Water Resources Research

Particle dynamics in a hydrodynamic separator subject to transient rainfall-runoff

Authors


Abstract

[1] Analysis of unit operations to separate particulate matter (PM) transported by urban drainage is challenged by coupled hydrologic and mass transport and is commonly based on statistical flow indices. In this study the response of a hydrodynamic separator (HS) to unsteady runoff is modeled with computational fluid dynamics (CFD). Flow is modeled by a k-ɛ model of turbulence with Lagrangian unsteady tracking for particle size distributions (PSDs). CFD results reproduced HS-captured PM mass within 10%. Validated unsteady CFD results are compared to steady flow and PM event mean concentrations, indicating that event-based flow statistics do not represent unsteady HS behavior. Mean and median flows underestimate effluent PM mass, while peak flow overestimates to a lesser magnitude depending on hydrologic and PM coupling. Unsteady flow and PSD coupling in the CFD model yield accurate predictive capability for PM separation by a physically validated unit operation (HS) compared to common event-based flow statistics. While steady flow indices do not reproduce PM behavior for unit operations loaded by unsteady urban drainage, such indices are pragmatic and heuristic for initial phase pilot-scale testing.

1. Introduction

[2] Anthropogenic and biogenic particulate matter (PM) transported in urban rainfall-runoff has been identified as a significant contributor to deterioration of surface water in the United States (U.S. Environmental Protection Agency (USEPA), Water quality assessment database 2000 305(b), 2000, available at http://www.epa.gov/305b/2000report/). Rainfall-runoff transports an entrained mixture of colloidal and noncolloidal PM, dissolved and complexed pollutants [Lee and Bang, 2000; Sansalone et al., 1998]. The temporal particle size distribution (PSD) and composition of PM delivered by rainfall-runoff varies significantly between events and can vary spatially within the same watershed [Sansalone, 2002].

[3] Given the variability of transport in rainfall-runoff, the concept of an event mean concentration (EMC) is recognized as the most common and pragmatic index for water chemistry and PM in storm water management [Strecker, 1998]. Many models have been developed to predict source area EMCs with EMCs serving as inputs to transport or treatment tools. Brezonik and Stadelmann [2002] developed regression models to predict EMCs from urban catchments. Chen and Adams [2006] developed an analytical model to estimate storm water EMCs on the basis of rainfall-runoff transformations and buildup-wash-off models; as an alternative to continuous simulations. May and Sivakumar [2008] suggest artificial neural networks can improve traditional statistical models in predicting EMCs. Such advances have allowed quantification and prediction of EMC-based responses for watersheds. However, subject to unsteady flows for which rainfall-runoff and PM transport are coupled phenomena in urban source area watersheds; the question is if a single EMC or flow statistic can reproduce treatment phenomena for a physical unit operation system.

[4] The state-of-the-practice in urban drainage treatment for PM separation tends toward application of wastewater clarification principles, which assume reasonably steady flow and reasonably constant primary influent PM granulometry [Wilson et al., 2007] allowing autosampling. In contrast, the rainfall-runoff process and coupled PM and dissolved constituent delivery are highly variable, and in situ unit operations are subject to such coupled and unsteady phenomena. Urban rainfall-runoff models such as the Storm Water Management Model (SWMM) [Rossman, 2007; Huber and Dickinson, 1988] use a variety of hydrographs and pollutograph input models. Such models that allow the coupling of complex hydrology and pollutant transport have greatly improved the efficacy of design considering the unsteady and interrelated loading parameters. However, the implementation of parallel unsteady modeling for urban drainage treatment design is only occasional at best. Huber [2006] reports that in many application of SWMM for modeling hydrodynamic devices, the functionality of the unit is based on a black box approach that neglects maintenance, malfunctioning, poor sizing and maximum treatment rates. Many times such an approach must rely on empirical formulae based on influent and effluent data for a given unit operation, and extensive calibration is required [Artina et al., 2007]. Urbonas [1995] synthesized and categorized a list of parameters for selection and design of unit operations to develop selection and comparison strategies. In addition, Tsihrintzis and Hamid [1997] report in their review of storm water management that no single class of unit operations and processes is applicable to every situation and identify the need for careful design based on a set of parameters which include inflow and outflow EMCs for water chemistry constituents.

[5] Hydrodynamic separation (HS) has been suggested as a viable urban drainage physical unit operation [Rushton, 2004, 2006; Brombach, 1987; Brombach et al., 1993; Pisano and Brombach, 1994; U.S. Environmental Protection Agency, 1999; Andoh and Saul, 2003]. Previous studies of PM separation mechanisms by HS units have ranged from simplified overflow rate theory [Weib, 1997] to semiempirical approaches based on assumptions of vortex flow behavior [Paul et al., 1991]. Fenner and Tyack [1997] and Fenner [1998] report that similitude analysis does not yield a single dimensionless group for HS scale up. Because of the complexity and variability of runoff and PM transport, analyses of HS units have been based on a pragmatic EMC approach. However, such an approach does not capture the PSD and hydrologic coupling as commonly facilitated through the use of automated samplers programmed on a flow-weighted basis [Rushton, 2004, 2006].

[6] A recent alternative to steady flow and EMC approaches is computational fluid dynamics (CFD) which utilizes numerical methods to solve the equations of fluid dynamics, the Navier-Stokes equations [Ferziger and Peric, 2002]. CFD techniques, while computationally intensive, allow examination of complex flows and PM transport. The application of a CFD to model PM-laden flows is an active research area [Curtis and van Wachem, 2004; van Wachem and Almstedt, 2003]. Pathapati and Sansalone [2007, 2009] developed an experimentally validated CFD approach to accurately describe behavior of a screened HS, across a range of steady flow rates for an influent of constant PSD at a constant concentration (EMC) typically observed in urban rainfall-runoff. This study extends the CFD modeling to unsteady rainfall-runoff events with transient flow rates, and variable but flow-coupled influent PSDs and PM concentrations.

2. Objectives

[7] The first objective of this study is to demonstrate the applicability of a CFD model for unsteady rainfall-runoff loadings to predict effluent PSDs and PM mass from a screened HS. In contrast, common urban drainage practices for PM control are often based on peak flow models and/or design storms coupled with an EMC of water chemistry or PM parameters. The common hypothesis of this lumped approach is that the characteristics of a time-variant coupled hydrology and PM transport are adequately represented by a single flow rate, such as the peak, mean or median. Therefore as a second objective, this hypothesis is tested by comparing event-based captured and effluent PM from a monitored empty bed–screened HS to (1) unsteady CFD model predictions of PM fate and (2) steady flow CFD model predictions using the mean, median and peak flow rates with the EMC of measured influent PM as the input parameter.

3. Methodology

3.1. Experimental Methodology

[8] This study examined a screened HS consisting of two cylindrical chambers, the inner “screen area” and the outer “volute area” separated by a static screen (with 2400 μm apertures) as illustrated in Figure 1. The flow inlet is tangential to the inner chamber and the bottom of the inner cylinder is a closed conical sump, resulting in the formation of a weak vortex in the screen area. As flow passes through the directional screen apertures flow can be weakly reversed as flow enters the outer volute area. PM separation by a screened HS is generally a function of the influent volumetric flow rate, the influent PSD, the influent PM concentration, the PM settling velocity, tangential and radial velocity distributions in the inner screen area, and screen aperture size and is primarily gravitational sedimentation for much of the PSD mass. The design flow rate (Qd) for the HS is 9.5 L/s and the hydraulic capacity of the HS is sized for the study watershed.

Figure 1.

Schematic representation of experimental site setup.

[9] A schematic process diagram of the experimental site setup is illustrated in Figure 1. The Baton Rouge, Louisiana, watershed consisted of two hydraulically parallel catchment areas that are paved urban source areas with a transportation land use. The catchment surfaces are constructed of Portland cement concrete (PCC). The drainage area is 1088 m2. A detailed description of the watershed and hydrology are available elsewhere [Sansalone et al., 2005; Sheng et al., 2008]. Kim and Sansalone [2008] describe in depth the experimental site, sampling, field analysis and lab analyses for the storms that are modeled in this paper, and only a brief summary of the procedure is presented here.

[10] Eight discrete rainfall-runoff events were monitored and treated by the screened HS. All storms were routed through a precleaned HS system in order to accurately monitor influent PM mass and PSD and conduct a mass balance after each event. Sampling started immediately when runoff was observed, and was performed on a flow-weighted basis, across the entire duration of the rainfall-runoff event. Influent was sampled at the drop box upstream of the screened HS and effluent was sampled at the outflow of the HS. All samples were taken manually, across the entire cross section of the outfall, in order to obtain a representative and complete PSD. The number of discrete samples of influent and effluent was chosen appropriately to provide a reasonable estimate of temporal variability of PM concentrations and PSDs with at least 14 to15 influent samples and 12 to 13 effluent samples were taken for each event. Total PM was obtained as a sum of sediment, settleable and suspended PM fractions. Sediment PM is defined as particles with a diameter greater than 75 μm [American Society for Testing and Materials (ASTM), 1993] The settleable fraction (∼25 μm < dp < 75 μm) comprises PM that settle out in a 60 min Imhoff cone analysis (standard method 2540F) [American Public Health Association, 1998] and suspended PM is from 1 to ∼25 μm [Kim and Sansalone, 2008].

[11] The measured percent removal (PRmeasured) for PM mass or number of particles was used as the index for comparison between the model and experimental data, and defined as follows:

equation image

For each storm across the HS, a mass balance error constraint of 10% on PM was imposed:

equation image

In this expression, Mi is the influent mass of particles, MHS is the mass of particles captured by the screened HS and Me is the effluent mass of particles, computed from the measured effluent SSC across the total treated effluent volume. All gravimetric measurements were carried out on a dry mass basis. A maximum mass balance error of 10% was established for each experimental run.

[12] The EMC for PM of a rainfall-runoff event is typically used as an index for event-based chemical concentration to calculate percent removal for storm water unit operations [Huber, 1993]:

equation image

In this expression, M is the total effluent mass over the entire duration of the event, V is the total volume of flow over the entire duration of the event, C is the flow-weighted mean concentration, c(t) is the time variable particulate-bound concentration, q(t) is the time variable flow rate.

3.2. Mutliphase Flow Modeling Methodology

[13] The behavior of the screened HS is modeled more accurately in three dimensions because of the simultaneous effects of lack of geometric symmetry, complex static screen geometry, vortex flow and gravitational forces on the motion of particles. The fluid flow equations solved by CFD are based on conservation of mass and momentum [Versteeg and Malalasekera, 1995] with details of these equations for the HS provided elsewhere [Pathapati and Sansalone, 2009].

[14] The inlet Reynolds number varied significantly as a function of time for a runoff events. In addition, there was high temporal variability (100 to 900,000) in the magnitude of Reynolds numbers calculated for the 20 August 2004 rainfall-runoff event. On the other hand, the magnitude and temporal variation of Reynolds numbers was low for the 14 October 2004 storm (100 to 2000). Therefore, there is the need for a turbulence model that can provide stable and accurate flow simulations across widely ranging and often rapidly changing inlet Reynolds numbers.

[15] In the standard k-ɛ model [Launder and Spalding, 1974; Rodi, 1993] for turbulent flow, a closed solution is obtained for the turbulent transport equations by relating Reynolds stresses to an eddy viscosity (μ). Newton's law of viscosity is applied to define the relationship between viscous stresses and “Reynolds stresses.” It was hypothesized that isotropy of Reynolds stresses can be reasonably assumed in the case of the HS.

[16] Previous studies in modeling swirling multiphase flows in hydrocyclones have employed two equation Reynolds averaged Navier-Stokes (RANS) models including the standard k-ɛ model for turbulence modeling of hydrocyclones [Nowakowski et al., 2004; Statie et al., 2001; Petty and Parks, 2001]. The standard k-ɛ model was used to successfully model steady flow as part of a previous study and supported with validation data for a screened HS under controlled steady testing [Pathapati and Sansalone, 2009]. The realizable k-ɛ model was tested in this study and was found to offer no improvement over the standard k-ɛ model. The shape of the screen apertures results in a weakly reversed flow direction in the outer volute chamber. The screen area open to flow is designed so that radial velocity through the screen is approximately an order of magnitude lower than the inlet velocity. The screen was modeled as a momentum sink term, and the detailed methodology is provided elsewhere [Pathapati and Sansalone, 2009].

3.2.1. Modeling the Particulate Phase

[17] Multiphase flows are modeled with a Eulerian-Eulerian approach or a Eulerian-Lagrangian approach [van Wachem and Almstedt, 2003] depending on the extent of coupling between phases, with the delimiter that a Eulerian-Eulerian approach is used for flows with particulate volume fractions (PVF) greater than 10%. Elghobashi [1991] proposed a regime map for appropriating the degree of interphase coupling, by analyzing length and time scales. Subsequently, it was determined that a Lagrangian approach to tracking the secondary phase is appropriate for flows with a low influent PVF which is the case in this study (0.2% < PVF < 3.2%). The transient flow field was computed utilizing the Eulerian approach for each time step. The measured influent particles were numerically injected at times that correspond to influent sampling times during storm event data collection. The Lagrangian DPM is derived from force balances based on Newton's law describing particle settling [Pathapati and Sansalone, 2009]:

equation image

In this expression,

equation image
equation image

In these expressions, u is fluid velocity, up is particle velocity, ρ is fluid density, ρp is particle density, dp is particle diameter, μ is viscosity, a1, a2, a3 are empirical constants for spherical particles as a function of the particle Reynolds number, Rep [Morsi and Alexander, 1972].

[18] Particle trajectories are obtained by integration of equation (4). For this study, particles of consistent morphology across the PSD were numerically injected across the entire flow across the inlet to the HS to represent measured particle transport across varied flow rates. PM data included PSDs determined by mechanical sieves and laser diffraction, and specific gravity (2.65) determined by helium pycnometry [Sansalone et al., 1998]. The PSD was measured for each influent and effluent discrete sample and modeled using a cumulative gamma distribution, to express the PM mass or volume fractions as a function of PM diameter. The probability density function of a two parameter gamma distribution is given by the following expression:

equation image

In this expression, ϕ is the shape factor and η is the scaling factor. The cumulative gamma distribution is thus represented as follows:

equation image

[19] Injections of particles into the CFD model were initiated at times corresponding to monitoring sampling times and weighted across monitoring sampling intervals. Particles were tracked over a time step equal to the fluid flow time step. Particles that remained in the HS after integrating over the specified tracking length were considered to have been separated the HS.

3.2.2. Discretization and Solution Schemes

[20] The computational domain was discretized as unstructured tetrahedral elements generated by TGrid [Qi and Lin, 2006]. The HS was divided into 3.86 million cells. A grid independent numerical solution was iteratively obtained using a finite volume method (FVM) and a cell-centered discretization scheme for a series of cell sizes to determine that 3.86 million cells were required for the computational domain. A second-order upwind scheme [Barth and Jespersen, 1989] solved for flow parameters.

[21] A first-order fully implicit scheme was used for time discretization. The fully implicit scheme is unconditionally stable and is suggested for transient CFD operations which do not involve chemical reactions [Ranade, 2001]. Flow data were measured at one minute intervals. In order to test the sensitivity of the solution to smaller time steps, continuous functions were utilized to model the measured flow data. For simple hydrographs such as the 20 August 2004 event, a gamma distribution function was utilized. For more complicated events, flow was modeled by splitting the hydrograph into piecewise continuous segments which allowed for accurate curve fitting. For example, the 5 June 2005 storm was modeled with a combination of quadratic and exponential functions. One minute time steps were required; smaller time steps did not significantly affect the flow solutions. The transient semi-implicit method for pressure linked equations (SIMPLE) algorithm [Patankar, 1980, pp. 126–131] accounted for pressure-velocity coupling. The criterion for iterative convergence was set at 1 × 10−3 [Ranade, 2001].

4. Results

[22] Hyetographs and influent hydrographs for the eight discrete events are presented in Figures 2 and 3. The unsteady and variable hydrology resulted in a variable PM mass and PSD transport signature for each event. Table 1 classifies each of these events as mass limited (ML) or flow limited (FL) on the basis of PM delivery [Sheng et al., 2008]. Events classified as ML had a first-order exponential delivery while FL events had a zero-order delivery of PM mass. CFD results indicate that the standard k-ɛ model used to model turbulent flow, coupled with the DPM allowed for accurate prediction of PM separation. Across the eight storms analyzed, the total PM removal efficiency of the HS ranged from 39% to 70% on an event basis. Influent and effluent mass loads are provided in Table 1. The PM clarification response of the HS is largely dependent on the influent PSD, in particular the coarse fraction. A significant fraction of the PSD is separated by gravitational settling for coarse PM and for flow rates less than design flow, while finer sediment size PM is settled at low flow rates with the potential for nominal inertial separation at flows near the hydraulic design flow rate of the HS.

Figure 2.

Influent hydrology for four discrete 2004 storm events.

Figure 3.

Influent hydrology for four discrete 2005 storm events.

Table 1. Summary of Measured and Modeled Particulate Matter Separation by the Screened HS for Eight Discrete Storm Eventsa
Rainfall-Runoff Event DateQpeak (L/s)Qmedian (L/s)Qmean (L/s)Runoff Duration (min)Total Runoff Volume (L)Temporal PM Transport ClassInfluent PM Mass (g)PM Separated MassPM Percent RemovalRPD Between Modeled and PM Massb
Measured (g)CFD Model (g)Measured (%)CFD Model (%)
  • a

    See Sheng et al. [2008]. ML designates mass-limited (first-order) hydrologic transport, and FL designates flow-limited (zero-order) hydrologic transport for particulate matter (PM). PM specific gravity ranged from 2.15 to 2.48 across the monitoring campaign and was quantified using helium pycnometry [Kim and Sansalone, 2008]. On the basis of the definition of relative percent difference (RPD) from equation (9), which in this case compares the CFD model result to measured PM mass separated by the HS as part of a material balance for each event, a positive RPD indicates that the CFD model overpredicted the PM mass captured.

  • b

    Modeled mass has unsteady CFD.

14 Mar 20046.40.6140824076ML49491950204539.441.34.9
24 Apr 20041.80.40.61997288ML32192269236970.573.64.4
20 Aug200417.50.65.14112286ML12005926709722063.368.27.6
14 Oct 20040.60.10.11691672FL54426428048.551.45.9
5 Jun 20059.40.31.9515856ML47582979324562.668.28.9
30 Jun 200513.81.63.67115117ML40441677185341.545.810.4
21 Aug 200517.37.17.910650002ML88384646497652.656.37.1
3 Oct 200512.113.1152615FL73829730840.241.83.8

[23] Figure 4 illustrates the dynamics of a specific PM size for the 20 August 2004 storm event. Snapshots of HS particle trajectories are illustrated for distinct hydrograph points. The median particle diameter by mass (d50m), 300 μm of the measured influent PSD is chosen for illustration. For this event the peak flow rate exceeded the hydraulic design flow rate by a factor of two. The PM residence time is not sufficient to promote complete gravitational settling; with 80% of the captured PSD coarser than 300 μm on a mass basis as determined from Figure 5. The combination of CFD and PSDs provides insight into the particle transport and fate of any given particle of known specific gravity, within a turbulent multidimensional (3-D) flow regime.

Figure 4.

Temporal particle trajectories calculated by a Lagrangian DPM for the screened HS for the 20 August 2004 storm. The peak flow rate Qmax was 17.5 L/s, and the total duration of the storm tmax was 50 min. Trajectories are illustrated for the particle diameter corresponding to d50m and equal to 300 μm. Measured particle density (ρp) is 2.65 g/cm3.

Figure 5.

Measured versus modeled particle size distributions of PM separated by the screened HS in 2004.

[24] Figures 5 and 6 illustrate the modeled and measured gravimetric PSD separated and retained by the HS. Unsteady CFD modeled results agree with measured data, across the PSD for each runoff events. Modeled and measured mass of PM separated by the HS is also summarized in each plot. With respect to the separated PM mass, the relative percent difference (RPD) was utilized to compare measured and modeled results, and RPD results calculated as follows:

equation image
Figure 6.

Measured versus modeled particle size distributions of PM separated by the screened HS in 2005.

[25] Since a material balance for PM mass was measured and demonstrated for each event around the full-scale physical model of the HS, the measured PM mass is the basis to compare CFD model results. Effluent, influent and separated PM mass are measured mass components in the PM mass balance verification for each event. The definition of relative percent difference (RPD) in equation (9) is utilized to provide a comparison with measured PM mass for the unsteady CFD modeled results, or alternately for the use of each flow statistic (mean, median and peak) in a steady CFD model. A positive RPD indicates the CFD model (either as an unsteady model or with constant flow) overpredicts the mass for effluent or captured PM.

[26] Results indicate the unsteady CFD model reproduces PM mass separated in the HS with an RPD of less than 10% with respect to measured values. The separated PM mass and RPD between measured and modeled PM separated in the HS is provided for each event in Table 1.

[27] Figures 7 and 8 illustrate simulation results for specific event-based steady flow rate statistics (mean, median and peak) and an EMC of PM mass compared to actual unsteady results. Events are described chronologically. The 14 March 2004 event was an extended lower-intensity storm, with dual peaks late in the storm event. While the peak flow rate was approximately 60% of the design flow rate, the mean flow rate was approximately 10% of the design flow rate. However, the overall measured removal efficiency is low compared to other storm events (39%). The influent PSD of the 14 March 2004 storm is predominantly in the range of suspended and settleable PM (d50m = 43 μm) which are not effectively separated by gravitational separation. Therefore, the low mean flow rate had less of an impact on PM separation. On an effluent basis, Table 2 compares effluent PM at mean, median and peak flows. Results utilizing these flow rates for total effluent PM in the top third of Table 2 indicate mean and median flow rates result in a very significant underestimation (negative RPD) of effluent PM mass, ranging from −11 to −124%, and −11 to −171%, respectively. In contrast, peak flow rates result in a range of underestimation to overestimation of effluent PM mass from −2% to +50% with respect to measured PM mass.

Figure 7.

Modeled versus measured effluent particle size distributions for four discrete 2004 storm events utilizing Qmean, Qpeak, and Qmedian.

Figure 8.

Modeled versus measured effluent particle size distributions for four discrete 2005 storm events utilizing Qmean, Qpeak, and Qmedian.

Table 2. Summary of Measured and Modeled Effluent Particulate Matter for the Fine Fraction of Particulate Matter and the Suspended Fraction Thereofa
Rainfall-Runoff Event DateUnsteady Q = f(t)Steady Q = QmeanSteady Q = QmedianSteady Q = Qpeak
Measured Influent PM Load (g)Measured Effluent PM Load (g)CFD Modeled Effluent PM Load (g)RPD (%)CFD Modeled Effluent PM Load (g)RPD (%)CFD Modeled Effluent PM Load (g)RPD (%)
  • a

    The CFD model used a constant flow statistic. Fine fraction of particulate matter (PM) is <75 μm, and the suspended fraction is <25 μm. A negative RPD represents an underprediction by the steady CFD model. Negative RPDs are shown in bold.

Effluent Mass Load Predictions for Given Total PM Influent as an EMC Across Runoff Duration of Each Event
14 Mar 2004494925931699−49.41493−70.12582−1.7
24 Apr 20043219976436−124.1360−171.3650−50.1
20 Aug 20041059243143596−16.73864−11.646467.2
14 Oct 2004544268127−52.6178−52.2203−31.7
5 Jun 2005475815821040−34.3755−109.4192217.7
30 Jun 2005404424951337−86.51764−41.425472.1
21 Aug 2005883848844081−19.74003−22544210.3
3 Oct 2005738382339−11.0342−11.444914.9
Effluent Mass Load Predictions for Fine (Settleable Plus Suspended) PM Fractions (<75 μm)
14 Mar 2004306824641699−31.01493−39.424530.4
24 Apr 20041046830435−47.5359−56.6650−21.6
20 Aug 20042966267528406.227051.127884.2
14 Oct 2004359254127−50.2178−30.0203−20.1
5 Jun 2005133215341009−34.3740−51.8192225.3
30 Jun 2005202219711311−33.51517−23.020373.4
21 Aug 2005371234193225−5.73203−6.335383.5
3 Oct 20054433323330.33350.939117.5
Effluent Mass Load Predictions for Suspended PM Fraction (<25 μm)
14 Mar 2004158414261275−10.61120−21.51420−0.4
24 Apr 2004386410344−16.1306−25.43778.0
20 Aug 20041059971115118.510437.510225.3
14 Oct 2004229214126−41.4174−19.0183−14.6
5 Jun 20054281265437−65.5347−72.548162.0
30 Jun 2005688773709−8.3706−8.77641.2
21 Aug 2005150315631429−8.61401−10.4125219.9
3 Oct 2005185187170−9.2171−8.61794.1

[28] The 24 April 2004 storm was also a sustained low-intensity storm, with a peak flow rate of approximately 10 percent of the design flow rate. However, a significant fraction of the influent PSD consisted of coarse PM transported during the initial portion of the storm. The combination of low flow rate and coarse PM resulted in the measurement of a high PM removal (70%). Table 2 illustrates that the mean, median or peak flow rates could not reproduce the measured PM separation, with the peak flow rate providing smallest yet still significant underestimation of effluent PM mass (RPD = −50.1%) as compared to the measured value.

[29] The 20 August 2004 storm was a high-intensity storm with the peak flow rate approximately twice the design flow rate (9.5 L/s). At this peak flow rate a weak vortex was created. The observed vortex suggests a nominal role for inertial separation augmenting the dominant mechanism of gravitational settling. Moreover, there was a disproportionate amount of coarse PM mass delivered in the initial portion of the storm, when flow rates were highest. The influent event-based PSD was very coarse with a d50m = 300 μm. As a result of the very coarse gradation a PM removal of 63% was measured. For high-intensity mass-limited events, peak flow reproduced the overall PM effluent mass better than the mean and median flow rates.

[30] The 14 October 2004 storm was a low-intensity and long-duration event. Under these conditions, the HS functions simply as a circular sedimentation tank. PM delivery was approximately flow limited, although a significant fraction of the dry deposition PM gradation was fine enough to be transported early in the event. Application of the mean, median or peak flow rate each underestimate effluent PM mass. The fine influent PSD (d50m = 45 μm) resulted in a measured PM removal of 49% despite low flow rates and longer hydraulic residence times.

[31] The 5 June 2005 storm had a maximum flow rate approximately equal to the design flow rate of the screened HS. The PM transport was mass limited for this high-intensity event, the influent d50m was 247 μm on an event basis, and the high runoff intensity peak flow delivered coarse PM. With this coarse influent PM, and a unimodal well-behaved hydrograph, it was hypothesized that the mean or the median flow rate could reproduce PM dynamics for the HS on an event basis. However, similar to the 20 August 2004 storm, the peak flow rate provides the best prediction of effluent PM mass, albeit an overestimation, even though the peak lasted for a fraction of the total duration of the storm. It is hypothesized that previously settled PM during the rising limb of the hydrograph, prior to the peak was resuspended and scoured from the unit by peak flow.

[32] The 30 June 2005 and 21 August 2005 storms had peak flow rates that were well above 125% of design flow rate, and by the same rationale applied to the 20 August 2004 storm, the peak flow rate shows the best agreement with measured data. The 3 October 2005 storm had a peak flow rate approximately 125% of the design flow rate. However, the PM mass delivery was proportional to the flow rate, across the entire event, and the influent PSD was finer (d50m = 58 μm). There was no significant difference between PM effluent mass predicted by the mean and the median flow rates. The mean and median steady flows underestimated effluent PM mass by ∼11% as compared to measured effluent PM. The peak flow model yields an overestimation of effluent PM mass (RPD = 14.9%) as a result of the finer influent PSD for both events.

[33] Table 2 illustrates in a tabular manner the magnitude of individual mass fractions in the effluent as do Figures 7 and 8 graphically for the entire gradation. In addition to the above comparisons for total PM mass in the effluent, a comparison was made to identify the differences between measured effluent PM mass fractions and the CFD models with steady flow statistics for PM mass fractions (suspended and settleable) described in the methodology. Two PM mass fractions are examined, collectively the suspended and settleable PM (<75 μm) fractions and separately, only the suspended PM (<25 μm) fraction. These results are presented in the middle and bottom sections of Table 2. The trends for the fine fractions (<75 μm) follows a similar pattern of underestimation and overestimation to the total PM previously discussed and shown in the top section of Table 2; but to a lesser magnitude. A similar pattern emerges for suspended PM (<25 μm) as shown in the bottom section of Table 2 but to a lesser degree than the combined fine fractions (settleable + suspended) < 75 μm. The largely consistent trend in decreasing magnitude with the fine PM fraction and the suspended PM fraction can be explained in large part because each of these fractions represent increasingly smaller mass fractions of the total PM [Kim and Sansalone, 2008]. Beyond effluent PM fractions, Table 3 illustrates that the unsteady CFD model predicts the effluent d50 for each event more precisely than the constant flow CFD models. The mean and median flows consistently underestimate effluent d50 with the peak flow generally overestimating the effluent d50 compared to the precise matching of measured and unsteady CFD results.

Table 3. Summary of Measured and CFD Modeled Particulate Matter Effluent d50m by the Screened HS for Eight Discrete Storm Eventsa
PSD IndexEvent Mean d50m (μm)
14 Mar 200424 Apr 200420 Aug 200414 Oct 20045 Jun 200530 Jun 200521 Aug 20053 Oct 2005
  • a

    PM, particulate matter, d50m; mass-based d50. The summary uses the unsteady CFD model or the measured EMC for influent PM for a constant Qmean, Qmedian, and Qpeak in a steady CFD model.

Measured
   Influent, Q = f(t)43233300452476910658
   Effluent, Q = f(t)2031521342394226
CFD modeled
   Effluent, Q = f(t), unsteady2032511341394323
   Effluent, Qmean, steady141238830233623
   Effluent, Qmedian, steady121048923283423
   Effluent, Qpeak, steady2320581050445035

5. Discussion

[34] Results indicate that rainfall-runoff transport and PSD are coupled phenomena in urban source area watersheds. Beyond a categorical analysis of this coupling on an event scale as mass limited (ML) or flow limited (FL), this coupling is physically dependent on urban source area watershed PM loading phenomena and the time distribution of the rainfall-runoff relationship and PM transport. For in situ treatment without upstream hydrologic attenuation of unsteady flows this coupling has a direct impact on treatment for preliminary unit operations such as the screened HS. Results indicate that the coupling of unsteady flow and resulting variability of PSDs are important simulation parameters. Results examined the use of steady flow statistics (mean, median and peak) for actual hydrographs demonstrating that there is no single steady flow rate statistic that can represent the unsteady runoff phenomena controlling the PM mass separation behavior of the HS, although peak flow was more accurate than mean or median. The complexity of real-time flow and PM monitoring as well as treatment results from the temporal coupling of unsteady rainfall-runoff and PSDs. Given the unsteady loadings, the physical model results and CFD model were validated through measurements of flow at one minute intervals, PSDs of influent, effluent and captured PM as well as a mass and volume balance across the screened HS. The use of a clean bed condition to model performance on an event scale does not take into account interevent scour, which has a demonstrable deleterious impact on screened HS behavior. Enumeration of interevent scour requires a separate CFD model. CFD results in this study illustrate the need to gather representative monitoring and sample information for quantification of flow, PSDs across the entire gradation, material balances, and enumeration of constituents or constituent phases/fractions across unsteady events. Additionally, while results indicate that steady flow with a constant EMC cannot reproduce the complexity of the unsteady and coupled hydrologic PM transport and treatment thereof, such controlled pilot-scaled testing of unit operations is a necessary precursor in the development, the testing and modeling phase of a unit operation. However, such controlled testing or modeling is not sufficient to provide an accurate description of unit operation behavior subject to variable and unsteady rainfall-runoff loadings. Testing protocols for controlled and unsteady loadings should be planned such that a robust database can be generated in order to support and incorporate simulation tools such as CFD and hydrologic models and continuous simulations of unit operations in such protocols. Without the support of the physical modeling database in this study to generate a validated unsteady event-based CFD model, demonstrating the misrepresentation of PM mass by steady flow statistics would have been difficult and tenuous. While current unit operations such as the screened HS do not include maintenance between events for captured PM and pollutants, such operational considerations are required on a reasonably frequent interval to ensure event-scale performance illustrated herein to maximize scour and changing water chemistry in the unit between events.

6. Conclusions

[35] Unsteady event-based monitoring of a screened hydrodynamic separator (HS) maintained with a clean sump between rainfall-runoff events indicates that the total PM removal efficiency for the HS ranged from 39 to 70% at an event scale. To eliminate the effects of resuspension and scour from previous event PM settling and to ensure a material balance for PM an event basis with a required PM mass recovery of 90%, the HS was cleaned between events and the separated PSD enumerated. Measured PM separation by the HS subject to these unsteady hydrologic and PM loadings was modeled at the event scale by the application of the standard k-ɛ turbulence model and a Lagrangian discrete phase model for PM. Event-scale results indicate that the measured and unsteady CFD model for PM separation by the HS agreed on the basis of PM mass captured across the entire measured particle size distribution (PSD) with a relative percent difference (RPD) between measured and model PM mass within ±10%. The CFD model reproduced measured results across the entire range of unsteady flow rates and influent PSD variability for mass-limited (ML) events where PM mass exhibits first-order transport as a function of volume, and for flow-limited (FL) events that exhibit zero-order transport. Furthermore, this study tested whether CFD simulations with a single steady flow rate and constant event mean concentration (EMC) of PM, physical model conditions commonly used in controlled pilot-scale testing of manufactured unit operations such as an HS, could reproduce the PM mass separation by the HS. The common steady flow statistics tested in these steady CFD simulations are the mean, median and peak flow from each hydrograph. Results indicate that the steady mean and median flow generally underestimated effluent PM mass to a significant extent (up to −124.1% as a RPD for the mean, and up to −171.3% for the median). In contrast, the deviation of steady peak flow results with respect to measured effluent PM mass were numerically smaller for effluent PM mass load differences. The peak flow RPDs ranged from −50.1 and +62% for underestimation and overestimation of effluent PM mass, respectively. Evaluation of the fine PM mass fractions (<75 μm) eluted from the HS indicated that as the PM fraction represented an increasingly smaller gravimetric fraction of total PM the underestimation or overestimation by all of the steady flow models decreased as compared to the total PM for that event. Results indicate that accurate modeling of a unit operation loaded by unsteady hydrologic and PM loadings requires a representative description of coupled unsteady flow and PSD variations throughout the event. The time distribution of influent runoff and PSDs has significant impacts on unit operations and models.

Notation
BMP

best management practices.

CFD

computational fluid dynamics.

HS

hydrodynamic separator.

UOP

unit operations and processes.

EMC

event mean concentration.

PM

particulate matter.

ID

internal diameter (m).

OD

outer diameter (m).

PVC

polyvinyl chloride.

PCC

Portland concrete cement.

SWMM

storm water management model.

M

total effluent mass over the entire duration of the storm.

V

total volume of flow over the entire duration of the storm.

C

flow-weighted mean concentration.

c(t)

time variable particulate-bound concentration.

q(t)

time variable flow rate.

vs

discrete particle settling velocity (m s−1).

dp

particle diameter (m).

SMx

source-sink terms in the x direction in the momentum equations.

SMy

source-sink terms in the x direction in the momentum equations.

SMz

source-sink terms in the x direction in the momentum equations.

Q

influent volumetric flow rate (L s−1).

Mi

mass of particles in the influent (g).

MHS

mass of particles captured by the screened HS (g).

Me

mass of particles in the effluent (g).

equation image

fluid velocity vector (m s−1).

U

steady mean value of velocity (m s−1).

Si

source term for the ith momentum equation.

u

fluid velocity (m s−1).

up

particle velocity (m s−1).

dp

particle diameter (m).

a1, a2, a3

empirical constants for smooth spherical particles as a function of Reynolds number.

Rep

particle Reynolds number.

NHS

number of particles that remain in the screened HS.

NI

number of particles injected at the inlet.

Qd

design hydraulic operating flow rate (L s−1).

Qmax

peak flow rate for the rainfall-runoff event (L s−1).

Qpeak

peak flow rate for the rainfall-runoff event (L s−1).

Qmedian

median flow rate for the rainfall-runoff event (L s−1).

Qmean

average flow rate for the rainfall-runoff event (L s−1).

PRmeasured

measured percent removal of influent mass load.

PRmodeled

modeled percent removal of influent mass load.

PSD

particle size distribution.

PVF

particle volume fraction (%).

DPM

discrete phase model.

SSC

suspended sediment concentration (mg L−1).

QA/QC

quality analysis/quality control.

ρ

fluid density (kg m−3).

ρp

particle density (kg m−3).

μ

viscosity (kg m−1 s−1).

ϕ

shape factor of the cumulative gamma distribution.

η

scaling factor of the cumulative gamma distribution.

Ancillary