Download Flume Friction f versus Re

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
Associate Professor of Environmental Engineering, Department of Civil and
Environmental Engineering, New Mexico Tech, Socorro, New Mexico 87801
1
2Graduate
Research Assistant, Department of Mineral Engineering, New Mexico
Tech, Socorro, New Mexico 87801
Significance of the Problem

Urban Stormwater Runoff
 Large areas of impervious or semiimpervious surfaces
 Major non-point source of pollutants
previously deposited during dry weather
 Runoff quantity typically high volume
and relatively short duration
Significance of the Problem

National Urban Runoff Program (19 cities)
 33 % lake contamination from runoff
 10 % river contamination from runoff
 Several priority pollutants found in at
least 10 % of samples collected
 e.g. #121 phenanthrene; #30 lead; #51
chloroform; #5 lindane; #23 arsenic
Modeling Background

Stormwater Water Quality Models
 Two-stage process
 Pollutant accumulation on catchment
surfaces during dry weather periods
 Pollutant washoff during rainfall and
subsequent runoff.
Modeling Background (cont’d)

Pollutant Washoff is the Critical Stage
 Transport limited process governed by
rainfall and runoff characteristics
 Dependent upon overland flow shear
stress (Nakamura, 1984)
 Dependent upon raindrop and runoff
energies (Vaze and Chiew, 2003)
Modeling Background (cont’d)

Typical Modeling Approach
 Estimate pollutant washoff empirically by
a first-order relationship (exponential)
 Washoff rate depends linearly on the
available accumulated pollutant mass,
on the rainfall intensity, and/or the
overland flow runoff rate (Alley, 1981;
Millar, 1999)
Modeling Background (cont’d)

Storm Water Management Model (SWMM)
 Algorithm uses exponential relationship
between pollutant washoff and runoff
volume (Huber and Dickinson, 1988)
 This type of model lacks a physical
basis for pollutant detachment from the
impervious surface
Modeling Background (cont’d)

Previous Research
 Mass flux of pollutants from a pervious
surface is a function of boundary shear
stress (Richardson and Parr, 1988)
 Pollutant mass flux increased linearly
as the product of shear velocity and the
square root of boundary permeability
increased
Research Objective

Two-fold Objective
 Examine rates of pollutant detachment
from an impermeable surface for various
chloride compounds and determine their
relationship to boundary shear stress
 Quantify a washoff coefficient under
varied hydraulic conditions for different
chloride compounds and, if possible, to
identify controlling factors
Research Methodology

Plexiglass Laboratory Flume
 2.44 m long by 20.3 cm wide
 Impermeable test section
 1.14 m long by 20. 3 cm wide
 Beach sand surface 0.4 to 0.8 mm
 Simulated overland flow and rainfall
 Rainfall module 1.0 m above flume
Research Methodology (cont’d)

Plexiglass Laboratory Flume (cont’d)
 Flowmeters
 Applied overland flow and rainfall
 Boundary Shear Stress (Re versus f)
 Lory depth gauges
 Flush-mounted hot film anemometer
Research Methodology (cont’d)

Tracer Chemicals
 Four inorganic chloride salts
 NaCl, KCl, LiCl, and CaCl2
 Spray applied to test section/air dried
• Fixed Cl areal density at t = 0
 Chloride analysis of flume effluent
 Orion specific-ion electrode
Research Methodology (cont’d)
Overland Flow Experiments
 2.27, 3.78, and 6.06 Lpm
 Laminar flow regime as Re
 Simulated Rainfall Experiments
 1.89, 3.78, and 6.06 Lpm overland flow
 Rainfall intensity 6.86 cm/hr
 Laminar flow regime as per Re

Description of Model

Mass Flux N = dP/dt = - kSfYP
 dP/dt = pollutant mass flux off the
impervious surface [M/L2T]
 k = washoff coefficient based only on
pollutant characteristics [L-1T-1]
 Sf = friction slope or slope of the water
surface profile [L/L]
Description of Model (cont’d)
Mass Flux (cont’d)
 Y= average runoff flow depth [L]
 P = areal pollutant density [M/L2]
 Friction Slope Sf = fV2/(8gY)
 V = average velocity (L/T)
 g = acceleration of gravity (L/T2)
 f = friction factor (unitless)

Description of Model (cont’d)
Boundary Shear Stress  = fV2/(8g )
2 2
  = unit weight of water [M/L T ]
 Actual Mass Flux N = CQ/A = CR
 C = chloride concentration [M/L3]
 Q = flow rate [L3/T]
 A = area of the impervious surface [L2]
 R = rate of runoff [L/T]

Description of Model (cont’d)

Unitless Mass Flux dN*/dt* = -{kDv/g}N*
2
 Dv = V* Y/3V
 Vertical momentum transfer coefficient
• V* = shear velocity (L/T) = V (f/8)
 k = washoff coefficient = -3mVg/V*2Y
 m = slope of unitless semi-log plot
• m = -kDv/g
Description of Model (cont’d)
Alternate Mass Flux N = dP/dt = - wRP
-1
 w = washoff coefficient [L ]
 P = areal pollutant density [M/L2]
 R = rate of runoff [L/T]
 Load Characteristic Curve
 YF = {[1 – exp(-wVF)]/ [1 – exp(-wVT)]}
 Derived from the mass flux equation

Description of Model (cont’d)

YF = {[1 – exp(-wVF)]/ [1 – exp(-wVT)]}
 YF = fraction of total chloride load for a
given runoff event [dimensionless]
 VF = cumulative runoff volume up to a
specified runoff time [L]
 VT = total runoff volume for a complete
runoff event [L]
Description of Model (cont’d)

Washoff Coefficient w
 Catchment specific and varies with
pollutant type; however, no physical basis
 Positive values of w can only produce
convex load characteristic curves
 Decreasing concentrations of a
constituent with increasing time after
runoff event starts (Alley, 1981)
Description of Model (cont’d)

Washoff Coefficients (w versus k)
 k = wR/
 For a given rate of runoff (R) and
constant unit weight of water (), the
boundary shear stress () of the
impervious surface is constant and,
thus, k is linearly proportional to w
Hydraulic Parameters
Salt
NaCl
Q (Lpm)
2.27
3.78
6.06
Y (cm)
0.47
0.50
0.56
Re
197
341
533
f
0.355
0.192
0.115
V* (cm/s)
0.88
1.05
1.16
NaCla
1.89
2.27
6.06
0.48
0.57
0.60
165
335
535
0.433
0.314
0.188
0.79
1.16
1.37
CaCl2
2.27
3.78
6.06
0.46
0.48
0.53
197
336
533
0.272
0.153
0.095
0.76
0.95
1.07
KCl
3.78
0.49
321
0.150
0.87
LiCl
3.78
0.50
317
0.115
0.76
Results and Discussion

Frictional Resistance of Test Surface
 Laminar flow regime (Re < 900)
 Smooth surface theoretical relationship
• f = 24/Re
 Parallel to theoretical relationship
• Higher boundary shear stress
Flume Friction f versus Re
friction factor (f)
1
0.1
NaCL
CaCl2
LiCl
NaCl rain
KCl
0.01
100
Reynolds Number (Re)
1000
Results and Discussion

Frictional Resistance (cont’d)
 Test surface became progressively less
rough as sand was removed during runoff
 Surface roughness phenomenon,
however, was accounted for in the
normalization procedure for mass flux
Results and Discussion

Observed Chloride Mass Flux
 Unitless mass flux versus time plots
 Normalized to flow-related parameters,
including flow depth, velocity, shear
velocity via a vertical momentum
transport coefficient
• Plots for a given chloride salt should
collapse to a single line
Washoff Coefficients (k and w)
Salt
NaCl
Q (Lpm)
0.6
1.0
1.6
Dv (m2/s)*106
2.90
2.71
2.58
k (m-1s-1)
1348
972
1197
w (mm-1)
0.065
0.040
0.038
NaCla
0.5
1.0
1.6
2.94
4.38
4.21
3894
2527
2608
0.181
0.127
0.114
CaCl2
0.6
1.0
1.6
2.18
2.11
2.08
708
705
441
0.025
0.024
0.018
KCl
1.0
1.97
1337
0.038
LiCl
1.0
1.52
1830
0.039
NaCl Mass Flux w/o Rainfall
100.0
6.06 Lpm
3.78 Lpm
2.27 Lpm
Unitless
+4
Flux x 10
10.0
1.0
0.1
0
10
20
Unitless Time x 10-3
30
CaCl2 Mass Flux w/o Rainfall
Unitless
+4
Flux x 10
100.0
6.06 Lpm
3.78 Lpm
2.27 Lpm
10.0
1.0
0
20
Unitless Time x 10-3
40
Monovalent Mass Flux at 3.78
Lpm w/o Rainfall
100.0
Unitless
+4
Flux x 10
NaCl
KCl
10.0
LiCl
1.0
0.1
0
10
20
Unitless Time x 10-3
30
Results and Discussion

Normalization Procedure
 Non-flow-related factors may have been
operative as there was not complete
coalescence of all the runoff data for a
given chloride salt
 Aqueous solubility, molecular weight,
molecular diffusivity, heats of solution,
and cation ionic radius were examined
Results and Discussion

Monovalent versus Divalent Chloride Salt
 Divalent chloride salt CaCl2*H2O
behaved significantly different than the
monovalent salt NaCl at same runoff rate
 Much lower washoff coefficient and
slower mass flux from the test surface
Mono- versus Divalent Mass
Flux at 3.78 Lpm w/o Rainfall
Unitless
+4
Flux x 10
100.0
CaCl2
NaCl
10.0
1.0
0.1
0
10
20
Unitless Time x 10-3
30
Results and Discussion

Washoff Coefficient k
 Akan (1987) describes the washoff
coefficient k as depending only on the
pollutant characteristics
 Chloride detachment of monovalent salts
( NaCl, KCl, and LiCl) was similar
 In general, higher overland flow rates
produced lower washoff coefficients
Results and Discussion

Simulated Rainfall with Overland Flow
 Washoff coefficient, k, was much higher
for the runs with superimposed simulated
rain compared to those without rainfall
 Casts some doubt on the postulate of
Nakamura (1984) and Akan (1987) that
pollutant detachment rate is a function
of pollutant characteristics and not
influenced by hydraulic conditions
NaCl Mass Flux at 3.78 Lpm
1000.0
Unitless
+4
Flux x 10
Simulated Rain
100.0
Without
Simulated Rain
10.0
1.0
0.1
0
10
20
Unitless Time x 10-3
30
Results and Discussion

Higher Mass Flux with Rainfall
 Raindrops retard the runoff flow because
a transfer of momentum is required to
accelerate the drops from zero velocity in
the horizontal direction up to the velocity
of overland flow
 Produces higher friction factor and
increased shear at the test surface
NaCl Mass Flux w/ Rainfall
1000
Unitless
+4
Flux x 10
6.06 Lpm
3.78 Lpm
100
1.89 Lpm
10
1
0
2
4
Unitless Time x 10-3
6
Results and Discussion

Simulated Rainfall with Overland Flow
 Rainfall intensity herein was constant
 Rainfall-induced turbulence over test
section appeared less dominant with
increasing overland flow rates
• e. g. increasing overland flow rates
may cause the rainfall effect to
become less pronounced
Results and Discussion

Washoff Coefficient w
 Varied over an order of magnitude with
simulated rainfall runs being the highest
 Range from 0.018 to 0.18 mm-1
 Typical washoff coefficient value in
simulation models is 0.18 mm-1 (Alley,
1981 and Millar, 1999)
 i.e. a 12.7 mm/hr runoff event removes
90 % of the pollutant in 1 hr
Results and Discussion

Washoff Coefficient (k versus w)
 Recall that by equating the two mass flux
models
 k = wR/
 For constant hydraulic conditions, k is
proportional to w
 Linear relationship observed
• r2 = 0.86
Comparison of Washoff
Coefficients (k versus w)
-1 -1
k (m s )
4000
y = 22549x
r2 = 0.86
3000
NaCl rain
NaCl
2000
CaCl2
1000
KCl
LiCl
0
0
0.05
0.1
w (mm-1)
0.15
0.2
Conclusions
Washoff coefficients were similar for each
monovalent chloride compound (NaCl,
KCl, and LiCl) at the same rate of runoff
 Detachment rates for the divalent chloride
compound CaCl2*H2O was approximately
one-half the monovalent NaCl
 In general, the washoff coefficient
decreased as the rate of runoff increased

Conclusions

Not possible to completely normalize the
data for different flow rates in the
dimensionless mass flux versus
dimensionless time semi-log plots
 Used a derived average vertical transport
coefficient based on a momentum and
mass transfer analogy for laminar flow
 Non-flow-related factors possible
Conclusions

Washoff coefficient significantly increased
with simulated rainfall superimposed on
overland flow
 Increased boundary shear stress
 Effect may be reduced at higher overland
flow with constant rainfall intensity
Recommendations

Perform additional experiments under
varied hydraulic conditions using overland
flow and overland flow with superimposed
simulated rainfall in order to clarify if the
washoff rate is a function of only pollutant
characteristics
Recommendations

Evaluate additional salt compounds with a
common cation and different anions to
determine if washoff coefficients are
correlated with any chemical and physical
property, e. g., LiBr and LiCl, or CaCl2 and
CaBr2
Recommendations
Examine detachment rates between various
monovalent and divalent compounds, such
NaCl and CaCl2, or NaBr and MgBr2
 Include more complex substances as tracers,
such as typical organics found in runoff
 Fertile grounds for research into pollutant
detachment rates

Acknowledgments

Funding for Research Provided by
 New Mexico Tech Research Council