An Investigation of Boundary Shear Stress and Pollutant Detachment From an Impervious Surface During...

An Investigation of Boundary Shear Stress and Pollutant Detachment

From an Impervious Surface During Simulated Urban Storm Runoff

C.P. Richardson1 and G.A. Tripp2

1Associate Professor of Environmental Engineering, Department of Civil and Environmental Engineering, New Mexico Tech, Socorro, New Mexico 87801 2Graduate Research Assistant, Department of Mineral Engineering, New Mexico Tech, Socorro, New Mexico 87801

Significance of the Problem

Urban Stormwater RunoffUrban Stormwater Runoff Large areas of impervious or semi-Large areas of impervious or semi-

impervious surfacesimpervious surfaces Major non-point source of pollutants Major non-point source of pollutants

previously deposited during dry weatherpreviously deposited during dry weather Runoff quantity typically high volume Runoff quantity typically high volume

and relatively short durationand relatively short duration

Significance of the Problem

National Urban Runoff Program (19 cities)National Urban Runoff Program (19 cities) 33 % lake contamination from runoff33 % lake contamination from runoff 10 % river contamination from runoff10 % river contamination from runoff Several priority pollutants found in at Several priority pollutants found in at

least 10 % of samples collectedleast 10 % of samples collectede.g. #121 phenanthrene; #30 lead; #51 e.g. #121 phenanthrene; #30 lead; #51

chloroform; #5 lindane; #23 arsenicchloroform; #5 lindane; #23 arsenic

Modeling Background

Stormwater Water Quality ModelsStormwater Water Quality Models Two-stage processTwo-stage process

Pollutant accumulation on catchment Pollutant accumulation on catchment surfaces during dry weather periodssurfaces during dry weather periods

Pollutant washoff during rainfall and Pollutant washoff during rainfall and subsequent runoff.subsequent runoff.

Modeling Background (cont’d)

Pollutant Washoff is the Critical StagePollutant Washoff is the Critical Stage Transport limited process governed by Transport limited process governed by

rainfall and runoff characteristicsrainfall and runoff characteristicsDependent upon overland flow shear Dependent upon overland flow shear

stress (Nakamura, 1984)stress (Nakamura, 1984)Dependent upon raindrop and runoff Dependent upon raindrop and runoff

energies (Vaze and Chiew, 2003) energies (Vaze and Chiew, 2003)


Typical Modeling ApproachTypical Modeling Approach Estimate pollutant washoff empirically Estimate pollutant washoff empirically

by a first-order relationship (exponential)by a first-order relationship (exponential)Washoff rate depends linearly on the Washoff rate depends linearly on the

available accumulated pollutant mass, available accumulated pollutant mass, on the rainfall intensity, and/or the on the rainfall intensity, and/or the overland flow runoff rate (Alley, 1981; overland flow runoff rate (Alley, 1981; Millar, 1999)Millar, 1999)


Storm Water Management Model (SWMM)Storm Water Management Model (SWMM) Algorithm uses exponential relationship Algorithm uses exponential relationship

between pollutant washoff and runoff between pollutant washoff and runoff volume (Huber and Dickinson, 1988)volume (Huber and Dickinson, 1988)This type of model lacks a physical This type of model lacks a physical

basis for pollutant detachment from the basis for pollutant detachment from the impervious surface impervious surface


Previous ResearchPrevious Research Mass flux of pollutants from a pervious Mass flux of pollutants from a pervious

surface is a function of boundary shear surface is a function of boundary shear stress (Richardson and Parr, 1988) stress (Richardson and Parr, 1988) Pollutant mass flux increased linearly Pollutant mass flux increased linearly

as the product of shear velocity and the as the product of shear velocity and the square root of boundary permeability square root of boundary permeability increased increased

Research Objective

Two-fold Objective Two-fold Objective Examine rates of pollutant detachment Examine rates of pollutant detachment

from an impermeable surface for various from an impermeable surface for various chloride compounds and determine their chloride compounds and determine their relationship to boundary shear stressrelationship to boundary shear stress

Quantify a washoff coefficient under Quantify a washoff coefficient under varied hydraulic conditions for different varied hydraulic conditions for different chloride compounds and, if possible, to chloride compounds and, if possible, to identify controlling factors identify controlling factors

Research Methodology

Plexiglass Laboratory FlumePlexiglass Laboratory Flume 2.44 m long by 20.3 cm wide2.44 m long by 20.3 cm wide Impermeable test sectionImpermeable test section

1.14 m long by 20. 3 cm wide1.14 m long by 20. 3 cm wideBeach sand surface 0.4 to 0.8 mmBeach sand surface 0.4 to 0.8 mm

Simulated overland flow and rainfallSimulated overland flow and rainfallRainfall module 1.0 m above flumeRainfall module 1.0 m above flume

Research Methodology (cont’d)

Plexiglass Laboratory Flume (cont’d)Plexiglass Laboratory Flume (cont’d) FlowmetersFlowmeters

Applied overland flow and rainfallApplied overland flow and rainfall Boundary Shear Stress (Re Boundary Shear Stress (Re versusversus f) f)

Lory depth gaugesLory depth gaugesFlush-mounted hot film anemometer Flush-mounted hot film anemometer


Tracer ChemicalsTracer Chemicals Four inorganic chloride saltsFour inorganic chloride salts

NaCl, KCl, LiCl, and CaClNaCl, KCl, LiCl, and CaCl22

Spray applied to test section/air driedSpray applied to test section/air dried

• Fixed Cl areal density at t = 0Fixed Cl areal density at t = 0 Chloride analysis of flume effluentChloride analysis of flume effluent

Orion specific-ion electrodeOrion specific-ion electrode


Overland Flow ExperimentsOverland Flow Experiments 2.27, 3.78, and 6.06 Lpm2.27, 3.78, and 6.06 Lpm Laminar flow regime as ReLaminar flow regime as Re

Simulated Rainfall ExperimentsSimulated Rainfall Experiments 1.89, 3.78, and 6.06 Lpm overland flow1.89, 3.78, and 6.06 Lpm overland flow Rainfall intensity 6.86 cm/hrRainfall intensity 6.86 cm/hr Laminar flow regime as per Re Laminar flow regime as per Re

Description of Model

Mass Flux Mass Flux N = dP/dt = - kSN = dP/dt = - kSffYPYP

dP/dt = pollutant mass flux off the dP/dt = pollutant mass flux off the impervious surface [M/Limpervious surface [M/L22T]T]

k = washoff coefficient based only on k = washoff coefficient based only on pollutant characteristics [Lpollutant characteristics [L-1-1TT-1-1]]

SSff = friction slope or slope of the water = friction slope or slope of the water

surface profile [L/L]surface profile [L/L]

Description of Model (cont’d)

Mass Flux (cont’d)Mass Flux (cont’d) Y= average runoff flow depth [L]Y= average runoff flow depth [L] P = areal pollutant density [M/LP = areal pollutant density [M/L22]]

Friction Slope Friction Slope SSff = fV = fV22/(8gY/(8gY))

V = average velocity (L/T)V = average velocity (L/T) g = acceleration of gravity (L/Tg = acceleration of gravity (L/T22)) f = friction factor (unitless)f = friction factor (unitless)


Boundary Shear Stress Boundary Shear Stress = = fVfV22/(8g/(8g ) ) = unit weight of water [M/L= unit weight of water [M/L22TT22]]

Actual Mass Flux N = CQ/A = CRActual Mass Flux N = CQ/A = CR C = chloride concentration [M/LC = chloride concentration [M/L33]] Q = flow rate [LQ = flow rate [L33/T]/T] A = area of the impervious surface [LA = area of the impervious surface [L22]] R = rate of runoff [L/T] R = rate of runoff [L/T]


Unitless Mass Flux Unitless Mass Flux dN*/dt* = -{kDdN*/dt* = -{kDvv/g}N*/g}N*

DDv v == V*V*22Y/3VY/3V

Vertical momentum transfer coefficientVertical momentum transfer coefficient

• V* = shear velocity (L/T) = V V* = shear velocity (L/T) = V (f/8)(f/8) k = washoff coefficient = -3mVg/V*k = washoff coefficient = -3mVg/V*22YY

m = slope of unitless semi-log plotm = slope of unitless semi-log plot

• m = -kDm = -kDvv/g /g


Alternate Mass Flux Alternate Mass Flux N = dP/dt = - wRPN = dP/dt = - wRP w = washoff coefficient [Lw = washoff coefficient [L-1-1]] P = areal pollutant density [M/LP = areal pollutant density [M/L22]] R = rate of runoff [L/T]R = rate of runoff [L/T]

Load Characteristic CurveLoad Characteristic Curve YYFF = {[1 – exp(-wV = {[1 – exp(-wVFF)]/ [1 – exp(-wV)]/ [1 – exp(-wVTT)]})]}

Derived from the mass flux equation Derived from the mass flux equation


YYFF = {[1 – exp(-wV = {[1 – exp(-wVFF)]/ [1 – exp(-wV)]/ [1 – exp(-wVTT)]})]}

YYFF = fraction of total chloride load for a = fraction of total chloride load for a

given runoff event [dimensionless]given runoff event [dimensionless] VVFF = cumulative runoff volume up to a = cumulative runoff volume up to a

specified runoff time [L]specified runoff time [L] VVTT = total runoff volume for a complete = total runoff volume for a complete

runoff event [L] runoff event [L]


Washoff Coefficient wWashoff Coefficient w Catchment specific and varies with Catchment specific and varies with

pollutant type; however, no physical basispollutant type; however, no physical basis Positive values of w can only produce Positive values of w can only produce

convex load characteristic curvesconvex load characteristic curvesDecreasing concentrations of a Decreasing concentrations of a

constituent with increasing time after constituent with increasing time after runoff event starts (Alley, 1981) runoff event starts (Alley, 1981)


Washoff Coefficients (w Washoff Coefficients (w versusversus k) k) k = wRk = wR//

For a given rate of runoff (R) and For a given rate of runoff (R) and constant unit weight of water (constant unit weight of water (), the ), the boundary shear stress (boundary shear stress () of the ) of the impervious surface is constant and, impervious surface is constant and, thus, k is linearly proportional to w thus, k is linearly proportional to w

Hydraulic Parameters

NaCl 2.27 0.47 197 0.355 0.88 3.78 0.50 341 0.192 1.05 6.06 0.56 533 0.115 1.16

NaCla 1.89 0.48 165 0.433 0.79 2.27 0.57 335 0.314 1.16 6.06 0.60 535 0.188 1.37

CaCl2 2.27 0.46 197 0.272 0.76 3.78 0.48 336 0.153 0.95 6.06 0.53 533 0.095 1.07

KCl 3.78 0.49 321 0.150 0.87

LiCl 3.78 0.50 317 0.115 0.76

Salt Q (Lpm) Y (cm) Re f V* (cm/s)

Results and Discussion

Frictional Resistance of Test SurfaceFrictional Resistance of Test Surface Laminar flow regime (Re < 900)Laminar flow regime (Re < 900)

Smooth surface theoretical relationshipSmooth surface theoretical relationship

• f = 24/Ref = 24/ReParallel to theoretical relationshipParallel to theoretical relationship

• Higher boundary shear stress Higher boundary shear stress

Flume Friction f versus Re

0.01

0.1

1

100 1000 Reynolds Number (Re)

frict

ion

fact

or (f

)

NaCL NaCl rainCaCl2 KClLiCl


Frictional Resistance (cont’d)Frictional Resistance (cont’d) Test surface became progressively less Test surface became progressively less

rough as sand was removed during runoffrough as sand was removed during runoffSurface roughness phenomenon, Surface roughness phenomenon,

however, was accounted for in the however, was accounted for in the normalization procedure for mass flux normalization procedure for mass flux


Observed Chloride Mass FluxObserved Chloride Mass Flux Unitless mass flux versus time plotsUnitless mass flux versus time plots

Normalized to flow-related parameters, Normalized to flow-related parameters, including flow depth, velocity, shear including flow depth, velocity, shear velocity via a vertical momentum velocity via a vertical momentum transport coefficienttransport coefficient

• Plots for a given chloride salt should Plots for a given chloride salt should collapse to a single line collapse to a single line

Washoff Coefficients (k and w)

NaCl 0.6 2.90 1348 0.065 1.0 2.71 972 0.040 1.6 2.58 1197 0.038

NaCla 0.5 2.94 3894 0.181 1.0 4.38 2527 0.127 1.6 4.21 2608 0.114

CaCl2 0.6 2.18 708 0.025 1.0 2.11 705 0.024 1.6 2.08 441 0.018

KCl 1.0 1.97 1337 0.038

LiCl 1.0 1.52 1830 0.039

Salt Q (Lpm) Dv (m2/s)*106 k (m-1s-1) w (mm-1)

NaCl Mass Flux w/o Rainfall

0.1

1.0

10.0

100.0

0 10 20 30

Unitless Time x 10-3

Unitle

ss

Flu

x x

10

+4

6.06 Lpm3.78 Lpm2.27 Lpm

CaCl2 Mass Flux w/o Rainfall

1.0

10.0

100.0

0 20 40


Unitle

ss

Flu

x x

10

+4

6.06 Lpm3.78 Lpm2.27 Lpm

Monovalent Mass Flux at 3.78 Lpm w/o Rainfall

0.1

1.0

10.0

100.0

0 10 20 30


Unitle

ss

Flu

x x

10

+4

NaCl

KCl

LiCl


Normalization ProcedureNormalization Procedure Non-flow-related factors may have been Non-flow-related factors may have been

operative as there was not complete operative as there was not complete coalescence of all the runoff data for a coalescence of all the runoff data for a given chloride saltgiven chloride saltAqueous solubility, molecular weight, Aqueous solubility, molecular weight,

molecular diffusivity, heats of solution, molecular diffusivity, heats of solution, and cation ionic radius were examinedand cation ionic radius were examined


Monovalent Monovalent versusversus Divalent Chloride Salt Divalent Chloride Salt Divalent chloride salt CaClDivalent chloride salt CaCl22*H*H22O O

behaved significantly different than the behaved significantly different than the monovalent salt NaCl at same runoff ratemonovalent salt NaCl at same runoff rateMuch lower washoff coefficient and Much lower washoff coefficient and

slower mass flux from the test surfaceslower mass flux from the test surface

Mono- versus Divalent Mass Flux at 3.78 Lpm w/o Rainfall

0.1

1.0

10.0

100.0

0 10 20 30


Unitle

ss

Flu

x x

10

+4

CaCl2NaCl


Washoff Coefficient kWashoff Coefficient k Akan (1987) describes the washoff Akan (1987) describes the washoff

coefficient k as depending only on the coefficient k as depending only on the pollutant characteristicspollutant characteristics

Chloride detachment of monovalent salts Chloride detachment of monovalent salts ( NaCl, KCl, and LiCl) was similar( NaCl, KCl, and LiCl) was similarIn general, higher overland flow rates In general, higher overland flow rates

produced lower washoff coefficientsproduced lower washoff coefficients


Simulated Rainfall with Overland FlowSimulated Rainfall with Overland Flow Washoff coefficient, k, was much higher Washoff coefficient, k, was much higher

for the runs with superimposed simulated for the runs with superimposed simulated rain compared to those without rainfallrain compared to those without rainfallCasts some doubt on the postulate of Casts some doubt on the postulate of

Nakamura (1984) and Akan (1987) that Nakamura (1984) and Akan (1987) that pollutant detachment rate is a function of pollutant detachment rate is a function of pollutant characteristics and not pollutant characteristics and not influenced by hydraulic conditionsinfluenced by hydraulic conditions

NaCl Mass Flux at 3.78 Lpm

0.1

1.0

10.0

100.0

1000.0

0 10 20 30


Unitle

ss

Flu

x x

10

+4

Simulated Rain

WithoutSimulated Rain


Higher Mass Flux with RainfallHigher Mass Flux with Rainfall Raindrops retard the runoff flow because Raindrops retard the runoff flow because

a transfer of momentum is required to a transfer of momentum is required to accelerate the drops from zero velocity in accelerate the drops from zero velocity in the horizontal direction up to the velocity the horizontal direction up to the velocity of overland flowof overland flowProduces higher friction factor and Produces higher friction factor and

increased shear at the test surfaceincreased shear at the test surface

NaCl Mass Flux w/ Rainfall

1

10

100

1000

0 2 4 6


Unitle

ss

Flu

x x

10

+4

6.06 Lpm

3.78 Lpm

1.89 Lpm


Simulated Rainfall with Overland FlowSimulated Rainfall with Overland Flow Rainfall intensity herein was constantRainfall intensity herein was constant

Rainfall-induced turbulence over test Rainfall-induced turbulence over test section appeared less dominant with section appeared less dominant with increasing overland flow ratesincreasing overland flow rates

• e. g. increasing overland flow rates e. g. increasing overland flow rates may cause the rainfall effect to may cause the rainfall effect to become less pronounced become less pronounced


Washoff Coefficient wWashoff Coefficient w Varied over an order of magnitude with Varied over an order of magnitude with

simulated rainfall runs being the highestsimulated rainfall runs being the highestRange from 0.018 to 0.18 mmRange from 0.018 to 0.18 mm-1-1

Typical washoff coefficient value in Typical washoff coefficient value in simulation models is 0.18 mmsimulation models is 0.18 mm-1-1 (Alley, (Alley, 1981 and Millar, 1999)1981 and Millar, 1999)i.e. a 12.7 mm/hr runoff event removes i.e. a 12.7 mm/hr runoff event removes

90 % of the pollutant in 1 hr 90 % of the pollutant in 1 hr


Washoff Coefficient (k Washoff Coefficient (k versusversus w) w) Recall that by equating the two mass flux Recall that by equating the two mass flux

modelsmodelsk = wRk = wR//

For constant hydraulic conditions, k is For constant hydraulic conditions, k is proportional to wproportional to wLinear relationship observedLinear relationship observed

• rr22 = 0.86 = 0.86

Comparison of Washoff Coefficients (k versus w)

y = 22549x

r2 = 0.86

0

1000

2000

3000

4000

0 0.05 0.1 0.15 0.2

w (mm-1)

k (

m-1s-1

) NaCl rain

NaCl

CaCl2

KCl

LiCl

Conclusions

Washoff coefficients were similar for each Washoff coefficients were similar for each monovalent chloride compound (NaCl, monovalent chloride compound (NaCl, KCl, and LiCl) at the same rate of runoffKCl, and LiCl) at the same rate of runoff

Detachment rates for the divalent chloride Detachment rates for the divalent chloride compound CaClcompound CaCl22*H*H22O was approximately O was approximately one-half the monovalent NaClone-half the monovalent NaCl

In general, the washoff coefficient In general, the washoff coefficient decreased as the rate of runoff increaseddecreased as the rate of runoff increased

Conclusions

Not possible to completely normalize the Not possible to completely normalize the data for different flow rates in the data for different flow rates in the dimensionless mass flux dimensionless mass flux versus versus dimensionless time semi-log plotsdimensionless time semi-log plots Used a derived average vertical transport Used a derived average vertical transport

coefficient based on a momentum and coefficient based on a momentum and mass transfer analogy for laminar flowmass transfer analogy for laminar flow

Non-flow-related factors possibleNon-flow-related factors possible

Conclusions

Washoff coefficient significantly increased Washoff coefficient significantly increased with simulated rainfall superimposed on with simulated rainfall superimposed on overland flowoverland flow Increased boundary shear stressIncreased boundary shear stress Effect may be reduced at higher overland Effect may be reduced at higher overland

flow with constant rainfall intensityflow with constant rainfall intensity

Recommendations

Perform additional experiments under Perform additional experiments under varied hydraulic conditions using overland varied hydraulic conditions using overland flow and overland flow with superimposed flow and overland flow with superimposed simulated rainfallsimulated rainfall in order to clarify if the in order to clarify if the washoff rate is a function of only pollutant washoff rate is a function of only pollutant characteristicscharacteristics

Recommendations

Evaluate additional salt compounds with a Evaluate additional salt compounds with a common cation and different anions to common cation and different anions to determine if washoff coefficients are determine if washoff coefficients are correlated with any chemical and physical correlated with any chemical and physical property, e. g., LiBr and LiCl, or CaClproperty, e. g., LiBr and LiCl, or CaCl22 and and

CaBrCaBr22

Recommendations

Examine detachment rates between various Examine detachment rates between various monovalent and divalent compounds, such monovalent and divalent compounds, such NaCl and CaClNaCl and CaCl

22, or NaBr and MgBr, or NaBr and MgBr22

Include more complex substances as tracers, Include more complex substances as tracers, such as typical organics found in runoffsuch as typical organics found in runoff Fertile grounds for research into pollutant Fertile grounds for research into pollutant

detachment rates detachment rates

Acknowledgments

Funding for Research Provided byFunding for Research Provided by New Mexico Tech Research CouncilNew Mexico Tech Research Council

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