Assessment of the minimal distance for placing household connections downstream of water distribution cross junctions

Numerical modeling plays a critical role in predicting and managing water quality parameters, including residual chlorine, in distribution networks. Research on mixing phenomena is essential for understanding the distribution of water quality parameters such as disinfectants and contaminants throughout the network. Over the past decade, this phenomenon has gained considerable attention, especially in the water industry.

Numerous experimental and numerical studies using cross and T-junctions have been conducted due to their relevance in several applications, including particle trajectory monitoring and controlling the diffusion of solute concentrations exiting the junctions throughout the water distribution network (Choi et al. 2008; Romero-Gomez et al. 2008; Walker et al. 2010; Shao et al. 2014, 2019; Yu et al. 2014, 2016; Hernandez et al. 2021). Results of these studies show that incomplete mixing occurs at cross junctions when two or more fluid streams intersect. Additionally, the results indicate that mixing efficiency depends on several factors, including flow rates, Reynold numbers (Re), fluid properties, and junction geometry. These factors collectively influence the blending of different inflow streams, making their comprehension crucial for optimizing mixing at cross junctions. A few works considered most relevant in the context of this research will be discussed later.

Ho & O'Rear (2009) conducted experiments based on conductivity measurements of the two effluents to investigate the mixing behavior within individual pipe joints in a water distribution system. The experiment involved a single-node mixing setup with two entrances for water, a tracing material (used to visualize mixing), and the measurement of water conductivity at two outlets. The main objective was to understand how mixing occurs within pipe joints, specifically evaluating different joint configurations, pipe diameters, and flow rates. Their findings showed that the conductivity values at the two outlets were not equal. This suggests that the mixing process within the pipe joints was not perfect, with differences in concentration or composition between both outlets.

Ho & Khalsa (2007) developed models for a small-scale 3 × 3 pipe network to evaluate both complete and incomplete mixing models in pipe junctions of water distribution networks. Computational fluid dynamics (CFD) simulations demonstrated that accurate predictions of spatially variable tracer concentrations throughout the network could be achieved when compared to experimental data. Incomplete mixing within cross junctions was observed due to the bifurcation of incoming flows, with the extent of bifurcation and mixing largely dependent on the relative flow rates entering the cross junction.

In contrast, the first version of the EPANET model (Rossman 2000), assuming complete mixing within the junctions, produced uniform concentrations throughout the network, differing significantly from the spatially variable concentrations observed in the experimental network. The EPANET model was modified after that to incorporate mixing correlations derived from previous single-joint experiments (Rossman et al. 2020). The results from this modified model accurately reflected incomplete mixing at the pipe junctions and aligned with the trends seen in the experimental data. Furthermore, additional CFD simulations demonstrated that networks consisting of T-junctions separated by at least several pipe diameters could be suitably modeled with complete-mixing assumptions.

Shao et al. (2019) studied experimentally the mixing phenomenon under laminar and transitional flow regimes, which is rarely reported. They reported that the average Reynolds number and the inflow Reynolds numbers ratio control the mixing degree at outlet pipe junctions. Austin et al. (2008) investigated the mixing phenomenon at cross junctions, exploring flow rates of 7.6 L/min or higher and at a wide range of Reynolds numbers within the turbulent regime. Their results indicated that the average dimensionless concentration and mass split through the outlets were 85 and 15%, respectively, suggesting incomplete mixing at the cross junction, unlike perfect mixing conditions where a mass split of 50% would be expected.

Solehati et al. (2014) conducted a numerical study to evaluate the mixing performance of a micro-channel T-junction with a wavy structure in comparison to a traditional straight micro-channel T-junction. The study yielded compelling results, demonstrating that the micro-channel with the wavy structure outperformed its conventional counterpart in terms of downstream mixing efficiency. The enhanced mixing observed in the micro-channel with the wavy structure was attributed to the presence of periodically reversed secondary flows generated by the curved wavy structure. These secondary flows created a chaotic flow within the micro-channel, significantly enhancing the mixing process.

Zughbi et al. (2003) carried out a numerical and experimental investigation of mixing in pipelines with side and opposed T-junction of different pipe diameters with cold water flowing in the main pipe and hot water through the tee. Their findings indicated that the downstream pipe length needed to achieve 95% mixing depends on the velocity ratio between the main pipe and the tee. Sun et al. (2020) conducted an experimental and numerical study on the mixing uniformity of water and saline solution injected as a tracer into the pipeline under turbulent conditions. They investigated the influence of pipe diameter, flow ratio, and Reynolds number on the mixing uniformity. The assessment of downstream uniformity was performed based on the coefficient of variation. Utilizing dimensional analysis, they derived an equation to predict the effective mixing length downstream from the tracer injection point within the proposed piping system.

Based on the previously discussed studies, it becomes evident that the water exiting a cross junction results from a combination of inlet flow rates, and often, incomplete mixing is observed with two inlets at 90°. In laboratory studies, cross junctions with short inlets and outlets have frequently been chosen, and therefore, most experiments have primarily focused on monitoring chlorine concentration variations at both outlets immediately after leaving the junction or until the pipe end. To our knowledge, no prior study has specifically examined the diffusion of chlorine concentration downstream from cross junctions.

Ongoing chlorine reactions with diverse organic or inorganic materials, including organic sediments, dissolved metals from corroded pipes, pipe materials, and microbial biofilms, within drinking water distribution pipes lead to chlorine decay (World Health Organization 2017). Consequently, chlorine concentrations at the inlet of cross junctions may exhibit fluctuations and decline below the minimum recommended levels at specific points within the distribution network, depending on the traveled path. On the other hand, it has been observed that flows with different concentrations in pipes (Zughbi et al. 2003; Ho & Khalsa 2007; Ho & O'Rear 2009; Sun et al. 2020) or channels (Solehati et al. 2014) need to travel a certain distance from the cross or T-junctions to achieve homogeneity. Therefore, in a real distribution network, household connections (carrying water from the public mains into homes) connected at any point downstream of cross junctions, where the effluents are not yet homogeneous, may carry inadequate chlorine concentrations. Nonetheless, there is a lack of reported data on chlorine concentration diffusion at points further downstream from cross junctions.

From the earlier discussion, the objective of this research is to determine the minimal distance at which household connections should be located to ensure the delivery of high-quality water. In order to fulfill the aim of this research, an experimental study was conducted to investigate the mixing phenomenon at a cross junction with two inlets at 90°, focusing on the interaction between water streams with different flow and chlorine concentration ratios at the inlets. Furthermore, CFD simulations were carried out to predict chlorine concentrations downstream of the cross junction, providing a detailed analysis of the distribution of chlorine concentration at various points across the conduit cross section. The statistical percent coefficient of variation (%CV) was used for a quantitative analysis of the degree of mixing, providing valuable insights into the homogeneity of the fluid within the pipe system after leaving the cross junction. Finally, a novel correlation was developed to determine the pipe length required to achieve the targeted mixing level of %CV = 5 downstream of cross junctions.

A B&C Electronics CL7635 advanced chlorine controller was used to measure (measuring range of 0.1–20 mg/L) and control residual chlorine in the experiment. A data logger (El-USB-4, Lascar Electronics) was connected to each device to collect the data for their analysis. The chlorine meters were connected through hoses to nozzles located upstream and downstream of the intersections. Finally, an Evans 4HME200 centrifugal pump was used to move the fluid from the reservoir to the storage tanks.

The flow control valves were previously adjusted by partially opening them to achieve the desired flow rate for 10 scenarios with varying inflows, ranging from 0.75 to 4.50 L/s at the North inlet and 0.45 to 2.40 L/s at the West inlet. This study involved 10 scenarios that simulated different inflow rates as water enters the cross junctions. In this scenario, the flows joined the cross junction at 90° (from North and West) and exited at the South and East outlets. The primary objective of the experiments was to investigate the downstream mixing of incoming flows as they pass through the cross junction. The flow rate and chlorine concentration were set for 10 scenarios with varying inflows ranging from 0.75 to 4.50 L/s at the North inlet and 0.45 to 2.40 L/s at the West inlet. Considering that the majority of water distribution systems operate in the turbulent regime, the experiments were performed in this regime.

During the experimental runs, clean (tap) water from the reservoir was pumped to the elevated storage tanks with a 4HME200 centrifugal pump. Sodium hypochlorite solution was added to the West and North storage tanks, resulting in chlorine concentrations ranging from 0.06 to 0.9 mg/L at the North and 0.50 to 1.65 mg/L at the West inlet. The solutions in each tank were mixed with a hand mixer. All experiments were conducted at the standard room temperature of 20 ± 3 °C and ambient pressure.

The chlorine decay was neglected in this study since each experiment was extended for about 3 min. Instantaneous flow rates were measured using the flow meters at each inlet and outlet of the cross junctions. In all scenarios, the flows entering the North pipe, containing a lower chlorine concentration, were higher than those in the West inlet pipe. Free chlorine concentrations were also measured at each inlet and outlet. In order to corroborate the repeatability of experimental measurements, each experiment was repeated at least twice, and average results are reported. Predicting the exact flow magnitudes entering a cross junction in an actual water distribution network is nearly unfeasible; therefore, replicating the identical magnitudes is highly improbable. Thus, our scenarios established diverse relationships among inflow rates. The pivotal factor underlying this choice is that the scenarios were conducted under turbulent conditions, a consistent occurrence in real distribution networks. The description of the different scenarios in terms of flow rate and initial chlorine concentration is presented in Table 1.

The term in Equation (10) represents the mass diffusion coefficient for species k in the mixture, and Sc_t is the effective Schmidt number for the turbulent flow. In this work, the standard Sc_t value (Sc_t = 0.7) included in Ansys-Fluent was used in simulations.

In the study of fluid flow in pipe networks, friction losses are an important parameter to consider. According to Prandtl's theory, friction losses occur in a relatively thin region near the solid walls, referred to as the boundary layer (Bird et al. 2007), which is typically divided into three sublayers: viscous, buffer, and turbulent. In this context, to capture the influence of the flow in various regions of the boundary layer, the dimensionless parameter Y⁺ is commonly employed in CFD simulations. This parameter relates the thickness of the boundary layer to the length of the computational cells close to the walls. According to Andersson et al. (2011), the values for Y⁺ commonly used are 0 < Y⁺ < 5 (viscous sublayer), 5 < Y⁺ < 30 (transition sublayer), and 30 < Y⁺ < 400 (turbulent sublayer). In this work, to account for friction losses in the viscous sublayer, the length of the elements adjacent to the solid wall satisfies Y⁺ < 1 for each examined computational mesh and all evaluated Reynolds numbers.

The commercial CFD package Ansys^©-Fluent 17.1 numerically simulates the present model with steady-state conditions and without gravitational effects. The standard κ-ε turbulence model with enhanced wall treatment for the near-wall condition was used for modeling the isothermal 3D turbulent flow. It has been reported that this model produces similar results for mixing in pipe cross junctions and T-junctions as the shear-stress transport (SST) turbulence model, with less computational effort (Walker et al. 2010; Santos-Violante et al. 2020). The standard pressure–velocity coupling, in conjunction with a coupled scheme, was utilized. High-order spatial discretization was applied to the pressure, momentum equations, turbulent kinetic energy, turbulent dissipation rate, and species transport equations.

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_k,m = 1.26 × 10⁻⁹m²/s, corresponding to chlorine's diffusion coefficient in water at 25 °C. In simulations, it was assumed that the tracer fluid (free chlorine in water) had the same viscosity (μ) and density as the main water flow, i.e., μ = 0.001 Pas and ρ = 998.3 kg/m³. Standard model constants predetermined in Fluent were used in all simulations. Each solution converged when all the scaled residuals remained constant, below 10⁻⁵. No convergence problems were observed during simulations, i.e., the equation residuals always gradually decayed until the desired convergence was achieved.

The focus of our study is the mixing of chlorine in pipelines downstream of cross junctions, which occurs over a duration of around 3 min. In contrast, the phenomenon of chlorine decay in water distribution systems extends over hours (Al-Jasser 2007; Romero-Gomez et al. 2008; Monteiro et al. 2014). Consequently, the decay of chlorine is considered non-significant in the context of our investigation and has been disregarded.

Two critical aspects in CFD simulations that play a fundamental role in the reliability and precision of the numerical results are the computational mesh independence analysis and the validation of the numerical data. The mesh characteristics have a significant impact on the accuracy of the results at the expense of computational efficiency. Therefore, the mesh independence analysis ensures that the simulation converges toward a stable solution at a reasonable computational cost. On the other hand, the validation of the numerical data with experimental information ensures the reliability of the numerical results.

Table 2 shows the six computational meshes that were built in order to ensure that numerical results were independent of the mesh density. The number of cells between the coarsest and finest mesh varies between 250,880 and 3,043,784, respectively. Numerical simulations for these six meshes were conducted at the highest Reynolds number (Re = 179,000) examined in this study.

Throughout all the scenarios, consistently higher levels of chlorine concentrations were observed at the South outlet. This phenomenon can be attributed to the obstruction of flow at the West inlet caused by the incoming flow from the North, which had a lower flow rate. As a result, the effluent at the South outlet primarily consisted of water from the West inlet flow, leading to an elevated chlorine concentration. Chlorine concentrations ranged from 0.40 to 1.32 mg/L at the South outlet and from 0.07 to 1.00 mg/L at the East outlet. Ho & O'Rear (2009) made the same observation in their study where the clean water inlet flow rate exceeds the tracer inlet flow rate. They pointed out that the higher momentum of clean water flows across the junction diverts the incoming flow of the tracer water.

Numerical simulations were carried out to describe the mixing phenomenon at cross junctions to predict chlorine (Cl₂) concentration at the outlets. The distribution of water flow lines and tracer contour concentrations in the cross junction for Scenario 5 is shown in Figure 7. It is important to note that, in this figure, the red and blue color indicates the high and low concentrations of Cl₂ coming from the West and North inlets, respectively, which were different for each examined scenario. It can be seen here that the higher momentum from the North inlet resulted in a portion of the flow crossing over the junction and exiting through the South outlet, while all the flow coming from the West diverts toward the South. This causes a partial mixture of the two inflows to the South, while to the East, there is only the inflow coming from the North.

In Scenario 6 (Figure 8(a)), with a Q_N/Q_W ratio of 1.90 and a Cl_2,N/Cl_2,W ratio of 0.26, a significant unmixing region was observed, indicated by the presence of distinct colors (blue, light blue, and green) immediately after the junction. Consequently, fluid uniformity remained compromised until the pipe end. Placing a household connection right after this cross junction could result in low-quality water delivery within the buildings, as achieving the intended homogeneity in mixing requires a specific downstream distance. Based on this example, the right placement for such a connection would be at the pipe's endpoint.

In Scenario 7 (Figure 8(b)), a lower value of Q_N/Q_W (1.33) was obtained. In this case, the incoming flow streams almost collide and exit through the adjacent pipe with some minor mixing. Consequently, a small unmixed area was observed, and the uniformity of the fluid was achieved closer to the junction compared to the previous test.

As shown in Figure 8(a) and 8(b), the area immediately downstream of the cross junction would carry an unmixed fluid with a lower disinfectant concentration (chlorine in the case of this study) since the fluid must travel some distance before achieving homogeneity.

Here, c_p is the local concentration of the tracer (free chlorine, in this case) at the pth mesh cell, and N is the number of evaluation mesh cells over the pipe cross-section. In this approach, the smaller the value of the coefficient of variation, the more homogeneous a tracer concentration is attained.

This equation was validated in the range 1.33 ≤ Q_N/Q_W ≤ 1.9 and 17,900 ≤ Re ≤ 179,000 (see Table 1), with R² = 0.97. However, for 1 ≤ Q_N/Q_W < 1.33, smaller initial values of %CV would be expected than the scenarios presented in Figure 9; therefore, the downstream pipe length required to achieve a coefficient of variation of 5% will be shorter. The majority of water distribution systems operate in a turbulent regime. Therefore, the obtained correlation (Equation (16)) can be reliably used under realistic operating conditions for 1 ≤ Q_N/Q_W ≤ 1.9 and 17,900 ≤ Re ≤ 179,000.

Due to the lack of data in the literature on the diffusion of chlorine concentration at locations further downstream from cross junctions, predictions from Equation (16) are compared with reported data on downstream mixing under turbulent conditions obtained from T-junctions by Zughbi et al. (2003) and Shao et al. (2014). Zughbi et al. (2003) observed that for a T-junction, the length of the pipe needed to achieve 95% mixing increases with the inlet velocity ratios, aligning with predictions from Equation (16). The term ‘length of the pipe for achieving 95% mixing’ in their study refers to the distance from the jet inlet to a point along the pipe where the measured quantity drops below 5% of the step input value. This concept is analogous to the coefficient of variation used in our study. When a side tee angle of 90° was utilized (refer to Figure (18) in Zughbi et al. 2003), which is more similar to our study involving a cross junction with two inlets at 90°, they reported that, for the various examined pipe diameters (ranging from 1 to 16 in), 11 pipe diameters were needed to achieve 95% mixing. For a double T-junction, simulation results reported by Shao et al. (2014) indicate that complete mixing of tracers occurs at a distance greater than 10 pipe diameters. Meanwhile, applying Q_N/Q_W = 1 in Equation (16), a distance of approximately 12.4 pipe diameters is required to achieve CV = 5%. Therefore, both reported results align well with those obtained in this study.

The degree of mixing of two fluids after leaving a cross junction is a crucial parameter in a water distribution system. It refers to how well two or more fluid streams mix after they intersect at a cross junction in a conduit. The level of mixing can significantly impact the quality and uniformity of the resulting fluid within the system.

Household connections represent an essential part of the water distribution network. Examining potential shifts in water quality parameters, particularly chlorine concentration, upon exiting the cross junction is significant for determining the right connection point along the main for the household. This analysis is crucial in preventing the delivery of water with undesirable or non-compliant chlorine concentrations.

The mixing phenomenon of incoming flows at pipe junctions plays a fundamental role in analyzing water quality within distribution networks, particularly in predicting solute transport. Experiments were carried out in a turbulent flow regime at a typical cross junction with two inlets (North and West) and two outlets (South and East). The present work explored a wide range of inflow rates, free chlorine concentrations, and Reynolds numbers, revealing incomplete solute mixing due to the bifurcation of the incoming flow. Additionally, a numerical study was performed using CFD, which yielded average relative errors between experimental and numerical results of chlorine concentrations at the outlets of 5%.

To evaluate the degree of mixing in junctions, a statistical method based on the coefficient of variation was applied. Simultaneous numerical data samples at various points across the conduit cross section, expressed as a percentage of the coefficient of variation, were collected. These data were gathered for different Q_N/Q_W and Cl_2,N/Cl_2,W ratios, allowing us to assess mixture quality downstream. The accepted criterion for composition uniformity (indicating a well-mixed system) is %CV < 5.

A linear correlation was established to determine the dimensionless pipe length required to achieve %CV = 5 as a function of Q_N/Q_W. Our findings suggest that Cl_2,N/Cl_2,W has minimal influence on downstream mixture quality, while Q_N/Q_W significantly affects it at distances less than 50 pipe diameters downstream.

Ensuring public health protection against contaminated water is of paramount importance. The results of this study enhance our understanding of how incoming flow rates and disinfectant ratios impact the mixing quality of effluents leaving junctions in water distribution systems. These findings can contribute to improving mathematical models for predicting disinfectant concentrations (chlorine) throughout the network and optimizing the placement of household connections downstream from cross junctions. In addition, the obtained correlation represents practical guidance for ensuring the delivery of safe and high-quality water to consumers.

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

The authors declare there is no conflict.