Optimizing Water Quality in Dead-Ends of Water Distribution Networks Using Passive Control Methods: A Computational Fluid Dynamics Simulation and Predictive Modeling Study

doi:10.21203/rs.3.rs-5175680/v1

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Optimizing Water Quality in Dead-Ends of Water Distribution Networks Using Passive Control Methods: A Computational Fluid Dynamics Simulation and Predictive Modeling Study

https://doi.org/10.21203/rs.3.rs-5175680/v1

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Dead-ends are points in water distribution networks (WDNs) where water flow is almost stagnant, leading to pipe corrosion and microbial growth, which degrade water quality. Controlling the contaminant dispersion in dead-ends is crucial for maintaining water quality. This research examined the use of passive control methods, specifically leading-edge spoilers, to improve water quality in dead-ends of WDNs. Computational fluid dynamics (CFD) was used to simulate and analyze the effect of spoilers on fluid flow and contaminant dispersion under different flow conditions. The results showed that spoilers significantly reduced contaminant concentrations and sped up water quality restoration. The optimal spoiler configuration was found to be twice the boundary layer thickness in height and angled at 30°, achieving control rates of 58% and 61.90% at low and high velocities, respectively. Predictive models developed from CFD data confirmed the effectiveness of spoilers in reducing YC town's WDN contaminants, and laboratory experiments demonstrated their minimal impact on hydraulic efficiency. Spoilers offer a cost-effective and environmentally friendly solution for improving water quality in WDNs.

Earth and environmental sciences/Environmental sciences

Physical sciences/Engineering

WDNs

Dead-ends

Contaminant Dispersion

Passive Control Methods

Leading-edge Spoilers

CFD

In Water Distribution Networks (WDNs), the relationship between the upstream main pipes and the downstream branch pipes is analogous to the trunk and branches of a tree, with many branches connected to the main trunk. When a branch pipe has no further connections downstream, it becomes what is referred to in this paper as a "dead-end." Situated at the extremities of the WDN and not forming a loop with other pipes, drinking water in these dead-ends is nearly stagnant ¹. As social distance increases, the average water age significantly increases², allowing water to soak the pipe walls for extended periods, leading to the corrosion of pipe walls ^3,4 and the breeding of microorganisms ^5,6. These conditions collectively degrade the quality of drinking water within these dead-ends. In many countries, water distribution systems consist of large, highly pressurized pipe networks that require an excessive amount of energy⁷. Contaminated water from dead-ends can flow back into the main pipes, potentially leading to discoloration in drinking water and posing risks to public health and safety ⁸. Implementing effective measures to prevent contaminants in dead-end branches from entering the main pipes is essential.

Standard methods for cleaning pipes include unidirectional flushing ⁹, ice slurry flushing ¹⁰, multi-phase flow pulse flushing^11,12, swabbing, pigging, and chemical methods. Although these methods can reduce contaminants attaching to pipe walls, they suffer from low efficiency, high energy consumption, high costs, and require lengthy service interruptions^13,14. In response to the global movement for low carbon^15,16, water utility companies must find more efficient, energy-saving, cost-effective, and non-stop water methods to manage contaminant diffusion in dead-ends.

A cavity is formed at the main pipe connecting to the dead-end, as shown in Fig. 1. The passive control method is among the cavities' most economical and practical fluid flow control techniques¹⁷. It involves installing the spoiler at the cavity's leading edge to alter the internal fluid flow, thereby controlling it without needing energy input¹⁸.

Passive control methods have been extensively utilized in areas such as reducing cavity noise^19–21, suppressing cavity resonance ²², and decreasing fluid resistance ^23,24. The effectiveness of various spoilers in controlling fluid flow has been well-documented across different applications. For instance, Zhang ²⁰ has demonstrated that elevating the shear layer is a primary mechanism for reducing cavity noise in high-speed flows when installing a spoiler. Li ²¹ has found that serrated leading-edge spoilers effectively suppress noise in partially open cavities. Chen ¹⁹has observed that passive controls like rectangular barriers and square-tooth spoilers also contribute to noise reduction in cavities. Bennett ²² has explored the suppression of resonance in partially enclosed cylindrical cavities affected by grazing flows using a fluidic spoiler. Schoelzel ²⁴ has optimized the design of parachutist spoiler-helmet configurations through numerical simulations, achieving an 18.9% reduction in drag coefficient and a more symmetrical flow field, which reduced lateral forces. Darabasz ²³ has installed inclined spoilers at the rear of a vehicle body to achieve drag reduction, with a reduction rate of 11.5%. Yu ²⁵ conducted wind tunnel experiments and numerical simulations on cavities above aircraft fuselages, finding that cylindrical spoilers significantly reduced pressure fluctuations within the cavity.

These studies show that installing an appropriate spoiler can effectively alter and control fluid flow states, thus reducing pressure fluctuations within the cavity. Pressure fluctuations within dead-end cavities in WDNs can lead to significant contaminant diffusion into main pipes. Additionally, installing spoilers provides a cost-effective and energy-efficient alternative to traditional pipe flushing methods. Therefore, installing spoilers at the leading edge of dead-end cavities has the potential to effectively control contaminant diffusion, offering a promising approach to improving drinking water quality.

The study initially employed Computational Fluid Dynamic (CFD) to analyze the impact of installing various leading-edge spoilers at the dead-end cavity under normal (low flow) and flushing (high flow) conditions. Subsequently, predictive models for contaminant diffusion, with and without spoilers, were developed based on the simulation results. Finally, utilizing a realistic hydraulic model of a WDN, the study compared contaminant diffusion before and after the spoilers' installation, thereby demonstrating this approach's effectiveness.

2.1 CFD Simulation

Numerical simulation is widely used for studying spoiler control laws in fluid flow research^24–26. In this study, CFD was employed to examine the effects of installing leading-edge spoilers at the dead-end cavity. The entire CFD simulation process consisted of the following steps: mathematical model development, geometric model setup, solution, and result post-processing.

2.1.1 Mathematical Model Development

The diffusion of contaminants at dead-ends is governed by three core principles: the conservation of mass, momentum, and energy.

Using Eq. (1) to model the conservation of mass ensures the conservation of mass in a transient, three-dimensional, and incompressible fluid flow.

$$\:\frac{\partial\:u}{\partial\:x}+\frac{\partial\:\nu\:}{\partial\:y}+\frac{\partial\:w}{\partial\:x}=0$$

Where u, v, and w denote the velocity vector components in the x, y, and z directions.

Additionally, using the Navier-Stokes equation to capture the conservation of momentum is shown as Eq. (2).

$$\:\begin{array}{c}\frac{\partial\:\left(\rho\:u\right)}{\partial\:t}+di\nu\:\left(\rho\:uu\right)=-\frac{\partial\:p}{\partial\:x}+\frac{\partial\:{\tau\:}_{xx}}{\partial\:x}+\frac{\partial\:{\tau\:}_{yx}}{\partial\:y}+\frac{\partial\:{\tau\:}_{zx}}{\partial\:z}+{F}_{x}\\\:\frac{\partial\:\left(\rho\:\nu\:\right)}{\partial\:t}+di\nu\:\left(\rho\:\nu\:u\right)=-\frac{\partial\:p}{\partial\:y}+\frac{\partial\:{\tau\:}_{xy}}{\partial\:x}+\frac{\partial\:{\tau\:}_{yy}}{\partial\:y}+\frac{\partial\:{\tau\:}_{zy}}{\partial\:z}+{F}_{y}\\\:\frac{\partial\:\left(\rho\:w\right)}{\partial\:t}+di\nu\:\left(\rho\:wu\right)=-\frac{\partial\:p}{\partial\:z}+\frac{\partial\:{\tau\:}_{xz}}{\partial\:x}+\frac{\partial\:{\tau\:}_{yz}}{\partial\:y}+\frac{\partial\:{\tau\:}_{zz}}{\partial\:z}+{F}_{z}\end{array}$$

Where ρ represents the fluid density, p represents the pressure on the fluid element, τ denotes the viscous stress, and F is the force acting on the fluid element.

Considering an incompressible fluid and the fact that heat exchange is negligible during contaminant diffusion, this study omitted the conservation of energy equation.

Furthermore, the transport of contaminants necessitates adherence to specific equations for component transport. In cases where the fluid system exhibits turbulence, the diffusion flux of a given substance, referred to as the ith substance, is described by Eq. (3).

$$\:{\overrightarrow{J}}_{i}=-(\rho\:{D}_{i,m}+\frac{{\mu\:}_{t}}{S{c}_{t}})\nabla\:{Y}_{i}-{D}_{T,i}\frac{\nabla\:T}{T}$$

Where $\:{\overrightarrow{J}}_{i}$ is the diffusive flux of the ith substance due to the concentration gradient and temperature gradient, D_i,m is the mass diffusion coefficient of substance i in the mixture, µ_t is the turbulent viscosity, Sc_t is the turbulent Schmidt number, Y_i is the mass partition coefficient of substance i, D_{T, i} is the thermal diffusion coefficient, and T is the temperature. This study used a default value of 0.7 for the turbulent Schmidt number.

2.1.2 Geometric Model Setup

Designing geometric models replicating real-world conditions is essential for obtaining realistic numerical simulation results. The geometric model included the dead-end, the main pipe, and the leading-edge spoiler, as depicted in Fig. 1. The main pipe was modeled with a length of 1,000 mm and a diameter of 200 mm, while the dead-end extended 500 mm with a diameter of 100 mm. The variables H and θ represent the spoiler's height and tilt angle. To develop these models using Creo CAD, a sophisticated 3D design software²⁷.

H was specifically designed based on the boundary layer thickness. The boundary layer thickness was calculated using Eq. (4).

$$\:\delta\:=0.37l\cdot\:R{e}^{-0.2}$$

Where δ donates the boundary layer thickness, l represents the cavity’s leading edge length. In this study, l determined to be 450 mm. This measurement was calculated by subtracting half of the pipe diameter at the dead-end (50 mm, as the diameter is 100 mm) from half of the total length of the geometric model of the main pipe (500 mm, as the total length is 1,000 mm).

Previous studies have varied the height and tilt angle of the spoiler to investigate the fluid flow control of spoilers with different design parameters^18,20. The study varied these two control parameters across 15 different conditions, including θ, set at 30°, 45°, and 60°, and H, set at 0.3δ, 0.5δ, δ, 1.5δ, and 2δ.

Utilizing ICEM CFD to generate the computational grid for the simulations²⁸. The density of the grid is a crucial factor that influences both the accuracy and the computational efficiency of the numerical calculations²⁹. Grid independence analysis is a crucial first step in defining grids in CFD analysis, with the aim of making simulation results independent of grids^30,31. Grid independence analysis was conducted to ensure the results were reliable and computationally feasible, and a grid of 134,435 cells was selected for the final simulations.

2.1.3 Solution

Using Ansys Fluent to carry out the CFD simulations is well-suited for modeling and analyzing fluid flow and related phenomena³². The boundary conditions were meticulously set to mimic realistic scenarios in water distribution systems.

Inlet Boundary

Configured as a velocity inlet where the flow direction was perpendicular to the boundary. The inlet was defined as contaminant-free to simulate the introduction of clean water into the system. This study considered two inflow velocities scenarios. The first was a nearly stagnant lower velocity, typical of daily conditions at dead-ends, set at 0.03 m/s. The second was a higher velocity of 1.2 m/s, often used during flushing operations to clear out accumulated contaminants ^11,33.

Outlet Boundary

Set as a pressure outlet to allow the fluid to exit the system under controlled pressure conditions.

Wall Boundaries

The pipe inner walls and the surfaces of the spoilers were treated as no-slip stationary walls, which means that the velocity of the fluid at these boundaries is zero, simulating the physical behavior of the fluid at solid boundaries.

Initial Concentration of Contaminants

Represented by iron ions, was uniformly set at 1 mol/m³ in the dead-end.

For the solver settings, a transient calculation method was chosen to capture the time-dependent behavior of the fluid flow and contaminant dispersion. The turbulence model employed was the Large Eddy Simulation (LES), which effectively predicts the larger energy-containing eddies in turbulent flows while modeling the minor scales³⁴. The SIMPLE algorithm provided more robust and faster convergence to manage pressure-velocity coupling. Transient discretization was set to First Order Implicit to ensure stability in the time-stepping process. Spatial discretization utilized a second-order upwind scheme, which balances accuracy and computational cost well. The subgrid-scale stress model was the Wall-Adapting Local Eddy-viscosity (WALE) model, which is particularly effective in near-wall turbulence modeling ³⁵.

2.1.4 Result post-processing

The data concerning the distribution of contaminant concentration and velocity fields were processed to analyze and visualize the results. The results were visualized using plots, which provide a clear and intuitive understanding of how contaminants disperse and how effectively the spoilers modify the flow to reduce contaminant levels. To quantitatively assess the effectiveness of the spoilers in controlling contaminants, a contaminant control rate, denoted as α, was introduced. This rate is defined by Eq. (5).

$$\:\alpha\:=\frac{C-{C}^{{\prime\:}}}{C}$$

Where C is the contaminant concentration at the outlet of the main pipe before installing the spoiler, and C’ is the concentration after installation.

2.2 Predictive Modelling of Contaminants

Predictive models with and without implementing a spoiler were developed to enhance the understanding and control of contaminant diffusion in water distribution systems. The numerical simulation experiments under various working conditions provided data to support the development of contaminant diffusion prediction models. The spoiler used in the simulations was set with an θ of 30° and an H of 1.5δ. These models aimed to predict the concentration of contaminants at the main pipe, considering several independent variables: initial concentration of contaminants within the dead-end, hydrodynamic pressure at the cavity, water velocity at the cavity entrance, and the dead-end's diameter. The variables were varied across multiple gradients, as outlined in Table 1.

Table 1

Gradient of the Respective Variables
Variable	Gradient
The initial concentration of contaminants within the dead-end (mol/m³)	0.1, 0.5, 1, 2, 4
Hydrodynamic pressure at the cavity (MPa)	0.1, 0.2, 0.3, 0.4, 0.5
Water velocity at the cavity entrance (m/s)	0.03, 0.1, 0.4, 0.8, 1.2
Dead-end’s diameter (mm)	50, 100, 150

This setup resulted in a total of 5 × 5 × 5 × 3 = 375 unique conditions for each model scenario (with and without spoiler), leading to 750 simulations. These simulations provided a comprehensive dataset that reflects a wide range of possible real-world conditions. The numerical results were fitted using linear regression and analyzed using the SPSS statistic for F-tests³⁶.

2.3 Case Profile

YC town's WDN is extensive, covering approximately 280 km and serving an area of about 43 km². It supports a population of around 36,000. The network includes 3,667 pipes and 3,616 nodes, as depicted in Fig. 2. Water is supplied from a single reservoir located in the north, and the system primarily relies on gravity flow for water distribution.

The predictive model developed was integrated into EPANET 2 ³⁷. This integration allowed the evaluation of the spoiler's control effects under realistic hydraulic conditions.

Nodes with a primary water demand of less than 0.001 L/s were preliminarily identified as dead-ends. After excluding non-terminal nodes, 533 nodes were deemed eligible for further analysis regarding the impact of spoilers.

In the simulations, tracer particles were used to model the movement of contaminants within the network. These particles did not undergo chemical reactions, and their concentration did not influence reaction rates. Consequently, the main reaction order was set to 0.

The pipe wall reaction coefficient was 0, indicating no interaction between the tracer particles and the pipe walls. Both decay and growth rates for chemical reactions were set to 0, focusing solely on the physical transport of contaminants without chemical alterations. The total duration for the simulation was set to 240 hours to observe the long-term effects of spoilers. Hydraulic time steps were set at 1 hour, and water quality time steps at 6 minutes, starting at 0:00 am.

3.1 Numerical Simulation Results

3.1.1 Analysis of Spoiler Mechanism

An analysis of the methods by which spoilers decrease or increase the spread of contaminants was conducted by studying concentration and velocity distribution diagrams, as depicted in Fig. 4. In all examined scenarios, the spoilers were set with a θ of 30°.

At an inflow velocity of 0.03 m/s with no spoiler (Fig. 4(a)), the shear layer collided with the rear edge of the cavity, leading to the separation of the shear layer. Some of the shear layers redirected deeper in the dead-end, creating a counterclockwise vortex at the cavity's entrance. This vortex caused a lower concentration of contaminants at the entrance than the deeper regions. Another portion of the shear layer bypassed the rear edge and continued downstream in the main pipe, carrying contaminants from the cavity.

At an inflow velocity of 0.03 m/s with a spoiler height of 1.5ẟ (Fig. 4(b)), the shear layer lifted from the spoiler, crossing over the cavity, creating a vortex behind the spoiler. The vortex core was located above the rear edge of the cavity, and the outflow from the vortex exited at the highest point of the spoiler, aligning with the inflow of the main pipe. The contaminants tended to be centered in the main pipe rather than clinging to the walls. This resulted in a reduced concentration of contaminants at the entrance of the dead-end, leading to decreased outflow contamination.

At an inflow velocity of 1.2 m/s with no spoiler (Fig. 4(c)), turbulence within the dead-end was heightened, resulting in a clockwise vortex at the rear edge of the cavity. This vortex brought contaminants from the depth of the dead-end into the counterclockwise vortex at the entrance, elevating the concentration of contaminants in this area. Subsequently, a shear layer bypassing the rear edge transported these contaminants into the main pipe.

At an inflow velocity of 1.2 m/s, with a spoiler height of 0.3ẟ (Fig. 4(d)), the shear layer experienced slight lifting after passing the spoiler, leading to partial exposure of the vortex at the entrance of the dead-end to the shear layer from the main pipe. As the shear layer bypassed the vortex at the dead-end entrance, more contaminants were transported into the main pipe.

At an inflow velocity of 1.2 m/s and with a spoiler height of 1.5δ (Fig. 4(e)), the higher spoiler led to the shear layer passing the cavity, resulting in a significant reduction in velocity and contaminant concentration at the entrance of the dead-end, compared to scenarios without a spoiler (Fig. 4(c)) or with a shorter spoiler (Fig. 4(d)). A smaller vortex was present behind the highest point of the spoiler. The shear layer from the main pipe protected this vortex from being exposed to the main pipe flow. As a result, few contaminants were diffused from the dead-end.

In summary, the spoiler’s height and inflow velocity significantly impact the efficiency of controlling contaminant dispersion. Spoilers are effective at lowering contaminant concentrations at lower inflow velocities. However, at higher inflow velocities, the spoiler’s height becomes a critical factor in controlling dispersion, with taller spoilers demonstrating superior performance in managing contaminants.

3.1.2 Analysis of Parameter Impact

Figure 3 depicts the impact of spoilers in managing the spread of contaminants. In trials without spoilers, the contamination control rate was practically 0%.

At a lower inflow velocity of 0.03 m/s, as depicted in Fig. 3(a), it was observed that the control rate (α) remained above 0% for all conditions, indicating the effective reduction of contaminant dispersion by spoilers. When the spoiler's tilt angle (θ) was kept constant, α increased with the spoiler height (H). With a constant H, different θ values resulted in two distinct trends in α. Specifically, at H = 0.3ẟ, an increase in θ led to a decrease in α, with the maximum α observed at 60°. Conversely, for H ≥ 0.5ẟ, α increased with θ, peaking at 30°. The difference in control rates between various θ values also widened as H increased, indicating that changes in H significantly impacted the spoilers' ability to control dispersion compared to adjustments in θ. Overall, at this lower inflow velocity, the spoiler with a θ of 30° and an H of 2ẟ was most effective, achieving an α of 58%.

In contrast, at a higher inflow velocity of 1.2 m/s, shown in Fig. 3(b), the influence of spoilers on pollution control became more intricate and could be classified into two distinct groups. Spoilers with H < ẟ proved ineffective and, in some cases, worsened contaminant dispersion. On the other hand, spoilers with H ≥ ẟ effectively controlled dispersion, with α increasing as H increased. The changes in θ did not consistently impact α at the same H. However, at a θ of 30°, the control effect of the spoiler was more prominent with increasing H, peaking at H = 2ẟ with an efficiency α of 61.90%. Workers may choose to flush out contaminants from dead-ends rather than controlling their dispersion when working at higher velocities. In these cases, spoilers play a beneficial role in promoting contaminant dispersion. Specifically, a spoiler with θ = 45°and H = 0.3 was most effective for facilitating pipe flushing operations.

3.1.3 Development of the Predictive Model

The results from the numerical simulations, as detailed in Table 1, were analyzed using linear regression to develop models that predict contaminant dispersion in WDNs. Both with and without the implementation of spoiler control, as outlined in Eq. (6).

$$\:Y=-0.266+0.916C+0.2612P-0.1v+0.003D$$

$$\:Y=-0.266+0.916C+0.2612P-0.1v+0.003D-0.328$$

C is the initial concentration of contaminants within the dead-end, P is the hydrodynamic pressure at the cavity, v is the water velocity at the cavity entrance, and D is the dead-end's diameter.

The effectiveness of these models was confirmed through F-tests, which yielded a P-value of 0.000, demonstrating a satisfactory fit to the observed data. Additionally, the Variance Inflation Factor (VIF) values were all below 10, indicating that the models were free from multicollinearity, further validating their robustness and reliability. These suggest that the constructed models are sound and can effectively be used to understand and predict contaminant dispersion under various conditions within WDNs.

3.2 Case Study Analysis

3.2.1 Comparison of Contaminant Control Effects

The dispersion of contaminants in the case of WDN was analyzed with and without spoilers. Contaminant concentration contour maps were created at various time intervals—12, 24, 72, and 240 hours, as depicted in Fig. 5.

In scenarios without a spoiler, contaminants were released directly into the WDN, leading to higher concentrations near the network's dead-ends, as shown in Fig. 5(a). Conversely, installing a spoiler decreased the peak concentrations at these critical times, as illustrated in Fig. 5(e). Although contaminants continued to spread as the upstream flow increased, the presence of a spoiler consistently mitigated the release of contaminants at the dead-end.

Comparative analysis at each time point revealed that the general direction and pattern of contaminant spread were similar in scenarios with and without spoilers emanating outward from the dead-end. This observation confirmed that while the spoiler did not alter the dispersion path, it significantly reduced contaminants' concentration and residence time within the network. Notably, by 240 hours post-pollution, water quality had nearly returned to normal levels in scenarios with spoilers, as seen in Fig. 5(h). In contrast, areas without spoilers displayed lingering pollution, as seen in Fig. 5(g), suggesting a more extended recovery period was required.

These findings underscore spoilers' effectiveness in reducing contaminant concentrations and accelerating water quality restoration within WDNs.

3.2.2 Resistance Impact Analysis

Installing spoilers within pipes probably leads to an increase in head loss. The local resistance coefficient of the spoiler was calculated using Eq. (7).

$$\:\zeta\:=\frac{200gh}{{\nu\:}_{\text{a}\text{v}\text{g}}^{2}}$$

Where ζ represents the local resistance coefficient, h is the pressure drop, g is the acceleration due to gravity, and v_avg is the average flow velocity downstream of the spoiler.

A spoiler with H = 1.5δ and θ = 30° was installed in a DN100 pipe in a controlled laboratory setting. Measurements of h and v_avg allowed for the determination of ζ for this configuration, which was found to be 1.2. Consequently, the local head loss induced by the spoiler at a velocity of 1.00 m/s was calculated to be 5.85 × 10^− 4 MPa. The head loss over a 1,000m stretch of a DN100 cast iron pipe is 2.06 × 10^− 2 MPa.

Despite the presence of the spoiler, the local head loss it causes is significantly smaller compared to the overall head loss along the pipe, nearly two orders of magnitude less. This analysis highlights that while spoilers effectively manage contaminant dispersion, their impact on the hydraulic efficiency of the WDN is minimal. Thus, spoilers can be considered a viable option for pollution control without substantially compromising the system's hydraulic performance.

The study utilized computational fluid dynamics (CFD) simulations to assess the impact of installing leading-edge spoilers at the dead-end within WDNs. The key findings are as follows:

Spoilers alter fluid dynamics in dead-end and main pipes, influencing the distribution of contaminants.

Spoilers can control the diffusion of contaminants from dead-end into main pipes under low and high inflow velocities. The optimal spoiler configuration, which is twice the height of the boundary layer thickness and angled at 30°, achieved control rates of 58% and 61.90% at low and high velocities, respectively. Conversely, at high velocities, spoilers shorter than half the boundary layer thickness inadvertently promote the diffusion of contaminants from dead-end pipes into main pipelines.

Based on the CFD simulation results, predictive models for contaminant diffusion in WDNs with and without spoilers were developed. Application of these models in the actual WDN of YC Town demonstrated that spoilers significantly reduce contaminant concentrations in dead-end pipes and accelerate water quality restoration. Despite increasing local resistance within the pipelines, spoilers have a minimal impact relative to the total resistance loss across the entire pipeline.

The study concludes that spoilers represent a cost-effective, efficient, and environmentally friendly solution for controlling contaminant diffusion and enhancing pipeline flushing efficiency. Future research could further explore the application of spoilers in different types of pipelines and under various operational conditions and optimize spoiler design parameters and shapes to enhance their effectiveness.

Funding:

This work was supported by the Key Research and Development Program of Heilongjiang Province of China [grant number 2022ZX01A06]; the State Key Laboratory of Urban Water Resource and Environment (Harbin Institute of Technology) [grant number 2024TS26]; and the Collaborative Innovation Achievement Project of Heilongjiang Province's " double world-class project " Disciplines [grant number LJGXCG2023-018].

Author Contribution

K.L. and J.G. wrote the main manuscript text and W.W. prepared figures. All authors reviewed the manuscript.

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No competing interests reported.

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Optimizing Water Quality in Dead-Ends of Water Distribution Networks Using Passive Control Methods: A Computational Fluid Dynamics Simulation and Predictive Modeling Study

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Abstract

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1 Introduction

2 Methods

2.1 CFD Simulation

2.1.1 Mathematical Model Development

2.1.2 Geometric Model Setup

2.1.3 Solution

2.1.4 Result post-processing

2.2 Predictive Modelling of Contaminants

2.3 Case Profile

3 Results and Discussion

3.1 Numerical Simulation Results

3.1.1 Analysis of Spoiler Mechanism

3.1.2 Analysis of Parameter Impact

3.1.3 Development of the Predictive Model

3.2 Case Study Analysis

3.2.1 Comparison of Contaminant Control Effects

3.2.2 Resistance Impact Analysis

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Funding:

Author Contribution

References

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