장 낮은 값을 나타냈습니다. 플로우 헤드 값은 305mm로 가장 높은 것으로 나타났는데, 이는 입출력 비율의 높은 토출량에 기인합니다. 또한, 웨어 높이에 대한 유수두 비율 H/P가 증가함에 따라 유출계수 Cd는 감소하였다.
베이스 노즈 모양이 다른 웨어의 흐름 조건을 비교해 보면, 스핀들 노즈 모양(PKW1.2S)의 웨어가 평면(PKW1.2), 반원통형(PKW1.2CL) 및 삼각형 모양의 PKW보다 성능이 우수한 것으로 관찰되었습니다. 베이스 노즈(PKW1.2TR) 결과는 반원통형 및 편평한 노즈를 특징으로 하는 모델이 노즈에 충격을 가할 때 눈에 띄는 흐름 편차와 급격한 중단을 나타냄을 강조했습니다.
그러나 삼각형 및 방추형 노즈를 장착한 모델에서는 이러한 효과가 크게 감소했습니다. 또한 PKW1.20보에 비해 PKW1.2S보와 PKW1.2TR보의 유출계수는 각각 27%, 20% 증가하였다.
Keywords
Piano Key Weir, Base Nose Shape, Flow Hydraulics, Numerical Model, Triangular Nose Shape, Flat Nose Shape, Semi-Cylindrical Nose Shape, Spindle Nose Shape
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Alireza Khoshkonesh1, Blaise Nsom2, Saeid Okhravi3*, Fariba Ahmadi Dehrashid4, Payam Heidarian5, Silvia DiFrancesco6 1 Department of Geography, School of Social Sciences, History, and Philosophy, Birkbeck University of London, London, UK. 2 Université de Bretagne Occidentale. IRDL/UBO UMR CNRS 6027. Rue de Kergoat, 29285 Brest, France. 3 Institute of Hydrology, Slovak Academy of Sciences, Dúbravská cesta 9, 84104, Bratislava, Slovak Republic. 4Department of Water Science and Engineering, Faculty of Agriculture, Bu-Ali Sina University, 65178-38695, Hamedan, Iran. 5 Department of Civil, Environmental, Architectural Engineering and Mathematics, University of Brescia, 25123 Brescia, Italy. 6Niccol`o Cusano University, via Don C. Gnocchi 3, 00166 Rome, Italy. * Corresponding author. Tel.: +421-944624921. E-mail: saeid.okhravi@savba.sk
Abstract
This study aimed to comprehensively investigate the influence of substrate level difference and material composition on dam break wave evolution over two different erodible beds. Utilizing the Volume of Fluid (VOF) method, we tracked free surface advection and reproduced wave evolution using experimental data from the literature. For model validation, a comprehensive sensitivity analysis encompassed mesh resolution, turbulence simulation methods, and bed load transport equations. The implementation of Large Eddy Simulation (LES), non-equilibrium sediment flux, and van Rijn’s (1984) bed load formula yielded higher accuracy compared to alternative approaches. The findings emphasize the significant effect of substrate level difference and material composition on dam break morphodynamic characteristics. Decreasing substrate level disparity led to reduced flow velocity, wavefront progression, free surface height, substrate erosion, and other pertinent parameters. Initial air entrapment proved substantial at the wavefront, illustrating pronounced air-water interaction along the bottom interface. The Shields parameter experienced a one-third reduction as substrate level difference quadrupled, with the highest near-bed concentration observed at the wavefront. This research provides fresh insights into the complex interplay of factors governing dam break wave propagation and morphological changes, advancing our comprehension of this intricate phenomenon.
이 연구는 두 개의 서로 다른 침식층에 대한 댐 파괴파 진화에 대한 기질 수준 차이와 재료 구성의 영향을 종합적으로 조사하는 것을 목표로 했습니다. VOF(유체량) 방법을 활용하여 자유 표면 이류를 추적하고 문헌의 실험 데이터를 사용하여 파동 진화를 재현했습니다.
모델 검증을 위해 메쉬 해상도, 난류 시뮬레이션 방법 및 침대 하중 전달 방정식을 포함하는 포괄적인 민감도 분석을 수행했습니다. LES(Large Eddy Simulation), 비평형 퇴적물 플럭스 및 van Rijn(1984)의 하상 부하 공식의 구현은 대체 접근 방식에 비해 더 높은 정확도를 산출했습니다.
연구 결과는 댐 붕괴 형태역학적 특성에 대한 기질 수준 차이와 재료 구성의 중요한 영향을 강조합니다. 기판 수준 차이가 감소하면 유속, 파면 진행, 자유 표면 높이, 기판 침식 및 기타 관련 매개변수가 감소했습니다.
초기 공기 포집은 파면에서 상당한 것으로 입증되었으며, 이는 바닥 경계면을 따라 뚜렷한 공기-물 상호 작용을 보여줍니다. 기판 레벨 차이가 4배로 증가함에 따라 Shields 매개변수는 1/3로 감소했으며, 파면에서 가장 높은 베드 근처 농도가 관찰되었습니다.
이 연구는 댐 파괴파 전파와 형태학적 변화를 지배하는 요인들의 복잡한 상호 작용에 대한 새로운 통찰력을 제공하여 이 복잡한 현상에 대한 이해를 향상시킵니다.
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험프 웨어는 수위 제어 및 배출 측정을 위한 기존의 수력 구조물 중 하나입니다. 상류 및 하류 경사로의 경사는 자유 및 침수 흐름 조건 모두에서 험프 웨어의 성능에 영향을 미치는 설계 매개변수입니다.
침수된 험프보의 유출 특성 및 수위 변화에 대한 램프 경사 및 유출의 영향을 조사하기 위해 일련의 수치 시뮬레이션이 수행되었습니다. 1V:1H에서 1V:5H까지의 5개 램프 경사를 다양한 업스트림 방전에서 테스트했습니다.
수치모델의 검증을 위해 수치결과를 실험실 데이터와 비교하였다. 수면수위 예측과 유출계수의 시뮬레이션 불일치는 각각 전체 범위의 ±10%와 ±5% 이내였습니다.
모듈 한계 및 방전 감소 계수의 변화에 대한 램프 경사의 영향을 연구했습니다. 험프보의 경사로 경사가 증가함에 따라 상대적으로 높은 침수율에서 모듈러 한계가 발생함을 알 수 있었다.
침수 시작은 방류 수위를 작은 증분으로 조심스럽게 증가시켜 모델링되었으며 그 결과는 모듈 한계의 고전적인 정의와 비교되었습니다. 램프 경사와 방전이 증가함에 따라 모듈러 한계가 증가하는 것으로 밝혀졌지만, 모듈러 한계의 고전적인 정의는 모듈러 한계가 방전과 무관하다는 것을 나타냅니다.
Hump weir 하류의 속도와 와류장은 램프 경사에 의해 제어되는 와류 구조 형성을 나타냅니다. 에너지 손실은 수치 출력으로부터 계산되었으며 정규화된 에너지 손실은 침수에 따라 선형적으로 감소하는 것으로 나타났습니다.
Hump weirs are amongst conventional hydraulic structures for water level control and discharge measurement. The slope in the upstream and downstream ramps is a design parameter that affects the performance of Hump weirs in both free and submerged flow conditions. A series of numerical simulations was performed to investigate the effects of ramp slope and discharge on discharge characteristics and water level variations of submerged Hump weirs. Five ramp slopes ranging from 1V:1H to 1V:5H were tested at different upstream discharges. The numerical results were compared with the laboratory data for verifications of the numerical model. The simulation discrepancies in prediction of water surface level and discharge coefficient were within ±10 % and ±5 % of the full range, respectively. The effects of ramp slope on variations of modular limit and discharge reduction factor were studied. It was found that the modular limit occurred at relatively higher submergence ratios as the ramp slope in Hump weirs increased. The onset of submergence was modeled by carefully increasing tailwater level with small increments and the results were compared with the classic definition of modular limit. It was found that the modular limit increases with increasing the ramp slope and discharge while the classic definition of modular limit indicated that the modular limit is independent of the discharge. The velocity and vortex fields in the downstream of Hump weirs indicated the formation vortex structure, which is controlled by the ramp slope. The energy losses were calculated from the numerical outputs, and it was found that the normalized energy losses decreased linearly with submergence.
Weirs have been utilized predominantly for discharge measurement, flow diversion, and water level control in open channels, irrigation canal, and natural streams due to their simplicity of operation and accuracy. Several research studies have been conducted to determine the head-discharge relationship in weirs as one of the most common hydraulic structures for flow measurement (Rajaratnam and Muralidhar, 1969 [[1], [2], [3]]; Vatankhah, 2010, [[4], [5], [6]]; b [[7], [8], [9]]; Azimi and Seyed Hakim, 2019; Salehi et al., 2019; Salehi and Azimi, 2019, [10]. Weirs in general are classified into two major categories named as sharp-crested weirs and weirs of finite-crest length (Rajaratnam and Muralidhar, 1969; [11]. Sharp-crested weirs are typically used for flow measurement in small irrigation canals and laboratory flumes. In contrast, weirs of finite crest length are more suitable for water level control and flow diversion in rivers and natural streams [7,[12], [13], [14]].
The head-discharge relationship in sharp-crested weirs is developed by employing energy equation between two sections in the upstream and downstream of the weir and integration of the velocity profile at the crest of the weir as:
where Qf is the free flow discharge, B is the channel width, g is the acceleration due to gravity, ho is the water head in free-flow condition, and Cd is the discharge coefficient. Rehbock [15] proposed a linear correlation between discharge coefficient and the ratio of water head, ho, and the weir height, P as Cd = 0.605 + 0.08 (ho/P).
Upstream and/or downstream ramp(s) can be added to sharp-crested weirs to enhance the structural stability of the weir. A sharp-crested weir with upstream and/or downstream ramp(s) are known as triangular weirs in the literature. Triangular weirs with both upstream and downstream ramps are also known as Hump weirs and are first introduced in the experimental study of Bazin [16]. The ramps are constructed upstream and downstream of sharp-crested weirs to enhance the weir’s structural integrity and improve the hydraulic performance of the weir. In free-flow condition, the discharge coefficient of Hump weirs increases with increasing downstream ramp slope but decreases as upstream ramp slope increases (Azimi et al., 2013).
The hydraulic performance of weirs is evaluated in both free and submerged flow conditions. In free flow condition, water freely flows over weirs since the downstream water level is lower than that of the crest level of the weir. Channel blockage or flood in the downstream of weirs can raise the tailwater level, t. As tailwater passes the crest elevation in sharp-crested weirs, the upstream flow decelerates due to the excess pressure force in the downstream and the upstream water level increases. The onset of water level raise due to tailwater raise is called the modular limit. Once the tailwater level passes the modular limit, the weir is submerged. In sharp-crested weirs, the submerged flow regime may occur even before the tailwater reaches the crest elevation [8,14], whereas, in weirs of finite crest length, the upstream water level remains unchanged even if the tailwater raises above the crest elevation and it normally causes submergence once the tailwater level passes the critical depth at the crest of the weir [7,17]. The degree of submergence can be estimated by careful observation of the water surface profile. Observations of water surface at different submergence levels indicated two distinct flow patterns in submerged sharp-crested weirs that was initially classified as impinging jet and surface flow regimes [14]. [8] analyzed the variations of water surface profiles over submerged sharp-crested weirs with different submergence ratios and defined four distinct regimes of impinging jet, surface jump, surface wave, and surface jet.
[18] characterized the onset of submergence by defining the modular limit as a stage when the free flow head increases by +1 mm due to tailwater rise. The definition of modular limit is somewhat arbitrary, and it is difficult to identify for large discharges because the upstream water surface begins to fluctuate. This definition did not consider the effects of channel and weir geometries. The experimental data in triangular weirs and weirs finite-crest length with upstream and downstream ramp(s) revealed that the modular limit varied with the ratio of the free-flow head to the total streamwise length of the weir [17]. Weirs of finite crest length with upstream and downstream ramps are known as embankment weirs in literature [1,19,20] and Azimi et al., 2013) [19]. conducted two series of laboratory experiments to study the hydraulics of submerged embankment weirs with the upstream and downstream ramps of 1V:1H and 1V:2H. Empirical correlations were proposed to directly estimate the flow discharge in submerged embankment weirs for t/h > 0.7 where h is the water head in submerged flow condition. He found that the free flow discharge is a function of upstream water head, but the submerged discharge is a function of submergence level, t/h [21]. studied the hydraulics of four embankment weirs with different weir heights ranging from 0.09 m to 0.36 m. It was found that submerged embankments with a higher ho/P, where P is the height of the weir, have a smaller discharge reduction due to submergence. Effects of crest length in embankment weirs with both upstream and downstream ramps of 1V:2H was studied in both free and submerged flow conditions [1]. It was found that the modular limit in submerged embankment weirs decreased linearly with the relative crest length, Ho/(Ho + L), where Ho is the total head and L is the crest length.
In submerged flow condition, the performance of weirs is quantified by the discharge reduction factor, ψ, which is a ratio of the submerged discharge, Qs, to the corresponding free-flow discharge, Qf, based on the upstream head, h [12]. In submerged-flow conditions, flow discharge can be estimated as:��=���
[1] proposed a formula to predict ψ that could be used for embankment weirs with different crest lengths ranging from 0 to 0.3 m as:�=(1−��)�where n is an exponent varying from 4 to 7 and Yt is the normalized submergence defined as:��=�ℎ−[0.85−(0.5��+�)]1−[0.85−(0.5��+�)]where H is the total upstream head in submerged-flow conditions [7]. proposed a simpler formula to predict ψ for weirs of finite-crest length as:�=[1−(�ℎ)�]�where m and n are exponents varying for different types of weirs. Hakim and Azimi (2017) employed regression analysis to propose values of n = 0.25 and m = 0.28 (ho/L)−2.425 for triangular weirs.
The discharge capacity of weirs decreases in submerged flow condition and the onset of submergence occurs at the modular limit. Therefore, the determination of modular limit in weirs with different geometries is critical to understanding the sensitivity of a particular weir model with tailwater level variations. The available definition of modular limit as when head water raises by +1 mm due to tailwater rise does not consider the effects of channel and weir geometries. Therefore, a new and more accurate definition of modular limit is proposed in this study to consider the effect of other geometry and approaching flow parameters. The second objective of this study is to evaluate the effects of upstream and downstream ramps and ramps slopes on the hydraulic performance of submerged Hump weirs. The flow patterns, velocity distributions, and energy dissipation rates were extracted from validated numerical data to better understand the discharge reduction mechanism in Hump weirs in both free and submerged flow conditions.
Section snippets
Governing equations
Numerical simulation has been employed as an efficient and effective method to analyze free surface flow problems and in particular investigating on the hydraulics of flow over weirs [22]. The weir models were developed in numerical domain and the water pressure and velocity field were simulated by employing the FLOW-3D solver (Flow Science, Inc., Santa Fe, USA). The numerical results were validated with the laboratory measurements and the effects of ramps slopes on the performance of Hump
Verification of numerical model
The experimental observations of Bazin [16,17] were used for model validation in free and submerged flow conditions, respectively. The weir height in the study of Bazin was P = 0.5 m and two ramp slopes of 1V:1H and 1V:2H were tested. The bed and sides of the channel were made of glass, and the roughness distribution of the bed and walls were uniform. The Hump weir models in the study of Seyed Hakim and Azimi (2017) had a weir height of 0.076 m and ramp slopes of 1V:2H in both upstream and
Conclusions
A series of numerical simulations was performed to study the hydraulics and velocity pattern downstream of a Hump weir with symmetrical ramp slopes. Effects of ramp slope and discharge on formation of modular limit and in submerged flow condition were tested by conducting a series of numerical simulations on Hump weirs with ramp slopes varying from 1V:1H to 1V:5H. A comparison between numerical results and experimental data indicated that the proposed numerical model is accurate with a mean
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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웨어의 두 가지 서로 다른 배열(즉, 직선형 웨어와 직사각형 미로 웨어)을 사용하여 웨어 모양, 웨어 간격, 웨어의 오리피스 존재, 흐름 영역에 대한 바닥 경사와 같은 기하학적 매개변수의 영향을 평가했습니다.
유량과 수심의 관계, 수심 평균 속도의 변화와 분포, 난류 특성, 어도에서의 에너지 소산. 흐름 조건에 미치는 영향을 조사하기 위해 FLOW-3D® 소프트웨어를 사용하여 전산 유체 역학 시뮬레이션을 수행했습니다.
수치 모델은 계산된 표면 프로파일과 속도를 문헌의 실험적으로 측정된 값과 비교하여 검증되었습니다. 수치 모델과 실험 데이터의 결과, 급락유동의 표면 프로파일과 표준화된 속도 프로파일에 대한 평균 제곱근 오차와 평균 절대 백분율 오차가 각각 0.014m와 3.11%로 나타나 수치 모델의 능력을 확인했습니다.
수영장과 둑의 흐름 특성을 예측합니다. 각 모델에 대해 L/B = 1.83(L: 웨어 거리, B: 수로 폭) 값에서 급락 흐름이 발생할 수 있고 L/B = 0.61에서 스트리밍 흐름이 발생할 수 있습니다. 직사각형 미로보 모델은 기존 모델보다 무차원 방류량(Q+)이 더 큽니다.
수중 흐름의 기존 보와 직사각형 미로 보의 경우 Q는 각각 1.56과 1.47h에 비례합니다(h: 보 위 수심). 기존 웨어의 풀 내 평균 깊이 속도는 직사각형 미로 웨어의 평균 깊이 속도보다 높습니다.
그러나 주어진 방류량, 바닥 경사 및 웨어 간격에 대해 난류 운동 에너지(TKE) 및 난류 강도(TI) 값은 기존 웨어에 비해 직사각형 미로 웨어에서 더 높습니다. 기존의 웨어는 직사각형 미로 웨어보다 에너지 소산이 더 낮습니다.
더 낮은 TKE 및 TI 값은 미로 웨어 상단, 웨어 하류 벽 모서리, 웨어 측벽과 채널 벽 사이에서 관찰되었습니다. 보와 바닥 경사면 사이의 거리가 증가함에 따라 평균 깊이 속도, 난류 운동 에너지의 평균값 및 난류 강도가 증가하고 수영장의 체적 에너지 소산이 감소했습니다.
둑에 개구부가 있으면 평균 깊이 속도와 TI 값이 증가하고 풀 내에서 가장 높은 TKE 범위가 감소하여 두 모델 모두에서 물고기를 위한 휴식 공간이 더 넓어지고(TKE가 낮아짐) 에너지 소산율이 감소했습니다.
Two different arrangements of the weir (i.e., straight weir and rectangular labyrinth weir) were used to evaluate the effects of geometric parameters such as weir shape, weir spacing, presence of an orifice at the weir, and bed slope on the flow regime and the relationship between discharge and depth, variation and distribution of depth-averaged velocity, turbulence characteristics, and energy dissipation at the fishway. Computational fluid dynamics simulations were performed using FLOW-3D® software to examine the effects on flow conditions. The numerical model was validated by comparing the calculated surface profiles and velocities with experimentally measured values from the literature. The results of the numerical model and experimental data showed that the root-mean-square error and mean absolute percentage error for the surface profiles and normalized velocity profiles of plunging flows were 0.014 m and 3.11%, respectively, confirming the ability of the numerical model to predict the flow characteristics of the pool and weir. A plunging flow can occur at values of L/B = 1.83 (L: distance of the weir, B: width of the channel) and streaming flow at L/B = 0.61 for each model. The rectangular labyrinth weir model has larger dimensionless discharge values (Q+) than the conventional model. For the conventional weir and the rectangular labyrinth weir at submerged flow, Q is proportional to 1.56 and 1.47h, respectively (h: the water depth above the weir). The average depth velocity in the pool of a conventional weir is higher than that of a rectangular labyrinth weir. However, for a given discharge, bed slope, and weir spacing, the turbulent kinetic energy (TKE) and turbulence intensity (TI) values are higher for a rectangular labyrinth weir compared to conventional weir. The conventional weir has lower energy dissipation than the rectangular labyrinth weir. Lower TKE and TI values were observed at the top of the labyrinth weir, at the corner of the wall downstream of the weir, and between the side walls of the weir and the channel wall. As the distance between the weirs and the bottom slope increased, the average depth velocity, the average value of turbulent kinetic energy and the turbulence intensity increased, and the volumetric energy dissipation in the pool decreased. The presence of an opening in the weir increased the average depth velocity and TI values and decreased the range of highest TKE within the pool, resulted in larger resting areas for fish (lower TKE), and decreased the energy dissipation rates in both models.
1 Introduction
Artificial barriers such as detour dams, weirs, and culverts in lakes and rivers prevent fish from migrating and completing the upstream and downstream movement cycle. This chain is related to the life stage of the fish, its location, and the type of migration. Several riverine fish species instinctively migrate upstream for spawning and other needs. Conversely, downstream migration is a characteristic of early life stages [1]. A fish ladder is a waterway that allows one or more fish species to cross a specific obstacle. These structures are constructed near detour dams and other transverse structures that have prevented such migration by allowing fish to overcome obstacles [2]. The flow pattern in fish ladders influences safe and comfortable passage for ascending fish. The flow’s strong turbulence can reduce the fish’s speed, injure them, and delay or prevent them from exiting the fish ladder. In adult fish, spawning migrations are usually complex, and delays are critical to reproductive success [3].
Various fish ladders/fishways include vertical slots, denil, rock ramps, and pool weirs [1]. The choice of fish ladder usually depends on many factors, including water elevation, space available for construction, and fish species. Pool and weir structures are among the most important fish ladders that help fish overcome obstacles in streams or rivers and swim upstream [1]. Because they are easy to construct and maintain, this type of fish ladder has received considerable attention from researchers and practitioners. Such a fish ladder consists of a sloping-floor channel with series of pools directly separated by a series of weirs [4]. These fish ladders, with or without underwater openings, are generally well-suited for slopes of 10% or less [1, 2]. Within these pools, flow velocities are low and provide resting areas for fish after they enter the fish ladder. After resting in the pools, fish overcome these weirs by blasting or jumping over them [2]. There may also be an opening in the flooded portion of the weir through which the fish can swim instead of jumping over the weir. Design parameters such as the length of the pool, the height of the weir, the slope of the bottom, and the water discharge are the most important factors in determining the hydraulic structure of this type of fish ladder [3]. The flow over the weir depends on the flow depth at a given slope S0 and the pool length, either “plunging” or “streaming.” In plunging flow, the water column h over each weir creates a water jet that releases energy through turbulent mixing and diffusion mechanisms [5]. The dimensionless discharges for plunging (Q+) and streaming (Q*) flows are shown in Fig. 1, where Q is the total discharge, B is the width of the channel, w is the weir height, S0 is the slope of the bottom, h is the water depth above the weir, d is the flow depth, and g is the acceleration due to gravity. The maximum velocity occurs near the top of the weir for plunging flow. At the water’s surface, it drops to about half [6].
Extensive experimental studies have been conducted to investigate flow patterns for various physical geometries (i.e., bed slope, pool length, and weir height) [2]. Guiny et al. [7] modified the standard design by adding vertical slots, orifices, and weirs in fishways. The efficiency of the orifices and vertical slots was related to the velocities at their entrances. In the laboratory experiments of Yagci [8], the three-dimensional (3D) mean flow and turbulence structure of a pool weir fishway combined with an orifice and a slot is investigated. It is shown that the energy dissipation per unit volume and the discharge have a linear relationship.
Considering the beneficial characteristics reported in the limited studies of researchers on the labyrinth weir in the pool-weir-type fishway, and knowing that the characteristics of flow in pool-weir-type fishways are highly dependent on the geometry of the weir, an alternative design of the rectangular labyrinth weir instead of the straight weirs in the pool-weir-type fishway is investigated in this study [7, 9]. Kim [10] conducted experiments to compare the hydraulic characteristics of three different weir types in a pool-weir-type fishway. The results show that a straight, rectangular weir with a notch is preferable to a zigzag or trapezoidal weir. Studies on natural fish passes show that pass ability can be improved by lengthening the weir’s crest [7]. Zhong et al. [11] investigated the semi-rigid weir’s hydraulic performance in the fishway’s flow field with a pool weir. The results showed that this type of fishway performed better with a lower invert slope and a smaller radius ratio but with a larger pool spacing.
Considering that an alternative method to study the flow characteristics in a fishway with a pool weir is based on numerical methods and modeling from computational fluid dynamics (CFD), which can easily change the geometry of the fishway for different flow fields, this study uses the powerful package CFD and the software FLOW-3D to evaluate the proposed weir design and compare it with the conventional one to extend the application of the fishway. The main objective of this study was to evaluate the hydraulic performance of the rectangular labyrinth pool and the weir with submerged openings in different hydraulic configurations. The primary objective of creating a new weir configuration for suitable flow patterns is evaluated based on the swimming capabilities of different fish species. Specifically, the following questions will be answered: (a) How do the various hydraulic and geometric parameters relate to the effects of water velocity and turbulence, expressed as turbulent kinetic energy (TKE) and turbulence intensity (TI) within the fishway, i.e., are conventional weirs more affected by hydraulics than rectangular labyrinth weirs? (b) Which weir configurations have the greatest effect on fish performance in the fishway? (c) In the presence of an orifice plate, does the performance of each weir configuration differ with different weir spacing, bed gradients, and flow regimes from that without an orifice plate?
2 Materials and Methods
2.1 Physical Model Configuration
This paper focuses on Ead et al. [6]’s laboratory experiments as a reference, testing ten pool weirs (Fig. 2). The experimental flume was 6 m long, 0.56 m wide, and 0.6 m high, with a bottom slope of 10%. Field measurements were made at steady flow with a maximum flow rate of 0.165 m3/s. Discharge was measured with magnetic flow meters in the inlets and water level with point meters (see Ead et al. [6]. for more details). Table 1 summarizes the experimental conditions considered for model calibration in this study.
Table 1 Experimental conditions considered for calibration
Computational fluid dynamics (CFD) simulations were performed using FLOW-3D® v11.2 to validate a series of experimental liner pool weirs by Ead et al. [6] and to investigate the effects of the rectangular labyrinth pool weir with an orifice. The dimensions of the channel and data collection areas in the numerical models are the same as those of the laboratory model. Two types of pool weirs were considered: conventional and labyrinth. The proposed rectangular labyrinth pool weirs have a symmetrical cross section and are sized to fit within the experimental channel. The conventional pool weir model had a pool length of l = 0.685 and 0.342 m, a weir height of w = 0.141 m, a weir width of B = 0.56 m, and a channel slope of S0 = 5 and 10%. The rectangular labyrinth weirs have the same front width as the offset, i.e., a = b = c = 0.186 m. A square underwater opening with a width of 0.05 m and a depth of 0.05 m was created in the middle of the weir. The weir configuration considered in the present study is shown in Fig. 3.
2.3 Governing Equations
FLOW-3D® software solves the Navier–Stokes–Reynolds equations for three-dimensional analysis of incompressible flows using the fluid-volume method on a gridded domain. FLOW -3D® uses an advanced free surface flow tracking algorithm (TruVOF) developed by Hirt and Nichols [12], where fluid configurations are defined in terms of a VOF function F (x, y, z, t). In this case, F (fluid fraction) represents the volume fraction occupied by the fluid: F = 1 in cells filled with fluid and F = 0 in cells without fluid (empty areas) [4, 13]. The free surface area is at an intermediate value of F. (Typically, F = 0.5, but the user can specify a different intermediate value.) The equations in Cartesian coordinates (x, y, z) applicable to the model are as follows:
�f∂�∂�+∂(���x)∂�+∂(���y)∂�+∂(���z)∂�=�SOR
(1)
∂�∂�+1�f(��x∂�∂�+��y∂�∂�+��z∂�∂�)=−1�∂�∂�+�x+�x
(2)
∂�∂�+1�f(��x∂�∂�+��y∂�∂�+��z∂�∂�)=−1�∂�∂�+�y+�y
(3)
∂�∂�+1�f(��x∂�∂�+��y∂�∂�+��z∂�∂�)=−1�∂�∂�+�z+�z
(4)
where (u, v, w) are the velocity components, (Ax, Ay, Az) are the flow area components, (Gx, Gy, Gz) are the mass accelerations, and (fx, fy, fz) are the viscous accelerations in the directions (x, y, z), ρ is the fluid density, RSOR is the spring term, Vf is the volume fraction associated with the flow, and P is the pressure. The k–ε turbulence model (RNG) was used in this study to solve the turbulence of the flow field. This model is a modified version of the standard k–ε model that improves performance. The model is a two-equation model; the first equation (Eq. 5) expresses the turbulence’s energy, called turbulent kinetic energy (k) [14]. The second equation (Eq. 6) is the turbulent dissipation rate (ε), which determines the rate of dissipation of kinetic energy [15]. These equations are expressed as follows Dasineh et al. [4]:
In these equations, k is the turbulent kinetic energy, ε is the turbulent energy consumption rate, Gk is the generation of turbulent kinetic energy by the average velocity gradient, with empirical constants αε = αk = 1.39, C1ε = 1.42, and C2ε = 1.68, eff is the effective viscosity, μeff = μ + μt [15]. Here, μ is the hydrodynamic density coefficient, and μt is the turbulent density of the fluid.
2.4 Meshing and the Boundary Conditions in the Model Setup
The numerical area is divided into three mesh blocks in the X-direction. The meshes are divided into different sizes, a containing mesh block for the entire spatial domain and a nested block with refined cells for the domain of interest. Three different sizes were selected for each of the grid blocks. By comparing the accuracy of their results based on the experimental data, the reasonable mesh for the solution domain was finally selected. The convergence index method (GCI) evaluated the mesh sensitivity analysis. Based on this method, many researchers, such as Ahmadi et al. [16] and Ahmadi et al. [15], have studied the independence of numerical results from mesh size. Three different mesh sizes with a refinement ratio (r) of 1.33 were used to perform the convergence index method. The refinement ratio is the ratio between the larger and smaller mesh sizes (r = Gcoarse/Gfine). According to the recommendation of Celik et al. [17], the recommended number for the refinement ratio is 1.3, which gives acceptable results. Table 2 shows the characteristics of the three mesh sizes selected for mesh sensitivity analysis.Table 2 Characteristics of the meshes tested in the convergence analysis
The results of u1 = umax (u1 = velocity component along the x1 axis and umax = maximum velocity of u1 in a section perpendicular to the invert of the fishway) at Q = 0.035 m3/s, × 1/l = 0.66, and Y1/b = 0 in the pool of conventional weir No. 4, obtained from the output results of the software, were used to evaluate the accuracy of the calculation range. As shown in Fig. 4, x1 = the distance from a given weir in the x-direction, Y1 = the water depth measured in the y-direction, Y0 = the vertical distance in the Cartesian coordinate system, h = the water column at the crest, b = the distance between the two points of maximum velocity umax and zero velocity, and l = the pool length.
The apparent index of convergence (p) in the GCI method is calculated as follows:
�=ln(�3−�2)(�2−�1)/ln(�)
(7)
f1, f2, and f3 are the hydraulic parameters obtained from the numerical simulation (f1 corresponds to the small mesh), and r is the refinement ratio. The following equation defines the convergence index of the fine mesh:
GCIfine=1.25|ε|��−1
(8)
Here, ε = (f2 − f1)/f1 is the relative error, and f2 and f3 are the values of hydraulic parameters considered for medium and small grids, respectively. GCI12 and GCI23 dimensionless indices can be calculated as:
GCI12=1.25|�2−�1�1|��−1
(9)
Then, the independence of the network is preserved. The convergence index of the network parameters obtained by Eqs. (7)–(9) for all three network variables is shown in Table 3. Since the GCI values for the smaller grid (GCI12) are lower compared to coarse grid (GCI23), it can be concluded that the independence of the grid is almost achieved. No further change in the grid size of the solution domain is required. The calculated values (GCI23/rpGCI12) are close to 1, which shows that the numerical results obtained are within the convergence range. As a result, the meshing of the solution domain consisting of a block mesh with a mesh size of 0.012 m and a block mesh within a larger block mesh with a mesh size of 0.009 m was selected as the optimal mesh (Fig. 5).Table 3 GCI calculation
The boundary conditions applied to the area are shown in Fig. 6. The boundary condition of specific flow rate (volume flow rate-Q) was used for the inlet of the flow. For the downstream boundary, the flow output (outflow-O) condition did not affect the flow in the solution area. For the Zmax boundary, the specified pressure boundary condition was used along with the fluid fraction = 0 (P). This type of boundary condition considers free surface or atmospheric pressure conditions (Ghaderi et al. [19]). The wall boundary condition is defined for the bottom of the channel, which acts like a virtual wall without friction (W). The boundary between mesh blocks and walls were considered a symmetrical condition (S).
The convergence of the steady-state solutions was controlled during the simulations by monitoring the changes in discharge at the inlet boundary conditions. Figure 7 shows the time series plots of the discharge obtained from the Model A for the three main discharges from the numerical results. The 8 s to reach the flow equilibrium is suitable for the case of the fish ladder with pool and weir. Almost all discharge fluctuations in the models are insignificant in time, and the flow has reached relative stability. The computation time for the simulations was between 6 and 8 h using a personal computer with eight cores of a CPU (Intel Core i7-7700K @ 4.20 GHz and 16 GB RAM).
3 Results
3.1 Verification of Numerical Results
Quantitative outcomes, including free surface and normalized velocity profiles obtained using FLOW-3D software, were reviewed and compared with the results of Ead et al. [6]. The fourth pool was selected to present the results and compare the experiment and simulation. For each quantity, the percentage of mean absolute error (MAPE (%)) and root-mean-square error (RMSE) are calculated. Equations (10) and (11) show the method used to calculate the errors.
MAPE(%)100×1�∑1�|�exp−�num�exp|
(10)
RMSE(−)1�∑1�(�exp−�num)2
(11)
Here, Xexp is the value of the laboratory data, Xnum is the numerical data value, and n is the amount of data. As shown in Fig. 8, let x1 = distance from a given weir in the x-direction and Y1 = water depth in the y-direction from the bottom. The trend of the surface profiles for each of the numerical results is the same as that of the laboratory results. The surface profiles of the plunging flows drop after the flow enters and then rises to approach the next weir. The RMSE and MAPE error values for Model A are 0.014 m and 3.11%, respectively, indicating acceptable agreement between numerical and laboratory results. Figure 9 shows the velocity vectors and plunging flow from the numerical results, where x and y are horizontal and vertical to the flow direction, respectively. It can be seen that the jet in the fish ladder pool has a relatively high velocity. The two vortices, i.e., the enclosed vortex rotating clockwise behind the weir and the surface vortex rotating counterclockwise above the jet, are observed for the regime of incident flow. The point where the jet meets the fish passage bed is shown in the figure. The normalized velocity profiles upstream and downstream of the impact points are shown in Fig. 10. The figure shows that the numerical results agree well with the experimental data of Ead et al. [6].
3.2 Flow Regime and Discharge-Depth Relationship
Depending on the geometric shape of the fishway, including the distance of the weir, the slope of the bottom, the height of the weir, and the flow conditions, the flow regime in the fishway is divided into three categories: dipping, transitional, and flow regimes [4]. In the plunging flow regime, the flow enters the pool through the weir, impacts the bottom of the fishway, and forms a hydraulic jump causing two eddies [2, 20]. In the streamwise flow regime, the surface of the flow passing over the weir is almost parallel to the bottom of the channel. The transitional regime has intermediate flow characteristics between the submerged and flow regimes. To predict the flow regime created in the fishway, Ead et al. [6] proposed two dimensionless parameters, Qt* and L/w, where Qt* is the dimensionless discharge, L is the distance between weirs, and w is the height of the weir:
��∗=���0���
(12)
Q is the total discharge, B is the width of the channel, S0 is the slope of the bed, and g is the gravity acceleration. Figure 11 shows different ranges for each flow regime based on the slope of the bed and the distance between the pools in this study. The results of Baki et al. [21], Ead et al. [6] and Dizabadi et al. [22] were used for this comparison. The distance between the pools affects the changes in the regime of the fish ladder. So, if you decrease the distance between weirs, the flow regime more likely becomes. This study determined all three flow regimes in a fish ladder. When the corresponding range of Qt* is less than 0.6, the flow regime can dip at values of L/B = 1.83. If the corresponding range of Qt* is greater than 0.5, transitional flow may occur at L/B = 1.22. On the other hand, when Qt* is greater than 1, streamwise flow can occur at values of L/B = 0.61. These observations agree well with the results of Baki et al. [21], Ead et al. [6] and Dizabadi et al. [22].
For plunging flows, another dimensionless discharge (Q+) versus h/w given by Ead et al. [6] was used for further evaluation:
�+=��ℎ�ℎ=23�d�
(13)
where h is the water depth above the weir, and Cd is the discharge coefficient. Figure 12a compares the numerical and experimental results of Ead et al. [6]. In this figure, Rehbock’s empirical equation is used to estimate the discharge coefficient of Ead et al. [6].
�d=0.57+0.075ℎ�
(14)
The numerical results for the conventional weir (Model A) and the rectangular labyrinth weir (Model B) of this study agree well with the laboratory results of Ead et al. [6]. When comparing models A and B, it is also found that a rectangular labyrinth weir has larger Q + values than the conventional weir as the length of the weir crest increases for a given channel width and fixed headwater elevation. In Fig. 12b, Models A and B’s flow depth plot shows the plunging flow regime. The power trend lines drawn through the data are the best-fit lines. The data shown in Fig. 12b are for different bed slopes and weir geometries. For the conventional weir and the rectangular labyrinth weir at submerged flow, Q can be assumed to be proportional to 1.56 and 1.47h, respectively. In the results of Ead et al. [6], Q is proportional to 1.5h. If we assume that the flow through the orifice is Qo and the total outflow is Q, the change in the ratio of Qo/Q to total outflow for models A and B can be shown in Fig. 13. For both models, the flow through the orifice decreases as the total flow increases. A logarithmic trend line was also found between the total outflow and the dimensionless ratio Qo/Q.
3.3 Depth-Averaged Velocity Distributions
To ensure that the target fish species can pass the fish ladder with maximum efficiency, the average velocity in the fish ladder should be low enough [4]. Therefore, the average velocity in depth should be as much as possible below the critical swimming velocities of the target fishes at a constant flow depth in the pool [20]. The contour plot of depth-averaged velocity was used instead of another direction, such as longitudinal velocity because fish are more sensitive to depth-averaged flow velocity than to its direction under different hydraulic conditions. Figure 14 shows the distribution of depth-averaged velocity in the pool for Models A and B in two cases with and without orifice plates. Model A’s velocity within the pool differs slightly in the spanwise direction. However, no significant variation in velocity was observed. The flow is gradually directed to the sides as it passes through the rectangular labyrinth weir. This increases the velocity at the sides of the channel. Therefore, the high-velocity zone is located at the sides. The low velocity is in the downstream apex of the weir. This area may be suitable for swimming target fish. The presence of an opening in the weir increases the flow velocity at the opening and in the pool’s center, especially in Model A. The flow velocity increase caused by the models’ opening varied from 7.7 to 12.48%. Figure 15 illustrates the effect of the inverted slope on the averaged depth velocity distribution in the pool at low and high discharge. At constant discharge, flow velocity increases with increasing bed slope. In general, high flow velocity was found in the weir toe sidewall and the weir and channel sidewalls.
On the other hand, for a constant bed slope, the high-velocity area of the pool increases due to the increase in runoff. For both bed slopes and different discharges, the most appropriate path for fish to travel from upstream to downstream is through the middle of the cross section and along the top of the rectangular labyrinth weirs. The maximum dominant velocities for Model B at S0 = 5% were 0.83 and 1.01 m/s; at S0 = 10%, they were 1.12 and 1.61 m/s at low and high flows, respectively. The low mean velocities for the same distance and S0 = 5 and 10% were 0.17 and 0.26 m/s, respectively.
Figure 16 shows the contour of the averaged depth velocity for various distances from the weir at low and high discharge. The contour plot shows a large variation in velocity within short distances from the weir. At L/B = 0.61, velocities are low upstream and downstream of the top of the weir. The high velocities occur in the side walls of the weir and the channel. At L/B = 1.22, the low-velocity zone displaces the higher velocity in most of the pool. Higher velocities were found only on the sides of the channel. As the discharge increases, the velocity zone in the pool becomes wider. At L/B = 1.83, there is an area of higher velocities only upstream of the crest and on the sides of the weir. At high discharge, the prevailing maximum velocities for L/B = 0.61, 1.22, and 1.83 were 1.46, 1.65, and 1.84 m/s, respectively. As the distance between weirs increases, the range of maximum velocity increases.
On the other hand, the low mean velocity for these distances was 0.27, 0.44, and 0.72 m/s, respectively. Thus, the low-velocity zone decreases with increasing distance between weirs. Figure 17 shows the pattern distribution of streamlines along with the velocity contour at various distances from the weir for Q = 0.05 m3/s. A stream-like flow is generally formed in the pool at a small distance between weirs (L/B = 0.61). The rotation cell under the jet forms clockwise between the two weirs. At the distances between the spillways (L/B = 1.22), the transition regime of the flow is formed. The transition regime occurs when or shortly after the weir is flooded. The rotation cell under the jet is clockwise smaller than the flow regime and larger than the submergence regime. At a distance L/B = 1.83, a plunging flow is formed so that the plunging jet dips into the pool and extends downstream to the center of the pool. The clockwise rotation of the cell is bounded by the dipping jet of the weir and is located between the bottom and the side walls of the weir and the channel.
Figure 18 shows the average depth velocity bar graph for each weir at different bed slopes and with and without orifice plates. As the distance between weirs increases, all models’ average depth velocity increases. As the slope of the bottom increases and an orifice plate is present, the average depth velocity in the pool increases. In addition, the average pool depth velocity increases as the discharge increases. Among the models, Model A’s average depth velocity is higher than Model B’s. The variation in velocity ranged from 8.11 to 12.24% for the models without an orifice plate and from 10.26 to 16.87% for the models with an orifice plate.
3.4 Turbulence Characteristics
The turbulent kinetic energy is one of the important parameters reflecting the turbulent properties of the flow field [23]. When the k value is high, more energy and a longer transit time are required to migrate the target species. The turbulent kinetic energy is defined as follows:
�=12(�x′2+�y′2+�z′2)
(15)
where ux, uy, and uz are fluctuating velocities in the x, y, and z directions, respectively. An illustration of the TKE and the effects of the geometric arrangement of the weir and the presence of an opening in the weir is shown in Fig. 19. For a given bed slope, in Model A, the highest TKE values are uniformly distributed in the weir’s upstream portion in the channel’s cross section. In contrast, for the rectangular labyrinth weir (Model B), the highest TKE values are concentrated on the sides of the pool between the crest of the weir and the channel wall. The highest TKE value in Models A and B is 0.224 and 0.278 J/kg, respectively, at the highest bottom slope (S0 = 10%). In the downstream portion of the conventional weir and within the crest of the weir and the walls of the rectangular labyrinth, there was a much lower TKE value that provided the best conditions for fish to recover in the pool between the weirs. The average of the lowest TKE for bottom slopes of 5 and 10% in Model A is 0.041 and 0.056 J/kg, and for Model B, is 0.047 and 0.064 J/kg. The presence of an opening in the weirs reduces the area of the highest TKE within the pool. It also increases the resting areas for fish (lower TKE). The highest TKE at the highest bottom slope in Models A and B with an orifice is 0.208 and 0.191 J/kg, respectively.
Figure 20 shows the effect of slope on the longitudinal distribution of TKE in the pools. TKE values significantly increase for a given discharge with an increasing bottom slope. Thus, for a low bed slope (S0 = 5%), a large pool area has expanded with average values of 0.131 and 0.168 J/kg for low and high discharge, respectively. For a bed slope of S0 = 10%, the average TKE values are 0.176 and 0.234 J/kg. Furthermore, as the discharge increases, the area with high TKE values within the pool increases. Lower TKE values are observed at the apex of the labyrinth weir, at the corner of the wall downstream of the weir, and between the side walls of the weir and the channel wall for both bottom slopes. The effect of distance between weirs on TKE is shown in Fig. 21. Low TKE values were observed at low discharge and short distances between weirs. Low TKE values are located at the top of the rectangular labyrinth weir and the downstream corner of the weir wall. There is a maximum value of TKE at the large distances between weirs, L/B = 1.83, along the center line of the pool, where the dip jet meets the bottom of the bed. At high discharge, the maximum TKE value for the distance L/B = 0.61, 1.22, and 1.83 was 0.246, 0.322, and 0.417 J/kg, respectively. In addition, the maximum TKE range increases with the distance between weirs.
For TKE size, the average value (TKEave) is plotted against q in Fig. 22. For all models, the TKE values increase with increasing q. For example, in models A and B with L/B = 0.61 and a slope of 10%, the TKE value increases by 41.66 and 86.95%, respectively, as q increases from 0.1 to 0.27 m2/s. The TKE values in Model B are higher than Model A for a given discharge, bed slope, and weir distance. The TKEave in Model B is higher compared to Model A, ranging from 31.46 to 57.94%. The presence of an orifice in the weir reduces the TKE values in both weirs. The intensity of the reduction is greater in Model B. For example, in Models A and B with L/B = 0.61 and q = 0.1 m2/s, an orifice reduces TKEave values by 60.35 and 19.04%, respectively. For each model, increasing the bed slope increases the TKEave values in the pool. For example, for Model B with q = 0.18 m2/s, increasing the bed slope from 5 to 10% increases the TKEave value by 14.34%. Increasing the distance between weirs increases the TKEave values in the pool. For example, in Model B with S0 = 10% and q = 0.3 m2/s, the TKEave in the pool increases by 34.22% if you increase the distance between weirs from L/B = 0.61 to L/B = 0.183.
Cotel et al. [24] suggested that turbulence intensity (TI) is a suitable parameter for studying fish swimming performance. Figure 23 shows the plot of TI and the effects of the geometric arrangement of the weir and the presence of an orifice. In Model A, the highest TI values are found upstream of the weirs and are evenly distributed across the cross section of the channel. The TI values increase as you move upstream to downstream in the pool. For the rectangular labyrinth weir, the highest TI values were concentrated on the sides of the pool, between the top of the weir and the side wall of the channel, and along the top of the weir. Downstream of the conventional weir, within the apex of the weir, and at the corners of the walls of the rectangular labyrinth weir, the percentage of TI was low. At the highest discharge, the average range of TI in Models A and B was 24–45% and 15–62%, respectively. The diversity of TI is greater in the rectangular labyrinth weir than the conventional weir. Fish swimming performance is reduced due to higher turbulence intensity. However, fish species may prefer different disturbance intensities depending on their swimming abilities; for example, Salmo trutta prefers a disturbance intensity of 18–53% [25]. Kupferschmidt and Zhu [26] found a higher range of TI for fishways, such as natural rock weirs, of 40–60%. The presence of an orifice in the weir increases TI values within the pool, especially along the middle portion of the cross section of the fishway. With an orifice in the weir, the average range of TI in Models A and B was 28–59% and 22–73%, respectively.
The effect of bed slope on TI variation is shown in Fig. 24. TI increases in different pool areas as the bed slope increases for a given discharge. For a low bed slope (S0 = 5%), a large pool area has increased from 38 to 63% and from 56 to 71% for low and high discharge, respectively. For a bed slope of S0 = 10%, the average values of TI are 45–67% and 61–73% for low and high discharge, respectively. Therefore, as runoff increases, the area with high TI values within the pool increases. A lower TI is observed for both bottom slopes in the corner of the wall, downstream of the crest walls, and between the side walls in the weir and channel. Figure 25 compares weir spacing with the distribution of TI values within the pool. The TI values are low at low flows and short distances between weirs. A maximum value of TI occurs at long spacing and where the plunging stream impinges on the bed and the area around the bed. TI ranges from 36 to 57%, 58–72%, and 47–76% for the highest flow in a wide pool area for L/B = 0.61, 1.22, and 1.83, respectively.
The average value of turbulence intensity (TIave) is plotted against q in Fig. 26. The increase in TI values with the increase in q values is seen in all models. For example, the average values of TI for Models A and B at L/B = 0.61 and slope of 10% increased from 23.9 to 33.5% and from 42 to 51.8%, respectively, with the increase in q from 0.1 to 0.27 m2/s. For a given discharge, a given gradient, and a given spacing of weirs, the TIave is higher in Model B than Model A. The presence of an orifice in the weirs increases the TI values in both types. For example, in Models A and B with L/B = 0.61 and q = 0.1 m2/s, the presence of an orifice increases TIave from 23.9 to 37.1% and from 42 to 48.8%, respectively. For each model, TIave in the pool increases with increasing bed slope. For Model B with q = 0.18 m2/s, TIave increases from 37.5 to 45.8% when you increase the invert slope from 5 to 10%. Increasing the distance between weirs increases the TIave in the pool. In Model B with S0 = 10% and q = 0.3 m2/s, the TIave in the pool increases from 51.8 to 63.7% as the distance between weirs increases from L/B = 0.61 to L/B = 0.183.
3.5 Energy Dissipation
To facilitate the passage of various target species through the pool of fishways, it is necessary to pay attention to the energy dissipation of the flow and to keep the flow velocity in the pool slow. The average volumetric energy dissipation (k) in the pool is calculated using the following basic formula:
�=����0��
(16)
where ρ is the water density, and H is the average water depth of the pool. The change in k versus Q for all models at two bottom slopes, S0 = 5%, and S0 = 10%, is shown in Fig. 27. Like the results of Yagci [8] and Kupferschmidt and Zhu [26], at a constant bottom slope, the energy dissipation in the pool increases with increasing discharge. The trend of change in k as a function of Q from the present study at a bottom gradient of S0 = 5% is also consistent with the results of Kupferschmidt and Zhu [26] for the fishway with rock weir. The only difference between the results is the geometry of the fishway and the combination of boulders instead of a solid wall. Comparison of the models shows that the conventional model has lower energy dissipation than the rectangular labyrinth for a given discharge. Also, increasing the distance between weirs decreases the volumetric energy dissipation for each model with the same bed slope. Increasing the slope of the bottom leads to an increase in volumetric energy dissipation, and an opening in the weir leads to a decrease in volumetric energy dissipation for both models. Therefore, as a guideline for volumetric energy dissipation, if the value within the pool is too high, the increased distance of the weir, the decreased slope of the bed, or the creation of an opening in the weir would decrease the volumetric dissipation rate.
To evaluate the energy dissipation inside the pool, the general method of energy difference in two sections can use:
ε=�1−�2�1
(17)
where ε is the energy dissipation rate, and E1 and E2 are the specific energies in Sects. 1 and 2, respectively. The distance between Sects. 1 and 2 is the same. (L is the distance between two upstream and downstream weirs.) Figure 28 shows the changes in ε relative to q (flow per unit width). The rectangular labyrinth weir (Model B) has a higher energy dissipation rate than the conventional weir (Model A) at a constant bottom gradient. For example, at S0 = 5%, L/B = 0.61, and q = 0.08 m3/s.m, the energy dissipation rate in Model A (conventional weir) was 0.261. In Model B (rectangular labyrinth weir), however, it was 0.338 (22.75% increase). For each model, the energy dissipation rate within the pool increases as the slope of the bottom increases. For Model B with L/B = 1.83 and q = 0.178 m3/s.m, the energy dissipation rate at S0 = 5% and 10% is 0.305 and 0.358, respectively (14.8% increase). Figure 29 shows an orifice’s effect on the pools’ energy dissipation rate. With an orifice in the weir, both models’ energy dissipation rates decreased. Thus, the reduction in energy dissipation rate varied from 7.32 to 9.48% for Model A and from 8.46 to 10.57 for Model B.
4 Discussion
This study consisted of entirely of numerical analysis. Although this study was limited to two weirs, the hydraulic performance and flow characteristics in a pooled fishway are highlighted by the rectangular labyrinth weir and its comparison with the conventional straight weir. The study compared the numerical simulations with laboratory experiments in terms of surface profiles, velocity vectors, and flow characteristics in a fish ladder pool. The results indicate agreement between the numerical and laboratory data, supporting the reliability of the numerical model in capturing the observed phenomena.
When the configuration of the weir changes to a rectangular labyrinth weir, the flow characteristics, the maximum and minimum area, and even the location of each hydraulic parameter change compared to a conventional weir. In the rectangular labyrinth weir, the flow is gradually directed to the sides as it passes the weir. This increases the velocity at the sides of the channel [21]. Therefore, the high-velocity area is located on the sides. In the downstream apex of the weir, the flow velocity is low, and this area may be suitable for swimming target fish. However, no significant change in velocity was observed at the conventional weir within the fish ladder. This resulted in an average increase in TKE of 32% and an average increase in TI of about 17% compared to conventional weirs.
In addition, there is a slight difference in the flow regime for both weir configurations. In addition, the rectangular labyrinth weir has a higher energy dissipation rate for a given discharge and constant bottom slope than the conventional weir. By reducing the distance between the weirs, this becomes even more intense. Finally, the presence of an orifice in both configurations of the weir increased the flow velocity at the orifice and in the middle of the pool, reducing the highest TKE value and increasing the values of TI within the pool of the fish ladder. This resulted in a reduction in volumetric energy dissipation for both weir configurations.
The results of this study will help the reader understand the direct effects of the governing geometric parameters on the hydraulic characteristics of a fishway with a pool and weir. However, due to the limited configurations of the study, further investigation is needed to evaluate the position of the weir’s crest on the flow direction and the difference in flow characteristics when combining boulders instead of a solid wall for this type of labyrinth weir [26]. In addition, hydraulic engineers and biologists must work together to design an effective fishway with rectangular labyrinth configurations. The migration habits of the target species should be considered when designing the most appropriate design [27]. Parametric studies and field observations are recommended to determine the perfect design criteria.
The current study focused on comparing a rectangular labyrinth weir with a conventional straight weir. Further research can explore other weir configurations, such as variations in crest position, different shapes of labyrinth weirs, or the use of boulders instead of solid walls. This would help understand the influence of different geometric parameters on hydraulic characteristics.
5 Conclusions
A new layout of the weir was evaluated, namely a rectangular labyrinth weir compared to a straight weir in a pool and weir system. The differences between the weirs were highlighted, particularly how variations in the geometry of the structures, such as the shape of the weir, the spacing of the weir, the presence of an opening at the weir, and the slope of the bottom, affect the hydraulics within the structures. The main findings of this study are as follows:
The calculated dimensionless discharge (Qt*) confirmed three different flow regimes: when the corresponding range of Qt* is smaller than 0.6, the regime of plunging flow occurs for values of L/B = 1.83. (L: distance of the weir; B: channel width). When the corresponding range of Qt* is greater than 0.5, transitional flow occurs at L/B = 1.22. On the other hand, if Qt* is greater than 1, the streaming flow is at values of L/B = 0.61.
For the conventional weir and the rectangular labyrinth weir with the plunging flow, it can be assumed that the discharge (Q) is proportional to 1.56 and 1.47h, respectively (h: water depth above the weir). This information is useful for estimating the discharge based on water depth in practical applications.
In the rectangular labyrinth weir, the high-velocity zone is located on the side walls between the top of the weir and the channel wall. A high-velocity variation within short distances of the weir. Low velocity occurs within the downstream apex of the weir. This area may be suitable for swimming target fish.
As the distance between weirs increased, the zone of maximum velocity increased. However, the zone of low speed decreased. The prevailing maximum velocity for a rectangular labyrinth weir at L/B = 0.61, 1.22, and 1.83 was 1.46, 1.65, and 1.84 m/s, respectively. The low mean velocities for these distances were 0.27, 0.44, and 0.72 m/s, respectively. This finding highlights the importance of weir spacing in determining the flow characteristics within the fishway.
The presence of an orifice in the weir increased the flow velocity at the orifice and in the middle of the pool, especially in a conventional weir. The increase ranged from 7.7 to 12.48%.
For a given bottom slope, in a conventional weir, the highest values of turbulent kinetic energy (TKE) are uniformly distributed in the upstream part of the weir in the cross section of the channel. In contrast, for the rectangular labyrinth weir, the highest TKE values were concentrated on the sides of the pool between the crest of the weir and the channel wall. The highest TKE value for the conventional and the rectangular labyrinth weir was 0.224 and 0.278 J/kg, respectively, at the highest bottom slope (S0 = 10%).
For a given discharge, bottom slope, and weir spacing, the average values of TI are higher for the rectangular labyrinth weir than for the conventional weir. At the highest discharge, the average range of turbulence intensity (TI) for the conventional and rectangular labyrinth weirs was between 24 and 45% and 15% and 62%, respectively. This reveals that the rectangular labyrinth weir may generate more turbulent flow conditions within the fishway.
For a given discharge and constant bottom slope, the rectangular labyrinth weir has a higher energy dissipation rate than the conventional weir (22.75 and 34.86%).
Increasing the distance between weirs decreased volumetric energy dissipation. However, increasing the gradient increased volumetric energy dissipation. The presence of an opening in the weir resulted in a decrease in volumetric energy dissipation for both model types.
Availability of data and materials
Data is contained within the article.
References
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In river engineering, the stepped spillway of a dam is an important component that may be used in various ways. It is necessary to conduct research dealing with flood control in order to investigate the method, in which energy is lost along the tiered spillways. In the past, several research projects on stepped spillways without baffles have been carried out utilizing a range of research approaches. In the present study, machine learning techniques such as Support Vector Machine (SVM) and Regression Tree (RT) are used to analyze the energy dissipation on rectangular stepped spillways that make use of baffles in a variety of configurations and at a range of channel slopes. The results of many experiments indicate that the amount of energy that is lost increases with the number of baffles that are present in flat channels with slopes and rises. In order to evaluate the efficiency and usefulness of the suggested model, the statistical indices that were developed for the experimental research are used to validate the models that were created for the study. The findings indicate that the suggested SVM model properly predicted the amount of energy that was dissipated when contrasted with RT and the method that had been developed in the past. This study verifies the use of machine learning techniques in this industry, and it is unique in that it anticipates energy dissipation along stepped spillways utilizing baffle designs. In addition, this work validates the use of machine learning methods in this field.
Keywords
Rectangular Stepped Spillways, Baffle Arrangements, Channel Slope, Support Vector Machine (SVM), Regression Tree (RT)
Introduction
To regulate water flows downstream of a dam, a spillway structure is employed, with stepped spillways preventing water from overflowing and causing damage to the dam. These spillways consist of a channel with built-in steps or drops. Flow patterns observed include nappe flow, transition flow, and skimming flow [1]. Numerous scholars have looked at the energy dissipation in stepped spillways [2-4]. Boes and Hager [5] looked at the benefits of stepped spillways, such as their simplicity of construction, less danger of cavitation, and smaller stilling basins at downstream dam toes owing to considerable energy loss along the chute. Hazzab and Chafic [7] conducted an experimental study on energy dissipation in stepped spillways and reported on flow configurations. Additionally, the Manksvill dam spillway was examined using a 1:25 scale physical wooden model [6]. For moderately inclined stepped channels, Stefan and Chanson [8] explored air-water flow measurements. Daniel [9] discussed how the existence of steps and step heights affect stepped spillways’ ability to dissipate energy. A comparison of the smooth invert chute flow with the self aerated stepped spillway. The energy dissipation in stepped spillways was investigated using various methods. Katourany [10] compared experimental findings to conventional USBR outcomes to examine the effects of different baffle widths, spacing between baffle rows, and step heights of baffled aprons. Salmasi et al. [11] assessed the energy dissipation of through-flow and over-flow in gabion stepped spillways, discovering that gabion spillways with pervious surfaces dissipated energy more efficiently than those with concrete walls. Other forms of stepped spillways, such as inclined steps and steps with end sills, were also quantitatively studied for energy dissipation [12]. Saedi and Asareh [13] examined how the number of drop stairs affected energy dissipation in stepped drops and suggested using stepped drops to increase energy dissipation by providing flow path roughness. Al-Husseini [14] found that decreasing the number of steps and downstream slopes led to an increase in flow energy dissipation, and that the use of cascade spillways reduced energy dissipation compared to the original step spillway. MARS and ANN methods were used to estimate energy dissipation in flow across stepped spillways under skimming flow conditions, with both models proving reliable [15]. Frederic et al. [16] evaluated the energy dissipation effectiveness and stability of the Mekin Dam spillway by confirming that flow did not result in transitional flow and by calculating safety factors at various intervals. A numerical model was developed to validate a physical model examining the impact of geometrical parameters on the dissipation rate in flows through stepped spillways [17]. The regulation of the rates of dissipation is studied using a particular kind of fuzzy inference system (FIS). The findings are compared with a predefined numerical database to determine the predicted energy dissipation under various circumstances. The findings show that the suggested FIS may be a useful tool for the operational management of dissipator structures while taking various geometric characteristics into account. Nasralla [18] studied the four phases of the spillway and conducted eighteen runs to enhance energy dissipation through the contraction-stepped spillway. The study considered alternative baffle placements, heights, and widths. The results showed that downstream baffles on the stepped spillway of the stilling basin improve energy dissipation. Using the Flow 3D software, Ikinciogullari [19] quantitatively analyzed the energy dissipation capabilities of trapezoidal stepped spillways using four distinct models and three different discharges. The findings showed that trapezoidal stepped spillways are up to 30% more efficient in dissipating energy than traditional stepped spillways. In previous works, only a few machine learning algorithms were used to forecast energy dissipation across a rectangular stepped spillway without baffles. Therefore, this study used machine learning approaches such as Support Vector Machine (SVM) and Regression Tree (RT) to predict energy dissipation across a rectangular stepped spillway with varied rectangular-shaped baffle configurations at different channel slopes. The study compared these models using statistical analysis to assess their efficiency in predicting energy dissipation over rectangular stepped spillways with baffles. 2. Materials and Methods 2.1. Experimental Setup The experiments were carried out at the Hydraulics laboratory of Delhi Technological University. The tests were performed in a rectangular tilting flume of 8m long, 0.30m wide and 0.40m deep which has a facility to make it horizontal and sloping as well (shown in Figure 1). The flume consists of an inlet section, an outlet section, and a collecting tank at the downstream end which is used to measure the discharge. Figure 2 depicts the model of a rectangular stepped spillway prepared using an acrylic sheet having a width of 0.30m, a height of 0.20m and a base length of 0.40m. A total of four steps were designed with a step height of 0.05m, the step length is 0.10m and rectangular-shaped baffles of length 0.10m and height of 0.05m were arranged in different manner. Figure 3 represents the different baffle arrangements used in the experimental work. At first, the experiment was conducted for no baffle condition. Thereafter the experiment was conducted for the first arrangement of three baffles, in which two baffles were placed at a distance of 0.10m from the toe of the spillway and a distance of 0.10m was maintained between the first two baffles and the third baffle was placed between the first two baffles at a distance of 0.20m from the toe of the spillway (figure 4a). After that, the experiment was conducted for the third arrangement of baffles which consists of five baffles, two more baffles were introduced at a distance of 0.30m from the toe of the spillway and a distance of 0.10m was maintained between them (figure 4b). The baffles used in the experiment were rectangular shaped which had a height of 0.05m and length of 0.10m. The experiments were conducted for five different discharges 2 l/s, 4 l/s, 6 l/s, 8 l/s and 10 l/s. For the purpose of determining the head values both upstream and downstream of the spillway model, a point gauge with a precision of 0.1mm was used. In order to determine the average velocities of the upstream and downstream portions, respectively, a pitot static tube was used in conjunction with a digital manometer.
Fine sediments enter into the river through various sources such as channel bed, bank, and catchment. It has been regarded as a type of pollution in river. Fine sediments present in a river have a significant effect on river health. Benthic micro-organism, plants, and large fishes, all are part of food chain of river biota. Any detrimental effect on any of these components of food chain misbalances the entire riverine ecosystem. Numerous studies have been carried out on the various environmental aspects of rivers considering the presence of fine sediment in river flow. The present paper critically reviews many of these aspects to understand the various environmental impacts of suspended sediment on river health, flora and fauna.
Introduction The existence of fine sediment in a river system is a natural phenomenon. But in many cases it is exacerbated by the manmade activities. The natural cause of fines being in flow generally keeps the whole system in equilibrium except during some calamites whereas anthropogenic activities leading to fines entering into the flow puts several adverse impacts on the entire river system and its ecology. Presence of fines in flow is considered as a type of pollution in water. In United States, the fine sediment in water along with other non point source pollution is considered as a major obstacle in providing quality water for fishes and recreation activities (Diplas and Parker 1985). Sediments in a river are broadly of two types, organic and inorganic, and they both move in two ways either along the bed of the channel called bed load or in suspension called suspended load and their movements depend upon fluid flow and sediment characteristics. Further many investigators have divided the materials in suspension into two different types. One which originates from channel bed and bank is called bed material suspended load and another that migrates from feeding catchment area is called wash load. A general perception is that wash loads are very fine materials like clay, silt but it may not always be true (Woo et al. 1986). In general, suspended materials are of size less than 2 mm. The impact of sand on the various aspects of river is comparatively less than that of silt and clay. The latter are chemically active and good carrier of many contaminants and nutrients such as dioxins, phosphorous, heavy and trace metals, polychlorinated biphenyl (PCBs), radionuclide, etc. (Foster and Charlesworth 1996; Horowitz et al. 1995; Owens et al. 2001; Salomons and Förstner 1984; Stone and Droppo 1994; Thoms 1987). Foy and Bailey-Watt (1998) reported that out of 129 lakes in England and Wales, 69% have phosphorous contamination. Ten percent lakes, rivers, and bays of United States have sediment contaminants with chemicals as reported by USEPA. Several field and experimental studies have been conducted considering, sand, silt, and clay as suspended material. Hence, the subject reported herein is based on considering the fine sediment size smaller than 2 mm. Fine sediments have the ability to alter the hydraulics of the flow. Presence of fines in flow can change the magnitude of turbulence, it can change the friction resistance to flow. Fines can change the mobility and permeability of the bed material. In some extreme cases, fines in flow may even change the morphology of the river (Doeg and Koehn 1994; Nuttall 1972; Wright and Berrie 1987). Fines in the flow adversely affect the producer by increasing the turbidity, hindering the photosynthesis process by limiting the light penetration. This is ultimately reflected in the entire food ecosystem of river (Davis-Colley et al. 1992; Van Niewenhuyre and Laparrieve 1986). In addition, abrasion due to flowing sediment kills the aquatic flora (Edwards 1969; Brookes 1986). Intrusion of fines into the pores of river bed reduces space for several invertebrates, affects the spawning process (Petts 1984; Richards and Bacon 1994; Schalchli 1992). There are several other direct or indirect, short-term or long-term impacts of fines in river. The present paper reports the physical/environmental significance of fines in river. The hydraulic significance of presence of fines in the river has been reviewed in another paper (Effect of fine sediments on river hydraulics – a research review – http://dx.doi.org/10.1080/09715010.2014.982001).
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A numerical study was performed on the embankment weir overflows with various surface roughness and tailwater submergence, to better understand the effects of weir roughness on discharge performances under the free and submerged conditions. The variation of flow regime is captured, from the free overflow, submerged hydraulic jump, to surface flow with increasing tailwater depth. A roughness factor is introduced to reflect the reduction in discharge caused by weir roughness. The roughness factor decreases with the roughness height, and it also depends on the tailwater depth, highlighting various relations of the roughness factor with the roughness height between different flow regimes, which is linear for the free overflow and submerged hydraulic jump while exponential for the surface flow. Accordingly, the effects of weir roughness on overflow discharge appear nonnegligible for the significant roughness height and the surface flow regime occurring under considerable tailwater submergence. The established empirical expressions of discharge coefficient and submergence and roughness factors make it possible to predict the discharge over embankment weirs considering both tailwater submergence and surface roughness.
자유 및 침수 조건에서 방류 성능에 대한 둑 거칠기의 영향을 더 잘 이해하기 위해 다양한 표면 거칠기와 테일워터 침수를 갖는 제방 둑 범람에 대한 수치 연구가 수행되었습니다.
자유 범람, 수중 수압 점프, 테일워터 깊이가 증가하는 표면 유동에 이르기까지 유동 체제의 변화가 캡처됩니다. 위어 거칠기로 인한 배출 감소를 반영하기 위해 거칠기 계수가 도입되었습니다.
조도 계수는 조도 높이와 함께 감소하고, 또한 테일워터 깊이에 따라 달라지며, 서로 다른 흐름 영역 사이의 조도 높이와 조도 계수의 다양한 관계를 강조합니다.
이는 자유 범람 및 수중 수압 점프에 대해 선형인 반면 표면에 대해 지수적입니다. 흐름. 따라서 월류 방류에 대한 웨어 조도의 영향은 상당한 조도 높이와 상당한 방수 침수 하에서 발생하는 표면 흐름 체제에 대해 무시할 수 없는 것으로 보입니다.
방류계수와 침수 및 조도계수의 확립된 실증식은 방류수 침수와 지표조도를 모두 고려한 제방보 위의 방류량을 예측할 수 있게 합니다.
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Mahdi Feizbahr,1Navid Tonekaboni,2Guang-Jun Jiang,3,4and Hong-Xia Chen3,4 Academic Editor: Mohammad Yazdi
Abstract
강을 따라 식생은 조도를 증가시키고 평균 유속을 감소시키며, 유동 에너지를 감소시키고 강 횡단면의 유속 프로파일을 변경합니다. 자연의 많은 운하와 강은 홍수 동안 초목으로 덮여 있습니다. 운하의 조도는 식물의 영향을 많이 받기 때문에 홍수시 유동저항에 큰 영향을 미친다. 식물로 인한 흐름에 대한 거칠기 저항은 흐름 조건과 식물에 따라 달라지므로 모델은 유속, 유속 깊이 및 수로를 따라 식생 유형의 영향을 고려하여 유속을 시뮬레이션해야 합니다. 총 48개의 모델을 시뮬레이션하여 근관의 거칠기 효과를 조사했습니다. 결과는 속도를 높임으로써 베드 속도를 감소시키는 식생의 영향이 무시할만하다는 것을 나타냅니다.
Abstract
Vegetation along the river increases the roughness and reduces the average flow velocity, reduces flow energy, and changes the flow velocity profile in the cross section of the river. Many canals and rivers in nature are covered with vegetation during the floods. Canal’s roughness is strongly affected by plants and therefore it has a great effect on flow resistance during flood. Roughness resistance against the flow due to the plants depends on the flow conditions and plant, so the model should simulate the current velocity by considering the effects of velocity, depth of flow, and type of vegetation along the canal. Total of 48 models have been simulated to investigate the effect of roughness in the canal. The results indicated that, by enhancing the velocity, the effect of vegetation in decreasing the bed velocity is negligible, while when the current has lower speed, the effect of vegetation on decreasing the bed velocity is obviously considerable.
1. Introduction
Considering the impact of each variable is a very popular field within the analytical and statistical methods and intelligent systems [1–14]. This can help research for better modeling considering the relation of variables or interaction of them toward reaching a better condition for the objective function in control and engineering [15–27]. Consequently, it is necessary to study the effects of the passive factors on the active domain [28–36]. Because of the effect of vegetation on reducing the discharge capacity of rivers [37], pruning plants was necessary to improve the condition of rivers. One of the important effects of vegetation in river protection is the action of roots, which cause soil consolidation and soil structure improvement and, by enhancing the shear strength of soil, increase the resistance of canal walls against the erosive force of water. The outer limbs of the plant increase the roughness of the canal walls and reduce the flow velocity and deplete the flow energy in vicinity of the walls. Vegetation by reducing the shear stress of the canal bed reduces flood discharge and sedimentation in the intervals between vegetation and increases the stability of the walls [38–41].
One of the main factors influencing the speed, depth, and extent of flood in this method is Manning’s roughness coefficient. On the other hand, soil cover [42], especially vegetation, is one of the most determining factors in Manning’s roughness coefficient. Therefore, it is expected that those seasonal changes in the vegetation of the region will play an important role in the calculated value of Manning’s roughness coefficient and ultimately in predicting the flood wave behavior [43–45]. The roughness caused by plants’ resistance to flood current depends on the flow and plant conditions. Flow conditions include depth and velocity of the plant, and plant conditions include plant type, hardness or flexibility, dimensions, density, and shape of the plant [46]. In general, the issue discussed in this research is the optimization of flood-induced flow in canals by considering the effect of vegetation-induced roughness. Therefore, the effect of plants on the roughness coefficient and canal transmission coefficient and in consequence the flow depth should be evaluated [47, 48].
Current resistance is generally known by its roughness coefficient. The equation that is mainly used in this field is Manning equation. The ratio of shear velocity to average current velocity is another form of current resistance. The reason for using the ratio is that it is dimensionless and has a strong theoretical basis. The reason for using Manning roughness coefficient is its pervasiveness. According to Freeman et al. [49], the Manning roughness coefficient for plants was calculated according to the Kouwen and Unny [50] method for incremental resistance. This method involves increasing the roughness for various surface and plant irregularities. Manning’s roughness coefficient has all the factors affecting the resistance of the canal. Therefore, the appropriate way to more accurately estimate this coefficient is to know the factors affecting this coefficient [51].
To calculate the flow rate, velocity, and depth of flow in canals as well as flood and sediment estimation, it is important to evaluate the flow resistance. To determine the flow resistance in open ducts, Manning, Chézy, and Darcy–Weisbach relations are used [52]. In these relations, there are parameters such as Manning’s roughness coefficient (n), Chézy roughness coefficient (C), and Darcy–Weisbach coefficient (f). All three of these coefficients are a kind of flow resistance coefficient that is widely used in the equations governing flow in rivers [53].
The three relations that express the relationship between the average flow velocity (V) and the resistance and geometric and hydraulic coefficients of the canal are as follows:where n, f, and c are Manning, Darcy–Weisbach, and Chézy coefficients, respectively. V = average flow velocity, R = hydraulic radius, Sf = slope of energy line, which in uniform flow is equal to the slope of the canal bed, = gravitational acceleration, and Kn is a coefficient whose value is equal to 1 in the SI system and 1.486 in the English system. The coefficients of resistance in equations (1) to (3) are related as follows:
Based on the boundary layer theory, the flow resistance for rough substrates is determined from the following general relation:where f = Darcy–Weisbach coefficient of friction, y = flow depth, Ks = bed roughness size, and A = constant coefficient.
On the other hand, the relationship between the Darcy–Weisbach coefficient of friction and the shear velocity of the flow is as follows:
By using equation (6), equation (5) is converted as follows:
Investigation on the effect of vegetation arrangement on shear velocity of flow in laboratory conditions showed that, with increasing the shear Reynolds number (), the numerical value of the ratio also increases; in other words the amount of roughness coefficient increases with a slight difference in the cases without vegetation, checkered arrangement, and cross arrangement, respectively [54].
Roughness in river vegetation is simulated in mathematical models with a variable floor slope flume by different densities and discharges. The vegetation considered submerged in the bed of the flume. Results showed that, with increasing vegetation density, canal roughness and flow shear speed increase and with increasing flow rate and depth, Manning’s roughness coefficient decreases. Factors affecting the roughness caused by vegetation include the effect of plant density and arrangement on flow resistance, the effect of flow velocity on flow resistance, and the effect of depth [45, 55].
One of the works that has been done on the effect of vegetation on the roughness coefficient is Darby [56] study, which investigates a flood wave model that considers all the effects of vegetation on the roughness coefficient. There are currently two methods for estimating vegetation roughness. One method is to add the thrust force effect to Manning’s equation [47, 57, 58] and the other method is to increase the canal bed roughness (Manning-Strickler coefficient) [45, 59–61]. These two methods provide acceptable results in models designed to simulate floodplain flow. Wang et al. [62] simulate the floodplain with submerged vegetation using these two methods and to increase the accuracy of the results, they suggested using the effective height of the plant under running water instead of using the actual height of the plant. Freeman et al. [49] provided equations for determining the coefficient of vegetation roughness under different conditions. Lee et al. [63] proposed a method for calculating the Manning coefficient using the flow velocity ratio at different depths. Much research has been done on the Manning roughness coefficient in rivers, and researchers [49, 63–66] sought to obtain a specific number for n to use in river engineering. However, since the depth and geometric conditions of rivers are completely variable in different places, the values of Manning roughness coefficient have changed subsequently, and it has not been possible to choose a fixed number. In river engineering software, the Manning roughness coefficient is determined only for specific and constant conditions or normal flow. Lee et al. [63] stated that seasonal conditions, density, and type of vegetation should also be considered. Hydraulic roughness and Manning roughness coefficient n of the plant were obtained by estimating the total Manning roughness coefficient from the matching of the measured water surface curve and water surface height. The following equation is used for the flow surface curve:where is the depth of water change, S0 is the slope of the canal floor, Sf is the slope of the energy line, and Fr is the Froude number which is obtained from the following equation:where D is the characteristic length of the canal. Flood flow velocity is one of the important parameters of flood waves, which is very important in calculating the water level profile and energy consumption. In the cases where there are many limitations for researchers due to the wide range of experimental dimensions and the variety of design parameters, the use of numerical methods that are able to estimate the rest of the unknown results with acceptable accuracy is economically justified.
FLOW-3D software uses Finite Difference Method (FDM) for numerical solution of two-dimensional and three-dimensional flow. This software is dedicated to computational fluid dynamics (CFD) and is provided by Flow Science [67]. The flow is divided into networks with tubular cells. For each cell there are values of dependent variables and all variables are calculated in the center of the cell, except for the velocity, which is calculated at the center of the cell. In this software, two numerical techniques have been used for geometric simulation, FAVOR™ (Fractional-Area-Volume-Obstacle-Representation) and the VOF (Volume-of-Fluid) method. The equations used at this model for this research include the principle of mass survival and the magnitude of motion as follows. The fluid motion equations in three dimensions, including the Navier–Stokes equations with some additional terms, are as follows:where are mass accelerations in the directions x, y, z and are viscosity accelerations in the directions x, y, z and are obtained from the following equations:
Shear stresses in equation (11) are obtained from the following equations:
The standard model is used for high Reynolds currents, but in this model, RNG theory allows the analytical differential formula to be used for the effective viscosity that occurs at low Reynolds numbers. Therefore, the RNG model can be used for low and high Reynolds currents.
Weather changes are high and this affects many factors continuously. The presence of vegetation in any area reduces the velocity of surface flows and prevents soil erosion, so vegetation will have a significant impact on reducing destructive floods. One of the methods of erosion protection in floodplain watersheds is the use of biological methods. The presence of vegetation in watersheds reduces the flow rate during floods and prevents soil erosion. The external organs of plants increase the roughness and decrease the velocity of water flow and thus reduce its shear stress energy. One of the important factors with which the hydraulic resistance of plants is expressed is the roughness coefficient. Measuring the roughness coefficient of plants and investigating their effect on reducing velocity and shear stress of flow is of special importance.
Roughness coefficients in canals are affected by two main factors, namely, flow conditions and vegetation characteristics [68]. So far, much research has been done on the effect of the roughness factor created by vegetation, but the issue of plant density has received less attention. For this purpose, this study was conducted to investigate the effect of vegetation density on flow velocity changes.
In a study conducted using a software model on three density modes in the submerged state effect on flow velocity changes in 48 different modes was investigated (Table 1).
Table 1
The studied models.
The number of cells used in this simulation is equal to 1955888 cells. The boundary conditions were introduced to the model as a constant speed and depth (Figure 1). At the output boundary, due to the presence of supercritical current, no parameter for the current is considered. Absolute roughness for floors and walls was introduced to the model (Figure 1). In this case, the flow was assumed to be nonviscous and air entry into the flow was not considered. After seconds, this model reached a convergence accuracy of .
Figure 1
The simulated model and its boundary conditions.
Due to the fact that it is not possible to model the vegetation in FLOW-3D software, in this research, the vegetation of small soft plants was studied so that Manning’s coefficients can be entered into the canal bed in the form of roughness coefficients obtained from the studies of Chow [69] in similar conditions. In practice, in such modeling, the effect of plant height is eliminated due to the small height of herbaceous plants, and modeling can provide relatively acceptable results in these conditions.
48 models with input velocities proportional to the height of the regular semihexagonal canal were considered to create supercritical conditions. Manning coefficients were applied based on Chow [69] studies in order to control the canal bed. Speed profiles were drawn and discussed.
Any control and simulation system has some inputs that we should determine to test any technology [70–77]. Determination and true implementation of such parameters is one of the key steps of any simulation [23, 78–81] and computing procedure [82–86]. The input current is created by applying the flow rate through the VFR (Volume Flow Rate) option and the output flow is considered Output and for other borders the Symmetry option is considered.
Simulation of the models and checking their action and responses and observing how a process behaves is one of the accepted methods in engineering and science [87, 88]. For verification of FLOW-3D software, the results of computer simulations are compared with laboratory measurements and according to the values of computational error, convergence error, and the time required for convergence, the most appropriate option for real-time simulation is selected (Figures 2 and 3 ).
Figure 2
Modeling the plant with cylindrical tubes at the bottom of the canal.
Figure 3
Velocity profiles in positions 2 and 5.
The canal is 7 meters long, 0.5 meters wide, and 0.8 meters deep. This test was used to validate the application of the software to predict the flow rate parameters. In this experiment, instead of using the plant, cylindrical pipes were used in the bottom of the canal.
The conditions of this modeling are similar to the laboratory conditions and the boundary conditions used in the laboratory were used for numerical modeling. The critical flow enters the simulation model from the upstream boundary, so in the upstream boundary conditions, critical velocity and depth are considered. The flow at the downstream boundary is supercritical, so no parameters are applied to the downstream boundary.
The software well predicts the process of changing the speed profile in the open canal along with the considered obstacles. The error in the calculated speed values can be due to the complexity of the flow and the interaction of the turbulence caused by the roughness of the floor with the turbulence caused by the three-dimensional cycles in the hydraulic jump. As a result, the software is able to predict the speed distribution in open canals.
2. Modeling Results
After analyzing the models, the results were shown in graphs (Figures 4–14 ). The total number of experiments in this study was 48 due to the limitations of modeling.
Flow velocity profiles for canals with a depth of 1 m and flow velocities of 3–3.3 m/s. Canal with a depth of 1 meter and a flow velocity of (a) 3 meters per second, (b) 3.1 meters per second, (c) 3.2 meters per second, and (d) 3.3 meters per second.
Figure 5
Canal diagram with a depth of 1 meter and a flow rate of 3 meters per second.
Figure 6
Canal diagram with a depth of 1 meter and a flow rate of 3.1 meters per second.
Figure 7
Canal diagram with a depth of 1 meter and a flow rate of 3.2 meters per second.
Figure 8
Canal diagram with a depth of 1 meter and a flow rate of 3.3 meters per second.
Flow velocity profiles for canals with a depth of 2 m and flow velocities of 4–4.3 m/s. Canal with a depth of 2 meters and a flow rate of (a) 4 meters per second, (b) 4.1 meters per second, (c) 4.2 meters per second, and (d) 4.3 meters per second.
Figure 10
Canal diagram with a depth of 2 meters and a flow rate of 4 meters per second.
Figure 11
Canal diagram with a depth of 2 meters and a flow rate of 4.1 meters per second.
Figure 12
Canal diagram with a depth of 2 meters and a flow rate of 4.2 meters per second.
Figure 13
Canal diagram with a depth of 2 meters and a flow rate of 4.3 meters per second.
Flow velocity profiles for canals with a depth of 3 m and flow velocities of 5–5.3 m/s. Canal with a depth of 2 meters and a flow rate of (a) 4 meters per second, (b) 4.1 meters per second, (c) 4.2 meters per second, and (d) 4.3 meters per second.
To investigate the effects of roughness with flow velocity, the trend of flow velocity changes at different depths and with supercritical flow to a Froude number proportional to the depth of the section has been obtained.
According to the velocity profiles of Figure 5, it can be seen that, with the increasing of Manning’s coefficient, the canal bed speed decreases.
According to Figures 5 to 8, it can be found that, with increasing the Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the models 1 to 12, which can be justified by increasing the speed and of course increasing the Froude number.
According to Figure 10, we see that, with increasing Manning’s coefficient, the canal bed speed decreases.
According to Figure 11, we see that, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of Figures 5–10, which can be justified by increasing the speed and, of course, increasing the Froude number.
With increasing Manning’s coefficient, the canal bed speed decreases (Figure 12). But this deceleration is more noticeable than the deceleration of the higher models (Figures 5–8 and 10, 11), which can be justified by increasing the speed and, of course, increasing the Froude number.
According to Figure 13, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of Figures 5 to 12, which can be justified by increasing the speed and, of course, increasing the Froude number.
According to Figure 15, with increasing Manning’s coefficient, the canal bed speed decreases.
Figure 15
Canal diagram with a depth of 3 meters and a flow rate of 5 meters per second.
According to Figure 16, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher model, which can be justified by increasing the speed and, of course, increasing the Froude number.
Figure 16
Canal diagram with a depth of 3 meters and a flow rate of 5.1 meters per second.
According to Figure 17, it is clear that, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher models, which can be justified by increasing the speed and, of course, increasing the Froude number.
Figure 17
Canal diagram with a depth of 3 meters and a flow rate of 5.2 meters per second.
According to Figure 18, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher models, which can be justified by increasing the speed and, of course, increasing the Froude number.
Figure 18
Canal diagram with a depth of 3 meters and a flow rate of 5.3 meters per second.
According to Figure 19, it can be seen that the vegetation placed in front of the flow input velocity has negligible effect on the reduction of velocity, which of course can be justified due to the flexibility of the vegetation. The only unusual thing is the unexpected decrease in floor speed of 3 m/s compared to higher speeds.
Comparison of velocity profiles with the same plant densities (depth 1 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 1 m; (b) plant densities of 50%, depth 1 m; and (c) plant densities of 75%, depth 1 m.
According to Figure 20, by increasing the speed of vegetation, the effect of vegetation on reducing the flow rate becomes more noticeable. And the role of input current does not have much effect in reducing speed.
Comparison of velocity profiles with the same plant densities (depth 2 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 2 m; (b) plant densities of 50%, depth 2 m; and (c) plant densities of 75%, depth 2 m.
According to Figure 21, it can be seen that, with increasing speed, the effect of vegetation on reducing the bed flow rate becomes more noticeable and the role of the input current does not have much effect. In general, it can be seen that, by increasing the speed of the input current, the slope of the profiles increases from the bed to the water surface and due to the fact that, in software, the roughness coefficient applies to the channel floor only in the boundary conditions, this can be perfectly justified. Of course, it can be noted that, due to the flexible conditions of the vegetation of the bed, this modeling can show acceptable results for such grasses in the canal floor. In the next directions, we may try application of swarm-based optimization methods for modeling and finding the most effective factors in this research [2, 7, 8, 15, 18, 89–94]. In future, we can also apply the simulation logic and software of this research for other domains such as power engineering [95–99].
Comparison of velocity profiles with the same plant densities (depth 3 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 3 m; (b) plant densities of 50%, depth 3 m; and (c) plant densities of 75%, depth 3 m.
3. Conclusion
The effects of vegetation on the flood canal were investigated by numerical modeling with FLOW-3D software. After analyzing the results, the following conclusions were reached:(i)Increasing the density of vegetation reduces the velocity of the canal floor but has no effect on the velocity of the canal surface.(ii)Increasing the Froude number is directly related to increasing the speed of the canal floor.(iii)In the canal with a depth of one meter, a sudden increase in speed can be observed from the lowest speed and higher speed, which is justified by the sudden increase in Froude number.(iv)As the inlet flow rate increases, the slope of the profiles from the bed to the water surface increases.(v)By reducing the Froude number, the effect of vegetation on reducing the flow bed rate becomes more noticeable. And the input velocity in reducing the velocity of the canal floor does not have much effect.(vi)At a flow rate between 3 and 3.3 meters per second due to the shallow depth of the canal and the higher landing number a more critical area is observed in which the flow bed velocity in this area is between 2.86 and 3.1 m/s.(vii)Due to the critical flow velocity and the slight effect of the roughness of the horseshoe vortex floor, it is not visible and is only partially observed in models 1-2-3 and 21.(viii)As the flow rate increases, the effect of vegetation on the rate of bed reduction decreases.(ix)In conditions where less current intensity is passing, vegetation has a greater effect on reducing current intensity and energy consumption increases.(x)In the case of using the flow rate of 0.8 cubic meters per second, the velocity distribution and flow regime show about 20% more energy consumption than in the case of using the flow rate of 1.3 cubic meters per second.
Nomenclature
n:
Manning’s roughness coefficient
C:
Chézy roughness coefficient
f:
Darcy–Weisbach coefficient
V:
Flow velocity
R:
Hydraulic radius
g:
Gravitational acceleration
y:
Flow depth
Ks:
Bed roughness
A:
Constant coefficient
:
Reynolds number
∂y/∂x:
Depth of water change
S0:
Slope of the canal floor
Sf:
Slope of energy line
Fr:
Froude number
D:
Characteristic length of the canal
G:
Mass acceleration
:
Shear stresses.
Data Availability
All data are included within the paper.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was partially supported by the National Natural Science Foundation of China under Contract no. 71761030 and Natural Science Foundation of Inner Mongolia under Contract no. 2019LH07003.
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The hydrodynamics of coral reefs strongly influences their biological functioning, impacting processes such as nutrient availability and uptake, recruitment success and bleaching. For example, coral reefs located in oligotrophic regions depend on upwelling for nutrient supply. Coral reefs at Sodwana Bay, located on the east coast of South Africa, are an example of high latitude marginal reefs. These reefs are subjected to complex hydrodynamic forcings due to the interaction between the strong Agulhas current and the highly variable topography of the region. In this study, we explore the reef scale hydrodynamics resulting from the bathymetry for two steady current scenarios at Two-Mile Reef (TMR) using a combination of field data and numerical simulations. The influence of tides or waves was not considered for this study as well as reef-scale roughness. Tilt current meters with onboard temperature sensors were deployed at selected locations within TMR. We used field observations to identify the dominant flow conditions on the reef for numerical simulations that focused on the hydrodynamics driven by mean currents. During the field campaign, southerly currents were the predominant flow feature with occasional flow reversals to the north. Northerly currents were associated with greater variability towards the southern end of TMR. Numerical simulations showed that Jesser Point was central to the development of flow features for both the northerly and southerly current scenarios. High current variability in the south of TMR during reverse currents is related to the formation of Kelvin-Helmholtz type shear instabilities along the outer edge of an eddy formed north of Jesser Point. Furthermore, downward vertical velocities were computed along the offshore shelf at TMR during southerly currents. Current reversals caused a change in vertical velocities to an upward direction due to the orientation of the bathymetry relative to flow directions.
Highlights
A predominant southerly current was measured at Two-Mile Reef with occasional reversals towards the north.
Field observations indicated that northerly currents are spatially varied along Two-Mile Reef.
Simulation of reverse currents show the formation of a separated flow due to interaction with Jesser Point with Kelvin–Helmholtz type shear instabilities along the seaward edge.
지금까지 Sodwana Bay에서 자세한 암초 규모 유체 역학을 모델링하려는 시도는 없었습니다. 이러한 모델의 결과는 규모가 있는 산호초 사이의 흐름이 산호초 건강에 어떤 영향을 미치는지 탐색하는 데 사용할 수 있습니다. 이 연구에서는 Sodwana Bay의 유체역학을 탐색하는 데 사용할 수 있는 LES 모델을 개발하기 위한 단계별 접근 방식을 구현합니다. 여기서 우리는 이 초기 단계에서 파도와 조수의 영향을 배제하면서 Agulhas 해류의 유체역학에 초점을 맞춥니다. 이 접근법은 흐름의 첫 번째 LES를 제시하고 Sodwana Bay의 산호초에서 혼합함으로써 향후 연구의 기초를 제공합니다.
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Melquisedec Cortés Zambrano*, Helmer Edgardo Monroy González, Wilson Enrique Amaya Tequia Faculty of Civil Engineering, Santo Tomas Tunja University. Address Av. Universitaria No. 45-202. Tunja – Boyacá – Colombia
Abstract
홍수는 지반이동 및 이동의 원인 중 하나이며, 급속한 도시화 및 도시화로 인해 이전보다 빈번하게 발생할 수 있다. 도시 배수 시스템의 특성은 집수 요소가 결정적인 역할을 하는 범람의 발생 및 범위를 정의할 수 있습니다. 이 문서는 7가지 유형의 화격자 유입구의 수력 유입 효율 및 배출 계수에 대한 수치 조사를 제시합니다. FLOW-3D® 시뮬레이터는 Q = 24, 34.1, 44, 100, 200 및 300 L/s의 유속에서 풀 스케일로 격자를 테스트하는 데 사용되며 종방향 기울기가 1.0인 실험 프로토타입의 구성을 유지합니다. %, 1.5% 및 2.0% 및 고정 횡단 경사, 총 126개 모델. 그 결과를 바탕으로 종류별 및 종단경사 조건에 따른 수력유입구 효율곡선과 토출계수를 구성하였다. 결과는 다른 조사에서 제안된 경험적 공식으로 조정되어 프로토타입의 물리적 테스트 결과를 검증하는 역할을 합니다.
Floods are one of the causes of ground movement and displacement, and due to rapid urbanization and urban growth may occur more frequently than before. The characteristics of an urban drainage system can define the occurrence and extent of flooding, where catchment elements have a determining role. This document presents the numerical investigation of the hydraulic inlet efficiency and the discharge coefficient of seven types of grate inlets. The FLOW-3D® simulator is used to test the gratings at a full scale, under flow rates of Q = 24, 34.1, 44, 100, 200 and 300 L/s, preserving the configuration of the experimental prototype with longitudinal slopes of 1.0%, 1.5% and 2.0% and a fixed cross slope, for a total of 126 models. Based on the results, hydraulic inlet efficiency curves and discharge coefficients are constructed for each type and a longitudinal slope condition. The results are adjusted with empirical formulations proposed in other investigations, serving to verify the results of physical testing of prototypes.
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Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced roughness coefficient and invert level changes
Maryam Bagheria, Seyed M. Ali Zomorodianb, Masih Zolghadrc, H. Md. Azamathulla d,* and C. Venkata Siva Rama Prasade a Hydraulic Structures, Department of Water Engineering, Shiraz University, Shiraz, Iran b Department of Water Engineering, College of Agriculture, Shiraz University, Shiraz, Iran c Department of Water Sciences Engineering, College of Agriculture, Jahrom University, Jahrom, Iran d Civil & Environmental Engineering, The University of the West Indies, St. Augustine Campus, Port of Spain, Trinidad e Department of Civil Engineering, St. Peters Engineering College, Hyderabad, India *Corresponding author. E-mail: azmatheditor@gmail.com
ABSTRACT
측면 분기기(흡입구)의 상류측에서 유동 분리는 분기기 입구에서 맴돌이 전류를 일으키는 중요한 문제입니다. 이는 흐름의 유효 폭, 분기 용량 및 효율성을 감소시킵니다. 따라서 분리구역의 크기를 파악하고 그 크기를 줄이기 위한 방안을 제시하는 것이 필수적이다.
본 연구에서는 분리 구역의 크기를 줄이기 위한 방법으로 분출구 입구에 7가지 유형의 조면화 요소와 4가지 다른 방류가 있는 3가지 다른 베드 인버트 레벨의 설치(총 84회 실험)를 조사했습니다. 또한 3D 전산 유체 역학(CFD) 모델을 사용하여 분리 구역의 흐름 패턴과 치수를 평가했습니다.
결과는 조도 계수를 향상시키면 분리 영역 치수를 최대 38%까지 줄일 수 있는 반면 드롭 구현 효과는 사용된 조도 계수에 따라 이 영역을 다르게 축소할 수 있음을 보여주었습니다. 두 방법을 결합하면 분리 구역 치수를 최대 63%까지 줄일 수 있습니다.
Flow separation at the upstream side of lateral turnouts (intakes) is a critical issue causing eddy currents at the turnout entrance. It reduces the effective width of flow, turnout capacity and efficiency. Therefore, it is essential to identify the dimensions of the separation zone and propose remedies to reduce its dimensions.
Installation of 7 types of roughening elements at the turnout entrance and 3 different bed invert levels, with 4 different discharges (making a total of 84 experiments) were examined in this study as a method to reduce the dimensions of the separation zone. Additionally, a 3-D Computational Fluid Dynamic (CFD) model was utilized to evaluate the flow pattern and dimensions of the separation zone.
Results showed that enhancing the roughness coefficient can reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on the roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%.
Key words
discharge ratio, flow separation zone, intake, three dimensional simulation
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Ramamurthy, A. S., Junying, Q. & Diep, V. 2007 Numerical and experimental study of dividing open-channel flows. Journal of Hydraulic Engineering. See: https://doi.org/10.1061/(ASCE)0733-9429(2007)133:10(1135). Seyedian, S., Karami Moghaddam, K. & Shafai Begestan, M. 2008 Determining the optimal radius in lateral intakes of 55° and 90° using variation of flow velocity. In: 07th Iranian Hydraulic Conference. Power & Water University of Technology (PWUT). (In Persian). Available from: https://civilica.com/doc/56251. Zolghadr, M. & Shafai Bejestan, M. 2020 Six legged concrete (SLC) elements as scour countermeasures at wing wall bridge abutments. International Journal of River Basin Management. doi: 10.1080/15715124.2020.1726357. Zolghadr, M., Zomorodian, S. M. A., Shabani, R. & Azamatulla Md., H. 2021 Migration of sand mining pit in rivers: an experimental, numerical and case study. Measurement. https://doi.org/10.1016/j.measurement.2020.108944
Investigating the impact of the vortex breaker on the hydraulics of the flow (empirical hydraulic coefficient) passing over the morning glory spillway Roozbeh Aghamajidi1 1– Assistant Professor, Faculty of Engineering, Islamic Azad University, Sepidan Unit, Fars, Iran Received: 05 November 2022; Revised: 11 December 2022; Accepted: 10 January 2023; Published: 11 January 2023
Abstract
In recent decades, many dams have been built. Due to the high need for water and the increasing soil erosion in different areas, the need and sensation to build a dam is quite obvious. In 1900, the number of large dams did not exceed 50. However, between 1950 and 1986, the number of large dams (more than 15 meters high) was more than 39,000. Since the 70s, the construction of dams has been developing more and more. This expansion has been more visible in the Asian, Central and South American regions. According to the construction purpose, each dam structure must be able to pass the volume of excess water caused by the flood, and for this purpose, various structures such as spillways are used. The spillways are different according to the type of exploitation and the type of project. In other words, there are different types of leaks. Which are one of these types of shaft spillway. The spillway of a morning glory consists of a circular crest that directs the flow to an inclined or vertical axis. The mentioned axis is connected to a conduct way with a low gradient. In this research, in order to investigate the performance of both vortex breakers on the hydraulic spillway of morning glory, several tests have been conducted with various types of vortex breakers. The results show that the best vorticity channel with a low height and length is an arrangement of 6, which increases the flow rate by 23%. It should be noted that increasing the thickness of the vortex breaker by more than 7% of the spillway radius does not have much effect on the increase of the hydraulic coefficient.
최근 수십 년 동안 많은 댐이 건설되었습니다. 물에 대한 높은 수요와 여러 지역에서 증가하는 토양 침식으로 인해 댐 건설의 필요성과 감각은 매우 분명합니다. 1900년에는 대형 댐의 수가 50개를 넘지 않았지만 1950년에서 1986년 사이에 대형 댐(높이 15미터 이상)의 수는 39,000개가 넘었습니다. 70년대 이후 댐 건설은 점점 더 발전해 왔습니다.
이러한 확장은 아시아, 중남미 지역에서 더 두드러졌습니다. 각 댐 구조물은 시공목적에 따라 홍수로 인한 과잉수량을 통과할 수 있어야 하며 이를 위해 여수로 등 다양한 구조물이 사용된다. 여수로는 개발 유형과 프로젝트 유형에 따라 다릅니다. 즉, 다양한 유형의 누출이 있습니다.
샤프트 여수로의 이러한 유형 중 하나입니다. 나팔꽃의 여수로는 흐름을 경사 또는 수직 축으로 향하게 하는 원형 마루로 구성됩니다. 언급된 축은 기울기가 낮은 전도 방식에 연결됩니다. 본 연구에서는 나팔꽃 수로에서 두 가지 와류 차단기의 성능을 조사하기 위해 다양한 유형의 와류 차단기로 여러 테스트를 수행했습니다.
그 결과 높이와 길이가 낮은 최적의 vorticity 채널은 6개 배열로 유량이 23% 증가하는 것으로 나타났다. 와류 차단기의 두께를 여수로 반경의 7% 이상 증가시키는 것은 수리 계수의 증가에 큰 영향을 미치지 않는다는 점에 유의해야 합니다.
Paula Beceiro (corresponding author) Maria do Céu Almeida Hydraulic and Environment Department (DHA), National Laboratory for Civil Engineering, Avenida do Brasil 101, 1700-066 Lisbon, Portugal E-mail: pbeceiro@lnec.pt Jorge Matos Department of Civil Engineering, Arquitecture and Geosources, Technical University of Lisbon (IST), Avenida Rovisco Pais 1, 1049-001 Lisbon, Portugal
ABSTRACT
물 흐름에 용존 산소(DO)의 존재는 해로운 영향의 발생을 방지하는 데 유익한 것으로 인식되는 호기성 조건을 보장하는 중요한 요소입니다.
하수도 시스템에서 흐르는 폐수에 DO를 통합하는 것은 공기-액체 경계면 또는 방울이나 접합부와 같은 특이점의 존재로 인해 혼입된 공기를 통한 연속 재방출의 영향을 정량화하기 위해 광범위하게 조사된 프로세스입니다. 공기 혼입 및 후속 환기를 향상시키기 위한 하수구 드롭의 위치는 하수구의 호기성 조건을 촉진하는 효과적인 방법입니다.
본 논문에서는 수직 낙하, 배경 및 계단식 낙하를 CFD(전산유체역학) 코드 FLOW-3D®를 사용하여 모델링하여 이러한 유형의 구조물의 존재로 인해 발생하는 난류로 인한 공기-물 흐름을 평가했습니다. 이용 가능한 실험적 연구에 기초한 수력학적 변수의 평가와 공기 혼입의 분석이 수행되었습니다.
이러한 구조물에 대한 CFD 모델의 결과는 Soares(2003), Afonso(2004) 및 Azevedo(2006)가 개발한 해당 물리적 모델에서 얻은 방류, 압력 헤드 및 수심의 측정을 사용하여 검증되었습니다.
유압 거동에 대해 매우 잘 맞았습니다. 수치 모델을 검증한 후 공기 연행 분석을 수행했습니다.
The presence of dissolved oxygen (DO) in water flows is an important factor to ensure the aerobic conditions recognised as beneficial to prevent the occurrence of detrimental effects. The incorporation of DO in wastewater flowing in sewer systems is a process widely investigated in order to quantify the effect of continuous reaeration through the air-liquid interface or air entrained due the presence of singularities such as drops or junctions. The location of sewer drops to enhance air entrainment and subsequently reaeration is an effective practice to promote aerobic conditions in sewers. In the present paper, vertical drops, backdrops and stepped drop was modelled using the computational fluid dynamics (CFD) code FLOW-3D® to evaluate the air-water flows due to the turbulence induced by the presence of this type of structures. The assessment of the hydraulic variables and an analysis of the air entrainment based in the available experimental studies were carried out. The results of the CFD models for these structures were validated using measurements of discharge, pressure head and water depth obtained in the corresponding physical models developed by Soares (2003), Afonso (2004) and Azevedo (2006). A very good fit was obtained for the hydraulic behaviour. After validation of numerical models, analysis of the air entrainment was carried out.
Key words | air entrainment, computational fluid dynamics (CFD), sewer drops
REFERENCES
Afonso, J. Dissipação de energia e rearejamento em quedas em colectores. M.Sc. Thesis, UTL/IST, Lisboa, Portugal. Almeida, M. C., Butler, D. & Matos, J. S. Reaeration by sewer drops. In: 8th Int. Conf. on Urban Storm Drainage, Sydney, Australia. Azevedo, R. I. Transferência de oxigénio em quedas guiadas em colectores. M.Sc. Thesis, IST, Lisboa, Portugal. Beceiro, P., Almeida, M. C. & Matos, J. Numerical Modelling of air-water flows in a vertical drop and a backdrop. In: 3rd IAHR Europe Congress, Porto, Portugal. Bombardelli, F. A., Meireles, I. & Matos, J. S. Laboratory measurements and multi-block numerical simulations of the mean flow and turbulence in the non-aerated skimming flow region of step stepped spillways. Environ. Fluid Mech. 11 (3), 263–288. Brethour, J. M. & Hirt, C. W. Drift Model for TwoComponent Flows. Flow Science, Inc., Los Alamos, NM, USA. Chamani, M. R. Jet Flow on Stepped Spillways and Drops. M.Sc. Thesis, University of Alberta, Alberta, Canada. Chanson, H. Air Bubble Entrainment in Free-Surface Turbulent Shear Flow. Academic Press Inc., California, USA. Chanson, H. Air bubble entrainment in open channels: flow structure and bubble size distribution. Int. J. Multiphase 23 (1), 193–203. Chanson, H. Hydraulics of aerated flows: qui pro quo? Journal of Hydraulic Research 51 (3), 223–243. Dufresne, M., Vazques, J., Terfous, A., Ghenaim, A. & Poulet, J. Experimental investigation and CFD modelling of flow, sedimentation, and solids separation in a combined sewer detention tank. Computer and Fluids 38, 1042–1049. Durve, A. P. & Patwardhan, A. W. Numerical and experimental investigation of onset of gas entrainment phenomenon. Chemical Engineering Science 73, 140–150. Felder, S. & Chanson, H. Air–water flows and free-surface profiles on a non-uniform stepped chute. Journal of Hydraulic Research 52 (2), 253–263. Flow Science FLOW-3D User’s Manuals Version 10.0. Vol.1/2. Flow Science Inc., Los Alamos, NM, USA. Granata, F., Marinis, G., Gargano, R. & Hager, W. H. Energy loss in circular drop manholes. In: 33rd IAHR Congress: Water Engineering for Sustainable Environment, British Columbia, Vancouver, Canada. Hirt, C. W. Modeling Turbulent Entrainment of air at A Free Surface. Flow Science Inc., Los Alamos, NM, USA. Hirt, C. W. & Nichols, B. D. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics 39, 201–225. Hirt, C. W. & Sicilian, J. M. A porosity technique for the definition of obstacles in rectangular cell meshes. In: Proc. 4th Int, Conf. Ship Hydro., National Academy of Science, Washington, DC, USA. Isfahani, A. H. G. & Brethour, J. On the Implementation of Two-Equation Turbulence Models in FLOW-3D. Flow Science Inc., Los Alamos, NM, USA. Kouyi, G. L., Bret, P., Didier, J. M., Chocat, B. & Billat, C. The use of CFD modelling to optimise measurement of overflow rates in a downstream-controlled dual-overflow structure. 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Experiments and 3D simulations of flow structures in junctions and of their influence on location of flowmeters. In: 12th International Conference on Urban Drainage, Porto Alegre, Brazil. Ozmen-Cagatay, H. & Kocaman, S. Dam-break flow in the presence of obstacle: experiment and CFD Simulation. Engineering Applications of Computational Fluid Mechanics 5 (4), 541–552. Shojaee Fard, M. H. & Boyaghchi, F. A. Studies of the influence of various blade outlet angles in a centrifugal pump when handling viscous fluids. American Journal of Applied Sciences 4 (9), 718–724. Soares, A. Rearejamento em Quedas em Colectores de Águas Residuais. M.Sc. Thesis, FCTUC, Coimbra, Portugal. Sousa, C. M. & Lopes, R. R. Hidráulica e rearejamento em quedas verticais em colectores. Estudo Experimental. Research Report, UTL/IST, Lisboa, Portugal. Sousa, V., Meireles, I., Matos, J. & Almeida, M. C. Numerical modelling of air-water flow in a vertical drop manhole. 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ROPELLANT 열 성층화 및 외부 교란에 대한 유체 역학적 반응은 발사체와 우주선 모두에서 중요합니다. 과거에는 결합된 솔루션을 제공할 수 있는 충분한 계산 기술이 부족하여 이러한 문제를 개별적으로 해결했습니다.1
이로 인해 모델링 기술의 불확실성을 허용하기 위해 큰 안전 계수를 가진 시스템이 과도하게 설계되었습니다. 고중력 환경과 저중력 환경 모두에서 작동하도록 설계된 미래 시스템은 기술적으로나 재정적으로 실현 가능하도록 과잉 설계 및 안전 요소가 덜 필요합니다.
이러한 유체 시스템은 열역학 및 유체 역학이 모두 중요한 환경에서 모델의 기능을 광범위하게 검증한 후에만 고충실도 수치 모델을 기반으로 할 수 있습니다. 상용 컴퓨터 코드 FLOW-3D2는 유체 역학 및 열 모델링 모두에서 가능성을 보여주었으며,1 따라서 열역학-유체-역학 엔지니어링 문제에서 결합된 질량, 운동량 및 에너지 방정식을 푸는 데 적합함을 시사합니다.
발사체의 복잡한 액체 가스 시스템에 대한 포괄적인 솔루션을 달성하기 위한 첫 번째 단계로 액체 유체 역학과 열역학을 통합하는 제안된 상단 단계 액체-수소(Lit) 탱크의 간단한 모델이 여기에 제시됩니다. FLOW-3D FLOW-3D 프로그램은 Los Alamos Scientific Laboratory에서 시작되었으며 마커 및 셀 방법에서 파생된 것입니다.3 현재 상태로 가져오기 위해 수년에 걸쳐 광범위한 코드 수정이 이루어졌습니다.2
프로그램은 다음과 같습니다. 일반 Navier-Stokes 방정식을 풀기 위해 수치 근사의 중앙 유한 차분 방법을 사용하는 3차원 유체 역학 솔버입니다. 모멘텀 및 에너지 방정식의 섹션은 특정 응용 프로그램에 따라 활성화 또는 비활성화할 수 있습니다.
코드는 1994년 9월 13일 접수를 인용하기 위해 무액체 표면, 복잡한 용기 기하학, 여러 점성 모델, 표면 장력, 다공성 매체를 통한 흐름 및 응고와 함께 압축성 또는 비압축성 유동 가정을 제공합니다. 1995년 1월 15일에 받은 개정; 1995년 2월 17일 출판 승인.
이 프로젝트의 주요 목표는 FLOW-3D를 사용하여 계단식 여수로에서 스키밍 흐름의 수치 모델링을 개발하는 것입니다. 이러한 구조의 설계는 물리적 모델링에서 얻은 경험적 표현과 CFD 코드를 지원하는 계단식 여수로를 통한 흐름의 수치 모델링에서 보완 연구를 기반으로 합니다. 수치 모델은 균일한 영역의 유속과 계단 여수로의 마찰 계수를 추정하는 데 사용됩니다(ϴ = 45º, Hd=4.61m). 흐름에 대한 자동 통기의 표현은 복잡하므로 프로그램은 공기 연행 모델을 사용하여 특정 제한이 있는 솔루션에 근접합니다.
The main objective of this project is to develop the numerical modeling of the skimming flow in a stepped spillway using FLOW-3D. The design of these structures is based on the use of empirical expressions obtained from physical modeling and complementary studies in the numerical modeling of flow over the stepped spillway with support of CFD code. The numerical model is used to estimate the flow velocity in the uniform region and the friction coefficient of the stepped spillway (ϴ = 45º, Hd=4.61m). The representation of auto aeration a flow is complex, so the program approximates the solution with certain limitations, using an air entrainment model; drift flux model and turbulence model k-ԑ RNG. The results obtained with numerical modeling and physical modeling at the beginning of natural auto aeration of flow and depth of the biphasic flow in the uniform region presents deviations above to 10% perhaps the flow is highly turbulent.
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Pages 541-551 | Received 03 Mar 2020, Accepted 07 May 2020, Published online: 21 May 2020
ABSTRACT
Dams fall in ‘installations containing dangerous forces’ because of their massive impact on the environment and civilian life and property as per International humanitarian law. As such, it becomes vital for hydraulic engineers to refurbish various solutions for dam rehabilitation. This paper presents a review of a new type of weir installation called Piano Key Weir (PKW), which is becoming popular around the world for its higher spillway capacity both for existing and new dam spillway installations. This paper reviews the geometry along with structural integrity, discharging capacity, economic aspects, aeration requirements, sediment transport and erosion aspects of Piano Key Weir (PKW) as compared with other traditional spillway structures and alternatives from literature. The comparison with other alternatives shows PKW to be an excellent alternative for dam risk mitigation owing to its high spillway capabilities and economy, along with its use in both existing and new hydraulic structures.
댐은 국제 인도법에 따라 환경과 민간인 생활 및 재산에 막대한 영향을 미치기 때문에 ‘위험한 힘을 포함하는 시설물’에 속합니다. 따라서 유압 엔지니어는 댐 복구를 위한 다양한 솔루션을 재정비해야 합니다.
이 백서에서는 PKW(Piano Key Weir)라는 새로운 유형의 둑 설치에 대한 검토를 제공합니다. PKW는 기존 및 신규 댐 방수로 설치 모두에서 더 높은 방수로 용량으로 전 세계적으로 인기를 얻고 있습니다.
이 백서에서는 구조적 무결성, 배출 용량, 경제적 측면, 폭기 요구 사항, 퇴적물 운반 및 PKW(Piano Key Weir)의 침식 측면과 함께 다른 전통적인 여수로 구조 및 문헌의 대안과 비교하여 기하학을 검토합니다.
다른 대안과의 비교는 PKW가 높은 여수로 기능과 경제성으로 인해 댐 위험 완화를 위한 탁월한 대안이며 기존 및 새로운 수력 구조물 모두에 사용됨을 보여줍니다.
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Beom-Jin Kim 1, Jae-Hong Hwang 2 and Byunghyun Kim 3,* 1 Advanced Structures and Seismic Safety Research Division, Korea Atomic Energy Research Institute, Daejeon 34057, Korea 2 Korea Water Resources Corporation (K-Water), Daejeon 34350, Korea 3 Department of Civil Engineering, Kyungpook National University, Daegu 41566, Korea
Hydraulic structures installed in rivers inevitably create a water level difference between upstream and downstream regions. The potential energy due to this difference in water level is converted into kinetic energy, causing high-velocity flow and hydraulic jumps in the river. As a result, problems such as scouring and sloping downstream may occur around the hydraulic structures. In this study, a FLOW-3D model was constructed to perform a numerical analysis of the ChangnyeongHaman weir in the Republic of Korea. The constructed model was verified based on surface velocity measurements from a field gate operation experiment. In the simulation results, the flow discharge differed from the measured value by 9–15 m3/s, from which the accuracy was evaluated to be 82–87%. The flow velocity was evaluated with an accuracy of 92% from a difference of 0.01 to 0.16 m/s. Following this verification, a flow analysis of the hydraulic structures was performed according to boundary conditions and operation conditions for numerous scenarios. Since 2018, the ChangnyeongHaman weir gate has been fully opened due to the implementation of Korea’s eco-environmental policy; therefore, in this study, the actual gate operation history data prior to 2018 was applied and evaluated. The evaluation conditions were a 50% open gate condition and the flow discharge of two cases with a large difference in water level. As a result of the analysis, the actual operating conditions showed that the velocity and the Froude number were lower than the optimal conditions, confirming that the selected design was appropriate. It was also found that in the bed protection section, the average flow velocity was high when the water level difference was large, whereas the bottom velocity was high when the gate opening was large. Ultimately, through the reviewed status survey data in this study, the downstream flow characteristics of hydraulic structures along with adequacy verification techniques, optimal design techniques such as procedures for design, and important considerations were derived. Based on the current results, the constructed FLOW-3D-based model can be applied to creating or updating flow analysis guidelines for future repair and reinforcement measures as well as hydraulic structure design.
하천에 설치되는 수력구조물은 필연적으로 상류와 하류의 수위차를 발생시킨다. 이러한 수위차로 인한 위치에너지는 운동에너지로 변환되어 하천의 고속유동과 수압점프를 일으킨다. 그 결과 수력구조물 주변에서 하류의 세굴, 경사 등의 문제가 발생할 수 있다.
본 연구에서는 대한민국 창녕함안보의 수치해석을 위해 FLOW-3D 모델을 구축하였다. 구축된 모델은 현장 게이트 작동 실험에서 표면 속도 측정을 기반으로 검증되었습니다.
시뮬레이션 결과에서 유량은 측정값과 9~15 m3/s 차이가 나고 정확도는 82~87%로 평가되었다. 유속은 0.01~0.16m/s의 차이에서 92%의 정확도로 평가되었습니다.
검증 후 다양한 시나리오에 대한 경계조건 및 운전조건에 따른 수리구조물의 유동해석을 수행하였다. 2018년부터 창녕함안보 문은 한국의 친환경 정책 시행으로 전면 개방되었습니다.
따라서 본 연구에서는 2018년 이전의 실제 게이트 운영 이력 데이터를 적용하여 평가하였다. 평가조건은 50% open gate 조건과 수위차가 큰 2가지 경우의 유수방류로 하였다. 해석 결과 실제 운전조건은 속도와 Froude수가 최적조건보다 낮아 선정된 설계가 적합함을 확인하였다.
또한 베드보호구간에서는 수위차가 크면 평균유속이 높고, 수문개구가 크면 저저유속이 높은 것으로 나타났다. 최종적으로 본 연구에서 검토한 실태조사 자료를 통해 적정성 검증기법과 함께 수력구조물의 하류 유동특성, 설계절차 등 최적 설계기법 및 중요 고려사항을 도출하였다.
현재의 결과를 바탕으로 구축된 FLOW-3D 기반 모델은 수력구조 설계뿐만 아니라 향후 보수 및 보강 조치를 위한 유동해석 가이드라인 생성 또는 업데이트에 적용할 수 있습니다.
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As a part of design process for hydro-electric generating stations, hydraulic engineers typically conduct some form of model testing. The desired outcome from the testing can vary considerably depending on the specific situation, but often characteristics such as velocity patterns, discharge rating curves, water surface profiles, and pressures at various locations are measured. Due to recent advances in computational power and numerical techniques, it is now also possible to obtain much of this information through numerical modeling. In this paper, hydraulic characteristics of Kavsak Dam and Hydroelectric Power Plant (HEPP), which are under construction and built for producing energy in Turkey, were investigated experimentally by physical model studies. The 1/50-scaled physical model was used in conducting experiments. Flow depth, discharge and pressure data were recorded for different flow conditions. Serious modification was made on the original project with the experimental study. In order to evaluate the capability of the computational fluid dynamics on modeling spillway flow a comparative study was made by using results obtained from physical modeling and Computational Fluid Dynamics (CFD) simulation. A commercially available CFD program, which solves the Reynolds-averaged Navier-Stokes (RANS) equations, was used to model the numerical model setup by defining cells where the flow is partially or completely restricted in the computational space. Discharge rating curves, velocity patterns and pressures were used to compare the results of the physical model and the numerical model. It was shown that there is reasonably good agreement between the physical and numerical models in flow characteristics.
수력 발전소 설계 프로세스의 일부로 수력 엔지니어는 일반적으로 어떤 형태의 모델 테스트를 수행합니다. 테스트에서 원하는 결과는 특정 상황에 따라 상당히 다를 수 있지만 속도 패턴, 방전 등급 곡선, 수면 프로파일 및 다양한 위치에서의 압력과 같은 특성이 측정되는 경우가 많습니다. 최근 계산 능력과 수치 기법의 발전으로 인해 이제는 수치 모델링을 통해 이러한 정보의 대부분을 얻을 수도 있습니다.
본 논문에서는 터키에서 에너지 생산을 위해 건설 중인 Kavsak 댐과 수력발전소(HEPP)의 수력학적 특성을 물리적 모델 연구를 통해 실험적으로 조사하였다. 1/50 스케일의 물리적 모델이 실험 수행에 사용되었습니다. 다양한 흐름 조건에 대해 흐름 깊이, 배출 및 압력 데이터가 기록되었습니다. 실험 연구를 통해 원래 프로젝트에 대대적인 수정이 이루어졌습니다.
배수로 흐름 모델링에 대한 전산유체역학의 능력을 평가하기 위해 물리적 모델링과 전산유체역학(CFD) 시뮬레이션 결과를 이용하여 비교 연구를 수행하였습니다. RANS(Reynolds-averaged Navier-Stokes) 방정식을 푸는 상업적으로 이용 가능한 CFD 프로그램은 흐름이 계산 공간에서 부분적으로 또는 완전히 제한되는 셀을 정의하여 수치 모델 설정을 모델링하는 데 사용되었습니다.
물리적 모델과 수치 모델의 결과를 비교하기 위해 배출 등급 곡선, 속도 패턴 및 압력을 사용했습니다. 유동 특성에서 물리적 모델과 수치 모델 간에 상당히 좋은 일치가 있는 것으로 나타났습니다.
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Publication: Canadian Journal of Civil Engineering
3 December 2008
Abstract
Throughout the design and planning period for future hydroelectric generating stations, hydraulic engineers are increasingly integrating computational fluid dynamics (CFD) into the process. As a result, hydraulic engineers are interested in the reliability of CFD software to provide accurate flow data for a wide range of structures, including a variety of different spillways. In the literature, CFD results have generally been in agreement with physical model experimental data. Despite past success, there has not been a comprehensive assessment that looks at the ability of CFD to model a range of different spillway configurations, including flows with various gate openings. In this article, Flow-3D is used to model the discharge over ogee-crested spillways. The numerical model results are compared with physical model studies for three case study evaluations. The comparison indicates that the accuracy of Flow-3D is related to the parameter P/Hd.
미래의 수력 발전소를 위한 설계 및 계획 기간 동안 유압 엔지니어는 전산유체역학(CFD)을 프로세스에 점점 더 많이 통합하고 있습니다. 결과적으로 유압 엔지니어는 다양한 여수로를 포함하여 광범위한 구조에 대한 정확한 흐름 데이터를 제공하는 CFD 소프트웨어의 신뢰성에 관심을 갖고 있습니다. 문헌에서 CFD 결과는 일반적으로 물리적 모델 실험 데이터와 일치했습니다. 과거의 성공에도 불구하고 다양한 게이트 개구부가 있는 흐름을 포함하여 다양한 여수로 구성을 모델링하는 CFD의 기능을 살펴보는 포괄적인 평가는 없었습니다. 이 기사에서는 Flow-3D를 사용하여 ogee-crested 방수로의 배출을 모델링합니다. 세 가지 사례 연구 평가를 위해 수치 모델 결과를 물리적 모델 연구와 비교합니다. 비교는 Flow-3D의 정확도가 매개변수 P/Hd와 관련되어 있음을 나타냅니다.
Résumé
Les ingénieurs en hydraulique intègrent de plus en plus la dynamique des fluides numérique (« CFD ») dans le processus de conception et de planification des futures centrales. Ainsi, les ingénieurs en hydraulique s’intéressent à la fiabilité du logiciel de « CFD » afin de fournir des données précises sur le débit pour une large gamme de structures, incluant différents types d’évacuateurs. Les résultats de « CFD » dans la littérature ont été globalement sont généralement en accord avec les données expérimentales des essais physiques. Malgré les succès antérieurs, il n’y avait aucune évaluation complète de la capacité des « CFD » à modéliser une plage de configuration des évacuateurs, incluant les débits à diverses ouvertures de vannes. Dans le présent article, le logiciel Flow-3D est utilisé pour modéliser le débit par des évacuateurs en doucine. Les résultats du modèle de calcul sont comparés à ceux des essais physiques pour trois études de cas. La comparaison montre que la précision du logiciel Flow-3D est associée au paramètre P/Hd.
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Analysis of behavior and hydraulic characteristics of flow over the dam spillway is a complicated task that takes lots of money and time in water engineering projects planning. To model those hydraulic characteristics, several methods such as physical and numerical methods can be used. Nowadays, by utilizing new methods in computational fluid dynamics (CFD) and by the development of fast computers, the numerical methods have become accessible for use in the analysis of such sophisticated flows. The CFD softwares have the capability to analyze two- and three-dimensional flow fields. In this paper, the flow pattern at the guide wall of the Kamal-Saleh dam was modeled by Flow 3D. The results show that the current geometry of the left wall causes instability in the flow pattern and making secondary and vortex flow at beginning approach channel. This shape of guide wall reduced the performance of weir to remove the peak flood discharge.
댐 여수로 흐름의 거동 및 수리학적 특성 분석은 물 공학 프로젝트 계획에 많은 비용과 시간이 소요되는 복잡한 작업입니다. 이러한 수력학적 특성을 모델링하기 위해 물리적, 수치적 방법과 같은 여러 가지 방법을 사용할 수 있습니다. 요즘에는 전산유체역학(CFD)의 새로운 방법을 활용하고 빠른 컴퓨터의 개발로 이러한 정교한 흐름의 해석에 수치 방법을 사용할 수 있게 되었습니다. CFD 소프트웨어에는 2차원 및 3차원 유동장을 분석하는 기능이 있습니다. 본 논문에서는 Kamal-Saleh 댐 유도벽의 흐름 패턴을 Flow 3D로 모델링하였다. 결과는 왼쪽 벽의 현재 형상이 흐름 패턴의 불안정성을 유발하고 시작 접근 채널에서 2차 및 와류 흐름을 만드는 것을 보여줍니다. 이러한 형태의 안내벽은 첨두방류량을 제거하기 위해 둑의 성능을 저하시켰다.
Introduction
Spillways are one of the main structures used in the dam projects. Design of the spillway in all types of dams, specifically earthen dams is important because the inability of the spillway to remove probable maximum flood (PMF) discharge may cause overflow of water which ultimately leads to destruction of the dam (Das and Saikia et al. 2009; E 2013 and Novak et al. 2007). So study on the hydraulic characteristics of this structure is important. Hydraulic properties of spillway including flow pattern at the entrance of the guide walls and along the chute. Moreover, estimating the values of velocity and pressure parameters of flow along the chute is very important (Chanson 2004; Chatila and Tabbara 2004). The purpose of the study on the flow pattern is the effect of wall geometry on the creation transverse waves, flow instability, rotating and reciprocating flow through the inlet of spillway and its chute (Parsaie and Haghiabi 2015a, b; Parsaie et al. 2015; Wang and Jiang 2010). The purpose of study on the values of velocity and pressure is to calculate the potential of the structure to occurrence of phenomena such as cavitation (Fattor and Bacchiega 2009; Ma et al. 2010). Sometimes, it can be seen that the spillway design parameters of pressure and velocity are very suitable, but geometry is considered not suitable for conducting walls causing unstable flow pattern over the spillway, rotating flows at the beginning of the spillway and its design reduced the flood discharge capacity (Fattor and Bacchiega 2009). Study on spillway is usually conducted using physical models (Su et al. 2009; Suprapto 2013; Wang and Chen 2009; Wang and Jiang 2010). But recently, with advances in the field of computational fluid dynamics (CFD), study on hydraulic characterist–ics of this structure has been done with these techniques (Chatila and Tabbara 2004; Zhenwei et al. 2012). Using the CFD as a powerful technique for modeling the hydraulic structures can reduce the time and cost of experiments (Tabbara et al. 2005). In CFD field, the Navier–Stokes equation is solved by powerful numerical methods such as finite element method and finite volumes (Kim and Park 2005; Zhenwei et al. 2012). In order to obtain closed-form Navier–Stokes equations turbulence models, such k − ε and Re-Normalisation Group (RNG) models have been presented. To use the technique of computational fluid dynamics, software packages such as Fluent and Flow 3D, etc., are provided. Recently, these two software packages have been widely used in hydraulic engineering because the performance and their accuracy are very suitable (Gessler 2005; Kim 2007; Kim et al. 2012; Milési and Causse 2014; Montagna et al. 2011). In this paper, to assess the flow pattern at Kamal-Saleh guide wall, numerical method has been used. All the stages of numerical modeling were conducted in the Flow 3D software.
Materials and methods
Firstly, a three-dimensional model was constructed according to two-dimensional map that was prepared for designing the spillway. Then a small model was prepared with scale of 1:80 and entered into the Flow 3D software; all stages of the model construction was conducted in AutoCAD 3D. Flow 3D software numerically solved the Navier–Stokes equation by finite volume method. Below is a brief reference on the equations that used in the software. Figure 1 shows the 3D sketch of Kamal-Saleh spillway and Fig. 2 shows the uploading file of the Kamal-Saleh spillway in Flow 3D software.
Review of the governing equations in software Flow 3D
Continuity equation at three-dimensional Cartesian coordinates is given as Eq (1).
where u, v, z are velocity component in the x, y, z direction; Ax, Ay, Az cross-sectional area of the flow; ρ fluid density; PSOR the source term; vf is the volume fraction of the fluid and three-dimensional momentum equations given in Eq (2).
where P is the fluid pressure; Gx, Gy, Gz the acceleration created by body fluids; fx, fy, fz viscosity acceleration in three dimensions and vf is related to the volume of fluid, defined by Eq. (3). For modeling of free surface profile the VOF technique based on the volume fraction of the computational cells has been used. Since the volume fraction F represents the amount of fluid in each cell, it takes value between 0 and 1.
Flow 3D offers five types of turbulence models: Prantl mixing length, k − ε equation, RNG models, Large eddy simulation model. Turbulence models that have been proposed recently are based on Reynolds-averaged Navier–Stokes equations. This approach involves statistical methods to extract an averaged equation related to the turbulence quantities.
Steps of solving a problem in Flow 3D software
(1) Preparing the 3D model of spillway by AutoCAD software. (2) Uploading the file of 3D model in Flow 3D software and defining the problem in the software and checking the final mesh. (3) Choosing the basic equations that should be solved. (4) Defining the characteristics of fluid. (5) Defining the boundary conditions; it is notable that this software has a wide range of boundary conditions. (6) Initializing the flow field. (7) Adjusting the output. (8) Adjusting the control parameters, choice of the calculation method and solution formula. (9) Start of calculation. Figure 1 shows the 3D model of the Kamal-Saleh spillway; in this figure, geometry of the left and right guide wall is shown.
Figure 2 shows the uploading of the 3D spillway dam in Flow 3D software. Moreover, in this figure the considered boundary condition in software is shown. At the entrance and end of spillway, the flow rate or fluid elevation and outflow was considered as BC. The bottom of spillway was considered as wall and left and right as symmetry.
Model calibration
Calibration of the Flow 3D for modeling the effect of geometry of guide wall on the flow pattern is included for comparing the results of Flow 3D with measured water surface profile. Calibration the Flow 3D software could be conducted in two ways: first, changing the value of upstream boundary conditions is continued until the results of water surface profile of the Flow 3D along the spillway successfully covered the measurement water surface profile; second is the assessment the mesh sensitivity. Analyzing the size of mesh is a trial-and-error process where the size of mesh is evaluated form the largest to the smallest. With fining the size of mesh the accuracy of model is increased; whereas, the cost of computation is increased. In this research, the value of upstream boundary condition was adjusted with measured data during the experimental studies on the scaled model and the mesh size was equal to 1 × 1 × 1 cm3.
Results and discussion
The behavior of water in spillway is strongly affected by the flow pattern at the entrance of the spillway, the flow pattern formation at the entrance is affected by the guide wall, and choice of an optimized form for the guide wall has a great effect on rising the ability of spillway for easy passing the PMF, so any nonuniformity in flow in the approach channel can cause reduction of spillway capacity, reduction in discharge coefficient of spillway, and even probability of cavitation. Optimizing the flow guiding walls (in terms of length, angle and radius) can cause the loss of turbulence and flow disturbances on spillway. For this purpose, initially geometry proposed for model for the discharge of spillway dam, Kamal-Saleh, 80, 100, and 120 (L/s) were surveyed. These discharges of flow were considered with regard to the flood return period, 5, 100 and 1000 years. Geometric properties of the conducting guidance wall are given in Table 1.Table 1 Characteristics and dimensions of the guidance walls tested
Results of the CFD simulation for passing the flow rate 80 (L/s) are shown in Fig. 3. Figure 3 shows the secondary flow and vortex at the left guide wall.
For giving more information about flow pattern at the left and right guide wall, Fig. 4 shows the flow pattern at the right side guide wall and Fig. 5 shows the flow pattern at the left side guide wall.
With regard to Figs. 4 and 5 and observing the streamlines, at discharge equal to 80 (L/s), the right wall has suitable performance but the left wall has no suitable performance and the left wall of the geometric design creates a secondary and circular flow, and vortex motion in the beginning of the entrance of spillway that creates cross waves at the beginning of spillway. By increasing the flow rate (Q = 100 L/s), at the inlet spillway secondary flows and vortex were removed, but the streamline is severely distorted. Results of the guide wall performances at the Q = 100 (L/s) are shown in Fig. 6.
Also more information about the performance of each guide wall can be derived from Figs. 7 and 8. These figures uphold that the secondary and vortex flows were removed, but the streamlines were fully diverted specifically near the left side guide wall.
As mentioned in the past, these secondary and vortex flows and diversion in streamline cause nonuniformity and create cross wave through the spillway. Figure 9 shows the cross waves at the crest of the spillway.
The performance of guide walls at the Q = 120 (L/s) also was assessed. The result of simulation is shown in Fig. 10. Figures 11 and 12 show a more clear view of the streamlines near to right and left side guide wall, respectively. As seen in Fig. 12, the left side wall still causes vortex flow and creation of and diversion in streamline.
The results of the affected left side guide wall shape on the cross wave creation are shown in Fig. 13. As seen from Fig. 3, the left side guide wall also causes cross wave at the spillway crest.
As can be seen clearly in Figs. 9 and 13, by moving from the left side to the right side of the spillway, the cross waves and the nonuniformity in flow is removed. By reviewing Figs. 9 and 13, it is found that the right side guide wall removes the cross waves and nonuniformity. With this point as aim, a geometry similar to the right side guide wall was considered instead of the left side guide wall. The result of simulation for Q = 120 (L/s) is shown in Fig. 14. As seen from this figure, the proposed geometry for the left side wall has suitable performance smoothly passing the flow through the approach channel and spillway.
More information about the proposed shape for the left guide wall is shown in Fig. 15. As seen from this figure, this shape has suitable performance for removing the cross waves and vortex flows.
Figure 16 shows the cross section of flow at the crest of spillway. As seen in this figure, the proposed shape for the left side guide wall is suitable for removing the cross waves and secondary flows.
Conclusion
Analysis of behavior and hydraulic properties of flow over the spillway dam is a complicated task which is cost and time intensive. Several techniques suitable to the purposes of study have been undertaken in this research. Physical modeling, usage of expert experience, usage of mathematical models on simulation flow in one-dimensional, two-dimensional and three-dimensional techniques, are some of the techniques utilized to study this phenomenon. The results of the modeling show that the CFD technique is a suitable tool for simulating the flow pattern in the guide wall. Using this tools helps the designer for developing the optimal shape for hydraulic structure which the flow pattern through them are important.
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by Faizal Yusuf, M.A.Sc., P.Eng. Specialist Engineer in the Hydrotechnical Department at BC Hydro
BC Hydro, a public electric utility in British Columbia, uses FLOW-3D to investigate complex hydraulics issues at several existing dams and to assist in the design and optimization of proposed facilities.
Faizal Yusuf, M.A.Sc., P.Eng., Specialist Engineer in the Hydrotechnical department at BC Hydro, presents three case studies that highlight the application of FLOW-3D to different types of spillways and the importance of reliable prototype or physical hydraulic model data for numerical model calibration.
W.A.C. Bennett Dam At W.A.C. Bennett Dam, differences in the spillway geometry between the physical hydraulic model from the 1960s and the prototype make it difficult to draw reliable conclusions on shock wave formation and chute capacity from physical model test results. The magnitude of shock waves in the concrete-lined spillway chute are strongly influenced by a 44% reduction in the chute width downstream of the three radial gates at the headworks, as well as the relative openings of the radial gates. The shock waves lead to locally higher water levels that have caused overtopping of the chute walls under certain historical operations.Prototype spill tests for discharges up to 2,865 m3/s were performed in 2012 to provide surveyed water surface profiles along chute walls, 3D laser scans of the water surface in the chute and video of flow patterns for FLOW-3D model calibration. Excellent agreement was obtained between the numerical model and field observations, particularly for the location and height of the first shock wave at the chute walls (Figure 1).
W.A.C에서 Bennett Dam, 1960년대의 물리적 수력학 모델과 프로토타입 사이의 여수로 형상의 차이로 인해 물리적 모델 테스트 결과에서 충격파 형성 및 슈트 용량에 대한 신뢰할 수 있는 결론을 도출하기 어렵습니다. 콘크리트 라이닝 방수로 낙하산의 충격파 크기는 방사형 게이트의 상대적인 개구부뿐만 아니라 헤드워크에 있는 3개의 방사형 게이트 하류의 슈트 폭이 44% 감소함에 따라 크게 영향을 받습니다. 충격파는 특정 역사적 작업에서 슈트 벽의 범람을 야기한 국부적으로 더 높은 수위로 이어집니다. 최대 2,865m3/s의 배출에 대한 프로토타입 유출 테스트가 2012년에 수행되어 슈트 벽을 따라 조사된 수면 프로필, 3D 레이저 스캔을 제공했습니다. FLOW-3D 모델 보정을 위한 슈트의 수면 및 흐름 패턴 비디오. 특히 슈트 벽에서 첫 번째 충격파의 위치와 높이에 대해 수치 모델과 현장 관찰 간에 탁월한 일치가 이루어졌습니다(그림 1).
The calibrated FLOW-3D model confirmed that the design flood could be safely passed without overtopping the spillway chute walls as long as all three radial gates are opened as prescribed in existing operating orders with the outer gates open more than the inner gate.
The CFD model also provided insight into the concrete damage in the spillway chute. Cavitation indices computed from FLOW-3D simulation results were compared with empirical data from the USBR and found to be consistent with the historical performance of the spillway. The numerical analysis supported field inspections, which concluded that deterioration of the concrete conditions in the chute is likely not due to cavitation.
Strathcona Dam FLOW-3D was used to investigate poor approach conditions and uncertainties with the rating curves for Strathcona Dam spillway, which includes three vertical lift gates on the right abutment of the dam. The rating curves for Strathcona spillway were developed from a combination of empirical adjustments and limited physical hydraulic model testing in a flume that did not include geometry of the piers and abutments.
Numerical model testing and calibration was based on comparisons with prototype spill observations from 1982 when all three gates were fully open, resulting in a large depression in the water surface upstream of the leftmost bay (Figure 2). The approach flow to the leftmost bay is distorted by water flowing parallel to the dam axis and plunging over the concrete retaining wall adjacent to the upstream slope of the earthfill dam. The flow enters the other two bays much more smoothly. In addition to very similar flow patterns produced in the numerical model compared to the prototype, simulated water levels at the gate section matched 1982 field measurements to within 0.1 m.
보정된 FLOW-3D 모델은 외부 게이트가 내부 게이트보다 더 많이 열려 있는 기존 운영 명령에 규정된 대로 3개의 방사형 게이트가 모두 열리는 한 여수로 낙하산 벽을 넘지 않고 설계 홍수를 안전하게 통과할 수 있음을 확인했습니다.
CFD 모델은 방수로 낙하산의 콘크리트 손상에 대한 통찰력도 제공했습니다. FLOW-3D 시뮬레이션 결과에서 계산된 캐비테이션 지수는 USBR의 경험적 데이터와 비교되었으며 여수로의 역사적 성능과 일치하는 것으로 나타났습니다. 수치 분석은 현장 검사를 지원했으며, 슈트의 콘크리트 상태 악화는 캐비테이션 때문이 아닐 가능성이 높다고 결론지었습니다.
Strathcona 댐 FLOW-3D는 Strathcona Dam 여수로에 대한 등급 곡선을 사용하여 열악한 접근 조건과 불확실성을 조사하는 데 사용되었습니다. 여기에는 댐의 오른쪽 접합부에 3개의 수직 리프트 게이트가 포함되어 있습니다. Strathcona 여수로에 대한 등급 곡선은 경험적 조정과 교각 및 교대의 형상을 포함하지 않는 수로에서 제한된 물리적 수리 모델 테스트의 조합으로 개발되었습니다.
수치 모델 테스트 및 보정은 세 개의 수문이 모두 완전히 개방된 1982년의 프로토타입 유출 관측과의 비교를 기반으로 했으며, 그 결과 가장 왼쪽 만의 상류 수면에 큰 함몰이 발생했습니다(그림 2). 최좌단 만으로의 접근 흐름은 댐 축과 평행하게 흐르는 물과 흙채움댐의 상류 경사면에 인접한 콘크리트 옹벽 위로 떨어지는 물에 의해 왜곡됩니다. 흐름은 훨씬 더 원활하게 다른 두 베이로 들어갑니다. 프로토타입과 비교하여 수치 모델에서 생성된 매우 유사한 흐름 패턴 외에도 게이트 섹션에서 시뮬레이션된 수위는 1982년 현장 측정과 0.1m 이내로 일치했습니다.
The calibrated CFD model produces discharges within 5% of the spillway rating curve for the reservoir’s normal operating range with all gates fully open. However, at higher reservoir levels, which may occur during passage of large floods (as shown in Figure 3), the difference between simulated discharges and the rating curves are greater than 10% as the physical model testing with simplified geometry and empirical corrections did not adequately represent the complex approach flow patterns. The FLOW-3D model provided further insight into the accuracy of rating curves for individual bays, gated conditions and the transition between orifice and free surface flow.
보정된 CFD 모델은 모든 게이트가 완전히 열린 상태에서 저수지의 정상 작동 범위에 대한 여수로 등급 곡선의 5% 이내에서 배출을 생성합니다. 그러나 대규모 홍수가 통과하는 동안 발생할 수 있는 더 높은 저수지 수위에서는(그림 3 참조) 단순화된 기하학과 경험적 수정을 사용한 물리적 모델 테스트가 그렇지 않았기 때문에 모의 배출과 등급 곡선 간의 차이는 10% 이상입니다. 복잡한 접근 흐름 패턴을 적절하게 표현합니다. FLOW-3D 모델은 개별 베이, 게이트 조건 및 오리피스와 자유 표면 흐름 사이의 전환에 대한 등급 곡선의 정확도에 대한 추가 통찰력을 제공했습니다.
John Hart Dam The John Hart concrete dam will be modified to include a new free crest spillway to be situated between an existing gated spillway and a low level outlet structure that is currently under construction. Significant improvements in the design of the proposed spillway were made through a systematic optimization process using FLOW-3D.
The preliminary design of the free crest spillway was based on engineering hydraulic design guides. Concrete apron blocks are intended to protect the rock at the toe of the dam. A new right training wall will guide the flow from the new spillway towards the tailrace pool and protect the low level outlet structure from spillway discharges.
FLOW-3D model results for the initial and optimized design of the new spillway are shown in Figure 4. CFD analysis led to a 10% increase in discharge capacity, significant decrease in roadway impingement above the spillway crest and improved flow patterns including up to a 5 m reduction in water levels along the proposed right wall. Physical hydraulic model testing will be used to confirm the proposed design.
존 하트 댐 John Hart 콘크리트 댐은 현재 건설 중인 기존 배수로와 저층 배수로 사이에 위치할 새로운 자유 마루 배수로를 포함하도록 수정될 것입니다. FLOW-3D를 사용한 체계적인 최적화 프로세스를 통해 제안된 여수로 설계의 상당한 개선이 이루어졌습니다.
자유 마루 여수로의 예비 설계는 엔지니어링 수력학 설계 가이드를 기반으로 했습니다. 콘크리트 앞치마 블록은 댐 선단부의 암석을 보호하기 위한 것입니다. 새로운 오른쪽 훈련 벽은 새 여수로에서 테일레이스 풀로 흐름을 안내하고 여수로 배출로부터 낮은 수준의 배출구 구조를 보호합니다.
새 여수로의 초기 및 최적화된 설계에 대한 FLOW-3D 모델 결과는 그림 4에 나와 있습니다. CFD 분석을 통해 방류 용량이 10% 증가하고 여수로 마루 위의 도로 충돌이 크게 감소했으며 최대 제안된 오른쪽 벽을 따라 수위가 5m 감소합니다. 제안된 설계를 확인하기 위해 물리적 수압 모델 테스트가 사용됩니다.
Conclusion
BC Hydro has been using FLOW-3D to investigate a wide range of challenging hydraulics problems for different types of spillways and water conveyance structures leading to a greatly improved understanding of flow patterns and performance. Prototype data and reliable physical hydraulic model testing are used whenever possible to improve confidence in the numerical model results.
다양한 유형의 여수로 및 물 수송 구조로 인해 흐름 패턴 및 성능에 대한 이해가 크게 향상되었습니다. 프로토타입 데이터와 신뢰할 수 있는 물리적 유압 모델 테스트는 수치 모델 결과의 신뢰도를 향상시키기 위해 가능할 때마다 사용됩니다.
About Flow Science, Inc. Based in Santa Fe, New Mexico USA, Flow Science was founded in 1980 by Dr. C. W. (Tony) Hirt, who was one of the principals in pioneering the “Volume-of-Fluid” or VOF method while working at the Los Alamos National Lab. FLOW-3D is a direct descendant of this work, and in the subsequent years, we have increased its sophistication with TruVOF, boasting pioneering improvements in the speed and accuracy of tracking distinct liquid/gas interfaces. Today, Flow Science products offer complete multiphysics simulation with diverse modeling capabilities including fluid-structure interaction, 6-DoF moving objects, and multiphase flows. From inception, our vision has been to provide our customers with excellence in flow modeling software and services.
이 연구에서 FLOW 3D 전산 유체 역학(CFD) 소프트웨어를 사용하여 파키스탄 Mirani 댐 방수로에 대한 에너지 소산 옵션으로 미국 매립지(USBR) 유형 II 및 USBR 유형 III 유역의 성능을 추정했습니다. 3D Reynolds 평균 Navier-Stokes 방정식이 해결되었으며, 여기에는 여수로 위의 자유 표면 흐름을 캡처하기 위해 공기 유입, 밀도 평가 및 드리프트-플럭스에 대한 하위 그리드 모델이 포함되었습니다. 본 연구에서는 5가지 모델을 고려하였다. 첫 번째 모델에는 길이가 39.5m인 USBR 유형 II 정수기가 있습니다. 두 번째 모델에는 길이가 44.2m인 USBR 유형 II 정수기가 있습니다. 3번째와 4 번째모델에는 길이가 각각 48.8m인 USBR 유형 II 정수조와 39.5m의 USBR 유형 III 정수조가 있습니다. 다섯 번째 모델은 네 번째 모델과 동일하지만 마찰 및 슈트 블록 높이가 0.3m 증가했습니다. 최상의 FLOW 3D 모델 조건을 설정하기 위해 메쉬 민감도 분석을 수행했으며 메쉬 크기 0.9m에서 최소 오차를 산출했습니다. 세 가지 경계 조건 세트가 테스트되었으며 최소 오류를 제공하는 세트가 사용되었습니다. 수치적 검증은 USBR 유형 II( L = 48.8m), USBR 유형 III( L = 35.5m) 및 USBR 유형 III 의 물리적 모델 에너지 소산을 0.3m 블록 단위로 비교하여 수행되었습니다( L= 35.5m). 통계 분석 결과 평균 오차는 2.5%, RMSE(제곱 평균 제곱근 오차) 지수는 3% 미만이었습니다. 수리학적 및 경제성 분석을 바탕으로 4 번째 모델이 최적화된 에너지 소산기로 밝혀졌습니다. 흡수된 에너지 백분율 측면에서 물리적 모델과 수치적 모델 간의 최대 차이는 5% 미만인 것으로 나타났습니다.
In this study, the FLOW 3D computational fluid dynamics (CFD) software was used to estimate the performance of the United States Bureau of Reclamation (USBR) type II and USBR type III stilling basins as energy dissipation options for the Mirani Dam spillway, Pakistan. The 3D Reynolds-averaged Navier–Stokes equations were solved, which included sub-grid models for air entrainment, density evaluation, and drift–flux, to capture free-surface flow over the spillway. Five models were considered in this research. The first model has a USBR type II stilling basin with a length of 39.5 m. The second model has a USBR type II stilling basin with a length of 44.2 m. The 3rd and 4th models have a USBR type II stilling basin with a length of 48.8 m and a 39.5 m USBR type III stilling basin, respectively. The fifth model is identical to the fourth, but the friction and chute block heights have been increased by 0.3 m. To set up the best FLOW 3D model conditions, mesh sensitivity analysis was performed, which yielded a minimum error at a mesh size of 0.9 m. Three sets of boundary conditions were tested and the set that gave the minimum error was employed. Numerical validation was done by comparing the physical model energy dissipation of USBR type II (L = 48.8 m), USBR type III (L =35.5 m), and USBR type III with 0.3-m increments in blocks (L = 35.5 m). The statistical analysis gave an average error of 2.5% and a RMSE (root mean square error) index of less than 3%. Based on hydraulics and economic analysis, the 4th model was found to be an optimized energy dissipator. The maximum difference between the physical and numerical models in terms of percentage energy absorbed was found to be less than 5%.
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본 연구에서는 범람으로 인한 토사댐 붕괴에 대한 테일워터 깊이의 영향을 실험적으로 조사하였다. 테일워터 깊이의 네 가지 다른 값을 검사합니다. 각 실험에 대해 댐 수심 측량 프로파일의 진화, 고장 기간, 침식 체적 및 유출 수위곡선을 관찰하고 기록합니다.
결과는 tailwater 깊이를 늘리면 고장 시간이 최대 57% 감소하고 상대적으로 침식된 마루 높이가 최대 77.6% 감소한다는 것을 보여줍니다. 또한 상대 배수 깊이가 3, 4, 5인 경우 누적 침식 체적의 감소는 각각 23, 36.5 및 75%인 반면 최대 유출량의 감소는 각각 7, 14 및 17.35%입니다.
실험 결과는 침식 과정을 복제할 때 Flow 3D 소프트웨어의 성능을 평가하는 데 활용됩니다. 수치 모델은 비응집성 흙댐의 침식 과정을 성공적으로 시뮬레이션합니다.
The influence of tailwater depth on earth dam failure due to overtopping is investigated experimentally in this work. Four different values of tailwater depths are examined. For each experiment, the evolution of the dam bathymetry profile, the duration of failure, the eroded volume, and the outflow hydrograph are observed and recorded. The results reveal that increasing the tailwater depth reduces the time of failure by up to 57% and decreases the relative eroded crest height by up to 77.6%. In addition, for relative tailwater depths equal to 3, 4, and 5, the reduction in the cumulative eroded volume is 23, 36.5, and 75%, while the reduction in peak discharge is 7, 14, and 17.35%, respectively. The experimental results are utilized to evaluate the performance of the Flow 3D software in replicating the erosion process. The numerical model successfully simulates the erosion process of non-cohesive earth dams.
Eroded height of the dam measured at distance of 0.7 m from the dam heel (cm)t
Total time of failure (sec)t1
Time of crest width erosion (sec)Zcrest
The crest height (cm)Vtotal
Total volume of the dam (m3)Veroded
Cumulative eroded volume (m3)RMSE
The statistical variable root- mean- square errord
Degree of agreement indexyu.s.
The upstream water depth (cm)yd.s
The downstream water depth (cm)H
Water surface elevation over sharp crested weir (cm)Q
Outflow discharge (liter/sec)Qpeak
Peak discharge (liter/sec)
1. Introduction
Earth dams are compacted structures composed of natural materials that are usually mined or quarried from local locations. The failures of the earth dams have proven to be deadly, destructive, and costly. According to People’s Daily, two earthen dams, Yong’an Dam and Xinfa Dam located in Hulun Buir City in North China’s Inner Mongolia failed on 2021, due to a surge in the water level of the Nuomin River caused by heavy rain. The dam breach affected 16,660 people, flooded 325,622 mu of farmland (21708.1 ha), and destroyed 22 bridges, 124 culverts, and 15.6 km of roadways. Also, the failure of south fork dam (earth and rock fill dam) near Johnstown on 1889 is considered the worst U.S dam disaster in terms of loss of life. The dam was overtopped and washed away due to unexpected heavy rains, releasing 20 million tons of water which destroyed Johnstown and resulted in 2209 deaths, [1], [2]. Piping or shear sliding, failure due to natural factors, and failure due to overtopping are all possible causes of earth dam failure. However, overtopping failure is the most frequent cause of dam failure. According to The International Committee on Large Dams (ICOLD, 1995), and [3], more than one-third of the total known dam failures were caused by dam overtopping.
Overtopping occurs as the result of insufficient flood design or freeboard in some cases. Extreme rainstorms can cause floods which can overtop the dam and cause it to fail. The size and geometry of the reservoir or the dam (side slopes, top width, height, etc.), the homogeneity of the material used in the construction of the dam, overtopping depth, and the presence or absence of tailwater are all elements that influence this type of failure which will be illustrated in the following literature. Overtopping failures of earth dams may be divided into several failure mechanisms based on the material composition and the inner structure of the dam. For cohesive earth dams because of low permeability, no seepage exists on the slopes. Erosion often begins at the earth dam toe during turbulent erosion and moves upstream, undercutting the slope, causing the removal of large chunks of materials. While for non-cohesive earth dams the downstream face of the dam flattens progressively and is often said to rotate around a point near the downstream toe [4], [5], [6] In the last few decades, the study of failures due to overtopping has gained popularity among researchers. The overtopping failure, in fact, has been widely investigated in coastal and river hydraulics and morpho dynamic. In addition, several laboratory experimental studies have been conducted in this field in order to better understand different involved factors. Also, many numerical types of research have been conducted to investigate the process of overtopping failure as well as the elements that influence this type of failure.
Tabrizi et al. [5] conducted a series of embankment overtopping tests to find the effect of compaction on the failure of a homogenous sand embankment. A plane breach process occurred across the flume width due to the narrow flume width. They measured the downstream hydrographs and embankment surface profile for every case. They concluded that the peak discharge decreased with a high compaction level, while the time to peak increased. Kansoh et al. [6] studied experimentally the failure of compacted homogeneous non-cohesive earthen embankment due to overtopping. They investigated the influence of different shape parameters including the downstream slope, the crest width, and the height of the embankment on the erosion process. The erosion process was initiated by carving a pilot channel into the embankment crest. They evaluated the time of embankment failure for different shape parameters. They concluded that the failure time increases with increasing the downstream slope and the crest width. Zhu et al. [7] investigated experimentally the breaching of five embankments, one constructed with pure sand, and four with different sand-silt–clay mixtures. The erosion pattern was similar across the flume width. They stated that for cohesive soil mixtures the head cut erosion was the most important factor that affected the breach growth, while for non-cohesive soil the breach erosion was affected by shear erosion.
Amaral et al. [8] studied experimentally the failure by overtopping for two embankments built from silt sand material. They studied the effect of the degree of compaction of the embankment and the geometry of the pilot channel carved at the centre of the dam crest. They studied two shapes of pilot channel a rectangular shape and triangular shape. They stated that the breach development is influenced by a higher degree of compaction, however, the pilot channel geometry did not influence the breach’s final form. Bereta et al. [9] studied experimentally the breach formation of five dam models, three of them were homogenous clay soil while two were sandy-clay mixtures. The erosion process was initiated by cutting a pilot channel at the centre of the dam crest. They observed the initiation of erosion, flow shear erosion, sidewall bottom erosion, and distinguished the soil mechanical slope mass failure from the head cut vertically and laterally during these tests. Verma et al. [10] investigated experimentally a two-dimensional erosion phenomenon due to overtopping by using a wooden fuse plug model and five different soils. They concluded that the erosion process was affected mostly by cohesiveness and degree of compaction. For cohesive soils, a head cut erosion was observed, while for non-cohesive soils surface erosion occurred gradually. Also, the dimensions of fuse plug, type of fill material, reservoir capacity, and inflow were found to affect the behaviour of the overall breaching process.
Wu and Qin [11] studied the effect of adding coarse grains to the downstream face of a non-cohesive dam as a result of tailings deposition. The process of overtopping during tailings dam failures is analyzed and its effect on delaying the dam-break process and disaster mitigation are investigated. They found that the tested protective measures decreased the breach area, the maximum breaching flow discharge and flow velocity, and the downstream inundated area. Khankandi et al. [12] studied experimentally the effect of reservoir geometry on dam break flow in case of dry and wet bed conditions. They considered four different reservoir shapes, a long reservoir, a wide, a trapezoidal shaped and one with a 90◦ bend all with identical water volume and horizontal bed. The dam break is simulated by the sudden gate removal using a pneumatic jack. They measured the variation of water level over time with ultrasonic sensors and flow velocity component with an acoustic Doppler velocimeter. Also, the experimental results of water level variation are compared with Ritters solution (1892) [13]. They stated that for dry bed condition the long and 90 bend reservoirs results are close to the analytical solution by ritter also in these two shapes a 1D flow is noticed. However, for wide and trapezoidal reservoirs a 2D effect is significant due to flow contraction at channel entrance.
Rifai et al. [14] conducted a series of experiments to investigate the effect of tailwater depth on the outflow discharge and breach geometry during non-cohesive homogenous fluvial dikes overtopping failure. They cut an initial notch in the crest at 0.8 m from the upstream end of the dike to initiate overtopping. They compared their results to previous experiments under different main channel inflow discharges combined with a free floodplain. They divided the dike breaching process into three stages: gradual start of overtopping flow resulting in slow initiation of dike erosion, deepening and widening breach due to large flow depth and velocity, finally the flow depth starts stabilizing at its minimal level with or without sustained breach expansion. They stated that breach discharge has lower values than in free floodplain tests. Jiang [15] studied the effect of bed slope on breach parameters and peak discharge in non-cohesive embankment failure. An initial triangular breach with a depth and width of 4 cm was pre-set on one side of the dam. He stated that peak discharge increases with the increase of bed slope and then decreases.
Ozmen-cagatay et al. [16] studied experimentally flood wave propagation resulted from a sudden dam break event. For dam-break modelling, they used a mechanism that permitted the rapid removal of a vertical plate with a thickness of 4 mm and made of rigid plastic. They conducted three tests, one with dry bed condition and two tests with tailwater depths equal 0.025 m and 0.1 m respectively. They recorded the free surface profile during initial stages of dam break by using digital image processing. Finally, they compared the experimental results with the with a commercially available VOF-based CFD program solving the Reynolds-averaged Navier –Stokes equations (RANS) with the k– Ɛ turbulence model and the shallow water equations (SWEs). They concluded that Wave breaking was delayed with increasing the tailwater depth to initial reservoir depth ratio. They also stated that the SWE approach is sufficient more to represent dam break flows for wet bed condition. Evangelista [17] investigated experimentally and numerically using a depth-integrated two-phase model, the erosion of sand dike caused by the impact of a dam break wave. The dam break is simulated by a sudden opening of an upstream reservoir gate resulting in the overtopping of a downstream trapezoidal sand dike. The evolution of the water wave caused from the gate opening and dike erosion process are recorded by using a computer-controlled camera. The experimental results demonstrated that the progression of the wave front and dike erosion have a considerable influence on each other during the process. In addition, the dike constructed from fine sands was more resistant to erosion than the one built with coarse sand. They also stated that the numerical model can is capable of accurately predicting wave front position and dike erosion. Also, Di Cristo et al. [18] studied the effect of dam break wave propagation on a sand embankment both experimentally and numerically using a two-phase shallow-water model. The evolution of free surface and of the embankment bottom are recorded and used in numerical model assessment. They stated that the model allows reasonable simulation of the experimental trends of the free surface elevation regardeless of the geofailure operator.
Lots of numerical models have been developed over the past few years to simulate the dam break flooding problem. A one-dimensional model, such as Hec-Ras, DAMBRK and MIKE 11, ect. A two-dimensional model such as iRIC Nay2DH is used in earth embankment breach simulation. Other researchers studied the failure process numerically using (3D) computational fluid dynamics (CFD) models, such as FLOW-3D, and FLUENT. Goharnejad et al. [19] determined the outflow hydrograph which results from the embankment dam break due to overtopping. Hu et al. [20] performed a comparison between Flow-3D and MIKE3 FM numerical models in simulating a dam break event under dry and wet bed conditions with different tailwater depths. Kaurav et al. [21] simulated a planar dam breach process due to overtopping. They conducted a sensitivity analysis to find the effect of dam material, dam height, downstream slope, crest width, and inlet discharge on the erosion process and peak discharge through breach. They concluded that downstream slope has a significant influence on breaching process. Yusof et al. [22] studied the effect of embankment sediment sizes and inflow rates on breaching geometric and hydrodynamic parameters. They stated that the peak outflow hydrograph increases with increasing sediment size and inflow rates while time of failure decreases.
In the present work, the effect of tailwater depth on earth dam failure during overtopping is studied experimentally. The relation between the eroded volume of the dam and the tailwater depth is presented. Also, the percentage of reduction in peak discharge due to tailwater existence is calculated. An assessment of Flow 3D software performance in simulating the erosion process during earth dam failure is introduced. The statistical variable root- mean- square error, RMSE, and the agreement degree index, d, are used in model assessment.
2. Material and methods
The tests are conducted in a straight rectangular flume in the laboratory of Irrigation Engineering and Hydraulics Department, Faculty of Engineering, Alexandria University, Egypt. The flume dimensions are 10 m long, 0.86 m wide, and 0.5 m deep. The front part of the flume is connected to a storage basin 1 m long by 0.86 m wide. The storage basin is connected to a collecting tank for water recirculation during the experiments as shown in Fig. 1, Fig. 2. A sharp-crested weir is placed at a distance of 4 m downstream the constructed dam to keep a constant tailwater depth in each experiment and to measure the outflow discharge.
To measure the eroded volume with time a rods technique is used. This technique consists of two parallel wooden plates with 10 cm distance in between and five rows of stainless-steel rods passing vertically through the wooden plates at a spacing of 20 cm distributed across flume width. Each row consists of four rods with 15 cm spacing between them. Also, a graph board is provided to measure the drop in each rod with time as shown in Fig. 3, Fig. 4. After dam construction the rods are carefully rested on the dam, with the first line of rods resting in the middle of the dam crest and then a constant distance of 15 cm between rods lines is maintained.
A soil sample is taken and tested in the laboratory of the soil mechanics to find the soil geotechnical parameters. The soil particle size distribution is also determined by sieve analysis as shown in Fig. 5. The soil mean diameter d50,equals 0.38 mm and internal friction angle equals 32.6°.
2.1. Experimental procedures
To investigate the effect of the tailwater depth (do), the tailwater depth is changed four times 5, 15, 20, and 25 cm on the sand dam model. The dam profile is 35 cm height, with crest width = 15 cm, the dam base width is 155 cm, and the upstream and downstream slopes are 2:1 as shown in Fig. 6. The dam dimensions are set as the flume permitted to allow observation of the dam erosion process under the available flume dimensions and conditions. All of the conducted experiments have the same dimensions and configurations.
The optimum water content, Wc, from the standard proctor test is found to be 8 % and the maximum dry unit weight is 19.42 kN/m3. The soil and water are mixed thoroughly to ensure consistency and then placed on three horizontal layers. Each layer is compacted according to ASTM standard with 25 blows by using a rammer (27 cm × 20.5 cm) weighing 4 kg. Special attention is paid to the compaction of the soil to guarantee the repeatability of the tests.
After placing and compacting the three layers, the dam slopes are trimmed carefully to form the trapezoidal shape of the dam. A small triangular pilot channel with 1 cm height and 1:1 side slopes is cut into the dam crest to initiate the erosion process. The position of triangular pilot channel is presented in Fig. 1. Three digital video cameras with a resolution of 1920 × 1080 pixels and a frame rate of 60 fps are placed in three different locations. One camera on one side of the flume to record the progress of the dam profile during erosion. Another to track the water level over the sharp-crested rectangular weir placed at the downstream end of the flume. And the third camera is placed above the flume at the downstream side of the dam and in front of the rods to record the drop of the tip of the rods with time as shown previously in Fig. 1.
Before starting the experiment, the water is pumped into the storage basin by using pump with capacity 360 m3/hr, and then into the upstream section of the flume. The upstream boundary is an inflow condition. The flow discharge provided to the storage basin is kept at a constant rate of 6 L/sec for all experiments, while the downstream boundary is an outflow boundary condition.
Also, the required tailwater depth for each experiment is filled to the desired depth. A dye container valve is opened to color the water upstream of the dam to make it easy to distinguish the dam profile from the water profile. A wooden board is placed just upstream of the dam to prevent water from overtopping the dam until the water level rises to a certain level above the dam crest and then the wooden board is removed slowly to start the experiment.
2.2. Repeatability
To verify the accuracy of the results, each experiment is repeated two times under the same conditions. Fig. 7 shows the relative eroded crest height, Zeroded / Zo, with time for 5 cm tailwater depth. From the Figure, it can be noticed that results for all runs are consistent, and accuracy is achieved.
3. Numerical model
The commercially available numerical model, Flow 3D is used to simulate the dam failure due to overtopping for the cases of 15 cm, 20 cm and 25 cm tailwater depths. For numerical model calibration, experimental results for dam surface evolution are used. The numerical model is calibrated for selection of the optimal turbulence model (RNG, K-e, and k-w) and sediment scour equations (Van Rin, Meyer- peter and Muller, and Nielsen) that produce the best results. In this, the flow field is solved by the RNG turbulence model, and the van Rijn equation is used for the sediment scour model. A geometry file is imported before applying the mesh.
A Mesh sensitivity is analyzed and checked for various cell sizes, and it is found that decreasing the cell size significantly increases the simulation time with insignificant differences in the result. It is noticed that the most important factor influencing cell size selection is the value of the dam’s upstream and downstream slopes. For example, the slopes in the dam model are 2:1, thus the cell size ratio in X and Z directions should be 2:1 as well. The cell size in a mesh block is set to be 0.02 m, 0.025 m, and 0.01 m in X, Y and Z directions respectively.
In the numerical computations, the boundary conditions employed are the walls for sidewalls and the channel bottom. The pressure boundary condition is applied at the top, at the air–water interface, to account for atmospheric pressure on the free surface. The upstream boundary is volume flow rate while the downstream boundary is outflow discharge.
The initial condition is a fluid region, which is used to define fluid areas both upstream and downstream of the dam. To assess the model accuracy, the statistical variable root- mean- square error, RMSE, and the agreement degree index, d, are calculated as(1)RMSE=1N∑i=1N(Pi-Mi)2(2)d=1-∑Mi-Pi2∑Mi-M¯+Pi-P¯2
where N is the number of samples, Pi and Mi are the models and experimental values, P and M are the means of the model and experimental values. The best fit between the experimental and model results would have an RMSE = 0 and degree of agreement, d = 1.
4. Results of experimental work
The results of the total time of failure, t (defined as the time from when the water begins to overtop the dam crest until the erosion reaches a steady state, when no erosion occurs), time of crest width erosion t1, cumulative eroded volume Veroded, and peak discharge Qpeak for each experiment are listed in Table 1. The case of 5 cm tailwater depth is considered as a reference case in this work.
Table 1. Results of experimental work.
Tailwater depth, do (cm)
Total time of failure, t (sec)
Time of crest width erosion, t1 (sec)
cumulative eroded volume, Veroded (m3)
Peak discharge, Qpeak (liter/sec)
5
255
22
0.21
13.12
15
165
30
0.16
12.19
20
140
34
0.13
11.29
25
110
39
0.05
10.84
5. Discussion
5.1. Side erosion
The evolution of the bathymetry of the erosion line recorded by the video camera1. The videos are split into frames (60 frames/sec) by the Free Video to JPG Converter v.5.063 build and then converted into an excel spreadsheet using MATLAB code as shown in Fig. 8.
Fig. 9 shows a sample of numerical model output. Fig. 10, Fig. 11, Fig. 12 show a dam profile development for different time steps from both experimental and numerical model, for tailwater depths equal 15 cm, 20 cm and 25 cm. Also, the values of RMSE and d for each figure are presented. The comparison shows that the Flow 3D software can simulate the erosion process of non-cohesive earth dam during overtopping with an RMSE value equals 0.023, 0.0218, and 0.0167 and degree of agreement, d, equals 0.95, 0.968, and 0.988 for relative tailwater depths, do/(do)ref, = 3, 4 and 5, respectively. The low values of RMSE and high values of d show that the Flow 3D can effectively simulate the erosion process. From Fig. 10, Fig. 11, Fig. 12, it can be noticed that the model is not capable of reproducing the head cut, while it can simulate well the degradation of the crest height with a minor difference from experimental work. The reason of this could be due to inability of simulation of all physical conditions which exists in the experimental work, such as channel friction and the grain size distribution of the dam soil which is surely has a great effect on the erosion process and breach development. In the experimental work the grain size distribution is shown in Fig. 5, while the numerical model considers that the soil is uniform and exactly 50 % of the dam particles diameter are equal to the d50 value. Another reason is that the model is not considering the increased resistance of the dam due to the apparent cohesion which happens due to dam saturation [23].
It is clear from both the experimental and numerical results that for a 5 cm tailwater depth, do/(do)ref = 1.0, erosion begins near the dam toe and continues upward on the downstream slope until it reaches the crest. After eroding the crest width, the crest is lowered, resulting in increased flow rates and the speeding up of the erosion process. While for relative tailwater depths, do/(do)ref = 3, 4, and 5 erosion starts at the point of intersection between the downstream slope and tailwater. The existence of tailwater works as an energy dissipater for the falling water which reduces the erosion process and prevents the dam from failure as shown in Fig. 13. It is found that the time of the failure decreases with increasing the tailwater depth because most of the dam height is being submerged with water which decreases the erosion process. The reduction in time of failure from the referenced case is found to be 35.3, 45, and 57 % for relative tailwater depth, do /(do)ref equals 3, 4, and 5, respectively.
The relation between the relative eroded crest height, Zeroded /Zo, with time is drawn as shown in Fig. 14. It is found that the relative eroded crest height decreases with increasing tailwater depth by 10, 41, and 77.6 % for relative tailwater depth, do /(do)ref equals 3, 4, and 5, respectively. The time required for the erosion of the crest width, t1, is calculated for each experiment. The relation between relative tailwater depth and relative time of crest width erosion is shown in Fig. 15. It is found that the time of crest width erosion increases linearly with increasing, do /Zo. The percent of increase is 36.4, 54.5 and 77.3 % for relative tailwater depth, do /(do)ref = 3, 4 and 5, respectively.
Crest height, Zcrest is calculated from the experimental results and the Flow 3D results for relative tailwater depths, do/(do)ref, = 3, 4, and 5. A relation between relative crest height, Zcrest/Zo with time from experimental and numerical results is presented in Fig. 16. From Fig. 16, it is seen that there is a good consistency between the results of numerical model and the experimental results in the case of tracking the erosion of the crest height with time.
5.2. Upstream and downstream water depths
It is noticed that at the beginning of the erosion process, both upstream and downstream water depths increase linearly with time as long as erosion of the crest height did not take place. However, when the crest height starts to lower the upstream water depth decreases with time while the downstream water depth increases. At the end of the experiment, the two depths are nearly equal. A relation between relative downstream and upstream water depths with time is drawn for each experiment as shown in Fig. 17.
5.3. Eroded volume
A MATLAB code is used to calculate the cumulative eroded volume every time interval for each experiment. The total volume of the dam, Vtotal is 0.256 m3. The cumulative eroded volume, Veroded is 0.21, 0.16, 0.13, and 0.05 m3 for tailwater depths, do = 5, 15, 20, and 25 cm, respectively. Fig. 18 presents the relation between cumulative eroded volume, Veroded and time. From Fig. 18, it is observed that the cumulative eroded volume decreases with increasing the tailwater depth. The reduction in cumulative eroded volume is 23, 36.5, and 75 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The relative remained volume of the dam equals 0.18, 0.375, 0.492, and 0.8 for tailwater depths = 5, 15, 20, and 25 cm, respectively. Fig. 19 shows a relation between relative tailwater depth and relative cumulative eroded volume from experimental results. From that figure, it is noticed that the eroded volume decreases exponentially with increasing relative tailwater depth.
5.4. The outflow discharge
The inflow discharge provided to the storage tank is maintained constant for all experiments. The water surface elevation, H, over the sharp-crested weir placed at the downstream side is recorded by the video camera 2. For each experiment, the outflow discharge is then calculated by using the sharp-crested rectangular weir equation every 10 sec.
The outflow discharge is found to increase rapidly until it reaches its peak then it decreases until it is constant. For high values of tailwater depths, the peak discharge becomes less than that in the case of small tailwater depth as shown in Fig. 20 which agrees well with the results of Rifai et al. [14] The reduction in peak discharge is 7, 14, and 17.35 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively.
The scenario presented in this article in which the tailwater depth rises due to unexpected heavy rainfall, is investigated to find the effect of rising tailwater depth on earth dam failure. The results revealed that rising tailwater depth positively affects the process of dam failure in terms of preventing the dam from complete failure and reducing the outflow discharge.
6. Conclusions
The effect of tailwater depth on earth dam failure due to overtopping is investigated experimentally in this work. The study focuses on the effect of tailwater depth on side erosion, upstream and downstream water depths, eroded volume, outflow hydrograph, and duration of the failure process. The Flow 3D numerical software is used to simulate the dam failure, and a comparison is made between the experimental and numerical results to find the ability of this software to simulate the erosion process. The following are the results of the investigation:
The existence of tailwater with high depths prevents the dam from completely collapsing thereby turning it into a broad crested weir. The failure time decreases with increasing the tailwater depth and the reduction from the reference case is found to be 35.3, 45, and 57 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The difference between the upstream and downstream water depths decreases with time till it became almost negligible at the end of the experiment. The reduction in cumulative eroded volume is 23, 36.5, and 75 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The peak discharge decreases by 7, 14, and 17.35 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The relative eroded crest height decreases linearly with increasing the tailwater depth by 10, 41, and 77.6 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The numerical model can reproduce the erosion process with a minor deviation from the experimental results, particularly in terms of tracking the degradation of the crest height with time.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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My name is Shaimaa Ibrahim Mohamed Aman and I am a teaching assistant in Irrigation and Hydraulics department, Faculty of Engineering, Alexandria University. I graduated from the Faculty of Engineering, Alexandria University in 2013. I had my MSc in Irrigation and Hydraulic Engineering in 2017. My research interests lie in the area of earth dam Failures.
Peer review under responsibility of Ain Shams University.