## Abstract

This work investigated the partition walls or baffles’ effects on hydraulic parameters and water retention time in a reservoir. According to this aim, the water system was equipped with remote sensing (RS), networked sensors, advanced modems, and data loggers. The study showed how to control hydraulic parameters by the Internet of things and RS. The higher retention time led to the probability growth of rebar oxidation in concrete in the presence of chlorine and increased the possibility of water loss. This work also showed how to decrease the probability of water leakage in reservoirs. The computational fluid dynamics analysis results showed that the two baffles case led to the emergence of three eddy currents in the three zones created. The better fluid interpenetration caused the reduction in retention time. In the areas where the vortex was formed, the number of eddy currents decreased and the retention time increased. Regression analysis showed that the *P* value was 0.998 and 0.977 for the inlet flow and outlet flow for the reservoir, respectively (two baffles case perpendicular to the flow direction). The curve estimation showed that the power function had a suitable correlation on the scatter diagram and with the best curve fit.

## HIGHLIGHTS

Analysis of water reservoir in the water system.

Access to the reservoir by (computational fluid dynamics) and regression analysis.

Baffles and control of water retention time in a reservoir.

Control of hydraulic parameters in a reservoir as a water supply.

Control of water retention time in a reservoir by remote sensing.

## ABBREVIATIONS

*ρ*Fluid density

*ui*Components of speed

Cartesian coordinate direction

- t
Time

*μ*Kinematic viscosity

- P
Pressure vector

*V*Velocity vector

*g*Gravity acceleration

Derivative of the velocity vector over time

*P*Average static pressure

*ρ g*Gravitational physical force

Tension tensor

Calm current stress tensor

Turbulent current stress tensor

Newtonian viscous stresses plus an additional tensor

Specific heat capacity at constant pressure

Temperature

*k*Thermal conductivity

Turbulent heat flux

*K*Kinetic energy of turbulence

*v*Dynamic viscosity

*TI*Intensity of perturbation with kinetic energy

*U*_{ref}Reference average flow rate

*S*_{M}Sum of physical forces

Effective viscosity

*P*Pressure

*ε*Vortex viscosity model

*k*Kinetic energy flow of energy

Fixed numeric

- , ,
*C*,_{Ɛ2}*C*_{Ɛ1} Constants

*P*,_{kb}*P*,_{Ɛb}P_{kb}*P*_{Ɛb}Influence of buoyancy forces

*P*_{k}Perturbation due to viscous forces

*ω*Specific rate of dissipation

*Q*Water flow rate

## INTRODUCTION

Reservoirs in the water distribution network are responsible for storing water for use in emergencies, firefighting, and controlling fluctuations in consumption. Several decisions such as the location, size, and type of reservoir operation in the design of the reservoir in water distribution networks should be made. In general, very few modelling studies have been done to investigate the flow inside the water storage tanks as well as the quality of the stored water (Walski 2000).

Mau *et al.* (1995) presented an explicit model for simulating water flow and water quality inside a reservoir. In their study, they defined three different behaviours (different scenarios) for the reservoir and examined the water quality in each case. They wrote mass transfer, mixing, and kinetic reaction relations for reservoirs. Then the obtained equations were solved numerically. They used two different numerical methods to solve the equations. Then, the amount of chloride and fluoride injected into the reservoir was calculated in certain points which were called sensitive points by using a numerical solution and measured experimentally. Then, by using experimental data, they verified the accuracy of the presented numerical method. The numerical data were in good agreement with the experimental data. Also, they calculated the concentration of fluoride and chloride for different reservoir volumes at a given point. Their article can be considered a primer on mathematical modelling of water reservoirs with appropriate accuracy. Therefore, their article is important from this point of view.

Rossmann (2000) considered four different models for the reservoir and examined the water flow and water quality in each case. He stated that the water quality inside the reservoir is highly dependent on the geometry of the flow and consequently on the geometry of the reservoir. He showed that the flow entering the reservoir leads to complete mixing of the flow inside the reservoir or not depending on the ratio of the momentum of the incoming flow to the buoyancy force of the incoming flow. A similar situation exists for output currents. He showed that there are only limited geometries in which complete mixing can take place, which, of course, is related to the volume of the reservoir and the ratio of its height to its base. Therefore, he finally defined the four factors of reservoir geometry, the number of inlets and outlets of the reservoir, and the ratio of height to base as four basic parameters in retention time. Rossmann & Grayman (2000) concluded that complete mixing can be achieved for cylindrical reservoirs with a ratio of height to diameter less than one, and in other reservoirs, complete mixing will never be established. They simulated the ideal reservoir for filling and emptying. In most of the cases investigated by them, the results of the geometry of the reservoir showed that a major part of the volume of the reservoir is located in a retention area, that is, an area between complete mixing and creep flow.

Yeung (2001) investigated the behaviour of several rectangular reservoirs using the computational fluid dynamics (CFD) method. He examined the pattern of the flow field and the age of water and showed that better mixing occurs in reservoirs with horizontal inlets than in vertical inlets at a high level. As the ratio of length to width increases in reservoirs with a vertical inlet, the flow characteristics move toward creeping flows at a faster rate.

Mahmood *et al.* (2005), using the CFD model, investigated different samples of existing reservoirs in the drinking water supply system of Virginia. They compared the obtained numerical results with experimental data obtained from measurements at different points of the reservoir. Their results showed that the CFD model has good accuracy in simulating the fluid flow inside the reservoir. It can be used to determine the proper location of reservoir inlets and outlets. They first examined the speed of the flow entering the reservoir and also the position of the pipe entering the reservoir on the mixing rate of the reservoir. For this purpose, they performed the simulation in a reservoir with a storage volume of 3.8 m^{3}. They assumed that a flow with a volumetric flow rate of 63 L per second enters the reservoir at a speed of 29 m/min through a vertical inlet with a diameter of 400 mm. They considered the fluid temperature inside the reservoir to be 20°C and the inlet fluid temperature to be 18°C. Then they calculated the concentration distribution inside the reservoir after 60 min using CFD.

Prasad (2010) designed a water distribution system with reservoirs. He explained a method for designing the water distribution network along with the correct selection of various elements such as pipes, pumps, and reservoirs. He used the genetic algorithm in a steady state to optimize the water distribution system. His objective function was to minimize the total cost. In his work, the total cost is defined as the sum of initial investment costs and energy costs. His goal was to determine the size of the pipes, the required pump, and the pump's operating time, and to choose the number of reservoirs and the capacity of the reservoirs so that the objective function is optimized. Finally, he used it to minimize the water retention time in the network as a quality parameter for the third objective function. His results showed that the design of the network in this way leads to a network with high capability so that the network obtained has optimal pipes and the best arrangement for reservoirs in high consumption points.

Marek *et al.* (2007) investigated the jet flow inside the reservoir by solving the averaged Navier–Stokes unsteady state equations. They stated that the mixing process inside the water reservoirs is a basic parameter in the quality of the stored water. They emphasized that various factors are effective on the mixing inside the reservoir, including the power of the inlet jet speed, nozzle diameter, and nozzle inlet angle. Their goal was to determine the optimal value for the nozzle angle and the diameter of the nozzle entering the reservoir. They compared the results of their simulations with the available experimental data and showed that the presented results were in good agreement with each other. They considered a cylindrical reservoir with one inlet and one outlet in three dimensions and investigated it numerically and experimentally. They investigated the influence of the angle and diameter of the inlet nozzle on the flow field. For this purpose, they obtained the contour of the velocity field in three cases. In the first case, the angle of the inlet nozzle was considered equal to 45 degrees and the diameter of the inlet nozzle was equal to 21 mm. As a result, the speed of the inlet jet was equal to 2.1 m/s. In the second case, the angle of the nozzle was considered equal to 45 degrees according to the previous case. In this case, the diameter of the inlet nozzle was considered equal to 8 mm, and as a result, the speed of the inlet jet was equal to 4.4 m/s. In the third case, the angle of the inlet nozzle was considered equal to 90 degrees and the diameter of the inlet nozzle was assumed to be equal to 8 mm. The velocity contour along the middle plane *y* = 0. They found that the most optimal mode is obtained when the nozzle angle is equal to 45 degrees and the inlet nozzle diameter is equal to 8 mm. As a result, they investigated the concentration of substances injected into the reservoir under these conditions to see how the distribution of the injected substances would be at different times. The concentration of the substance injected into the reservoir can be considered as a measure of the retention time of the water inside the tank. That is, the areas that do not change after the injection the water remain in stagnation condition and the quality of the water decreases.

Van Zyl & Haarhoff (2007) presented a random analysis method for the size of reservoirs based on the reliability criterion. They performed a sensitivity analysis to estimate the critical parameters for the size of the reservoirs (reliability of the reservoir). The results showed that water demand has the greatest effect on the size of the reservoir. In this research, they showed that the fire reserve had the least effect on the size of the reservoir. The main purpose of the study was to check the reliability of Yeovile city reservoirs under different conditions. Therefore, the operation code of the water distribution system was tested in different conditions and calculations for different capacities. They checked how many times a year the water distribution system may fail (failure means the lack of supply of water required by the network), how long the failure will be, and what the maximum time the system will fail. They introduced the average number of network failures per year and the duration of network failures per year as two basic parameters for evaluating the water distribution system and by comparing these two parameters for reservoirs with different capacities, the optimal number and capacity of reservoirs. They presented the average annual network failure time and the reservoir capacity.

Gualtieri (2009) compared the hydrodynamics as well as the turbulence of the flow inside a cylindrical storage tank. He investigated the problem in a two-dimensional mode and assumed that the flow is stable and also the flow is unstable. He investigated the problem for four different configurations of the reservoir and compared their hydraulic performance. He numerically investigated the problem once in a steady state and once in a transient state. Then, for four different geometries of the baffle inside the columnar reservoir, the mixing rate was compared with each other.

Some researchers designed baffle to improve fluid mixing in the reservoir (Nasyrlayev *et al.* 2020).

On the basis of numerical simulation results, they manufactured the two sets of polycarbonate perforated baffles that yielded the highest performance. A comparison of numerical and experimental results demonstrated that the numerical model developed was reliable in simulating the flow through the perforated baffles and the associated mixing level in the contact reservoir. Numerical simulations indicated that the jet flow structure through the perforated baffle penetrates into the recirculation zones in the neighbouring chambers and turns the dead zones into active mixing zones. Furthermore, large-scale turbulent eddies shed by the perforations contribute to the mixing process in the chambers of the reservoir. With the use of the perforated baffle design, it was shown that the hydraulic efficiency of the tank was improved from average to superior.

Martínez-Solano *et al.* (2006) defined a method based on CFD to simulate a two-dimensional flow inside a rectangular reservoir. They considered a rectangular reservoir with dimensions of 20 m × 25 m, a height of 3 m, and a volume of 1,500 m^{3}, which has an inlet, an outlet, and a place for injecting. The flow rate at the entrance was considered equal to 50 L per second, and for the system to work in stable mode, accordingly, the flow rate at the outlet must be equal to 50 L per second. They considered the diameter of the inlet and outlet pipes to be equal to 250 mm assuming that the injected materials are added by a third pipe with a diameter of 40 mm. They assumed that the inlet velocity of the inlet pipe and the injection pipe was equal to 1 m/s. They considered the resilience provided by Todini (2000) as their goal to increase the availability of water when pipes break. Their goal was to design a water distribution system with high reliability and overall cost. They used a multi-objective optimization algorithm and defined total cost, reliability, and water quality as objective functions. They defined three types of distribution systems and calculated the total cost for each and compared them.

The key findings of the previous works can be organized into the following items:

The location, size, and type of reservoir operation in the design of the reservoir in water distribution networks should be made (Walski 2000).

The experimental data are used to verify the accuracy of the numerical method (Mau

*et al.*1995).The number of inlets and outlets of the reservoir, and the ratio of height to base are effective in retention time (Rossmann & Grayman 2000).

The CFD analysis showed in reservoirs with horizontal inlets, better mixing occurs than vertical inlets at a high level (Yeung 2001).

The CFD model has good accuracy in simulating the fluid flow inside the reservoir (Mahmood

*et al.*2005),The design of the network by genetic algorithm in a steady state to optimize the water distribution system leads to a network with high capability so that the network obtained has optimal pipes and the best arrangement for reservoirs in high consumption points (Prasad 2010).

Various factors are effective on the mixing inside the reservoir, including the power of the inlet jet speed, nozzle diameter, and nozzle inlet angle (Marek

*et al.*2007).A sensitivity analysis to estimate the critical parameters for the size of the reservoirs (reliability of the reservoir) showed that water demand has the greatest effect on the size of the reservoir (Van Zyl & Haarhoff 2007).

A comparison of the hydrodynamics as well as the turbulence of the flow inside a cylindrical storage tank showed the problem in a two-dimensional mode and assumed the flow is stable and also the flow is unstable (Gualtieri 2009).

Numerical simulations indicated that the jet flow structure through the perforated baffle penetrated the recirculation zones in the neighbouring chambers and turned the dead zones into active mixing zones. Furthermore, large-scale turbulent eddies shed by the perforations contribute to the mixing process in the chambers of the reservoir (Nasyrlayev

*et al.*2020).A method based on CFD was used to simulate a two-dimensional flow inside a rectangular reservoir (Martínez-Solano

*et al.*2006).

The comparison of the previous works showed the following limitations:

Very few modelling studies have been done to investigate the flow inside the water reservoir as well as the CFD analysis for smart control of water supply based on RS and the Internet of things (IoT).

In the present work, according to the limitations of the previous works of other researchers, the 1,500 m^{3} rectangular concrete reservoir was selected to improve the advanced techniques for smart control of retention time in the reservoirs. The average water retention time in the reservoir was 8 h. The water inlet velocity as well as the injection rate of the plug was achieved to reach a flow rate of 50 L per second at about 1 m per second. The length of the pipes was equal to 4 m and its length was 3 m outside the reservoir and 1 m inside the reservoir. Also, the inlet, outlet, and injection pipes were assumed to be in the middle height of the reservoir, and the distance of the inlet pipe from the side wall was equal to 0.5 m. The distance of the outlet pipe from its side wall was assumed to be equal to 0.5 meters. For the inlet pipe, the inlet velocity condition was used. For the walls of the reservoir, the non-slip condition was used. The value of the wall roughness was assumed to be 0.1 mm. For the free surface, the symmetry boundary condition was used. This condition increased the number of required iterations and decreased the degree of convergence in the problem. Then the zero shear stress boundary condition was used. This boundary condition somewhat improved the solution criteria. Therefore, it can be concluded that this boundary condition is more appropriate. The output pressure limit condition was used for the reservoir output. In this case, no partition walls (baffles) were intended for the reservoir. This case was considered as the base. Results showed that increasing the angle of baffle plates was strongly effective in increasing the eddy currents formed. As can be seen, few researchers have investigated the hydraulic properties of the reservoir and the effect of different parameters on the mixing inside the reservoir. The research done in this area is often done for the reservoir with one inlet and one outlet. Therefore, there has been no research in which the effect of the number of inputs and outputs on the mixing inside the reservoir has been seen. In the present work, the aim is to investigate the simultaneous effect of the water flow rate of the inlet and outlet and the baffles arrangement on the mixing process inside the reservoir, which has not been investigated before.

## MATERIALS AND METHODS

Generally, the water reservoirs in minimum and maximum demand are inevitable. A hydraulic model can simulate the flow and the quality of water inside the reservoir. It can define the different behaviours of the reservoir. The hydraulic model examines the state of water flow. The relationships between mass transfer, mixing, and kinetic reaction for reservoirs can be found. The obtained equations are solved numerically for the state of water flow. This can be considered the beginning of mathematical modelling of water storage reservoirs with appropriate accuracy. Today, the CFD model is an accurate method for investigating the effect of different parameters on the state of water flow and water retention time in the corners of the reservoirs.

### Methodology

^{3}rectangular concrete reservoir with a 25-m length and 20-m width was studied for water retention time. The height of the water reservoir was 3 m. The diameter of the inlet and outlet pipes was 25 cm, the diameter of the injection pipe of the plug was 4 cm, and the inlet and outlet water flow rate was measured at about 50 L/s. These data were detected by the RS flowmeters. The variation of hydraulic parameters including velocity and water retention time was investigated related to the simulation of the position of baffles in the concrete reservoirs. This work tried to improve the advanced techniques for the control of retention time in the reservoirs. The research method was stated in the form of the chart in Figure 1.

The main purpose of this work is to determine the impact of reservoir design specifications on hydraulic behaviour. Therefore, determining the dimensions, number, and optimal angles for the baffles was also considered in this work, and as a research hypothesis, the option angle of the baffles and their effect on the field and flow lines were investigated.

In the management of water system facilities based on meta data management, the development and application of advanced technologies in all areas of software and hardware in the facility can have a positive impact on system performance and efficiency. The application of state-of-the-art technologies such as IoT can also provide scientific guidance and enhance the technical and hygienic safety factor of the installation systems. In the case of water system control, RS through IoT can sense the spatial structure of fluid in water reservoirs. This method provides a mathematical model which makes the possibility of online investigation for fluid conditions such as laminar conditions, transient conditions, and turbulence conditions (Kelly *et al.* 2013; Zhou *et al.* 2013; Andrade & de Freitas Rachid 2022).

The IoT is a new concept in the world of technology and communications, but IoT was first used by Kevin Ashton in 2007, describing a world in which everything, including inanimate objects, is used to have a digital identity and allow computers to organize and manage them. The Internet now connects all people, but with the IoT, all things are connected. The new economic law in the age of networks in year four addressed the issue of small smart nodes (such as open and closed sensors) that are connected to the World Wide Web (Asli 2023a, 2023b). In the 21st century, with the international water and energy-saving attitude, the international community requires the use of networked sensors, the IoT based on the geospatial information system for the management of water systems. Water loss and energy loss are important threats to cities (Lü *et al.* 2014; Kudzh & Tsvetkov 2017; Asli 2022, 2023a, 2023b; Asli & Hozouri 2021). The present work showed that the smart management of water system facilities is a new topic in the field of control and optimization of water retention time in a reservoir. The awareness of this subject is especially important for facility engineers.

Today, due to the need to reduce water loss and increase water quality, as well as advances in numerical calculation methods in the last decade, much research has been done in different parts of the world on how to reduce water retention time or age in water supply networks and reservoirs. Increasing the age of water in the presence of chlorine causes oxidation of rebar in concrete reservoirs and water pipelines increasing the possibility of water leakage based on the guide to operation and maintenance of water reservoirs. One of the available ways is to improve the hydraulic condition of concrete tanks, which was discussed in the present work. The subject was in line with the implementation of water loss management and includes the following items.

Water loss reduction in the water facilities: More water retention time causes more possibility of oxidation of rebel. The oxidation of rebel leads to water leakage through concrete reservoirs.

Durability of the water distribution system: The water leakage through concrete reservoirs leads to instability of the water distribution.

### Materials

The computational model is based on solving the mass conservation of mass equations and the Navier–Stokes equations for fluid motion. Therefore, if the flow is turbulent, the turbulent flow equations are added to the basic equations. Numerical methods used in the computational model are the finite element method (FEM), finite volume method (FVM), and finite difference method (FDM). Therefore, the FVM is more used in modelling incompressible flows. The CFD software output based on the FVM was used for modelling in the present work. The reservoir was meshed by using the CFD software. For roughness, 0.1 mm was considered for the inner wall of the tank, and it was assumed that the water level inside the tank was constant. Unstructured mesh type was used to mesh the volume inside the tank, and for this purpose, mesh with hexagonal (octagonal) cells was used. Mesh with different dimensions and types were examined, and the duration and number of repetitions required for the convergence of the problem in each case were compared with each other to use the best type of mesh. Finally, the view of meshing criteria embedded in CFD software was used.

#### Boundary conditions

#### Formulation

For simulation, input turbulence parameters such as input kinetic energy (*k*) and turbulence intensity (IT) at the input were specified. Turbulence intensity was defined as the ratio of the square root of the oscillating velocity to the mean velocity of the flow. Also, the length of the perturbation was a physical parameter that was proportional to the size of the flow eddies.

In this work, the computational model was based on solving the conversion of mass equations and the Navier–Stokes equations for fluid motion. Therefore, if the flow was turbulent, the turbulent flow equations were added to the basic Equations (1)–(7):

*g*is the gravity acceleration, and expresses the complete derivative of velocity vector with respect to time.where expresses the tension tensor, which is defined as follows:where and express the laminar current stress tensor and the turbulent current stress tensor, respectively.

*C _{Ɛ}*

_{1}

*, C*

_{Ɛ}_{2}

*,*, ,

*σ*, and

*ε*are constants.

*P*and

_{kb}*P*exert the influence of the Boeing forces.

_{Ɛb}*P*produces turbulence due to viscous forces. Generally, instantaneous fluid flow equations are simulated. This type of modelling is the most complete case. Numerical methods used in the computational model are the FEM, FVM, FDM, and spectral methods. Therefore, the FVM is more used in modelling incompressible flows. In this work, computational software based on the FVM was used for modelling. The 1,500 m

_{k}^{3}rectangular concrete reservoir was meshed by using computational software. For roughness, the value of 0.1 mm was considered. For the inner wall of the reservoir, it was assumed that the water level inside the tank was constant. Unstructured mesh type was used to mesh the volume inside the tank, and for this purpose, mesh with hexagonal (octagonal) cells was used. Mesh with different dimensions and types were examined, and the duration and number of repetitions required for the convergence of the problem in each case were compared with each other to use the best type of mesh. Finally, the view of meshing criteria embedded in computational software was used.

#### Research tools

This work was carried out in July 2018. The water system was equipped with measuring and RS tools such as ultrasonic flow meters (UFMs), modems, and data loggers. The IoT was used for rapid data intercommunication due to flow conditions and retention time in reservoirs. The IoT covered equipment that connected information through the Internet. In this work, the water inlet flow rate into the reservoir was measured and recorded by data loggers. The modems were applied for data transmission through data loggers to program logic control. The hydraulic model for analysis of fluid interpenetration was recognized by numerical analysis such as the FVM (Asli *et al.* 2010).

## RESULTS AND DISCUSSION

*et al.*2015; Vardy

*et al.*2015; Lema

*et al.*2016). The main purpose of this work is to investigate the retention time and velocity profiles in the reservoir to determine the stagnation points and optimize the geometry, and to avoid the complexity of the model, the injection of additives was omitted. Flow lines were checked to determine stationary points and points with high retention times (Figure 3).

### Sensitivity analysis

As shown in Figure 2, the meshing around the inlet, outlet, and injection pipes was more compact. Due to the formation of the boundary layer around the pipes and also the sensitivity of the flow in these points, the number of meshes was increased in these points so that the phenomena that occur can be well observed. The meshing of the problem included 601,508 nodes and 2,027,645 elements.

### Calibrate the model

Seven criteria were considered in the meshing software to check the quality of meshing. Of these seven criteria, four criteria – element quality, shape factor, error rate, and orthogonality – were more important. This process examined the quality of meshing from the perspective of these four criteria.

Most of the elements had a quality of around 0.88. Also, the number of elements that had a quality of less than 0.75 was very small. Therefore, it can be concluded that the meshing quality of the problem was suitable from the point of view of the quality criterion of the element.

### Statistical technique and speed vector simulation

*et al.*2014; Tao 2014; Seetharamu & Hoboken 2017; Yousif

*et al.*2023; Zenkner & Navarro-Martinez 2023). Regression as a statistical technique was used for estimation and forecasting in the present work. Regression introduced the use of one variable to perform the prediction for another variable. In the following, flow lines and velocity vectors for baffle plates with a distance of 5 m are checked.

### Hypothesis

^{3}rectangular concrete reservoir. The diameter of the inlet and outlet pipes was 250 mm, the diameter of the injection pipe of the plug was 40 mm, and the inlet and outlet water average flow rate was measured at about 50 L/s (Tables 1 and 2).

Time (h) . | Inlet flow (L/s) . | Outlet flow (L/s) . | Time (h) . | Inlet flow (L/s) . | Outlet flow (L/s) . |
---|---|---|---|---|---|

1 | 45 | 42 | 13 | 89 | 52 |

2 | 63 | 57 | 14 | 94 | 78 |

3 | 83 | 56 | 15 | 89 | 76 |

4 | 15 | 12 | 16 | 52 | 49 |

5 | 19 | 12 | 17 | 42 | 31 |

6 | 52 | 45 | 18 | 58 | 43 |

7 | 58 | 55 | 19 | 28 | 23 |

8 | 38 | 32 | 20 | 73 | 71 |

9 | 63 | 55 | 21 | 48 | 42 |

10 | 52 | 53 | 22 | 26 | 22 |

11 | 94 | 76 | 23 | 45 | 39 |

12 | 86 | 77 | 24 | 75 | 71 |

Time (h) . | Inlet flow (L/s) . | Outlet flow (L/s) . | Time (h) . | Inlet flow (L/s) . | Outlet flow (L/s) . |
---|---|---|---|---|---|

1 | 45 | 42 | 13 | 89 | 52 |

2 | 63 | 57 | 14 | 94 | 78 |

3 | 83 | 56 | 15 | 89 | 76 |

4 | 15 | 12 | 16 | 52 | 49 |

5 | 19 | 12 | 17 | 42 | 31 |

6 | 52 | 45 | 18 | 58 | 43 |

7 | 58 | 55 | 19 | 28 | 23 |

8 | 38 | 32 | 20 | 73 | 71 |

9 | 63 | 55 | 21 | 48 | 42 |

10 | 52 | 53 | 22 | 26 | 22 |

11 | 94 | 76 | 23 | 45 | 39 |

12 | 86 | 77 | 24 | 75 | 71 |

Equation . | Model summary . | Parameter estimates . | |||||||
---|---|---|---|---|---|---|---|---|---|

R^{2}
. | F
. | df1 . | df2 . | Sig. . | Constant . | b1 . | b2 . | b3 . | |

Linear | 0.878 | 157.871 | 1 | 22 | 0.000 | 3.776 | 1.109 | ||

Logarithmic | 0.816 | 97.486 | 1 | 22 | 0.000 | −94.403 | 40.322 | ||

Inverse | 0.637 | 38.581 | 1 | 22 | 0.000 | 84.164 | −976.151 | ||

Quadratic | 0.878 | 75.605 | 2 | 21 | 0.000 | 1.824 | 1.210 | −0.001 | |

Cubic | 0.878 | 48.004 | 3 | 20 | 0.000 | 2.199 | 1.175 | 0.000 | −6.62 × 10^{−006} |

Compound | 0.874 | 153.249 | 1 | 22 | 0.000 | 16.837 | 1.023 | ||

Power | 0.936 | 320.833 | 1 | 22 | 0.000 | 1.708 | 0.906 | ||

S | 0.846 | 121.202 | 1 | 22 | 0.000 | 4.592 | −23.605 | ||

Growth | 0.874 | 153.249 | 1 | 22 | 0.000 | 2.824 | 0.023 | ||

Exponential | 0.874 | 153.249 | 1 | 22 | 0.000 | 16.837 | 0.023 | ||

Logistic | 0.874 | 153.249 | 1 | 22 | 0.000 | 0.059 | 0.977 |

Equation . | Model summary . | Parameter estimates . | |||||||
---|---|---|---|---|---|---|---|---|---|

R^{2}
. | F
. | df1 . | df2 . | Sig. . | Constant . | b1 . | b2 . | b3 . | |

Linear | 0.878 | 157.871 | 1 | 22 | 0.000 | 3.776 | 1.109 | ||

Logarithmic | 0.816 | 97.486 | 1 | 22 | 0.000 | −94.403 | 40.322 | ||

Inverse | 0.637 | 38.581 | 1 | 22 | 0.000 | 84.164 | −976.151 | ||

Quadratic | 0.878 | 75.605 | 2 | 21 | 0.000 | 1.824 | 1.210 | −0.001 | |

Cubic | 0.878 | 48.004 | 3 | 20 | 0.000 | 2.199 | 1.175 | 0.000 | −6.62 × 10^{−006} |

Compound | 0.874 | 153.249 | 1 | 22 | 0.000 | 16.837 | 1.023 | ||

Power | 0.936 | 320.833 | 1 | 22 | 0.000 | 1.708 | 0.906 | ||

S | 0.846 | 121.202 | 1 | 22 | 0.000 | 4.592 | −23.605 | ||

Growth | 0.874 | 153.249 | 1 | 22 | 0.000 | 2.824 | 0.023 | ||

Exponential | 0.874 | 153.249 | 1 | 22 | 0.000 | 16.837 | 0.023 | ||

Logistic | 0.874 | 153.249 | 1 | 22 | 0.000 | 0.059 | 0.977 |

## CONCLUSIONS

Insufficient control of hydraulic parameters in a reservoir as a water supply case can lead to abnormal fluid conditions and high retention time. Conversely, by the fluid parameters control, the low retention time will be acquired in a reservoir. The fluid retention time may be lower or higher than the standard time. In this work, the effect of the distance of the baffles from each other on the flow field was investigated. It was shown that the reduction of baffles leads to a weakening of the vortex strength, especially in the second and third regions. Increasing the number of baffle plates is strongly effective in increasing the eddy currents formed.

This work studied the 15-degree baffles with two variants of the distance of each other that affect eddy currents in the three areas of the reservoir. In the first variant, the two baffles with a 5-m distance from each other were used, and an eddy current formed in the second area of the reservoir. The flow velocity in the corners was reduced so much that in the corners of the second area, stagnation points were formed and the age and time of water retention time in these points increased. Then for the second variant, the two baffles with a 10-m distance were considered. In this case, more eddy currents were generated. As a result, this situation was better than before. The case of two baffles with a 10-m distance from each other led to the emergence of three eddy currents in the three areas created by the two baffle plates. This led to better flow mixing, and it reduced the retention time in the areas where the vortex was formed. If the areas formed by the baffle plates from the left are called one, two, and three, then in the lower corner of the second area and especially in the upper corner of the third area, stagnation points were formed. In this case, the fluid retention time was increased slightly. Investigation of the effect of the distance of the baffles from each other on the flow field showed that the distance reduction of baffles led to a weakening of vortex strength, especially in the second and third areas.

### Suggestions for future research

To use corrugated baffles and investigate the effect of the size and height of baffles on the flow field, a supplementary study should be done. Increasing the age of water can cause oxidation of rebar in concrete in the presence of chlorine and increase the possibility of water leakage and loss and economic losses. The following items are suggested to those who are interested in studying the use of corrugated baffles as well as the effect of the size and height of baffle plates on the flow field:

If additives are injected into the reservoir, it is necessary to study the concentration of these materials in the corners, and as a result, how many disadvantages have this type of reservoir?

In oblique baffle cases with an angle of 10 and 15 degrees, the number of eddy currents and the stationary points can be studied.

Can the use of three baffles with equal distance and completely vertical position create the maximum number of vortices and reduce the residence time and static points?

## ACKNOWLEDGEMENTS

The authors thank all specialists for their valuable observations and advice, and the referees for recommendations that improved the quality of this paper.

## DATA AVAILABILITY STATEMENT

All relevant data are included in the paper or its Supplementary Information.

## CONFLICT OF INTEREST

The authors declare there is no conflict.