## ABSTRACT

Hydrodynamic separators are commonly used to control the total suspended solid concentration in stormwater before being discharged to natural water bodies. The separator studied in this paper, featuring a swirling flow generated by tangential inlet and outlet connections, was analyzed for its sediment removal efficiency in relation to sediment and flow rates. For the separator studied in this paper, the numerical model showed that the flow field was favorable for the sediments to gather at the center and settle. A higher flow rate or a smaller sediment diameter corresponded to a lower removal rate and vice versa. The dimension improvement for increasing the sediment removal rate was also studied. It was found that increasing the diameter of the separator showed a higher sediment removal rate compared with corresponding increase in the height of the separator. A dimensionless parameter *J* was proposed to assess the sediment removal rate of a separator, which may be used for designing and optimizing such a device. The removal rate is positively correlated with the *J* value. When the *J* value reaches 0.5 or above, the sediment removal rate exceeds 80%, which is a good initial target value for designing this type of separator.

## HIGHLIGHTS

Provided an experimentally validated computational fluid dynamics model.

Changing the diameter has a greater impact on the removal rate of hydrodynamic separators than changing the height.

The

*J*value can be used to evaluate the solids removal efficiency of a hydrodynamic separator.

## INTRODUCTION

With the rapid urbanization and emerging effects of climate change, cities, and urban areas are facing the challenge of urban flooding caused by the increased hydraulic loads caused by the increased magnitude and intensity of extreme rainfall events, increased urban imperviousness levels, and internal urban drainage system (UDS) failures (Mugume *et al.* 2015). Conventional UDSs are designed to safely collect and convey stormwater runoff to wastewater treatment plants or receiving water bodies while minimizing inconvenience, flood damages, and health risks to the public (Butler *et al.* 2018; Mugume *et al.* 2024).

Discharging untreated stormwater to natural water bodies may lead to eutrophication (Helmreich & Horn 2009; Angrill *et al.* 2017), produce malodorous black water, increase turbidity, reduced light penetration, blanketing of the bed (Suarez & Puertas 2005; Binns *et al.* 2019) and have influences on biodiversity (Kim *et al.* 2007; Sazakli *et al.* 2007). However, the ability of these systems to remove sediment varies with particle sizes, so it is important to know the particle size distributions in real-world stormwater (Charters *et al.* 2015). Therefore, ensuring the water quality released is one of the essential criteria in most current design guidelines. Most national or local authority regulations in various countries limit the sediment content in stormwater to a certain level given the adsorption of pollutants and the negative impact of the sediment itself, and the removal rate of sediments is generally one of the key requirements in most design guidelines (USEPA 2016; EPCOR 2020). Therefore, removing sediments from stormwater before releasing them to natural water bodies is a necessary process for stormwater management (Mamoon *et al.* 2019).

A hydrodynamic separator is one of the options for sediment control in stormwater treatment before releasing to natural water bodies. The main mechanism for sediment removal is to generate a flow field in a chamber that is favorable for the sediment to settle before exit (Andoh & Saul 2003; Yu & Lee 2009; Kiringu & Basson 2021). These devices separate sediments and floating from stormwater through vortex principles caused by swirling flow fields, and therefore have no moving parts which requires low maintenance. However, they are mostly effective at removing heavy sediments from stormwater, and less effective on fine sediments (USEPA 1999). Therefore, it is crucial to understand and predict the performance of such a separator to guide the design and operation. This assertion is supported by research from Bright *et al.* (2020), highlighting the importance of analyzing sediment transport mechanisms.

Commercial separators are available on the market and most products use swirling flow for the separation process. Traditional collection tanks and catch basin inserts mainly rely on the principle of gravity separation, showing overall satisfactory performance in capturing large debris, retaining plankton, and minimizing sedimentation in UDSs (Tang *et al.* 2016; Yang *et al.* 2022). Charbeneau *et al.* (2004) summarized 18 commercial products, and it was found that more than half of the systems (10 devices) used swirling flow, seven used multiple chambers, and only one used filtration technique. Mohseni & Fyten (2008) systematically analyzed the performance of a commercial separator and proposed that the sediment removal efficiency was a function of the Péclet number. It serves as a pivotal indicator for the efficiency of sediment removal across a diverse spectrum of flow rates, sediment dimensions, densities, and fluid viscosities, as investigated by Carlson *et al.* (2006) and Wilson *et al.* (2009). At present, most commercial products have single design and limited compatibility, and thus may not be able to always reach ideal results (Vialle *et al.* 2015). Therefore, it is useful to conduct a study on the movement of sediments and its removal efficiency in a generalized separator under different flow conditions.

Computational fluid dynamics (CFD) has been increasingly utilized for elucidating the intricate dynamics of sediment–water interaction, primarily due to its ability to provide a granular level of detail that is often infeasible to achieve through experimental means alone. This advanced computational technique allows for a comprehensive analysis of flow patterns and the optimization of system design parameters, which is particularly beneficial in scenarios where physical prototyping is costly or impractical (Sansalone & Pathapati 2009; Rodi 2017; Ganjare & Patwardhan 2023). The efficacy of CFD in urban drainage-related applications has been articulated by Ta (1999), Faram & Harwood (2000), and Harwood (2006), who collectively substantiate the compatibility and advantages of CFD simulation for the design and analysis of UDSs. Notably, Lee *et al.* (2010) leveraged CFD technology to rigorously assess the performance of a hydrodynamic stormwater separator, with a particular emphasis on the impact of underflow on the separator's efficacy. Similarly, Peng *et al.* (2019) adeptly employed CFD simulations to scrutinize the influence of various geometric ratios of separator diameter to height on sediment removal rates, thereby enhancing the understanding of the underlying fluid dynamics and facilitating the informed design of such separators. It is worth noting that their research primarily focused on separators with relatively small dimensions, where the precision and control offered by CFD were especially advantageous for revealing subtle design sensitivities that are otherwise challenging to discern through traditional experimental approaches.

Most previous studies focused solely on the bulk sediment removal efficiency rather than proposing a method to evaluate the sediment removal rate of such a hydrodynamic separator device (Andoh 2005; Pathapati & Sansalone 2009). In this study, the main objective was to comprehensively assess the sediment removal rate of a swirling-type hydrodynamic separator and propose a way of assessing the device for optimizing the design. The separator tested in this study was designed with inlet and outlet pipes tangential to a chamber for generating a swirling flow. The reason for this design is to avoid extra structures in the chamber impeding the inflow and causing potential flooding issues. The results of physical experiments as well as numerical modeling were presented to predict the performance of the separator for different sediment sizes. The design parameters and ways of assessing the separators in the removal of specific sediment diameters are proposed at the end. These study findings could improve the design and operational guidelines of these separators and contribute to the development of more sustainable stormwater management in cities.

## METHODS

### Physical experiment

*D*) of 500 mm. The inlet and outlet pipes have a diameter of 150 mm and connect to the separator tangentially to generate a swirling flow, and the length for the inlet and outlet pipes are 3 and 1 m, respectively. The distance between the centerline of the inlet and outlet pipes is 350 mm. The invert of the inlet and outlet pipe is 350 mm above the bottom of the separator. The sediment-adding port is 50 mm in diameter and 150 mm upstream of the upper part of the inlet pipe to the separator. A screw feeder was used for the sediment injection. The input voltage was adjusted to ensure a steady sediment injection at a mass rate of 4 g/s. At the outlet, a sediment-capturing system is installed for avoiding the sediment exiting the outlet from entering the inlet.

The flow field was measured by an Acoustic Doppler velocimetry (ADV) (Nortek Vector) with a range of ±4 m/s and accuracy of ±0.5% at a sampling frequency of 200 Hz. A turbulent characteristics analysis was performed, and the turbulence statistics and second-order quantities were found converged for the measurement. Prior to the measurement, the apparatus was run for 10 min before collecting the velocity data to ensure the measurement reached the equilibrium state of the system.

During the experiment, the sediment–water mixture was collected manually at the outlet using an 800-mL beaker. The mixture was then dried in an oven (DHG9240A heating and drying oven) and weighed using a high-precision electronic scale (QUINTIX35-1CN). The procedure for the experiments was as follows: (1) start the pump for 10 min to stabilize the flow field and measure the flow rate using bucket method; (2) turn on the sediment-adding device to evenly add sediment into the flow; (3) collect sediment–water mixture using the beaker at every 10 s interval at the outlet, run the pump for 2.5 min, and obtain 15 beakers of sediment–water mixture; (4) dry sediment–water mixture in the oven and weigh by the electronic scale. For each experiment runs, the total weight of the sediment deposited at the bottom of the separator, and that captured by the beaker at the outlet generally equals to 250 g.

Due to the laboratory scale model used in this study and the unclear scale effect of water sand multiphase flow, errors may occur in the prototype size separator. However, this experiment can preliminarily clarify the dynamics of the particles in such separators, evaluate their separation efficiency, and ultimately propose optimization methods.

### CFD model setup

Ansys Fluent is an advanced CFD simulation software developed by ANSYS, Inc. It is extensively applied across a variety of engineering disciplines, including aerospace, automotive, chemical engineering, environmental engineering, and biomedical fields, for simulating and analyzing flows, heat transfer, chemical reactions, combustion, and related physical processes. This study used Ansys Fluent (ANSYS 2020. R2) for CFD simulation.

The geometry of the numerical model was 1:1 to the physical model. Velocity inlet boundary condition was used at the water inlet and the outlet was set as a pressure boundary condition. The wall was modeled as a no-slip wall, assuming zero fluid velocity at the wall. A uniform size tetrahedral mesh was generated with three inflation layers near the wall for boundary layer. The mesh sizes ranged from 4 to 8 mm, and the *y* + values for water flow at the first grid near the wall ranged between 10.23 and 14.61. Reynolds-averaged Navier–Stokes (RANS) equations were solved with volume of fluid (VOF) model for air and water flow given free surface flow in the system. The renormalization group (RNG) *k*–*ε* model was selected as the turbulent model given its adaptability to various flow conditions and good predictive performance. The sediment motion was modeled using the discrete phase model (DPM) which combined the Eulerian method for fluid motion and the Lagrangian method for sediment motion.

With respect to the solution method, standard SIMPLE algorithm was used as the pressure–velocity coupling method. Transient mode with time step of 0.05 s was selected for the simulation, which corresponded to a Courant number of about 1.9. The advection scheme was second-order upwind for the transient model. The sediment was modeled with a Rosin–Rammler diameter distribution, and the injection type was normal direction at the surface of injection. The sediment was introduced through the sediment inlet at a rate of 4 g/s for a duration of 64 s. The simulation then continued for an additional 84 s to allow for sufficient time for the sediment to settle or escape through the outlet.

Mesh independent test was conducted at inflow rate of 10 L/s (i.e. Run 0). Four progressive mesh levels were generated with node numbers of 358245, 513389, 790546, and 1228467. The monitoring point for velocity and static pressure was at the center of the separator 100 mm above the bottom. As the node number increased, the relative velocity differences between two consecutive mesh levels were 4.01%, 0.52%, and 0.27%. The corresponding pressure differences were 2.03%, 0.70%, and 0.34%. Further increasing the node number did not significantly change the flow velocity and pressure. Therefore, the model with node number 790546 was selected for further simulations. The corresponding order of accuracy was roughly 1.60 based on the Richardson Extrapolation from the classic CFD handbook (Ferziger & Peric 2002).

Tables 1 and 2 present the experimental conditions and CFD model conditions for this study, respectively. Run 0 is model validation and mesh independent test case where the measured flow field in the physical experimental model is compared with the simulated flow field by the CFD model at a flow rate of 10 L/s. Runs A to E are for the sediment removal efficiency of physical and CFD models. Run F explores the separation efficiency of mixed sediment in the hydrodynamic separator. Based on the physical experimental model, Runs M to N numerically assess the modifications of the separator for further improving the sediment removal efficiency. For Runs M and N, the height of the hydrodynamic separator was increased by 1.2 and 1.5 times, respectively, for Runs M1 and N1. Similarly, the diameter of the hydrodynamic separator increased by 1.2 and 1.5 times for Run M2 and N2, respectively. The height-to-diameter ratio of the laboratory size is 1.4 and M1, N1, M2, and N2 are 1.68, 2.10, 1.17, and 0.93, respectively.

Run . | Sediment size (μm) . | Q (L/s)
. | H (m)
. | D (m)
. |
---|---|---|---|---|

0 | N/A | 10 | 0.7 | 0.5 |

A1 | 75 | 3, 5, 7 | 0.7 | 0.5 |

B1 | 100–200 | |||

C1 | 200–500 | |||

D1 | 400–800 | |||

E1 | 500–1,000 | |||

F | 75–1,000 | 7 | 0.7 | 0.5 |

Run . | Sediment size (μm) . | Q (L/s)
. | H (m)
. | D (m)
. |
---|---|---|---|---|

0 | N/A | 10 | 0.7 | 0.5 |

A1 | 75 | 3, 5, 7 | 0.7 | 0.5 |

B1 | 100–200 | |||

C1 | 200–500 | |||

D1 | 400–800 | |||

E1 | 500–1,000 | |||

F | 75–1,000 | 7 | 0.7 | 0.5 |

Run . | Sediment size (μm) . | Q (L/s)
. | H (m)
. | D (m)
. |
---|---|---|---|---|

0 | N/A | 10 | 0.7 | 0.5 |

A2 | 75 | 3, 5, 7 | 0.7 | 0.5 |

B2 | 100–200 | |||

C2 | 200–500 | |||

D2 | 400–800 | |||

E2 | 500–1,000 | |||

M1 | 75, 100–200, 200–500, 400–800, 500–1,000 | 3, 5, 7 | 0.84 | 0.5 |

N1 | 1.05 | 0.5 | ||

M2 | 75, 100–200, 200–500, 400–800, 500–1,000 | 0.7 | 0.6 | |

N2 | 0.7 | 0.75 |

Run . | Sediment size (μm) . | Q (L/s)
. | H (m)
. | D (m)
. |
---|---|---|---|---|

0 | N/A | 10 | 0.7 | 0.5 |

A2 | 75 | 3, 5, 7 | 0.7 | 0.5 |

B2 | 100–200 | |||

C2 | 200–500 | |||

D2 | 400–800 | |||

E2 | 500–1,000 | |||

M1 | 75, 100–200, 200–500, 400–800, 500–1,000 | 3, 5, 7 | 0.84 | 0.5 |

N1 | 1.05 | 0.5 | ||

M2 | 75, 100–200, 200–500, 400–800, 500–1,000 | 0.7 | 0.6 | |

N2 | 0.7 | 0.75 |

*et al.*(2015) found that in urban runoff, the diameter of solid particles mainly ranges from 10 to 1,000 μm. Therefore, the sediments in this study are divided into five groups: 75, 100–200, 200–500, 400–800, and 500–1,000 μm. Each of the five graded sediment was screened using a standard sieve. The screening result is shown in the dotted line in Figure 2 along with the mixed sediment in solid line. The suspended solid level in the initial rainwater specified in the surface water environmental quality standards (EPB 2002) ranges from 154 to 1,367 mg/L. To ensure that the sediment content at the experimental inlet is relatively close to reality, a total sediment addition of 250 g was chosen for the experiment, with a mass rate of 4 g/s and duration of 64 s. It corresponds to a sediment content ranging from 571 to 1,333 mg/L which is close to the actual sediment content in prototype systems. One of the assumptions in the present study is that the sediment is well mixed with water without settlement when entering the separator. When the system becomes stratified due to the high sediment contents, the excessive sediment would settle before entering the separator and hence may result in a higher sediment removal rate.

### CFD model validation

Additionally, with respect to sediment removal rate, the difference between the measured and simulated value of the experiment for Runs A–E is maximum at 12.36% with a minimum of 0.2%, and the average difference is less than 10%. This indicates that the CFD model can describe the behavior of hydrodynamic separators and reliably predict their performance. Several factors can contribute to the differences between the experimental and simulated results. These factors include fluctuations in the flow rate of the water pump, measurement errors on the water surface, and the influence of placing the ADV in the water, which can affect the flow field. These discrepancies highlight the challenges in precisely replicating real-world conditions in a simulation and the inherent limitations of experimental measurements.

## RESULTS AND DISCUSSION

### Flow field analysis

*Q*= 7 L/s. From Figure 4, when the fluid enters the separator from the inlet pipe, some of the fluid is directly directed to the outlet, accounting for about 50%, and the flow direction is tangential to the separator wall. The flow then reaches the cylindrical section, where it undergoes a circular motion, forming a vortex center approximately 45° to the bottom. Due to the action of inertial forces, the fluid moves along the wall with relatively higher velocity toward the center of the circle, forming an external vortex. After the flow reached the bottom, the fluid direction then begins to redirect to upwards, forming an internal vortex that eventually discharged from the outlet pipeline. With an inlet velocity of about 0.4 m/s for almost full pipe flow at

*Q*= 7 L/s, the hydraulic retention time hence increased to an average of about 25 s in the separator from the CFD model. Compared with the hydraulic retention time of roughly 1 s for flow with 0.4 m/s velocity to pass the separator with diameter of 0.5 m, the hydraulic retention time increases by 30 times in the separator. The increased hydraulic retention time helps the sediments to settle in the separator and therefore can have a higher sediment removal rate.

The velocity distribution for *Q* = 7 L/s is shown in Figure 4(b). The overall velocity in the flow field ranges from 0 to 0.5 m/s. The figure shows the tangential velocity distribution curve of the hydrodynamic separator at different sections. At higher than 0.25 m from the bottom, the tangential velocity in the hydrodynamic separator is the highest near the wall, at 0.45 m/s, which is roughly equal to the inlet velocity. For lower elevation, the low-velocity zone gradually moves toward the inlet. Such velocity distribution helps the separation of solid sediments from water, and at the same time, it makes the sediments move toward at the center, and finally precipitate at the bottom.

### Sediment removal rate

Also, the sediment content at the outlet remains relatively high for smaller sediments. For sediment with diameter of 75 μm, the sediment content of the mixture continuously increased during the sediment-adding time 0–50 s, then reached its peak at 50, 50, and 40 s for *Q* = 3, 5, and 7 L/s, respectively. Notably, the maximum sediment content occurred about 10 s before the cessation of sediment addition, rather than simultaneously. This is primarily attributed to the delay of the sediments given the period for water flow from the sediment addition to the tailgate is about 10 s. Within the next 30 s, the sediment content at the outlet decreased and approached a low value of 50 mg/L. In comparison, the sediment with a diameter of 100–200 μm has similar pattern except for the value and the occurrence time of maximum sediment content. For sediments with diameter larger than 200 μm, the sediment content at the outlet varied little during all the observation time for all cases. This can be explained that larger sediments have greater mass and inertia and hence are hardly impacted by water flow. The sediments are collected by the separator and less follows the flow to the outlet. Therefore, there is no significant difference in their removal efficiency under different flow conditions for sediment with larger diameters. In contrast, sediments with smaller diameter are subjected to stronger eddy current and shear forces, resulting in a decrease in their separation effect as the flow rate increases.

Inside the separator, the water is forced to rotate due to the tangential inlet configuration, forming a swirling flow. As the flow rate increases, the water velocity in the hydrodynamic separator increases, resulting in a greater shear force and vortex intensity. Due to the increased shear and eddy currents, smaller diameter sediments are more susceptible to the turbulence from eddy currents, resulting in a decrease in their deposition and removal efficiency in the separator. Due to the high mass and inertia, larger diameter sediments can better maintain themselves in the vortex and ultimately deposit at the bottom of the separator. In contrast, sediments with smaller diameters are subjected to stronger vortex forces, making it difficult to maintain a stable trajectory in the vortex, thereby increasing the difficulty of their separation.

*Q*= 7 L/s, the overall removal efficiency of the sediment mix was 80.22% which is in between Runs B and C. The size distribution for the sediments left in the separator was measured and shown in Figure 7. Compared with the size distribution before the experiment, the curve rotates anticlockwise direction which corresponds to a decrease proportion of smaller sediments. Specifically, the passing percentage for diameter less than 75 μm decreases by 57% from about 7.63% to 3.26% while the change for sediments less than 500 μm decreases by 5.9% from 73.49% to 69.25%. It means that sediments with larger diameter were left in the separator. The median diameter for the sediments before and after the experiment increases from roughly 300–450 μm which also shows that sediments with larger diameter are subject to remain in the separator.

### Separator optimization

*H*), the separator with increased diameter (

*D*) has a more significant influence on the improvement of sediment removal efficiency especially on sediments with a diameter less than 200 μm.

From Figure 8, it is noticeable that for sediment size greater than 200 μm, the sediment removal efficiency reaches 100% for both increased *H* and *D* cases. With respect to sediment diameter less than 200 μm, when the *H* of the separator increased by 1.2 times, the removal rate increased slightly compared with the original case. The averaged improvement for sediment less than 200 μm was 3, 3, and 7% respectively for *Q* = 3, 5, and 7 L/s. Similarly, when the diameter of the separator increased by 1.2 times, the removal rate of sediments increased by 17, 13, and 15% respectively for *Q* = 3, 5, and 7 L/s. When the *H* of the hydrodynamic separator is increased by 1.5 times, the removal rate of sediments of 6%, 6%, and 9% for *Q* = 3, 5, and 7 L/s, respectively. For separator with 1.5*D*, the average removal rate increases by 28%, 20%, and 23% for *Q* = 3, 5, and 7 L/s, respectively. Therefore, diameter increases responses to a better performance on sediment removal especially for sediments with relatively small diameters.

*Q*= 7 L/s with improved size are shown in Figure 9. It shows that the velocity distribution of the separator as well as the angle and direction of the vortex has a slight change compared with the laboratory-size hydrodynamic separator. The analysis of the flow field in the hydrodynamic separator with increasing separator diameter reveals that the flow velocity at the separator wall ranges from 0.13 to 0.36 m/s, which is lower compared with the laboratory-size separator. Additionally, the flow velocity in the separator with increasing height reaches 0.4 m/s. In addition, the mean diameter of its vortices also increased by 20% and 50% for the 1.2

*D*and 1.5

*D*cases, respectively compared with the original case, indicating an increased room for the sediments to settle. For the height variation cases, due to the change in the depth of the cylinder, the settling distance and settling time of the sediments increase.

It can be concluded that increasing the diameter of the separator can provide a larger cross-sectional area and reduce the flow velocity of the fluid in the hydrodynamic separator. A lower flow velocity can increase the settling time of sediments, thereby increasing the residence time of sediments in the separator and improving the sediment removal efficiency. In addition, increasing the height of the separator can also help reduce fluid vortices and turbulence, minimize sediment suspension and resuspension, and further enhance the separation efficiency but the effect is smaller than increasing the diameter. Therefore, larger diameter hydrodynamic separators can more effectively settle larger diameter sediments, allowing them to deposit more quickly to the bottom of the separator. In contrast, increasing the separator height only affects the residence time of sediments, but does not significantly change their settling speed. Therefore, the increase in diameter has a greater impact on sediment removal compared with the height of the separator. Further research is needed to fully understand the sediment removal in real-size separators.

### Efficiency comparison

*et al.*2009):where

*D*and

*h*are the diameter and depth of the separator, respectively,

*Q*is the flow rate and

*V*is the settlement velocity of sediment which can be calculated by the following equation proposed by Cheng (1997).where

_{s}*d*is the sediment size,

_{p}*ρ*and

_{s}*ρ*are the density of sediment and water, respectively. In addition,

_{w}*ν*is the kinetic viscosity of water. When the measured removal efficiency is plotted by the Péclet number, a removal efficiency function for a specific stormwater treatment device can be developed and can be written as:where

*R*,

*a,*and

*b*are fitting parameters. In particular, the parameter

*R*indicates the removal rate as the Péclet number approaches infinity,

*a*is the initial slope of the curve at

*P*= 0 and

_{e}*b*is a measure of the curvature in the function at

*P*=

_{e}*R*/

*a*.

*V*

_{s}) for each sediment size group is taken, ranging from 0.0035 to 0.088 m/s. Figure 10 is a plot of the experimental and simulation data on the removal efficiency versus Péclet number, along with Yang

*et al.*(2022). The figure illustrates that the experimental data have similar trends for different set-ups. For all experimental data, sediment removal efficiencies exhibit an increase from 0% to approximately 100% for Péclet number ranging from 0.1 to 10. From the trend of scatter, the sediment removal rate is a positive correlation with Péclet number and the gradient of the change in the efficiency varies from small to large and finally returns to small. This situation signifies that the sediment removal efficiency remains relatively stable at very low or high values of flow rates, settling velocities, and outlet diameters. However, it undergoes rapid variations when transitioning between these extreme values. For example, the sediment removal rate rises rapidly when the Péclet number is between 0.1 and 1 and increases slowly in the range of 95–100% after Péclet number reaches 1.

Table 3 shows the fitting parameter of Equation (3). The sediment removal rate of the unimproved model falls between the improved models. Its parameter values are *R* = 0.99, *a* = 3.24, and *b* = 1.07. Compared with the improved models, it has a larger value of *a* and a smaller value of *b*. This may lead to a larger initial slope but smaller curvature, resulting in a moderate sediment removal rate. For 1.2*D* and 1.5*D* cases, the *a* value changes to more than 2.0 and the *b* value increases to 1.3 indicating a rapid increase in the removal rate with a higher curvature and the removal rate tends to approach *R* more quickly than the original design as well as the 1.2*H* and 1.5*H* design, which is desired in normal operation conditions. In contrast, the 1.2*H* and 1.5*H* models share the same *R* value at *R* = 1, but the values of *a* and *b* are between the original model and the 1.2*D* and 1.5*D* model. This may result in a moderate initial slope and curvature, leading to a sediment removal rate performance in between the original design and separator diameter variation cases. The model of Yang *et al.* (2022) exhibits the lowest sediment removal rate with *R* = 0.97, *a* = 0.58, and *b* = 5.74. This may result in a smaller initial slope although a significantly larger curvature, leading to a decreased sediment removal rate. Therefore, the sediment removal rate of the improved model is higher than that of the unimproved model. The ratio of Hazen number (defined as: ) and Péclet number is *h/D*. Therefore, for a separator with a given geometric dimension, the Hazen number and Peclet number can be used interchangeably for assessing the removal rate.

Setup . | R
. | a
. | b
. |
---|---|---|---|

Original design | 0.99 | 3.24 | 1.07 |

1.2D | 1 | 2.78 | 1.3 |

1.5D | 1 | 2.36 | 1.4 |

1.2H | 1 | 1.98 | 1.18 |

1.5H | 1 | 1.57 | 1.22 |

Yang et al. (2022) | 0.97 | 0.58 | 5.74 |

Setup . | R
. | a
. | b
. |
---|---|---|---|

Original design | 0.99 | 3.24 | 1.07 |

1.2D | 1 | 2.78 | 1.3 |

1.5D | 1 | 2.36 | 1.4 |

1.2H | 1 | 1.98 | 1.18 |

1.5H | 1 | 1.57 | 1.22 |

Yang et al. (2022) | 0.97 | 0.58 | 5.74 |

### Evaluation of sediment removal efficiency of hydraulic separator

*J*written as:where

*C*is the length of the route for the flow to travel from the inlet to the outlet of the separator, as shown as

*C*

_{50}in Figure 11,

*V*

_{s}is the sediment settling velocity calculated by Equation (2),

*h*is the elevation difference between water surface at the inlet pipe and the invert of the downstream pipe, and

*V*

_{0}is the inlet water velocity.

The *J* value is a dimensionless parameter calculated based on the size of the hydraulic separator, the settling velocity of sand sediments, and the water velocity rather than a curve fitting. The physical meaning of the value is the ratio between the ‘time for the water to travel from the inlet to the outlet in the separator’ and the ‘time for the sediments to settle from the inlet water surface to the invert of the downstream pipe’. This parameter provides a key indicator when designing or optimizing such a hydraulic separator. The dynamic similarity does not apply to the *J* value since the value itself takes the dimension of the geometry into consideration. Ideally, for flow condition with *J* > 1, the time for sediments to settle below the invert of the downstream pipe is less than the time for water to travel from the inlet to the outlet and hence corresponds to a higher removal rate compared with the *J* < 1 cases. In an actual separator, due to the complex swirling flow field, the interaction between water flow and sediments can be complicated and hard to predict. The *J* value does not always have to be higher than one for a satisfactory sediment removal rate. Nevertheless, Equation (4) still provides a straightforward way of assessing the performance of a hydrodynamic separator.

For the tested cases in the present study, for a separator with diameter of 500 mm, which corresponds to *C* = 0.785 m, inflow rate of 3 L/s with half full pipe flow in a 150 mm diameter inlet pipe, which results in *V*_{0} = 0.34 m/s and *h* = 0.075 m. For sediment with diameter of 150 μm, the settling velocity *V*_{s} is 0.012 m/s. For the above case, Equation (4) yields a *J* value of 0.36 which is less than 1 and the actual measured sediment removal rate was 65.80%. For sediment diameter of 250 μm, the settling velocity is 0.027 m/s, and the *J* value increases to 0.83 which corresponds to a measured removal rate of 98.60%. Therefore, with *J* value increasing, the performance of the hydrodynamic separator increases.

In the context of separator dimension optimization cases, when the separator diameter is increased by 1.2 and 1.5 times compared with the original design, for the same flow condition above, the *J* value increases to 0.43 and 0.54 for sediment diameter of 150 μm which corresponds to a removal rate of roughly 80% and 90%, respectively. For larger sediments at 250 μm, the *J* value increases to 1.00 and 1.25, respectively for 1.2*D* and 1.5*D*, all of which reaches about 100% removal rate. For separator height modification, since it does not affect the physical parameters in Equation (4), the *J* value remains the same as the original design and the measured removal efficiency only improved slightly to roughly from 65.8% to 70% and from 98.6% to 99% for sediment diameter of 150 and 250 μm, respectively. For engineering applications, one can design or optimize a hydrodynamic separator if the flow condition is given. The design flow rate of the system and the flow depth can determine the inlet velocity *V*_{0}, and the elevation difference *h*. The local sediment size distribution can be measured, and the median diameter can be used to determine the *V*_{s}. Once the preliminary design is completed, the *C* can be determined and the *J* value for the design can be therefore calculated. The goal of the design is to adjust design parameters to achieve a higher *J* value while still satisfying the design requirements such as footprint, budget, construction, and accessibility.

*J*value for the tested cases. From the figure, it can be clearly observed that there is a positive correlation between the removal efficiency and

*J*value. As the

*J*value exceeds 0.6, the corresponding removal efficiency approaches 100%. Based on our experimental and numerical work, it can be found that when the

*J*value reached above 0.5, the sediment removal rate already reached above 80% and it may be a good preliminary target value for designing such a separator.

## CONCLUSIONS

This study has investigated the performance of a hydrodynamic separator by physical experiments and CFD simulations. After a systematic analysis and discussion, the following conclusions can be drawn. The validated CFD model reveals that the swirling flow field provides a tendency for the sediments to gather to the center of the separator and settle which improves the removal efficiency especially for larger sediments with higher mass and inertial. The physical experiment shows that under different flow conditions, the sediment with diameter greater than 200 μm experiences a relatively stable high removal efficiency above 90%.

In addition, it was found that increasing the diameter of the separator generates a more significant increase in the removal efficiency under the same flow conditions compared with the cases increasing the height of the separator. The physical and CFD experiment also found a positive correlation between the sediment removal rate and Péclet number, indicating that Péclet number can effectively predict the removal efficiency of sediments in hydrodynamic separators.

A way of assessing the design and performance of hydrodynamic separators are proposed by using a dimensionless parameter *J*. The removal rate is positively correlated with the *J* value. When the *J* value reaches 0.5 or above, the sand removal rate has reached over 80%. When the *J* value exceeds 0.6, the corresponding removal rate approaches 100%, the key to design the separator is to make the *J* value at a reasonable higher range while still satisfying the design requirements such as footprint, budget, construction, accessibility, etc. Engineers and researchers can therefore optimize the design and operation of hydrodynamic separators to improve the efficient removal of solid sediments from water flow. In addition, our research also provides important references for future research and engineering practice to improve the separation efficiency.

Nevertheless, there are still gaps that have not been yet addressed in this study. First, the scale effect of the sediment and water interaction is still missing. This study features a lab-scale model for both physical and CFD model. Although the flow field, removal efficiency and some theoretical equations were proposed, the actual performance of a larger prototype scale model is to be assessed. Second, the design of the separator in the present study is more of a conceptual design without a prototype scale model verified and hence a prototype device installed in real-storm system is to be monitored for a better understanding of the performance of the swirling-type hydrodynamic separator.

## ACKNOWLEDGEMENTS

This study is supported by the Key R&D Program of Zhejiang Province (2020C03082). The authors would also like to acknowledge the technical support from Weidong Li, Zi Ye, and Jingyan Mao.

## 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.