Prediction of chlorine concentration of flows exiting pipe in cross junctions: experimental and numerical study

Numerical modeling is a fundamental tool in managing water quality in the distribution network. One of its immediate advantages is that it can provide information on the behavior of water quality parameters in the whole network. Therefore, water utility operators can take safety measures to ensure better water management, and also make it possible to verify the extent to which water quality standards are maintained in the distribution network.

The transport and diffusion of water quality parameters within a network depend primarily on the hydraulic operation and the mixing phenomenon at cross junctions where different incoming flows and concentrations may exist. A detailed study of the intersection's flow pattern and geometric configuration is essential to understand this phenomenon better.

Many researchers have studied this phenomenon, which plays a vital role in water quality modeling. Their results show that at junctions that receive water from several pipes, the mixing can be considered instantaneous and perfect (Fowler & Jones 1991; Mays 2004). EPANET (Rossman 2000), a public domain, water distribution system modeling software package, assumes complete mixing of a solute such as free chlorine at a pipe junction.

Conversely, many researchers have conducted experiments that proved that the mixing at cross junctions is not perfect (Ho et al. 2007; Austin et al. 2008; Shao et al. 2014). As a result, the concentration of water quality parameters exiting the node in various directions could differ. Ho & O'Rear (2009) found that relative flows in and out of the junction can significantly affect the degree of mixing. Van Bloemen Waanders et al. (2005) emphasized that the flows in cross junctions tend to bifurcate and reflect off one another rather than mix completely.

Diverse other authors carried out experimental and numerical studies through computational fluid dynamics (CFD) using salt tracers (Song et al. 2009; Liu et al. 2011; Shao et al. 2014; Yu et al. 2014; Hernández-Cervantez et al. 2018), dyes (Ho & O'Rear 2009) and chlorine as soluble tracer (Mompremier et al. 2015) for concentration distribution analysis. It has been pointed out that the use of chlorine as solute turns out to be somewhat complicated; however, this is one of the most commonly used methods for water chlorine disinfection in real water distribution networks. Therefore, the result of interest is to address studies using chlorine directly as solute. Santos-Violante et al. (2020) conducted a CFD study in the turbulent regime of mixing phenomena in cross junctions by using chlorine as a solute tracer. They reported a good concordance with experimental measurements of chloride concentrations at the outlets reported by Mompremier et al. (2015).

One of the most critical aspects of the study of mixing at cross junctions is estimating the concentration of solute water that exits the junctions. To achieve this, the development of analytical equations that describe the behavior of flows is crucial. Unfortunately, much research conducted on this phenomenon has not resulted in analytical equations to estimate the chlorine concentration in the node's water.

and are the dimensionless concentrations of the east and North outlets.

in which, C_E and C_S are concentrations at the East and South outlets, respectively.

Finally, Mompremier et al. (2017) performed mixing scenarios using chlorine in different cross junction configurations. They investigated different combinations of flows, concentrations and, configurations to assess mixing phenomena at cross junctions. The study also sheds light on how the concentration of microorganism (total coliform and E. coli) can vary greatly in the same water network system due to the impact of the mixing of water with different physicochemical characteristics. The present research aims to determine a dimensionless concentration coefficient R based on experimental data and CFD simulations to develop an analytical equation to predict chlorine concentration in outlet cross junctions. In addition, the predictions of the analytical equation were compared with experimental results and CFD.

This study involved a scenario that simulated different inflow rates as water enters the cross junctions. The flows enter the cross junction at 90° (from North and West) and exit at South and East outlets. The principal goal of the experiments was to study the behavior of the incoming flows before leaving the cross junctions. Experiments with varying inflows (ranging from 0.36 to 2.70 L/s at North inlet and 0.18–1.68 L/s at West inlet) and varying chlorine concentrations were carried out. However, ten of them that were found to be more relevant in the context of this investigation are reported in this paper. During the experiments, clean water from the reservoir was pumped to the elevated storage tanks using a 4HME200 centrifugal pump. Sodium hypochlorite solution (at 13%) was added to the West and North storage tanks, which resulted in chlorine concentrations that ranged from 1.25 to 1.80 mg/L at the North inlet and 0.50–1.42 at the West inlet. The solutions in each tank were mixed using a manual mixer. Descriptions of the scenarios in terms of chlorine concentrations and flow rate at inlets are presented in Table 1.

Table 1

Description of scenarios in terms of flow rate and chlorine concentration at the inlets

.	Q North [L/s] .	Q West [L/s] .	[mg/L] .	[mg/L] .
Experiment 1	0.360	0.180	1.75	0.70
Experiment 2	0.582	0.360	1.65	0.70
Experiment 3	0.840	0.420	1.75	0.75
Experiment 4	0.500	0.320	1.25	0.87
Experiment 5	1.050	0.540	1.80	1.42
Experiment 6	1.440	0.720	1.65	0.80
Experiment 7	2.400	1.440	1.25	0.85
Experiment 8	2.150	1.050	1.75	0.75
Experiment 9	2.340	1.680	1.55	0.80
Experiment 10	2.700	1.320	1.39	0.50

.	Q North [L/s] .	Q West [L/s] .	[mg/L] .	[mg/L] .
Experiment 1	0.360	0.180	1.75	0.70
Experiment 2	0.582	0.360	1.65	0.70
Experiment 3	0.840	0.420	1.75	0.75
Experiment 4	0.500	0.320	1.25	0.87
Experiment 5	1.050	0.540	1.80	1.42
Experiment 6	1.440	0.720	1.65	0.80
Experiment 7	2.400	1.440	1.25	0.85
Experiment 8	2.150	1.050	1.75	0.75
Experiment 9	2.340	1.680	1.55	0.80
Experiment 10	2.700	1.320	1.39	0.50

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In all the experiments, incoming flow rates and chlorine concentration at the North inlet were higher than in the West pipe. The flow meters measured instantaneous flow rates at each inlet and outlet of the cross junctions. Free chlorine concentrations were also measured at each inlet and outlet. An advanced system (CL763, B&C electronics, Italy) that detects chlorine concentration in the range of 0.1–20 mg/L was installed in the cross junction (at inlets and outlets), designed for continuous inflow measurement of residual chlorine in solution. The collected signals were transferred to a data logger (El-USB-4, Lascar Electronics, USA) connected to each controller and a PC for analysis. Every experiment was repeated twice to obtain the average results.

In which,

In simulations, the mesh quality is an important aspect to consider since it determines the accuracy and convergence of the numerical computation. The discretization of the cross-junction volume was done using a mesh with only hexahedral cells, and all employed meshes had a maximum cell skewness of 0.8. Extra refinement was implemented in the near-wall region using the inflation tool incorporated in Ansys©-Meshing to capture detailed current velocity gradients in the wall proximities, as can be seen in Figure 3. The boundary between the different computational regions was conformal, i.e., the grid node location was identical at the boundary. A mesh independence analysis was performed to verify that the numerical results are independent of the mesh density at the highest Reynolds number examined in this study (Re = 110780), resulting in a mesh containing approximately 1,500,000 elements, which can be considered independent. For each computational mesh, the first layer thickness adjacent to the wall along the axial locations was displaced by a value below 1 of the wall function, i.e., Y + <1, for the range of exanimated Reynolds numbers (7380 ≤ Re ≤ 110780).

A fully developed turbulent velocity profile was imposed in both inlets as a boundary condition by programming a C⁺⁺ User-Defined Function (UDF). This strategy ensured that both inlet flows would achieve a fully developed state before entering the cross junction. Instead of using the known values of the tracer concentrations in the inlets (showed in Table 1), a tracer mass fraction of one (1) was imposed as a boundary condition in the North inlet, while in the West inlet, a tracer mass fraction of zero was imposed.

In which, and are, respectively, the area-weighted average tracer mass fraction in each outlet boundary surface (East and South) extracted from simulations. Pressure outlet boundary conditions were imposed at the pipe outflows (South and East) with a gauge pressure equal to zero. In addition, non-slip boundary conditions were set on all wall surfaces.

The standard k-epsilon turbulence model with enhanced wall treatment for the near-wall treatment was used for modeling the three-dimensional turbulent flow. It has been reported that this model produces similar results for mixing in cross-pipe junction and T-junction compared with the shear-stress transport (SST) turbulence model with less computational expense (Walker et al. 2010; Santos-Violante et al. 2020). The species transport model incorporated in Ansys©-Fluent was used to predict the solute concentrations at the outlets. The binary diffusion coefficient of the tracer species in the fluid was D = 1.26 × 10 − 9 m²/s, which corresponds to the diffusion coefficient of chlorine in water at 25 °C. It was assumed that the tracer fluid (free chlorine in water) had the same viscosity (μ) and density (ρ) as the main water flow, i.e., μ = 0.001 Pa·s and ρ = 998.3 kg/m³. Standard model constants predetermined in Fluent were used in all simulations.

Finally, Ansys©-Fluent 17.1 software was used in all numerical simulations with steady-state conditions. The standard pressure–velocity together with the coupled scheme was employed for the pressure–velocity coupling. A high-order spatial discretization was used for the pressure and equations of momentum, turbulent kinetic energy, turbulent dissipation rate, and species transport. The solutions were considered converged when the residual of the equations reached a value below 10⁻⁵.

The initial chlorine concentration of the water entering the junctions could be considered a determining factor of the outflow's chlorine concentration. For example, in experiment 5, chlorine concentrations at the North and West inlets were 1.80 mg/L and 1.60 mg/L, respectively, while in experiment 6, 1.42 mg/L at the North inlet and 0.80 mg/L at the West inlet. On the other hand, the inflow rates in the North inlet were approximately two times greater than in the West (in both experiments). Therefore, the effluent leaving the East outflow contained a higher chlorine concentration as it mainly contained water from the North inflow. Consequently, in these experiments where the value of chlorine at the East outlet depends on the value of the North entrance. As a result, the higher the chlorine concentration is in the North inflow stream, the higher it will be in the East outflow. The same trend was observed in the other experiments.

Reynolds number (Re) ranged from approximately 14324 to 110780 (North inlets) and from approximately 7380 to 68934 at West inlet, indicating turbulent flow through all pipes. The results show that Re number (especially, in turbulent flow) does not govern the cross junction mixing level. For example, in experiment 3, the North and West chlorine concentrations were 1.75 and 0.75 mg/L, and Re numbers were 33400 and 17200, respectively; the mixing was incomplete. The East and South outlets had chlorine concentrations of 1.27 and 1.63 mg/l, respectively. Therefore, it is logical to expect that the increased turbulence intensity enhances mixing with the increase of the Re numbers. Results of experiment 8, however, are not corroborated with this approach. While chlorine concentrations at North and West inlets were similar to those measured in experiments 3 (1.75 and 0.75), the increase of Re at inlets (85500 and 41800) would be expected to increase chlorine concentration at the South outlet. The results, however, indicate that chlorine concentration at the South outlet was similar to that obtained in experiment 3 (with only a minimal difference of 0.02 mg/L). The results of this study with those obtained by Shao et al. (2019). In their experimental study on mixing phenomenon at cross junction. They observed that under Re < 1,500 or laminar flow regime, the mixing is reduced as the Reynolds number increases. In transient flow (500 < Re < 3,000), mixing increases with increasing Reynolds numbers; and finally, in the turbulent flow of Re the >3,000, the degree of mixing is constant or invariant of flow variations.

The numerical simulation results show that the incoming flow rate is the principal parameter influencing the mixing. As illustrated in Figures 5 and 6, the trend maintains reasonable proximity to the tracer distribution in all experiments. In addition, the results show errors lower than 8% at East outlets and lower than 12% at South outlets with respect to the experimental measurements.

As illustrated in Figure 7, the trend seen with both models is similar, indicating that the proposed analytical equations describe the mixing phenomenon observed in the cross junctions. Furthermore, the relative error between experimental and numerical findings (analytical equations of this study) is below 1% at East outlets and less than 8% at South outlets, proving the proposed model's goodness. The results agree with those obtained by Santos-Violante et al. (2020), who conducted a 3D CFD study of mixing in cross junctions with two adjacent inlets and proposed the implementation of an internal device inside the cross junction to improve the mixing in the two outlet flows.

Finally, the analytical equations developed as part of this study were used to predict exit concentrations of an experimental study reported by Ho & O'Rear (2009). Their study explored the effect of alternative configurations on solute mixing in junction adjacent inlets with equal pipe sizes. The boundary conditions were as follows:

⁠; the normalized concentration of the tracer was 1 mg/L, and the normalized concentration of the clean water was 0. ⁠.

As a result, the normalized concentration was 1 mg/L for effluent adjacent to the Q tracer and 0.55 mg/L for effluent opposite the Q tracer. Furthermore, Equations (11) and (14) predicted the normalized effluent concentrations. The predicted values were 0.99 and 0.543 mg/L in both outlets respectively. A relative error of less than 2% at both outlets was observed. Obtained results suggest that the analytical equations can be used as a good representation of experimental data.

The obtained results validated the analytical equations developed in this study that predict solute concentrations in the outlets. Experiments were carried out with varying flow and chlorine concentrations at the inlet pipes in which solute mixing is incomplete due to the bifurcation of the incoming adjacent flows. A dimensionless concentration R was calculated for each scenario in order to provide a means to determine the outlet concentrations based on the inlet concentrations. For example, chlorine concentration at the East outlet was calculated by multiplying R by the chlorine concentration of the North inlet. In addition, a solute mass balance was performed within the cross junction to predict the concentration at the South outlet. Finally, the k–e turbulence model with enhanced wall treatment, solved by the Ansys© 17.1 -Fluent software, was employed to validate the analytical equations proposed in this study to predict the chlorine concentrations leaving the junction. Experimental and CFD simulation results assessed the effectiveness of the analytical equation formulated in this study. One of the limitations of these equations is that they (analytical equations) can only be used when the higher incoming flow rates have a higher chlorine concentration. In future studies, it is suggested to conduct experiments with higher incoming flow rates containing lower chlorine concentration. It is also suggested to perform more experiments with a greater flow range, unequal pipe diameters, and higher chlorine doses. Decisions on protecting public health against drinking water contamination threats have become necessary. The results of this study can help to prepare water utility operators for making these critical decisions during an intense course of emergency. Finally, it has been shown that the CFD method can readily and reliably evaluate the mixing phenomenon in cross junctions as a complement to experimental measurements.

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

The authors declare there is no conflict.