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, Flow-3D 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 (Bed-Load) 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 1.
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 one-dimensional velocity factor over the bars. For simplifying the energy head, some authors considered a horizontal energy level over the bottom intake (Torabi et al. 2; Vargas 3; Brunella et al. 4; Righetti & Lanzoni 5; Garcia 6; Drobir et al. 7) and others considered a parallel energy level ( Noseda 8; Dagan 9; Hamedi et al. 10).
Orth et al.9 provided the first investigation of the flow field over bottom intake. Different flows on a 20% sloping channel with five different rack geometries, including the simple T-shaped, the T with a top triangle profile, the semicircular bar, the circular bar and the ovoid profile was investigated. The ovoid bar profile had the least wetted length, where the t- shaped bar had the poorest diverting performance. The bottom slope of the rack had only a small effect on rack occlusion.
Righetti and Lanzoni 5 studied the hydraulic design of Bottom racks made by longitudinal bars, analyzing the data obtained from a systematic series of experiments carried out in a laboratory flume. For each run they measured the diverted discharge, the water surface longitudinal profile and they obtained discharge coefficient to be used to determine the rate of change of the diverted discharge. They also drove a physically based relationship relating the overall diverted discharge to the length of the rack, the void ratio, the discharge coefficient measured under static conditions, the specific head of the stream approaching the rack, and a modified Froude number. The robustness of the proposed relationship is confirmed by the comparison between the discharges calculated through the proposed relationship and those measured in an extensive series of experiments.
∆Q=C_qo ωWL√(2gH_o ) (a/2 L/H_o F_(H_O )+1)tanh[b_o (√2-F_(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  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. 4 conducted experimental tests in a rectangular channel, 0.5 m wide and 7 m long. According to the extended laboratory observation, the effect of various parameters, such as the bottom slope, the rack geometry and the rack porosity, was explored. In addition, a novel approach to determine the discharge coefficient of a rack structure was developed. Finally, the intake channel below the bottom rack was investigated and several interesting features were found, including a significant flow instability that may have a strongly adverse effect on the rack performance.
Kumar et al.11 carried out an experimental study on the discharge characteristics of a trench weir consisting of flat bars under free and submerged flow. They evolved the following relationship for discharge ratio (Cd) based on observation and under constant conditions.
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 1 conducted experimental tests, in which they developed the following equation for discharge coefficient:
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 12 performed a set of experiments in order to develop a methodology to estimate head loss through trash racks in open channel by considering the variable parameters such as bar diameter, clear spacing between bars, inclination angle and unit discharge. Head loss during trash rack is a key parameter to design geometrical arrangement of the bars. Josiah et al. proposed a new head loss equation based on the experimental findings to estimate the head loss through trash racks made up of circular bars.
∆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 13 obtained the discharge coefficient by setting different discharges of sediment and clean water flow over bottom intakes and derived a dimensionless relation for discharge coefficient. A rectangular channel with 8 meters long and 0.4 m wide and three kinds of bottom grids with three opening ratios of 0.3, 0.35 and 0.4 were built. Bottom grids were placed at the bottom of the channel with three different slopes (20%,30%, and 56%). Sediment was sized to transport as bed load. They derived relations for the discharge coefficient for both sediment and clean water flow.
In the classical numerical modeling authors considered one-dimensional and two-dimensional models to analyse the hydraulic of turbulent flow and sediment transport. Nevertheless, over the bottom intakes, the flow becomes highly three-dimensional so that three-dimensional models were developed and considered (Castillo & Carrillo 14).
Kuntzmann and Bouvard 9 presented a first computational approach for the free-surface profile over bottom racks by assuming constant energy head and a conventional orifice equation. The spatial distribution of discharge as a function of the streamwise coordinate resulted in an ordinary differential equation of the sixth degree, which was solved for the horizontal bottom rack.
Castillo et al. 15 carried out numerical simulations with CFD methodology. They analyzed the increment in the wetted rack length due to the sediment transport. Different sediment concentrations, from 1.0% to 5.0% in volume, void ratios from 0.16 to 0.60, flow rates, and rack slopes were all considered.
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 16:
dy/dx=(So-Sf-(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(E-y)) and rearranging the terms in the resulting equation, one obtains:
Integration of Equation 3 yields:
can be determined from the flow conditions at the upstream of the bottom rack which yields:
x=E/ɛCd(y1/E √(1-y1/E)-y/E √(1-y/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).
Dimensional analysis :
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:
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 non-dimensional 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 v-notch 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.
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 non-uniform gradation (combination of D75=5mm and D75=8mm) which is transported as bed-load under the range of allowed discharges (Fig. 4). The series of tests were conducted under the same conditions as clean flow.
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 finite-element scheme program FLOW-3D.
The experimental conditions modeled in Flow3-d 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.
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 zero-roughness (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 17.
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 run-time considrations). The grid convergence method for selecting mesh sizes is used and inspiered by Zahani et al. and Zeidi et al.18,19,20
|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|
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 k-ε model, the ReNormalization Group (RNG), the Large Eddy Simulation (LES) model and the Prandtl ’ s one-equation 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.
|verage||Qd ( Num)||Qd ( Exp)||Test no||turbulence model|
Results and discussion:
The value of discharge coefficient was calculated from the following equation, using the measured data:
Where E was computed from upstream flow conditions. Table 3. shows a summary of the experimental results.
|Test no||Ɛ||Fr o||mm)||Slope%||Re||Cd (experimental )|
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=0.759-0.543(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.Table 4. Comparison between measured diverted discharge and computed diverted discharge using the proposed relation.
|Row||Qd (Experimental)||Qd (proposed relation)||Error%|
For the sediment flow, the following relation is obtained for discharge coefficient:
C_d=0.652-0.528(ε)-0.019*(L/y_o )-0.00169(S_L )
RMSE=13.35% ,〖 R〗^2=80%
Table 5. shows a comparison between measured discharge coefficient and computed discharge coefficient using the proposed relation for sediment flow. As it can be seen, proposed relation led to a mean of 4.36% difference with measured discharge coefficient that is acceptable and confirms the function of numerical model. Also discharge coefficient of proposed relation plotted against measured discharge coefficient in figure 9.
|Test no||Ɛ||y0||slope||Cd(measured)||Cd(fitting relation)||% error|
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.
|Standard deviation||Average error||Fitting relation to estimate discharge coefficient||Sediment/clean 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.
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