Modeling Particulate Matter Resuspension and Washout from Urban Drainage Hydrodynamic Separators

Pathapati, Subbu-Srikanth; Sansalone, John J.

doi:10.1061/(ASCE)EE.1943-7870.0000427

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TECHNICAL PAPERS

May 14, 2011

Modeling Particulate Matter Resuspension and Washout from Urban Drainage Hydrodynamic Separators

Authors: Subbu-Srikanth Pathapati [email protected] and John J. Sansalone, M.ASCE [email protected]Author Affiliations

Publication: Journal of Environmental Engineering

Volume 138, Issue 1

https://doi.org/10.1061/(ASCE)EE.1943-7870.0000427

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Abstract

Given the spatial complexity of urban drainage systems, the numerous system appurtenances and unit operations are a maintenance challenge. Maintenance can be the Achilles heel for best management practices (BMPs), and washout is of crucial importance for hydrodynamic separators (HS) that commonly function as preliminary unit operations to separate coarse particulate matter (PM) in urban systems. This study combines physical and computational fluid dynamics (CFD) models to quantify washout from two common HS types; screened (SHS) and baffled (BHS). Washout of particle size distributions (PSDs) for a range of flows is examined. Trajectory analysis of PM illustrates entrainment and washout as a function of PSDs and PM deposit depth. Velocity distributions identify washout-critical PM sizes and areas. Bed profiles are modeled by integrating velocity distributions across washout areas. A Shields washout criterion contradicts physical and CFD results, illustrating the portability challenges of open-channel approaches to nonuniform complex flows in BMPs. The driving parameter for washout is flow intensity at the PM deposit interface. The physically validated CFD model reproduces washout as a function of PSD and flow rate. A baffled HS provides volumetric isolation of deposited PM and generates low washout as tested with a fine hetero-disperse PSD. In comparison to the low washout of the baffled HS for a finer and hydraulically isolated PM deposit, a screened HS generates higher washout for a coarse monodisperse PM deposit, and over 50% of the volumetric domain has an upward velocity vector.

Introduction

Anthropogenic particulate matter (PM) transported in urban runoff is a significant contributor to deterioration of surface water (USEPA 2000). Protection of receiving waters from runoff PM and PM-associated chemicals such as nutrients and metals through separation and storage in a unit operation is challenged by factors such as hetero-dispersivity of PM, changing inter-event water chemistry, and intra-event washout. Whereas deleterious impacts of washout have been recognized for decades, physical testing of unit operations for washout susceptibility as part of a comprehensive design and management approach is recent (Guo et al. 2008; Gulliver et al. 2008).

Currently, large-scale models can address overall sediment yield. Some models apply the universal soil loss equation (Novotny and Olem 1994), whereas others apply the Shields criterion. Jennings (2003) presented a two-dimensional (2-D) depth-averaged finite element model for washout in an urban lake, by using the RMA2 module, a two-dimensional depth-averaged hydrodynamic model for computing water surface elevations and horizontal velocity components, in which vertical accelerations are small and velocity vectors generally point in the same direction U.S. Army Corps of Engineers [(USACE) 2000]. Although spatially invariant vertical velocities may be assumed in large water bodies, this is not the case in hydrodynamic separators (HS) examined in this paper.

In this study it is hypothesized that the scale and complexity of washout in unit operations such as an HS can be quantified by a physically validated computational fluid dynamics (CFD) modeling approach. Olsen and Kjellesvig (1998) combined the solutions of incompressible Navier-Stokes (N-S) equations around a cylinder with a standard

k - ε

turbulence model, with a formula for bed sediment concentration as a function of local stress. Yeganeh et al. (2000) used a 2-D Euler-Lagrangian coupled two-phase model without including interparticle interactions to simulate bed-load transport under high bottom shear. Zhao and Fernando (2007) used a Euler-Euler approach with interparticle and particle-fluid interactions. The aforementioned studies are performed for 2-D or very small scale three-dimensional (3-D) geometries. Another consideration for Eulerian-Eulerian approaches is applicability at very low particulate volume fractions (Elgobashi 1991).

Pathapati and Sansalone (2009a, 2009b) applied CFD to model PM separation by a screened HS and a media filter with computational times of 3 h, but for clean-bed systems. However, computational requirements of large-scale time-variant CFD simulations can be significant. For instance, a recent study (Duc and Rodi 2008) in which contraction washout is modeled, reported computational times up to 221 h. A less computationally-intensive CFD method to estimate washout from a unit operation in the form of effluent mass load is needed.

Objectives

The first objective of the study is to measure the washout of predeposited PM of known particle size distributions (PSDs) from two different HS types, a baffled and screened HS, across a range of steady influent flow rates. The second objective is to investigate the propensity for washout from the two HS units, by analyzing predicted velocity distributions from physically validated CFD models, and compare these results with an empirical Shields approach. The third objective is to develop a CFD model, utilizing an Euler-Lagrangian approach to simulate overall washout in the form of effluent mass load. The fourth and final objective is to investigate the possibility of determining the shape of washout from integrated velocity distributions across washout-critical areas.

Methodology

Physical Modeling Background

This study examines a screened HS consisting of two concentric cylindrical chambers separated by a static-screen with 2,400 μm openings, as illustrated in Fig. 1. The HS inlet is tangential to the inner chamber. Flow exits the cross-flow screen, which imparts a weak reversal in direction, into the outer chamber. The outer chamber functions primarily as a settling tank and flow exits the outer chamber through an effluent weir and outlet section. PM separation by the HS is a function of discrete particle settling velocity, the PSD, flow rate, the hydraulic residence time, and the screen aperture openings. PM separation is predominantly by discrete settling. The design flow rate (

Q_{d}

) for the screened HS in this study is

31.1 L / s

. The bottom sump of the HS is a cylindrical section. Three bed depths of PM are examined and illustrated in Fig. 1. The surface overflow rate (SOR) for the screened HS at flow rates of

31.1 L / s

and

38.8 L / s

, is

0.87 cm / s

and

1.09 cm / s

, respectively. In comparison, the baffled HS has a diameter of 122 cm and a depth of 182 cm. The sediment chamber had an overall surface area of

11, 674 {cm}^{2}

and a volume of 1,778.3 L, and the design flow rate was

9.05 L / s

. The design flow rate specified for the two different HS are the design flow rates provided by the manufacturer. The design flow rate is on the basis of the hydraulic capacity of each unit beyond which flow bypass occurs. Regulatory testing protocols for manufactured best management practices (BMPs) such as the HS by technology acceptance reciprocity protocol (TARP) (State of Pennsylvania 2003) specify flow rates as a percent of the manufacturer design flow rate to test for scour, and this convention is adopted in this study. A single bed depth of PM is studied as depicted in Fig. 1. The SOR for the baffled HS at flow rates of 9.05 L/s and

11.1 L / s

, is

0.77 cm / s

and

0.95 cm / s

, respectively. The PSDs of the preloaded bed PM are measured a priori and shown in Fig. 2. Textural classification is conducted for each PSD. The PSD of the screened HS is poorly graded (relatively monodisperse) sand (SP) and the PSD for the baffled HS is a hetero-disperse sandy silt (SM). The measured

d_{50 m}

of the SP and SM are 110 µm and 9.2 µm, respectively. The run times used for each test are provided in Table 1. In this study, PM-free water is run through the HS for at least four residence times, similar to methods reported in previous studies (Nauman and Buffham 1983). Melville and Chiew (1999) determined that the scour depth after 10% of the time to scour equilibrium is approximately 80% of the equilibrium scour depth at high approach flow velocities.

Fig. 1. Experimental modeling utilized in this study: (a) experimental setup for measuring washout; (b) profile view of baffled hydrodynamic separators and screened hydrodynamic separators with sediment; BHS is baffled hydrodynamic separator, SHS is screened hydrodynamic separator, $h_{BHS}$ is the effective height of water in the BHS, $h_{SHS}$ is the effective height of water in the SHS, $h_{PM}$ , $h_{PM, s}$ and $h_{PM, v}$ are the depths of PM deposits in the BHS, SHS, sump and SHS volute, respectively, SOR is the surface overflow rate ( $cm / s$ )

Fig. 2. Influent particle size distributions of preloaded PM for the SHS and BHS

Table 1. Measured and Modeled Effluent Mass Loads and Concentrations as a Function of Flow Rate and Depth of Preloaded Sediment in the SHS and BHS

Screened HS (SP), $Q_{d} = 31.1 L / s$ , $γ = 46.88$ , $β = 2.36$ , $d_{50 m} = 110 μ m$
Run #	$Q$	Duration	PM deposit depth		Effluent mass load			Effluent concentration			Effluent PSD
	$Q$	Duration	Sump	Volute	Measured	Modeled	RPD	Measured	Modeled	RPD	$γ$	$β$	$d_{50 m}$
	$L / s$	min	cm	cm	g	g	%	$[mg / L]$	$[mg / L]$	%	$γ$	$β$	$d_{50 m}$
SHS1	38.8	12	23	0	3215	3060	4.8	117	112	4.3	8.44	11.38	82.2
SHS2	31.1	15	23	0	2760	2690	2.5	103	99	3.9	6.29	14.75	79.1
SHS3	31.1	15	46	0	4510	4323	4.1	174	165	5.2	8.28	11.56	82.1
SHS4	38.8	12	46	0	5482	5421	1.1	197	192	2.5	6.50	14.33	79.7
SHS5	31.1	15	23	2.5	2979	2780	6.7	106	96	9.4	7.11	13.35	81.5
SHS6	38.8	12	23	2.5	3161	3077	2.7	115	106	7.8	5.67	16.23	78.5
SHS7	38.8	12	46	2.5	5482	5732	$- 4.6$	199	203	$- 2.0$	7.56	12.71	82.7
SHS8	31.1	15	46	2.5	5011	5323	$- 6.2$	179	188	$- 5.1$	6.40	14.47	79.1
Baffled HS (SM), $Q_{d} = 9.0 L / s$ $γ = 0.8115$ , $β = 18.60$ , $d_{50 m} = 9.2 μ m$
BHS1	9.0	25	12.7		761	743	2.4	52	50	3.8	1.47	2.34	2.4
BHS2	11.3	20	12.7		893	812	9.1	63	61	3.2	2.41	1.28	2.6

Physical Modeling Methodology

The methodology is identical for the screened and baffled HS but described only for the screened HS. Before each test, the entire system is cleaned with potable water and drained. The HS is then pluviated with a PM mixture of a known PSD, to a predetermined bed depth shown in Fig. 1. The HS is filled with potable water at a low flow rate to ensure no resuspension of bed PM. Intra-event storage of runoff and PM by an HS unit is the typical in situ condition for a HS unit. After achieving a steady flow rate with fluctuations of less than

+ 1 %

of the target flow rate, flow is diverted to the screened HS.

Influent volume is maintained constant for each run, and 20 duplicated full cross-section flow effluent samples. Suspended sediment concentration (SSC) is measured for each sample. SSC analysis is carried out by filtering each sample through a nominal 1 µm fiberglass filter. The magnitude of washout is subsequently evaluated by effluent mass load and effluent concentration. All influent is clean potable water with no PM added, as verified by SSC analysis by. PSDs are measured with a laser diffraction analyzer by using Mie scattering theory.

Computational Fluid Dynamics Background

The screened HS is modeled more accurately in 3-D, attributed to the simultaneous effects of lack of geometric symmetry, complex static-screen geometry, vortex flow, and gravitational forces on the motion of particles. Although the geometry of the baffled HS can possibly be simplified owing to the symmetry, measured velocity profiles by using acoustic Doppler velocimetry (ADV) as part of a separate study showed significant difference in geometrically symmetric planes.

Liang et al. (2005) suggest that a standard

k - ε

model is suited for scour predictions. Studies of swirling multiphase flows in hydro-cyclones have employed two-equation Reynold's-averaged Navier-Stokes (RANS) models. Pathapati and Sansalone (2009b) modeled turbulent flow in a screened HS with a standard

k - ε

model.

Computational Fluid Dynamics Methodology

The fluid flow equations that are solved in CFD are on the basis of conservation of mass and momentum:

Continuity: \frac{\partial (ρ Φ)}{\partial t} + div (ρ Φ \bar{u}) = 0

(1)

X-momentum: \frac{\partial (ρ u)}{\partial t} + div (ρ u \bar{u}) = - \frac{\partial p}{\partial x} + div (μ grad (u)) + S_{M x}

(2)

Y-momentum: \frac{\partial (ρ v)}{\partial t} + div (ρ v \bar{u}) = - \frac{\partial p}{\partial y} + div [μ grad (v)] + S_{M y}

(3)

Z-momentum: \frac{\partial (ρ w)}{\partial t} + div (ρ w \bar{u}) = - \frac{\partial p}{\partial y} + div [μ grad (w)] + S_{M z}

(4)

In the above expressions,

p

= pressure;

μ

= viscosity; and

S_{M x}

,

S_{M y}

,

S_{M x}

are source/sink terms to account for surface forces such as viscous and pressure forces, and body forces such as gravitational and centrifugal forces in the

x

,

y

and

z

directions, respectively.

In the current study the emphasis is not on the time-evolution of washout, but on the overall equilibrium washout. Therefore, the focus is on steady-state solutions. The standard

k - ε

model has been presented extensively in previous studies (Rodi 1993) and only a summary is provided. In the standard

k - ε

model turbulent flow, a closed solution is obtained for transport equations by relating Reynolds stresses to an eddy viscosity (

μ

). The transport equations of the standard

k - ε

model are expressed as follows.

\frac{\partial}{\partial t} (ρ k) + \frac{\partial}{\partial x_{i}} (ρ k u_{i}) = \frac{\partial}{\partial x_{j}} [(μ + \frac{μ_{t}}{σ_{k}}) \frac{\partial k}{\partial x_{j}}] + G_{k} + G_{b} - ρ ε + S_{k}

(5)

For

ε

:

\frac{\partial}{\partial t} (ρ ε) + \frac{\partial}{\partial x_{i}} (ρ ε u_{i}) = \frac{\partial}{\partial x_{j}} [(μ + \frac{μ_{t}}{σ_{ε}}) \frac{\partial ε}{\partial x_{j}}] + C_{1 ε} \frac{ε}{k} (G_{k} + C_{3 ε} G_{b}) - C_{2 ε} ρ \frac{ε^{2}}{k} + S_{ε}

(6)

In these expressions,

G_{k}

represents generation of

k

attributable to the mean velocity gradients;

G_{b}

is generation of

k

attributable to buoyancy;

C_{1 τ}

,

C_{2 τ}

and

C_{3 τ}

are constants (Launder and Spalding 1974);

σ_{k}

and

σ_{τ}

are the turbulent Prandtl numbers for

k

and

ε

, respectively; and

S_{k}

and

S_{τ}

are source terms. Values of

C_{1 τ}

,

C_{2 τ}

,

C_{3 τ}

,

σ_{k}

and

σ_{τ}

used in the model are 1.44, 1.92, 0.09, 1.0, and 1.3, respectively (Launder and Spalding 1974).

In modeling the free surface of flow, the writers have modeled the top surface as a fixed shear-free wall defined by a zero normal velocity and zero normal gradients of all variables (Dufresne et al. 2009; Goula et al. 2008; Jayanti and Narayanan 2004; Adamsson et al. 2003). This method makes the following assumptions.

1.

The physical and numerical modeling is carried out for steady flow, steady-state cases, in which changes in the free surface have a negligible effect on the variable of interest, the PM elution from the HS. In addition, previous research for HS units (Fenner and Tyack 1997) reports the absence of a predominant free surface in such devices. In this study, the baffled hydrodynamic separators (BHS) and screened hydrodynamic separators (SHS) have surface areas of

1.14 m^{2}

and

3.56 m^{2}

, respectively.

2.

In addition, modeling of air-water interaction is unlikely to have any significant effect on the overall CFD model owing to the relatively small surface area of HS units.

The physical depth of water in the HS is used to delineate the location of the top surface as function of flow rate for each HS. The depth of water in the HS is obtained by measurement after a steady flow rate is achieved. Following this, with grid generation, a surface is created at the measured flow height at a given flow rate. Although specifying boundary conditions, this surface is treated as a wall with no shear specified in

x

,

y

, and

z

directions, mimicking a free surface.The screen apertures shape result in a weakly reversed flow direction in the outer chamber; 40% of the screen area is open and radial velocity through the screen is an order of magnitude lower than the inlet velocity. The screen is modeled as a perforated (2,400 μm) plate, with values of inertial resistance in

x

,

y

, and

z

directions, assuming negligible viscous resistance. The domain is discretized as an unstructured mesh composed of tetrahedral elements, and grid convergence is achieved at a grid density of 2.14 million cells for the screened HS and 5 million cells for the baffled HS. Flow solutions are obtained by using a finite-volume approach, and a second order upwind scheme. The semi-implicit method for pressure-linked equations (SIMPLE) algorithm (Patankar 1980) is utilized to account for pressure-velocity coupling.

Multiphase flows are modeled with an Euler-Euler approach or an Euler-Lagrangian approach (van Wachem et al. 2003), depending on the extent of coupling between phases. On the basis of the regime map proposed by Elgobashi (1991) for appropriating the degree of interphase coupling, an Euler-Lagrangian approach is suitable for the dilute nature of the PM-laden flow in this study. In this approach, the flow field is solved by using the Eulerian approach. Subsequently, particles are tracked by using a Lagrangian discrete phase model (DPM). The DPM is derived from force balances on the basis of classical Newton’s (turbulent and transitional regimes) and Stokes (laminar regimes) laws describing PM settling, and is summarized by the following equations.

\frac{d u_{p}}{d t} = F_{D} (u - u_{p}) + \frac{g_{x} (ρ_{p} - ρ)}{ρ_{p}} + F_{x}

(7)

F_{d} = \frac{18 μ}{ρ_{p} d_{p}^{2}} \frac{C_{D} {Re}_{p}}{24}

(8)

C_{D} = a_{1} + \frac{a_{2}}{{Re}_{p}} + \frac{a_{3}}{{Re}_{p}^{2}}

(9)

R_{p} \equiv \frac{ρ d_{p} | u_{p} - u |}{μ}

(10)

in which

u

, = fluid velocity;

u_{p}

= particle velocity;

ρ

= fluid density;

ρ_{p}

= particle density;

d_{p}

= particle diameter;

μ

= viscosity;

a_{1}, a_{2}, a_{3}

are constants for particles as a function of the Reynolds number (Morsi et al. 1972); and

R_{p}

= particle Reynolds number.

The washout from the PM sediment bed is modeled as follows from Fig. 3.

1.

A steady-state, grid independent solution is obtained for the flow field in the HS.

Following this step ‘layers’ are created in the region of the computational domain consisting of the pluviated PM bed. This is carried out by creating a group of planes such that the interval size between these layers or surfaces is equal to approximately one particle diameter. These layers are created for each particle size in the PSD.

2.

The number of points and layers available to place particles to simulate the sediment bed are a function of mesh density. For example, by using an interval size of 25 µm across, 230 mm sediment depth yields approximately 9,200 layers. With a mesh density of 2.1 million cells, this resulted in the availability of approximately 27,384 points per layer for the SHS.

3.

The mesh size ranges from 1-3 cm and tetrahedral mesh volume is

0.12 {cm}^{3}

for a total volume of

196, 058 {cm}^{3}

and

277, 935 {cm}^{3}

for the BHS and SHS respectively, with a total mesh size of

2.1 e + 06

and

5 e + 06

of the SHS and BHS respectively, at grid convergence. Further refinement of the mesh did not result in significant change in PM elution (

α = 0.05

).

4.

The tracking length for tracking particles is determined by simulating a tracer study. A neutrally buoyant ‘tracer’ is input into each surface, and tracking length is iteratively modified until

+ 1 %

of tracer is eluted from the unit, similar to a single pulse input tracer study (Levenspiel 1998). In this manner, an unbiased tracking length is obtained from each layer. This tracking length is applied uniformly for each particle size, for example a 25 µm particle is tracked with the same length as a 250 µm particle. As an example, by using these criteria for the SHS results in a top-most layer with a tracking length of 6 m, whereas the bottom-most layer has a tracking length of 8.5 m. In comparison, the BHS has a tracking length of 7 m for the top-most layer, and the bottom-most layer has a tracking length of 9 m.

5.

Following this, particles are ‘placed’ at nodes across all the layers for the entire depth of the pluviated PM bed. Particles are defined as silica particles of diameters associated with the PSDs utilized, and a measured specific gravity of 2.63 as determined by helium pycnometry. When particles are placed at these nodes, and tracked with discrete phase model the ambient fluid dynamics will either resuspend the particles or allow the particles to settle. Those particles that are resuspended can then be eluted from the HS or can resettle elsewhere in the HS. The number of particles that remain in the HS after determining the unbiased tracking length are considered as retained.

6.

This process is repeated for each individual particle size. This study uses 17 particle sizes. The appropriate weighting is assigned to each particle size on the basis of the PSD analyzed on the basis of the percent distribution of PSD in the SM and SP gradations, as depicted in Fig. 2.

7.

Following this, the effluent mass load is calculated as follows.

Effluent Mass Load = \int_{0}^{d p} \int_{0}^{n} (N_{released} - N_{retained}) d n

(11)

d n = \frac{HPM}{d_{p}}

(12)

Fig. 3. Models of washout: (a) schematic of washout, pre- and post-CFD modeling; (b) schematic of washout modeling methodology by integrating across surfaces (not to scale); $H_{PM, s}$ = depth of predeposited PM in the sump, $d n$ = interval between plane surfaces, $d_{p}$ = particle diameter

In the above expressions,

N_{released}

and

N_{retained}

are the number of particles released per surface and the number of particles that are not eluted from the HS; ‘

n

’ = total number of layers of placement, respectively;

d n

= interval between surfaces;

H_{PM}

= prewashout sediment depth in each HS: and

d_{p}

= particle diameter.

Without a priori knowledge of the scour depth, layers or plane surfaces are created for each particle size at regular intervals across the entire depth of PM sediment bed. However, if the scour topography is precisely measured, these layers can be reduced to a depth that incorporated the depth of scour but did not include the entire PM sediment bed depth, thus reducing the computational effort.

Results

CFD results are examined on the basis of fluid velocities and pathlines, velocity vectors, isosurfaces of velocities, and normalized frequency distributions. Fig. 4(a) depicts velocity vectors in the screened HS. There is no underflow in the HS, and there is a vortex created in the inner screen chamber. The vortex vectors of the inner screening area create high velocities that are reflected upward. However, in the outer chamber, velocity magnitudes are lower and more uniform. Fig. 4(b) depicts velocity vectors in the baffled HS. In contrast, fluid velocities at the bottom of the baffled HS are more uniform and of low magnitudes. These results indicate that a larger fraction of the fluid volume is mobilized in the screened HS compared to the baffled HS. In addition, the bottom region of the screened HS has higher flow velocity magnitudes as compared to the baffled HS. The lower zone of the baffled HS is predominantly quiescent without volumetric utilization. The comparison suggests that washout likely occurs to a greater extent in the screened HS than in the baffled HS.

Fig. 4. Velocity vectors in the interior of (a) screened hydrodynamic separators and (b) baffled hydrodynamic separators

Fig. 5 summarizes frequency distributions of the mean fluid velocities in the inner and outer volute chamber of the screened HS, and in the baffled HS. It is evident that there is a wider distribution of velocities in the screened area of the screened HS as opposed to the volute area. This is attributed to the presence of a forced vortex, and possible secondary currents in the screen area. Mechanistically, separation mechanisms in the screened area tend toward inertial separation of gross solids and size exclusion for large PM by the 2,400 μm static-screen. The volute area, with a narrow distribution of lower velocities, is more conducive to discrete particle settling and also to washout. Similar to the volute area in the screened HS, th e mean fluid velocities in the baffled HS also exhibit a narrow range and lower velocities, which suggest appropriate conditions for discrete particle settling. On the basis of these results, Fig. 5 suggests settling throughout the baffled HS and washout in the screened HS inner chamber and, to a lesser degree, in the volute section.

Fig. 5. Normalized mean fluid velocity distributions inside the inner screened hydrodynamic separators and outer volute area of screened hydrodynamic separators, and the entire domain of the baffled hydrodynamic separators; bin sizes are consistent for screened baffled hydrodynamic separators and baffled hydrodynamic separators; negative velocities indicate an upwards direction (opposite to gravity)

Effluent Mass Load and Particle Size Distributions at Equilibrium Washout

The potential for resuspension and washout of predeposited PM (SP) in the screened HS is examined as a function of the flow rates corresponding to 100% (

38.8 L / s

) and 125% (

31.1 L / s

) of the design flow rate and as a function of sediment depth in the HS sump and volute chambers. Table 1 summarizes physical conditions and results from washout tests for the screened HS. Influent potable water is sampled and the SSC does not deviate significantly from

0 mg / L

. Sump depths of 23 cm and 46 cm correspond 50% and 100% of total sump depth. It is observed that that depth of PM in the sump influences washout more significantly than an increase in flow rate from

31.1 L / s

to

38.8 L / s

. Effluent PM concentrations ranged from

103 mg / L

for a flow rate of

31.1 L / s

and PM depth of 23 cm, to

197 mg / L

for a flow rate of

38.8 L / s

and a PM depth of 46 cm. There is no significant change in washout for tests that included predeposited PM in the outer volute region. This is supported by the velocity distributions described previously in which the velocities are less in the outer volute region with less potential for washout.

The washout from the baffled HS is influenced by the PSD of the settled PM. There also is an increase in washout as flow rate increases from 100% (

9 L / s

) to 125% (

11.3 L / s

) of design flow rate. Effluent concentrations of PM are provided in Table 1. In comparison to the screened HS, the overall washout is significantly less for the baffled HS owing to the uniformly low velocity distributions in the baffled HS, in particular in the lower quiescent zone of the sump. Relative percent differences (RPD) are utilized to compare measured and CFD modeled results, and are calculated as follows.

RPD (%) = 100 * (\frac{measured-modeled}{measured})

(13)

The CFD model is able to reproduce measured results, with all RPDs below 10%.

Measured and modeled effluent PSDs are compared in Fig. 6. The model predicts effluent particle gradations. Plots illustrate the dependence of effluent PM mass washed out on the PSD of predeposited sediment for both HS units.

Fig. 6. Measured and modeled effluent particle size distributions in the screened hydrodynamic separators (left column) for different initial conditions (SHS 1 to SHS 11, elaborated in Table 1) and baffled hydrodynamic separators (right column) for different initial conditions (BHS 1 to BHS 5, elaborated in Table 1)

The minimum SP gradation particle size retained by the screened HS is approximately 120 µm as compared to approximately 20 µm retained by the baffled HS. The influent and effluent PSDs are modeled as cumulative gamma distributions. The probability density function of a gamma distribution is given by the following expression. A gamma probability density function represents PM separation as a function particle diameter, symbolized as “

x

”.

f (x) = \frac{(\frac{x}{β})^{γ - 1} e^{(- \frac{x}{β})}}{(β) Γ (γ)}

(14)

γ

and

β

are shape and scaling factor, respectively; and

F (x)

= cumulative gamma distribution.

F (x) = \int_{0}^{x} f (x) d x

(15)

With a CFD model that reproduces measured physical model data, the CFD model is utilized to compare washout from the screened HS at 100% and 125% of the design flow rates of the baffled HS, with SM as the influent particle gradation (a much finer and hetero-disperse PSD than the SP). In parallel, the baffled HS is examined at 100% of the design flow rate of the screened HS, with SP as the predeposited PM. Results are provided in Table 2. Washout from the screened HS is much higher than from the baffled HS, at the same flow rate, notwithstanding that the screened HS has a larger unit diameter, and higher unit surface area than the baffled HS. The baffled HS showed negligible washout with the SP gradation at 100% and 125% of design flow rates. The baffled HS illustrates a negligible amount of washout (effluent of

1.2 mg / L

), even at the higher flow rate (100% of

Q_{d}

of the screened HS,

31.1 L / s

). Washout also is modeled for the more quiescent volute area of the screened HS, with the sump and volute loaded with the finer SM gradation. Results for SHS 11 from Table 2 illustrate high washout even from the volute region of the HS for this finer PSD. However, it is clear that a large portion of the washout occurs from the turbulent screen area. The baffled HS and the volute area of the screened HS are relatively quiescent and similar to each other in velocity distributions, as shown in Fig. 5. For the SM gradation, Table 2 indicates the

d_{50}

of PM eluted from the baffled HS is finer than 10 μm, whereas the same threshold is 49 μm for the screened HS. This suggests the existence of short circuiting of flow in the volute area. However, even with a coarser PSD, the screened HS has greater washout than the baffled HS with a finer predeposited PM.

Table 2. Model Predictions of Effluent Mass Loads and Concentrations as a Function of Flow Rate and Depth of Preloaded Sediment in the SHS and BHS

Run #	$Q$	PM deposit depth		Modeled results		Effluent PSD
	$Q$	Sump	Volute	Effluent mass load	Effluent concentration	$γ$	$β$	$d_{50 m}$
	$L / s$	cm	cm	g	$[mg / L]$	$γ$	$β$	$d_{50 m}$
Screened HS (SP), $Q_{d} = 31.1 L / s$ , $γ = 46.88$ , $β = 2.36$ , $d_{50 m} = 110 μ m$
SHS9	31.1	23	0	18200	665	0.88	14.93	9.1
SHS10	31.1	46	0	36400	1330	0.92	13.02	9.3
SHS11	31.1	0	2.5	8963	327	1.04	22.41	10.9
Baffled HS (SM), $Q_{d} = 9.0 L / s$ , $γ = 0.8115$ , $β = 18.60$ , $d_{50 m} = 9.2 μ m$
BHS3	9.0	12.7		0	0	n/a	n/a	n/a
BHS4	11.3	12.7		0	0	n/a	n/a	n/a
BHS5	31.1	12.7		18	1.2	195.3	0.27	49

Fig. 7 compares trajectories of washed out discrete particles of selected diameters for the screened HS and baffled HS. Figs. 7(a), (b), and (c) correspond to particle diameters of 300 µm, 53 µm, and 10 µm, respectively. As illustrated in Fig. 7(a) 300 µm particles are not washed out in either HS. However, in the screened HS, the velocities in the sump are high enough to cause washout, although the quiescent conditions in the volute area is more washout-neutral than the sump. From Figs. 7(b) and (c), there is significant washout of PM in the settleable and suspended fractions in the screened HS. Resuspension and washout of these particles is significantly less for the baffled HS.

Fig. 7. Washed out particle trajectories inside the screened hydrodynamic separators (left column) and baffled hydrodynamic separators (right column) for (a) $d_{p} = 300 μ m$ , (b) $d_{p} = 50 μ m$ , and (c) $d_{p} = 10 μ m$

Shape of Washout

The shape of washout on the basis of velocities is predicted by integrating across the depth of the area of the deposited PM surfaces. Fig. 8(a) provides integrated radial velocity distributions delineated across the outer volute area and the sump of the screened HS. There are higher velocities toward the sump perimeter as opposed to the center, which translates to more washout toward the perimeter as opposed to the center. Results match visually-observed washout patterns at the end of each physical model run. Observed volute area washout patterns are not as pronounced and are more diffuse. Velocities in the volute area are low and support this observation. Fig. 8(b) illustrates fairly uniform velocity distributions in the baffled HS that do not translate to a predominance of washout in any given region. There is a slight peak corresponding to the baffled HS area directly below the effluent drop-pipe, suggesting washout potential directly underneath. This can further be verified from visual inspection of the location of washout from Fig. 7.

Fig. 8. Velocity distributions corresponding to washout shape in (a) screened hydrodynamic separators and (b) baffled hydrodynamic separators

Conclusions

This study examines washout from two common hydrodynamic separators (HS) for two PSDs of predeposited PM, across a range of flow rates. For the screened HS, measured effluent PM ranged from

103 mg / L

for a flow rate of

31.1 L / s

and PM depth of 23 cm, to

197 mg / L

for a flow rate of

38.8 L / s

and a PM depth of 46 cm. The results indicate that the PM depth in the screened HS has a more significant influence on washout than the increase in flow rate for the coarse monodisperse SP gradation. The results indicate that washout from the baffled HS is influenced by the PSD, and there is an increase in washout with increasing flow rate. Even with the finer SM gradation, the washout from the baffled HS is significantly less than the screened HS, and in comparison ranges from

25 mg / L

to

63 mg / L

. When comparing the effluent PSD from the baffled and screened HS, the effluent PSD from the screened HS is consistently coarser for the screened HS whether both units are preloaded with an SM or SP gradation.

The applicability of the Shield’s criterion in predicting incipient motion is tested with the aid of predicted CFD frequency distributions of mean velocities and velocity vectors. The results indicate that for a wide range of particle sizes from 300 µm to finer than 10 µm, the Shield’s diagram predicts that washout should not occur, even utilizing the maximum velocity values. This is contradicted by measured and CFD modeled results.

The CFD model reproduces physically modeled results for effluent PM yield in terms of mass and concentration, and effluent PSD. The RPD between measured and modeled data is below 10% for each HS unit. The smallest PM size not washed out by the screened and baffled HS is 120 and 20 µm for the SP gradation, and 49 and 10 μm for the SM gradation, respectively. Postprocessing Lagrangian particle trajectory results show regions of initiation, entrainment, and pathways for washout as a function of PM diameter. Although coarser PM is not washed out from either HS, finer-size PM is eluted to a significantly larger degree by the screened HS as opposed to the baffled HS. The results indicate that greater than 50% of the domain consists of upward velocities (negative) in the screened HS. The percentage of velocities in a given unit operation can be utilized to obtain an approximation of the PM sizes washed out. Such results can enable a designer to identify areas of high velocities and pressure gradients, and therefore try to mitigate these phenomena via retrofits such as baffles or through unit redesign.

Finally, this study investigates the shape of washout by integrating velocity distributions. Integrated velocity distributions predict higher velocities toward the perimeter of the sump as opposed to the center, which implies higher washout toward the periphery of the sump. This prediction matches the observed washout patterns in the sump region of the screened HS and can give a general index for the shape of washout. The CFD method to quantify washout from HS units is promising in terms of computational time. Computational time for one steady simulation for an HS with 2.14 million cells is 3 h on a Pentium Xeon 3.2 Ghz workstation. Although computational resources are of interest, a crucial variable to stakeholders is effluent mass yield from washout. The use of a validated CFD model can help this effort to a greater degree of accuracy than empirical approaches illustrated, although simpler approaches can be readily implemented until CFD is increasingly adopted. Washout from unit operations (BMPs) directly affects event-based and long-term performance and is of prime concern owing to the challenges of BMP maintenance and residual management. Although many BMPs can meet regulatory requirements upon installation, without frequent maintenance there is performance deterioration owing to changing inter-event water chemistry and intra-event washout and hydraulic response, as shown in this paper by high washout from the screened HS.

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Published In

Journal of Environmental Engineering

Volume 138 • Issue 1 • January 2012

Pages: 90 - 100

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Received: Dec 24, 2009

Accepted: May 12, 2011

Published online: May 14, 2011

Published in print: Jan 1, 2012

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Subbu-Srikanth Pathapati [email protected]

Postdoctoral Researcher, Environmental Engineering Sciences, Univ. of Florida, Engineering School of Sustainable Infrastructure and Environment (ESSIE), 220 Black Hall, Gainesville, FL 32611. E-mail: [email protected]

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John J. Sansalone, M.ASCE [email protected]

Professor, Environmental Engineering Sciences, Univ. of Florida, Engineering School of Sustainable Infrastructure and Environment (ESSIE), 220 Black Hall, Gainesville, FL 32611 (corresponding author). E-mail: [email protected]

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Modeling Particulate Matter Resuspension and Washout from Urban Drainage Hydrodynamic Separators

Abstract

Introduction

Objectives

Methodology

Physical Modeling Background

Physical Modeling Methodology

Computational Fluid Dynamics Background

Computational Fluid Dynamics Methodology

Results

Effluent Mass Load and Particle Size Distributions at Equilibrium Washout

Shape of Washout

Conclusions

References

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Abstract

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Shape of Washout

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