Hydraulic modeling of a compact stormwater treatment device applying concepts of dynamic similitude Open Access

Due to increasing knowledge of pollutant pathways, new urban stormwater management practices have been developed in recent decades, which are commonly referred to as best management practices (BMPs), stormwater control measures (SCM) or low impact development (LID) (Fletcher et al. 2015). These include compact treatment devices (CTDs) integrated into the underground stormwater sewer system, which treat stormwater in a decentralized or semicentralized manner and are often designed for the treatment of road runoff. Road runoff is known to be heavily polluted with particulate matter and soluble pollutants. Particulate matter is often generated by tire, brake and road wear and consists to a large extent of particles in the spectrum of ≤63 μm (Gelhardt et al. 2017). Additionally, the transport of many pollutants can also be attributed to particulate matter, since they are partly present in particle-bound or particulate form (Maniquiz-Redillas & Kim 2014; Huber et al. 2016). The retention of fine particulate matter ≤63 μm in CTDs is therefore a decisive criterion for their effectiveness and has recently been defined as a target parameter for stormwater treatment in German worksheets (DWA & BWK 2020). Therefore, some CTDs combine an upstream sedimentation with a filter stage within a single system (CTD-SF) to achieve the highest possible retention of fine particulate matter. The upstream sedimentation stage reduces the filter load and can thus extend the time until the filter clogs (Herr & Sansalone 2015). The lifetime of the filter stage is an important operating cost factor, as it determines the maintenance intervals. Therefore, evaluating the effectiveness of the sedimentation stage in a CTD-SF is critical because it directly affects the filter loading and thus the life of the filter stage. In addition, filtration mechanisms depend on a number of variables, of which the size of the particles in the influent and the grain size of the filter medium play an important role (Kandra et al. 2015).

However, there is little information on the different separation mechanisms in CTD-SFs, and most of the investigations have been performed on the less complex CTDs without a filter stage. Existing information on CTDs comes either from laboratory tests developed and conducted for the purpose of design approval or, less frequently, from in situ field studies. While in situ studies can provide important information on the retention to be expected in the field, they are often subject to greater measurement uncertainties under highly variable conditions (Langeveld et al. 2012; Lieske et al. 2021). Full-scale laboratory tests allow testing under controlled conditions. However, they require test rigs with appropriate hydraulic capacity and capabilities for automated metering of larger quantities of test material (Boogaard et al. 2015; Neupert et al. 2021). Here, too, some uncertainties may still exist due to partial volume sampling of large quantities of volume flow (Dufresne et al. 2010; Neupert et al. 2021). Some devices (CTDs and CTD-SFs) on the market are designed for catchment areas of up to 30,000–45,000 m² with a maximum hydraulic treatment capacity of roughly 45 to 70 L s⁻¹, respectively (Sommer et al. 2015). The volume of filter substrate used in CTD-SFs can range from about 0.4 to 0.03 L m⁻² catchment area depending on the device (Grüning & Schmitz 2018). For CTD-SFs, the investigation of sedimentation efficiency is particularly challenging, since it requires a representative measurement upstream of the filter stage or access to the sedimentation chamber. In addition, it can generally be assumed that the flow resistance of the filter stage influences the flow through the upstream sedimentation chamber (Stricker et al. 2022). Therefore, the effectiveness of the sedimentation chamber cannot be accurately assessed without the presence of the filter stage. To date, there are no full-scale laboratory studies on the effectiveness of a sedimentation stage in CTD-SFs. Studies based on in situ measured data on the effectiveness of the sedimentation stage in CTD-SFs have previously been conducted on smaller systems with catchment areas of 500 and 1,000 m² (Herr & Sansalone 2015; Liu & Sansalone 2019). Herein, the authors found that over an operating period of more than one year, 77 and 87% of the particulate matter was retained in the sedimentation stage. A single in situ study investigated a CTD-SF connected to a catchment area of 10,000 m². Thereby, a 71% removal was calculated by a mass balance derived by drawing samples from the influent, the effluent and below the filter bed (Wichern et al. 2017). In addition to the challenge of transferring in situ results to other sites (Spelman & Sansalone 2018), it is uncertain to what extent efficiencies can be transferred to other system types: all CTDs and CTD-SFs are industrial products of different manufacturers and therefore vary in size and type. Furthermore, it is unclear how and whether basic principles of existing dimensioning recommendations of rectangular sedimentation basins can be used for the general dimensioning of these systems. Rectangular sedimentation basins are usually sized on the basis of surface loading rate (EPA 1986; DWA & BWK 2020), which is derived from model concepts of classic sedimentation theories (Hazen 1904; Camp 1946). Therefore, in the context of dimensioning, a uniform horizontal flow in a rectangular basin is often assumed. If applicable to CTD-SFs, these mathematical models of classic sedimentation theory may provide information on the removal efficiency without difficult measurements underneath the filter stage (Herr & Sansalone 2015). However, the flow patterns in CTDs and CTD-SFs are often far from ideal in the sense of the classical sedimentation theory because they are built for much smaller footprints than rectangular basins. Previous studies of CTDs showed that classical mathematical models often need adjustment to the specific device (Boogaard et al. 2015; Liu & Sansalone 2019).

The objective of this study is to determine the removal efficiency of particulate matter in the sedimentation stage in a CTD-SF designed for catchment areas up to 10,000 m², although in practice the CTD-SF is often connected to smaller catchments. By this, not only the removal of particulate matter in the sedimentation stage but also the filter load can be determined, which allows conclusions on the expected lifetime of the filter stage. However, accessing data from the sedimentation chamber underneath a filter stage remains a difficult task on large full-scale systems. For this reason, this study presents an alternative approach by investigating a CTD-SF by physical hydraulic modeling. Thereby, small-scale physical models are built and tested under laboratory conditions. Usually, the physical models are designed in accordance with the geometric features of the original, i.e. the device in full-scale. Contrary to full-scale investigations, hydraulic physical modeling is cost and time-saving since it significantly reduces the quantity of volume flow to be sampled. Most importantly, it allows direct access to the sedimentation chamber, which is hard to achieve on a full-scale CTD-SF. However, transferring results from small-scale models to the full-scale original demands the investigation of valid upscaling laws. Therefore, the decision to physically model a CTD-SF added a central objective to this study: Is it possible to transfer data of removal efficiency obtained from model tests to the full-scale of a CTD-SF?

Generally, the results of the hydraulic model tests are scaled to the original by applying relationships derived from the principles of dynamic similitude. These relationships are expressed as nondimensional numbers (e.g. Reynolds number) that characterize, by their numerical value, the nature of the flow under consideration. In the field of stormwater treatment, physical hydraulic modeling was used for studies of rectangular sedimentation basins (Thompson 1969; Kawamura 1981; Stovin & Saul 1994; Sekimoto 2008; Takamatsu et al. 2010) and for vortex separators (Weiß & Michelbach 1996). The validity of nondimensional numbers can either be checked by comparing the model results to the original or by comparing them to a geometrically similar model on a different length scale (Emori & Schuring 1977). The latter one benefits from reduced cost and improved accessibility of the involved physical processes, whereas the direct comparison with the full-scale is mostly avoided.

In summary, the objectives of this study are as follows:

• (i)

  Physical hydraulic modeling of the sedimentation process in a compact treatment device with combined sedimentation and filtration and investigation of valid upscaling laws for sedimentation.

• (ii)

  Evaluation of particle-size-specific removal efficiencies of Millisil W4 in the sedimentation stage and testing the applicability of mathematical models of classical sedimentation theory.

• (iii)

  Site-specific prediction of the filter load after preliminary sedimentation for the full-scale.

In these equations, U is the characteristic velocity (m s⁻¹), L is the characteristic length (m), ρ_w is the density of water (kg m⁻³), ρ_p is the density of particulate matter (kg m⁻³), is the kinematic viscosity (m² s⁻¹), v_s is the settling velocity (m s⁻¹), is the surface loading rate (m h⁻¹), which is defined as the ratio of flow rate to the settling area of the device.

The Reynolds number indicates the conditions under which the ratio of viscous forces to inertial forces is the same in both model and original. Moreover, it indicates the transition from laminar to turbulent flow, which greatly influences the inside flow patterns. The densiometric Froude number expresses the condition for the similarity of buoyant and inertia forces. However, Reynolds and Froude similarity spells out conflicting model design requirements (Emori & Schuring 1977). The Hazen number expresses the relation of the settling time scale and the hydraulic retention time scale, which is represented by the surface loading rate (Hazen 1904; Camp 1946). For instance, when the numerical value of the Hazen number is the same in the model and the original, the ratio of settling velocity and surface loading rate is identical. Throughout the literature, the Hazen number is a common nondimensional group used to predict and scale removal efficiencies in settling devices (Hazen 1904; Thompson 1969; Weiß & Michelbach 1996; Takamatsu et al. 2010; Li & Sansalone 2021). Moreover, it proved to be a robust nondimensional group for a set of different rectangular basin configuration and loading conditions (Li & Sansalone 2021). However, scaling solely on Hazen number contradicts also with Reynolds similarity, which may lead to an overestimation of removal efficiency when scaling the removal efficiency from the model to the full-scale (Weiß 1997). Thompson (1969) achieved similarity between two rectangular tank geometries of the same model family by scaling with Hazen number. In addition, his study did not show a dependence of Reynolds or Froude number on the removal efficiency. This however may be due to the fact that the Reynolds number already was above a critical value. Exceeding this value, Thompson (1969) suggests, will diminish the influence of the Reynolds number and can make the flow pattern independent of Reynolds number (Clements et al. 1969). This is also indicated by Kobus (1984) who suggests that a relaxation of Reynolds number is tolerable, as long as it exceeds a critical value. Within this constraint, the modeling of gravity-driven flows by Froude similarity may be preferable over Reynolds similarity because it allows maintaining macroscopic turbulent features of the flow while also enabling Froude similarity. This approach was used by Sekimoto (2008) who modeled the removal efficiencies in two differently scaled models of a water-driven sedimentation basin using Froude number, while the Reynolds number in the smaller model still exceeded 20,000. However, by applying just the Froude number similarity between both models, the similarity was not achieved with respect to the removal of small particles (<200 μm), which are of major concern for the treatment of polluted road runoff in separate sewer systems. In this study, scaling laws are verified by comparing two differently scaled physical models of the same CTD-SF to each other (Thompson 1969; Emori & Schuring 1977; Sekimoto 2008).

In this study, two physical hydraulic models of the full-scale CTD-SF under investigation were built at different scales. Herein the small model (model A) and the large model (model B) are built with shaft diameters of 0.29 and 0.49 m, respectively. Since the full-scale device has a diameter of L = 2.4 m, the ratio of length scales is 1:8.3 for model A and 1:4.9 for model B. All other geometric features were scaled using these ratios. Both models are depicted in Figure 1(a). Since the aim of this study is to investigate the removal efficiency by sedimentation, the modeling of the filter stage was relaxed to some extent. Therefore, the only property of the filter stage in the full-scale device that is considered in the models is its ability to balance the flow along the filter surface by providing flow resistance and thereby affecting the flow pattern in the sedimentation chamber. Modeling any internal processes of the filter stage in this setup was discarded and is best done in a standalone experiment. To include filter resistance in the model, filter mats from aquarium supplies (Pondlife Hanako Koi, Germany) were used. These have an open foam structure with 30 PPI (pores per inch). The thickness of the filter mats in model B corresponds to 3 cm. To provide some additional resistance to the higher momentum in model A, the thickness was doubled in model A to 6 cm. The filter mats were placed on a filter media support (12 × 12 mm). To prevent the filter mats from lifting, they were weighted with coarse gravel (d = 25–40 mm), see Figure 1(b) and 1(c).

Four assumptions were used to further reduce complexity of the models: (i) a condition of the full-scale CTD-SF is investigated in which the pressure drop by the filter, i.e. water column height in front of the baffle (Δh) is negligibly small in comparison with other geometric length scales. This condition can be expected for the full-scale device at low particulate filter load and/or low volumetric flow rates and allows to achieve the geometric similarity between models and CTD-SF as long as the observed water column height goes towards zero (Δh → 0). This assumption holds true for both models A and B, since the water column height in front of the baffle is negligible small under experimental conditions, see Figure 1(b) and 1(c). (ii) Secondly, it is assumed that the filter stage is isotropic, i.e. the filter permeability and thus the pressure drop across the filter depth is the same at any location. (iii) Thirdly, steady-state conditions, i.e. constant inflow and outflow rates are investigated. (iv) Fourth, it is assumed that the flow pattern in the sedimentation chamber is relatively insensitive to the magnitude of the filter resistance as long as a filter is present.

Although Reynolds similarity is chosen to generate similar flow patterns, a drawback of this approach is that the sedimentation process is not scalable by Hazen number if the settling velocity is the same in the models and the full-scale device. This can be seen from the fact that model A is operated at a higher surface loading rate than model B, while both are again operated at higher surface loading rates than the full-scale device, see Table 1. However, if the same particle material is used and is not scaled in accordance with the geometric relationship of model A and model B, the settling velocity of a particle with a specific diameter remains constant in both models. Consequently, both models are operated at different Hazen numbers concerning particles with the same diameter, which prevents a direct comparison. To avoid this obstacle, the removal efficiency in this experimental setup is determined for very fine particle classes that approximate the behavior of individual particles (see SI for more information). Since each particle-size corresponds to an individual settling velocity, this results in a set of different Hazen numbers. Assuming that scaling with the Hazen number can be performed for basin types that deviate from the classic rectangular basins, the removal efficiency is expected to be the same for the same numerical value of the Hazen number in both models of the CTD-SF. To test this hypothesis in the framework of this study, the particle-size-specific removal efficiencies by sedimentation are evaluated in models A and B. For the tests, the standard material Millisil W4 was used as particulate matter. The applied measurements and methods are described in section 2.4. Additionally, the determination of the Hazen number requires the settling velocities of the considered particles. These are calculated according to a type I settling behavior and Newton's equation (Bolognesi et al. 2012) using the Kaskas equation for the drag coefficient (Goossens 2019), see SI for additional information.

To control if Reynolds similarity produces similar flow patterns in the given geometry, tracer experiments are carried out in models A and B. Thereby, the tracer is injected into the inlet and measured at the outlet. As stated, the modeling of the CTD-SF in this publication does only include the filter resistance towards the flow, i.e. the effect of the filter resistance on the flow within the preliminary sedimentation stage. Following this concept, the internal flow inside the filter media is not modeled. Since the filter mats are between injection and measurement point, they can therefore cause distortion of the tracer signal and prevent a comparison. A measurement in both models A and B underneath the filter mats was discarded, since the invasive measurement can likewise cause distortion of the tracer signal. Thus, the similarity of flow patterns could only be evaluated for both models without filter mats. However, if the tracer signals indicate similar flow patterns in both models at the same Reynolds number, i.e. at the same ratio of inertial to viscous forces, then it can be assumed that these forces are also governing the flow pattern even when a filter is included.

Tracer experiments were initially conducted at different sodium chloride concentrations of 25, 50 and 100 g L⁻¹ on model B. The goal was to find the tracer concentration that would provide the best recovery rate without changing the flow field due to density differences between the tracer solution and the water. The results are depicted in Figure S3 showing that a concentration of 100 g L⁻¹ changes the tracer signal, while concentrations of 25 and 50 g L⁻¹ produce identical results. In this case, the tracer solution with a concentration of 100 g L⁻¹ preferentially follows the flow near the bottom, which is the fastest path to the outlet of the system in this setup (without filter mats). However, with higher concentrations, the recovery rate of the tracer experiments improved from 84 to 94%, for 25 to 50 g L⁻¹, respectively.

To investigate the applicability of classical theoretical models, the removal efficiencies are calculated according to Equation (6) assuming a CSTR and PFR basin. Herein, the CSTR assumption significantly underestimates the removal efficiencies of the sedimentation chamber, while the assumption of an ideal PFR tends to overestimate the removal efficiencies. A best fit for the classical mathematical model was achieved for n = 3.5, which corresponds to three and a half CSTRs in series, see Figure 5(b). The results coincide with the investigations of Liu & Sansalone (2019) who found that the classical CSTR model of Hazen underestimates removal efficiencies in a hydrodynamic separator for stormwater treatment. Testing different CTDs and comparing them to the classical Hazen model, Boogaard et al. (2015) suggest that deviations from the mathematical model can be referred to the effectively used settling area. Quantitatively, the removal efficiency of the sedimentation chamber of the CTD-SF in this study is in the order of magnitude of the removal efficiencies determined by Boogaard et al. (2015). Generally, the results match with the observation of Li & Sansalone (2021), who determined that the Hazen number is a relatively robust parameter for scaling removal efficiencies in clarification basins. However, within their results, this did not imply that the predictions of classical theoretical models were correct. This reflects the results of this study since the Hazen number is able to achieve similarity. Nevertheless, the classical theoretical model needs calibration with respect to the characteristics of device.

The results in Figures 6 and 7 are relevant to properly dimensioning CTD-SFs concerning catchment area, filter area and filter structure. Thereby, the filter stage in CTD-SFs is only partly loaded by particulate matter in the road runoff since a preliminary sedimentation retains larger particles. Additionally, it can be expected that particulate matter loaded to the filter stage in CTD-SFs is rather fine compared to particulate matter in untreated road runoff. Since both particle size and the mass of particulate matter loaded to the filter are important parameters that affect the lifetime of a filter stage, the sedimentation stage is likely to slow down the process of filter clogging. To what extent, however, also depends on the properties of the filter material (Kandra et al. 2015). Consequently, studies investigating the lifetime of a CTD-SF as a result of mechanical clogging should consider the loading conditions and the properties of the filter material.

In the present study, a compact stormwater treatment device combining sedimentation and filtration is investigated by physical hydraulic modeling. Verification of scaling laws is carried out by comparing the results of two geometrically similar small-scale models at different length scales. Thereby, tracer experiments confirm that Reynolds number similarity produces similar flow patterns in both models. Moreover, the Hazen number successfully creates the similarity of particle-size-specific removal efficiencies in the sedimentation chamber even when the flow pattern deviates from the theoretical concept of a uniform flow in a rectangular basin. However, models of classical sedimentation theory cannot be used without calibration and may otherwise incorrectly predict removal efficiencies in compact stormwater treatment devices. Upscaling to the full-scale shows that, on average, the filter stage is only loaded with one-fourth of the total particulate matter in the inlet of the device. Furthermore, even at rainfall intensities of 15 L s⁻¹ ha⁻¹, about 88% of the particles in the influent of the filter still belong to the spectrum of particles ≤63 μm. These results are obtained assuming a PSD of Millisil W4 and a type I settling behavior. Other values may result under different boundary conditions. However, it becomes clear that sedimentation upstream of a filter is of relevant importance in CTDs. Overall, physical hydraulic modeling was able to provide information on the functionality of CTDs with combined sedimentation and filtration without the effort of full-scale measurements. Future investigations may extend the range of volume flows tested in this study. Additionally, the information generated on small-scale models may be used to complement numerical modeling studies.

This work was supported by the Ministry for Culture and Science of the State of North-Rhine Westphalia (NRW, Germany) through the joint project ‘Future Water’ (project number: 321-8.03-215-116439).

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

The authors declare there is no conflict.