Numerical Simulations of the Flow Field of a Submerged Hydraulic Jump over Triangular Macroroughnesses
Abstract
:1. Introduction
2. Submerged Hydraulic Jump
3. Materials and Methods
3.1. Input Parameters for Numerical Models
3.2. Experimental Model
3.3. CFD Analysis
3.4. Turbulence Model
3.5. Boundary Conditions in the Computational Domain
3.6. Computational Grid and Grid Convergence Analysis
4. Results and Discussions
4.1. Validity of the Numerical Model Results
4.2. Longitudinal Profile of Streamlines
4.3. Velocity Profiles
4.4. Bed Shear Stress
4.5. Turbulent Kinetic Energy (TKE) and Energy Loss
5. Conclusions
 The flow patterns in the triangular macroroughnesses in the developed and developing regions are the same with smaller areas in comparison with the smooth bed in submerged hydraulic jump conditions. The triangular macroroughnesses lead to the formation of another clockwise eddy flow in the cavity region between the macroroughnesses.
 For distances equal to T/I = 1, 0.5 and 0.33, the velocity vector distribution displays a clockwise eddy in the cavity region, where the magnitude of velocity is much smaller than the mean flow velocity. Increasing the distance between triangular macroroughnesses (T/I = 0.25 and 0.2), two eddies of different sizes are formed in the cavity region.
 When the distance between the triangular macroroughnesses is long enough, the velocity distribution has recovered by the time that the flow arrives at the next roughness. However, in the short distance, the flow arrives at the next roughness without adequate recovery of the velocity distribution. Hence, with decreasing distance between macroroughnesses, the rate of increase in the frictional coefficient decreases.
 In the triangular macroroughnesses, the maximum velocity at a specified section in the submerged jump leads to higher values than the free jump. In addition, for both types of bed (smooth and rough) in the submerged jump, the maximum velocity distance from the bed is decreased due to increasing depth and eddy flow. In the submerged jump, the boundary layer thickness is less than the free jump.
 The turbulence region on the smooth bed is created with the distance from the gate and occurs near free surface roller area, whereas on the macroroughnesses, the turbulence begins near a gate with greater intensity and limited sweep region that is the result of a counterclockwise circulating in free surface roller and clockwise eddy flow in the space between the macroroughnesses.
 The bed shear stress coefficient and energy loss of the submerged jump on the triangular macroroughnesses is larger than that found on the smooth bed that increased with the increase in inlet Froude numbers. The highest and lowest bed shear stress coefficient and energy loss occur in T/I = 0.50 and 0.20 with the increasing distance of roughness elements compared to a smooth bed.
 The reduction in the length of the jump and the submerged and tailwater depths given by the presence of triangular macroroughnesses with nearroughness elements can be used in the design of stilling basins with a resulting decrease in their size, i.e., length and height.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Reference  Shape BedChannel Type Jump Type  Channel Dimension (m)  Roughness (mm)  Fr_{1}  Investigated Flow Properties 

Ead and Rajaratnam [10] 
 CL^{1} = 7.60 CW^{2} = 0.44 CH^{3} = 0.60 
 4–10 

Tokyay et al. [11] 
 CL = 10.50 CW = 0.253 CH = 0.432 
 5–12 

Izadjoo and ShafaiBejestan [14] 
 CL = 1.2, 9 CW = 0.25, 0.50 CH = 0.40  Baffle with trapezoidal cross section (RH: 13 and 26)  6–12 

Abbaspour et al. [12] 
 CL = 10 CW = 0.25 CH = 0.50 
 3.80–8.60 

ShafaiBejestan and Neisi [13] 
 CL = 7.50 CW = 0.35 CH = 0.50  Lozenge bed  4.50–12 

Elsebaie and Shabayek [18] 
 CL = 9 CW = 0.295 CH = 0.32 
 50 

SamadiBoroujeni et al. [19] 
 CL = 12 CW = 0.40 CH = 0.40 
 6.10–13.10 

Ahmed et al. [20] 
 CL = 24.50 CW = 0.75 CH = 0.70 
 1.68–9.29 

Nikmehr and Aminpour [15] 
 CL = 12 CW = 0.25 CH = 0.50 
 5.01–13.70 

Ghaderi et al. [17] 
 CL = 4.50 CW = 0.75 CH = 0.70 
 1.70–9.30 

Present study  Rectangular channel Smooth and rough beds Submerged jump  CL = 4.50 CW = 0.75 CH = 0.70 
 1.70–9.30 

Bed Type  Q (l/s)  I (cm)  T (cm)  d (cm)  y_{1} (cm)  y_{4} (cm)  Fr_{1}= u_{1}/(gy_{1})^{0.5}  S  Re_{1}= (u_{1}y_{1})/υ 

Smooth  30, 45      5  1.62–3.83  9.64–32.10  1.7–9.3  0.26–0.50  39,884–59,825 
Triangular macroroughnesses  30, 45  4, 8, 12, 16, 20  4  5  1.62–3.84  6.82–30.08  1.7–9.3  0.21–0.44  39,884–59,825 
Models  Bed Type  Q (l/s)  d (cm)  y_{1} (cm)  u_{1} (m/s)  Fr_{1} 

Numerical and Physical  Smooth  45  5  1.62–3.83  1.04–3.70  1.7–9.3 
T/I = 0.5  45  5  1.61–3.83  1.05–3.71  1.7–9.3  
T/I = 0.25  45  5  1.60–3.84  1.04–3.71  1.7–9.3 
Mesh  Nested Block Cell Size (cm)  Containing Block Cell Size (cm) 

1  0.55  1.10 
2  0.65  1.30 
3  0.85  1.70 
Parameters  Amounts 

f_{s}_{1} ()  7.15 
f_{s}_{2} ()  6.88 
f_{s}_{3} ()  6.19 
K ()  5.61 
E_{32} (%)  10.02 
E_{21} (%)  3.77 
GCI_{21} (%)  3.03 
GCI_{32} (%)  3.57 
GCI_{32}/r^{p} GCI_{21}  0.98 
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Ghaderi, A.; Dasineh, M.; Aristodemo, F.; Aricò, C. Numerical Simulations of the Flow Field of a Submerged Hydraulic Jump over Triangular Macroroughnesses. Water 2021, 13, 674. https://doi.org/10.3390/w13050674
Ghaderi A, Dasineh M, Aristodemo F, Aricò C. Numerical Simulations of the Flow Field of a Submerged Hydraulic Jump over Triangular Macroroughnesses. Water. 2021; 13(5):674. https://doi.org/10.3390/w13050674
Chicago/Turabian StyleGhaderi, Amir, Mehdi Dasineh, Francesco Aristodemo, and Costanza Aricò. 2021. "Numerical Simulations of the Flow Field of a Submerged Hydraulic Jump over Triangular Macroroughnesses" Water 13, no. 5: 674. https://doi.org/10.3390/w13050674