This study investigated the hydraulic characteristics of stormwater sumps and their design optimization for sediment retention using physical experiments. Particle image velocimetry was utilized to measure the flow field, and the use of internal structures was investigated for improving solids retention. Results indicate that these internal structures can significantly improve the sediment removal efficiency of suspended solids with an average size of 125 μm, resulting in an efficiency improvement of 20–30%. Additionally, a modified Péclet number was proposed to more accurately evaluate the sediment removal efficiency of stormwater sumps, and recommendations were provided for further improving and optimizing sump design. This study provides insights into the hydraulic characteristics of stormwater sumps and has important implications for optimizing and designing particle removal systems for various industrial and environmental applications.

  • The study demonstrates that incorporating enhancements leads to a substantial increase (20–30%) in the efficiency of removing suspended solids in stormwater sumps.

  • The study introduces a modified dimensionless number that provides a more precise evaluation of sediment removal efficiency in stormwater sumps.

  • The study highlights that scaling, with a ratio of up to 6, can reasonably predict particle removal efficiency.

Urban stormwater runoff is one of the major sources of urban water pollution, comprising particulate matters of varying sizes, heavy metals, and organic matters (Aryal & Lee 2009). These sedimentary particles are the primary carriers of pollutants and pathogens and their direct discharge to receiving water can lead to varying degrees of contamination. Catchbasin sumps are an essential component of stormwater collection networks, which have proven to be effective in retaining floatables, capturing large debris, and reducing the buildup of deposition in sewers (Lager et al. 1977; Hvitved-Jacobsen et al. 2010). Underground stormwater treatment devices were also commonly used to reduce suspended solids (Roseen et al. 2005; Fassman 2006). In comparison to end-of-pipe treatment devices, stormwater sumps occupy a smaller land footprint, which is highly desirable in densely populated urban areas (Field et al. 2003; Erickson et al. 2013). In addition, sumps can be used in series to achieve multi-stage solids control. Therefore, maximizing the capability of existing sumps to remove sediment is an intriguing area of interest, such as incorporating simple inserts and the like (Aronson et al. 1983; Brar et al. 2016). An optimal modified stormwater sump must not only enhance its particulate retention efficiency but also minimize its impact on drainage capacity and its maintenance cost (Pitt & Field 2004).

Numerous studies on the standard sump, by laboratory testing, field monitoring, and/or computational fluid dynamics modeling, reveal that the configuration and size, inflow rate, and particle settling velocity are all important factors in determining the sediment removal efficiency of sumps (Wilson et al. 2007; Pathapati & Sansalone 2009; Howard et al. 2012; Kaushal et al. 2012; McIntire et al. 2012). Nondimensional parameters were found to be useful to analyze the overall functionality and efficiency of sumps, including the Hazen number, Froude number, and Péclet number (Wilson et al. 2009; Guo 2017; Yang et al. 2022). Howard et al. (2012) evaluated the removal efficiency of standard stormwater sumps of varying sizes and found that the sumps can effectively remove suspended sediment from stormwater runoff, although not as effectively as dedicated hydrodynamic separators. The relationships between the removal efficiency and system parameters were identified by an integral approach in earlier studies, and there is still a lack of quantified information and in-depth analysis on hydraulic characteristics of the flow field in the sump that are crucial for optimizing and novel designs.

A number of sump inserts and/or internal structures were studied to improve the management of wet-weather flow solids (Pitt & Field 2004; Andoh et al. 2007; Brar et al. 2016). Various sump inserts were found to be useful for gross solids removal, although considerable variability has been reported in the results (Lau et al. 2001; Walch et al. 2004; Alam et al. 2018; Basham et al. 2019). Filter fabrics were used with special care for capturing fine particulates, as they get clogged so quickly that the maintenance cost becomes an issue (Pitt & Field 2004). When dealing with a large flow rate, catchbasin inserts are inclined to cause flow choking and scouring contamination (Walch et al. 2004; Brar et al. 2016). A hooded outlet design was recommended as it can withstand extreme flows with little scouring losses in Pitt & Field (2004). A few internal structure add-ons were tested and found to provide a good balance between solids control and hydraulic performance (Howard et al. 2011; Ma & Zhu 2014). However, most of such designs lack a well-defined physical foundation and are challenging to continuously optimize using established metrics in order to attain better performance. This difficulty is due, in part, to the absence of a determined functional relationship between the flow features and solids movement, especially for sumps.

The present study aimed to investigate the flow characteristics of a sump with and without modifications and to provide insight into the solids retention efficiency as a function of various physical characteristics, including particle size, settling velocity, flow rate, and sump geometry. In laboratory testing, a particle image velocimetry (PIV) device was employed to quantify and analyze the flow field. Additionally, the study explored scaling relationships for predicting the performance of stormwater sumps of different sizes.

Experimental setup

The experimental model consists of two pipes and a circular sump made of plexiglass (Figure 1). The sump has an inner diameter (D) of 20 cm and a total height of 40 cm. The inlet and outlet pipes both have a diameter of 4 cm. The inlet pipe invert is positioned 26.3 cm above the bottom of the sump and 1 cm above the outlet pipe invert. An electronic flow meter (TM20SQ9GMB, Flomec GPI TM) with a 0.5% full-scale accuracy measured the inlet flow rate, and the flow meter has a range of 3.6–76 L/min. The sand feeder employed a pre-mixing process that involved mixing particulates and water to form a slurry. This mixture was then dispensed at a controlled rate through a regulating valve. The sand feeder was positioned 18.0 cm upstream of the sump to guarantee thorough intermixing of the slurry before its introduction into the sump. This arrangement also promotes the unobstructed entry of all particles into the sump, thus preventing any potential sedimentation within the upstream conduit. According to Guo (2017), two conditions must be fulfilled in the experimental testing: (1) the inlet flow should be turbulent and (2) the Weber number should be higher than a critical value of 100 to prevent the surface tension from affecting the flow field. These conditions were satisfied by the model used in this study, despite its relatively small sizes.
Figure 1

Schematic of the experimental setup.

Figure 1

Schematic of the experimental setup.

Close modal

Sump with internal structures

In order to improve the efficiency of sediment removal by the sump, internal structures were designed as shown in Figure 2. The upper part was intended to generate vortex generation and the lower part was for sediment settling. The plate separates the flow and produces two vortices in opposite directions within the constraints of the plate and the side wall. The effect of the vortices is to transport the particulate matter downward rapidly. The principle of the inclined plate sedimentation tank (Saleh & Hamoda 1999) was adopted, which enabled the rapid deposition of sediment on the inclined plates. The particles then slid down to the sump bottom through the gaps between the plates.
Figure 2

Illustration of the stormwater sump with internal structures: (a) photograph of the experimental apparatus; (b) detailed design.

Figure 2

Illustration of the stormwater sump with internal structures: (a) photograph of the experimental apparatus; (b) detailed design.

Close modal

Testing details

It was discovered that over 50% of particles had a diameter greater than 125 μm in German & Svensson (2002). Additionally, Sansalone et al. (2010) conducted statistical surveys and found that roughly 10% of particles were less than 100 μm in diameter, while particles with diameters between 100 and 400 μm constituted approximately 25–60% of the distribution. Therefore, for the experiments in this study, non-cohesive quartz sand particles with a density of 2,650 kg/m³ were selected within a size range of 100–150 μm, with a mean value of 125 μm. The discharge range associated with free surface conditions is Q = 0.1–0.3 L/s, while the discharge range related to full pipe flow conditions is Q = 0.4–0.5 L/s. To conduct removal efficiency testing, sediment was continuously fed into the entrance pipe in the form of slurry, with a sand feeding rate in the range 36–286 mg/s (Table 1). The sediment concentration of the incoming flow was in the range of 72–2,860 mg/L. The quantity of sediment particles fed into the pipeline was pre-determined by weight. The captured solids in the sump were collected, dried by a drying chamber (DHG-9240A Heating and Drying Oven), and then weighed by a high precision electronic scale (QUINTIX35-1CN). Therefore, the removal efficiency, conventionally defined as the ratio of the sediment particles retained in the sump to the total introduced, was assessed using a mass-based method.

Table 1

Experimental cases

No.Feeding rate fd (mg/s)Q (L/s)C (mg/L)
36–286 0.1 360–2,860 
0.2 180–1,430 
0.3 120–953 
0.4 90–715 
0.5 72–572 
No.Feeding rate fd (mg/s)Q (L/s)C (mg/L)
36–286 0.1 360–2,860 
0.2 180–1,430 
0.3 120–953 
0.4 90–715 
0.5 72–572 

A camera (SONY FDR-AX60) with a high resolution of 3,840 × 2,160 was used to record the flow field at 50 frames per second and the two-dimensional PIV technique was applied to obtain the velocity field in the sump. The particles with a diameter of 10 μm and density of 1,010 kg/m3 were chosen as PIV tracers. The particle size and density ensured minimal interference with the flow while allowing for reliable tracking and measurement of flow velocities. Following the approach of Beg et al. (2018), to minimize the error caused by refraction through the curved manhole wall, the sump was put within a square acrylic tank filled with water, in front of which the camera lens was positioned. The laser was directed from the top of the sump as a laser sheet with a thickness of approximately 5 mm. To ensure the relative stability of the water flow, we conducted continuous operation for approximately 20 min. During this period, the stability of the system was assessed by measuring the stability of the liquid level of the sump. To ensure the reproducibility of the experiment, each operating condition was replicated at least three times.

Flow field in a conventional sump

The flow dynamics within the sump exert a significant influence on particle motion. As illustrated in Figure 3, particles exit the sump through two distinct pathways: some are swiftly carried to the outlet, called short-circuiting (Howard et al. 2012), while others initially enter the sump, driven downward by the circulation and then propelled toward the outlet. However, the intensity of these vortices experiences varying degrees of modulation contingent on the inflow rate. Figure 3 displays two typical flow patterns under different flow rates. Under lower flow conditions, a substantial vortex forms in the lower right quadrant (Figure 3(a)). Conversely, higher flow rates result in a reduction of the dominant vortex and a phenomenon known as vortex splitting (Figure 3(b)).
Figure 3

Typical mean velocity field in ordinary sump; measurements taken below the outlet pipe in the sump centerline plane. (a) Q = 0.1 L/s; Experiment A, (b) Q = 0.3 L/s; Experiment C.

Figure 3

Typical mean velocity field in ordinary sump; measurements taken below the outlet pipe in the sump centerline plane. (a) Q = 0.1 L/s; Experiment A, (b) Q = 0.3 L/s; Experiment C.

Close modal
To investigate the relationship between the flow field and the particle removal rate, we present the velocity distribution along the central longitudinal section of the flow field in Figure 4. The velocity distribution provides insights into how flow velocities vary across this specific cross-sectional plane, contributing to a better understanding of the underlying dynamics. The diameter of the sump, D, and the inflow velocity, Ujet, were used to normalize the horizontal location and the vertical component of velocity, respectively. The study revealed that the velocity profiles demonstrated a self-similar pattern, with downward flow primarily occurring within a zone extending from the downstream wall to 0.2D inside. The maximum vertical velocity downward, for the sump under investigation, was approximately 40% of the average inflow velocity, whereas the upward velocity was approximately 10%.
Figure 4

Mean vertical velocities measured in the middle section (y = 0.5H), and turbulent kinetic energy in the sump. (a) Vertical velocity profiles under different rates, y = 0.5H; (b) vertical velocity profiles at different heights, Q = 0.3 L/s; (c) integrated results of turbulent kinetic energy in the sump.

Figure 4

Mean vertical velocities measured in the middle section (y = 0.5H), and turbulent kinetic energy in the sump. (a) Vertical velocity profiles under different rates, y = 0.5H; (b) vertical velocity profiles at different heights, Q = 0.3 L/s; (c) integrated results of turbulent kinetic energy in the sump.

Close modal

Eddy diffusion is a crucial parameter for assessing particle retention efficiency, which can be directly related to the fluctuating component of the velocity (Siegel et al. 1990). It follows that the eddy diffusion can be represented by the turbulent intensity or the total kinematic energy (TKE). In Figure 4(c), we have provided the values of calculated turbulent kinetic energy (TKE) corresponding to the different test cases. The data in this figure clearly demonstrate a noticeable trend: as the discharge rate increases, there is a corresponding rise in the TKE values. This observation implies that the intensity of eddy diffusion also increases as the discharge rate is raised.

However, to satisfy the request for further discussion and explanation, we need to delve deeper into the implications of this relationship. The connection between TKE and eddy diffusion is pivotal in understanding the mechanisms at play here. Eddy diffusion refers to the dispersion caused by turbulent eddies in a fluid flow. When the TKE increases, it signifies a higher level of turbulence within the flow field. This heightened turbulence leads to greater mixing and diffusion of particles or substances present in the fluid.

The relationship between TKE and eddy diffusion can be attributed to the fact that higher TKE values indicate a more energetic flow, with stronger and more frequent eddies. These turbulent eddies contribute significantly to particle transport and dispersion, influencing factors such as particle retention and mixing efficiency. Therefore, the observed correlation between increasing discharge, rising TKE, and enhanced eddy diffusion highlights the sensitivity of particle behavior to fluid dynamics.

In conclusion, while the presented data clearly illustrate the connection between rising TKE and increasing discharge, a more comprehensive analysis reveals that this relationship is intricately tied to the concept of eddy diffusion. The heightened TKE values signify a more turbulent flow, resulting in amplified eddy diffusion, which in turn has notable implications for particle retention efficiency and mixing patterns.

Figure 5 shows the horizontal velocity variation in depth along the vertical centerline of the sump. The discrepancy between the experimental data in the present study and that in Howard et al. (2012) can be attributed to the sump size and configuration. For the sump in Howard et al. (2012), the characteristic length ratios are h/D = 1 and D/d = 3, whereas for the sump in this study, h/D = 1.3 and D/d = 5. These differences resulted in a reduction of approximately 20% in the maximum velocity of the bottom flow.
Figure 5

Horizontal velocity with respect to depth along the vertical centerline of the sump.

Figure 5

Horizontal velocity with respect to depth along the vertical centerline of the sump.

Close modal

Flow field in the improved sump

The flow field in the improved sump is shown in Figure 6. Due to the presence of the internal structures, the flow has to pass through the bottom region/passage below the baffle. This area has an effectively larger cross-sectional area compared to the inlet, resulting in a pronounced reduction in the average velocity within it. The average velocity was approximately 1/10 of the inflow, which provided favorable conditions for particle sedimentation. It is worth noting that once the particles are captured by the inclined plate, a higher velocity is required to re-suspend them. The rising flow on the right side had a larger velocity near the outlet, while the velocity away from the out was relatively smaller or even reversed. It can be seen from the profile velocity data that both the forward and reverse velocity of the upwelling flow were proportional to the flow rate (Figure 7).
Figure 6

The mean velocity field within the improved sump was analyzed along the longitudinal cross-section. (a) Q = 0.1 L/s; Experiment A, (b) Q = 0.3 L/s; Experiment C.

Figure 6

The mean velocity field within the improved sump was analyzed along the longitudinal cross-section. (a) Q = 0.1 L/s; Experiment A, (b) Q = 0.3 L/s; Experiment C.

Close modal
Figure 7

Flow field features in the sump with internal structures: (a) Vertical velocity profiles along the horizontal centerline in the region to the right (downstream) of the baffle (y = 0.5H); (b) maximum values of normalized vertical velocity versus normalized Q, where d is the inflow pipe diameter.

Figure 7

Flow field features in the sump with internal structures: (a) Vertical velocity profiles along the horizontal centerline in the region to the right (downstream) of the baffle (y = 0.5H); (b) maximum values of normalized vertical velocity versus normalized Q, where d is the inflow pipe diameter.

Close modal

Sediment removal efficiency

To evaluate the effectiveness of particle removal in sumps and underground settling devices, the Péclet number (Equation (1)) is utilized. This number represents the ratio of settling to mixing by turbulent diffusion (Dhamotharan et al. 1981) and has been used by Mohseni & Fyten (2007) and Wilson et al. (2009) to scale removal efficiency in underground settling devices.
(1)
where Vs is the settling velocity, h is the water depth in the sump, D is the diameter of the sump, and Q is the inflow rate. Settling velocity can be calculated following Cheng (1997):
(2)
where ν is the kinematic viscosity of water; ds is the particle diameter; ρs is the particle density with a value of 2,650 kg/m3 in the present study; ρ0 is the water density with a value of 1,000 kg/m3 here; g is the gravitational constant.
The solids removal efficiency (η) for standard sumps has been related to the Péclet number and inflow Froude number (Wilson et al. 2009; Howard et al. 2011). Assuming that the removal rate approaches 100% when the flow tends to zero, the equation to describe the relationship between η and Pe/ can be written as follows:
(3)
where B and b are parameters to be determined. To determine the fitness of Equation (3) to the data in Figure 8, the Nash–Sutcliffe coefficient (NSC) was calculated according to the following equation.
(4)
where ηi presents the measured value, ηc the simulated value, and η0 the mean of the measured value. The closer the NSC value is to one, the higher the correlation between the predicted value and the measured data. The values of the fitting curve parameters B and b in Figure 8 are 1.22 and 3.7, respectively. The corresponding NSC is 0.9.
Figure 8

Parameter Pe/ versus efficiency η for standard sumps.

Figure 8

Parameter Pe/ versus efficiency η for standard sumps.

Close modal
The inflow Froude number is applied as a scaling parameter (Howard et al. 2011; Ma & Zhu 2014), which was defined as Frjet = Ujet/(gD)0.5, where Ujet is the mean velocity of the inflow. The Froude number obtained from the experiments plotted against dimensionless flow rates is given in Figure 9, indicating that the inlet flow velocity (Ujet) and number remained essentially the same before and after the improvement.
Figure 9

Mean velocity of the inflow and jet Froude number for a variety of flow rates. (a) Velocity of inflow versus flow rate, (b) inflow jet Froude number versus flow rate.

Figure 9

Mean velocity of the inflow and jet Froude number for a variety of flow rates. (a) Velocity of inflow versus flow rate, (b) inflow jet Froude number versus flow rate.

Close modal
It should be recognized that the empirical function for assessing the removal efficiency needs to be applicable to both standard and improved sumps. The normalized parameter Pem, which can be expressed as:
(5)
where Uc is the characteristic flow velocity. For the ordinary sumps, the average velocity at the inlet can be selected as the characteristic value, which is the discharge divided by the cross-sectional area of the flow. This characteristic velocity exhibits a dual significance. First, it is the inflow that drives the flow field inside the sump, consequently influencing the sedimentation of particles therein. Second, it correlates with the quantity of particles that are entrained and carried away by the water flow directly. However, in an improved sump with internal structures, the average velocity entering the settling zone is chosen as the characteristic velocity.
From Figure 10(a), it can be observed that using the commonly used Péclet number fails to unify the data from various studies. The recalculated Pem/ values are plotted in Figure 10(b), and the equation for the solid line that well fits the data was obtained by regression analysis as follows:
(6)
The fitting has an NSC = 95.31% for η.
Figure 10

Relationships between the removal efficiency and (a) Pe/; (b) Pem/.

Figure 10

Relationships between the removal efficiency and (a) Pe/; (b) Pem/.

Close modal
Data from this experiment show that variations in particle concentration have negligible influence on the removal rate at the same flow rate (Figure 11). The possible sources of variability include measurement errors, experimental uncertainties, and natural variations in particle size and shape. To assess the variability of the measurement data, the standard deviation of the removal rates was calculated for each particle concentration. The maximum standard deviation value is 0.02, indicating that the data are consistent and reliable.
Figure 11

Effect of inflow concentration on sediment removal rate.

Figure 11

Effect of inflow concentration on sediment removal rate.

Close modal

Scale effect analysis

Scale effects refer to the disparities between experimental outcomes and real-world scenarios attributed to differences in scale. When investigating sediment removal efficiency in a stormwater sump, acknowledging and addressing these scale effects is crucial. Therefore, it is imperative to scrutinize these effects thoroughly to gain a deeper understanding of their influence on sediment removal efficiency.

The hybrid scaling formula proposed by Fenner & Tyack (1997) can be applied as follows.
(7)
where the subscripts A and B indicate prototype and model, respectively; dp is the mean particle diameter in mm; and Lr is the length ratio of scale A to scale B. The results obtained from the scale model in this study can be adjusted using Equation (7) to facilitate the comparison with findings from studies conducted at varying scales. In the experiments conducted in the present study, the diameter of the sump D = 20 cm, whereas in the study by Howard et al. (2012), two setups were employed with diameters of D = 30 and 120 cm, respectively. Consequently, the comparison of results in Figure 12 was based on Lr = 1.5 and Lr = 6.0.
Figure 12

Particle removal efficiencies at different flow rates: comparison of the estimated values after using the model scaling in this study and the experimental data from Howard et al. (2012) for (a) Lr = 1.5 and (b) Lr = 6.0; comparison between ordinary and improved sumps for (c) Lr = 1.5 and (d) Lr = 6.0.

Figure 12

Particle removal efficiencies at different flow rates: comparison of the estimated values after using the model scaling in this study and the experimental data from Howard et al. (2012) for (a) Lr = 1.5 and (b) Lr = 6.0; comparison between ordinary and improved sumps for (c) Lr = 1.5 and (d) Lr = 6.0.

Close modal

It can be observed in Figure 12(a) and 12(b) that when the model is scaled up by 1.5 times, the predicted values agree well with the experimental results in Howard et al. (2012). When the model is scaled up by six times (to the standard size), there are notable differences at low flow rates, and the discrepancies reduce as the efficiencies both approach zero at high flow rates, as expected. For instance, at a flow rate of 50 L/s, the predicted retention rate is about 10% higher than the actual value, and this gap will further decrease as the flow rate increases.

Figure 12(c) and 12(d) illustrate the changes in sediment retention rates obtained by upscaling the improved model. Following sump enhancements, the sediment retention rate for a sump with a diameter of 120 cm increased from 20 to 50% under a flow rate of 50 L/s, marking an efficiency improvement of approximately 30%. It is evident that the particle removal efficiency of stormwater sumps with proper internal structures increases significantly.

To enhance the retention efficiency of stormwater sumps, two general approaches have been explored in previous studies. Howard et al. (2011) achieved promising results by reducing the inlet flow rate through the incorporation of Saint Anthony Falls Laboratory (SAFL) baffles, which proved particularly effective during low flow rates. On the other hand, Ma & Zhu (2014) adopted a different strategy by partitioning the rectangular sump into multiple channels, thereby increasing the particle retention rate by extending the residence time. Their comparative analysis demonstrated an efficiency improvement of approximately 10%. In our experiments, an innovative device was introduced that applies the principle of inclined plate sedimentation to further enhance retention efficiency. By reducing the settling distance, this approach yielded a substantial increase in the retention rate, measuring over 30% for a large flow rate range. These findings underscore the significance of exploring various retention-enhancing techniques, each offering unique advantages in stormwater sump design. As future research endeavors continue, it is essential to evaluate the feasibility and potential synergies of integrating multiple techniques to achieve even higher retention rates and foster sustainable urban water management practices.

The data from previous studies, such as Saddoris et al. (2010), Howard et al. (2011), and McIntire et al. (2012), suggest an empirical relationship that exists between particulate removal efficiency and Pe/Fr2 in conventional sumps. The current study further confirms this relationship holds even in optimized sumps, with only necessary corrections for the dominant dimensionless parameters. The addition of internal structures substantially alters certain parameters related to particulate removal efficiency. Once the parameters are uniformly described for both conventional and optimized sumps, the empirical formulas become universal and can guide sump optimization.

The small scale of the physical model used here necessitated careful comparison to previous larger-scale experimental data to quantify scale effects. This analysis delineates the application scope of conclusions from the current study. Accounting for scale dependencies enables first-order estimation of particulate removal efficiency in full-scale systems based on empirical relationships.

The findings of this study, especially the relationship equation between Pem/Fr2 and sediment removal rate after modification, offer data-based guidance for the design and improvement of stormwater sumps. It should be noted that, in practical applications, as the bottom space fills up, there is a risk of captured solids causing clogging or being washed out. Further investigations are warranted to optimize the volume allocated for sediment storage.

This paper presents hydraulic characteristics of conventional and improved storm sumps and examines the corresponding solids removal efficiency. The following conclusions can be drawn:

  • (1)

    The adoption of the enhanced model, which incorporates methodologies such as lengthening the water flow path, attenuating flow velocity, and facilitating particle adhesion, yields a substantial increase in the particle removal efficiency of stormwater wells. The observed efficiency improvement achieved with the upgraded model is approximately in the range of 20–30%.

  • (2)

    The results demonstrate that using the modified Péclet number (Pem) provides a better estimation of particle retention rates. The addition of internal structures can be considered as effectively modifying Pem. Overall, the modified Peclet number enables unified empirical modeling of particle retention rates across sump configurations by encapsulating the effects of internal structures on the effective settling parameters.

  • (3)

    When the scale ratio (prototype size : model size) is small, particle removal efficiency can be modeled with reasonably good accuracy. However, for scale ratios greater than 6, scale effects become significant and should be considered in the modeling to properly represent particle removal efficiency.

This investigation was supported by the Ningbo Young Technology Innovation Leading Talent Program (2023QL028), Natural Science Foundation of China (52009087), the Natural Science Foundation of Zhejiang Province (LGF19E090005, LY21E090003) and the key Research and Development Program of Zhejiang Province (2020C03082).

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

The authors declare there is no conflict.

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