Bottom intakes are the most useful structure for diverting the flow of steep rivers and providing specific amount of water for hydropower usage. It is crucial to obtain optimum of physical parameters in order to divert desired discharge with minimum possibility of occlusion. Numerical models can simulate flow and turbulence transport equations at any complex geometries. Numerical methods based on Computational Fluid Dynamics (CFD), are one of the most common methods of numerical simulation that is used in water structures. According to the capabilities of numerical methods, complex modes of flow field over bottom intakes can be analyzed. In the present study, Flow3D software is used to investigate the experimental results of the previous researcher for sediment and clean water flow over bottom intake with circular bars numerically. This study is carried out in a total of 27 models for clean water and 9 models of sediment flow (BedLoad) at different approaching flow conditions. Parameters of roughness, size of computational cell, turbulence transport equation, Bed Load Transport equation and bed load coefficient has been calibrated. Validation procedure proved that the accuracy and performance of numerical models appear to be acceptable for designing intake systems. For each test, the discharge coefficient is computed, then by using dimensional analysis, a dimensionless relation derived from the dependent and independent variables and compared with the measured discharge coefficient. Estimating the discharge coefficient by the proposed equation in clean water flow performed a mean error of 6.4 percent and for sediment flow led to a mean error of 4.3 percent.
Bottom intakes are structures that are used for diverting river flow generally for the goal of generating electricity in hydropower. The water is supplied from the small mountain rivers with steep slopes and intensive sediment transport. The intake structure must be simple from the construction point of view and requires less maintenance work after the construction. Bottom intakes must be able to divert the maximum flow discharge at all time with the minimum quantity of sediment and minimum possibility of occlusion. Bottom intake is the most suitable structure which can satisfy all the items mentioned above. This structure consists of a diversion channel below the river bed in on the side of the river, and a metal structure consists of bars on top of the diversion channel (Fig. 1).
Diversion channel transports the water to the penstock of hydropower. The function of bottom intakes is depended on different factors, such as approaching flow conditions, the size and shape of bars (shape function), the longitudinal slope, opening ratio (spacing between bars). Although this structure is the most useful structure for diverting river flow, some of its design criteria for optimum structure design needs to be studied. In the present study a rectangular channel with a circular opening in the bottom constructed to divert sediment and to produce an intake structure
In the previous studies, there are some simplifying assumptions, such as hydrostatic pressure distribution over the racks in the flow direction, a progressive decrease of the flow during the bottom intake and onedimensional velocity factor over the bars. For simplifying the energy head, some authors considered a horizontal energy level over the bottom intake (Torabi et al.
Orth et al.
Righetti and Lanzoni
∆Q=C_qo ωWL√(2gH_o ) (a/2 L/H_o F_(H_O )+1)tanh[b_o (√2F_(H_o ) )^(b_1 ) ]
Where the coefficients b_o and b_1 appearing in the hyperbolic tangent were obtained by minimizing the sum of the errors between the computed and measured total discharge diverted (estimated value: b_o=1.5, b_1=0.6093), ω= void ratio, W= channel width, C_qo= the experimental values measured under static conditions, H_o= the specific head of the stream approaching the rack, F_(H_O )= modified Froude number. Kumar and Ahmad [15] studied in the laboratory the percentage of solids passing through the rack. The authors considered the longitudinal rack slope, different water flows, the ratio between the size of sediments, and the bar clearance (from 0.18 to 0.83).
Brunella et al. [3]
Kumar et al.
C_d=0.4710.124×ln(S/t)0.194×S_r0.01×(ω/t)
Where S is clear spacing of rack bars, t represents the thickness of flat bars, S_r stands for the slope of rack and ω is width of flat bars. They compared discharge ratio obtained from derived relation with the experimental data.
Kamanbedast and Shafai Bejestan
C_d=0.223ε^(0.79) 〖Fr〗^(0.295) (∅/L)^0.054 〖(Y_1/L)〗^(0.0043)
Where Cd is the coefficient discharge, ε represents the area opening, F_r stands for the Froude number, ∅ represents the bar diameter, Y_1 stands for the flow depth and L is the length of rack.
Josiah et al
∆h/(V^2/2g)=0.1923〖(sinα)〗^0.05 〖(P)〗^0.15 〖(qg/V^3 )〗^1.56
Where V= approach velocity α= inclination angle from channel bed P=blockage ratio q= unit discharge
Bina and Saghi
In the classical numerical modeling authors considered onedimensional and twodimensional models to analyse the hydraulic of turbulent flow and sediment transport. Nevertheless, over the bottom intakes, the flow becomes highly threedimensional so that threedimensional models were developed and considered (Castillo & Carrillo
Kuntzmann and Bouvard
Castillo et al.
Although it seems that bottom intake has been studied in the past, there are so many questions regarding the estimating diverted discharge of bottom intakes to design a structure with optimum or desired intake ratio using numerical models with minimum cost. Therefore, the purpose of the present study is to investigate the effects of geometrical parameters of bottom intake and to approach flow conditions on the discharge coefficient and to contribute with new ideas for better structure design.
The governing equations for the flow in a river with a lateral outflow through a bottom screen are as follow. Hosseini et al. in 2019 investigated on energy equation
Continuity equation:
dQ/dx=Q_i=Cd.ɛ.√2gE
Energy equation:
dy/dx=(SoSf(aQ/(gA^2 ))(dQ/dx))/(1〖Fr〗^2 )
In this equation:
Q is the discharge in the main channel; Qi is the diverted flow discharge (passing through bottom rack); ɛ is the opening ratio of the screen; C_d is discharge coefficient; E is the specific energy of the flow over the screen and is the sum of the flow depth (y) and velocity head (V^2/2g); Y is the flow depth on the screen; So is the screen slope; Sf is the slope of energy grade line; A is the flow area cross section in the main channel; Fr is the Froude number which is defined as v⁄gy in which v is the flow velocity.
To determine the water surface profile over the screen, both equations must be solved. The analytical solution for these equations is possible through use of a few assumptions. The first assumption is that since the length of bottom rack generally is short, consequently the effect of channel and friction slopes on the flow profile can be assumed to be negligible. This assumption reveals that the value of specific energy (E) is constant. The second assumption is that the channel shape is wide and the discharge coefficient is constant. Applying these assumptions and substituting Eqation1 into each and calculating Q from specific energy definition which is zg by Q=By√(2g(Ey)) and rearranging the terms in the resulting equation, one obtains:
dy/dx=(2ɛCd√(E(Ey)))/(3y2E)
Integration of Equation 3 yields:
x=y/ɛCd √(1y/E)+constant.
can be determined from the flow conditions at the upstream of the bottom rack which yields:
x=E/ɛCd(y1/E √(1y1/E)y/E √(1y/E))
Therefore, it can be seen that discharge coefficient is an important factor in determining the intake flow discharge (Equation5) and water surface computations (Equation2).
Before setting the numerical simulation of experimental tests, a general relationship has to be developed. This can be done by using the dimensional analysis. Discharge coefficient ( Cd) can be shown as follows:
C_d=f_1 (ρ,μ,g,ε,s_L,L,y_0,V_0,e_l/d)
Where C_d is discharge coefficient; ρ is the specific mass of water; μ is dynamic viscosity of the fluid; g is acceleration of gravity; ε is the opening ratio; y_0 is depth of approaching flow; L is the rack length; V_0 is approaching flow velocity; e_l stands for clear space of longitudinal bars; d is the bar diameter and s_L for longitudinal slope of bottom intake. By applying the dimensional analysis (buckingham π theorem), the nondimensional equation can be developed (Equation 7). After simplification of above equation and eliminating the parameters with constant values in this study, following function can be obtained:
C_d=f(μ/(ρV_O y_o ),(gy_o)/(V_o^2 ),ε,s_L,L/y_o ,e_l/d)
Bina’s physical model consists of a 0.4 m wide, 0.5 m deep and 8 m long flume with Plexiglas walls that allows for the inspection of the flow and perform minimum roughness. Three kinds of bottom screens with different opening ratio of 0.3, 0.35 and 0.4 were built and installed at the end of the flume (30 cm long and 40 cm wide). Bottom screens are made of longitudinal and cross bars (grid) with circular shape ( ∅8mm). A pipe was connected to the bottom of the flume to transport the diverted water into the sump. A vnotch weir at the downstream end of the channel, measures the discharge and the discharge passing through the screen. Fig. 2 shows the sketch of the experimental setup.
Sketch of the experimental setup
View of experimental model
After installing one of the bottom racks at the desired slope, the flow was allowed to enter the flume by gradual opening of the entrance valve until the flow discharge reaches the desired discharge (Fig. 3). This situation was kept constant for one hour. During this time, water surface elevation was measured in the flume, especially above the bottom rack. The diverted flow discharge was also measured. Then, flow discharge in the flume was increased and the same variables were measured. The same procedure was followed for three more discharges. Afterwards, the bottom rack was installed at a new slope and the above mentioned tests were repeated. The above procedures were followed by installing a new model of bottom rack with three new opening ratio.
To investigate the performance of bottom racks when the sediment is passing over the rack tests have been repeated in more restricted condition. In these series sediment was placed on the bed of upstream flume of the bottom rack with nonuniform gradation (combination of D75=5mm and D75=8mm) which is transported as bedload under the range of allowed discharges (Fig. 4). The series of tests were conducted under the same conditions as clean flow.
view of sediment bed load considerations
The computational fluid dynamics (CFD) programs solve the fluid mechanic problems, providing lots of data and flexibility. However, the numerical models still present a level of mismatch when modelling some hydraulic phenomena. Hence, it is necessary to validate numerical results with experimental data. Some certain Laboratory tests were considered to validate simulations in order to evaluate the accuracy of the finiteelement scheme program FLOW3D.
The experimental conditions modeled in Flow3d Software with suitable boundary conditions. Parameters such as roughness, size of computational cell, turbulence transport equation, Bed Load Transport equation and bed load coefficient calibrated to match the experimental and numerical results.
View of a modelling test
It ’ s important to set suitable boundary conditions for computional enviromet to apply exact lobratoar conditions on model. In this case, Volume Flow Rate boundary condition considered for inlet of the mesh grid that provide the possibility to set the discharge and depth of the inlet flow. WALL boundary condition setted for the flume wall that was made of plexiglas in the lobratoar. This type of boundary provides rigorous and zeroroughness (as what plexiglas provides). For the outlet faces of the grid, OUTFLOW boundery is considersd in order to observe the discharge of the diverted flow and remaining flow at the end of flume. Fig. 6 shows the considered boundry conditions of cumputional grid.
Zeidi et al. defined a robust way of assigning boundary condition, including assigning wall bounday condition, pressure difference boundary condition and velocity inlet boundary condition which is used in the current study [26]
View of applied boundary condition
To test the accuracy of the numerical simulations data, diverted discharges of the intake were compared by using different mesh sizes and thus obtaining mesh sizes sufficiently insensitive to the results (Table 1). The analysis was based on the diverted discharge obtained after stabilization of measured discharge with a tolerance of 0.005 l/s. The comparison with the laboratory measurements shows good agreement for the mesh sizes smaller than 4mm.
Also it can be seen that 2.5 mm and 2 mm mesh sizes make tolerable differences in diverted discharge. As there are no outstanding differences between the results obtained with the smaller mesh size, the 2.5 mm mesh size is used to analyze the rest of the models (based on runtime considrations). The grid convergence method for selecting mesh sizes is used and inspiered by Zahani et al. and Zeidi et al.
Numerical Qd
Experimental Qd
Test no.
size of cell=٢ mm
size of cell=٢.٥ mm
size of cell=٣ mm
size of cell=٤ mm
size of cell=٥ mm
size of cell=٦ mm
٢٥.٦١٠
٢٥.٦١١
٢٥.٧٤٢
٢٥.٩٧٩
٢٤.٧٦٥
٢٦.٥١٠
٢٥.٥٩٨٤
81
View of applied mesh grid
Due to the different behavior of the turbulence models in complex flow conditions around the bottom intake, the influence of the turbulence model has also been tested with four of the turbulence models: the standard kε model, the ReNormalization Group (RNG), the Large Eddy Simulation (LES) model and the Prandtl ’ s oneequation model. Three experimental tests are used and Table 2. compares the values of the numerical and experimental diverted discharge by using different turbulence models. For the cases considered, There are no outstanding differences between the four turbulence models and the experimental measurements. However, the RNG turbulence model made less difference between experimental and numerical diverted discharge.
Qd ( Num)
Qd ( Exp)
Test no
turbulence model
0.973
23.2153
١٩.٥٦٣٩
66
Prandtl
26.3646
25.5984
81
28.2354
24.8094
246
0.986
22.1650
١٩.٥٦٣٩
66
kɛ
26.4254
25.5984
81
27.3645
24.8094
246
0.998
20.5582
١٩.٥٦٣٩
66
RNG
25.9709
25.5984
81
25.1139
24.8094
246
0.990
19.3657
١٩.٥٦٣٩
66
LES
25.9932
25.5984
81
24.2364
24.8094
246
The value of discharge coefficient was calculated from the following equation, using the measured data:
C_d=Q_i/(ε√2gE)
Where E was computed from upstream flow conditions. Table 3. shows a summary of the experimental results.
View of a modelling test.







60  0.4  1.53  33  56.98  28701  0.1951 
66  0.4  2.28  47  56.98  72793  0.2219 
63  0.4  1.55  47  56.98  49550  0.2433 
103  0.4  1.57  49  27.24  53312  0.2811 
106  0.4  1.48  68  27.24  82322  0.3563 
100  0.4  1.54  35  27.24  31552  0.2082 
83.1  0.3  1.54  47  56.2  49059  0.2805 
233  0.4  1.54  48  21.16  50883  0.2813 
236  0.4  1.5  67  21.16  81691  0.3771 
230  0.4  1.53  31  21.16  26135  0.1799 
86.1  0.3  1.51  61  56.2  71047  0.3188 
80.1  0.3  1.55  35  56.2  31697  0.2487 
81  0.3  1.51  66  57.36  79985  0.432 
82  0.3  1.54  49  57.36  52222  0.345 
80  0.3  1.53  34  57.36  30141  0.2665 
256  0.3  1.5  67  20.14  81529  0.4295 
253  0.3  1.54  53  20.14  58837  0.3775 
250  0.3  1.54  40  20.14  38688  0.3101 
76  0.4  1.51  65  57.36  78279  0.2872 
73  0.4  1.53  48  57.36  50546  0.2524 
70  0.4  1.51  34  57.36  29723  0.2124 
93  0.4  1.54  48  27.34  50747  0.2901 
97  0.4  1.5  63  27.34  74414  0.3575 
90  0.4  1.53  35  27.34  31375  0.2277 
243  0.4  1.55  49  21.5  52748  0.299 
246  0.4  1.49  64  21.5  75651  0.3584 
240  0.4  1.54  35  21.5  31586  0.2369 
For clean water flow, based on numerical results (diverted discharges), discharge coefficient of each test is calculated. By multiple linear fitting of dimensionless parameters, using SPSS Statistical software, the following relation is obtained for discharge coefficient:
C_d=0.7590.543(ε)0.03*(L/y_o )0.013(e_L/d)0.00147(S_L )
RMSE=7.75% ,〖 R〗^2=93.5%
3d. In this relation, the effect of Reynolds number on discharge coefficient has been neglected in comparison with Bina’s proposed relation.
Discharge coefficient values of proposed relation in this study against experimental values of discharge coefficient plotted in Fig. 8. Also table 4. is a comparison between measured diverted discharge and computed diverted discharge using the proposed relation. It can be seen that accuracy of proposed relation is acceptable.
Row  Qd (Experimental)  Qd (proposed relation)  Error% 
1  11.1834  10.838  17.4 
2  19.5639  21.396  9.4 
3  16.7888  16.743  0.3 
4  19.9222  20.86  4.7 
5  28.8521  28.001  2.9 
6  12.3353  13.072  6.0 
7  14.18  15.495  9.3 
8  30.537  28.574  6.4 
9  10  10.909  9.1 
0  18.1585  20.003  10.2 
11  10.8832  10.489  3.6 
12  17.8102  16.141  9.4 
13  11.4497  9.894  13.6 
14  25.5964  24.943  2.6 
15  20.2832  20.55  1.3 
16  14.4968  15.256  5.2 
17  20.2832  21.537  6.2 
18  15.4633  15.676  1.4 
19  10.8732  9.145  15.9 
20  17.8102  18.42  3.4 
21  24.81  23.919  3.6 
22  11.8894  12.032  1.2 
23  18.504  19.462  5.2 
24  12.3353  12.526  1.5 
mean  17.25039  17.26171  6.4 
discharge coefficient of proposed relation for sediment flow(Cd_c) against measured discharge coefficient(Cd_a).
Ratio of diverted discharge to total input discharge (Q_d/Q_t ) against total input discharge (Q_t) for every three opening ratio of bottom intakes is plotted in Figures 10, 11 and 12.
Ratio of diverted discharge to total input discharge against total input discharge for ?=0.3.
Ratio of diverted discharge to total input discharge against total input discharge for ?=0.35.
Ratio of diverted discharge to total input discharge against total input discharge for ?=0.4.
Standard deviation
Average error
Fitting relation to estimate discharge coefficient
Sediment/clean flow
٠.٠٣١٤
٦.٤%
Clean flow
٠.٠٣١٣
٤.٣%
Sediment flow
• Estimating discharge coefficient with proposed relation for clean flow led to a mean error of 6.4% in comparison with measured values.
• Estimating discharge coefficient with proposed relation for sediment flow led to a mean error of 4.3% in comparison with measured values.
• Following factors increases discharge coefficient of bottom intake:
1) Less longitudinal slope of bottom intake, 2) more opening ratio of bottom screen and 3) Less Froude number.