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EXPERIMENTAL AND NUMERICAL ANALYSIS OF STORMWATER UNIT OPERATIONS AND PROCESSES

By

SUBBU-SRIKANTH PATHAPATI

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2008

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© 2008 Subbu-Srikanth Pathapati

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To my grandfather, the late Pathapati Subba Rao

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ACKNOWLEDGMENTS

First and foremost, I extend my gratitude to my advisor, Dr. John Sansalone, for his

continued support, encouragement and guidance. In addition to academic knowledge, I have

learned the elements of a distinguished work ethic from him. I will take these experiences with

me, in all my future career endeavors.

I extend my sincere appreciation to the members of my graduate committee: Dr. James

Heaney, Dr. Ben Koopman and Dr. Jennifer Curtis for their interest, advice and insight. I am

forever in debt to them for their guidance.

I thank my dear colleagues and friends who have helped me in the lab and in the field:

Dr. Jong-Yeop Kim, Dr. Bo Liu, Dr. Gaoxiang Ying, Natalie Magill, Robert Rooney, Adam

Winberry, Dr.Ki-Joon Jeon, Saurabh Raje, Ruben Kertesz, Tingting Wu, Sandeep Gulati ,Hwan-

chul Cho, Giuseppina Garofalo, Josh Dickenson, Paul Indeglia, Dr. Tianpeng Guo , Dr. Xuheng

Kuang, Will Barlett, and Matt McGaugh.

I thank the many friends I have made during these years, for being there for me

throughout and would like to name a few of these: Dr. Srinivas Gopal Krishna, Ashwin Chittoor,

Chetan Salimath, Arpit Mathur, Bharath Thiruvengadachari, Karthik Bharat, Avinash Rajendran,

Kishore Menon, Rupa Nair,.Sruti Ramnath Aditya, Preeti Bhuvan, Aditya Ramachandran,

Praveen Sampath, Jayaram Balasubramanian, Karthik Chepudira, and many others.

I thank my mother Mrs. Lakshmi Govindaraju, my aunt Ms. Padma Pathapati, my

grandmother, Mrs. Sundari Pathapati, and to my uncle Mr. Kotesh Govindaraju for their support.

I thank Dr. Phillip Barkley of the University of Florida Health Center for taking care of

me. I express my sincere gratitude to Dr. Jocelyn Lee of the University of Florida Health Center,

for her tremendous kindness, insight and compassion.

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TABLE OF CONTENTS

page

ACKNOWLEDGMENTS ...............................................................................................................4

LIST OF TABLES...........................................................................................................................8

LIST OF FIGURES .........................................................................................................................9

LIST OF ABBREVIATIONS........................................................................................................11

ABSTRACT...................................................................................................................................17

1 GLOBAL INTRODUCTION.................................................................................................19

2 EXPERIMENTAL MODIFICATION OF A STORMWATER HYDRODYNAMIC SEPARATOR FOR ENHANCED PARTICLE SEPARATION ...........................................25

Introduction.............................................................................................................................25 Background.............................................................................................................................27 Objectives ...............................................................................................................................28 Methodology...........................................................................................................................29

Experimental Site Setup ..................................................................................................29 Influent Particle Gradation ..............................................................................................30 Field Test Procedure........................................................................................................31 Laboratory Analyses........................................................................................................32 Geometric Configurations ...............................................................................................33 Tracer Analysis................................................................................................................35

Results and Discussions..........................................................................................................38 Treatment Influent Flow Rate at 25 % of Design Flow Rate ..........................................38 Treatment Influent Flow Rate at 75 % of Design Flow Rate ..........................................39 Treatment Influent Flow Rate at 125 % of Design Flow Rate ........................................41 Discussion........................................................................................................................42 Tracer Study Results........................................................................................................43

Conclusions.............................................................................................................................46

3 CFD MODELING OF A STORMWATER HYDRODYNAMIC SEPARATOR.................63

Introduction.............................................................................................................................63 Objectives ...............................................................................................................................67 Methodology...........................................................................................................................68

Pilot-scale Testing Setup .................................................................................................68 Influent Particle Gradation ..............................................................................................68 Field Test Procedure........................................................................................................69 Laboratory Analyses........................................................................................................70 Computational Fluid Dynamics Methodology ................................................................71 Modeling Fluid Flow.......................................................................................................71

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Modeling the Static Screen..............................................................................................73 Modeling the Particulate Phase .......................................................................................75 Discretization of Geometry .............................................................................................76 Discretization of Governing Equations ...........................................................................77 Solution Schemes ............................................................................................................77

Results and Discussions..........................................................................................................78 PSD Results .....................................................................................................................78 CFD Model Results .........................................................................................................78 Post-processing CFD Model Results: Particle Dynamics and Hydrodynamics ..............80 Dynamics of a Particle with dp= 450 µm ........................................................................82 Dynamics of a Particle with dp= 25 µm ..........................................................................82

Conclusions.............................................................................................................................83

4 COMBINING PARTICLE ANALYSES AND CFD MODELING TO PREDICT HETERO-DISPERSE PARTICULATE MATTER FATE AND PRESSURE DROP IN A PASSIVE RAINFALL-RUNOFF RADIAL FILTER........................................................94

Introduction.............................................................................................................................94 Objectives ...............................................................................................................................96 Methodology...........................................................................................................................97

Experimental Setup .........................................................................................................97 Media Characteristics ......................................................................................................98 Prototype Test Procedure ................................................................................................98 Laboratory Analyses........................................................................................................99 Pressure Head Measurements........................................................................................101 Computational Fluid Dynamics Model .........................................................................101 Modeling Flow in Porous Media...................................................................................102 Modeling the Particulate Phase .....................................................................................104 Discretization and Solution Schemes ............................................................................106

Results and Discussions........................................................................................................106 Experimental Results.....................................................................................................106 CFD Model Results .......................................................................................................107 Particle Separation.........................................................................................................107 Head loss and Pressure Distributions ............................................................................108

Conclusions...........................................................................................................................110

5 MODELING HYDRAULICS AND PARTICLE DYNAMICS OF A STORMWATER HYDRODYNAMIC SEPARATOR FOR TRANSIENT INFLUENT LOADS..................123

Introduction...........................................................................................................................123 Objectives .............................................................................................................................126 Methodology.........................................................................................................................127

Experimental Methodology ...........................................................................................127 Multiphase Flow Modeling Methodology.....................................................................129 Modeling the Particulate Phase .....................................................................................134 Discretization and Solution Schemes ............................................................................136

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Results and Discussions........................................................................................................136 Conclusions...........................................................................................................................140

6 A PARTICLE SEPARATION MODEL OF A VOLUMETRIC CLARIFYING FILTER FOR SOURCE AREA RAINFALL-RUNOFF PARTICULATE MATTER ......................148

Introduction...........................................................................................................................148 Media filtration of rainfall-runoff..................................................................................148 Modeling Approach.......................................................................................................151

Objectives .............................................................................................................................152 Methodology.........................................................................................................................152

VCF and Watershed Configuration ...............................................................................152 Data Acquisition and Management ...............................................................................154 Influent and Effluent Sampling and Analysis ...............................................................156 Multiphase flow Modeling Methodology......................................................................158 Modeling the Particulate Phase .....................................................................................161 Discretization and Solution Schemes ............................................................................163 Time Discretization .......................................................................................................164

Results and Discussion .........................................................................................................165 Event-Based Hydrologic Loadings and Response ........................................................165 Filter Media Cartridge Head Loss Modeling Results....................................................166 Separation of Particulate Matter Modeling Results.......................................................167

Conclusions...........................................................................................................................169

7 GLOBAL CONCLUSIONS .................................................................................................182

LIST OF REFERENCES.............................................................................................................185

BIOGRAPHICAL SKETCH .......................................................................................................192

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LIST OF TABLES

Table page 2-1 Comparison of target particle size distribution with calculated and measured gradation

utilizing 5 different Silica particle gradations....................................................................49

2-2 Experimental matrix for optimization of the screened HS....................................................50

2-3 Clarification response or particle separation (expressed as SSC removal efficiency) of different configurations to the influent particle gradation .................................................51

2–4 Indices for characterizing hydraulic response across flow rates representing 25%, 75% and 125% of Qd , where Qd is the design flow rate............................................................52

3-1 Summary comparison of pilot-scale measurements, CFD modeled results, and overflow rate (Q/A) model results.....................................................................................................86

4-1 Summary of SSC results for RCF tested with a Sil-co-Sil 106 gradation at a nominal concentration of 200 mg/L. EBCT is the mean fluid empty bed contact time. ...............113

5-1 Summary of measured and modeled particulate matter (PM) separation by the screened HS for four discrete storm events. ...................................................................................141

5-2 Summary of measured and modeled particulate matter (PM) separation by the screened HS for four discrete storm events, using the measured EMC..........................................141

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LIST OF FIGURES

Figure page 2-1 Experimental setup for testing the screened HS.. ..............................................................53

2-2 Geometry of the screened HS.. ..........................................................................................54

2-3 Plots of target influent particle size distribution. ...............................................................55

2-4 Clarification response of different configurations across flow rates. ................................56

2-5 Particle Size Distributions of separated particles at Q = 0.25*Qd. ....................................57

2-6 Particle Size Distributions of separated particles at Q = 0.75*Qd.. ...................................58

2-7 Particle Size Distributions of separated particles at Q = 1.25*Qd.. ...................................59

2-8 Tracer study at a flow rate Q = 0.25*Qd. ...........................................................................60

2-9 Tracer study at a flow rate Q = 0.75*Qd. ...........................................................................61

2-10 Tracer study at a flow rate Q = 1.25*Qd ............................................................................62

3-1 Full scale experimental setup for testing a screened HS....................................................87

3-2 Observed phase shift in particle size distribution from influent to effluent. .....................88

3-3 Demonstration of grid independence. ................................................................................89

3-4 Measured vs. modeled Δ Mparticles. .....................................................................................90

3-5 Comparison of measured versus modeled results as a function of Q ................................91

3-6 Particle trajectories calculated by a Lagrangian DPM for the screened HS......................92

3-7 Modeled velocity distributions within the screened HS ....................................................93

4-1 Process flow diagram for steady flow operation of the radial filter cartridge. ................114

4-2 Profile view of the radial cartridge filter (RCF) apparatus ..............................................115

4-3 Measured media size expressed as a Gaussian frequency histogram.. ............................116

4-4 Observed phase shift in particle size distribution from influent to effluent. ...................117

4-5 Comparison of measured versus modeled results as a function of influent flow rate .....118

4-6 Head loss (ΔH) as a function of influent flow rate (Q)....................................................119

4-7 Measured vs. modeled Δ particle mass in the effluent of the RCF..................................120

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4-8 Head loss (ΔH) and pressure distributions in the RCF. ...................................................121

4-9 CFD predictions of trajectories of fluid and particles inside the RCF.............................122

5-1 Plan and side view of detailed geometry of a screened HS. ............................................142

5-2 Experimental site for monitoring rainfall-runoff from an urban highway.......................143

5-3 Influent hydrology for four discrete storm events ...........................................................144

5-4 Measured vs. modeled particle size distributions separated by the screened HS. ...........145

5-5 Temporal particle trajectories calculated by a Lagrangian DPM for the screened HS....146

5-6 Modeled versus measured particle size distributions for four storm eventsn. .................147

6-1 Plan view of experimental site and Volumetric Clarifying Filter (VCF) system. ...........171

6-2 Location of the pressure transducers installed in the Volumetric Clarifying Filter.........172

6-3 Measured media size expressed as a Gaussian frequency histogram. .............................173

6-4 Profile and plan views of a section of the computational grid of the VCF system..........174

6-5 Hydrographs and hyetographs for 5 real-time rainfall runoff events ..............................175

6-6 Measured vs. modeled cartridge head loss profiles as a function of normalized time. ...176

6-7 Comparison of head loss as a function of surface loading rate (SLR).............................177

6-8 Head loss (ΔH) and pressure distributions in the VCF....................................................178

6-9 Comparison of measured and modeled temporal variation in effluent mass...................179

6-10 Measured versus modeled effluent concentrations as function of storm elapsed time....180

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LIST OF ABBREVIATIONS

A Effective surface area of the filter media (m2)

321 ,, aaa Empirical constants for smooth spherical particles as a function of Reynolds

number

(AOCM)p Aluminum oxide coated media with a pumice substrate

Ai Effective area of the inlet throat

As Effective screen area

BMP Best management practices

2C Inertial resistance factor, (m-1)

ε1C , ε2C , ε3C Empirical constants in the standard k-ε model

C(t) Tracer concentration at time t

Ceff Effluent concentration (mg L-1)

CFD Computational fluid dynamics

Ci-IN Concentration of influent during time period i (L s-1)

Cj-EFF Concentration of influent during time period j (L s-1)

CSO Combined sewer overflow

CV Control volume

sd Diameter of the screen apertures (m)

md Granular media particle diameter (m)

pd Particle diameter (m)

d15m Particle diameter at which 15% of particle gradation mass is finer

d50m Median particle diameter based on mass

d50m Particle diameter at which 50% of particle gradation mass is finer

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d85m Particle diameter at which 85% of particle gradation mass is finer

Deff Duration of effluent (min)

Dinf Duration of influent (min)

dp Particle diameter

DPM Discrete phase model

Drain Duration of rainfall (min)

E(t) Residence time distribution function

EBCT Empty bed contact time (s)

ECD Equivalent circular diameter

EMC Event mean concentration

ER Efficiency ratio (%)

F(t) Cumulative Residence time distribution function

kG Generation of k due to the mean velocity gradients

bG Generation of k due to buoyancy

HS Screened hydrodynamic separator

ID Inner diameter (cm)

IDs Inner diameter of the screen area (m)

IDv Inner diameter of the volute area (m)

k Turbulent kinetic energy per unit mass, (m2s-2)

mK Physico-chemical property of media

)(' iLK Loss coefficient through perforated plate in the ith direction (m-1)

)(iLK Loss factor through perforated plate in the ith direction (m-1)

L Length of the packed bed (m)

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Lx Length in the x-direction (m)

Ly Length in the y-direction (m)

m Number of effluent measurements

MDI Morrill Dispersion Index

Me Mass of particles in the effluent

Mi Mass of particles in the Influent

iM Mass of particles in the Influent (g)

RCFM Mass of particles captured by the RCF (g)

HSM Mass of particles captured by the Screened HS (g)

IN Number of particles injected at the inlet

HSN Number of particles that remain in the screened HS

RCFN Number of particles that remain in the screened RCF

n Number of influent measurements

OD Outer diameter (cm)

PM Particulate matter

PR % removal (%)

PSD Particle size distribution

PVF Particle volume fraction (%)

Q Influent volumetric flow rate (L s-1)

QA/QC Quality assurance and Quality control

Qd Design hydraulic operating flow rate (L s-1)

Qeff-avg Average effluent flow rate (L s-1)

Qeff-max Maximum effluent flow rate (L s-1)

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Qinf-avg Average influent flow rate (L s-1)

Qinf-max Maximum influent flow rate (L s-1)

Qmax Peak flow rate for the rainfall-runoff event (L s-1)

Qmean Average flow rate for the rainfall-runoff event (L s-1)

Qmedian Median flow rate for the rainfall-runoff event (L s-1)

AQ / Surface loading rate (m s-1)

pRe Particle Reynolds number

mediaRe Porous media Reynolds number

RCF Radial cartridge filter

RTD Residence Time Distribution

SLR Surface loading rate, (Lm-2m-1)

SSC Suspended Sediment Concentration

kS , εS User-defined source terms in the standard k-ε model

ΦS Source/sink term in the generalized scalar conservation equation;

iS Source term for the i th momentum equation

t Time measured from “time 0”

t50 Time at which 50 % of tracer had passed through the reactor

t90 Time at which 90 % of tracer had passed through the reactor

tmean Mean hydraulic residence time from tracer measurements

tp Time at which peak concentration is observed

U Steady mean value of velocity, (m s-1)

u Fluid velocity (m s-1)

u Fluid velocity vector, (m s-1)

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)(tu′ Fluctuating component superimposed on it, (m s-1)

wvu ′′′ ,, Vector components of velocity fluctuations due to turbulence, (m s-1)

pu Particle velocity (m s-1)

UOP Unit operations and processes

sv Discrete particle settling velocity (m s-1)

rv Radial velocity component in the screening area (m s-1)

tv Tangential velocity component in the screening area (m s-1)

magv Velocity magnitude in the cell, (m s-1)

2xv Square of the velocity through the plate, considering that the plate is ‘x’ % open

to flow in the given direction, (m2s-2)

2Σv Square of the velocity through the plate, considering that the plate is 100 % open

to flow in the given direction, (m2s-2)

sv Superficial velocity through the porous media (m s-1)

V Volume of the unit

VCF Volumetric clarifying filter

Vi-IN Volume of influent during time period i (L s-1)

Vj-EFF Volume of effluent during time period j (L s-1)

vr Radial velocity component in the screen area

vs Discrete particle settling velocity

vt Tangential velocity component in the screen area

τ Hydraulic residence time (s)

ε Rate of dissipation of turbulent kinetic energy per unit mass (m2s-3)

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iv Velocity in the i th momentum equation (m s-1)

kσ , εσ Turbulent Prandtl numbers for k andε , respectively

Γ Diffusion coefficient (m2s-1)

ρ Fluid density (kg m-3)

Φ Fluid property per unit mass

τ Hydraulic residence time (s)

pρ Particle density (kg m-3)

α Permeability (m2)

η Porosity (%)

pΔ Pressure loss through the plate (Pa)

μ Viscosity (kg m-1s-1)

particlesMΔ Particle separation efficiency (%)

μ t Eddy viscosity (kg m-1s-1)

η2 Removal efficiency

σ2 Variance of the RTD function

σ2/τ2 Peclet number equivalent

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

EXPERIMENTAL AND NUMERICAL ANALYSIS OF STORMWATER UNIT

OPERATIONS AND PROCESSES

By

Subbu-Srikanth Pathapati

May 2008

Chair: John J. Sansalone Major: Environmental Engineering Sciences

Anthropogenic particulate matter (PM) transported in urban rainfall-runoff has been

identified as a significant contributor to overall deterioration of surface water in the USA

(USEPA 2000). Rainfall-runoff transports an entrained mixture of colloidal PM, non-colloidal

PM, dissolved and complexed pollutants (Sansalone et al. 2007, Lee and Bang 2000, Sansalone

et al.. 1998, Igloria et al.. 1997, Sansalone and Buchberger 1997). PM transported by runoff act

as reactive surfaces for adsorbing, desorbing and leaching organics and metals as well as

phosphorus and other nutrients (Sansalone 2002). Separation of PM by unit operations and

processes (UOPs) for in-situ treatment of rainfall-runoff is challenged by factors such as the

stochastic nature of hydrologic and pollutant loads and concerns such as availability of land and

infrastructural resources (Liu et al.. 2001).

This study aimed at understanding the hydrodynamic and clarification response of

innovative UOPs for urban stormwater management – hydrodynamic separators and volumetric

filters by means of a coupled experimental and modeling approach. A screened HS is a type of

HS that utilizes a combination of inertial separation, discrete particle (Type I) settling, and size

exclusion by means of a static screen to effect particle separation. A passive radial cartridge filter

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(RCF) utilizing aluminum-oxide coated media with a pumice substrate (AOCM)p was also

tested. All tests were conducted for a known influent particle size distribution and concentration

across the entire range of operating flow rates.

Computational fluid dynamics (CFD) utilizes numerical methods to solve the fundamental

equations of fluid dynamics, i.e. the Navier-Stokes equations (Versteeg et al.. 1995). This study

applied the principles of CFD to predict the particle separation behavior of a screened HS for

dilute multiphase flows, to a scientifically acceptable degree of accuracy. PM separation of the

HS and RCF were modeled for both steady and transient influent flow rates and particulate

loading. The Reynolds averaged Navier-Stokes equations were closed by applying a two

equation turbulence model, and a Lagrangian discrete phase model was used to examine the

particle clarification response. The absolute relative % difference (RPD) between measured and

modeled data was less than 10 %. The CFD model was stable and accurate, demonstrating grid

independence. Post-processing the CFD predictions provided an in-depth insight into the

mechanistic behavior of the screened HS and RCF by means of three dimensional hydraulic

profiles, particle trajectories and pressure distributions. A CFD approach is the next step in

understanding and designing UOPs for urban stormwater, and has far-reaching results compared

to traditional ‘black-box’ approaches.

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CHAPTER 1 GLOBAL INTRODUCTION

Anthropogenic particulate matter (PM) transported in urban rainfall-runoff has been

identified as a significant contributor to overall deterioration of surface water in the USA

(USEPA 2000). Rainfall-runoff transports an entrained mixture of colloidal PM, non-colloidal

PM, dissolved and complexed pollutants (Sansalone et al. 2007, Lee and Bang 2000, Sansalone

et al.. 1998, Igloria et al.. 1997, Sansalone and Buchberger 1997). The temporal particle size

distribution (PSD) and chemical composition of particulate matter (PM) delivered by runoff from

a rainfall-runoff event varies significantly between different geographical regions and even with

spatial variation in the same watershed. (Sansalone 2002).

A major issue that needs to be addressed while designing stormwater unit operations and

processes (UOPs) is the dearth of available land for construction, especially in highly polluted

urban areas. In light of this, many new devices have been introduced, which have the advantage

of a small-footprint and ease of new installation or retrofit to existing infrastructure. This

dissertation is a coupled experimental and numerical approach to characterizing the particulate

matter separation by various UOPs, for screened hydrodynamic separators and small scale as

well as large scale granular medium volumetric filtration systems, for controlled and real-time

influent hydrology and granulometry.

Hydrodynamic separators (HS) are one such class of UOPs that broadly rely on centrifugal

forces in addition to gravitational force to separate particles (Brombach et al.. 1987, Brombach et

al.. 1993, Pisano et al.. 1994, USEPA 1999, Andoh et al.. 2003). An attractive feature of a HS is

the potential for longer particle trajectories per given unit surface area in comparison with

traditional unit operations and processes (UOPs) such as settling basins. . A screened HS is a

variant on the HS principle, and uses the combined separation mechanisms of vortex induced

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inertial separation, screening and sedimentation and has been used in recent years as a device for

treating stormwater runoff (Rushton 2004, Rushton 2006), and oil/grease removal (Stenstrom

and Lau 1998). This study examined a simple screened HS consisting of two annular cylindrical

chambers separated by a static screen consisting of a regular array of apertures. The flow inlet is

tangential to the inner cylindrical chamber. The screen apertures allow vortex flow to exit the

inner screen chamber and enter the outer volute chamber. The geometry of the screen results in a

weakly reversed flow direction in the outer annular area, termed the ‘volute area’. Particle

separation by this HS configuration is a function of the discrete particle settling velocity, particle

diameter, influent volumetric flow rate, radial velocity components in the screening area,

tangential velocity components in the screening area, hydraulic residence time, and the diameter

of the screen apertures. The design flow rate (Qd) for the screened HS used in this study is 9.5

L/s.

Various filtration configurations including infiltration and exfiltration through fixed

granular medium (including soil) systems have been suggested as viable solutions for meeting

runoff quantity and quality regulations for watersheds (Colandini 1999, Sansalone 1999, Li et al..

1999, Colandini et al.. 1995, Geldof et al.. 1994, Schueler 1987). Recently, Hipp et al. (2006)

suggested that removable filter inserts, which are mechanistically different from typical fixed

bed granular medium filters, may be viable preliminary unit operations due to easier

maintenance. While granular filtration has demonstrated advantages for improving water quality,

there is a requirement for careful design, analysis and prototype testing, as well as regular

maintenance to ensure optimal hydraulics for quantity control. Performance (mass and size of

PM separated) of a granular medium filter depends on the influent surface loading rate, total

surface area of the media , the influent volumetric flow rate, effective porosity, particle diameter,

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granular media diameter, empty bed contact time (EBCT) (AWWA 1990) and physical,

chemical and surficial properties of the media, such as adsorption properties, media (internal)

porosity, and morphology. (Tien 1989). Oxide coated media has been found to be effective at

reducing turbidity, phosphorus and microbes in water and wastewater treatment (Ayoub et al.

2001, Chen et al. 1998, Ahammed et al. 1996). Recently, the use of oxide coated media has been

extended to runoff treatment (Erickson et al. 2007, Sansalone et al. 2004). In this study,

aluminum oxide coated media with a pumice substrate (AOCM)p was utilized for physical

filtration. Granular filtration mechanisms have been classified into surficial straining,

sedimentation, interception, inertial impaction, diffusion, hydrodynamic and electrostatic

interaction (Wakeman et al.. 2005). Filtration dynamics are widely assumed to be dependent on

the surface loading rate (SLR) and with increasing SLR, macroscopic mechanisms tend to

predominate the separation process, due to reduced contact times. The radial flow rapid-rate

filter used in this study was operated at surface loading rates (SLR) ranging from 24 to 189

L/m2-min, which is higher than SLR’s of typical rapid sand filters (83 L/m2-min) (Reynolds et al.

1995).

Typical stormwater design approaches are extensions of wastewater tank design principles,

which assume ideal to predictable influent quantitative and qualitative loads. It is clear that the

rainfall-runoff process and the associated particulate and dissolved matter delivery is a highly

variable process and therefore unit operations for stormwater PM management have to be

designed to operate across rapidly changing flow and particle concentrations. Existing

stormwater models such as the stormwater management model (SWMM) (Rossman 2007) use

idealized influent hydrographs and pollutographs. While these have greatly improved the

efficacy of design considering the complex and inter-related design parameters, they are not

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equipped to provide an in-depth hydrodynamic and particle clarification profile of the UOP for

transient loads.

Existing literature does not provide a detailed and fundamental insight into the functioning

of UOPs, including hydrodynamic separators. Previous studies have ranged from simplified

overflow rate theory (Weib 1997) to semi-empirical approaches based on broad assumptions of

vortex flow behavior (Paul et al.. 1991). This lack of information leads to difficulties in scaling

and implementation of these devices. Fenner et al.. (1997, 1998) report that similitude analysis

does not yield a single dimensionless group that can be used in scale-up of a HS.

Hydraulic optimization has long been in practice in engineering, for instance, in

wastewater treatment, particularly in the design and analysis of grit chambers, primary and

secondary clarifiers. For instance, weirs and baffles have been used as energy dissipating devices

and to optimize flow paths to minimize short-circuiting and hydraulic instability (Tchobanoglous

et. al, 2003) . Improvement of swirl concentrators/vortex chambers has been an ongoing process.

Researchers have utilized baffles, bars and other appendages to optimize solid separation

(Alquier et al. 1982) by minimizing eddies, short-circuiting and dead spaces. Furthermore,

fundamental design methodologies have been suggested to optimize vortex separation, based on

the characteristics of the vortex flow (Paul et al. 1991).

Computational fluid dynamics utilizes numerical methods to solve the fundamental

equations of fluid dynamics, i.e. the Navier-Stokes equations (Versteeg et al.. 1995). The

applicability and efficacy of CFD techniques have closely followed corresponding leaps in

computational power. While traditionally being in the realm of Aerospace and Process

engineering, CFD is now used in design and optimization of UOPs in environmental

engineering. Computational fluid dynamics (CFD) has found applications in environmental

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engineering in recent years, specifically in water and wastewater treatment (Do-Quang et al.

1998).

CFD approaches to model particle-laden flows is an active research area (Curtis et al..

2004, van Wachem et al.. 2003), including hydrodynamic separators. Faram et al.. (2003)

utilized a Reynolds Stress Model (RSM) to model turbulent flow and a Lagrangian Discrete

Phase Model (DPM) to model behavior of the particulate phase. Okamoto et al.. (2002) studied

particle separation by a vortex separator using a k-ε model to model flow and an Algebraic Slip

Mixture (ASM) model for the particulate phase. Lim et al.. (2002) used CFD-predicted velocity

profiles to study behavior of flocs in a vortex separator, with a Renormalization Group (RNG) k-

ε turbulence model. Tyack et al.. (1999) compared measured velocity profiles in a vortex

separator to those predicted by a Renormalization Group (RNG) k-ε turbulence model.

Tung et al. (2004) studied deep bed filtration for a sub-micron/nano-particle suspension

utilizing a microscopic approach wherein different types of media packing were modeled.

However, macroscopic approaches to modeling filter media are needed to model practical

systems where packing schemes are most commonly random and unstructured. Li et al. (1999)

applied a 2-D numerical model to simulate variably saturated flow in a partial exfiltration

system. Sansalone et al.. (2005) applied a 2-D numerical model to simulate the transient

hydrodynamics of a partial exfiltration system for rainfall-runoff clarification. However, a

macroscopic CFD based approach to simulate the 3-D hydrodynamic and clarification response

of a granular medium filter is much needed in order to understand passive radial filtration, which

may not be fully described by a simplified 2-D approach, due to lack of ideal symmetric flow

conditions.

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It should be noted that albeit studies dealing with the application of CFD in understanding

the multiphase dynamics that occur in a hydrodynamic separator are few in number, this is

clearly not the case with wastewater unit operations such as settling tanks (Jayanti et al. 2004,

Naser et al. 2005, Deininger et al. 1998, Brouckaert et al. 1999, Brestscher et al. 1992, Zhou et

al. 1994, Szalai et al. 1994, Karl et al., 1999) and for CSO pollution abatement devices such as

storage chambers (Stovin et al., 1996, 1998, 2002).

In order that an engineer be aided in designing UOPs with complex hydraulics and particle

transport, it is imperative that there be a coupled experimental and numerical modeling method

that can:

• Predict the particle separation behavior of the UOP through the application of an appropriate flow and particulate phase model, within reasonable computational limits, to a scientifically acceptable degree of accuracy.

• A targeted experimental matrix that adheres to effective and practical QA/QC constraints, to experimentally characterize the UOP in order to effectively verify and validate the numerical model and to provide any data required for calibrating the model.

• Apply to steady, as well as temporally transient quantitative and qualitative hydraulic and pollutant loads.

25

CHAPTER 2 EXPERIMENTAL MODIFICATION OF A STORMWATER HYDRODYNAMIC

SEPARATOR FOR ENHANCED PARTICLE SEPARATION

Introduction

Non-point source pollution has emerged as a significant issue of concern in recent years.

Various studies have shown that urban stormwater runoff is one of the major reasons for the

deterioration of water bodies in the USA (USEPA 2000). The physical and chemical nature of

stormwater pollutants has been studied, and it has been reported that a significant fraction of

pollution from runoff can be attributed to particulate matter (Sansalone 2002). Control of

particulate pollutants is an especially challenging task in an urban environment, due to complex

watershed characteristics and hydrology. In addition, land-availability and infrastructure

constraints have only compounded the problem and have led to research and development of

innovative technologies for in-situ and ex-situ control of pollution, such as hydrodynamic vortex

separators (Brombach et al. 1987, Brombach et al. 1993, Pisano et al. 1994, EPA 1999, Andoh et

al. 2003).

A unique feature of hydrodynamic separators is that the particle trajectory in such systems

is many degrees of magnitude longer than in traditional Unit Operations (UOPs) such as settling

basins (Field et al. 1996).The probability of particles being separated within a given volume is

thus, degrees of magnitude greater. It should be noted that the studies mentioned previously have

dealt with performance evaluation of hydrodynamic separators based only on experimental data.

One type of HS utilizes a combination of UOPs, namely, inertial separation due to vortex

action, size exclusion by screening, and discrete particle (Type I) settling. This device, referred

to as a screened HS or simply HS for this document, has been used in recent years as a device for

treating stormwater runoff CSO outfalls (Heist et al.. 2003), and oil & grease removal (Stenstrom

and Lau 1998).

26

Analysis of storage chambers and hydrodynamic separators for CSO treatment has been

carried out by both experimental and numerical approaches (Tyack et al. 1999, Faram et al.

2002, Okamoto et al. 2003). Hydraulic optimization has long been in practice in engineering, for

instance, in wastewater treatment, particularly in the design and analysis of grit chambers,

primary and secondary clarifiers. For instance, weirs and baffles have been used as energy

dissipating devices and to optimize flow paths to minimize short-circuiting and hydraulic

instability (Tchobanoglous et. al, 2003) . Improvement of swirl concentrators/vortex chambers

has been an ongoing process. Researchers have utilized baffles, bars and other appendages to

optimize solid separation (Alquier et al. 1982) by minimizing eddies, short-circuiting and dead

spaces. Furthermore, fundamental design methodologies have been suggested to optimize vortex

separation, based on the characteristics of the vortex flow (Paul et al. 1991).

Studies agree that the predominant variables affecting the performance of a HS are the

settling velocity characteristics of the influent particles and the flow rates at which the device is

loaded, and that improved solid separation can be effected by lengthened particle trajectories or

increased particle residence time (Field et al.. 1996). This study aims at optimizing the particle

removal performance of a screened HS by means of geometric modifications. These

modifications were based on hypotheses built upon increasing particle residence time in the unit,

reduction in flow instability and short-circuiting. The study was conducted for an influent

particle gradation typically issued by regulatory bodies. A concentration of 200 mg/L was chosen

and the tests were conducted for 8 different configurations, across three flow rates representing

25, 75 and 125 %, respectively, of the maximum hydraulic operating flow rate or design flow

rate (Qd) of the unit under test. The tests were conducted under steady-state flow regimes, to

better distinguish the effects of different configurations on solid separation.

27

Background

A schematic of the screened HS is provided in Figure 2. The device consists of two

concentric cylindrical chambers, the inner screen area, and the outer annular volute area. The

inlet is tangential to the inner cylindrical chamber. The inner cylindrical chamber is equipped

with a static separator screen, with perforations elongated in shape and are aligned with the

longer axis in the vertical direction. Furthermore, the shape of the apertures, results in reversed

flow direction in the outer volute chamber. The screen area open to flow is designed in a manner

that would cause the radial velocity through the screen to be of an order of magnitude lower than

the inlet velocity. The resultant higher ratios of tangential to radial velocities prevent particles

from exiting through the apertures (Wong, 1997), and allow them to settle to the sump, via

circular helical paths of progressively decreasing radii. This mechanism is at its most favorable

level when the energy of the driving vortex is optimal and is subsequently seen to be higher at

flow rates closer to the design flow rate (Qd). The flow path through the screened HS is

continuous and steady. A unique characteristic of a screened HS is that it does not rely on

secondary currents due to vortex action, as with traditional vortex separators. The action of

secondary currents is countered by providing a filtration mechanism in the form of a perforated

screen. This has been suggested to provide higher particle separation rates as opposed to

traditional vortex separators (Schwarz and Wells, 1999). Overall, the performance of a screened

HS can be summarized as being dependent on the following variables, as shown in the following

expression.

),,,,,,( strpsparticles dvvQdvfM τ=Δ (2-1)

In this expression, particlesMΔ is the particle separation efficiency (%); sv is the discrete

particle settling velocity [LT-1]; pd is the particle diameter[L];Q is the influent volumetric flow

28

rate [L3T-1]; rv is the radial velocity component in the screen area [LT-1]; tv is the tangential

velocity component in the screen area [LT-1];τ is the hydraulic residence time [T]; and sd is the

diameter of the screen apertures [L].

The ratio of the radial to tangential velocities in the screen area was expressed as follows.

i

s

t

r

AA

vv

α (or) ⎟⎟⎠

⎞⎜⎜⎝

⎛=

i

s

t

r

AA

kvv

* (2-2)

In this expression, sA is the effective screen area [L2]; iA is the effective area of the inlet

throat [L2]; and k is a dimensionless coefficient proportional toQ .

Previous studies in particle behavior in vortices (Julien et al..,1986) have suggested that in

steady vortices, there exists a equal diffusive flux acting opposite to the centrifugal flux pushing

particles toward the outside of the vortex, for both free and forced vortices, and at equilibrium,

these two fluxes are equal. Other studies (Davila et al..2000) have suggested the dependence of

particle motion in a vortex on the particle Froude number, and terminal settling velocity. Studies

in modeling the performance of hydrodynamic separators (Fenner et al. 1997, Fenner et al. 1998)

have suggested that no single dimensionless group can be used in describing, and scaling the

solid separation performance. Other such studies used a simplified overflow rate theory

approach(Weib, 1997).For this study, the overall performance of the screened HS was evaluated

on the basis of equations 1 and 2, keeping sd constant at 2400 µm, and with pre-determined

values of pd and sv .

Objectives

The first objective of this study was experimental characterization of the clarification

response of a prototype screened HS to an influent particle gradation, at a concentration of 200

mg/L, commonly observed in urban runoff, as a function of geometric modifications that affect

29

performance indicating variables described in the previous section. A second objective was to

study the effect of varying the dimensionless ratio of is AA / on solid separation performance,

and to develop preliminary design criteria for creating optimal ratios of tr VV / .The third and

major objective of this study was to suggest a geometric modification that would optimize the

overall solid separation performance of the screened HS, across flow rates representing 25, 75

and 125 % respectively, of the maximum hydraulic operating flow rate (Qd),with the unit filled

to its residual treatment capacity, and with an allowable error rate of +10% by mass. The fourth

objective was to characterize variations in hydrodynamic response of the modified geometric

configuration in comparison with a baseline unit, from Residence Time Distribution (RTD)

curves obtained by a tracer study.

Methodology

Experimental Site Setup

Figure 3-1 contains a schematic plan view of the instrumented experimental setup. A

storage tank (Storage tank A) with an approximate capacity of 4000 L was used as a reservoir for

influent potable water. Three sludge pumps located in Storage Tank A, with capacities of 6.94

L/s each were used to generate influent flow. The sludge pumps were used in appropriate

combinations to generate flow across the entire treatment range with an error of less than + 2%.

Flow rates were measured in a 5.08 cm (2-inch) Parshall flume located downstream of the

storage tank. Depth of flow in the Parshall flume was measured with a 70 KHz ultrasonic sensor

manufactured by American Sigma Inc, and data was recorded real-time by an American Sigma

data logger. The Parshall flume was re-calibrated volumetrically over the entire flow rate range,

with triplicate measurements, at an error less than or equal to +1%, and this re-calibrated

relationship between depth of water in the flume and the corresponding volumetric flow rate was

30

used in place of the standard relationship for a 5.08 cm (2-inch) Parshall flume. This was done to

account for any errors that might arise due to the complicated upstream plumbing at this specific

experimental site. Influent particles and Sodium Chloride (NaCl) tracer were injected at the drop-

box located immediately downstream of the 5.08 cm (2-inch) Parshall flume and immediately

upstream of the screened HS. Flow was routed to the screened HS utilizing a system of gate

valves located immediately downstream of the “drop-box” and immediately upstream of the

screened HS.

The overall diameter of the screened HS was 89.3 cm and the diameter of the inner screen

area was 49.5 cm. The height of the unit was 96.5 cm. The residual storage volume of the unit

was approximately 408 L, based on the depth of liquid in the unit under quiescent conditions,

and the maximum hydraulic operating volumetric flow rate(Qd) was 9.4 L/s. The static separator

screen consisted of apertures with a sd of 2400 µm. A storage tank (Storage tank B) with an

approximate capacity of 4000 L was used as a storage reservoir for effluent from the Screened

HS, and was located immediately downstream of the unit.

Influent Particle Gradation

The clarification response of a screened HS has been identified to be dependent on the

characteristics of the influent particle gradation (Kim et al., 2005). Particle gradations commonly

seen in urban runoff vary significantly based on the demography, geography, and land-use

characteristics of a watershed. The influent particle gradation that was used in this study is one

that is typically seen in urban runoff. The particle size distribution of the influent solids by mass

is shown in Figure 3. It is noted that approximately over 50 % by mass of this gradation, is finer

than 75 µm. By a widely accepted standard of classification, over 50 % by mass of this gradation

can be said to consist of settleable-suspended particles.

31

Five different test gradations of silica particles were obtained from the US Silica Company

and each of the 5 test gradations were first sieved to separate out particles too coarse and too fine

between specific sieve increments. These sieved gradations were combined to meet the specified

test gradation. Once combined and mixed, the five sieved final particle components of the final

gradation were sieved again down to 25 μm, and the fraction finer than 25 μm was analyzed

using laser diffraction. Measured results were then compared to the target gradation and to the

calculated gradation. Results of the target gradation, the calculated gradation and the measured

gradation are depicted in Figure 3 and Table 1. The mass of particle mixture to be added was

chosen so as to achieve a 200 mg/L influent concentration, based on 4000-L of influent. QA/QC

checks were periodically made to ensure consistency of the influent particle gradation.

Field Test Procedure

The following describes the field test procedure. The storage tanks, the recirculation pipes

and the screened HS were cleaned thoroughly by pumping potable water through the system.

This was done to ensure that any previously deposited particles or any extraneous particles were

removed from the system prior to starting the test. Storage tank A was then filled with about

4000 L of water, and the screened HS was filled to its residual storage capacity of approximately

408 L. The valves on the recirculation system were calibrated with tap water and set to the

desired flow rate (25, 75, and 125 % of Qd). The desired test flow rates were achieved through

the use of either one or two 110-gpm recirculation pumps. Calibrated flow measurements were

made throughout each run. The moment of time at which flow was diverted to the screened HS,

was noted as “Time 0”. Addition of influent particles at the drop-box was started immediately at

“Time 0”. The run time for each test was calculated based on available influent volume of

approximately 4000 L, and flow rate tested. Flow was diverted to the screened HS and influent

particle addition into the drop-box upstream of the Screened HS commenced immediately at

32

“time 0”.The rate of particle injection was consistent across the test running time, on a

gravimetric and granulometric basis. Ten replicate 2-L effluent samples were collected for water

quality and SSC analyses, at the outfall of the effluent pipe into storage tank B. Separately, 100

gallons of effluent (10 of 5-gallon with replicate) were captured and recovered in 55-gallon

polypropylene tanks, at the same sampling frequency as the 2-L samples, in order to recover

sufficient particle mass to carry out effluent particle gradations.

Laboratory Analyses

Two 20-L composite effluent samples (A and B) were prepared from 10 individual

replicate (A and B) 2-L samples. The entire measured volume of each replicate composite

sample was then filtered using a 1.2-μm glass fiber filter. Total suspended solids (TSS) were thus

measured as suspended sediment concentration (SSC). Particles captured by the screened HS

from each run were completely recovered as wet slurry from the unit. Effluent particles captured

in two 55-gallon polypropylene tanks were also recovered as wet slurry. After each run, a known

amount of coagulant ferric chloride was added to the screened HS and the two 55-gallon

polypropylene tanks, in order to accelerate the settling process of particles. At least 5 hours of

settling time was allowed before slurry recovery.

The recovered particle slurry was then transported to the laboratory and dried at 40 C. The

dried particle mass was weighed and the SSC removal efficiency was calculated as effluent mass

was computed from the measured effluent SSC corresponding to total volume. A mass balance

check was performed on the SSC removal efficiency as,

Mass Balance Error = %10)(

100 ±≤⎥⎦

⎤⎢⎣

⎡ +−×

i

eHSi

MMMM

(2-3)

33

In this expression iM is the mass of particles in the Influent [M]; HSM is the mass of

particles captured by the screened HS [M]; and eM is the mass of particles in the effluent [M].

If the mass balance error criterion was satisfied, the SSC removal efficiency was calculated

as,

⎟⎟⎠

⎞⎜⎜⎝

⎛×=

i

HS

MM

100η (2-4)

The dried particle mass was then sieved using graded sieves to obtain particle size

distributions according to ASTM D422 for sieve analysis (ASTM 1993). Sieve numbers were

chosen appropriate to the influent gradation. The sieve numbers used were #30, #50, #100, #140,

#200, #270, #400, #500 and the pan. Mass balances were determined for each mechanical sieve

analysis and mass balance errors were in the range of 1 to 2 % by mass.

Geometric Configurations

The screened HS is a variation on the hydrodynamic separation principle, and its

predominantly distinguishing feature is that this UOP, unlike traditional vortex separators, does

not rely on secondary currents created by a vortex, to effect particle separation. It ensues that the

rotary flow patterns that occur in the screened HS are different. The presence of a static screen,

and the absence of an underflow, creates a steady and continuous flow path through the device.

The device functions closest to optimal operation under steady flow conditions. Therefore, a

main aspect of the modifications in the inner separation/screening chamber was to not impede

the steady and continuous flow through the device by providing baffles as attenuating devices.

Modifications involving the area of the inlet, and the effective screen area, did not aim at

impeding flow. These modifications were aimed at increased ratios of tangential to radial

velocities, in terms of magnitude alone, and did not interfere with directional aspects of flow

34

within the device. Modifications in the outer volute chamber were aimed at lengthening particle

trajectory out of the system. With these constraints in mind, eight different geometric

modifications were made to the existing unit.

The first modification involved fixing a 5 cm (2-inch) “effluent weir baffle” to the unit.

The “effluent weir baffle” is a sheet metal baffle placed at the outlet of the device. The principal

goal of this was to reduce possible short-circuiting and to lengthen the path of travel of particles

out of the unit. This does not alter the volume of the unit. The effluent baffle was hypothesized to

improve solid separation performance mainly at higher flow rates. The second modification was

placing a “sump baffle”. The “sump baffle” is a baffle placed on top of the sump portion of the

inner screen area. The hypothesis tested here was that this would reduce probable re-suspension

of deposited particles by scouring.

The third modification was a 5 cm (2-inch) “submergence baffle”. This was fixed at the

outlet, to increase the height of water inside the unit, thereby increasing the volume of water

inside the unit by a small amount. The dimensionless ratio of screen area to inlet throat area,

is AA / was tested as a viable design parameter. By modifying iA by friction-fitting hard

Styrofoam wedges, the inlet flow velocity was increased, by creating a nozzle-like effect. The

hypothesis tested here was that this would decrease the number of particles exiting the screen via

the apertures, due the increased tangential velocities. The screen area sA was changed by

blocking the screen with high-strength adhesive non-permeable tape.

Various combinations of the above modifications were tested. Overall, eight different

configurations from “A” to “H” were tested. Configuration “A” included only the “effluent weir

baffle”. Configuration “B” included the “effluent weir baffle” and the “sump baffle”.

Configuration “C” included the “effluent weir baffle”,” sump baffle” and “submergence baffle”.

35

Configuration “D” included the “effluent weir baffle”, “submergence baffle” and screen area

reduced by 37 % from the top. Configuration “E” included the “effluent weir baffle”, screen area

reduced by 37 % from the top, and throat area reduced by 17 %. Configuration “F” included the

“effluent weir baffle” and the “submergence baffle”. Configuration “G” included the effluent

weir baffle, and throat area reduced by 26 %. Finally, Configuration “H” included a “effluent

weir baffle”, screen area reduced by 18 %, and throat area reduced by 17 %. The choice of

configurations was an iterative process, based on the results of the previous configuration. A

detailed description of the experimental matrix and dimensions of modifications is provided in

Table 1 and the accompanying description.

Tracer Analysis

A tracer study was conducted to determine hydraulic residence time distributions (RTD).

Concentrated Sodium Chloride (NaCl) solution was used as a tracer. A known volume of tracer

was injected as a single pulse into the drop box upstream of the screened HS. The methodology

for tracer injection followed the exact same steps as for influent particle injection, described in

the previous section, with the tracer slug injection taking the place of the influent particles. A

calibration curve was developed to establish the relationship between concentrations and

conductivity. The concentrations were thus calculated from conductivity measurements. Prior to

tracer injection, the conductivity of the potable water used for testing was measured. For

continuous real-time measurement of conductivity at the effluent sampling point, a calibrated

conductivity probe, manufactured by YSI Inc., was used. The conductivity probe was placed so it

was fully submerged at the outfall of the effluent pipe. The tracer study was run at a constant

flow rate, until the conductivity dropped back to the background (potable water) conductivity.

The screened HS was thoroughly cleaned with potable water, after every run. Each tracer run

was run in triplicate and validated by a mass balance check, with the allowable error rate set at +

36

5% by mass. Discrete measurements were taken every one second, and the mean residence time

was approximated as (Tchobanoglous et. al, 2003),

∫

∫∞

∞

=

0

0

)(

)(

dttC

dtttCtmean (2-5)

In the expression, meant is the mean detention time from tracer measurements [T]; t is time

measured from “time 0” [T] ; )(tC is tracer concentration at time t [LT-1].The theoretical

residence time was calculated as

QV

=τ (2-6)

In the expression, V is the volume of the unit [ L3]; and Q is the Influent flow rate [L3T-1].

The residence time distribution function E(t) was calculated as

∫∞=

0

)(

)()(dttC

tCtE (2-7)

And consequently the cumulative RTD function F (t) was calculated as

∫=t

dttEtF0

)()( (2-8)

Previous studies on Residence Time Distributions in hydrodynamic separators

(Alkhaddar et al. 2001) suggest that the hydrodynamic separator behaves as a incompletely

mixed plug flow reactor, and different models, such as the Axial Dispersion Model (ADM), and

Tanks-in-series Model (TISM) were used to describe the data. In this study, the aim was to

compare the RTD of the optimized configuration relative to the baseline configuration. Therefore

the following parameters were used (Levenspiel, 1972; Letterman, 1999),

37

Morrill Dispersion Index (MDI) = 1090 / tt (2-9)

Volumetric Efficiency = MDI/1 (2-10)

Index of short-circuiting = τ/it (2-11)

Index of modal retention time = τ/pt (2-12)

Index of average retention time = τ/50t (2-13)

Hazen’s N = (t50 ) / (t50 - tp) (2-14)

In the above expressions, it is the time at which tracer first appears; pt is the time at which

peak concentration is observed; 50t is the time at which 50 % of tracer had passed through the

reactor; and 90t is the time at which 90 % of tracer had passed through the reactor.

The Morrill Dispersion Index is close to 1 for a plug-flow reactor. Higher values indicate

deviations from plug-flow towards complete-mixing, and result in lower volumetric efficiency.

The indices of short-circuiting and modal retention time vary from 0 to 1 from complete-mixing

to plug flow. The index of average retention time provides a measure of the skew of the curve.

Values greater than 1 indicate skew to the right and values less than 1 indicate skew to the left.

The variance (σ2) was calculated from equation (4) as,

∫

∫∞

∞

−=

0

0

2

2

)(

)()(

dttC

dttCtt mean

σ (2-15)

A Peclet number equivalent was adopted (Alquier et al. 1982), and defined as equal to

22 /τσ . This was used to distinguish between the modified and baseline configurations. A

higher value of the Peclet number equivalent would indicate improved plug-flow behavior.

38

Results and Discussions

Treatment Influent Flow Rate at 25 % of Design Flow Rate

Figure 4 depicts particle separation performance removal at 25% of design flow rate across

configurations. It was noticed that, at this flow rate, the screened HS functions primarily as a

circular tank, and the primary mechanism of solid separation is gravitational sedimentation. The

improvement in performance over a baseline unit at this low flow rate was seen to be minimal,

and not very significant. This response was consistent across configurations. The %age of

separated solid captured by the screen area and by the volute area did not vary significantly

across all configurations except Configuration B and Configuration C, which exhibited a

noticeable tendency for increased captured of solids in the Volute area as opposed to the screen

area. This can be attributed to the reason that the “Sump Baffle”, was a geometric modification

common to these two configurations. The baffle was intended to prevent re-suspension of settled

particles, by reducing the area of the sump exposed to flow. However, at low flow rates, such as

25% of design flow rate, the benefits of reduced scouring are not significant. At this flow rate,

particles tend to have more vertical trajectories, as opposed to vortex-driven circular trajectories

seen at higher flow rates. This results in a fairly uniform deposition of particles over the entire

surface area of the sump. In this case, this resulted in reduced distance from the screen apertures

to the particles deposited on the baffle, as opposed to particles deposited in the sump, and

subsequently these particles were re-suspended and pushed out of the screen, where they were

captured in the volute area.

This is supported by the particle size distributions by mass of recovered solid particles

from the screen area, volute area, and from the sampled effluent, as seen in Figure 5. It is seen

that, as this flow rate, the particle size distributions by mass across configurations exhibit similar

trends. Any deviations in parameters such as d15m, d50m, and d85m are minor and do not

39

significantly alter the overall SSC removal efficiency. It would be useful to note that, at this flow

rate, the solids captured by the Screened HS tend to be closer to the Influent particle size

distribution as compared to particle size distributions at higher flow rates (Figure 6 and Figure

7), i.e., the d15m, d50m, and d85m are noticeably finer at 25% of design flow rate as compared to

75% an 125% of design flow rate. The overall SSC removal efficiency ranged from 48 to 52.7%,

across configurations. Detailed results are listed in Table 2.

Treatment Influent Flow Rate at 75 % of Design Flow Rate

Figure 4 depicts particle separation performance at 75% of design flow rate across

configurations. The noticeable difference is that the difference in functionality of the screened

HS starts to surface at this flow rate as compared to lower flow rates. At 75% of design flow rate,

the energy of the driving influent flow is sufficient to create a vortex in the screened HS.

However, the significance of vortex flow as a performance affecting variable can be quantified

as being higher than at lower flow rates, and lower than at higher flow rates. Although there is

sufficient energy to create and sustain a vortex, the distribution of associated surface velocities,

tangential and radial velocities is of a magnitude lower than at higher flow rates. That is, the

static screening separation mechanism that is dependent on higher ratios of tangential to radial

velocities is not pronounced or fully utilized. With particle separation being directly influenced

by velocity distributions within the unit, the overall solid separation mechanism at an influent

flow rate of 75% of design flow rate can be said to be a combination of screening and

sedimentation, with a greater emphasis on gravitational sedimentation mechanisms than on

mechanisms of hydrodynamic separation. There is improvement over a baseline setting by about

6 %, for Configuration A.

Other configurations do not differ significantly from one another. Figure 6 depicts the

particle size distributions by mass across configurations for a flow rate of 75 % of design flow

40

rate. The most noticeable trend is that in comparison with the lower flow rates discussed

previously, the particle size distribution tends to capture a lesser fraction of the influent

gradation, and it tends to capture a coarser portion of the influent gradation. This is supported by

the visibly coarser values taken by d15m, d50m, and d85m. Configuration A performed best,

capturing about 45 % of influent gradation, in the screened HS. Consequently, the particle size

distribution curve for Configuration A is seen to capture a higher number of fine particles as

compared to the baseline setting.

It is seen that the %age of particles captured by the screen area as opposed to the volute

area varies significantly across some configurations, unlike with a lower flow rate. The reasons

for the variation in Configuration B can be attributed to the deleterious effect of the Sump baffle

in preventing particles from settling to the bottom of the sump, as expressed in detail in the

preceding section. Configuration C resulted in decreased particle capture in the screen area,

partly due the same reason as with Configuration B. An additional reason for lowered

performance is described as follows. Under a baseline condition in itself, there was a slightly

higher liquid depth in the Volute area as opposed to the Screen area, at steady state. These

measurements were made with a 2.5 psi pressure transducer, manufactured by Druck Inc, as part

of a different study. Under the condition where a submergence baffle was used, the overall depth

of liquid in the Screened HS was increased further. The corresponding increase in the effective

volume meant that, a higher amount of energy would be necessary to create and sustain a vortex

equivalent in magnitude to that seen with configurations that did not cause increased liquid

depth. Therefore, any appreciative effect of increased liquid depth was negated by the absence of

sufficient energy to create and sustain a vortex. This is an observation common to Configurations

“C’ and “F”, both of which employed a submergence baffle. A glance at the particle size

41

distributions in Figure 6 reveals that Configuration B, C and F captured less fine particles than

Configuration A. On the other hand, Configurations D, E, G and H do not show any significant

deviation from the Baseline configuration, despite reduced screen area and inlet throat area. This

is because, the effect of these parameters comes into play only in a situation where there exists a

vortex that creates flow regimes that are conducive to hydrodynamic separation, such as flow

rates close to the design flow rate. These effects are examined in further detail in the succeeding

section on Tracer analysis.

Treatment Influent Flow Rate at 125 % of Design Flow Rate

Figure 4 depicts particle separation performance at 125% of design flow rate across

configurations. . For the given volume of the screened HS, there is a significant improvement in

particle separation performance over a baseline unit, across configurations. The experimental

results presented in Table 3 clearly indicate the change in solid separation mechanisms in that

they tend predominantly towards hydrodynamic separation and screening as opposed to at lower

flow rates, where the effects of gravitational sedimentation were predominant. The particle size

distributions of the particles captured in the screen area, volute area and the effluent are depicted

in Figure 7. An observation that is consistent across configurations is that there is a clear shift in

the particle size distribution of capture particles towards a coarser particle diameter as is

evidenced by the d15m, d50m, and d85m. All configurations with the exclusion of D, E and H

showed a marked improvement in capture of fine particles compared to a baseline setting, at an

almost equal level. Configurations B and C, which did not function as well as the other

configurations, at lower flow rates, did not have any deleterious effects on SSC removal. The

location and geometry of the sump baffle allows it to work optimally, when particles do not

settle on the baffle itself. At lower flow rates, particle trajectories were not predominantly

influenced by hydrodynamic separation. Therefore, particles tended to settle on the baffle itself

42

and hence be re-suspended. On the other hand, at the highest flow rate, the particle settling

trajectories are circular helical paths of progressively decreasing radii, enabling particles to settle

into the sump through the center region of the inner screen area. Thus, particles were not

deposited on the baffle, instead, settled to the bottom of the sump.

Configurations D, E and H involved modifications to the screen area, which resulted in

increased differential pressure through the screen and higher radial velocities as opposed to

tangential velocities in the screen area, thus causing particles to exit the screen area. It is

interesting to note that Configuration “E” performed slightly better than Configuration “D”, at

solid separation. This indicates the effect of increased tangential velocities due to the “nozzle-

like effect” of the decreased throat area.

A consistent characteristic of particle size distribution curves for the tested configurations

is that almost all configurations showed a clear increase in the capture of finer particles, in the

volute chamber, compared to a baseline setting. This was conclusive evidence to identify the

beneficial effects of the Effluent weir baffle, which was the common element to all these

configurations. The effluent weir baffle clearly increased the capture of finer particles in the

volute chamber, by lengthening the trajectory of particles out of the screened HS.

Discussion

From the point of view of assessing the performance of the screened HS, equation (2)

provides a preliminary method that can be extended to design. This has been ratified by the

improved performance of Configuration “G” which the highest is AA / among the configurations

that involved modifications to sA and iA , and consequently high solid separation at flow rates

close to dQ .Another observation is that Configuration ”H”, performed at a significantly lower

level as opposed to other configurations, while maintaining the same is AA / .

43

This leads to the conclusion that is AA / is a non-singular parameter, and dependent largely

on the dimensions of a given unit. It is seen that, for this particular Screened HS, designing a

screen which allows 40 % of the inner volume of flow to pass through, is best to promote ideal

ratios of rt VV / . Further reduction of the inlet throat area tA however, leads to excessive and

deleterious head build-up upstream of the screened HS. It was also noted that increasing is AA / ,

by reducing tA did not have significantly enhancing effects on performance compared to the

baseline is AA / at a flow rate of 1.25* dQ , while causing lowered performance at a flow rate of

0.75* dQ , due to excessive head buildup upstream and inadequate energy of the incoming flow.

Tracer Study Results

At the beginning of the run, the vortex is not formed and the process of hydrodynamic

separation has not reached a steady state. At a given flow rate which is not conducive to the

creation of a vortex, short circuiting does occur at the initial portion of the tracer study and this is

largely dependent on the location of the outlet with respect to the inlet. The outlet is located to

provide the longest path for an individual particle out of the system, under a condition of

hydrodynamic separation in steady state. However, the location of the outlet will result in short-

circuiting under conditions other than those conducive to steady state hydrodynamic separation.

Such conditions exist in the period of time that is required for an ideal vortex to develop,

measured from Time “0”. There is a clear indication of short-circuiting even for a baseline unit

as is observed in the tracer C (t) and F curves in Figures 8, 9 and 10. However, even with short-

circuiting in the initial portion of the RTD curve, the screened HS has mean residence times

almost twice in magnitude to the theoretical residence time based on the volume of the screened

HS.

44

At an influent flow rate of 25 % of design flow rate, there was an increase of

approximately 5 % in average hydraulic residence time for the best modified configuration

(Configuration A) over the baseline configuration. However, this did not have a significant effect

on the % SSC removal efficiency of the unit. This is a clear indication of the influent particle

size distribution as a predominant factor in determining the performance of the screened HS. A

large fraction (50 %) of the influent particle gradation consists of particles that would be

classified as settleable and suspended particles, and their removal would require an increase in

residence time that is disproportional to the given unit, at the given volume. Therefore, the

particle separation process tended towards that predicted by overflow rate theory. However, it

should be noted that for the given volume, the measured hydraulic residence time is greater than

the theoretical residence time. Based on this, it would be apt to state that the performance of the

screened HS at this flow rate is marginally better than that of a circular tank of similar volume,

owing to the geometry of the unit. An interesting point to note about the C (t) curve at a flow rate

of 25 % of Qd is that the peak concentration is seen to be lower than that of tracer responses at

higher flow rates, and there is a “tailing” effect. This is explained by comparing the F curves for

these three flow rates. It is seen that the deviation from plug flow increases with decreasing flow

rate. At the lowest flow rate, the entire volume is not utilized, due to the presence of dead spaces.

This is also indicated by the fact that the residence time increase at the lowest flow rate for the

screened HS in comparison to the theoretical residence time is lower in magnitude at lower flow

rates, than at higher flow rates. Also to be noted is that any difference between commonly used

indices for analyzing tracer curves, presented in Table 4, do not translate into any significant

difference in solid separation performance, for the given influent particle size gradation.

45

At and inflow rate of 75 % of Qd, there is a difference in hydrodynamic response,

immediately indicated by the higher peak concentration in the C (t) curve. As discussed

previously in the section describing SSC removal results, this flow rate can be designated as a

threshold flow rate for transition to steady state hydrodynamic separation from solid separation

influenced more by gravitational forces than by vortex action. The variances (σ2), of the C (t)

curves for an optimized setting (Configuration A) and the baseline setting do not differ

significantly. A glance at the F curve shown in Figure 9 reveals the mechanistic behavior of the

unit at 75 % of design flow rate. There was an increase in hydraulic residence time of about 8 %

over a baseline setting. The normalized cumulative tracer concentration was noted for

Configuration A and the baseline setting, at values of the independent variable, t, representing

multiples of the theoretical residence time (τ). This was chosen as the time allowed for the flow

regime to tend towards steady state hydrodynamic separation, in a magnitude proportional to the

magnitude of the vortex. A look at values of F (n*τ) with n taking values 1 to 5, indicates a clear

separation between the F curves of an optimized setting versus a baseline setting, with increasing

flow rate. For instance, for an n value of 2, the corresponding (1-F) value for the optimized

setting indicates that 37 % of tracer molecules remained in the reactor for time 2* τ or greater

whereas for a baseline setting, 31 % remained in the reactor. This clearly indicates the effect of

the effluent weir baffle as the flow reaches steady-state.

For an influent flow rate of 125 % of Qd, the trend towards plug flow behavior is more

pronounced than with the lower two flow rates. The tracer response curves for this flow rate are

shown in Figure 10. At this flow rate, there is adequate energy to generate a vortex conducive to

hydrodynamic separation. At this flow rate, the primary and predominant solid separation

mechanism is hydrodynamic separation. The variances (σ2), of the C (t) curves for an optimized

46

setting (Configuration A) and the baseline setting do not differ significantly, as with 75 % of

design flow rate. The normalized cumulative tracer concentration was noted for Configuration A

and the baseline setting, at values of the independent variable, t, representing multiples of the

theoretical residence time (τ), as described in the previous section. Values of F (n*τ) with n

taking values 1 to 6, indicates a more pronounced separation between the F curves of an

optimized setting versus a baseline setting, with increasing flow rate. For instance, for an n value

of 3, the corresponding (1-F) value for the optimized setting indicates that 15 % of tracer

molecules remained in the reactor for time 2* τ or greater whereas for a baseline setting, 11 %

remained in the reactor. Overall, there was an increase of about 10 % in residence time for

Configuration “A” as compared to a baseline setting.

From Table 4, it is noted that while commonly used indices such as the σ2/ τ2, Morrill

Dispersion Index, Hydraulic efficiency based on MDI, and t50/ τ do not show differ significantly

between the best modified configuration and the baseline configuration, across flow rates, there

is a clear lag introduced in the RTD curve by using an effluent baffle, as is evident from the t10,

t50, t90 and tp . The modal retention time index tp / τ, shows a tendency for the modified

configuration to tend towards plug flow as compared to the baseline setting. Although most other

indices do not differ significantly between the modified and baseline configurations, it should be

noted that they do indicate favorable conditions in the modified configuration.

In summary, the provision of the effluent weir baffle in Configuration “A” resulted in an

increase in hydraulic residence time compared to a baseline setting, with increasing flow rate.

Conclusions

The clarification response of a screened HS to an influent particle gradation, at a

concentration commonly observed in urban runoff, was studied across flow rates representing 25,

75 and 125 % of the maximum hydraulic operational flow rate. This study concludes that

47

although the screened HS is primarily a hydrodynamic separator, the variables that affect particle

separation differ significantly from that of a typical vortex separator. This can be attributed to the

absence of an underflow, and the presence of a static screen. Therefore, the approach to

optimizing the performance of the screened HS should be one suited to its mechanisms, and

geared towards satisfying the constraints set by the given influent particle size gradation.

The solid separation performance of the screened HS was seen to vary significantly with

changes in the dimensionless ratio of is AA / (Screen area/Inlet throat area) was tested. It was

concluded that, for this particular screened HS, designing a screen which allows 40 % of the

inner volume of flow to pass through, is best to promote ideal ratios of rt VV / .

The best modified configuration for enhanced particle separation was Configuration “A”.

The resulting increased residence time was confirmed by means of a tracer study. The effluent

weir baffle had a significant impact on the residence time at the higher flow rate of 125 % of the

design flow rate, with residence time increased by approximately 10 %. Although the average

residence time shows a marked increase even at lower flow rates, particle removal was mainly

enhanced at the higher flow rate. Using the effluent baffle increased the residence time of

particles which may have otherwise exited the system at high flow rates, thereby increasing the

chances of them remaining trapped in the unit. There was an increase of about 10% in SSC

removal efficiency at 125% of design flow rate under the optimized setting.

It would be beneficial for stormwater treatment facilities that employ such devices to

optimize them for the targeted removal performance, for the characterized influent particle size

gradation, across the entire range of operating flow rates, and with the device filled to its residual

treatment capacity, as is the case in real situations, in between periodic cleanouts of the device.

These would ensure a more structured and defensible approach to utilizing these devices for

48

treating real-time storm events. The importance of hydraulic optimization is all the more

imminent considering that this provides a resourceful and scientific approach to maximizing the

functionality of a hydrodynamic separator, without expensive geometric modifications.

49

Table 2-1 Comparison of target particle size distribution with calculated and measured gradation utilizing 5 different Silica particle gradations

Silica particle gradations Mass Fraction

Particle Size 20/30 H-85 SCS 250

SCS 51

MUS 10 SUM Calculated Target Measured

(microns) (g) (g) (g) (g) (g) (g) % % % 500-1000 40.4 3.8 0 0 0 44.2 5 5 5 250-500 0 40 0 0 0 40 5 5 5 100-250 0 160 76 0 0 235.6 28 30 35 50-100 0 36 92 13.2 0 141.2 17 15 15

8-50 0 0.4 32 166.8 8 207.2 25 25 22 2-8 0 0.4 0 75 52 127.4 15 15 13 1-2 0 0 0 21 20 41 5 5 5

SUM(g) 40.4 240 200 276 80 836.6 100 100 100

50

Table 2-2 Comparison of target particle size distribution with calculated and measured gradation utilizing 5 different Silica particle gradations. Experimental matrix for optimization of the screened HS

Details of Geometric Modifications

Run # Setting Q EBa SPBb SMBc sA d

[m2] iA e

[m2] i

sA

A

O-1 0.25* Qd N N N 0.5334 0.0106 50 O-2 0.75* Qd N N N 0.5334 0.0106 50 O-3

Baseline 1.25* Qd N N N 0.5334 0.0106 50

3 0.25* Qd Y N N 0.5334 0.0106 50 1 0.75* Qd Y N N 0.5334 0.0106 50 2

A 1.25* Qd Y N N 0.5334 0.0106 50

6 0.25* Qd Y Y N 0.5334 0.0106 50 5 0.75* Qd Y Y N 0.5334 0.0106 50 4

B 1.25* Qd Y Y N 0.5334 0.0106 50

8 0.25* Qd Y Y Y 0.5334 0.0106 50 7 0.75* Qd Y Y Y 0.5334 0.0106 50 9

C 1.25* Qd Y Y Y 0.5334 0.0106 50

14 0.25* Qd Y N Y 0.3340f 0.0106 31 13 0.75* Qd Y N Y 0.3340f 0.0106 31 15

D 1.25* Qd Y N Y 0.3340f 0.0106 31

17 0.25* Qd Y N N 0.3340f 0.0089g 38 18 0.75* Qd Y N N 0.3340f 0.0089g 38 16

E 1.25* Qd Y N N 0.3340f 0.0089g 38

19 0.25* Qd Y N Y 0.5334 0.0106 50 12 0.75* Qd Y N Y 0.5334 0.0106 50 20

F 1.25* Qd Y N Y 0.5334 0.0106 50

23 0.25* Qd Y N N 0.5334 0.0078h 68 22 0.75* Qd Y N N 0.5334 0.0078h 68 21

G 1.25* Qd Y N N 0.5334 0.0078h 68

26 0.25* Qd Y N N 0.4437i 0.0089g 50 25 0.75* Qd Y N N 0.4437i 0.0089g 50 24

H 1.25* Qd Y N N 0.4437i 0.0089g 50

51

Table 2-3 Clarification response or particle separation (expressed as SSC removal efficiency) of different configurations to the influent particle gradation (Figure 2.3), across flow rates representing 25%, 75% and 125% of design flow rate, for an influent concentration of 200 mg/L. Details of configurations are provided in Table 2-2.

Details of Experimental Setup Particle separation

Flow Rate

Influent Conc.

Screened Particles

Mass

Volute Particles

Mass

Δ Particle Mass

Mass Balance

Error Run # Setting % Qd [mg/L] [g] [g] [%] [%]

O-1 0.25*Qd 200 225.8 160.1 47.1 7.8 O-2 0.75*Qd 200 149.2 154.6 38.9 9.6 O-3

Baseline 1.25*Qd 200 67.3 136.4 28.7 7.1

3 0.25*Qd 200 210.5 208.8 52.5 -6.3 1 0.75*Qd 200 164.9 200.2 45.6 2.1 2

A 1.25*Qd 200 107.8 197.6 38.2 3

6 0.25*Qd 200 177.7 209.5 48.4 -0.7 5 0.75*Qd 200 134.2 205.3 42.4 1.8 4

B 1.25*Qd 200 114.7 196.5 38 1.5

8 0.25*Qd 200 174.8 229.2 50.5 -5.8 7 0.75*Qd 200 105.6 202.1 38.5 3.5 9

C 1.25*Qd 200 89.1 199.6 36.1 2

14 0.25*Qd 200 221.4 184.3 50.7 -8.1 13 0.75*Qd 200 142.9 182 40.6 -3.7 15

D 1.25*Qd 200 86.9 118.1 25.6 7.4

17 0.25*Qd 200 210.5 199.9 51.3 -2.7 18 0.75*Qd 200 156.8 156.8 39.2 0 16

E 1.25*Qd 200 76.9 160.3 29.6 5.4

19 0.25*Qd 200 214.6 206.6 52.7 -0.5 12 0.75*Qd 200 135 188.8 40.5 1.8 20

F 1.25*Qd 200 144 177.9 37.2 0.4

23 0.25*Qd 200 205.2 179.1 48 -5.8 22 0.75*Qd 200 145.5 155.4 37.6 -2 21

G 1.25*Qd 200 140.5 168.6 38.6 7.4

26 0.25*Qd 200 205.8 205.6 51.4 -9.1 25 0.75*Qd 200 128.7 176.7 38.2 -2.7 24

H 1.25*Qd 200 95.5 76.6 21.5 4.9

52

Table 2–4. Indices for characterizing hydraulic response across flow rates representing 25%, 75% and 125% of Qd , where Qd is the design flow rate

Q Q=0.25* Qd Q=0.75* Qd Q=1.25* Qd Configuration A(Optimal) Baseline A(Optimal) Baseline A(Optimal) Baseline

τ 192 192 64 64 38.4 38.4 tmean (s) 320 308 119 111 77 70

ti(s) 26 20 28 25 20 21 tp (s) 215 178 47 42 31 28 t10 (s) 110 107 45 45 31 29 t50(s) 292 274 103 95 62 57 t90(s) 614 530 218 198 133 119 MDI 5.58 4.95 4.84 4.40 4.29 4.10

1/MDI 0.18 0.20 0.21 0.23 0.23 0.24 ti / τ 0.14 0.10 0.44 0.39 0.52 0.55 tp / τ 1.12 0.93 0.73 0.66 0.81 0.73 σ2/ τ2 0.31 0.32 0.30 0.30 0.29 0.29 t50/ τ 1.52 1.43 1.61 1.48 1.61 1.48

Hazen's N 3.79 2.85 1.84 1.79 2.00 1.97

53

Figure 2-1 Experimental setup for testing the screened HS. The diameter of the HS was 89.3 cm

and the diameter of the inner screen area was 49.5 cm. The height of the unit was 96.5 cm. The storage capacity of the screened HS under quiescent conditions was 408 L. The screen aperture size for the screened HS used in this study was 2400 μm.

70 KHz ultrasonic sensor

Drop-box (Influent particle injection)

Diversion valve

HS

Recirculation system

Re-circ. pumps

Storage tank B (4000 L)

Storage tank A (4000 L)

Effluent

Inf. OD=15 cm

ID=20 cm

54

Figure 2-2 Geometry of the screened HS. A) Plan and side view of detailed geometry of a

screened HS. B) Typical fluid flow profile inside a screened HS.

Outer Annular Chamber (Volute Area)

Inner Chamber (Screening Area)

Inlet

Inner Chamber (Screening Area)

Outlet

Outer annular chamber (Volute Area)

Cross-flow Screen

Conical Sump

A

B

55

Figure 2-3 Plots of target influent particle size distribution, calculated and measured gradation

utilizing a mixture of five different US Silica Sands (20/30,H-85,Min-U-Sil 10, Sil-Co-Sil 51 and Sil-Co-Sil 250). Details of the granulometric characteristics of the silica sands are provided in Table 2.1. The specific gravities of particles across the gradation were not seen to significantly deviate from 2.65 g/cm3.The resulting gradation was verified by mechanically dry sieving the prepared mixture (ASTM method D422).

Particle diameter (μm) 1101001000

Perc

ent f

iner

by

mas

s (%

)

0

10

20

30

40

50

60

70

80

90

100

Target InfluentCalculated InfluentMeasured Influent

56

Percent of Qd (L/s)

0 25 50 75 100 125

CEf

fluen

t [m

g/L]

60

80

100

120

140

160

180

Δ Pa

rticl

e m

ass (

%)

0

20

40

60

80

100 Baseline A B C D E F G H

(A)

(B)

Figure 2-4 Clarification response of different configurations to for the non-cohesive sandy silt

influent particle gradation across flow rates representing 25%, 75% and 125% of design flow rate, for an influent concentration of 200 mg/L. A) Measured separated particle mass in the HS. Δ particle mass denotes particle mass expressed as % of mass in the influent that was captured in the HS. B) Effluent concentrations measured as SSC [mg/L]. SSC is suspended sediment concentration.

57

Perc

ent f

iner

by

mas

s (%

)

0

20

40

60

80

100InfluentBaseline ABCDEFGH

Screen area

Particle diameter (μm) 101001000

Perc

ent f

iner

by

mas

s (%

)

0

20

40

60

80

100

Volute area

Figure 2-5 Particle Size Distributions by mass, of separated particles as a function of modified

configurations Baseline, A, B, C, D, E, F, G, H, for an influent concentration of 200 mg/L, a screen aperture size of 2400 microns, at a flow rate of Q = 0.25*Qd. A) Screen area. B) Volute area.

A

B

58

Perc

ent f

iner

by

mas

s (%

)

0

20

40

60

80

100

InfluentBaseline ABCDEFGH

Screen area

Particle diameter (μm) 101001000

Perc

ent f

iner

by

mas

s (%

)

0

20

40

60

80

100

Volute area

Figure 2-6 Particle Size Distributions by mass, of separated particles as a function of modified configurations Baseline, A, B, C, D, E, F, G, H, for an influent concentration of 200 mg/L, a screen aperture size of 2400 microns, at a flow rate of Q = 0.75*Qd. A) Screen area. B) Volute area.

A

B

59

Perc

ent f

iner

by

mas

s (%

)

0

20

40

60

80

100

InfluentBaseline ABCDEFGH

Screen area

Particle diameter (μm) 101001000

Perc

ent f

iner

by

mas

s (%

)

0

20

40

60

80

100

Volute area

Figure 2-7 Particle Size Distributions by mass, of separated particles as a function of modified

configurations Baseline, A, B, C, D, E, F, G, H, for an influent concentration of 200 mg/L, a screen aperture size of 2400 microns, at a flow rate of Q = 1.25*Qd. A) Screen area. B) Volute area.

A

B

60

0 0 0 0 0 0 0 0

Trac

er (N

aCl)

[mg/

L]

0

20

40

60

80

100

120

140

160

Configuration [A]Baseline

Q=0.25*Qd

Figure 2-8 Tracer study of Configuration [A] (modified) and the baseline configuration at a flow rate Q = 0.25*Qd.

.

Elapsed Time (sec)

020

040

060

080

010

0012

0014

00

Cum

ulat

ive

RTD

, F

0.0

0.2

0.4

0.6

0.8

1.0

61

Figure 2-9 Tracer study of Configuration [A] (modified) and the baseline configuration at a flow

rate Q = 0.75*Qd.

Trac

er (N

aCl)

Con

cent

ratio

n [m

g/L]

0

50

100

150

200

250

E lapsed T im e (sec)

0 100 200 300 400

Cum

ulat

ive

Res

iden

ce T

ime

Dis

tribu

tion

,F

0.0

0.2

0.4

0.6

0.8

1.0

Q =0.75*Q d

Q =0.75*Q d

Configuration [A]Baseline

Configuration [A]Baseline

62

Figure 2-10 Tracer study of Configuration [A] (modified) and the baseline configuration at a flow rate Q = 1.25*Qd

Trac

er (N

aCl)

Con

cent

ratio

n [m

g/L]

0

50

100

150

200

250

Elapsed T im e (sec)

0 50 100 150 200 250 300

Cum

ulat

ive

Res

iden

ce T

ime

Dis

tribu

tion

,F

0.0

0.2

0.4

0.6

0.8

1.0

Q =1.25*Q d

Q =1.25*Q d

Configuration [A]Baseline

Configuration [A]Baseline

63

CHAPTER 3 CFD MODELING OF A STORMWATER HYDRODYNAMIC SEPARATOR

Introduction

Particulate matter (PM) transported in urban rainfall-runoff has been identified as a

significant contributor to overall deterioration of surface waters (USEPA 2000). Rainfall-runoff

transports a hetero-disperse distribution of PM that ranges from colloidal to debris-size PM as

well as PM-associated contaminants (Sansalone et al. 2007, Lee and Bang 2000, Sansalone et al..

1998, Igloria et al.. 1997, Sansalone and Buchberger 1997). Particle size distribution (PSD) of

PM delivered by runoff varies with flow rate and spatial position along a flow path, with urban

source areas providing the more hetero-disperse yet coarser PSDs (Kim and Sansalone 2008).

One of the most significant advances in the field of urban runoff management is with

respect to modeling hydrologic and hydraulic processes in these urbanized systems. Existing

urban runoff models such as the Stormwater Management Model (SWMM) (Rossman 2007,

Huber 1988), utilized worldwide, and variations thereof, have greatly improved the efficacy of

hydrologic and hydraulic design and analysis in highly complex urban drainage systems. While

this has been a major advancement in the field of urban drainage, it is outside the current scope

of such models to provide in-depth hydrodynamic and particle clarification profiles for a

geometrically and hydrodynamically-complex unit operation loaded by hetero-disperse PM.

Many conventional urban runoff analysis methods for clarification of PM are extensions of

historical settling or wastewater tank principles, which often assume ideal overflow theory and

reasonably steady influent hydraulic as well as PM characteristics with time (Cristina et al.

2003). However, differing flow rates generated by rainfall-runoff processes, hetero-disperse PM

not amenable to a single gravimetric aggregate index such as TSS, and the geometric and

hydrodynamic complexity of unit operations require more representative models and

64

measurements; with the commensurate complexity added by such representations. Wastewater

and drinking water practices have incorporated models and measurements of representative

complexity. However, the development of representative models and measurements for

stormwater treatment unit operations have lagged behind the proliferation of best management

practices (BMPs) installations largely designed, analyzed and permitted based on index or

empirical concepts (Sansalone 2005). The terminology, BMP, generally elicits a more

qualitative and empirical evaluation of treatment that has been based on %-removal and

examination of unit operations as lumped “black-box” systems (Sansalone 2005). While

treatment BMPs evolved from large surface area detention/retention basins designed originally to

mitigate flow and volume, a class of preliminary treatment manufactured BMPs have focused on

small-footprint unit operations minimize land costs without hydrologic control. As a result,

small-footprint unit operations without hydrologic control have proliferated over the last decade.

Screened hydrodynamic separators (HS) as preliminary treatment for coarse PM (> 75 μm) and

trash/debris; fall into this category of unit operations (Rushton 2004, Rushton 2006, Stenstrom

and Lau 1998). In a HS gravitational settling and to a lesser extent inertial forces and size

exclusion separates coarse PM (Brombach et al.. 1987, Brombach et al.. 1993, Pisano et al..

1994, USEPA 1999, Andoh et al.. 2003). The HS provides the potential for longer particle

trajectories per given unit surface area in comparison to traditional BMPs such as

detention/retention basins.

Despite thousands of HS installations in North America over the last decade, existing

literature does not provide fundamental insight into performance of an HS other than %-

reduction information with an HS treated as a lumped black-box. Previous studies in the

literature have ranged from overflow rate theory (Weib 1997) to semi-empirical approaches

65

based on broad assumptions of vortex flow behavior (Paul et al.. 1991). The lack of mechanistic

evaluations and use of lumped index methodologies have led to difficulties in HS scaling and

implementation. Fenner et al.. (1997, 1998) report that similitude analysis does not yield a

single dimensionless group that can be used in scale-up of a HS. These approaches can be

contrasted with CFD approaches to examine PM fate in treatment unit operations such as the HS.

CFD approaches to model particle-laden flows are an active research area (Curtis et al..

2004, van Wachem et al.. 2003) for many hydraulic systems including a HS. Faram et al.. (2003)

utilized a Reynolds Stress Model (RSM) to model turbulent flow and a Lagrangian Discrete

Phase Model (DPM) to model PM fate. Lim et al.. (2002) used CFD-predicted velocity profiles

to study behavior of flocs in a vortex separator with a Renormalization Group (RNG) k-ε

turbulence model. Tyack et al.. (1999) compared measured velocity profiles in a vortex

separator to those predicted by a Renormalization Group (RNG) k-ε turbulence model.

However, many of these CFD modeling studies did not couple representative PM measurements

with the numerical approach. Limiting the modeling approach, for example with an overflow rate

evaluation of an HS, or limiting the representativeness of measurements, for example with

indices such as TSS and auto sampling has resulted in most HS studies as %-removal evaluations

of a black-box unit.

This study examined a HS with two cylindrical chambers illustrated in plan in Figure 3-1.

The flow inlet is tangential to the inner cylindrical chamber and the two chambers are separated

by a static screen. The static screen consists of a regular array of apertures. These apertures

allow flow to exit the inner screen chamber and enter the volute chamber. The inner cylindrical

chamber, along with the screen and the sump area are designated the ‘screen area’. The outer

66

less turbulent annular area is the ‘volute area’. PM separation by this HS configuration is

primarily a function of various parameters, as expressed in the following equation.

),,,,,,( strpsparticles dvvQdvfM τ=Δ (3-1)

In this expression, particlesMΔ is the mass of particles separated, sv is the discrete particle

settling velocity, pd is the mass-based particle diameter, Q is the influent volumetric flow rate,

rv is the radial velocity component in the screening area, tv is the tangential velocity component

in the screening area,τ is the hydraulic residence time, and sd is the diameter of the screen

apertures.

The screened HS has no underflow, and therefore the mechanisms of hydrodynamic

separation are different from typical vortex-based separators, where secondary currents play an

important part in PM separation. The screen of the HS consists of apertures of diameter 2.4 mm.

These apertures are not expected to ‘screen’ particles wherein there is interaction with the screen

wall in the form of reflection, interception or straining, for particles with diameters less than the

aperture size of 2.4 mm. In this study the mass-based d50 of the influent PSD is 78 μm). The PM

separation mechanism in the screening area or the inner chamber of the screened HS is

summarized as follows. The aperture geometry allows for increased tangential fluid velocities as

opposed to increased radial fluid velocities. Particles that enter the screening area have a

tendency to exit the screen, advecting with velocities proportional to the radial fluid velocity. As

the particles travel outwards from the center and towards the screen, the radial fluid velocity

component is significantly weaker in comparison to the tangential fluid velocity component.

Therefore, a fraction of particles do not possess adequate momentum to pass through the screen.

This phenomenon has been termed as “inertial separation” in the rest of this paper.

67

Objectives

This study has four objectives. The first objective is to couple a pilot-scale HS

configuration utilizing representative PSD sampling and analysis as well as measured PM

material balances with the development of a CFD-based HS model. In this first objective the

CFD-based HS model is validated by concentration, mass and PSD measurements for pilot-scale

testing conducted across the operating flow rate range of the HS. The second set of objectives

evaluates the role of flow rate and PSD, across the hydraulic operating range of the HS, on the

separation of PM as a function of particle size (important for examining trapped and exported

PSDs for O & M and chemical partitioning during storage). The third objective is to examine

spatially-distributed particle trajectories in the HS and settling velocity frequency distributions

within the HS to Newtonian and Stokesian models. In this objective the HS is examined as a

unit operation where the multiple (screened and volute) chambers have unique sedimentation

roles for PM in contrast to a conventional examination of the HS as a lumped black-box. The

fourth objective is to quantify differences between validated CFD-based model results with

results based on examining the HS as a lumped system with a conventional overflow rate model.

As part of this fourth objective, PM is represented as the entire measured PSD (providing a direct

comparison to the CFD-based model at each flow rate), or based on a gravimetric index of the

PSD (the mass-based median of the PSD; the d50m) and therefore providing an evaluation of how

the modeled performance utilizing an index measurement deviates from measured PSD results.

(It is further noted that most index-based measurements such as TSS provide no indication of the

d50m).

68

Methodology

Pilot-scale testing setup

Figure 3-1 illustrates the schematic plan view of the instrumented full-scale HS as part of

the pilot-scale testing configuration. The flow control valves and pump were calibrated (with

volume and time) across the entire flow rate range of 0.16 to 23.4 L/s. A Parshall flume was also

calibrated volumetrically over the entire flow rate range, with triplicate measurements, at an

error less than +1%. A known and constant gradation of influent particles were injected at the

free-flow drop-box located immediately downstream of the Parshall flume and immediately

upstream of the HS. The overall diameter of the HS is 1.524 m and the diameter of the inner

screened chamber area is 0.65 m. The height of the HS is 1.82 m. The empty HS sump storage

volume is approximately 1580 L. The design hydraulic operating volumetric flow rate (Qd) is

15.89 L/s based on the manufactured specification. The HS tested was hydraulically-sized based

on hydrologic loadings from the impervious 1088 m2 watershed at the pilot-scale facility located

in Baton Rouge, LA. The static cross-flow cylindrical screen with a diameter of 0.65 m

consisted of apertures, each with a d50 of 2.4 mm. The overall screen area that was open to flow

(through these non-clogging apertures) was approximately 40 % of the total screen area of

0.5334 m2.

Influent Particle Gradation

The clarification response of the HS is highly dependent on the influent PSD (Kim et al.. 2004);

in this study the textural classification is non-cohesive sandy silt. The influent mass-based PSD

is illustrated in Figure 3-2. It is noted that approximately over 50 % by mass of this gradation, is

finer than 75 µm and therefore, over 50 % by mass of this gradation consists of settleable

(nominally ~25 to 75 �m) and suspended particles (nominally 1 to ~25 �m) (Kim and

Sansalone 2008). The influent PSD was prepared by a weighted combination of commercially-

69

available gradations of solid sub-rounded silica particles. The dry mass of particle mixture was

added to each experimental run based on approximately 38,000 L of influent ( 25 ± 4 ºC) to

achieve a 200 mg/L influent concentration, which is a typically observed concentration in runoff

at this paved source area watershed (Sansalone et al.. 2005). Periodic QA/QC checks of influent

PSD and concentration were conducted to ensure consistency of the influent particle gradation.

Field Test Procedure

Before each treatment run the storage tanks, the recirculation pipes and the HS were

cleaned and washed thoroughly by pumping potable water through the system. The desired test

flow rates and velocities were achieved through the use of the influent pump and the

recirculation system to vary flows. Calibrated flow control valves were operated to achieve the

desired flow rate. Flow measurements were validated throughout each run and a cumulative

volumetric balance was based on a Druck pressure sensor in each influent supply tank. Druck

pressure sensors (2 psi, resolution of 0.5 mm) were installed on the influent (sump) side and

volute side of the screen as well as at the outer diameter of the volute chamber before effluent

discharge from the volute area. PM with the influent gradation shown in Figure 3-2 was injected

just upstream of the inlet of the HS, after achieving a steady influent flow rate with fluctuations

of less than +1 % of the target flow rate. The rate of particle injection was constant on a

gravimetric and granulometric PSD basis. 10 duplicated 2 L effluent samples were collected for

water quality and suspended sediment concentration (SSC) analyses, at the outfall of the effluent

pipe. Approximately 400 L of effluent, representing 10 duplicated 20 L samples, was collected

and composited into several 210 L polypropylene tanks, at the same sampling frequency as the 2

L samples, in order to recover sufficient particle mass to carry out effluent particle gradations.

70

Laboratory Analyses

Two 20 L composite effluent samples (A and B) were prepared from the 10 individual

replicate (A and B) 2 L samples. The entire measured volume of each replicate composite

sample was then filtered using a nominal 1 μm glass fiber filter. Since the entire volume was

examined of each replicate composite sample was analyzed the gravimetric index of total

suspended solids (TSS) was equivalent to suspended sediment concentration (SSC) without the

inherent sampling and analysis errors associated with TSS. Particles captured in the screened HS

from each run were completely recovered as wet slurry from the HS screened area and volute

area separately, and these areas cleaned for the next run. Effluent PM captured in the 210 L

polypropylene tanks was also recovered as separate slurries. At least 5 hours of quiescent

settling was allowed before slurry recovery. The recovered PM slurry was transported to the

laboratory, dried at 40°C and the mass was recovered. Total effluent mass was computed from

the measured sample effluent SSC for the total volume treated. A flow volume totalizer was

used as a check of the incremental flow volume measurements for each treatment run. A mass

balance check requiring at least a 90+% recovery across the HS was performed based on SSC.

Mass Balance Error = %10100)(±≤×⎥

⎦

⎤⎢⎣

⎡ +−

i

eHSi

MMMM (3-2)

In this expression, iM is the mass of particles in the influent , HSM is the mass of particles

captured by the screened HS and eM is the mass of particles in the effluent , computed from the

measured effluent SSC corresponding to total treated volume. All gravimetric particle

measurements were carried out on a dry mass basis. With the mass balance error criterion (≤ 10

%) satisfied, the particle removal efficiency ( particlesMΔ ) is calculated.

71

100)()(

×=Δi

HSparticles M

MM (3-3)

The dried PM mass was mechanically sieved to obtain a PSD according to a modified

method for ASTM D422 (sieve analysis) (ASTM 1993, Sansalone et al.. 1998). Sieves utilized

included the #30, #50, #100, #140, #200, #270, #400, #500 and the pan. Mass balances were

determined for each analysis and mass balance errors were in the range of 1 to 2 % by dry mass

for all PSDs.

Computational Fluid Dynamics Methodology

The hydrodynamics and particle dynamics of the HS vary as a function of x, y and z spatial

coordinates. As a result, a three dimensional (3-D) approach was required. The generalized 3-D

scalar conservation equation for a control volume (CV) with volume )( zyxV ∂∂∂= is utilized.

(Versteeg et al.., 1995)

Φ+ΦΓ=Φ+∂

Φ∂ Sgraddivudivt

)()()( ρρ (3-4)

In this expression, Φ is any fluid property per unit mass, such as mass fraction, velocity,

etc; u is the fluid velocity, Γ is the diffusion coefficient, and ΦS is the source/sink term.

zw

yv

xuudiv

∂∂

+∂∂

+∂∂

=)( (3-5)

The mass continuity equation is obtained by assigning a value of 1 to Φ .

( ) 0=+∂∂ udiv

tρρ (3-6)

Modeling Fluid Flow

The dominant flow regime is turbulent in the HS. The Reynolds numbers range from 102

to 105, indicating the requirement of a turbulence model that can effectively model flows that

range from laminar to transitional to fully turbulent. A Reynolds averaged Navier-Stokes or

72

RANS approach (Ferziger et al.. 2002) was utilized to resolve turbulent flow. The RANS

approach is based on “time averaging” the Navier-Stokes equations. This process yields

additional terms in the standard transport equations, termed the “Reynolds stresses”. A k-ε

model (Launder and Spalding 1974) accounted for the effects of turbulence on mean 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 illustrate the relationship between

viscous stresses and “Reynolds stresses”. It should be noted that eddy viscosity (µt) is a non-

physical quantity, and is expressed by the following equation.

⎟⎟⎠

⎞⎜⎜⎝

⎛=

ερμ

2kft (3-7)

In this expression, k is the turbulent kinetic energy per unit mass.

)(5.0 222 wvuk ′+′+′= , [L2T-2] (3-8)

In this expression, wvu ′′′ ,, are vector components of velocity fluctuations due to

turbulence and ε is the dissipation rate of turbulent kinetic energy per unit mass. Vortex-

induced flows in the HS did not exhibit secondary currents and flows are not highly swirling.

The standard k-ε model has been suggested as a robust approach in situations where the swirl

velocities are not large (Mohammadi and Pironneau 1994) but has also been applied in the case

of hydrocyclones with highly swirling flows (Nowakowski et al.. 2004, Statie et al.. 2001, Petty

et al.. 2001). The full Reynolds Stress Model (RSM), the realizable and renormalized k-ε models

were tested, and did not suggest any improvement that might warrant the increased

computational power and time. The standard k-ε model equations are expressed for k and ε,

respectively.

73

kbkjk

t

ji

iSGG

xk

xku

xk

t+−++

⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

⎟⎟⎠

⎞⎜⎜⎝

⎛+

∂∂

=∂∂

+∂∂ ρε

σμμρρ )()( (3-9)

εεεεε

ερεεσμμρερε S

kCGCG

kC

xxu

xt bkj

t

ji

i+−++

⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

⎟⎟⎠

⎞⎜⎜⎝

⎛+

∂∂

=∂∂

+∂∂ 2

231 )()()( (3-10)

kG represents generation of k due to the mean velocity gradients; bG is generation of

k due to buoyancy; ε1C , ε2C and ε3C are constants ; kσ and εσ are the turbulent Prandtl

numbers for k andε , respectively; kS and εS are user-defined source terms. The constants were

determined by Launder and Spaulding (1974). It was hypothesized that isotropy of Reynolds

stresses can be assumed reasonably in the case of the HS. Values of ε1C , ε2C , ε3C , kσ and εσ in

the model were 1.44, 1.92, 0.09, 1.0 and 1.3 respectively (Launder et al.. 1974). The no-slip

boundary condition, along with effects of viscous blocking and kinematic damping creates large

gradients in variables near the HS walls. To account for these phenomena semi-empirical “wall

functions” for the k-ε model were used (Launder et al.. 1974).

Modeling the static screen

The shape of the screen apertures results in a weakly reversed flow direction in the volute

chamber. The screen area open to flow is designed so that screen radial velocity is approximately

an order of magnitude lower than the inlet velocity. The non-cohesive, inorganic and granular

nature of stormwater PM, and large 2.4 mm apertures results in a screen that non-clogging, at

least for stormwater. Meshing the screen with structured or unstructured meshing schemes

places severe constraints on time and computational power. To overcome this difficulty, the

static screen was modeled as a porous perforated plate with the addition of a momentum source

term to the standard fluid flow equations. This momentum sink contributes to the pressure

gradient in the porous computational cell, creating a pressure drop that is proportional to the fluid

74

velocity in the cell. The source term is composed of two parts: a viscous loss term and an inertial

loss term. For simple homogeneous media, the sink term is expressed by the following equation.

⎟⎠⎞

⎜⎝⎛ +−= imagiii vvCvS ρ

αμ

21

2 (3-11)

In this equation, iS is the source term for the i th momentum equation, α is the

permeability, iC2 is the inertial resistance factor, iv is the velocity in the i th momentum equation,

magv is the velocity magnitude in the computational cell. The pressure drop through the screen

was measured experimentally with pressure transducers and it was found that the head loss was

38.1 mm (150 mm across the entire HS) at design flow rates. Given the HS height of 1.82 m,

these head loss values are low. The viscous resistance term was assumed to be negligible and the

source term was then modeled considering only the inertial resistance term, and the inertial

resistance factor per unit thickness of the plate, i.e. )(2 iC was calculated for the x, y and z

directions as described by the following equation (FLUENT 2005).

nK

C iLi

)(')(2 = (3-12)

In this equation, n is the plate thickness, and )(' iLK is calculated in the following equation.

2

2

)()(' *n

miLiL v

vKK = (3-13)

In this equation, 2mv is the square of the velocity through the plate, considering that the

plate is ‘m’ % open to flow in the given direction and 2nv is the square of the velocity through the

plate, considering that the apertures are 100 % open to flow in the given direction. )(iLK is the loss

factor in the ith direction and is calculated from the following equation.

( )2)( oiLscreen vKp ρ=Δ (3-14)

75

In this expression, pΔ is the measured pressure loss through the static screen. 2C is

calculated based on the %ages of screen area open to flow described previously for the x and y

directions. The inertial resistance in the z-direction is theoretically infinite. However, to specify

2C in the z-direction, a value sufficiently large enough (twice the order of magnitude of the

largest value of 2C ) was used. The assumption is that the porous cells (apertures) are 100%

open, indicating that there is no physical/geometric obstruction to flow through the apertures.

Modeling the Particulate Phase

Typically, multiphase flows are modeled with an Eulerian-Eulerian approach or an

Eulerian-Lagrangian approach (van Wachem et al.. 2003). The latter is commonly accepted to be

suited to modeling dilute flows, defined as flows with a particulate volume fraction (PVF) less

than 10% (Brennen 2005), which is the case in this study (PVF << 0.1 %). In this approach, the

flow field was solved using the Eulerian approach. Following this, particles were tracked using a

Lagrangian Discrete Phase Model (DPM). The DPM is derived from force balances based on

classical Newton’s (Turbulent and transitional regimes) and Stokes’ (Laminar regimes) laws

describing particle motion, and is summarized by the following equation.

xp

pxpD

p Fg

uuFdt

du+

−+−=

ρρρ )(

)( (3-15)

In this expression,

dF 24Re18

2pD

pp

Cdρμ

= (3-16)

232

1 ReRe ppD

aaaC ++= (3-17)

76

In the above expressions , u is the fluid velocity, pu is the particle velocity, ρ is the fluid

density, pρ is the particle density, pd is particle diameter, μ is the viscosity, 321 ,, aaa are

empirical constants that apply to smooth spherical particles as a function of the Reynolds number

(Morsi et al.., 1972) and pRe is the particle Reynolds number. Particle trajectories are obtained

by integration. For this study, particles of consistent morphology were injected across the entire

flow cross-section immediately above the inlet to the HS to obtain comparable particle

trajectories across varied flow rates, by reducing uncertainty in initial spatial location. Particles

were defined as silica particles of diameters associated with the sieves utilized and a measured

specific gravity of 2.65 as determined by helium pycnometry (Sansalone et al. 1998). Particles

were tracked for a specific length for each flow rate, based on hydraulic residence times

calculated by injecting neutrally buoyant submicron ‘tracer’ particles. Particles that remained in

the HS after integrating over the specified length were considered to have been separated by the

HS. Particle removal was thus defined by the following equation.

100×=ΔI

HS

NNp (3-18)

In this expression, HSN is the number of particles that remain in the screened HS, and IN is

the number of particles injected at the inlet.

Discretization of Geometry

The computational geometry of the screened HS was generated using GAMBIT, a pre-

processing software for FLUENT. Boundary conditions were specified in this step. It is

important to note that the free surface of the flow was specified as a shear-free wall, while

assigning boundary conditions. The computational geometry was discretized using an

unstructured mesh with tetrahedral elements. The TGrid (Qi et al.. 2006) algorithm was used to

77

generate the mesh. Progressively finer meshes were tested, with 0.4, 1.96 and 2.10 million cells

respectively, to examine the effects of computational mesh sizes on particle separation

predictions. Localized mesh refinements were not utilized. The HS mesh is shown in Figure 3-

1.

Discretization of Governing Equations

A Finite Volume Method (FVM) was used to convert the governing equations to algebraic

equations. The governing equations were integrated over each control volume to yield discrete

equations. A cell-centered scheme was used in the process of discretization. Values of cell faces

were computed using a Second-Order Upwind Scheme (Barth et al.. 1989). “Upwinding”

implies that the face values are obtained from upstream cell quantities relative to the normal

velocity. The Second-Order Upwind Scheme is typically suggested as a requirement to procure

accurate results with unstructured meshing schemes.

Solution Schemes

Pressure-velocity coupling is an issue that must be addressed during the process of

obtaining a sequential solution to the momentum and continuity equations. The SIMPLE (Semi-

Implicit Method for Pressure Linked Equations) algorithm (Patankar 1980) was used to introduce

a pressure term in the continuity equation. Various other algorithms have been devised for

effecting pressure-velocity coupling, such as the SIMPLEC (Vandoormaal et al.. 1984.) and

PISO (Issa 1986) algorithms, but did not provide any significant improvement in convergence

from the SIMPLE algorithm for the HS. The SIMPLE algorithm was chosen as the consistent

approach to pressure-velocity coupling across the range of operating flow rates. The criterion for

iterative convergence was set at 1x10-3, which is a typical constraint for multiphase flows which

do not consider chemical kinetics (Ranade 2002).

78

Results and Discussions

PSD results

Figure 3-2 illustrates the phase shift in particle size distribution from influent (left) to

effluent (right) as transformed by the HS. Particles in the effluent are finer than in the influent,

as a result of the separation mechanisms of the HS. As flow rates increase, effluent particles are

progressively coarser as compared to the finer effluent PSDs for the lower flow rates. Results

also indicate the finer effluent PSDs (at lower flow rates) are significantly less hetero-disperse.

The median particle size based on mass (d50m) is commonly selected as an index for a PSD and

this index is plotted in upper plot of Figure 3-3-2. The d50m of the effluent PSD is significantly

finer than that of the influent d50m across the entire flow rate range. The overall separation

mechanisms of the HS can be categorized into three primary mechanisms. These mechanisms are

discrete particle (Type I) settling, size exclusion and inertial separation. While gravitational

settling and to a lesser extent size exclusion are the predominant separation mechanisms at lower

flow rates, inertial separation contribute to overall particle separation at higher inflow rates.

CFD model results

Refining the HS mesh from 0.4 million to 1.96 million cells, resulted in an improvement in

model predictions, as illustrated in Figure 3-3. However, further refinement of the mesh had

little effect on improving overall model performance, confirming that the solution is grid

independent. Model results are presented in two parts. The first part consists of modeled particle

separation efficiencies at given flow rates, for individual particle sizes, and these results are

summarized in Figures 4. The second results set is depicted in Figure 3-5, where results are

compared on the basis of overall separation efficiency expressed as Δ particle mass (gravimetric

mass of SSC in the effluent) and effluent concentrations (Ceff) expressed as SSC.

79

The first presentation of results of the CFD model is further grouped into three categories

based on flow rates. The first category consists of the lowest flow rates (approximately 1 to 10

% of the HS design flow rate, Qd = 15.89 L/s), where gravitational sedimentation effects

predominate. The second category consists of intermediate flow rates (approximately 25 to 75 %

of Qd), where gravitational sedimentation and exclusion by the deflective screen are the

predominant separation mechanisms, and inertial separation effects are low. It is observed that

up to approximately 50% of Qd that the coarse fraction (> 75 μm) of the PSD is effectively

separated. The third category consists of high flow rates (approximately 100 to 150 % of Qd,

where the effects of inertial separation and increased particle residence times as a result of

lengthened particle trajectories are increasingly important with respect to gravitational

sedimentation. Absolute relative % difference (RPD) was chosen as a parameter to compare

measured and modeled data. RPD was calculated from the following equation.

100data Measured

data) Modeled-data (Measured RPD Absolute ×= (3-19)

Results in Figure 3-4 indicate that for the first category of flow rates, 0.16 L/s, 0.79 L/s and

1.59 L/s, there is agreement between measured and modeled data, with absolute RPD’s lesser

than 4 %. It is noted that the CFD model predicts particle separation behavior effectively across

the entire PSD. In the second category of flow rates, 3.97 L/s, 7.94 L/s and 11.92 L/s, results

demonstrate agreement between measured and modeled with an RPD < 10%, although the model

tends to slightly overestimate removal of coarser PM. In the high flow rate category, 15.89 L/s,

19.87 L/s and 23.34 L/s, results demonstrate agreement but there is a tendency for CFD to over

predict removal of coarser PM. However, the overall RPD still remained < 10%. In the field of

urban drainage these results are noteworthy given that the flow rates range over two orders of

magnitude and the hetero-disperse influent PSD ranges by almost three orders of magnitude in

80

particle size. Results are also of significant value given that the current paradigm of

measurement for design, analysis and permitting for BMP performance is the index parameter

TSS; although only occasionally a specific gravity or size index (such as d50m) are ascribed.

The second set of results, Figure 3-5, compares model and measured results of effluent

PM mass and concentration. Effluent measured and modeled concentrations are compared, for

an influent SSC of 200 mg/L, across the entire range of inflow rates. Range bars associated with

measured data represent the standard deviation between replicated effluent samples. Results

indicate that the model predictions of SSC reproduce the measured data with an absolute RPD <

10 %. Figure 3-5 also compares the overall particle separation by the screened HS is expressed in

terms of gravimetric SSC mass in the effluent, Δ particle mass. Model and measured results

agree with an absolute RPD < 10%. Range bars indicate the overall mass balance error (MBE)

associated with the SSC measurements for each pilot-scale test at a given flow rate. CFD results

are compared and contrasted to conventional methods in Table 3-1 for the HS and loadings of

this study. While the table summarizes the agreement between measured and CFD results, the

table also illustrates deviation for the conventional overflow rate model (Q/A). Furthermore

results indicate that despite the use of a lumped black-box model such as overflow rate,

knowledge of a PSD for the PM loading provides a far more reasonable (albeit less accurate than

CFD) set of results than the convention use of a lumped index such as a d50m for PM. It is further

noted that in most conventional analyses, even a d50m is not available for gravimetric indices

such as TSS.

Post-processing CFD model results: Particle dynamics and hydrodynamics

Figure 3-6 illustrates the particle trajectories calculated by a Lagrangian DPM for the

screened HS, for an influent flow rate (Q) of 3.97 L/s. This flow rate was chosen as a typical

flow rate on the basis of its frequency of occurrence in typical stormwater flows and on the HS

81

hydraulic design capacity for watershed at this pilot-scale facility (Sansalone et al.. 2005). Three

particle sizes were chosen for illustration, 450 μm in the sediment size range (medium sand), 75

mm as the nominal particle size that “differentiates” coarse and fine PM (differentiates sediment

and settleable PM), and 25 μm as the nominal size that “differentiates” settleable and suspended

PM size ranges. Plot (a), (b) and (c) depict particle trajectories for a particle diameter (dp) of

450, 75 and 25 µm respectively. The dependence of particle separation on particle size is clear. It

can be observed for the coarse end of the size spectrum that particles are influenced

predominantly by gravitational forces whereas for the fine end of the size spectrum the

suspended particle behavior is largely a function of inertial hydrodynamic forces.

Figure 3-7 illustrates HS velocity distributions, for particles injected at the inlet

geometric centroid. Plots (a) and (b) illustrate the spatial variation of particle velocity. A

neutrally buoyant ‘tracer’ particle was chosen to represent fluid velocity in a comparable

Lagrangian frame of reference. Distance traveled by a tracer particle, from the injection point

(geometric centroid of the inlet) to the outlet of the HS, was recorded as the overall path length

of a fluid ‘particle’. The distances traveled by discrete PM sizes were normalized to the overall

path length.

Plots (c) through (f) illustrate the mechanistic aspects of particle separation in the HS

through normalized frequency distributions of particle velocities. Due to the difference in

mechanisms within the screen and volute area, results are presented separately. Plot (c) and plot

(d) represent particle velocities in the screen area for a 450 µm and 25 µm particle respectively,

while plot (e) and plot (f) represent particle settling velocities (vs) within the volute area for the

450 µm and 25 µm particle respectively. Qualitative variations in the histograms are highlighted

by dotted numbered circles. In explaining particle behavior, it should be noted from Figure 3-6

82

path lines that the inlet velocity vector is exactly aligned in the y-direction. Thus, the inertial

force is predominantly represented by the y component of the velocity vector.

Dynamics of a particle with dp= 450 µm

Plot (a) depicts the particle velocities of a 450 µm particle relative to fluid velocity, as a

function of the normalized path length. The initial fluctuations in particle velocity of the 450 µm

particle are attributed to the sliding of the particle along the turbulent boundary layer at the

bottom of the inlet. The point where the inlet pipe opens tangentially into the inner screening

chamber is located at a distance close to 18% of the total normalized path length. Following this,

the particle falls into the screen area, and its motion is almost entirely affected by gravitational

forces and correspondingly, in plot (c), number ‘1’ indicates that the particle velocity that occurs

with the highest frequency does not diverge significantly from Vs predicted by Newton’s law

(indicated by the bulls-eye symbol in the plot). In addition, it is noted that the geometric centroid

of this distribution lies close to Vs predicted by Newton’s law. As the particle settles in the inner

screening chamber, the particle trajectory tends to be closer to the screen due to higher radial

velocities compared to tangential velocities and it escapes the screen, to finally settle at the

bottom of the volute area. This corresponds to the number ‘7’ in plot (e) which indicates that the

predominant velocities of a 450 µm particle in the volute area are close to zero, indicating that

the particle has been separated by gravitational settling. Having escaped the screen, the particle

settles into the volute area with a velocity in the range of that indicated by number ‘8’.

Dynamics of a particle with dp= 25 µm

Plot (b) shows the relative particle velocities of a 25 µm particle relative to fluid velocity,

plotted as a function of the normalized path length. It is seen that a 25 µm particle essentially

follows the fluid pathlines and is not separated by the HS. Plots (d) and (f) indicate a wider

distribution of particle velocities in the HS for the 25 µm particle as opposed to a 450 µm

83

particle, leading to the inference that a 25 µm particle is largely affected by the characteristics of

the flow regime. The following observations were made regarding the spatial location of

occurrence of velocities. Firstly, in the screen area, in Plot (d) the number ‘2’ indicates the low

velocities occurring at the center of the screen area and the number ‘3’ indicates the increase in

velocities as the particle approaches the screen. Number ‘4’ occurs at the screen, and is

dominated by the y-component of velocity. Number ‘5’ shows the increase in velocity towards

screen. This occurs closer to the screen than number ‘3’. Number ‘6’ occurs at the inlet to the

screened HS. This is inferred from the magnitude of the velocity, which is equal to the inlet

velocity of 0.08 m/s. In plot (f), number ‘9’ indicates velocities at the outlet of the HS, where the

y-component is less predominant. Number ‘10’ indicates the decrease in velocities from the

screen towards the outlet, and highlight ‘11’ indicates the velocity at the screen, for the 25 µm

particle. It is noted that the centroid of the distributions for both the screen and volute areas for a

25 µm particle diverges significantly from a value of Vs predicted by Newton’s law.

The fate of PM in the HS can be influenced by the point of injection. The trajectory

analysis dealt with a geometrically representative injection point, mainly for the purpose of

illustrating how CFD results are utilized to examine a geometrically-complex unit operation.

Conclusions

In the field of urban drainage treatment, the conventional practice is to evaluate

treatment BMPs as lumped “black-box” units examined by overflow rate models for PM indices,

sampled by automated samplers, examined based on indices such as TSS, with results

characterized by %-removal. In contrast, this study utilized PSDs, mass balances, CFD, unit

operation concepts and spatially-distributed evaluation of a commonly-deployed screened HS

unit operation instead of these conventional treatment paradigms of urban drainage. This study

applied the principles of CFD, using a Finite Volume Method (FVM), to model PM behavior of

84

the geometrically and hydrodynamically-complex HS, using a standard k-ε model to account for

effects of flow turbulence and resolve the RANS equations, and a Lagrangian discrete phase

model (DPM) to track particles. The static screen was modeled as a porous cylinder by adding

appropriate source terms to the flow equations. The CFD model was validated with pilot-scale

data across the operating range of flow rates and PSDs. PM data were collected from

representative manual sampling and resolved into PSDs, concentration and mass; with mass

balances conducted for each pilot-scale test and each PSD analysis; in contrast to more

commonly utilized indices such as TSS. Each test was further evaluated with pressure sensor,

flow and volume measurements. CFD model validation results for PM concentration, mass and

PSDs were within 10% of the pilot-scale measured data. Model grid stability and independence

were demonstrated. Post-processing results provided insight into the mechanistic HS behavior

by means of 3-D hydraulic profiles and particle trajectories and allows re-designs to further

mitigate short-circuiting.

Results demonstrate that while coarse PM on the order of several hundred

microns are separated by the HS at design flows, settleable and suspended particles are largely

eluted from the HS even at flow rates less than design flow and under clean unit conditions of

this study (therefore scouring of previous sediments did not occur). The ability of the CFD

model to reproduce treatment results across a range of flow rates and PSDs suggest that the

validated model can serves as a foundation upon which design alternatives can be proposed. A

validated CFD-based iterative approach to design of this HS as a preliminary unit operation has

the potential to provide reduced prototyping costs with improved performance, as a result of

carefully designed experimental matrices, focused on meeting coarse PM control requirements

for downstream treatment units. It is noted that for this study, most parameters required for the

85

CFD model were measured. The only parameters that were provided in the model were the

inertial resistance coefficients. These were obtained by physical measurement of aperture areas

of the screen, these areas being open to flow. The pressure drop across the static screen was also

measured. The apertures geometry and distribution was uniform throughout the screen.

This study demonstrated the ability of a CFD approach to model effluent mass,

concentration and PSDs of PM from the HS. In the field of urban drainage treatment, it has been

argued that this level of agreement between measured and modeled is not achievable. None the

less, this level of agreement was achieved through the combination of a validated CFD model

and representative measurement of flow, granulometric and geometric quantities coupled with

material balances; as well as resolution of PM into a PSD through the common practice of

mechanical sieve analysis with the companion mass balances. Clearly the need to resolve PM

into a PSD is an important conclusion from Table 3-1. Table 3-1 also illustrates that despite the

simplicity of an overflow rate model, that even for a complex screened HS a significant fraction

of the PM separation performance of the HS is simple discrete (Type I) gravitational settling.

Even with a simple overflow model, resolution of PM into a PSD allows gravitational settling to

be identified as the most significant mechanism for coarse PM separation of a screened HS.

Study results indicate that a screened HS is a preliminary unit operation that may have potential

to protect downstream primary unit operations, units capable of more significant PM

concentration reductions and finer PM capture. While the HS unit was evaluated under clean

sump and volute conditions, the capture of PM by HS units require regular maintenance and

management to prevent scour and mitigate the lability of separated coarse PM to repartition PM-

bound contaminants back to captured runoff stored in such units between runoff events.

86

Table 3-1 Summary comparison of pilot-scale measurements, CFD modeled results, and overflow rate (Q/A) model results utilizing either the event representative influent PSD (an NJCAT gradation), or utilizing the d50m(78.1 μm) (median particle size of influent gradation based on mass) of overall % mass separated or effluent PM concentration [mg/L] by the screened HS (2.4 mm apertures) as a function of influent flow rate. The influent concentration and dry PM mass were 200 mg/L and 3145 g respectively for each pilot-scale run at each flow rate shown.

% (%) of influent PM mass separated by the screened HS

Effluent PM concentration [mg/L]

Overflow Model (Q/A)

Overflow Model (Q/A)

Influent Flow Q (L/s) Measured CFD

Model PSD d50m Measured CFD

Model PSD d50m 1.59 65.8 71.3 100.0 100.0 64.5 63.2 0.0 0.0 3.97 64.1 65.5 81.8 100.0 68.0 75.9 40.0 0.0 7.94 62.2 58.8 73.7 100.0 92.4 90.6 57.7 0.0 11.92 47.9 50.0 63.7 100.0 90.1 109.9 79.7 0.0 15.89 41.3 46.4 56.5 100.0 125.3 117.8 95.7 0.0 19.87 36.5 42.2 52.5 79.5 117.6 127.0 104.4 45.2

87

Figure 3-1 Full scale experimental setup for testing a screened HS (drawing not to scale) and computational grid of the HS (Inset).

5.486 m

OD = 0.304

Sump

Inlet reservoir

(V =37854 L)

0.71 m

Influent reservoir

(V = 37854 L)

Flow control valve

Effluent sampling

6.0 m

15cm Parshall flume (75 KHz ultrasonic)

0.76 m

Pump (Capacity 69.39 L/s)

3.8 m

Drop Box

OD = 0.304 m

5.5 m

IDs = 0.65 m

Lx = 0.87 m

OD = 0.304 m

OD = 0.152 m

Ly=0.76 m

0 1 2 012

IDv= 1.524 m

Recirculation valve

-1

0

Volute -2

88

Particle diameter (μm) 1101001000

Perc

ent f

iner

by

parti

cle

dry

mas

s (%

)

0

20

40

60

80

100

0.16 L/s0.79 L/s1.59 L/s3.97 L/s7.94 L /s11.92 L/s15.89 L/s19.87 L/s23.34 L/s31.17 L/s38.93 L/s

Flow rate, Q (L/s)0 10 20 30 40

Efflu

ent d

50(μ

m)

0

20

40

60

80Influent d50(78.1 μm)

Flow,

Q+

50

Figure 3-2 Observed phase shift in particle size distribution from influent to effluent via the

screened HS. The influent gradation is that of the NJCAT protocol.

89

Figure 3-3 Demonstration of grid independence. Results depict measured vs. modeled Δ particle

mass separated by the HS expressed as % finer by mass at an influent flow rate (Q) of 15.89 L/s, as a function of progressively finer meshes.

RPD1= 25.77

Particle diameter (μm)

101001000

% F

iner

by

mas

s

0

20

40

60

80

100

MeasuredModeled1 - 4e+05 cellsModeled2 - 1.96e+06 cellsModeled3 - 2.78e+06 cells

RPD2= 2.25RPD3= 5.29

Q = 15.89 L/s

Absolute RPD

90

Figure 3-4 Measured vs. modeled Δ Mparticles separated by the HS expressed as % finer by mass

as a functoin of Q, [L3T-1] for a volute area diameter of 1.524 m, at an influent concentration of 200 mg/L. The mass-based error associated with each measured PSD is in the range of 1 to 2% of the entire gradation mass and is distributed across the gradation; although the distribution of error was not measured. Therefore the individual error bars are not shown.

% F

iner

by

mas

s

0

20

40

60

80

100MeasuredModeled

% F

iner

by

mas

s

0

20

40

60

80

100

Particle Diameter (μm)101001000

% F

iner

by

mas

s

0

20

40

60

80

100

Q = 15.89 L/s

Q = 19.87 L/s

Q = 23.34 L/s

Absolute RPD = 2.25

AbsoluteRPD = 6.64

AbsoluteRPD = 9.48

% F

iner

by

mas

s

0

20

40

60

80

100

MeasuredModeled

% F

iner

by

mas

s

0

20

40

60

80

100

Particle Diameter (μm)101001000

% F

iner

by

mas

s

0

20

40

60

80

100

Q = 3.97 L/s

Q = 7.94 L/s

Q = 11.92 L/s

Absolute RPD = 8.43

Absolute RPD = 9.52

Absolute RPD = 1.06

% F

iner

by

mas

s

0

20

40

60

80

100

MeasuredModeled

% F

iner

by

mas

s

0

20

40

60

80

100

Particle Diameter (μm)101001000

% F

iner

by

mas

s

0

20

40

60

80

100

Q = 0.16 L/s

Q = 0.79 L/s

Q = 1.59 L/s

Absolute RPD = 1.41

Absolute RPD = 3.81

Absolute RPD = 0.48

91

Q (L/s)0 4 8 12 16 20 24

Cef

fluen

t [m

g/L]

0

25

50

75

100

125

0

25

50

75

100

125

[C] MeasuredModeledΔM Measured

Absolute RPD = 7.67

Δ Mparticles (%

)

Absolute RPD = 8.40

Figure 3-5 Comparison of measured versus modeled results as a function of Q, [L3T-1] for non-

cohesive sandy silt influent particle gradation.

92

Figure 3-6 Particle trajectories calculated by a Lagrangian DPM for the screened HS, for an

influent flow rate (Q) of 3.97 L/s. Plot (a) , (b) and (c) depict particle trajectories for particles with a diameter (dp) of 450 µm, 75 µm and 25 µm respectively. Particle density(ρp) is 2.65 g/cm3.

C

Screen

Volute

Sump

A

Screen

Sump

B

Screen

Volute

Sump

93

Figure 3-7 Modeled velocity distributions within the screened HS for an influent Q of 3.97 L/s.

Plots (a) and (b) are particle velocities relative to fluid velocities integrated across the computational domain for a particle injected at the geometric centroid of the inlet, for a particle with dp of 450 µm and for a particle with dp of 25 µm respectively. Plots (c) and (d) are frequencies of particle velocities in the screen area for particle diameters (dp) of 450 µm and 25 µm respectively. Plots (e) and (f) are frequencies of particle velocities in the volute area for dp of 450 µm and 25 µm respectively.

Screen

Normalized path length

0.0 0.2 0.4 0.6 0.8 1.0

Parti

cle

velo

city

(m/s

)

0.00

0.03

0.06

0.09

0.12Fluid450 μm

Normalized path length

0.0 0.2 0.4 0.6 0.8 1.0

Parti

cle

velo

city

(m/s

)

0.00

0.03

0.06

0.09

0.12Fluid25 μm

Screen

Vs,Newton

Vs,Newton

Nor

mal

ized

freq

uenc

y

0.0

0.1

0.2

0.3

0.4

0.5450 μm screen area

Particle Velocity (m/s)

0.00 0.03 0.06 0.09 0.12

Nor

mal

ized

freq

uenc

y

0.0

0.1

0.2

0.3

0.4

0.5450 μmvolute area

Nor

mal

ized

freq

uenc

y

0.00

0.04

0.08

0.12

0.16

Particle velocity (m/s)

0.00 0.03 0.06 0.09 0.12

Nor

mal

ized

Fre

quen

cy

0.00

0.04

0.08

0.12

0.16

25 μmscreen area

25 μmvolute area

Vs,N

ewto

nV

s,New

ton

Vs,N

ewto

nV

s,New

ton

(a) (b)

(c) (d)

(e) (f)

1

2

3

4

5

6

7

89

10

11

94

CHAPTER 4 COMBINING PARTICLE ANALYSES AND CFD MODELING TO PREDICT HETERO-

DISPERSE PARTICULATE MATTER FATE AND PRESSURE DROP IN A PASSIVE RAINFALL-RUNOFF RADIAL FILTER

Introduction

Anthropogenic particulate matter (PM) transported in urban rainfall-runoff has been

identified as a significant contributor to overall deterioration of surface water in the USA

(USEPA 2000). Rainfall-runoff transports an entrained mixture of colloidal PM, non-colloidal

PM, dissolved and complexed pollutants (Sansalone et al. 2007, Lee and Bang 2000, Sansalone

et al.. 1998, Igloria et al.. 1997, Sansalone and Buchberger 1997). PM transported by runoff act

as reactive surfaces for adsorbing, desorbing and leaching organics and metals as well as

phosphorus and other nutrients (Sansalone 2002). Separation of PM by unit operations and

processes (UOPs) for in-situ treatment of rainfall-runoff is challenged by factors such as the

stochastic nature of hydrologic and pollutant loads and concerns such as availability of land and

infrastructural resources (Liu et al.. 2001). Empirical or ‘black-box’ approaches are based on

gross assumptions and thus their application to treatment unit prototyping may mask the actual

mechanistic behavior of a UOP.

Various filtration configurations including infiltration and exfiltration through fixed

granular medium (including soil) systems have been suggested as viable solutions for meeting

runoff quantity and quality regulations for watersheds (Colandini 1999, Sansalone 1999, Li et al..

1999, Colandini et al.. 1995, Geldof et al.. 1994, Schueler 1987). Recently, Hipp et al. (2006)

suggested that removable filter inserts, which are mechanistically different from typical fixed

bed granular medium filters, may be viable preliminary unit operations due to easier

maintenance. While granular filtration has demonstrated advantages for improving water quality,

there is a requirement for careful design, analysis and prototype testing, as well as regular

95

maintenance to ensure optimal hydraulics for quantity control (Keblin et al.. 1997). Performance

(mass and size of PM separated) of a granular medium filter depends on the following broad

parameters (Tien 1989).

),,,,,/( τη mmpparticles KddAQfM =Δ (4-1)

In this expression, particlesMΔ is the mass of particles separated, AQ / is the influent surface

loading rate, A is the total surface area of the media , Q is the influent volumetric flow rate, η is

the effective porosity, pd is the mass-based particle diameter, md is the diameter of the granular

media, τ is the empty bed contact time (EBCT) (AWWA 1990) and mK includes physical,

chemical and surficial properties of the media, such as adsorption properties, media (internal)

porosity, and morphology. Oxide coated media has been found to be effective at reducing

turbidity, phosphorus and microbes in water and wastewater treatment (Ayoub et al. 2001, Chen

et al. 1998, Ahammed et al. 1996). Recently, the use of oxide coated media has been extended to

runoff treatment (Erickson et al. 2007, Sansalone et al. 2004). In this study, aluminum oxide

coated media with a pumice substrate (AOCM)p was utilized for physical filtration.

Granular filtration mechanisms have been classified into surficial straining, sedimentation,

interception, inertial impaction, diffusion, hydrodynamic and electrostatic interaction (Wakeman

et al.. 2005). Filtration dynamics are widely assumed to be dependent on the surface loading rate

(SLR) and with increasing SLR, macroscopic mechanisms tend to predominate the separation

process, due to reduced contact times. The radial flow rapid-rate filter used in this study was

operated at surface loading rates (SLR) ranging from 24 to 189 L/m2-min, which is higher than

SLR’s of typical rapid sand filters (83 L/m2-min) (Reynolds et al. 1995).

Computational fluid dynamics (CFD) has found applications in environmental engineering

in recent years, specifically in water and wastewater treatment (Do-Quang et al. 1998). CFD is a

96

method to solve the Navier-Stokes equations for coupled fluid and particle dynamics by a series

of discretization techniques and algorithms (Anderson 1995). Tung et al. (2004) studied deep bed

filtration for a sub-micron/nano-particle suspension utilizing a microscopic approach wherein

different types of media packing were modeled. However, macroscopic approaches to modeling

filter media are needed to model practical systems where packing schemes are most commonly

random and unstructured. Li et al. (1999) applied a 2-D numerical model to simulate variably

saturated flow in a partial exfiltration system. Sansalone et al.. (2005) applied a 2-D numerical

model to simulate the transient hydrodynamics of a partial exfiltration system for rainfall-runoff

clarification. However, a macroscopic CFD based approach to simulate the 3-D hydrodynamic

and clarification response of a granular medium filter is much needed in order to understand

passive radial filtration, which may not be fully described by a simplified 2-D approach, due to

lack of ideal symmetric flow conditions.

Objectives

CFD approaches to modeling granular filtration of rainfall-runoff are relatively new. Due

to the water quality and hydraulic requirements encountered in building rainfall-runoff PM

control systems in urban areas, there is the opportunity to utilize recent advances to examine the

behavior of rainfall-runoff filters. This study hypothesized that computational tools such as

CFD, and measurement tools such as laser diffraction for PM analysis can provide examination

and allow accurate prediction for separation of PM as a function of particle size and head loss

behavior of filtration systems. Moreover, passive rapid rate filters have not been well understood

mechanistically. The goal of this study was to demonstrate that a calibrated and validated CFD

model can simulate the prototype performance of a passive radial cartridge filter (RCF) that

utilizes (AOCM)p for treating a representative rainfall-runoff particle size distribution (PSD) and

concentration. The efficiency of the RCF is hypothesized to decrease as a function of flow rate,

97

under maintainable head loss conditions for such a system deployed in the field. The first

objective is to apply CFD to predict particle separation behavior and head loss response of the

RCF through application of an appropriate flow and particulate phase model, within reasonable

computational limits, to a scientifically acceptable degree of accuracy. The second objective is to

compare the results of the numerical model to paired experimental results. A process of

verification and validation was undertaken, in order to confirm the validity of the numerical

model, as the third objective. The fourth objective was to examine the head-loss behavior and

pressure distributions in the RCF based on the validated particle separation model.

Methodology

Experimental Setup

Figure 4-1 illustrates the schematic plan view of the instrumented RCF as part of the

experimental setup. A storage tank with a capacity of approximately 40,000 L was utilized as a

reservoir for influent potable water. A centrifugal pump with a capacity of 414 L/min was used

to generate influent flow. The flow measurement system consisted of a calibrated 5 cm multi-jet

water velocity meter (DLJ Multi-jet). The flow control valve system facilitated flow rates

ranging from 11.34 L/min to 90.7 L/min, which represent 11% and 114% of the design flow rate

(Qd) respectively. The RCF was contained in a cylindrical test tank which served as a container

to stabilize the inflow and ensure saturated filtration. The total volume of the RCF was 72.9 L

and the additional volume of the test tank around the RCF was approximately 57 L to the top of

the RCF. The diameter and height of the RCF are 0.4572 m and 0.5588 m, respectively. The

media was contained between an outer mesh and non-reactive impervious polypropylene discs

on top and bottom of the cartridge. Tank dimensioning was based on the representative

elemental volume of an RCF under field deployment conditions in single or multiple

applications. The scaled geometry of the RCF is shown in Figure 4-2.

98

Media Characteristics

Engineered (AOCM)p was utilized as the granular media. The distribution of media

diameter (dp) was obtained by digital image analysis and utilization of Image Pro Plus v 6.2

Image Analysis Software. Image analysis results were utilized to calculate an equivalent circular

diameter (ECD) as follows (Holdich 2002). The ECD is defined as the diameter of a sphere

having the same projection area as the object. The resolution of the imaging method was 10.1

mega-pixels.

π/4AECD = (4-2)

In this expression, A is the projected area of the media. Figure 4-3 illustrates a frequency

histogram for the media tested. A three-parameter Gaussian distribution was fit to the data (R2 =

0.93). The additional parameter accounts for the area under the curve, which is not equal to 1.

The mean media size is 3.56 mm ± 0.8 mm for a sample size (n) of 2551. The specific gravity of

the pumice based media with was 2.35 (Farizoglu 2003). The media was pluviated into the

cartridge so that the cartridge contained 49830.4 g of dry media at full capacity for each

experimental run. Triplicate measurements of total clean bed porosity (η) of the RCF with media

produced a mean of 0.71 and standard deviation of 0.041 by volume. Of this total porosity the

internal porosity of the media was measured in triplicate by mercury porosimetry (ASTM 2003)

with a mean of 0.37 and a standard deviation of 0.022. The total porosity includes all available

pore areas in the media and media bed, but not necessarily the effective porosity available for a

given flow rate.

Prototype Test Procedure

Each filtration experiment was started with a clean filter bed. As a secondary unit

operation filters are operated under steady flows and steady flows were achieved through the use

99

of the influent pump and the recirculation system to establish differing levels of influent flow.

Flow control valves were calibrated to reach flow rates ranging from 0.16 to 23.36 L/s. Flow

measurements were validated throughout each run and a cumulative volumetric balance was

performed after each run. The PM suspension was prepared with Sil-co-Sil 106, a non-cohesive

silt manufactured by US Silica and used as a common filtration test material. The influent

particle gradation had a specific gravity of 2.65 as determined by helium pycnometry. Figure 4-

3 depicts the particle size distribution (PSD) by mass of the influent; typical of a gradation that is

largely settleable and suspended in rainfall-runoff (Sansalone and Kim 2007). The mass-based

d50 of the influent particle gradation was 16.3 μm. Over 85 % of the PSD by mass consists of

settleable particles, as determined by laser diffraction.

A slurry delivery system was designed to inject the influent particle size distribution on a

temporally consistent mass and granulometric basis. The slurry delivery system consisted of a

polypropylene slurry tank with a capacity of 20 L, an electronic mixer system in order to

maintain the homogeneity of the influent suspension, and a variable flow-rate peristaltic pump.

The appropriate dry mass of particles to be added to the slurry tank and the rate of injection

into the RCF was calculated depending on the influent flow rate being tested in order to deliver a

constant nominal influent concentration of 200 mg/L (Sansalone et al. 1998, Sansalone 2002).

Upon achieving the desired influent flow rate, particles were injected at the inlet of the RCF. 10

discrete duplicated 2 L influent and effluent samples were collected at regular sampling intervals

designed for each individual experiment based on flow rate and run times.

Laboratory Analyses

For each run 10 discrete samples were subsequently combined to form duplicate (A and B)

20 L composites for water quality and suspended sediment concentration (SSC) analyses. SSC

analysis was conducted in accordance with Standard Method 2540 D (ASTM 1997). PSDs of the

100

influent and effluent were measured using a laser diffraction analysis based on Mie scattering

theory (Finlayson-Pitts et al. 2000). The particle size range was from 1.0 μm to 250 μm, and was

applicable to sediment concentration range of 1 to 1000 mg/L with a resolution < 1 mg/L. The

particle separation efficiency of the filter is defined in terms of the average event mean

concentration (EMC) for PM over the time period of the influent flow (Huber 1993).

∫

∫== t

t

tq

dttqtc

VMEMC

0

0

)(

)()( (4-3)

In this expression, M is the total effluent mass load over the entire duration of the test, V is

the total volume of flow over the entire duration of the test, C is the flow weighted mean

concentration, c (t) is the time variable particulate-bound concentration, q (t) is the time variable

flow rate and t is time. The overall efficiency ratio was calculated as follows.

EMCinlet averageEMCoutlet average - EMCinlet average

=ER (4-4)

Urbonas (1995) suggested the following equation for calculating the % removal by using

inflow and outflow loads.

100)(

)()(

1

11 ו

•−•=

−=

−

−=

−−=

−

∑

∑∑

INi

n

iINi

EFFj

m

jEFFjINi

n

iINi

CV

CVCVPR (4-5)

In this expression, Vi-IN and Vj-EFF are the volume of influent flow and effluent flow during

the sampling periods i and j respectively; Ci-IN and Cj-EFF are average concentrations associated

with periods i and j respectively; and n and m are the total number of influent and effluent

measurements taken during event, respectively. The effluent concentration (Ceff) and effluent

101

particle mass load have been used to represent the separation efficiency of the RCF. For the

purpose of QA/QC, a mass balance error constraint of 10% was imposed.

Mass Balance Error = %10100)(±≤×⎥

⎦

⎤⎢⎣

⎡ +−

i

eRCFi

MMMM (4-6)

In this expression, iM is the influent mass of particles, RCFM is the mass of particles

captured by the RCF and eM is the effluent mass of particles, computed from the measured

effluent SSC across the total treated 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.

Pressure Head Measurements

The variations in the height of the water column in the central discharge pipe (hi) of the

RCF and the outer manometer (ho) was measured by the use of 1 psi pressure sensors

manufactured by Druck Inc. Real-time data was acquired via a CR1000 datalogger,

manufactured by Campbell Scientific Inc. Thus, head loss (ΔH) in the radial direction was

calculated as follows.

io hhH −=Δ (4-7)

In this expression, h0 is the water column height in the outer manometer and hi is the water

column height in the central discharge pipe, normalized to the same reference location.

Computational Fluid Dynamics Model

While the geometry of the RCF suggested a simplified two dimensional CFD model, the

hydrodynamics and particle dynamics vary as a function of x, y and z spatial coordinates. As a

result, a three dimensional (3-D) approach was required. The generalized 3-D scalar conservation

equation for a control volume (CV) with volume )( zyxV ∂∂∂= is utilized. (Ferziger et al.., 2002)

102

Φ+ΦΓ=Φ+∂

Φ∂ Sgraddivudivt

)()()( ρρ (4-8)

The RCF was thus modeled by adding a momentum sink term to the flow equations. This

sink contributes to the pressure gradient in the porous computational cell, creating a pressure

drop that is proportional to the fluid velocity in a computational cell. The source term is

composed of two parts: a viscous loss term and an inertial loss term.

⎟⎟⎠

⎞⎜⎜⎝

⎛+−= ∑ ∑

= =

3

1

3

1 21

j jjijjiji vvCvDS ρμ (4-9)

In this expression, iS is the source term for the i th momentum equation, α is

permeability, iC2 is the inertial resistance factor, iv is the velocity in the i th momentum equation,

v is the velocity in a computational cell. For isotropic porous media the above equation can be

expressed in the following form.

⎟⎠⎞

⎜⎝⎛ +−= 2

2 21 vCvSi ρ

αμ (4-10)

In this expression, α is the permeability [L2] and C2 is the inertial resistance coefficient.

Modeling Flow in Porous Media

The dominant flow regime is laminar to transitional in the RCF. The Reynolds number for

flow in the media was calculated as follows.

μηρ)1(

Re−

= smmedia

vd (4-11)

In this expression, md is media particle diameter, μ is the fluid viscosity, η is the porosity

of the packed bed (not media porosity), sv is the superficial velocity through the packed bed

and ρ is fluid density. The Reynolds numbers were found to range from approximately 5 to 30.

103

Porous media may be modeled with a macroscopic or a microscopic approach (Ranade

2002). In the latter approach, the micro-scale pore structure is taken into account. A microscopic

approach demands tedious computational resources and is typically used as a benchmark

problem, as opposed to modeling practical systems. On the contrary, the macroscopic or lumped

approach considers the entire filter bed as isotropic or non-isotropic porous media. This approach

is characterized by pertinent lumped parameters such as the effective porosity (η), inertial and

viscous resistance coefficients. The geometry of the media can be accounted for by utilizing bed

porosity distributions, such as Mueller’s distribution (Mueller 1992), or by assuming

homogeneous distribution of pores between media. With uniform pluviation in the RCF and

uniform size gradation for the media a uniform pore distribution was assumed in this model.

Previous studies have shown that the standard k-ε model (Launder and Spalding 1974) for

turbulent flow has worked well in both micro and macroscopic approaches to solving flow in

porous media (Antohe et al. 1997). The transport equations of the standard k-ε model are

expressed as follows.

kbkjk

t

ji

iSGG

xk

xku

xk

t+−++

⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

⎟⎟⎠

⎞⎜⎜⎝

⎛+

∂∂

=∂∂

+∂∂ ρε

σμμρρ )()( (4-12)

For ε:

εεεεε

ερεεσμμρερε S

kCGCG

kC

xxu

xt bkj

t

ji

i+−++

⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

⎟⎟⎠

⎞⎜⎜⎝

⎛+

∂∂

=∂∂

+∂∂ 2

231 )()()( (4-13)

In these expressions kG represents generation of k due to the mean velocity gradients;

bG is generation of k due to buoyancy; ε1C , ε2C and ε3C are constants ; kσ and εσ are the

turbulent Prandtl numbers for k andε , respectively; kS and εS are user-defined source terms.

The constants were determined by Launder and Spaulding (1974). The values

104

of ε1C , ε2C , ε3C , kσ and εσ used in the model were 1.44, 1.92, 0.09, 1.0 and 1.3 respectively

(Launder et al.. 1974). The free surface of the flow was modeled as a shear-free boundary.

Flow in porous media has been traditionally modeled analytically by comparison to

pipe/conduit flow by specifying analogous parameters such as the hydraulic diameter and

roughness coefficient. Laminar flow (Re < 10) through porous media has been successfully

modeled by applying Darcian-type equations. Models such as Blake-Plummer and Carman-

Kozeny equations were developed to account to transitional flow regimes. These models were

extended by Ergun (1952) to account for turbulent flow. The Ergun equation for packed beds

applies to flow regimes from laminar to turbulent and is expressed by the following equation.

233

2

2

)1(75.1)1(150s

ms

m

vd

vdL

pη

ηρη

ημ −+

−=

Δ (4-14)

In this expression, pΔ is the pressure drop across the media, L is the length of the packed

bed, μ is the fluid viscosity, md is media particle diameter, η is the total porosity of the packed

bed, v is the superficial velocity through the packed bed and ρ is fluid density. Comparing

equations 9 and 14, α and C2 can be expressed as follows.

2

32

)1(150 ηηα−

= md (4-15)

32)1(5.3

ηη−

=md

C (4-16)

Modeling the Particulate Phase

Brennen (2005) suggests a Eulerian-Lagrangian approach (van Wachem et al.. 2003) to

model multiphase flows with a particulate volume fraction (PVF) less than 10% which is the

case in this study (PVF << 0.1 %). In this approach, the flow field is first solved using a

continuum approach and subsequently particles are tracked using a Discrete Phase Model

105

(DPM). The DPM is derived from force balances based on Newton’s (Turbulent and transitional

regimes) and Stokes’ (laminar regimes) laws for particle motion, and summarized by the

following equation.

xp

pxpD

p Fg

uuFdt

du+

−+−=

ρρρ )(

)( (4-17)

DF 24Re18

2pD

pp

Cdρμ

= (4-18)

232

1 ReRe ppD

aaaC ++= (4-19)

In the above expressions , u is the fluid velocity, pu is the particle velocity, ρ is the fluid

density, pρ is the particle density, pd is particle diameter, μ is the viscosity, 321 ,, aaa are

empirical constants that apply to smooth spherical particles as a function of the Reynolds number

(Morsi et al.., 1972) and pRe is the particle Reynolds number. Sub-spherical silica particles of a

specific gravity of 2.65 were injected at regular intervals across the entire cross section of the

inlet to the RCF. Neutrally buoyant tracer particles were utilized to calculate an unbiased particle

tracking length. Particles that remained in the RCF system after integrating over the specified

length were considered to have been separated. Particle removal was defined by the following

equation.

100×=ΔI

RCF

NN

P (4-20)

In this expression, RCFN is the number of particles that remain in the RCF, and IN is the

number of particles injected at the inlet.

106

Discretization and Solution Schemes

The computational domain was discretized using an unstructured mesh with tetrahedral

elements, generated by TGrid (Qi et al.. 2006). Numerical solutions were obtained using a Finite

Volume Method (FVM) and a cell-centered scheme used for discretization. A Second-Order

Upwind Scheme (Barth et al.. 1989) was used solve for flow parameters. The SIMPLE (Semi-

Implicit Method for Pressure Linked Equations) algorithm (Patankar 1980) accounted for

pressure-velocity coupling. The criterion for iterative convergence was set at 1x10-3 (Ranade

2002).

Results and Discussions

Experimental Results

Figure 4 illustrates the phase shift in mass-based PSD from influent (left) to effluent (right)

as transformed by the RCF as a function of flow rate. The d50 of the effluent PSD is visibly finer

than that of the influent, and the phase shift increases with decreasing flow rate. This leads to the

hypothesis that at lower flow rates and lower head required to facilitate complete radial filtration,

gravitational settling is an important mechanism of particle separation in the RCF system

whether deployed as a single cartridge or in an volumetric filter system. Effluent concentrations

ranged from 30 to 58 mg/L for flow rates ranging from 11.3 L/min to 90.1 L/min respectively,

for a steady influent concentration of 200 mg/L, as shown in plots A and B of Figure 4-5. The

SSC removal results are presented in Table 4-1. Figure 4-6 illustrates the overall clean bed head

loss for the RCF as a function of flow rates. The head loss ranged from 1.2 cm to 3.9 cm for flow

rates of 22.7 L/min (SLR = 48 L/m2-min) to 90.8 L/min (SLR = 189 L/m2-min). The maximum

standard deviation was 1.9 cm for a flow rate of 79.5 L/min. These head loss values are

relatively low due to the media d50, the reasonable media uniformity and the clean bed total

porosity of 0.71.

107

CFD Model Results

Grid independence was achieved for the solutions at a mesh size of 3.01 million cells.

Therefore model results were run with a mesh size of 3.01 million cells. Modeled results were

compared with experimental data by means of an absolute relative % difference (RPD). Absolute

RPD was calculated from the following equation.

100*data Measured

data) Modeled-data (Measured (%) RPD Absolute = (4-21)

Particle Separation

In order to interpret the overall PM separation (as SSC) by the RCF, two approaches were

followed, the first is a comparison on the basis of effluent concentrations, and the second is a

comparison on the basis of effluent mass load. Figure 4-5 is a comparison of measured and

modeled clarification response of the RCF. Plot A is a comparison of measured and modeled

effluent concentrations. The range bars on the measured data represent the standard deviation

between replicate samples. Plot B compares modeled and measured effluent gravimetric dry

mass loads. Range bars are used to include the overall mass balance error (MBE) from the

experiment. In summary, there is good agreement between measured and modeled data. The

absolute RPD is well under 5% in both cases. All experimental runs yielded a mass balance

error that was less than 10% with the recovery of all particles filtered, settled or eluted.

Modeled and measured effluent PSDs are compared in Figure 4-7 for flow rates ranging

from 11.4 L/min to 90.4 L/min. Model results are in good agreement with measurements as a

function of dp ( Maximum RPD < 4 %). The three lower flow rates on the left in Figure 4-7

correspond to a range of Reynolds numbers that indicate a predominantly laminar flow regime,

while the three higher flow rates on the right in Figure 4-7 correspond to a transitional flow

regime. One important aspect of the model is that it accounts for the variation of porosity as a

108

function of flow rate by implicitly accounting for the available flow path across a given section

of the porous media. This is due to the solution of the complete N-S equations across the entire

computational domain, as opposed to black-box type calculations. The modeled and

experimental results agree demonstrating that finer particles are not separated by the RCF, with

increasing flow rate.

Head loss and Pressure Distributions

Figure 4-6 compares measured and modeled head loss in the radial direction of the filter

(ΔH). Results indicate agreement between measured and modeled head loss (absolute RPD =

9.1%) illustrating that the model is capable of predicting head loss despite representing the media

with a spherical geometry. This can be attributed to the predominantly laminar to mildly

transitional nature of the flow, where the viscous resistance component is negligible (Darby

2002).

With the aid of the calibrated and validated CFD model, pressure distributions

represented as head loss along the radial and vertical directions were computed and are

illustrated in Plots (A) and (B) respectively of Figure 4-8. The head loss varies inversely with

distance from the center of the RCF as illustrated in Plot (A). This variation displays a linear

trend with the slope increasing as a function of flow rate. The overall head loss across the entire

radial distance is equal in magnitude to the overall modeled head loss.

Plot (B) illustrates pressure distributions along a line parallel to the z-axis and located at

the geometric mid-point of the RCF in the radial direction, at one-half the annular thickness of

the media section of the cartridge (r/2). Results indicate that for low flow rates the pressure

distribution is fairly uniform. However, beyond a flow rate of 45.4 L/min, there is a parabolic

profile for pressure distributions as a function of depth, with the minimum pressure at the top and

bottom ends (no-flow boundaries) of the RCF. A check was performed for conservation of

109

energy across the entire RCF using Bernoulli’s theorem, with local velocities obtained from the

CFD model. This check supported the validity of the modeled distributions. The pressure

distributions may be explained as follows. The center effluent outlet of the RCF never flowed

full and remained open to the atmosphere. Therefore, the RCF configuration is analogous to an

inverted well, with flow pumped out in the direction of gravitational force. At the top surface, the

parabolic profile of the drawdown is due the head-loss created by the porous media. At the

bottom of the RCF, there is also a pressure differential from inside to outside of the cartridge.

This is in line with typical drawdown in pumped wells as expressed by the Theis equation

(Freeze et al.. 1979). The maximum differential occurred at 90.9 L/min and is 0.3 kPa.

CFD was used to examine not only the pressure distributions but also the hydrodynamic

and particulate loadings under which the RCF was tested and is operated given that

manufacturers of such systems claim a uniform pressure distribution and treatment from top to

bottom of the RCF. Figure 4-9 provides a 3-D picture of particle dynamics within the RCF

system for a flow rate of 45.4 L/min. Results indicate that the overall surface area of the filter is

not loaded uniformly, even in a single cartridge configuration. For instance, sediment-sized

particle (dp of 75 μm) results in Plot (D) demonstrate that more than 75% of the overall RCF

surface area is not being utilized. With decreasing particle size, a larger portion of the overall

available surface area of the filter is being utilized. Plot (B) shows the trajectories of a suspended

particle (dp=10 μm), the particle is strongly coupled with the hydrodynamics depicted in plot (A)

and a larger portion of the filter surface is available for filtration. However, as illustrated in Plot

(C), for a slight increase in particle diameter (dp = 25 μm), approximately 50% less surface area

is utilized. This provides insight into the actual mechanisms in the RCF system. Gravitational

effects are important even for this fine PSD and uniform filtration with depth does not occur. At

110

low flow rates, gravitational settling is the predominant mechanism of particle separation in the

system whether deployed as a single cartridge in a tank or in an volumetric filter system of

multiple filters. Results also indicate that depending on flow rate and particle size, a significant

fraction of the RCF surface area may not be utilized, and not utilized uniformly. Pressure or

head distributions along the axes of a granular filter are often difficult to measure and are often

approximated based on various assumptions. These assumptions range from Darcian flow

regimes to modeling flows with capillary tube analogs as in the Carman-Kozeny model. With the

aid of the calibrated and validated CFD model, pressure distributions represented as head loss

along the radial and vertical directions were computed and this served to better understand the

mechanistic behavior of the porous bed.

Conclusions

This study applied laser diffraction measurements of particle size distributions (PSDs)

and the principles of CFD using a Finite Volume Method (FVM) to model the particle separation

behavior of a passive radial cartridge filter (RCF) using aluminum oxide coated media

(AOCM)p,. The CFD approach employed a standard k-ε turbulence model to resolve turbulent

flow and a Lagrangian discrete phase model (DPM) to track particles. The uniform sub-

spherical porous media with a d50 of 3.56 mm, a total bed porosity of 0.71 and a media (internal)

porosity of 0.37 was modeled by adding a sink term to the momentum equations. The loading to

the RCF was a fine silt gradation with a d50 of 16.3 µm and a concentration of 200 mg/L and

flow rates ranging from 11.4 L/min (SLR= 24 L/m2-min) to 90.8 L/min (SLR = 189 L/m2-min).

The model was validated with data across a range of flow rates, PSDs, and head-loss

distributions. Predictions from the CFD model were within 10% of measurements and the CFD

solution was grid independent.

111

This study demonstrated that a CFD model could reproduce the fate of a hetero-disperse

PSD as a function of particle size for mass, concentration and head loss behavior of a RCF for

typical runoff loading rates, PSDs, and suspended sediment concentration (SSC) levels.

A steady state solution was obtained for flow through the RCF and clean bed conditions

were implemented in the experiment and in the model. CFD predictions provided an in-depth

insight into the mechanistic behavior of the RCF by means of three dimensional hydraulic

profiles, particle trajectories and radial and axial pressure distributions.

Results demonstrate that while the overall RCF particle removal for the silt sized hetero-

disperse influent gradation (SSC = 200 mg/L) ranged from 88% (effluent SSC = 66.7 mg/L) to

72% (effluent SSC = 50.2 mg/L) for flow rates ranging from 11.4 L/min to 90.9 L/min.

The maximum head loss did not exceed 5 cm even at the highest flow rate for the porous

(AOCM)p with a mean diameter of 3.56 mm. The low head loss allows a smaller media diameter

to be utilized that would further reduce effluent concentrations at the expense of a higher head

loss. Pressure distributions obtained from the CFD indicate that effects of gravity on particle

trajectory and separation are significant across the entire range of flow rates, specifically for the

settleable fraction of PM. Results demonstrate that the pressure distributions and loadings were

not uniform with depth in the RCF system.

The ability of the CFD model to reproduce treatment results across a range of flow rates

and PSDs suggest that the calibrated/validated model can serve as a foundation upon which

design alternatives can be proposed. A calibrated/validated CFD-based iterative approach to

design of this RCF as a unit operation has the potential to provide reduced prototyping costs with

improved performance, as a result of carefully designed experimental matrices, focused on PM

control requirements for effluent discharges.

112

This study combined PSD measurements using laser diffraction, media porosimetry, image

analysis and material balances as well as more conventional gravimetric SSC measurements of

PM and pressure sensor measurement. Such data are needed in the calibration and validation

process for a defensible porous media CFD model of a RCF.

113

Table 4-1 Summary of SSC results for RCF tested with a Sil-co-Sil 106 gradation at a nominal concentration of 200 mg/L. EBCT is the mean fluid empty bed contact time.

Q Surface Loading

Rate

Influent SSC

Effluent SSC

SSC Removal

FluidEBCT

(L/min) L/m2-min [mg/L] [mg/L] (%) min 11.4 24 202.8 50.2 86 4.42 22.8 48 203.7 54.4 85 2.21 34.2 72 195.5 52.5 80.7 1.47 45.6 95.4 193.4 64.7 78.4 1.11 68.4 142.8 202.4 69.3 76.7 0.74 79.2 165.6 202.4 68.8 75.1 0.64 90.6 189.6 209.3 66.7 71.4 0.56

114

Figure 4-1 Process flow diagram/experimental setup for steady flow operation of the radial filter

cartridge (not to scale).

PM slurry tank [C = 200 mg/L]

Mixer

Centrifugal pump (Capacity: 6.9 L/s)

5 cm velocity water meter (DLJ multi-jet)

Influent reservoir

(V=40,000 L) Variable flow

peristaltic pump Constant head tank

Filter Cartridge (V = 72.9 L)

Effluent

Influent

115

Figure 4-2 Profile view of the radial cartridge filter (RCF) apparatus.

Z

X

X (m)

Inlet

Filter cartridge

0

0.15

0.30

0.45

0.60

0.75

0.90

1.05

1.20

0 0.4 0.2 -0.2 -0.4

Z (m)

Outlet

ΔH

116

Figure 4-3 Measured media size expressed as a Gaussian frequency histogram. The average

media size was found to be 3.56 ±0.8 mm. A three parameter Gaussian distribution was used to model the data; a = 5.283, b= 0.6392. x0=3.435.

dp (mm)

0 1 2 3 4 5 6 7

Nor

mal

ized

Fre

quen

cy

0

2

4

6

8

R2=0.93

2))(5.0( 0

* bxx

eay−

−=

117

Figure 4-4 Observed phase shift in particle size distribution from influent to effluent via the

radial cartridge filter (RCF).

Particle diameter (μm) 1101001000

Perc

ent f

iner

by

parti

cle

dry

mas

s (%

)

0

20

40

60

80

100

Influent11.4 L / min22.8 L / min34.2 L / min45.6 L / min68.4 L / min79.8 L / min91.2 L / min

Q+

50

Influent Effluent

RCF

118

Q (L/s)0 15 30 45 60 75 90

Cef

fluen

t [m

g/L]

0

25

50

75

100

0

25

50

75

100

[C] MeasuredModeledΔΜ Measured

Absolute RPD = 2.1

Δ Mparticles (%

)

Absolute RPD = 6.25

Figure 4-5 Comparison of measured versus modeled results as a function of influent flow rate

(Q) for the non-cohesive influent particle gradation for an influent concentration of 200 mg/L. Absolute RPD is the absolute relative % difference between experimental and numerical model data.

119

Figure 4-6 Comparison of measured versus modeled filter head loss (ΔH) as a function of

influent flow rate (Q) for the non-cohesive influent particle gradation at an influent concentration of 200 mg/L; Error bars represent the standard deviation between replicated measurements. Q is the influent flow rate, [L3T-1]; Absolute RPD is the absolute relative % difference between experimental and numerical model data.

Q (L/min)

0 20 40 60 80 1000

5

10

15

20

MeasuredModeled

ΔH (c

m)

Absolute RPD = 9.1

120

%

Fin

er b

y m

ass

0

20

40

60

80

100

% F

iner

by

mas

s

0

20

40

60

80

100

Particle Diameter (μm)

101001000

% F

iner

by

mas

s

0

20

40

60

80

100

Q = 11.4 L/min

Absolute RPD =0.08

Measured Mass = 141 gModeled Mass = 141.1 g

Q = 22.7 L/min

Absolute RPD = 1.17

Measured Mass = 116.5 gModeled Mass = 117.7 g

Q = 34.1 L/min

Absolute RPD = 1.95

Measured Mass = 149.6 gModeled Mass = 152.5 g

Figure 4-7 Measured vs. modeled Δ particle mass in the effluent of the RCF expressed as %

finer by mass at influent flow rates (Q), [L3T-1] of 11.4 L/s, 22.7 L/s, 34.1 L/s, 68.1.4 L/s, 79.5 L/s and 90.9 L/s at an influent concentration of 200 mg/L. Absolute RPD is the absolute relative % difference on a mass basis between experimental and numerical model data.

% F

iner

by

mas

s

0

20

40

60

80

100

% F

iner

by

mas

s

0

20

40

60

80

100

Particle Diameter (μm)

101001000

% F

iner

by

mas

s

0

20

40

60

80

100

Q = 68.1 L/min

Absolute RPD =2.6

Measured Mass = 179.4 gModeled Mass = 184.1 g

Q = 79.5 L/min

Absolute RPD = 3.65

Measured Mass = 194 gModeled Mass = 186.9 g

Q = 90.9 L/min

Absolute RPD = 3.84

Measured Mass = 221.8 gModeled Mass = 230.3 g

Measured Modeled

121

Figure 4-8 Head loss (ΔH) and pressure distributions in the RCF. Plot (A) illustrates predictions of head-loss across the RCF from the CFD model. Plot (B) illustrates predictions of pressure distributions along the vertical (Z) axis of the RCF. Q1, Q2, Q3, Q4, Q5, and Q6 represent flow rates of 22.7, 34.1, 45.4, 68.1, 79.6, and 90.9 L/min respectively. The order of flow rates in (B) is the same as in Plot (A); (r, φ) and (0, φ) represent the radius and center of the RCF respectively, in radial coordinates; (r/2, 0, zn) and (r/2, 0, zo) represent the top and the bottom of the mid-point of the RCF respectively, in Cartesian coordinates

Radial distance (cm)

0 5 10 15 20

Δ H

(cm

)

0

1

2

3

4

5

6(r, φ) (0, φ) (r/2, 0, zn)

Cartridge depth (cm

)

Q6

Q5

Q4

Q3

Q2

Q1

Q+

(A)

Q+

(B)

0 0.05

0

10

20

30

40

50 0.10 0.15 0.20 0.25 0.30

(r/2, 0, z0) Gage Pressure (kPa)

122

Figure 4-9 CFD predictions of trajectories of fluid and particles inside the RCF, shaded on the

basis of residence time, τ [T]; Plot (A) describes the pathlines of fluid particles of negligible mass; Plots (B) through (D) describe the pathlines of inert spherical particles of diameters (dp) 10 µm, 25 µm and 75 µm respectively. Particle density(ρp) is 2.65 g/cm3.Qd is 45.4 L/min.

(A) Fluid pathlines (B) dp = 10 µm

Influent

Effluent

Influent

Effluent

Influent

Effluent

Influent

Effluent

(C) dp = 25 µm (D) dp = 75 µm

Filter media

Filter media τ (s)

τ (s)

123

CHAPTER 5 MODELING HYDRAULICS AND PARTICLE DYNAMICS OF A STORMWATER

HYDRODYNAMIC SEPARATOR FOR TRANSIENT INFLUENT LOADS

Introduction

Anthropogenic particulate matter (PM) transported in urban rainfall-runoff has been

identified as a significant contributor to overall deterioration of surface water in the USA

(USEPA 2000). Rainfall-runoff transports an entrained mixture of colloidal PM, non-colloidal

PM, dissolved and complexed pollutants (Sansalone et al. 2007, Lee and Bang 2000, Sansalone

et al.. 1998, Igloria et al.. 1997, Sansalone and Buchberger 1997). The temporal particle size

distribution (PSD) and chemical composition of particulate matter (PM) delivered by runoff from

a rainfall-runoff event varies significantly between different geographical regions and even with

spatial variation in the same watershed. (Sansalone 2002).

A major issue that needs to be addressed while designing stormwater unit operations and

processes (UOPs) is the dearth of available land for construction, especially in highly polluted

urban areas. In light of this, many new devices have been introduced, which have the advantage

of a small-footprint and ease of new installation or retrofit to existing infrastructure.

Hydrodynamic separators (HS) are one such class of UOPs that broadly rely on centrifugal

forces in addition to gravitational force to separate particles (Brombach et al.. 1987, Brombach et

al.. 1993, Pisano et al.. 1994, USEPA 1999, Andoh et al.. 2003). An attractive feature of a HS is

the potential for longer particle trajectories per given unit surface area in comparison with

traditional unit operations and processes (UOPs) such as settling basins. . A screened HS is a

variant on the HS principle, and uses the combined separation mechanisms of vortex induced

inertial separation, screening and sedimentation and has been used in recent years as a device for

treating stormwater runoff (Rushton 2004, Rushton 2006), and oil/grease removal (Stenstrom

and Lau 1998).

124

This study examined a simple screened HS consisting of two cylindrical chambers as

illustrated in plots (a) and (b) of Figure 5-1. The flow inlet is tangential to the inner cylindrical

chamber. The chambers are separated by a static screen. The static screen consists of a regular

array of apertures. The inner cylindrical chamber, along with the screen and the sump chamber

are designated as the ‘screen area’. The screen apertures allow vortex flow to exit the inner

screen chamber and enter the outer volute chamber. The geometry of the screen results in a

weakly reversed flow direction in the outer annular area, termed the ‘volute area’. Particle

separation by this HS configuration is a function of various parameters, as expressed in the

following equation.

),,,,,,( strpsparticles dvvQdvfM τ=Δ (5-1)

In this expression, particlesMΔ is the mass of particles separated, sv is the discrete particle

settling velocity, pd is the mass-based particle diameter, Q is the influent volumetric flow rate,

rv is the radial velocity component in the screening area, tv is the tangential velocity component

in the screening area,τ is the hydraulic residence time, and sd is the diameter of the screen

apertures. The design flow rate (Qd) for the screened HS used in this study is 9.5 L/s.

Typical stormwater design approaches are extensions of wastewater tank design principles,

which assume ideal to predictable influent quantitative and qualitative loads. It is clear that the

rainfall-runoff process and the associated particulate and dissolved matter delivery is a highly

variable process and therefore unit operations for stormwater PM management have to be

designed to operate across rapidly changing flow and particle concentrations. Existing

stormwater models such as the stormwater management model (SWMM) (Rossman 2007) use

idealized influent hydrographs and pollutographs. While these have greatly improved the

efficacy of design considering the complex and inter-related design parameters, they are not

125

equipped to provide an in-depth hydrodynamic and particle clarification profile of the UOP for

transient loads.

Existing literature does not provide a detailed and fundamental insight into the functioning

of hydrodynamic separators. Previous studies have ranged from simplified overflow rate theory

(Weib 1997) to semi-empirical approaches based on broad assumptions of vortex flow behavior

(Paul et al.. 1991). This lack of information leads to difficulties in scaling and implementation of

these devices. Fenner et al.. (1997, 1998) report that similitude analysis does not yield a single

dimensionless group that can be used in scale-up of a HS.

Computational fluid dynamics utilizes numerical methods to solve the fundamental

equations of fluid dynamics, i.e. the Navier-Stokes equations (Versteeg et al.. 1995). The

applicability and efficacy of CFD techniques have closely followed corresponding leaps in

computational power. While traditionally being in the realm of Aerospace and Process

engineering, CFD is now used in design and optimization of UOPs in environmental

engineering.

CFD approaches to model particle-laden flows is an active research area (Curtis et al..

2004, van Wachem et al.. 2003), including hydrodynamic separators. Faram et al.. (2003)

utilized a Reynolds Stress Model (RSM) to resolve turbulent flow and a Lagrangian Discrete

Phase Model (DPM) to model behavior of the particulate phase. Okamoto et al.. (2002) studied

particle separation by a vortex separator using a k-ε model to resolve flow and an Algebraic Slip

Mixture (ASM) model for the particulate phase. Lim et al.. (2002) used CFD-predicted velocity

profiles to study behavior of flocs in a vortex separator, with a Renormalization Group (RNG) k-

ε turbulence model. Tyack et al.. (1999) compared measured velocity profiles in a vortex

separator to those predicted by a Renormalization Group (RNG) k-ε turbulence model.

126

It should be noted that albeit studies dealing with the application of CFD in understanding

the multiphase dynamics that occur in a hydrodynamic separator are few in number, this is

clearly not the case with wastewater unit operations such as settling tanks (Jayanti et al. 2004,

Naser et al. 2005, Deininger et al. 1998, Brouckaert et al. 1999, Brestscher et al. 1992, Zhou et

al. 1994, Szalai et al. 1994, Karl et al., 1999) and for CSO pollution abatement devices such as

storage chambers (Stovin et al., 1996, 1998, 2002).

An experimentally validated CFD approach was used previously to accurately describe the

performance of a screened HS, across a range of steady flow rates and geometric configurations

for an influent of known particle size distribution at a concentration typically observed in real-

time storm events. The next step lies in extending this model to real-time rainfall-runoff events

with coupled and transient flow rates, influent particle size distributions and influent PM

concentrations.

Objectives

The first objective of this study was to model the overall particulate matter separation

across a real-time rainfall-runoff event for a hydrodynamic separator by the application of an

appropriate turbulent flow model. The subsequent objective was to compare predicted results

with measured PM removal data. The applicability of the model across different transient

quantitative and qualitative loads was to be tested as the third objective. Typical stormwater

basin designs are based on influent flow rates calculated from return storms, and on event mean

concentrations (EMC) of water quality parameters. Therefore, as the fourth and final objective,

this approach was compared to the real-time performance of the UOP by a CFD simulation with

the same model, for a steady influent flow rate, for the EMC of the PM and the event-mean

(representative) influent PSD.

127

Methodology

Experimental Methodology

The experimental site is illustrated in Figure 5-2. The catchment area was a stretch of

elevated urban highway (Interstate-10) over City Park Lake in Baton Rouge, Louisiana,

constructed from Portland cement concrete (PCC ). The overall drainage area was approximately

1088 m2. A detailed description of the catchment is available elsewhere (Sansalone et al.. 2005).

The overall experimental setup consists of the following components – a system of pipes and

troughs to deliver rainfall-runoff from the catchment, a 5.08 cm (2 inch) Parshall flume equipped

with a 70 KHz ultrasonic sensor for measuring flow rates, a gate valve to divert flow to the

screened HS.

Four discrete rainfall-runoff events were monitored and treated by the screened HS. All

storms were routed through a pre-cleaned system in order to accurately monitor PM mass

balance. The static screen aperture size used was 2.4 mm for all storms with the exception of the

20 Aug 2004 storm, where an aperture size of 1.2 mm was used. 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 truly representative

and complete particle size distribution. The number of discrete samples of influent and effluent

was chosen appropriately to provide a reasonable estimate of temporal particulate concentrations

(McBean et al.. 1997).

The total particulate matter was obtained as a sum of the mass of sediment, settleable and

suspended particle fractions. Sediment particles are defined as particles with a diameter greater

128

than 75μm (ASTM 1993). The settleable fraction (25μm<dp<75μm) comprises particles that

settle out in an 60 minutes Imhoff cone analysis (Standard Method 2540F, APHA 1998).

Those particles remaining in suspension after 60 minutes complete the suspended fraction

(1μm<dp<25μm) (APHA1998). This classification is based on the particle transport mechanisms

(Tchobanoglous et al.. 2003) that are associated with particles as a function of their diameter.

The sediment particle fraction is influenced mainly by gravitational forces while settleable

fraction particle transport is influenced to a larger degree by velocity gradients in the surrounding

liquid. The suspended particles display a more random behavior and are more likely advect with

fluid flow.

Suspended-sediment concentration (SSC) analysis was conducted in accordance with

Standard Method 2540 D (ASTM 1997). PSDs of the influent and effluent were measured using

a laser diffraction analysis based on Mie scattering theory (Finlayson-Pitts et al. 2000). The

particle size range was from 1.0 μm to 250 μm, and was applicable to sediment concentration

range of 1 to 1000 mg/L with a resolution < 1 mg/L. The contribution of coarser particles to the

temporal influent PSD was calculated from the separated HS particles and the temporal effluent

PSD.

The % removal (PR) for the overall total particulate matter was used as the index for

comparison between the model and experimental data, and was defined as follows.

% Removal = 100×⎥⎦

⎤⎢⎣

⎡

i

HS

MM

(5-2)

For the purpose of QA/QC, a mass balance error constraint of 10% was imposed.

Mass Balance Error = %10100)(±≤×⎥

⎦

⎤⎢⎣

⎡ +−

i

eHSi

MMMM (5-3)

129

In this expression, iM is the influent mass of particles, HSM is the mass of particles

captured by the screened HS and eM is the effluent mass of particles, computed from the

measured effluent SSC across the total treated 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.

The event mean concentration (EMC) for PM over the time period of a rainfall-runoff

event is typically used as an indicator of overall water quality and to calculate % removal for

stormwater UOPs (Huber 1993).

∫

∫== t

t

tq

dttqtc

VMEMC

0

0

)(

)()( (5-4)

In this expression, M is the total effluent mass load over the entire duration of the test, V is

the total volume of flow over the entire duration of the test, C is the flow weighted mean

concentration, c (t) is the time variable particulate-bound concentration, q (t) is the time variable

flow rate.

Multiphase Flow Modeling Methodology

The behavior of the screened HS is modeled more accurately in three dimensions, due to

the simultaneous effects of the complex static screen geometry, the vortexing flow and

gravitational forces on the instantaneous motion of particles. The fluid flow equations that are

solved by CFD are based on fundamental laws of conservation of mass, momentum and energy.

CFD provides a group of numerical techniques to solve non-linear partial differential equations

of flow, i.e. the Navier-Stokes equations. Versteeg et al. (1995) define the general conservation

equation for any fluid property Ф for a control volume )( zyxV ∂∂∂= is as follows.

130

Φ+ΦΓ=Φ+∂

Φ∂ Sgraddivudivt

)()()( ρρ (5-5)

In this expression, u is the fluid velocity, Γ is the diffusion coefficient, and ΦS is the

source/sink term.

zw

yv

xuudiv

∂∂

+∂∂

+∂∂

=)( (5-6)

In this expression, u, v and w are the velocity vectors in the x, y and z directions

respectively. The momentum equations for three dimensions are obtained by incorporating u, v

and w into equation 2.

X-momentum: MxSugraddivxpuudiv

tu

++∂∂

−=+∂

∂ ))(()()( μρρ (5-7)

Y-momentum: MySvgraddivypuvdiv

tv

++∂∂

−=+∂

∂ ))(()()( μρρ (5-8)

Z-momentum: MzSwgraddivypuwdiv

tw

++∂∂

−=+∂

∂ ))(()()( μρρ (5-9)

In the above expressions, p is the pressure, μ is the viscosity, and MzMyMx SSS ,, 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.

The inlet Reynolds number was found to vary significantly as a function of time for the

four rainfall-runoff events. There was high temporal variability (1e+02 to 9e+05) in the

magnitude of Reynolds numbers calculated for the 20 Aug 2004 rainfall-runoff event. On the

other hand, the magnitude and temporal variation of Reynolds numbers was low for the 14 Oct

2004 storm (1e+02 to 2e+03). 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 number.

131

The standard k-ε model was used to resolve turbulent flow for the HS, based on previous

studies with hydrocyclones (Nowakowski et al.. 2004, Statie et al.. 2001, Petty et al.. 2001) and

the screened HS at steady flow rates. Mohammadi et al. (1994) provide a detailed analysis into

the k- ε model and confirm the applicability across a wide range of flow regimes. In the standard

k-ε model (Launder and Spalding 1974) 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 illustrate the relationship between viscous stresses and “Reynolds

stresses”. It should be noted that eddy viscosity (µt) is a non-physical quantity, and is expressed

by the following equation.

⎟⎟⎠

⎞⎜⎜⎝

⎛=

ερμ

2kft (5-10)

In this expression, k is the turbulent kinetic energy per unit mass, calculated as follows.

)(5.0 222 wvuk ′+′+′= , [L2T-2] (5-11)

In this expression wvu ′′′ ,, are vector components of velocity fluctuations due to turbulence

and ε is the dissipation rate of turbulent kinetic energy per unit mass. The transport equations of

the standard k-ε model are expressed in the following equations. For k:

kbkjk

t

ji

iSGG

xk

xku

xk

t+−++

⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

⎟⎟⎠

⎞⎜⎜⎝

⎛+

∂∂

=∂∂

+∂∂ ρε

σμμρρ )()( (5-12)

For ε:

εεεεε

ερεεσμμρερε S

kCGCG

kC

xxu

xt bkj

t

ji

i+−++

⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

⎟⎟⎠

⎞⎜⎜⎝

⎛+

∂∂

=∂∂

+∂∂ 2

231 )()()( (5-13)

In these expressions kG represents generation of k due to the mean velocity gradients;

bG is generation of k due to buoyancy; ε1C , ε2C and ε3C are constants ; kσ and εσ are the

132

turbulent Prandtl numbers for k andε , respectively; kS and εS are user-defined source terms.

The constants were determined by Launder and Spaulding (1974). It was hypothesized that

isotropy of Reynolds stresses can be assumed reasonably in the case of the HS. The values

of ε1C , ε2C , ε3C , kσ and εσ used in the model were 1.44, 1.92, 0.09, 1.0 and 1.3 respectively

(Launder et al.. 1974). The no-slip boundary condition, along with effects of viscous blocking

and kinematic damping creates large gradients in solution variables near the walls of the HS. To

account for these phenomena in the turbulence model, semi-empirical “wall functions” for the k-

ε model were used (Launder et al.. 1974).

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. Approximately 40 %

of the screen area is effectively open to flow. Meshing the static screen, with structured or

unstructured meshing schemes places severe constraints on time and computational power. To

overcome this difficulty, the static screen was modeled as a porous perforated plate with the

addition of a momentum source term to the standard fluid flow equations. This momentum sink

contributes to the pressure gradient in the porous computational cell, creating a pressure drop

that is proportional to the fluid velocity in the cell. The source term is composed of two parts: a

viscous loss term and an inertial loss term. For simple homogeneous media, the sink term is

expressed by the following equation.

⎟⎠⎞

⎜⎝⎛ +−= imagiii vvCvS ρ

αμ

21

2 (5-14)

In this expression, iS is the source term for the i th momentum equation, α is the

permeability, iC2 is the inertial resistance factor, iv is the velocity in the i th momentum equation,

133

magv is the velocity magnitude in the computational cell. It is important to note that the primary

assumption is that the porous cells are 100% open, i.e. the actual geometry of the screen is

represented by a resistance component.

The pressure drop through the screen was measured experimentally for steady flow rates

ranging form 1 to 150 % of the design flow rate with pressure transducers and it was found that

the head loss was less than 150 mm even at higher flow rates, across the static screen. The

viscous resistance term was assumed to be negligible and the source term was then modeled

considering only the inertial resistance term, and the inertial resistance factor per unit thickness

of the plate, i.e. )(2 iC was calculated for the x, y and z directions as described by the following

equation (FLUENT 2005).

nK

C iLi

)(')(2 = (5-15)

In this expression, n is the thickness of the plate, and )(' iLK is a coefficient calculated from

the following equation.

2

2

)()(' *Σ

=vv

KK oiLiL (5-16)

In this expression, 2xv is the square of the velocity through the plate, considering that the

plate is ‘o’ % open to flow in the given direction and 2Σv is the square of the velocity through the

plate, considering that the plate is 100 % open to flow in the given direction. )(iLK is the loss

factor in the ith direction and is calculated from the following equation.

( )2)( oiL vKp ρ=Δ (5-17)

In this expression, pΔ is the measured pressure loss through the static screen. 2C is

calculated based on the %ages of screen area open to flow described previously for the x and y

134

directions. The inertial resistance in the z-direction is theoretically infinite. However, to specify

2C in the z-direction, a value sufficiently large enough to not cause numerical instability (twice

the order of magnitude of the largest value of 2C ) was used.

Modeling the Particulate Phase

Multiphase flows are modeled with an Eulerian-Eulerian approach or an Eulerian-

Lagrangian approach (van Wachem et al.. 2003) depending on the extent of coupling between

phases. Elgobashi (1991) proposed a regime map for appropriating the degree of inter-phase

coupling, by analyzing length and time scales. Subsequently, it was determined that a Lagrangian

approach to tracking the secondary phase is most appropriate for flows with a low influent

particulate volume fraction which is the case in this study (0.2 %< PVF < 3.2 %).

The transient flow field was modeled utilizing the Eulerian approach, for each time step.

Subsequently, the influent particles were injected at times that correspond to influent sampling

times during storm data collection.

The Eulerian-Lagrangian approach was chosen to model the behavior of particles in the

computational domain of the HS. In this approach, the flow field was solved using the Eulerian

approach. Following this, particles were tracked using a Lagrangian Discrete Phase Model

(DPM). The DPM is derived from force balances based on classical Newton’s (Turbulent and

transitional regimes) and Stokes (Laminar regimes) laws describing particle motion, and is

summarized by the following equation.

xp

pxpD

p Fg

uuFdt

du+

−+−=

ρρρ )(

)( (5-18)

dF 24Re18

2pD

pp

Cdρμ

= (5-19)

135

232

1 ReRe ppD

aaaC ++= (5-20)

μρ uud pp

p

−≡Re (5-21)

In equations 5-18 through 5-21, u is the fluid velocity, pu is the particle velocity, ρ is the

fluid density, pρ is the particle density, pd is particle diameter, μ is the viscosity, 321 ,, aaa are

empirical constants that apply to smooth spherical particles as a function of the Reynolds number

(Morsi et al.., 1972) and pRe is the particle Reynolds number.

Particle trajectories are obtained by integration of equation 21. For this study, particles of

consistent morphology were injected across the entire flow cross-section immediately above the

inlet to the HS to obtain comparable particle trajectories across varied flow rates, by reducing

uncertainty in initial spatial location. Particles were defined as silica particles of diameters

associated with the sieves utilized and a measured specific gravity of 2.65 as determined by

helium pycnometry (Sansalone et al. 1998). Particles were tracked for a specific length for each

flow rate, based on hydraulic residence times calculated by injecting neutrally buoyant

submicron ‘tracer’ particles. Particles that remained in the HS after integrating over the

specified length were considered to have been separated by the HS. Particle removal was thus

defined by the following equation.

100*I

HS

NNp =Δ (5-22)

In this expression, HSN is the number of particles that remain in the screened HS, and IN is

the number of particles injected at the inlet.

136

Discretization and Solution Schemes

The computational domain was discretized using an unstructured mesh with tetrahedral

elements, generated by TGrid (Qi et al.. 2006). The volume of the HS was divided into total of

3.86 million cells, after ensuring grid convergence. Numerical solutions were obtained using a

Finite Volume Method (FVM) and a cell-centered scheme used for discretization. A Second-

Order Upwind Scheme (Barth et al.. 1989) was used solve for flow parameters.

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). The flow data were measured for discrete time

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

Aug 2004 event, a Weibull function was utilized. For more complicated storms, the runoff

hydrograph was modeled by splitting the hydrograph into piecewise continuous segments which

allowed for accurate curve fitting. For example, the 05 June 2005 storm was modeled with a

combination of quadratic and exponential functions. All the storms were modeled successfully

with a time step Δt of 30 seconds. Smaller time steps did not significantly affect the flow

solutions. The transient SIMPLE (Semi-Implicit Method for Pressure Linked Equations)

algorithm (Patankar 1980) accounted for pressure-velocity coupling. The criterion for iterative

convergence was set at 1x10-3 (Ranade 2002).

Results and Discussions

The influent hydrographs and hyetographs of the four discrete storm events are presented

in Figure 5-3. The varying hydrology resulted in a distinct particle transport signature for each

storm. Among the four storms analyzed, the screened HS had a total PM removal efficiency that

ranged from 48% to 57%. Influent and effluent mass loads are provided in Table 5-1. The total

137

particulate clarification response of the screened HS is greatly dependent on the influent particle

size gradation. Coarse particles are separated by gravitational settling at low flow rates, while

finer particles are separated by vortex-induced inertial separation, which is more effective at high

flow rates close to the design flow rate of the screened HS.

Figure 5-4 illustrates the modeled and measured gravimetric particle size distributions of

the total PM separated by the screened HS. The modeled results agree very well with the

experimental data, across the four discrete rainfall-runoff events. The absolute relative %

difference was utilized to compare measured and modeled results, and was calculated as follows.

data Measureddata) Modeled-data (Measured*100 RPD Absolute = (5-23)

CFD simulations reproduced the overall separated particle size distribution within 10 % of

the measured value. The overall mass and relative % difference for measured and modeled PM is

provided for each storm in Table 5-1.

The temporal variations in the position of a given particle are illustrated in Figure 5-5. The

20 Aug 2004 storm was chosen, and particle trajectories in the HS were obtained from post-

processing CFD results. The particle diameter chosen was 300 μm, which is the median particle

diameter by mass (d50m ) of the influent PSD. The peak flow rate of the 20 Aug storm was twice

in magnitude of the design operational flow rate. The hydraulic residence time is not sufficient to

offset the effect of advective transport, and promote gravitational settling for the coarse particle.

This type of illustration provides an in-depth insight into the particle transport of any given

particle of known specific gravity, within a turbulent flow regime.

Bertrand et al.. (1998) classified rainfall-runoff events into mass-limited and flow-limited

events based on temporal pollutant mass delivery. For mass-limited events, mass delivery is

skewed toward the initial portion of the event, while mass delivery tends to follow the

138

hydrograph for flow-limited events. This classification was applied to the storms in this study, in

order to facilitate a discussion of their PM clarification responses to different steady influent

flow rates, chosen to test the practical usability of a supposedly representative singular value for

influent flow rate, in lieu of simulating an entire rainfall-runoff event.

Figure 5-6 illustrates the results of simulating different influent flow rates. The 20 august

2004 storm was a high intensity storm with the peak flow rate being close to twice the design

flow rate of 9.5 L/s. At higher flow rates, there is enough driving force to create and sustain a

forced vortex. This suggests the predominance of inertial or separation as opposed to

gravitational settling. Moreover, there was a disproportionate amount of mass delivered in the

initial portion of the storm, when the flow rates were high. Further, the influent particle

distribution was predominated by coarser particles (d50m = 300 μm). Due to the aforementioned

reasons, it is not surprising that the peak flow rate reproduces the overall PM separation better

than the mean and median flow rates.

The 03 October 2005 storm had a maximum flow rate that was close to 125% of the design

flow rate. However, the mass delivery was proportional to the flow rate, across the entire event,

and the influent PSD was finer (d50m = 58 μm). In light of this, there was no significant

difference between PM separation predicted by the mean and median flow rates. However, there

is a greater digression from measured PM removal utilizing the peak flow rate.

The 05 June 2005 storm had a maximum flow rate that was almost identical to the design

flow rate of the screened HS. The particulate transport was mass-limited and the d50m of the

influent was 247 μm. With this coarser influent, we find that neither the mean nor the median

influent flow rates are able to accurately reproduce the particle dynamics of the screened HS

across the storm. However, similar to that observed with the 20 August 2004 storm, we find that

139

the peak flow rate provides the best prediction, thus bolstering the hypothesis of increased

inertial separation as opposed to gravitational settling at flow rates close to or greater than the

design flow rate.

The 14 Oct 2004 storm was a very low intensity and long duration storm. Under these

conditions, the screened HS functions more as a circular sedimentation tank. However, the

particle delivery was mass limited, owing to a dry deposited particle gradation that was fine

enough to advect with the low intensity sheet flow on the paved surface of the watershed.

However, we notice that the mean, median or peak flow rate fall short of predicting the actual

PM performance. The reason for this can be attributed to the fine influent particle gradation (d50m

= 45 μm), which still leaves a large fraction of the influent mass in the suspended particle size

range, which are separated more as a function of velocity gradients than on increased hydraulic

residence times. Table 5-2 provides a comparison of the PM separation at different flow rates.

From a quantitative design point of view, it becomes apparent that no one flow rate can be

considered representative, as the predictions of the PM separation behavior of the UOP vary

significantly using the mean, median and peak influent flow rates. The influent hydrographs

range from slightly skewed Gaussian distributions to extended random pulses across a long

period of time. Any intuitive assumption that the median flow rate is likely to be most

representative was proved to be inapplicable across storms with varying hydrographs. This ties in

to the prevailing question of how much of a rainfall-runoff event needs to be treated. While

practical design initiatives call for specific quantitative and qualitative loads, the actual

functionality of the UOP is heavily influenced by the coupled variations in flow and influent

particle size and mass distributions.

140

Conclusions

Particulate matter separation by a screened hydrodynamic separator for transient hydraulic

and particulate loads observed in a real-time rainfall-runoff event was modeled by the

application of the standard k-ε turbulence model and a Lagrangian discrete phase model. Four

discrete rainfall-runoff events were modeled individually and the modeled results agreed very

well with the measured data (Absolute RPD <10%). The CFD model was applicable across the

entire range of flow rate and influent PSD variations and was able to accurately model both

mass-limited and flow limited rainfall-runoff events. Modeling the unsteady flow across the

entire duration of the storm was tested against using a single design flow rate and the event mean

concentration of PM for each event. It was observed that the PM separation behavior of the UOP

varies significantly using the mean, median and peak influent flow rates. Accurate modeling

calls for including the flow variations across the entire treated volume of runoff.

141

Table 5-1 Summary of measured and modeled particulate matter (PM) separation by the screened HS for four discrete storm events. Hydrologic and PM indices - Experimental measurements and model predictions

Separated mass % removal Qp Qave V Inf. mass Measure Model Measure Model RPD Storm

Event (L/s) (L/s) (L) (g) (g) (g) (g) (g) (%)

20-Aug-

04 17.5 5.1 12286 10592 6249.3 6691.7 59.0 63.2 -7.1 3-

Oct-05 12.1 3.1 2615 738 354.2 397.3 48.0 53.8 -3.7 5-

Jun-05 9.4 1.9 5856 4758 3187.9 3449.3 67.0 72.5 -8.2 14-Oct-04 0.6 0.1 1672 544 277.4 310.2 51.0 57.0 -5.6

Table 5-2 Summary of measured and modeled particulate matter (PM) separation by the

screened HS for four discrete storm events, using the measured EMC for influent PM, for Qmean, Qpeak and Qmedian

Effluent mass load predictions for given Influent EMC

Q = f(t) Qmean Qmedian Qpeak

Measured Model RPD Model RPD Model RPD

Storm Event

(g) (g) (%) (g) (%) (g) (%) 20-Aug-04 4313.9 3595.5 16.7 3864 11.6 4646.15 -7.2 3-Oct-05 381.9 339.9 11 342.2 11.4 448.8 -14.9 5-Jun-05 1581.8 1039.7 34.3 755.2 109.4 1921.8 -17.7

14-Oct-04 267.8 126.8 52.6 178 52.2 203.4 31.7

142

(a) (b) Figure 5-1 Plot (a) Plan and side view of detailed geometry of a screened HS. Plot (b) Typical

fluid flow profile inside a screened HS.

Outer Annular Chamber (Volute Area)

Inner Chamber (Screening Area)

Outer annular chamber (Volute Area)

Static Screen

Inlet

Inner Chamber (Screening Area)

OutletStatic Screen

Conical Sump

143

Figure 5-2 Experimental site for monitoring rainfall-runoff from an urban highway.

t

Q

I

dp

Δm

dp

Δm

Influent

Effluent

70 KHz ultrasonic sensor

Drop-box (Influent samples)

Diversion valveOD=15 cm

ID=20 cm

5 cm Parshall flume

Runoff from catchment Runoff from catchment

144

t/tmax0.0 0.2 0.4 0.6 0.8 1.0

Q/Q

max

0.00.20.40.60.81.0

Imax = 121.9 mm/hr Qmax = 17.5 L sec-1

I/Im

ax

0.0

0.5

Q/Q

max

0.00.20.40.60.81.0

20 Aug 2004 event tmax = 50 min

I/Im

ax

0.0

0.5

Imax = 2.2 mm/hr Qmax = 0.6 L sec-1

14 Oct 2004 event tmax = 200 min

I/Im

ax

0.0

0.5

t/tmax

0.0 0.2 0.4 0.6 0.8 1.0

Q/Q

max

0.00.20.40.60.81.0

Imax = 45.7 mm/hr Qmax = 9.4 L sec-1

05 Jun 2005 event tmax = 56 min

I/Im

ax

0.0

0.5

Q/Q

max

0.00.20.40.60.81.0

03Oct 2005 event tmax = 15 min

Imax = 61.0 mm/hr Qmax = 12.1 L sec-1

Figure 5-3 Influent hydrology for four discrete storm events.

145

% F

iner

by

mas

s

0

20

40

60

80

100

Measured Modeled

% F

iner

by

mas

s

0

20

40

60

80

100

Particle Diameter (μm)

10100100010000

% F

iner

by

mas

s

0

20

40

60

80

100

Absolute RPD =7.1

ΔMexperiment = 6249 gΔMmodel = 6669 g

Absolute RPD = 3.7

ΔMexperiment = 354 gΔMmodel = 367 g

Absolute RPD = 8.2

ΔMexperiment = 3188 gΔMmodel= 3449 g

Measured Modeled

Particle Diameter (μm)

10100100010000

% F

iner

by

mas

s

0

20

40

60

80

100

Absolute RPD = 5.6

ΔMexperiment = 277 gΔMmodel = 310 g

20 Aug 04 03 Oct 05

05 Jun 05 14 Oct 04

Figure 5-4 Measured vs. modeled particle size distributions of particles separated by the

screened HS.

146

Figure 5-5 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 minutes. Trajectories are calculated for the particle diameter corresponding to d50m and equal to 300 μm. Particle density (ρp) is 2.65 g/cm3.

a) ti = 0.30*tmax, Qt=0.25*Qmax b) ti = 0.36*tmax, Qt=0.50*Qmax

d) ti = 0.64*tmax, Qt=0.10*Qmax c) ti = 0.44*tmax, Qt=1.0*Qmax

Inflow

Inflow

Inflow

Inflow

Outflow

Outflow Outflow

Outflow

147

Figure 5-6 Modeled versus measured particle size distributions for four storm events utilizing

Qmean, Qpeak and Qmedian.

% F

iner

by

mas

s

0

20

40

60

80

100

% F

iner

by

mas

s

0

20

40

60

80

100

Particle Diameter (μm)

110100100010000

% F

iner

by

mas

s

0

20

40

60

80

100

Particle Diameter (μm)

110100100010000

% F

iner

by

mas

s

0

20

40

60

80

100

20 Aug 04 03 Oct 05

05 Jun 05 14 Oct 04

QMean

QMedian

QPeak

InfluentEffluent

148

CHAPTER 6 A PARTICLE SEPARATION MODEL OF A VOLUMETRIC CLARIFYING FILTER FOR

SOURCE AREA RAINFALL-RUNOFF PARTICULATE MATTER

Introduction

Anthropogenic particulate matter (PM) transported in urban rainfall-runoff has been

identified as a contributor to deterioration of surface water in the USA (USEPA 2000). Rainfall-

runoff transports an entrained mixture of colloidal, suspended, settleable and sediment fractions

of PM, with the associated chemical constituents distributed across this PM (Sansalone et al

2007, Lee and Bang 2000, Sansalone et al. 1998, Igloria et al. 1997, Sansalone and Buchberger

1997). PM transported by runoff act as reactive surfaces for adsorbing, desorbing and leaching

these chemical constituents which include organics, metals as well as nutrients (Sansalone 2002).

Separation of PM by unit operations and processes (UOPs) for in-situ treatment of rainfall-runoff

is challenged by factors such as the stochastic nature of hydrologic loads, variability and

complexity of PM and chemical constituents and practical constraints such as land area and

infrastructure (Liu et al. 2001).

Media filtration of rainfall-runoff

Various filtration configurations including infiltration and exfiltration through fixed

granular media such as sand, soil or engineered media systems have been suggested as viable

solutions for meeting hydrologic and chemistry regulations for watersheds (Colandini 1999,

Sansalone 1999, Li et al. 1999, Colandini et al. 1995, Geldof et al. 1994, Sansalone and Teng

2005). Engineered media such as oxide coated media has been found to be effective at reducing

chemical constituents in wastewater and source area rainfall-runoff (Ayoub et al. 2001, Teng and

Sansalone 2004, Sansalone and Teng 2004,). Recently, the use of oxide coated media has been

extended to in-situ and ex-situ runoff treatment (Erickson et al 2007, Sansalone et al. 2004, Liu

149

et al. 2005a, Liu et al. 2005b). In this study, aluminum oxide coated media with a pumice

substrate (AOCM)p was utilized for ex-situ physical filtration of source area rainfall-runoff.

Recently, Hipp et al. (2006) suggested that removable filter inserts may be a viable

preliminary unit operation due to ease of maintenance. While granular filtration has

demonstrated advantages for improving water chemistry through PM capture, such advantages

require careful design, analysis and prototype testing, as well as regular maintenance to ensure

acceptable hydraulic capacity (Keblin et al. 1997). Performance (mass and size of PM separated)

of a granular medium filter depends on the following broad parameters (Tien 1989).

)τ,K,d,dη,f(Q/A,ΔM mmpparticles = (6-1)

In this expression, ΔΜparticles is the mass of particles separated, Q/A is the influent surface

loading rate, A is the total surface area of the media , Q is the influent volumetric flow rate, ηis

the effective porosity, dp is the mass-based particle diameter, dm is the diameter of the granular

media, τ is the empty bed contact time (EBCT) (AWWA 1990) and Km includes physical,

chemical and surficial properties of the media, such as adsorption properties, media (internal)

porosity, and morphology.

Granular filtration mechanisms can be classified into surficial straining, sedimentation,

interception, inertial impaction, diffusion, hydrodynamic and electrostatic interaction (Wakeman

et al. 2005). Filtration dynamics are widely assumed to be dependent on the surface loading rate

(SLR) and with increasing SLR, macroscopic mechanisms tend to dominate the separation

process, due to reduced contact times. The radial flow rapid-rate filter used in this study was

operated at surface loading rates (SLR) ranging from 24 to 189 L/m2-min, which is higher than

SLR’s of typical rapid sand filters (83 L/m2-min) (Reynolds et al 1995).

150

Primary issues faced of designing a filtration system for stormwater PM control is the issue

of excessive head-loss due to long-term retention of trapped particles in the packed filter bed and

unsteady flow rates if there is not upstream hydraulic attenuation of flow. Farizoglu (2003)

reported that head-losses increase proportional to the square of the influent flow rate. Given the

large variability of flow rates within and between hydrologic events head loss considerations are

a challenge in the design of field scale filtration systems to achieve a pre-determined level of

clarification. Reddi (1997) reported that fine PM in runoff is a contributor to clogging of filters,

and eventual head buildup. As the filter progressively clogs, filter ripening occurs and

progressive clogging has the potential to cause deterioration of the filtration mechanism, due to

the modified and increasingly non-ideal hydrodynamics.

Many urban stormwater modeling approaches are extensions of wastewater treatment

principles which assume steady flow and PM loads. This is the case for many stormwater unit

operations and regulatory testing and modeling protocols assuming steady flow and load. While

controlled testing, required in many regulatory tests, is a necessary building block to examine

and compare unit operation behavior to controlled loads in lieu of the uncertainty and stochastic

nature of field loadings; ultimately unit operations are loaded by highly variable and

uncontrolled runoff processes. The associated PM and chemical constituent delivery in runoff

events are highly variable processes. Therefore stormwater unit operations and their models

must support rapidly changing flows and PM characteristics even when upstream volumetric

clarification is provided. The stormwater management model (SWMM) (Huber 1988) has made

very significant advances over simplified peak flow models and greatly improved the design and

modeling of volumetric controls even for complex hydrology and urban drainage systems.

However while the current version of SWMM can model complex hydrologic and variable PM

151

(as a lumped parameter, TSS) loads and examine volumetric attenuation, it is beyond the scope

of the current version to provide in-depth hydrodynamic, head loss and PM clarification profiles

of a filtration unit operation for transient loads and variable particle size distributions (PSDs).

Modeling Approach

Numerical modeling of water and wastewater treatment processes has found many

applications in the past several decades (Do-Quang et al. 1998). For treatment systems where

hydrodynamics play an important role, numerical methods have been developed to solve the

Navier-Stokes equations for coupled fluid and particle dynamics by a series of discretization

techniques and algorithms (Anderson 1995). Such approaches to model dilute particle-laden

flows and granular media filtration of such flows is an active research area (Curtis et al. 2004,

van Wachem et al. 2003).

Tung et al. (2004) studied deep bed filtration for a sub-micron/nano-particle suspension

utilizing a microscopic approach wherein different types of media packing were modeled.

However, macroscopic approaches to modeling filter media are needed to model practical

systems where packing schemes are most commonly random and unstructured. Li et al. (1999)

applied a 2-D numerical model to simulate variably saturated flow in a partial exfiltration

system. Sansalone and Teng (2005) applied a 2-D numerical model to simulate the transient

hydrodynamics of a linear partial exfiltration system containing oxide-coated media and

cementitious permeable pavement subject to direct unsteady rainfall-runoff loadings in order to

examine the PM clarification in this in-situ system. In the approach of the present study a

macroscopic-basis is utilized to simulate the 3-D hydrodynamic and clarification response of a

series of clustered radial filter cartridge without resorting to the assumptions of symmetric

loading and response within the clustered system. Furthermore, the modeling combines the

unsteady hydrodynamic inputs and corresponding variable PSD characteristics of PM; such

152

unsteady and variable behavior being characteristic of actual rainfall-runoff events. Therefore

this study not only examines the 3-D spatial complexity of the clustered filter VCF system, but

also examines the VCF response subject to uncontrolled and coupled hydrologic and PM

loadings.

Objectives

This study focuses on the PM filtration and head loss response of a VCF system to direct

and unsteady rainfall-runoff loadings from an urban paved source area watershed dominated by

traffic loadings. There are three sets of objectives in this study for the five events monitored and

modeled in this study. Between these events the VCF was off-line and was not subject to any

loading. With the VCF directly loaded by unsteady direct runoff and variable PM, the first

objective was to examine the VCF hydraulic response including flow changes, head loss and

surface loading rate (SLR) this series of five events. The second objective was to examine the

temporal response of the VCF for the d50m of the PSD. The final set of objectives was to

examine the event-based behavior of the VCF in modifying the influent concentration and mass

of PM.

Methodology

VCF and Watershed Configuration

The instrumented VCF received direct unsteady runoff from a source area urban paved

watershed in urban Baton Rouge, Louisiana. The upstream urban drainage system was designed

to intercept lateral pavement sheet flow from a concrete-paved watershed consisting of two

identical eastbound and westbound catchments, each having a contributing area of 544 m2. The

watershed was dominated by traffic and the average daily traffic (ADT) for eastbound and

westbound I-10 was 142,000 vehicles. Rainfall was recorded with a tipping bucket rain gage and

data-logger in increments of 0.254 mm (0.01 inch). Mean annual precipitation in Baton Rouge,

153

Louisiana is 1460 mm/year. Further details of the watershed, hydrology and water chemistry and

loads can be found elsewhere (Dean et al. 2005, Sansalone et al. 2005). During 2006 the

watershed was loaded by 59 rainfall-runoff events with five events monitored and treated in a

series in April and May by the VCF. Since the VCF was an off-line unit, events not treated

bypassed the VCF and were directly discharged into City Park Lake. Prior to treating the first

event of 21 April 2006, the VCF had only been loaded by potable water for hydrodynamic

testing. The main VCF components were a clarification vault and five radial downflow media

filtration cartridges, shown in Figure 6-1 and 6-2. The five cartridges with aluminum-coated

media are housed in a 116.8 cm by 212.2 cm vault surface area. This structure contained the

influent and effluent pipes as well and internal manifold delivering treated effluent runoff to the

effluent drop box. Pressure transducers are installed at the influent Parshall flume, system vault,

cartridge center pipe, effluent box and effluent V-notch weir.

Runoff was collected through direct piping from the watershed catch basins and expansion

joint, and entered the VCF through an influent delivery system which includes a 5.08 cm (2-

inch) Parshall flume and a 36.6 cm by 79.2 cm drop box for sampling. Runoff that entered the

VCF influent box was transported directly to the bottom of the vault beneath the radial

cartridges. When the water surface elevation in the vault reached the operating level (slide gate

was in the closed position), a float valve was triggered through buoyancy and the orifice plate

opened gradually. Runoff then flowed through the filter cartridges driven by the differential head

and drained into the perforated drain tubes located at the cartridge center and then to the collector

manifold. The manifold was plumbed to a float-controlled slide gate that sets the VCF flow

control to achieve a balance between flow and driving head level. After an event, detained runoff

continued draining through each cartridge, manifold and the slide gate until the vault water

154

surface was below the bottom of the filter cartridges. When runoff ended, the float controlled

slide gate closed until the next runoff event. Runoff was retained in the VCF up to the bottom of

the filter cartridges.

Data Acquisition and Management

Druck pressure transducers connected to a Campbell-Scientific CR 1000 were used in the

VCF for real-time water level monitoring. Water levels inside and outside the media cartridges

were monitored using two 2.5 psi (17.2 kPa) transducers. A single 5.0 psi (34.5 kPa) transducer

was located at the bottom of effluent drop box. Each transducer was calibrated, assigned

appropriate multipliers and offsets; with pressure data acquired every 10 seconds. Transducer

data were converted to flow using a calibrated head-discharge relationship for the influent 50.8

mm Parshall flume and the effluent 60o V-notch weir summarized in equation 1 and 2,

respectively and the VCF stage-storage provided in equation 3. Components are illustrated in

Figures 1 and 2.

8619.2

8.30462.74

2tan2

158

⎟⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛=

ZhgCQ ud

θ (6-2)

6548.1

8.30407.31 ⎟

⎠⎞

⎜⎝⎛==

ZKhQ u (6-3)

ZAV e= Ae = 2.48 m2 (Z < 0.1780 m)

ZAV e+= 061.0 Ae = 2.13 m2 (0.1780 m < Z < 0.5840 m)

ZAV e+= 540.0 Ae = 1.31 m2 (0.5840 m < Z< 1.1428 m) (6-4)

ZAV e+−= 397.0 Ae = 2.13 m2 (Z > 1.1428 mm)

155

In these equations Cd is the effective discharge coefficient, g is the gravitational constant

[L/T2], θ is the v-notch angle, h is the head [L] above the v-notch invert, u is an exponent, Z is

the head [L] above the VCF invert (datum), Q is the discharge [L3/T], K is an index of VCF

storage surface area, V is VCF storage volume (m3), and Ae = effective VCF surface area (m2).

An event volume balance is conducted to ensure volume conservation. A volume balance error

(VBE) criterion of ± 10%. VINF, VEFF, VS and Vs represent influent, effluent, storage and

sampling volumes, respectively.

( )100(%) ×

−−−=

INF

sSEFFINF

VVVVV

VBE (6-5)

Radial cartridge filters (RCF) and (AOCM)p

The total volume of each RCF was 72.9 L with the diameter and height of the RCF are

0.4572 m and 0.5588 m, respectively. The media was contained between an outer mesh and non-

reactive impervious polypropylene discs on top and bottom of the cartridge. Engineered

(AOCM)p was utilized as the granular media. This media had a pumice-substrate with an

aluminum oxide coating. The distribution of media diameter (dp) was obtained by digital image

analysis and utilization of Image Pro Plus v 6.2 Image Analysis Software. Image analysis results

were utilized to calculate an equivalent circular diameter (ECD) as follows (Holdich 2002). The

ECD is defined as the diameter of a sphere having the same projection area as the object. The

resolution of the imaging method was 10.1 mega-pixels.

π/4AECD = (6-6)

In this expression, A is the projected area of the media. Figure 6-3 illustrates a frequency

histogram for the media tested. A three-parameter Gaussian distribution fit the data (R2 = 0.93).

The additional parameter accounts for the area under the curve, which is not equal to 1. The

156

mean media size is 3.56 mm ± 0.8 mm for a sample size (n) of 2551. The specific gravity of the

pumice-based media was 2.35. The media was pluviated into the cartridge so that the cartridge

contained 49830.4 g of dry media at full capacity for each experimental run. Triplicate

measurements of total clean bed porosity (η) of the RCF with media produced a mean of 0.71

and standard deviation of 0.041 by volume. Of this total porosity the internal porosity of the

media was measured in triplicate by mercury porosimetry (ASTM 2003) with a mean of 0.37 and

a standard deviation of 0.022. The total porosity includes all available pore areas in the media

and media bed, but not necessarily the effective porosity available for a given flow rate.

Influent and Effluent Sampling and Analysis

Five discrete rainfall-runoff events in a series were monitored and treated by the VCF. For

each event sampling started immediately when runoff was observed, and was performed on a

time basis for the entire duration of runoff. Influent was sampled at the influent drop box of the

VCF and effluent was sampled at the outflow of the VCF. All samples were taken manually,

across the entire cross-section of the influent and effluent to ensure representative sampling. The

number of discrete samples of influent and effluent was chosen appropriately to provide a

reasonable estimate PM concentrations. PM was measured by two methods; gravimetrically as

the sum of the sediment (> 75 μm), settleable (~25 to 75 mm) and suspended (1 to ~ 25 μm)

fractions and utilizing laser diffraction for particle volume % for each particle size; generating

PSDs. The total PM was obtained as a sum of the mass of sediment, settleable and suspended

PM fractions which also generated the suspended sediment concentration (SSC). The

methodology is described elsewhere (ASTM 1993, ASTM 1998, APHA 1998, Kim and

Sansalone 2008a, Sansalone and Kim 2008b). PSDs of the influent and effluent were measured

using a laser diffraction analysis and Mie scattering theory (Finlayson-Pitts et al 2000). The

157

particle size range was reported from 0.02 μm to 2000 μm, in 100 increments and was applicable

to PM concentration range of 1 to 1000 mg/L with a resolution < 1 mg/L. The contribution of

coarser particles to the temporal influent PSD was calculated from the separated VCF particles

and the temporal effluent PSD.

The PSD measured for each influent and effluent discrete sample by laser diffraction.

The relative percent difference (RPD) is used to compare model and experimental results and is

follows. For the purpose of QA/QC, a mass balance error constraint of 10% was imposed on PM

data.

Mass Balance Error (MBE) = %10100)(

±≤×⎥⎦

⎤⎢⎣

⎡ +−

i

eVCFi

MMMM

(6-7)

In this expression, iM is the influent mass of PM, VCFM is the mass of PM captured by the

VCF and eM is the effluent mass of PM, computed from the measured effluent PM across the

total treated volume. All gravimetric measurements were carried out on a dry mass basis. The

event mean concentration (EMC) for PM over the time period of a rainfall-runoff event is

typically used as an indicator of overall water quality and to calculate percent removal for

stormwater unit operations (Huber 1993).

∫

∫== t

t

tq

dttqtc

VMEMC

0

0

)(

)()( (6-8)

In this expression, M is the total effluent mass load over the entire duration of the test, V is

the total volume of flow over the entire duration of the test, C is the flow weighted mean

concentration, c (t) is the time variable particulate-bound concentration, q (t) is the time variable

flow rate.

158

Multiphase flow modeling methodology

While the geometric symmetry of a single RCF suggested a simplified two dimensional

model, the hydrodynamics and particle dynamics vary as a function of x, y and z spatial

coordinates, as does the physical clustering of five RCF in parallel. As a result, a three

dimensional (3-D) approach was required. The fluid flow equations were solved based on

fundamental laws of conservation of mass, momentum and energy. The Navier-Stokes equations

were solved using numerical techniques of computational fluid dynamics. Versteeg et al (1995)

define the general conservation equation for any fluid property Ф for a control volume

)( zyxV ∂∂∂= is as follows.

Φ+ΦΓ=Φ+∂

Φ∂ Sgraddivudivt

)()()( ρρ (6-9)

In this expression, u is the fluid velocity, Γ is the diffusion coefficient, and ΦS is the

source/sink term.

zw

yv

xuudiv

∂∂

+∂∂

+∂∂

=)( (6-10)

In this expression, u, v and w are the velocity vectors in the x, y and z directions

respectively. The momentum equations for three dimensions are obtained by incorporating u, v

and w into equation 6-9.

X-momentum: MxSugraddivxpuudiv

tu

++∂∂

−=+∂

∂ ))(()()( μρρ (6-11)

Y-momentum: MySvgraddivypuvdiv

tv

++∂∂

−=+∂

∂ ))(()()( μρρ (6-12)

Z-momentum: MzSwgraddivypuwdiv

tw

++∂∂

−=+∂

∂ ))(()()( μρρ (6-13)

159

In the above expressions, p is the pressure, μ is the viscosity, and MzMyMx SSS ,, 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.

The RCF was modeled by adding a momentum sink term to the flow equations. This sink

contributes to the pressure gradient in the porous computational cell, creating a pressure drop

that is proportional to the fluid velocity in a computational cell. The source term is composed of

two parts: a viscous loss term and an inertial loss term.

⎟⎟⎠

⎞⎜⎜⎝

⎛+−= ∑ ∑

= =

3

1

3

1 21

j jjijjiji vvCvDS ρμ (6-14)

In this expression, iS is the source term for the i th momentum equation, α is

permeability, iC2 is the inertial resistance factor, iv is the velocity in the i th momentum equation,

v is the velocity in a computational cell. For isotropic porous media the above equation can be

expressed in the following form.

⎟⎠⎞

⎜⎝⎛ +−= 2

2 21 vCvSi ρ

αμ (6-15)

In this expression, α is the permeability [L2] and C2 is the inertial resistance coefficient.

The dominant flow regime is laminar to transitional in the RCF. The Reynolds number for

flow in the media was calculated as follows.

μηρ)1(

Re−

= smmedia

vd (6-16)

In this expression, md is media particle diameter, μ is the fluid viscosity, η is the porosity

of the packed bed (not media porosity), sv is the superficial velocity through the packed bed

and ρ is fluid density. The Reynolds numbers were found to range from approximately 5 to 30.

160

Previous studies have shown that the standard k-ε model (Launder and Spalding 1974) for

turbulent flow has worked well in both micro and macroscopic approaches to solving flow in

porous media (Antohe et al 1997). The transport equations of the standard k-ε model are

expressed as follows.

kbkjk

t

ji

iSGG

xk

xku

xk

t+−++

⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

⎟⎟⎠

⎞⎜⎜⎝

⎛+

∂∂

=∂∂

+∂∂ ρε

σμμρρ )()( (6-17)

For ε:

εεεεε

ερεεσμμρερε S

kCGCG

kC

xxu

xt bkj

t

ji

i+−++

⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

⎟⎟⎠

⎞⎜⎜⎝

⎛+

∂∂

=∂∂

+∂∂ 2

231 )()()( (6-18)

In equations 6-17 and 6-18, kG represents generation of k due to the mean velocity

gradients; bG is generation of k due to buoyancy; ε1C , ε2C and ε3C are constants ; kσ and εσ

are the turbulent Prandtl numbers for k andε , respectively; kS and εS are user-defined source

terms. The constants were determined by Launder and Spaulding (1974). The values

of ε1C , ε2C , ε3C , kσ and εσ used in the model were 1.44, 1.92, 0.09, 1.0 and 1.3 respectively

(Launder et al. 1974). The free surface of the flow was modeled as a shear-free boundary.

Porous media may be modeled with a macroscopic or a microscopic approach (Ranade

2002). In the latter approach, the micro-scale pore structure is taken into account. A microscopic

approach demands tedious computational resources and is typically used as a benchmark

problem, as opposed to modeling practical systems. On the contrary, the macroscopic or lumped

approach considers the entire filter bed as isotropic or non-isotropic porous media. This approach

is characterized by pertinent lumped parameters such as the effective porosity (η), inertial and

viscous resistance coefficients. The geometry of the media can be accounted for by utilizing bed

porosity distributions, such as Mueller’s distribution (Mueller 1992), or by assuming

161

homogeneous distribution of pores between media. With uniform pluviation in the RCF and

uniform size gradation for the media a uniform pore distribution was assumed in this model.

Flow in porous media has been traditionally modeled analytically by comparison to

pipe/conduit flow by specifying analogous parameters such as the hydraulic diameter and

roughness coefficient. Laminar flow (Re < 10) through porous media has been successfully

modeled by applying Darcian-type equations. Models such as Blake-Plummer and Carman-

Kozeny equations were developed to account to transitional flow regimes. These models were

extended by Ergun (1952) to account for turbulent flow. The Ergun equation for packed beds

applies to flow regimes from laminar to turbulent and is expressed by the following equation.

233

2

2

)1(75.1)1(150s

ms

m

vd

vdL

pη

ηρη

ημ −+

−=

Δ (6-19)

In this expression, pΔ is the pressure drop across the media, L is the length of the packed

bed, μ is the fluid viscosity, md is media particle diameter, η is the total porosity of the packed

bed, v is the superficial velocity through the packed bed and ρ is fluid density. Comparing

equations 9 and 14, α and C2 can be expressed as follows.

2

32

)1(150 ηηα−

= md (6-20)

32)1(5.3

ηη−

=md

C (6-21)

Modeling the particulate phase

Multiphase flows are modeled with an Eulerian-Eulerian approach or an Eulerian-

Lagrangian approach (van Wachem et al. 2003) depending on the extent of coupling between

phases. Elgobashi (1991) proposed a regime map for appropriating the degree of inter-phase

coupling, by analyzing length and time scales. Subsequently, it was determined that a Lagrangian

162

approach to tracking the secondary phase is most appropriate for flows with a low influent

particulate volume fraction which is the case in this study (PVF < 3.0 %).

The transient flow field was modeled utilizing the Eulerian approach, for each time step.

Subsequently, the influent particles were injected at times that correspond to influent sampling

times during storm data collection.

The Eulerian-Lagrangian approach was chosen to model the behavior of particles in the

computational domain of the VCF. In this approach, the flow field was solved using the Eulerian

approach. Following this, particles were tracked using a Lagrangian Discrete Phase Model

(DPM). The DPM is derived from force balances based on classical Newton’s (Turbulent and

transitional regimes) and Stokes (Laminar regimes) laws describing particle motion, and is

summarized by the following equation.

xp

pxpD

p Fg

uuFdt

du+

−+−=

ρρρ )(

)( (6-22)

dF 24Re18

2pD

pp

Cdρμ

= (6-23)

232

1 ReRe ppD

aaaC ++= (6-24)

μρ uud pp

p

−≡Re (6-25)

In equations 6-22 through 6-25, u is the fluid velocity, pu is the particle velocity, ρ is the

fluid density, pρ is the particle density, pd is particle diameter, μ is the viscosity, 321 ,, aaa are

empirical constants that apply to smooth spherical particles as a function of the Reynolds number

(Morsi et al., 1972) and pRe is the particle Reynolds number.

163

Particle trajectories are obtained by integration of equation 6-22. For this study, particles

of consistent morphology were injected across the entire flow cross-section immediately above

the inlet to the VCF to obtain comparable particle trajectories across varied flow rates, by

reducing uncertainty in initial spatial location. Particles were defined as silica particles of

diameters associated with the sieves utilized and a measured specific gravity of 2.65 as

determined by helium pycnometry (Sansalone et al 1998). The cumulative gamma distribution

function described in the previous section was used to model the relative mass fractions as a

function of particle diameter. Particles were tracked for a specific length for each flow rate,

based on hydraulic residence times calculated by injecting neutrally buoyant submicron ‘tracer’

particles. Particles that remained in the VCF after integrating over the specified length were

considered to have been separated by the VCF. Particle removal was thus defined by the

following equation.

100*I

HS

NNp =Δ (6-26)

HSN is the number of particles that remain in the VCF, and IN is the number of particles

injected at the inlet.

Discretization and Solution Schemes

The computational domain was discretized using an unstructured mesh with tetrahedral

elements, generated by TGrid (Qi et al. 2006). The volume of the VCF was divided into total of

5.18 million cells, after ensuring grid convergence. Numerical solutions were obtained using a

Finite Volume Method (FVM) and a cell-centered scheme used for discretization. A Second-

Order Upwind Scheme (Barth et al. 1989) was used solve for flow parameters. The spatial

discretization is shown in Figure 6-4 for the VCF.

164

Time Discretization

The flow data were measured for discrete time intervals. In order to test the sensitivity of

the solution to smaller time steps, continuous functions were utilized to model the measured flow

data. The runoff hydrograph was modeled by splitting the hydrograph into piecewise continuous

segments which allowed for accurate curve fitting.

An important consideration to make while choosing a time discretization approach was to

account for the high variability between the magnitudes of influent flow as a function of time.

In a given storm event, the flow rates can change multiple times, and this change can be

rapid, or gradual in time. In light of this, two time discretization approaches were tested.

The first approach was to use a first-order fully implicit scheme for time discretization.

The fully implicit scheme is unconditionally stable and is suggested for transient operations

which do not involve chemical reactions (Ranade 2001). The second approach was to use an

advanced adaptive time stepping approach, which involved modification of the time step based

on the truncation error of the time integration scheme, estimated from a predictor-corrector type

of algorithm (Gresho et al 1980). At each time step, a predicted solution is obtained using an

explicit method , such as the Adams-Bashforth method (Ferziger et al 2002), and this is used as

the initial condition for the next time step. The correction is computed using the implicit

formulation, and the truncation error is the difference between the predicted and the corrected

solutions. A preset truncation error tolerance is chosen, and is used as the constraint within

which the time step can be changed.

The transient SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm

(Patankar 1980) accounted for pressure-velocity coupling. The criterion for iterative

convergence for the flow field solution was set at 1x10-3 (Ranade 2002).

165

Results and Discussion

Event-Based Hydrologic Loadings and Response

Five consecutive rainfall-runoff events loading the VCF were captured, monitored,

analyzed and the results modeled. The event hyetographs and corresponding hydrographs are

shown in Figure 6-5. With the exception of the very low intensity event of 06 May 2006 with an

initial lag time of 39 minutes there was a rapid runoff response to rainfall loadings characterized

by an initial lag time of less than 3 minutes for all other events. These results are similar to

previous results reported for this watershed (Sansalone et al. 2005). Irrespective of rainfall

intensity, the runoff response (the hydraulic loading to the VCF) was highly unsteady for all

events and for two events multiple distinct hydrograph peaks were generated. Event runoff

durations loading the VCF ranged from 50 to 170 minutes. All volume balance errors (VBE)

were in the range of ± 10% except for the 06 May event which only generated 495 L (14.7%

VBE) of runoff with flow depth monitoring data approaching the lower detection limit in the

Parshall flume. Traffic is the dominant anthropogenic activity in the watershed that influenced

the rainfall-runoff relationship and PM loadings to the VCF. Therefore traffic was measured as

vehicles during storm (vds) to provide an index for the influence on the rainfall-runoff

relationship and also PM loadings (as SSC) (Sansalone et al. 1998, Sansalone et al. 2005). The

vds values ranged from 4429 for the 21 April 2006 event to 8938 for the 29 April 2006 event.

Traffic was also the dominant source of abstractions during a rainfall-event causing deflection of

rainfall and re-entrainment and deflection of the runoff. The initial watershed losses accounted

for approximately 0.5 mm of rainfall and the rainfall-runoff relationship for the watershed

required rainfall depths to be greater than 1.0 mm to provide sufficient runoff volume for initial

sampling.

166

Filter media cartridge head loss modeling results

From the pressure transducer data collected for inflow, outflow, inside of cartridge, outside

of cartridge and the effluent drop box a complete hydraulic profile across the VCF treatment

system during each event is constructed. As an in-situ unit operation the VCF is not backwashed

by intent during the period of monitoring. A primary interest is the head loss across the filter

cartridges as a function of flow rate and surface loading rate for each rainfall-runoff event.

These results are summarized in Figure 6-6 for the five events illustrated. Head loss values

remained below 200 mm during all events and the head loss profiles generally mimicked the

hydrographs. Measured and modeled head loss profiles were similar with a RPD generally less

than 15%. As shown in Figure 6-7, the unsteady event mean head loss is nominal; less than 40

mm and generally following a linear trend as a function of event mean surface loading rate

(SLR). The unsteady event mean head loss is compared to head loss results for steady flow rate

conditions of this same system under pilot scale testing. The steady flow rate head loss results

are consistently lower than the unsteady event head loss below 150 L/min-m2, but appear to

converge beyond this level.

With the aid of the calibrated and validated CFD model, pressure distributions represented

as head loss along the radial and vertical directions were computed and are illustrated in Plots

(A) and (B) respectively of Figure 6-8. The head loss varies inversely with distance from the

center of the RCF as illustrated in Plot (A). This variation displays a linear trend with the slope

increasing as a function of flow rate. The overall head loss across the entire radial distance is

equal in magnitude to the overall modeled head loss.

Plot (B) illustrates pressure distributions along a line parallel to the z-axis and located at

the geometric mid-point of the RCF in the radial direction, at one-half the annular thickness of

the media section of the cartridge (r/2). A check was performed for conservation of energy

167

across the entire RCF using Bernoulli’s theorem, with local velocities obtained from the CFD

model. This check supported the validity of the modeled distributions. There is a clear parabolic

drawdown towards the center of the cartridge, proportional to increasing peak flow rates.

This is in contrast with steady flow model results for a single radial cartridge filter (RCF),

discussed in detail in Chapter 4. Whereas for a steady state simulation, beyond a flow rate of

45.4 L/min, there is a parabolic profile for pressure distributions as a function of depth, with the

minimum pressure at the top and bottom ends (no-flow boundaries) of the RCF. The center

effluent outlet of the RCF never flowed full and remained open to the atmosphere. Therefore, the

RCF configuration was analogous to an inverted well, with flow pumped out in the direction of

gravitational force. At the top surface, the parabolic profile of the drawdown is due the head-loss

created by the porous media. At the bottom of the RCF, there is also a pressure differential from

inside to outside of the cartridge. This is in line with typical drawdown in pumped wells as

expressed by the Theis equation (Freeze et al. 1979).

However, in the case of the VCF, the pressure differential from the inside to the outside of

the cartridge is not severe, as the effluent, which is open to the atmosphere, is located in the far-

field, sufficiently distant to eliminate any drawdown at the bottom of the cartridge. An important

result was that the head loss for each individual cartridge remained similar across the entire

duration of each individual storm event. This clearly indicates that irrespective of the asymmetric

cartridge layout in the tank, the tank does provide uniform hydraulic loading for each cartridge.

Separation of particulate matter modeling results

The varying hydrology resulted in a distinct particle transport signature for each storm..

Among the five storms analyzed, the VCF was successful at separating a large portion of the

influent PM. The overall particle separation is most effective for sediment sized particles.

However, even for the finer settleable and suspended particles, the VCF proved effective in

168

separating the influent PM. The model was able to accurately predict the overall PM separation

across each individual storm event, with the RPD remaining below 15%.

Figure 6-9 and figure 6-10 provide a comparison of measured and modeled temporal

effluent mass loads and concentrations respectively. Bertrand et al. (1998) classified rainfall-

runoff events into mass-limited and flow-limited events based on temporal pollutant mass

delivery. For mass-limited events, mass delivery is skewed toward the initial portion of the

event, while mass delivery tends to follow the hydrograph for flow-limited events. The five

storms accommodate both mass and flow-limited kinds of particle transport. For the 21 April

2006 event, the effluent mass load, and SSC remained relatively invariant as a function of time,

irrespective of the change in influent SSC, suggesting that PM separation mechanisms in the

VCF are independent of the influent concentration. This behavior is noticed for all but the 29

April 2006 and 06 May 2006 events, suggesting the possible difference in influent and effluent

PSDs. Figure 6-10 is a plot of measured and modeled effluent d50m as function of time. In this

figure, we notice that for the 29 April 2006 storm, the particle size distribution in the effluent

changes as a function of time. This can be attributed to the complex multiple-peaked hydrograph,

with a very high flow rate (25.3 L/s) and an influent volume of almost 50,000 L . The 06 May

2006 storm on the other hand was a very low intensity storm (Qmax=0.3 L/s), and delivered

approximately 500 L of water. These two storms represent two extremes, both in flow rates and

volume of influent delivered. These results suggest that the influent concentration is truly a

function of the particle size distribution transported by the storm, wherein the higher flow rates

transport a PSD that is inclusive of sediment, settleable and suspended fractions, while low flow

rates mainly deliver suspended fractions. The CFD model is able to accurately predict the

169

temporal variation of effluent mass, effluent concentration and effluent d50m across varying

influent flows and particle concentrations, for both mass and flow-limited events.

Conclusions

In-situ control of hydrology and PM are major considerations for many watersheds and

receiving water systems. Volumetric clarification-type BMPs that can provide storage through

detention/retention operational management are more frequently incorporating media filtration as

a unit operation. These systems can provide some degree of volumetric and peak flow

attenuation, provide preliminary or primary clarification of PM; and with filtration provide

secondary treatment to separate PM and nutrients associated with PM.

This study examined the behavior of a volumetric clarifying filter (VCF) loaded by a

paved source area watershed dominated by transportation, in which some fraction of the influent

runoff is stored in the VCF between events. In this study five source area rainfall-runoff events

are monitored and treated real time; and the role of runoff storage and filtration on the separation

of PM is examined and modeled. Despite the significant variability between the five events,

delivery of PM mass (as SSC) generally resulted in a mass-limited (first-order) transport based

on runoff volume for this source area watershed.

In this study the VCF is operated in an undrained condition; where some fraction of runoff

from the previous event remains as stored volume until mixed with influent from a new event;

typical of many below-grade in-situ BMPs. As a result, hydrologic attenuation by the VCF is

muted. Mean head loss across the filters of the VCF is low (< 40 mm), due to the coarse uniform

size gradation of the engineered media. Event-based mean head loss increases nearly linearly

with the corresponding event mean surface loading rate for the VCF. The temporal variation of

filter head loss across an event can be clearly discerned as a function of flow rate. Since there is

no backwashing of the VCF system during the study period and any increase in head loss is not

170

discernable in comparison to head loss due to flow rate variations. This result suggests that the

vertical orientation of the radial-flow cartridges and utilization of the coarse uniform media did

not generate a significant “schmutzdecke” on the vertical inflow surfaces of the filter. Despite

the media remaining in a moist condition (but above the storage water surface) for the entire

study period results do not indicate significant biological clogging. Results indicate that the

VCF is capable of significant load reductions of PM as SSC with effluent concentrations at or

below 30 mg/L on an event basis. For both head loss and PM treatment results, the numerical

model was capable of reproducing the behavior of this VCF system to highly variable and

unsteady flow during a series of five consecutive events.

171

Figure 6-1 Plan view of experimental site and Volumetric Clarifying Filter (VCF) system, CB

represents catch basin and 304.8 in the equation represents unit conversion (mm to ft) factor.

Data logger

5.1

cm

Pars

hall

Flum

e

Watershed •PCC pavement •1088 m2 (2 x 544 m2) •2% surface slope •ADT=142,000 (east and west)

Tee

10.2 cm Φ PVC pipe from east CB @ 10 % slope

Drop box

6 % 31 cm Φ sloped open PVC trough under expansion joint

10.2 cm Φ PVC pipe from west CB @ 10 % slope

15 cm Φ PVC pipe @ 6 % slope

212.

1 cm

45

.7 c

m

Eff

luen

t

1

2

Influent 9

3

4 5 6 7 8 10 11

116.8 cm

1. Influent box 2. Radial flow cartridge 3. Baffle 4. Vault drainage pipe 5. Float valve 6. Effluent drop box

7 Orifice 8 Effluent pipe 9 Influent delivery pipe

10. Effluent V-notch weir 11. Effluent drainage pipe

5.1 cm Parshall flume

Dis

char

ge (L

/s)

02468

10

6548.1

8.30407.31 ⎟

⎠⎞

⎜⎝⎛×= XY

60o V-notch weir

Stage (mm)0.0 0.1 0.2 0.3 0.4 0.5

Dis

char

ge (L

/s)

02468

10

0 30 60 90 120 150

8619.2

8.30462.74 ⎟

⎠⎞

⎜⎝⎛×= XY

VCF Stage-Storage

0 300 600 900 120

Stor

age

(L)

0

500

1000

1500

2000

2500

Voverflow= 2180 L

Stage (mm)

172

H1 (Parshall flume pressure head) mm H2 (Outside cartridge pressure head) mm H3 (Inside cartridge pressure head) mm H4 (Outlet box pressure head) mm H5 (V-notch pressure head) mm Note (1) & (5) measured by CS420-L Pressure Transducer (6.9 kPa) (2) & (3) measured by CS420-L Pressure Transducers (17.2 kPa) (4) measured by CS420-L Pressure Transducers (34.5 kPa) Real-time Data acquisition: CR1000 Datalogger (Cambell Scientific) Media size (d50) : 3.56 ± 0.25 mm Media hydraulic conductivity (k) : 1.44 ± 0.17 cm/s Media macro porosity (ηm) : 0.37 ± 0.018

Figure 6-2 Location of the pressure transducers installed in the Volumetric Clarifying Filter

(VCF) system. d50, k and ηm represent the median size, hydraulic conductivity and macro porosity of the media (AOCM)P used in this study.

393.7 mm

H5 184 mm

H4 177.8m

558.8 mm

H3 H2

H1

Data logger

Parshall flume

System vault Cartridge center

drainage pipe Effluent

box V-notch weir

173

Figure 6-3 Measured media size expressed as a Gaussian frequency histogram. The average

media size was found to be 3.56 ±0.8 mm. A three parameter Gaussian distribution was used to model the data; a = 5.283, b= 0.6392. x0=3.435.

dp (mm)

0 1 2 3 4 5 6 7

Nor

mal

ized

Fre

quen

cy

0

2

4

6

8

R2=0.93

2))(5.0( 0

* bxx

eay−

−=

174

Figure 6-4 Profile and plan views of a section of the computational grid of the VCF system.

Y

Z

Y

X

175

Figure 6-5 Hydrographs and hyetographs for 5 real-time rainfall runoff events

I/Im

ax0.0

0.5

Q/Q

max

0.00.20.40.60.81.0

Imax = 91.4 mm/hr Qmax = 13.3 L sec-1

21 April 2006 tmax = 70 min

I/Im

ax

0.0

0.5

Q/Q

max

0.00.20.40.60.81.0

Imax = 259.1 mm/hr Qmax = 25.3 L sec-1

29 April 2005 tmax = 170 min

Imax = 1.0 mm/hr Qmax = 0.3 L sec-1

I/Im

ax

0.0

0.5

Q/Q

max

0.00.20.40.60.81.0

06 May 2006tmax = 92 min

I/Im

ax

0.0

0.5

t/tmax

0.0 0.2 0.4 0.6 0.8 1.0

Q/Q

max

0.00.20.40.60.81.0

Imax = 61.0 mm/hr Qmax = 9.1 L sec-1

07 May 2006 tmax = 68 min

I/Im

ax

0.0

0.5

Imax = 30.5 mm/hr Qmax = 6.5 L sec-1

27 May 2006 tmax = 31 min

t/tmax

0.0 0.2 0.4 0.6 0.8 1.0

Q/Q

max

0.00.20.40.60.81.0

27 May 2006tmax = 50 min

176

Figure 6-6 Measured vs. modeled cartridge head loss profiles as a function of normalized time. RPD is the relative percent difference between measured and modeled data.

27 May 2006

t/tmax0.0 0.2 0.4 0.6 0.8 1.0

Q/Q

max

0.00

0.25

0.50

0.75

1.00

Hea

d lo

ss (m

m)

0

50

100

150

200

HydrographMeasuredModeled

RPD = 15. 4 %

21 April 2006H

ead

loss

(mm

)

0

50

100

150

200RPD = 12. 3 %

29 April 2006

Q/Q

max

0.00

0.25

0.50

0.75

1.00RPD = 11. 3 %

07 May 2006

t/tmax.0 0.2 0.4 0.6 0.8 1.0

Q/Q

max

0.00

0.25

0.50

0.75

1.00RPD = 13. 2 %

06 May 2006

Hea

d lo

ss (m

m)

0

50

100

150

200RPD = 10. 4 %

177

Event mean SLR (L/m2-min)0 50 100 150 200

Mea

sure

d m

ean

head

loss

(mm

)

0

20

40

60

80

100Pilot-scale steady flow testingUnsteady runoff flows in VCF

Figure 6-7 Comparison of head loss as a function of surface loading rate (SLR) for steady flow

testing and for unsteady event flows for the same radial flow cartridges. Transient flow SLR and head loss is determined corresponding to the mean flow rate of real-time storm events and arranged in an ascending fashion corresponding to 6 May 2006 (lowest SLR), 21 April 2006, 27 May 2006, 7 May 2006 and 29 April 2006 event (highest SLR), respectively.

178

Figure 6-8 Head loss (ΔH) and pressure distributions in the VCF. Plot (A) illustrates predictions

of head-loss across the VCF from the CFD model. Plot (B) illustrates predictions of pressure distributions along the vertical (Z) axis of the VCF. S1, S2, S3, S4, and S5 represent storms corresponding to 21 April 2006, 27 April 2006, 06 May 2006, 07 May 2006 and 27 May 2006 storms respectively. Qp is the peak flow rate of the storms. The order of flow rates in (B) is the same as in Plot (A); (r, φ) and (0, φ) represent the radius and center of the VCF respectively, in radial coordinates; (r/2, 0, zn) and (r/2, 0, zo) represent the top and the bottom of the mid-point of the RCF respectively, in Cartesian coordinates.

Gage pressure (kPa)

Radial distance (mm)

0 50 100 150 200

Δ H

(mm

)

0

10

20

30

40

50(r, φ) (0, φ) (r/2, 0, zn)

Cartridge depth (m

m)

S2

S4 S5

S1

S3

Qp+

(A) (B)

0 0.1

0

0.2 0.3 0.4 0.5 0.6

(r/2, 0, z0)

Qp+

500

400

300

200

100

179

Figure 6-9 Comparison of measured and modeled temporal variation in effluent mass. Error bars

represent standard deviation and are contained within the symbols.

29 April 2006

Q/Q

max

0.0

0.2

0.4

0.6

0.8

1.0Measured Mmax=387 g

Modeled Mmax=360 g

21 April 2006

0 0 0 2 0 4 0 6 0 8 1 0

Efflu

ent M

/Mm

ax

0.0

0.2

0.4

0.6

0.8

1.0

HydrographModeled effluentMeasured effluent

Measured Mmax=14 g

Modeled Mmax=12 g

06 May 2006

Efflu

ent M

/Mm

ax

0.0

0.2

0.4

0.6

0.8

1.0 Measured Mmax= 14.8 gModeled Mmax=16.7 g

07 May 2006

Q/Q

max

0.00

0.25

0.50

0.75

1.00Measured Mmax= 35 g

Modeled Mmax= 32 g

27 May 2006

t/tmax

0.0 0.2 0.4 0.6 0.8 1.0

Q/Q

max

0.0

0.2

0.4

0.6

0.8

1.0

Efflu

ent M

/Mm

ax

0.0

0.2

0.4

0.6

0.8

1.0 Measured Mmax=29 g

Modeled Mmax=26 g

180

Figure 6-10 Measured versus modeled effluent concentrations as function of storm elapsed time.

RPD is relative percent difference between measured and modeled data.

29 April 2006

Q/Q

max

0.00

0.25

0.50

0.75

1.00tmax=170 min

Qmax=25.3 L/s

RPD = 10.5 %

06 May 2006

log 10

Efflu

ent S

SC [m

g/L]

10

100

1000

tmax=92 min

Qmax=0.3 L/s

RPD = -15.2 %

07 May 2006

t/tmax

0.0 0.2 0.4 0.6 0.8 1.0

Q/Q

max

0.00

0.25

0.50

0.75

1.00tmax= 68 minQmax= 9.1 L/sRPD = 9.1 %

27 May 2006

t/tmax

0.0 0.2 0.4 0.6 0.8 1.0

Q/Q

max

0.00

0.25

0.50

0.75

1.00

log 10

Efflu

ent S

SC [m

g/L]

10

100

1000tmax=50 min

Qmax=6.5 L/s

RPD = 14.4 %

21 April 2006

0 0 0 2 0 4 0 6 0 8 1 0

log 10

Efflu

ent S

SC [m

g/L]

10

100

1000

HydrographModeled effluentMeasured effluentMeasured influent

tmax=70 minQmax=13.3 L/s

RPD = 8.0 %

181

Figure 6-11 Measured vs. modeled effluent d50 as a function of time for 5 storm events

21 April 2006Ef

fluen

t d50

m ( μ

m)

0

100

200

300

400

500tmax=70 min

Qmax=13.3 L/s29 April 2006

Q/Q

max

0.0

0.2

0.4

0.6

0.8

1.0tmax=170 minQmax=25.3 L/s

06 May 2006

Efflu

ent d

50m

( μm

)

0

100

200

300

400

500tmax=92 minQmax=0.3 L/s

07 May 2006

t/tmax

0.0 0.2 0.4 0.6 0.8 1.0

Q/Q

max

0.0

0.2

0.4

0.6

0.8

1.0tmax=68 minQmax=9.1 L/s

27 May 2006

t/tmax

0.0 0.2 0.4 0.6 0.8 1.0

Q/Q

max

0.0

0.2

0.4

0.6

0.8

1.0

Efflu

ent d

50m

( μm

)

0

100

200

300

400

500

HydrographMeasuredModeled

tmax=50 minQmax=0.3 L/s

182

CHAPTER 7 GLOBAL CONCLUSIONS

This dissertation focused on a coupled experimental and numerical approach to

characterize particulate matter separation by stormwater unit operations and processes for steady

and transient hydrologic, hydraulic and pollutant loadings. A screened hydrodynamic separator

and a radial cartridge filter were the two UOPs that were tested.

The CFD model was validated with experimental data across a range of flow rates and particle

size distributions, PSDs. Predictions from the numerical model were found to lie within 10 % of

the measured data. Grid independence for the numerical model was demonstrated. This study

demonstrated that a CFD model of the behavior of an HS for typical stormwater flow rates,

particle size gradations and levels of SSC could reproduce the PSD and SSC response of a

screened HS. Post-processing the CFD predictions provided an in-depth insight into the

mechanistic behavior of the screened HS by means of three dimensional hydraulic profiles and

particle trajectories. Results demonstrate that while coarse particles are separated, settleable and

suspended particles are largely eluted from the HS, even under clean sump and conditions of this

study. The ability of the CFD model to reproduce treatment results across a range of flow rates

and PSDs suggest that the calibrated and validated model can serves as a foundation upon which

design alternatives can be proposed. A calibrated/validated CFD-based iterative approach to

design of this HS as a preliminary unit operation has the potential to provide reduced prototyping

costs with improved performance, as a result of carefully designed experimental matrices,

focused on meeting coarse particulate control requirements for downstream treatment units.

Particulate matter separation by a screened hydrodynamic separator for transient

hydraulic and particulate loads observed in a real-time rainfall-runoff event was modeled by the

application of the standard k-ε turbulence model and a Lagrangian discrete phase model. Four

183

discrete rainfall-runoff events were modeled individually and the modeled results agreed very

well with the measured data (Absolute RPD <10%). The CFD model was applicable across the

entire range of flow rate and influent PSD variations and was able to accurately model both

mass-limited and flow limited rainfall-runoff events. Modeling the unsteady flow across the

entire duration of the storm was tested against using a single design flow rate and the event mean

concentration of PM for each event. It was observed that the PM separation behavior of the UOP

varies significantly using the mean, median and peak influent flow rates. Accurate modeling

calls for including the flow variations across the entire treated volume of runoff.

This study demonstrated that a CFD model could reproduce the fate of a hetero-disperse

PSD as a function of particle size for mass, concentration and head loss behavior of a RCF for

typical runoff loading rates, PSDs, and suspended sediment concentration (SSC) levels. A

steady state solution was obtained for flow through the RCF and clean bed conditions were

implemented in the experiment and in the model. CFD predictions provided an in-depth insight

into the mechanistic behavior of the RCF by means of three dimensional hydraulic profiles,

particle trajectories and radial and axial pressure distributions.

The ability of the CFD model to reproduce treatment results across a range of flow rates

and PSDs suggest that the calibrated/validated model can serve as a foundation upon which

design alternatives can be proposed. A calibrated/validated CFD-based iterative approach to

design of this RCF as a unit operation has the potential to provide reduced prototyping costs with

improved performance, as a result of carefully designed experimental matrices, focused on PM

control requirements for effluent discharges.

This study combined PSD measurements using laser diffraction, media porosimetry,

image analysis and material balances as well as more conventional gravimetric SSC

184

measurements of PM and pressure sensor measurement. Such data are needed in the calibration

and validation process for a defensible porous media CFD model of a RCF.

Overall, a CFD approach to modeling the pollutant removal characteristics of UOPs is a

state-of-the-art approach to reducing the uncertainty that results from assuming ideal conditions,

thus providing a more effective method for pollution control.

185

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BIOGRAPHICAL SKETCH

Subbu-Srikanth Pathapati received his Bachelor’s degree in electrical and electronics

engineering from the University of Madras, Chennai, India in 2001 and came to United States of

America in Spring 2003 to pursue a graduate degree Sri Pathapati will receive the degree of

Doctor of Philosophy in environmental engineering from the University of Florida in May 2008.

His doctoral research was focused on experimentation and numerical modeling of urban

stormwater particulate matter control unit operations and processes. He worked under the

guidance of Dr. John J. Sansalone in the Department of Environmental Engineering and

Sciences.