Flow control in a multichamber settling basin by sluice gates driven by a CFD and an ancillary analytical model

Unequal ﬂ ow distribution between the chambers of a three-chamber settling basin causes its malfunction and endangers the turbines of a small hydropower plant. To equalize the ﬂ ows, sluice gates are used. To ﬁ nd their positions, the following methodologies are considered: (1) measurements combined with trial-and-error method (TAE), (2) measurements with regression analysis (RA), (3) CFD model combined with TAE, (4) CFD model with RA, (5) CFD model supported by a one-dimensional ﬂ ow model, and (6) CFD model with an analytical model. The additional models and RA are intended to speed up the solution ﬁ nding. From the previous list, only the sixth methodology is applicable. The ﬁ rst four are not because of the weir design, and the ﬁ fth because of the three-dimensional ﬂ ow character. Initially, the CFD model of the side-weir intake was developed and validated. Afterward, the analytical model, which consists of a system of three pressure drop equations for three parallel and partly imaginary streams, is formed. The local ﬂ ow resistances in the analytical model are determined by the CFD model combined with RA. To equalize the ﬂ ows, three solutions with (i) ﬁ x, (ii) ﬁ x in a range of ﬂ ows, and (iii) variable positions of the sluice gates are analyzed. with ﬁ x and one with variable gate positions), the optimal is chosen.


INTRODUCTION
Side intake structures are widely used to divert water from rivers that carry large amounts of sediments. Simple Tjunctions are side intakes without damming that are suitable to divert small amounts of water. These intakes are pre- and Michelazzo et al. ().
If the usage of diverted water requires a limited amount of sediments with a specified size, settling basins are usually placed after the intake structures. Where the available space for intake structures is inadequate, instead of constructing long and narrow basins, multichamber settling basins are used. Their use is preferable from the operational point of view (Bishwakarma ).
A flow control problem at a side-weir intake with a three-chamber settling basin is addressed in the paper. There were only small amounts of settled sediments in the third chamber. Measurements showed that at the installed flow rate of 5.65 m 3 /s, the distribution of flows among the chambers is 16.00, 37.97, and 46.03% in the first, second, and third chambers, respectively. The unequal flow distribution among the chambers is identified as the main reason for the malfunctioning of the settling basin. The distribution causes that the average water velocities in the second, and especially in the third chamber (see Figure 2), exceed the maximal design velocity. During 5 years of operation, the problem decreased electricity production by 8%. A potentially more severe problem caused by nonsettled sediments is the endangerment of two turbines, each with a capacity of 1.35 MW. The turbines are parts of a combined system, which is described in detail in Karamarković et al. (2018).  The boundary conditions were adjusted so as the relative error between the flow measurements and the model predictions defers less than 8.5%. This limit is equal to the calculated measurement uncertainty, which is defined by several ISO standards (BS ISO 5168 2005; BS ISO 1088 2007; ISO 748 2007) (see Equation (3)).
The idea was to use the CFD model to find the solution with the help of an as simple as possible analytical model, which would be used as a tugboat that would navigate the     It was assumed that the use of sluice gates would disturb downstream velocity profile and create backflow and vortices. Tranquilizing racks are used to prevent these disturbances by the dissipation of turbulent kinetic energy.
In each chamber, the use of three rows of tranquilizing racks made of 'V' shaped bars is analyzed. Figure 4 shows the design, geometry, and positions of tranquilizing racks, whose characteristics are taken based on the model given The CFD model and the measurements showed that below 3.67 m 3 /s, the average water velocity in each chamber is lower than the designed value. These three solutions are verified, and the optimal among them is chosen by the cost-benefit analysis.

CFD MODEL VERIFICATION
To analyze the present state, a CFD model of the side water intake is used. Figure   The mesh consists of 2,432,345 nodes and 1,372,530 elements, each with an average volume of 1.98 × 10 À4 m 3 .
The minimum length of a side of an element is 5 mm, whereas the maximum one is 120 mm.
The commercially available software Ansys (CFD Simulation Software | ANSYS Fluids n.d.) and its integration module CFX (ANSYS CFX: Turbomachinery CFD Simulation n.d.), according to the defined geometry, boundary conditions, and the mesh, performed the numerical simulation of water flow through the weir intake in steady-state conditions. The absolute convergence criterion that the residual is less than 1.0 × 10 À4 is used for all the simulations.

Measurement procedure
As the water's surface is free (no flow under pressure), the

Measurement of cross-sectional area
The cross-sectional areas of water were determined by the measuring rod BOSH GR 500 Professional (GR 500 Professional Measuring Rod | Bosch n.d.).  748 2007): where v surface and v bed are velocities close to the surface of the water and the bottom of the channel, and

Computation of discharge
The mid-section method (Herschy ) as a part of arithmetic methods is used for the computation of discharge.
In each of the three chambers, for the defined number of verticals n ¼ 13, the total discharge is calculated as follows: where v n is the mean vertical velocity in the observed segment defined by Equation (1)

Verification of the model
The model was verified by three particular measurement sessions at different rates of discharge, which were constant and approximately 100, 72, and 52% of the installed flow.
The velocity measurement plan, which is schematically shown in Figure 6, was used for these measurements.  To find the positions of the sluice gates, the total flow is divided into three parallel streams from the inlet to the outlet sections (see Figure 4(a)). These streams are imaginary in the inlet and outlet sections and real in the chambers. As the streams are parallel, their pressure drops are equal to the total pressure drop between the inlet and outlet sections, i.e., Δp 1 ¼ Δp 2 ¼ Δp 3 , and are calculated by: In Equations (4)-(6) for the i-th streamline (subscript   Table 2 shows the regression coefficients and the corresponding p-values in the t-test, which were used for their evaluation (Birkes & Dodge ). As the t-tests are far enough from 0 and the p-values are substantially below 0.05, the regression coefficients are significant (Birkes & Dodge ).
where C 0 , C 1 , C 2 , C 3 , C 4 , and C 5 are regression constants given in Table 2, h x (m) is the depth of the channel, x (m) is the depth to which the gate is immersed into water, ρ ¼ 999:45 (kg=m 3 ) is the average water density during the year, at 12 C (The Engineering ToolBox n.d.), and w (m=s) is the average water velocity at the inlet.  Table 3 shows the comparison of minor loss coefficients obtained by Equation (7)

Common inlet zone
From the common inlet zone, the diverted flow exits divided into three streams (see Figures 1, 2, and 4a), which enter the chambers of the settling basin. Because of the unique geometry of the zone, the minor pressure loss coefficient was not found in the literature. The same methodology as in the previous case is applied (CFD simulations þ RA). Figure 9 shows the 3D model with simulation details,    matches the desired conditions. In each case, there were eight simulations. The regression model consists of four predictor variables and five regression constants. Equation (8) describes well the simulation results as R 2 > 0.999987. The three predictor variables are the square differences of the average velocities at the entrance and at the three corresponding exits each divided by the appropriate radius of the curvature, and the fourth is the water flow rate at the entrance. Table 4 shows the values and that the regression coefficients are significant as their p-values are below 0.5 and the t-tests enough above zero, which is in agreement with Birkes & Dodge ().
where k ¼ 1 ÷ 3 is the number of the chamber, Q in (m 3 =s)is the total flow rate at the entrance, w in (m=s) is the average water velocity at the entrance to the zone, w i (m=s) is the average water velocity entering the ith chamber, R i (m) is the radius that connects the middles of the ith third (from right to  left) of the inlet section and the ith chamber, and C i (i ¼ 0 ÷ 4) are regression constants that are given in Table 4.

Outlet zone
Three separated flows from the settling basin entre, and the total flow laterally exits the outlet zone (see Figures 4(a) and 11). As it was already explained, this resistance could not be described by a one-dimensional flow analogy. Therefore, CFD simulations were done as in the previous cases. In these simulations, the flow rates were varied in the range from 0.65Q in to Q in , with the step 0.05Q in for the two similar cases as in the inlet zone: (1) for free inflow into the zone and (2) for equal inflows from the chambers into the outlet zone. The first case matches the present, whereas the second matches the desired conditions. Figure 12 shows simulation results for the two characteristic flows.
The assumed regression model (Equation (9)) describes well the simulation results as R 2 > 0.999986. It is analogous to Equation (8), which is used to describe the simulation results for the common inlet zone. In Equation (9), the three predictor variables are assumed to be the squared differences of water velocities at the exit and the entrance from each chamber divided by the corresponding distance between the middle of each entrance and the exit from the zone. The fourth predictive variable is the total flow at the exit of the zone. Table 5 shows the values and that the regression coefficients are significant as their p-values are below 0.5 and the t-tests enough above zero, which is in agreement with Birkes & Dodge (). where w out (m=s) is the average water velocity at the outlet of the zone, w i (m=s) is the average water velocity entering the outlet zone from the ith chamber, and C i (i ¼ 0 ÷ 4) are regression constants that are given in Table 5. Figure Figure 14 show the verification of previously mentioned results by the CFD model. Table 6 shows that the usage of sluice gates equalizes the flow rates and average velocities among the chambers. However, their usage impacts the downstream velocity profiles, which are shown in Figure 14 for all the chambers in eight equidistant sections at the installed flow rate. The flow

CONCLUSIONS
The main conclusions regarding the problem are as follows: 1. The existing sluice gates can be used to control the flows through the settling chambers. Their application equalizes flow rates and average velocities among the 2. All three analyzed solutions, two with fix and one with variable positions of the sluice gates, are applicable and all have a small impact on the electricity production.
Consequently, the cheapest solution that uses permanent positions of the sluice gates is preferable.
3. The geometrical and flow symmetry eliminates the need for flow control in multichamber settling basins.
4. Compared with the pressure losses in the inlet and outlet zones of a multichamber settling basin, the losses in the settling chambers are much smaller. Therefore, in this type of basins, the different widths could not be used to equalize flows through the settling chambers.  The main conclusions regarding the problem and the applied methodology for its solving are as follows: -If the intake design enables reliable flow measurements, their combination with RA is the easiest and the least time-consuming way to solve this kind of problem.
-If verified CFD models exist for similar flow control problems, the solution finding could be speeded up by combining the model with RA.
-In flow control problems, where proper measurements are not possible, as in the presented case, the solution finding with the CFD model could be speeded up using a simple analytical or 'data-driven' model.
-Equation (7) can be used to calculate pressure drops at open-channel sluice gates.