- Email: [email protected]
Longitudinal dispersion coefficient for mixing in open channel flows with submerged vegetation
Ecological Engineering 145 (2020) 105721
Contents lists available at ScienceDirect
Ecological Engineering journal homepage: www.elsevier.com/locate/ecoleng
Longitudinal dispersion coefficient for mixing in open channel flows with submerged vegetation
T
Jaehyun Shina, Jin Yu Seoa, Il Won Seob,
⁎
a
Department of Civil and Environmental Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, South Korea Department of Civil and Environmental Engineering, Institute of Construction and Environmental Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, South Korea
b
ARTICLE INFO
ABSTRACT
Keywords: Vegetated flow Vertical shear Longitudinal dispersion coefficient Submergence ratio Stem density Shear stress
An experimental investigation was conducted to analyze the flow and pollutant mixing characteristics in the vegetated channel, in which the velocity data was collected by micro acoustic Doppler velocimeter, and pollutant dispersion data was obtained through tracer tests in an open channel with submerged vegetation. The effects of submergence ratio (Sr = 2.0–3.5), and stem density (M = 0.4–5.9) on the vertical distribution of the stream-wise velocity and the turbulent shear stress were analyzed. The results of the flow experiments showed that the intensity of velocity deviation became larger with increasing stem density and decreasing submergence ratio. The turbulent shear stress at the exchange zone also increased with submergence ratio, as well as with increasing stem density. The calculation results of the longitudinal dispersion coefficient based on the vertical velocity profile data showed that as the submergence ratio and stem density increased, the dispersion coefficients increased linearly. This monotonic increase of the velocity-based dispersion coefficient differed from former research, in which concentration-based dispersion coefficient values approached a constant value in a higher submergence ratio of over 2. Comparison of the velocity-based longitudinal dispersion coefficients with concentration-based coefficients in this research demonstrated that the velocity-driven coefficient had a linear relation with the concentration-driven coefficients, with smaller values than the concentration-based dispersion. This difference can be explained by the fact that concentration-driven dispersion coefficient included the storage effects due to the submerged vegetation, while the velocity-driven coefficient only accounted for shear flow effects.
1. Introduction In conventional river management practices, the aquatic plants had been removed from the waterways to enhance the transport and conveyance of flood flow. However, in recent years, river vegetation is preserved because aquatic plants improve the quality of water through nutrient uptake and oxygen production, and can also act as natural treatment plants that filter and dilute land-source pollutants through physical and biological process (Kadlec and Knight, 1966; MacDonald, 1994). In natural channels where the plants coexist within the water body, the vegetation both in emergent and submerged conditions dramatically alters the flow dynamics and mixing of pollutants (Ghisalberti and Nepf, 2002). Vegetation also affects the deposition of sediments, which aids in the removal of absorbed contaminants while reduced bed shear stress prevents the resuspension of polluted sediments (Palmer et al., 2004; Schultz et al., 2002).
⁎
As the vegetation affects the vertical velocity profile, the type of plant and the density of canopy serve as important factors in changes to the flow dynamics (Ghisalberti and Nepf, 2002). The effects of vegetation on flow have been studied by many researchers via laboratory experiments and numerical models with rigid cylinder, flexible vegetation prototypes, and natural vegetation on open-channel flows. To find the velocity characteristics in vegetated channels several researches for analytical equations and modeling were conducted, such as Shimizu and Tsujimoto (1994) which utilized different turbulence closure schemes to model the vertical velocity profile. Klopstra et al. (1997) proposed analytical expressions to represent the flow velocity profile in various roughness flume experiments using a logarithmic form. Baptist et al. (2007) also developed equations with genetic programming to describe analytical expressions for vegetation resistance. Yang and Choi (2010) proposed a velocity relationship to predict the velocity distribution in two-layer flow in vegetation. Also, field
Corresponding author. E-mail address: [email protected] (I.W. Seo).
https://doi.org/10.1016/j.ecoleng.2020.105721 Received 5 September 2019; Received in revised form 27 December 2019; Accepted 7 January 2020 0925-8574/ © 2020 Elsevier B.V. All rights reserved.
Ecological Engineering 145 (2020) 105721
J. Shin, et al.
Fig. 1. Schematic diagram of flow characteristics of submerged vegetation flow: a) Streamwise velocity, b) Turbulent shear stress, c) Turbulent diffusion coefficient; Solid line means flow characteristics in case of vegetated flow and dotted line indicates the case of non-vegetated flow. (Adapted from Raupach et al., 1996)
vegetation. Hamidifar et al. (2015) calculated the longitudinal mixing using image processing to estimate the tracer concentration in compound open channels in smooth and vegetated floodplains to find out that vegetation can delay peak concentration up to 500%. Since these research efforts used only the tracer tests to calculate the longitudinal dispersion coefficients, they did not use the velocity measurements directly so the effects of vertical shear contributions from the velocity deviations over fast and slow zones were not fully addressed. With the advancement of velocity measurement equipment velocity profiles could be easily obtained, and 2D dispersion coefficients could be calculated effectively using the equation by Fischer et al. (1979). The equations assumed that the shear dispersion were more dependent on the vertical deviation of velocity than molecular diffusion, and calculated the two-dimensional coefficients using triple integration to the deviation of 2D vertical velocities. Although this method had been applied to open channels (Carr and Rehmann, 2007) or laboratory experiments (Lee and Seo, 2013) the application to vegetated channels have not been conducted previously. Also, the former studies related to analysis of velocity characteristics in vegetated channels did not find its effects to mixing in channels. Thus, direct calculation of the longitudinal dispersion coefficients from the detailed velocity measurements (Fischer et al., 1979), where both the effects of the vertical velocity deviation and the vertical distribution of the turbulent diffusion coefficient were considered, needs to be compared with the results by the concentration-based method. The objective of this study is to analyze the effect of submerged aquatic plants on longitudinal mixing in waterways by observation of the vertical velocity profile in vegetated channels. The experiments were conducted with different vegetation submergence ratio, and canopy density, and the detailed velocity profile was measured using a micro acoustic Doppler velocimeter (ADV) for each cases. The calculation of the longitudinal dispersion coefficient based on the velocity profile data was compared with the concentration-based method from the tracer experiment data.
experimental surveys of vegetation affect to flow velocity in natural rivers (Errico et al., 2019) or in a large fluvial lake (Bulat et al., 2019) have been conducted previously. These studies showed that vegetation and canopy drag would reduce velocities in these open channels. Other studies conducted additional mixing experiments in vegetated channels to show that the reduced velocities could cause particulates and contaminants to settle out of the water body. Various approaches have been proposed to analyze these effects, and the analyses were based on the two-layer method to describe flow through submerged vegetation. Fig. 1 shows that in these methods, the flow domain was usually divided into three layers: one through the vegetation called the “vegetation layer”, the “surface layer” above the vegetation, and the “shear layer” in between. In the case of canopy density, dense submerged canopies caused an inflection point of the velocity profile at the top of the canopy between the two layers due to the shear layer effect (Ghisalberti and Nepf, 2002; Nepf and Ghisalberti, 2008). The density of the vegetation would affect the position of the inflection point and the velocity difference of the vegetation layer and the surface layer (Ghisalberti and Nepf, 2004). Therefore, to find the characteristics of vegetation effect on flow and contaminant mixing, careful research of the changes of vertical velocity profile by vegetation and canopy density should be undertaken. Fig. 1 shows that in addition to the canopy density, the submergence ratio of vegetation also significantly affects the vertical profile of stream-wise velocity, in which the stream-wise velocity decreases in the vegetated zone and increases sharply in the upper water body above the vegetation. This causes increase of the vertical shear, and pollutant particles to spread faster than in non-vegetated channels. Because the velocity profile in submerged vegetation is different from a logarithmic form over the full depth, as plotted by a dotted line in Fig. 1, the traditional treatment of longitudinal dispersion in open channels without vegetation cannot be directly applied to vegetated ones. The longitudinal dispersion in flows with emergent and submerged vegetation has been studied by several researchers based on tracer tests in which they calculated longitudinal dispersion coefficients using either the moment-based method (Aris, 1956), or the routing method (Fischer, 1968; Fischer et al., 1979). The studies for mixing in vegetation included studies such as Nepf et al. (1997) which showed the increase of vertical shear in vegetation would also increase the longitudinal dispersion. White and Nepf (2003) showed that the unsteady recirculation zone close to vegetation cylinders, and velocity defect behind each cylinders affected the longitudinal mixing in tracer experiments. Lightbody and Nepf (2006) maintained that the size of the vertical velocity will vary inversely with canopy drag in vegetated channels. Later, Shucksmith et al. (2011) developed a mathematical model to predict the longitudinal mixing in real vegetation and found the mixing layer size to be related with the growing
2. Theoretical backgrounds 2.1. Flow and mixing characteristics in vegetated flows Fig. 1 shows that in submerged vegetated flows, as aforementioned, the flow field can be split into three distinct zones: a slow-moving zone through the vegetation (vegetation layer), a faster free-flow zone over the top of the canopy (surface layer), and a shear layer zone in-between (shear layer). The flow above the vegetation behaves as a turbulent shear layer, while the vegetation compared within the non-vegetated channels retards the flow within the vegetated or wake zone. A logarithmic law (Kouwen et al., 1969) can describe the velocity profile in 2
Ecological Engineering 145 (2020) 105721
J. Shin, et al.
the layer above the vegetation. The shear layer in-between has the maximum turbulent shear stress among the three layers as the velocities rapidly increase. Studies showed that this shear layer transported the mass pollutant more efficiently than momentum transport (Ghisalberti and Nepf, 2002). In addition, vortices dominated the vertical transport between the surface layer and vegetation layer (Ghisalberti and Nepf, 2009), which led to faster vertical transport of pollutants in the shear layer. The submergence ratio of the vegetation, Sr, in open channels in which Sr is defined as the ratio of water depth divided by the vegetation height, affects the vertical velocity profile. If the submergence ratio is small, i.e. the depth of the vegetation layer is large compared to the total depth of the channel, the retardation of the velocity profile becomes more prominent. In the cases where the submergence ratio is larger, the stem height would be smaller compared to the water depth, therefore the surface layer in Fig. 1a) would be larger compared to the vegetation layer, and the vertical velocity shear gets smaller. Former research showed that as the submergence ratio increased, the effects of retardation decreased (Shucksmith et al., 2010). The vertical velocity profile in flows with submerged vegetation is also dependent on the canopy density (Ghisalberti and Nepf, 2002). There are two types of behavior according to the canopy density: if bed drag is larger than canopy drag, then the mean velocity profile follows a turbulent logarithmic velocity profile in sparse density. If the bed drag is smaller than canopy drag, then the discontinuity in drag generates a region of shear resembling a free shear layer causing an inflection point at the top of the canopy in dense submerged canopies (Ghisalberti and Nepf, 2002; Nepf and Ghisalberti, 2008). In vegetated channels, the main source of velocity shear is between the vegetated and surface layers (Shucksmith et al., 2011). In the case of sparse vegetation, the velocity difference between the vegetated and surface layers is lower than for the case of dense vegetation. Also, the less dense and deeply submerged canopies' turbulent motions of vortices in the mixing layer penetrate the entire canopy height, and transfer mass and momentum between the main channel and the canopy; the vertical velocity profiles with the inflection point in vegetated channels makes the flow susceptible to instability leading to the generation of vortices within the layers. Thus, in the case of sparse density canopy, the vertical velocity profile shows a boundary-layer form without the inflection point. The submerged vegetation also produces difference in normalized turbulent stress in the channels (Raupach et al., 1996) where the vegetated layer and surface layer is generated as depicted in Fig. 1b). Nepf and Ghisalberti (2008) and Shucksmith et al. (2010) showed in their experiments that the maximum Reynolds turbulent stress occurred at the vegetation top; but without vegetation, the peak is located near the bottom of the channel, as plotted by the dotted line in Fig. 1b), typically shown for the turbulent stress for fully developed flow. For vegetated flows, as shown in Fig. 1b), the highest point of Reynolds turbulent stress is located at the shear layer along with the inflection point in the vertical velocity profile. Since the estimated Reynolds turbulent stress can be used as the numerator, and the velocity gradient as the denominator to calculate the turbulent diffusivity coefficient, using the Reynolds analogy that the mixing coefficients for mass transport and momentum transport are the same for the fully turbulent flow (Fischer, 1966). A solid line in Fig. 1c) can depict the typical profile of the turbulent diffusion coefficient. Thus, the vertical profile of the turbulent diffusion coefficient for vegetated flows is different from that for nonvegetated flows, since the maximum point of the turbulent diffusion coefficient is located in the middle of the depth without vegetation, while the profile of the turbulent stress with vegetation has two peak values as shown in Fig. 1c) due to the velocity gradient of the flow. Mixing in vegetated flows is caused by a combination of diffusion and dispersion processes by velocity shear with contribution from trapping mechanisms by the vegetation. The vegetation layer would create a relatively low velocity field where a fraction of the contaminant would be trapped in the vegetation, and released after the
main cloud has passed (Nepf et al., 1997). Due to these characteristics of vegetated flow, the range of dispersion coefficients related to longitudinal mixing has a wide range, which reflects the large influence that different hydraulic and physical parameters have on the mixing processes (Shucksmith et al., 2011). In the case of dense vegetation, the vortices generated in the flow did not penetrate to the channel bed so the longitudinal mixing was comparatively higher than for the sparsely vegetated channels (Shucksmith et al., 2010), while some submerged cases did not show a clear trend in the changes to the longitudinal mixing coefficient (Nepf et al., 2007). An experimental study with the model vegetation by Murphy et al. (2007) showed that when the submerged ratio was higher than 2.0, the non-dimensionalized longitudinal mixing coefficient became approximately constant with depth, while in the experiment by Shucksmith et al. (2010), when Sr is lower than 2.0, longitudinal dispersion coefficient monotonically increased with increasing Sr. The relative importance of the shear dispersion could outweigh the importance of dispersion due to exchange between the vegetated layer and surface layer, with higher submergence ratio. 2.2. Calculation of dispersion coefficients 2.2.1. Mixing in open channel flows Mixing in open channel flows is caused by a combination of diffusion and dispersion processes with additional contribution from the effect of dead zones. Shear dispersion is the spreading of solute due to the spatial variation of primary velocities in the channel. For the modeling of solute dispersion in the intermediate region in the open channel flow, the two-dimensional (2D) depth-averaged advectiondispersion equation (ADE) has frequently been used (Rutherford, 1994). The 2D advection-dispersion equation derived by depth-averaging the three-dimensional transport equation for natural channels could be shown in the curvilinear coordinate system as the following (Lee and Seo, 2013):
C C C 1 C 1 C + us + un = hDL + hDT t s n h s s h n n
(1)
where C is the depth-averaged concentration; us and un are the depthaveraged velocities in the streamwise and span-wise directions, respectively; DL is the longitudinal dispersion coefficient; DT is the transverse dispersion coefficient; h is the local depth; s is the streamwise direction; n is the spanwise direction; and t is time. The depth-averaged velocities are the following:
us =
1 h
0
un =
1 h
0
h
us dz
(2a)
un dz
(2b)
h
where us and un are the point velocities in the streamwise and span-wise directions, respectively; and z is the vertical distance from the channel bottom as shown in Fig. 1. 2.2.2. Velocity-based dispersion coefficient To use the 2D ADE for the analysis of contaminant transport in the shallow flows of rivers, the appropriate dispersion coefficients should be provided. The analysis undertaken by Taylor, 1954 remains the most commonly used method to describe mixing using dispersion coefficients in turbulent open channel flow. Assuming that the shear dispersion is more dependent on the vertical deviation of velocity than molecular diffusion, the two-dimensional coefficients could be derived as follows (Fischer et al., 1979):
3
DL =
1 h
0
DT =
1 h
0
h
h
us
un
z 0
z
z
z 0
1 0
1 z
z 0
us dzdzdz
un dzdzdz
(3a) (3b)
Ecological Engineering 145 (2020) 105721
J. Shin, et al.
where εz is the vertical turbulent diffusion coefficient; us and un are the deviation of the local velocity from the depth-averaged velocities, us and u¯n in the s and n directions respectively as shown in Fig. 1a). The deviation of velocities is the following:
us = us
us
(4a)
un = un
un
(4b)
2.2.3. Concentration-based dispersion coefficients When concentration data from tracer tests are available, the dispersion coefficients can be calculated by either applying moment-based methods (Seo et al., 2006) or routing procedures (Fischer et al., 1979). For the calculation of both longitudinal and transverse dispersion coefficients from concentration curves of 2D tracer tests, the 2D steamtube routing procedure (2D STRP) is more viable than moment methods because it can calculate the dispersion coefficients based on the dosage profile, which is converted from the concentration-time curves obtained from tracer tests (Baek and Seo, 2010). In this method, the stream-tube method was used with a fixed value of discharge attached to a fixed streamline, by moving the coordinate system back and forth across the cross-section along with the flow; thus, it could efficiently deal with the lateral migration of the water flow in irregularly curved rivers and the tracer cloud in meandering rivers (Seo et al., 2016). The equation for 2D STRP is shown below:
The turbulent diffusion coefficients εz were derived from the equations of vertical shear stress based on the Reynolds analogy that the mixing coefficients for mass transport and momentum transport are the same for the fully turbulent flow (Fischer, 1966). z
ux uz
=
dus dz
(5)
where
u x uz =
1 T
T 0
ux uz dt
(6a)
ux = ux
us
(6b)
uz = u z
w
(6c)
us =
1 T
0
w=
1 T
0
T
T
u x dt
(6d)
uz dt
(6e)
C (s2 , , t ) =
exp
{
4 BC (s2
0
·exp
( 4BC (s2
)2 s1 )
d
U2 (t¯2 t¯1 4DL (t¯2
t + )2 t¯1 )
}d
s1 ) (8)
where C(s2, η, t) is a temporal profile of the predicted concentration at the downstream section, s2; C(s1, ω, τ) is the temporal profile of measured concentration at the upstream section, s1; τ is the dummy time variable of integration; and t1 , t2 are the mean times of passage in sections s1 and s2, respectively. ω is the normalized dummy variable of integration; and η is the dimensionless discharge, U is the averaged velocity for each stream-tube, and Bc is the bulk dispersion coefficient, which is defined as:
where ux and uz are the instantaneous velocities and us and w are the time-averaged velocities in the steamwise and vertical direction, respectively. Using the Reynolds analogy, Elder (1959) derived expressions for longitudinal mixing for boundary layer flow based on the logarithmic profile of velocity and diffusivity in an infinitely wide channel as below:
DL = 5.93HU
C (s1 , , )U t¯1 )
4 DL (t¯2
1
Bc =
Hs 2Us DT Qs 2
(9)
where Qs is the span-averaged value of the flow discharge, Hs is the span-averaged value of the cross-sectional average depth of the river H, Us is the span-averaged value of the cross-sectional averaged velocity, and ψ is the normalized shape factor with the range 1.0–3.6 (Beltaos, 1980). Multiple regression techniques were used to fit the predicted concentration to the measured concentration since the two parameters are determined simultaneously through only one equation Eq. (8). Since this method used the actual contaminant dispersion data, the irregularities of the channel and storage effects due to the submerged vegetation were reflected in the dispersion coefficient results.
(7)
where H shows the cross-section averaged flow depth, and U∗ represents the boundary shear velocity. Although this value has many assumptions in its calculation, it had been widely used in many modeling applications due to its simplicity and applicability. However, in vegetated channels, the effect of aquatic plants changes the logarithmic form of the velocity as shown in Fig. 1a). Hence, other experimental values must be used for the longitudinal dispersion coefficient. In recent years, since with the advancement of velocity measurement equipment such as the Acoustic Doppler velocimeter (ADV) and Acoustic Doppler current profiler (ADCP), velocity profiles can be easily obtained, and 2D dispersion coefficients can be calculated more effectively using Eq. (3). However, the dispersion research using this method was usually focused on the calculation of the longitudinal dispersion coefficient of the one-dimensional mixing assuming the contaminants have gone through full lateral mixing in the far field. (Bogle, 1997; Carr and Rehmann, 2007; Shen et al., 2010; Kim, 2012). They used the acoustic Doppler current profilers to measure the longitudinal velocity in order to estimate the longitudinal dispersion coefficient as an alternative to the tracer test approach. Lee and Seo (2013) conducted the utilization of ADV for the laboratory experiment, which used the data from laboratory flume experiments on a meandering channel to use the vertical velocity profiles to predict the longitudinal and transverse dispersion coefficients. Other research efforts by Launay et al. (2015) and Zhu et al. (2017) were based on the measured velocity of longitudinal flow, and its shear dispersion due to the longitudinal flow distribution. In the case for transverse dispersion coefficients, Jung et al. (2019) measured large rivers in an experiment without considering vegetation. Since these research efforts were conducted under non-vegetated flows, the present research compared the velocity-based method and the concentration-based method in vegetated channels.
3. Experiments 3.1. Experimental set-up The experiments were carried out in a re-circulating flume of 12 m length, 0.3 m width, and with a fixed slope of 0.004 as shown in Fig. 2a). At the head tank, five honeycomb sheets were utilized to eliminate the swirl and provide a stable and uniform flow to the channel with similar setup with previous experiments (Ghisalberti and Nepf, 2002). The water discharge was supplied using the pump that has a capacity of (0.6 to 7.5) L/s, and the water depth was controlled by the tailgate. Artificial vegetation was installed between (5 and 7) m downstream from the head tank. This initial reach prevented the occurrence of large-scale disturbances due to vegetation, and allowed the development of a constant flow in the test section. Fig. 2b) shows that to study the velocity profiles and pollutant mixing in the vegetated flows, the model plants made of acrylic cylinders with a diameter of 6 mm and 0.1 m height were mounted onto acrylic boards of 2 m length, 0.3 m width, and 0.01 m height. The spacing of the acrylic cylinders was different between the lateral and 4
Ecological Engineering 145 (2020) 105721
J. Shin, et al.
Fig. 2. Schematic diagram, photos and results of experiments: a) Schematic diagram of experiment, b) Photo of installed vegetation, c) Photo of tracer cloud (NaCl solution with potassium permanganate).
stream-wise directions depending on the stem density. To analyze the effect of the vegetation on the characteristics of flow and pollutant mixing, the stem density was selected as (0.40, 0.85, 1.53, 2.97 and 5.94) m−1, in which the stem density is defined as
M = ad
Table 1 Summary of experimental conditions and results.
(10)
where a(m−2) is the number of cylinders per unit area, in stems per square meter; and d(m) is the cylinder diameter. Besides the stem density, the submergence ratio, Sr, the ratio of the water depth to the stem height, H/hV, was also selected as a significant parameter in the analysis of the velocity structure and mixing mechanism of the vegetated flow. Here, hV is the height of the model vegetation, and H is the water depth. In this experiment, four different conditions of the submergence ratio were tested in the range (2.0 to 3.5). Sr in this study was set to higher values than 2.0 in order to validate the results of Murphy et al. (2007), in which when Sr > 2.0, the longitudinal dispersion coefficient approached a constant value. Table 1 summarizes these experimental conditions, along with the results of the longitudinal dispersion coefficient calculated from the velocity profile data.
5
Case
Sr
M (m−1)
U (m/s)
IVD (m/s)
DLV (m2/s)
DLV/HU∗
S120 S121 S122 S123 S124 S131 S132 S133 S140 S141 S142 S143 S144 S151 S152 S153
2.0
0.40 0.85 1.53 2.97 5.94 0.85 1.53 2.97 0.40 0.85 1.53 2.97 5.94 0.85 1.53 2.97
0.119 0.118 0.114 0.110 0.114 0.099 0.103 0.102 0.082 0.082 0.085 0.084 0.086 0.069 0.069 0.070
0.0191 0.0234 0.0271 0.0327 0.0330 0.0113 0.0150 0.0210 0.0064 0.0097 0.0119 0.0168 0.0184 0.0075 0.0094 0.0124
0.0059 0.0124 0.0197 0.0256 0.0318 0.0149 0.0248 0.0335 0.0173 0.0205 0.0268 0.0417 0.0490 0.0371 0.0382 0.0430
3.77 6.02 8.63 7.66 8.98 7.16 10.4 10.6 11.5 12.0 10.9 15.5 15.0 21.7 17.0 16.9
2.5 3.0
3.5
Ecological Engineering 145 (2020) 105721
J. Shin, et al.
3.2. Velocity measurements
Table 2 Summary of dispersion study.
To collect the data of the stream-wise velocity at a number of vertical points in the cross sections of the vegetated reach of the channel, an acoustic Doppler velocity meter (SONTEK; 16 MHz Micro ADV) with down-looking probes was used as shown in Fig. 2a). The figure shows that the velocity profiles were measured at the centerline in six cross sections. The velocities were measured from the water surface down to the point at 1 cm above the bottom with (2 or 3) cm intervals, and more densely inside the vegetation zone with 1 cm intervals. At each point of the velocity measurement, the velocity was sampled for 120 s at the sampling rate of 25 Hz (Velasco et al., 2003) to make a total of 3000 samples at each point. This sampling duration of 120 s was selected through time scale analysis for the mean velocity. Later from the 3000 instantaneous values of the three-dimensional velocities, the turbulence-averaged velocities and turbulence shear stress were calculated using Eqs. 5 and 6. Fig. 2a) also shows that the velocities in the upper zone from the water surface to the water depth of 6 cm could not be measured, because the distance to the sampling point of Micro ADV was 5 cm away from the sensor. The unmeasured velocities near the water surface were extrapolated by applying the logarithmic law since the surface layer of vegetated flow follows the logarithmic form (White and Nepf, 2003).
Cp (ppm)
tp (sec)
tc (sec)
σ2 (ppm)2
DLC (m2/s)
DLC/HU∗
S120
C1 C2 C1 C2 C1 C2 C1 C2 C1 C2
30.62 17.27 23.03 12.32 27.90 18.99 30.01 19.96 35.79 16.85
41.25 54.75 41.50 56.25 41.50 56.50 47.50 59.25 42.25 56.00
43.44 57.87 43.38 59.02 43.17 58.07 50.68 61.81 43.57 57.73
23.66 31.09 13.49 43.03 16.38 27.20 31.81 46.17 11.41 52.46
0.0104
6.65
0.0109
5.29
0.0202
8.85
0.0293
8.76
0.0337
9.52
S122 S123 S124
Cp: peak concentration (ppm) of the tracer curve. tp: peak time of tracer. tc: centroid time of tracer. σ2: variance of C-T curve. a Same NaCl solution input with mixture of water, potassium permanganate, and ethanol used for all cases.
submergence ratio were carried out in order to analyze their effects on the velocity profiles in the submerged vegetated flows. The velocity profiles for four different submergence ratios and up to five different stem density cases were collected. Fig. 3 plots the vertical distributions of the normalized velocity versus the dimensionless depth for different submergence ratio and stem density. This figure shows that the vertical distributions of the normalized velocity were similar for different submergence ratio and stem density in which the stream-wise velocity was retarded by the vegetation stem while the velocity in the surface layer increased with increasing vertical coordinate Z/H, taking the logarithmic profile. In the interface between the two layers, the velocity increased very sharply; and this large velocity gradient was closely related to the velocity fluctuations that induced the high turbulent shear stresses at the shear layer as shown in Fig. 5. Fig. 3 also demonstrates that as the submergence ratio increased, the slope of the velocity profile, dus , got steeper. The variation of the dz vertical profile of the stream-wise velocity with the stem density change showed the same trend as the submergence ratio. As the submergence ratio increased, the deviation of the normalized velocity from the depth-averaged value became smaller, which means that stem height was the significant factor for the vertical deviation of the stream-wise velocity. As the stem density increased, the velocity deviation got larger, which means that the stem density was also the essential factor for the vertical deviation of the stream-wise velocity, as was the stem height. To quantify the variation of the velocity deviation, the amount of velocity deviation over the whole flow depth was analyzed using the intensity of velocity deviation (IVD), as defined by the equation given below (Fischer et al., 1979):
The tracer study was conducted to obtain the concentration-time curves, which were used to calculate the concentration-based longitudinal dispersion coefficient in which the 2D stream tube routing method was applied. Tracer experiments were carried out by releasing a dye with an instantaneous injection as a vertical line source at the upstream point of the vegetated section. As the tracer, NaCl solution was used, and it consisted of a mixture of water, potassium permanganate, and ethanol, with the later added to render the solute neutrally buoyant in the channel. At two downstream sections, the NaCl cloud was measured using the electrical conductivity meter (KENEK; MKTS2–50-04) with a sampling rate of 15 Hz. The conductivities provide voltage through the voltage amplification system, and then the voltage was converted to concentration (ppm) from a data acquisition system that was logged on a computer, as shown in Fig. 2a). The two sets of five conductivity sensors were positioned at the upstream and downstream sections of the test area, Sec. C1 and Sec. C2. The NaCl concentration was measured at mid-depth of the vegetation layer and surface layer at Sec. C1 and C2. These sections were located at (7 and 9) m downstream from the injection point respectively, ensuring the complete vertical mixing of the injected tracer. The criteria for the complete vertical mixing of the tracer cloud were checked using the equation given below:
IVD =
¯ 2 UH z
Section
S121
3.3. Concentration measurements
L = 0.1
Casea
(11)
1 H
H 0
us 2dz
1/2
(12)
Fig. 4 plots the variation of IVD against the submergence ratio and the stem density. Fig. 4a) shows that as Sr increased, IVD was decreasing exponentially, which was already found in the variation of the vertical velocity profiles shown in Fig. 3. Fig. 4b) also shows that with increasing stem density, IVD was increasing. In this case, the rate of increase of IVD was rather gradual or linear, compared to the rapid decrease of IVD with increasing Sr.
where εz is the vertical turbulent diffusion coefficient, H is the water depth, U¯ is the depth-averaged streamwise velocity, L is the length required for complete vertical mixing. Fig. 2c) indicates that the tracer cloud was moving downstream, maintaining full mixture over the entire water depth. Table 2 summarizes the experimental conditions of the tracer experiment, along with the statistical parameters and longitudinal dispersion coefficients calculated from the concentration curves.
4.2. Calculation of the dispersion coefficient using the vertical velocity profile
4. Results and discussions
The measured vertical velocity distribution were used to calculate the longitudinal dispersion coefficient by Eq. (3a)), and this coefficient was named the velocity-based dispersion coefficient, DLV. To complete the calculation of the triple integration of Eq. (3a)), the vertical
4.1. Analysis of the velocity profile As listed in Table 1, 16 runs with different stem density and 6
Ecological Engineering 145 (2020) 105721
J. Shin, et al.
Fig. 3. Variation of vertical velocity distributions with stem density for different submergence ratio.
turbulent diffusion coefficient, εz needed to be determined. In the vegetated flows of this study, assuming that the turbulent transport of mass and momentum is equivalent, Eq. (5) was incorporated into Eq. (3a)) to calculate the longitudinal dispersion coefficient considering the vertical variations of both velocity and turbulent diffusion coefficient as sketched in Fig. 1. Fig. 5 represents vertical distributions of the Reynolds turbulent stress for different submergence ratio and stem density cases. In this figure, the vertical profile of the turbulent shear stress showed the Gaussian distribution in which the maximum turbulent shear stress z occurred at the top of the canopy which is the shear layer, i.e., h = 1,
and decreased exponentially with increasing vertical coordinate. This profile is completely different from the linear one as maintained by previous researchers, including Righetti and Armanini (2002), that the distribution of shear stress above vegetation followed a linear trend between the vegetation top and the free surface. In the vegetation zone, the turbulent shear stress showed almost zero near the flume wall, and with increasing vertical coordinate, it increased exponentially. Fig. 5 shows that with decreasing submergence ratio and increasing stem density, the Reynolds turbulent stress increased. The turbulent diffusion coefficient was calculated using Eq. (5), and plotted against z/H in Fig. 6. This figure shows that, unlike the vertical distribution of the Reynolds turbulent stress shown in Fig. 5, maximum
v
7
Ecological Engineering 145 (2020) 105721
J. Shin, et al.
Fig. 4. Variation of IVD with stem density and submergence ratio.
Fig. 5. Vertical distributions of Reynolds turbulent stress along with stem density. 8
Ecological Engineering 145 (2020) 105721
J. Shin, et al.
Fig. 6. Vertical distributions of turbulent diffusion coefficient along with stem density.
values of εz occurred near the water surface of the surface layer not at z the top of the canopy, h = 1. At the shear layer, as shown in Fig. 3, the v slope of the velocity profile, which is the denominator in Eq. (5), was the largest even though the Reynolds turbulent stress had the maximum z value, which produced the small values of εz at h = 1. v Table 1 lists the longitudinal dispersion coefficients calculated by Eq. (3a)), and Fig. 7 plots them against the stem density and the
submergence ratio. Table 1 also shows the dimensionless values of DLV that were calculated using the shear velocity given as:
U =
max
=
(
u x uz )max (13)
where τmax is the maximum Reynolds stress which is located at the top of the vegetation (Murphy et al., 2007). Fig. 7a) reveals that, unlike the
Fig. 7. Variation of velocity-based longitudinal dispersion coefficient with stem density and submergence ratio. 9
Ecological Engineering 145 (2020) 105721
J. Shin, et al.
Fig. 9. Time concentration curves for Case S123. a) Upstream section C1, b) Downstream section C2.
turbulent diffusion coefficient and turbulent shear stress in the calculation of the velocity-based longitudinal dispersion coefficient had greater effect in higher submergence ratio, which caused the difference from the former result of the longitudinal dispersion coefficients calculated by the moment method (Murphy et al., 2007) applied to the concentration data, while for higher density the results remained similar. 4.3. Calculation of the dispersion coefficient using concentration curves
Fig. 8. Comparison of longitudinal dispersion coefficients calculated from velocity and concentration data.
In the dispersion study, the concentration-time curves were obtained at five lateral points in two sections, C1 and C2, as shown in Fig. 2. Fig. 9 plots the typical concentration-time curves measured at Sections C1 and C2 for Case S123, in which the concentration-time curves were smoothed by applying the moving average method. This figure shows that the concentration-time curves represent an asymmetric distribution, and the peak concentration was found in the center of the channel. As the tracer cloud moved downstream, the variance of the concentration-time curves increased, and showed a longer tail of concentration due to submerged vegetation, as shown in Fig. 9. Table 2 lists the statistical parameters of the concentration-time curves at the channel center for each case, along with the longitudinal dispersion coefficient calculated by Eq. (8). Table 2 also shows that as M increases, the variance increment between Sec. C1 and Sec. C2 increases, which meant that the longitudinal dispersion was also increasing. In this study, the stream-tube routing procedure (STRP) was used to calculate the longitudinal dispersion coefficient based on the dosage profiles, which were converted from the two-dimensional concentration-time curves shown in Fig. 9 (Seo et al., 2016). In the calculation of the dispersion coefficient by Eq. (8), the time-concentration curve at the downstream section was calculated with the input of the measured time-concentration curves at the upstream section. The predicted curve was repeatedly fitted with the measured curve at Section C2 (downstream), until the optimal value of the dispersion coefficients was found with nonlinear multiple regression technique, to find the longitudinal and transverse dispersion coefficient at the same time. The results of the longitudinal dispersion coefficients calculated from the concentration data, named the concentration-based
intensity of the velocity deviation, DLV was increasing as the submergence ratio, Sr, increased for all cases of the stem density. The reason for this increase of DLV was considered to be that as Sr increased, the turbulent diffusion coefficient, εz, which is a denominator in Eq. (3a)), increased more rapidly than the velocity deviation, us′. Fig. 7b) shows that in the case of stem density, DLV was increasing with increasing stem density, M, which is also true for the intensity of the velocity deviations IVD. Thus, in this case of the stem density change, the intensity of the velocity deviation was increasing more rapidly than the turbulent diffusion coefficient. This was similar to former research (Murphy et al., 2007) that maintained that for higher density canopies, the dispersion coefficients were higher. These results clearly illustrated that in the vegetated flow, the roles of the turbulent diffusion coeffiux uz , were as significant as cient, εz, and the turbulent shear stress, the effect of the velocity deviation, us′, in the calculation of the longitudinal dispersion coefficient from the vertical profiles of the streamwise velocity. The results of Fig. 7a) were plotted with the experimental results from former research (Murphy et al., 2007) in Fig. 8a). The vegetation densities for the former experiments were comparable as the values ranged (1.5 to 4.8), while this research had values of (0.85 to 2.97). The comparison result showed that in the former experiment, the dimensionless longitudinal dispersion coefficient values approached a constant value in higher submergence ratio Sr > 2, while the current research using velocity-based calculation results showed a linear increase with higher submergence ratio. This shows that the role of the 10
Ecological Engineering 145 (2020) 105721
J. Shin, et al.
coefficient, DLC, were listed in in Table 2, and plotted in Fig. 8b) along with the velocity-based dispersion coefficient, DLV. The results show a linear relation between the velocity-based dispersion coefficient, DLV, and the concentration based coefficient DLC, even though the DLC values were somewhat larger than those of DLV. The larger values of the longitudinal dispersion coefficients driven by the concentration curves could be due to the additional mixing effect by storage zones of the submerged vegetation, while the velocity driven coefficients only accounted for the shear flow effects which was shown in open channel experiments without considering vegetation (Jung et al., 2019). Although the former research (Jung et al., 2019) compared transverse dispersion coefficients, a similar result was shown with longitudinal dispersion, but with the introduction of vegetation the reason for storage zones was more evident in these experiment results. Former studies (Nepf et al., 1997) have also maintained that the storage zones of the submerged vegetation could be generated from physical obstruction associated with plant stems, and this study showed the effects of the vegetation to storage zones and mixing using both velocity-based and concentration-based methods. Since results from both methods are comparable to each other, it shows the feasibility for using the velocity driven method as an alternative to the traditional high-cost concentration driven method in vegetated channels.
concentration-based coefficients, DLC, had higher values than the velocity-based dispersion coefficients, DLV. These differences could be explained by the fact that concentration-driven dispersion coefficient included the additional mixing mainly by storage effects due to the submerged vegetation, while the velocity-based coefficient only accounts for shear flow effects. This finding suggests that the velocitybased method can be used to obtain the longitudinal dispersion coefficient in vegetated open channel flows, without performing the highcost tracer test. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement This research is supported by the BK21 PLUS research program of the National Research Foundation of Korea and also supported by the Korea Ministry of Environment (MOE) as “Chemical Accident Response R&D Program (2018001960001).” This research work was conducted at the Institute of Engineering Research and Institute of Construction and Environmental Engineering in Seoul National University, Seoul, Korea.
5. Conclusions
References
The mixing characteristics of pollutants in open channel flows with submerged vegetation were investigated through velocity measurements and tracer experiments. The effects of the submergence ratio and stem density on the vertical distribution of the stream-wise velocity and the turbulent shear stress were analyzed, and the longitudinal dispersion coefficients calculated from both the velocity and concentration data were compared. The experimental results show that the vertical distributions of the stream-wise velocity were similar for different submergence ratio and stem density in which the velocity was retarded by the vegetation stem while the velocity in the surface layer increased with water depth taking the logarithmic profile. At the shear layer, the velocity increased very sharply, and this large velocity gradient was closely related to the velocity fluctuations that induced the large turbulent shear stresses at the interface between vegetation and surface layers. Both the intensity of velocity deviation and the turbulent shear stress tended to increase with increasing submergence ratio and with increasing stem density. The longitudinal dispersion coefficient was calculated using two different methods: the first one, named the velocity-based dispersion coefficient, DLV, was calculated from the velocity profile data, and the second one, named the concentration-based dispersion coefficient, DLC, was calculated from the concentration-time data. The results of the velocity-based dispersion coefficient show that, unlike the intensity of the velocity deviation, DLV was increasing as the submergence ratio, Sr, increased for all cases of the stem density. Compared to former research, this monotonic increase of the velocity-based dispersion coefficient was different from the concentration-based dispersion coefficients, where the values approached a constant value in higher submergence ratio over 2.0. The reason for this increase of DLV was considered to be the turbulent diffusion coefficient, εz, which is a denominator in the dispersion equation, decreased more rapidly than the velocity deviation, us′, as Sr increased. Also, DLV was increasing with increasing stem density, M, which is also true for the intensity of the velocity deviations IVD. These results indicate that in the vegetated flow, variation of the turbulent diffusion coefficient needs to be adequately considered, as well as the distribution of the velocity deviation, in the calculation of the longitudinal dispersion coefficient from the vertical profiles of the stream-wise velocity. As the stem density increased, the concentration-based longitudinal dispersion coefficients, DLC, also increased. The comparison of the two dispersion coefficients shows a linear relation between DLC and DLV. The
Aris, R., 1956. On the dispersion of a solute in a fluid flowing through a tube. Proceed. Royal Soc. A. 235 (1200), 67–77. Baek, K.O., Seo, I.W., 2010. Routing procedures for observed dispersion coefficients in two-dimensional river mixing. Adv. Water Resour. 33 (12), 1551–1559. Baptist, M.J., Babovic, V., Rodriguez, U.J., Uittenbogaard, R.E., Mynett, A., Verwey, A., 2007. On inducing equations for vegetation resistance. J. Hydraul. Res. 45 (4), 435–450. Beltaos, S., 1980. Transverse mixing tests in natural streams. J. Hydraul. Div. 106 (10), 1607–1625. Bogle, G.V., 1997. Stream velocity profiles and longitudinal dispersion. J. Hydraul. Eng. 123 (9), 816–820. Bulat, M., Biron, P.M., Lacey, J.R., Botrel, M., Hudon, C., Maranger, R., 2019. A three‐dimensional numerical model investigation of the impact of submerged macrophytes on flow dynamics in a large fluvial lake. Freshw. Biol. 64 (9), 1627–1642. Carr, M.L., Rehmann, C.R., 2007. Measuring the dispersion coefficient with acoustic doppler current profilers. J. Hydraul. Eng. 133 (8) 997–982. Elder, J.W., 1959. The dispersion of marked fluid in turbulent shear flow. 5, 544–560. Errico, A., Lama, G.F.C., Francalanci, S., Chirico, G.B., Solari, L., Preti, F., 2019. Flow dynamics and turbulence patterns in a drainage channel colonized by common reed (Phragmites australis) under different scenarios of vegetation management. Ecol. Eng. 133, 39–52. Fischer, H.B., 1966. Longitudinal dispersion in laboratory and natural streams. In: W M Keck Laboratory of Hydraulics and Water Resources Report, https://doi.org/10. 7907/Z9F769HC. Fischer, H.B., 1968. Dispersion predictions in natural streams. J Sanit Eng 94 (SA5), 927–943. Fischer, H.B., List, E.J., Koh, R.C.Y., Imberger, J., Brooks, N.H., 1979. Mixing in Inland and Coastal Waters. Academic Press, New York. Ghisalberti, M., Nepf, H., 2002. Mixing layers and coherent structures in vegetated aquatic flows. J. Geophys. Res. 107 (C2), 3011. Ghisalberti, M., Nepf, H., 2004. The limited growth of vegetated shear layers. In: Water Resour. Res, doi:tp10.1029/2003WR002776. Ghisalberti, M., Nepf, H., 2009. Shallow flows over a permeable medium: the hydrodynamics of submerged aquatic canopies. Transp. Porous Media 78, 309–326. Hamidifar, H., Omid, M.H., Keshavarzi, A., 2015. Longitudinal dispersion in waterways with vegetated floodplain. Ecol. Eng. 84, 398–407. Jung, S.H., Seo, I.W., Kim, Y.D., Park, I., 2019. Feasibility of Velocity-based Method for Transverse Mixing Coefficients in River Mixing Analysis. J. Hydraul. Eng. 145 (11), 04019040. Kadlec, R., Knight, R., 1966. Treatment wetlands. Lewis publishers, FL. Kim, D., 2012. Assessment of longitudinal dispersion coefficients using acoustic Doppler current profilers in large river. J. Hydro-environment Res. 6 (1), 29–39. Klopstra, D., Barneveld, H.J., Noortwijk, J.M., Velzen, E.H., 1997. Analytical model for hydraulic roughness of submerged vegetation. In: Proc 27th IAHR Congress, pp. 775–780. Kouwen, N., Unny, T., Hill, H., 1969. Flow retardance in vegetated channels. J. Irrig. Drain. 95 (2), 329–342. Launay, M., Le Coz, J., Camenen, B., Walter, C., Angot, H., Dramais, G., Faure, J.B., Coquery, M., 2015. Calibrating pollutant dispersion in 1-D hydraulic models of river networks. J. Hydro Environ. Res. 9 (1), 120–132.
11
Ecological Engineering 145 (2020) 105721
J. Shin, et al. Lee, M.E., Seo, I.W., 2013. Spatially variable dispersion coefficients in meandering channels. J. Hyraul. Eng. 139 (2), 141–153. Lightbody, A., Nepf, H., 2006. Prediction of velocity profiles and longitudinal dispersion in emergent salt marsh vegetation. Limnol. Oceanogr. 51 (1), 218–228. MacDonald, L., 1994. Water pollution solution: build a marsh. Am. For. 100 (7), 26–29. Murphy, E., Ghisalberti, M., Nepf, H.M., 2007. Model and laboratory study of dispersion in flows with submerged vegetation. Water Resour. Res. 43 (5). Nepf, H.M., Ghisalberti, M., 2008. Flow and transport in channels with submerged vegetation. Acta. Geophysica. 56 (3), 753–777. Nepf, H., Mugnier, C., Zavistoski, R., 1997. The effects of vegetation on longitudinal dispersion. Estuar. Coast. Shelf Sci. 44, 675–684. Nepf, H., Ghisalberti, M., White, B., Murphy, E., 2007. Retention time and dispersion associated with submerged aquatic canopies. Water Resour. Res. 43 (4). Palmer, M., Nepf, H., Petterson, T., Ackerman, J., 2004. Observations of particle capture on a cylindrical collector: Implications for particle accumulation and removal in aquatic systems. Limnol. Oceanogr. 49, 76–85. Raupach, M., Finnigan, J.J., Brunet, Y., 1996. Coherent eddies and turbulence in vegetation canopies: the mixing-layer analogy. In Boundary-layer meteorology 25th anniversary volume, Springer. Dordrecht. 1970–1995, 351–382. Righetti, M., Armanini, A., 2002. Flow resistance in open channel flows with sparsely distributed bushes. J. Hydrol. 269 (1–2), 55–64. Rutherford, J.C., 1994. River Mixing. Wiley, Chichester, UK. Schultz, M., Kozerski, H.P., Pluntke, T., Rinke, K., 2002. The influence of macrophytes on sedimentation and nutrient retention in the lower river spree. Water Res. 37, 569–578. Seo, I.W., Baek, K.O., Jeon, T.M., 2006. Analysis of transverse mixing in natural streams under slug tests. J. Hydraul. Res. 44 (3), 350–362.
Seo, I.W., Choi, H.J., Kim, Y.D., Han, E.J., 2016. Analysis of two-dimensional mixing in natural streams based on transient tracer tests. J. Hydraul. Eng. 142 (8). Shen, C., Niu, J., Anderson, E.J., Phanikumar, M.S., 2010. Estimating longitudinal dispersion in rivers using acoustic Doppler current profilers. Adv. Water Resour. 33 (6), 615–623. Shimizu, Y., Tsujimoto, T., 1994. Numerical analysis of turbulent open-channel flow over a vegetation layer using a k-ɛ turbulence model. J. Hydrosci. Hydraul. Eng. 11 (2), 57–67. Shucksmith, J.D., Boxall, J.B., Guymer, I., 2010. Effects of emergent and submerged natural vegetation on longitudinal mixing in open channel flow. Water Resour. Res. 46 (4). Shucksmith, J.D., Boxall, J.B., Guymer, I., 2011. Determining longitudinal dispersion coefficients for submerged vegetated flow. Water Resour. Res. 47 (10). Taylor, G., 1954. The dispersion of matter in turbulent flow through a pipe. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 223 (1155), 446–468. Velasco, D., Bateman, A., Redondo, J.M., Demedina, V., 2003. An open channel flow experimental and theoretical study of resistance and turbulent characterization over flexible vegetated linings. Flow Turbul Combust 70 (1–4), 69–88. White, B.L., Nepf, H.M., 2003. Scalar transport in random cylinder arrays at moderate Reynolds number. J. Fluid Mech. 487, 43–79. Yang, W., Choi, S., 2010. A two-layer approach for depth-limited open-channel flows with submerged vegetation. J. Hydraul. Res. 48 (4), 466–475. Zhu, Z., Motta, D., Jackson, P.R., Garcia, M.H., 2017. Numerical modeling of simultaneous tracer release and piscicide treatment for invasive species control in the Chicago Sanitary and Ship Canal. Environ. Fluid Mech. 17 (2), 211–229.
12
Contents lists available at ScienceDirect
Ecological Engineering journal homepage: www.elsevier.com/locate/ecoleng
Longitudinal dispersion coefficient for mixing in open channel flows with submerged vegetation
T
Jaehyun Shina, Jin Yu Seoa, Il Won Seob,
⁎
a
Department of Civil and Environmental Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, South Korea Department of Civil and Environmental Engineering, Institute of Construction and Environmental Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, South Korea
b
ARTICLE INFO
ABSTRACT
Keywords: Vegetated flow Vertical shear Longitudinal dispersion coefficient Submergence ratio Stem density Shear stress
An experimental investigation was conducted to analyze the flow and pollutant mixing characteristics in the vegetated channel, in which the velocity data was collected by micro acoustic Doppler velocimeter, and pollutant dispersion data was obtained through tracer tests in an open channel with submerged vegetation. The effects of submergence ratio (Sr = 2.0–3.5), and stem density (M = 0.4–5.9) on the vertical distribution of the stream-wise velocity and the turbulent shear stress were analyzed. The results of the flow experiments showed that the intensity of velocity deviation became larger with increasing stem density and decreasing submergence ratio. The turbulent shear stress at the exchange zone also increased with submergence ratio, as well as with increasing stem density. The calculation results of the longitudinal dispersion coefficient based on the vertical velocity profile data showed that as the submergence ratio and stem density increased, the dispersion coefficients increased linearly. This monotonic increase of the velocity-based dispersion coefficient differed from former research, in which concentration-based dispersion coefficient values approached a constant value in a higher submergence ratio of over 2. Comparison of the velocity-based longitudinal dispersion coefficients with concentration-based coefficients in this research demonstrated that the velocity-driven coefficient had a linear relation with the concentration-driven coefficients, with smaller values than the concentration-based dispersion. This difference can be explained by the fact that concentration-driven dispersion coefficient included the storage effects due to the submerged vegetation, while the velocity-driven coefficient only accounted for shear flow effects.
1. Introduction In conventional river management practices, the aquatic plants had been removed from the waterways to enhance the transport and conveyance of flood flow. However, in recent years, river vegetation is preserved because aquatic plants improve the quality of water through nutrient uptake and oxygen production, and can also act as natural treatment plants that filter and dilute land-source pollutants through physical and biological process (Kadlec and Knight, 1966; MacDonald, 1994). In natural channels where the plants coexist within the water body, the vegetation both in emergent and submerged conditions dramatically alters the flow dynamics and mixing of pollutants (Ghisalberti and Nepf, 2002). Vegetation also affects the deposition of sediments, which aids in the removal of absorbed contaminants while reduced bed shear stress prevents the resuspension of polluted sediments (Palmer et al., 2004; Schultz et al., 2002).
⁎
As the vegetation affects the vertical velocity profile, the type of plant and the density of canopy serve as important factors in changes to the flow dynamics (Ghisalberti and Nepf, 2002). The effects of vegetation on flow have been studied by many researchers via laboratory experiments and numerical models with rigid cylinder, flexible vegetation prototypes, and natural vegetation on open-channel flows. To find the velocity characteristics in vegetated channels several researches for analytical equations and modeling were conducted, such as Shimizu and Tsujimoto (1994) which utilized different turbulence closure schemes to model the vertical velocity profile. Klopstra et al. (1997) proposed analytical expressions to represent the flow velocity profile in various roughness flume experiments using a logarithmic form. Baptist et al. (2007) also developed equations with genetic programming to describe analytical expressions for vegetation resistance. Yang and Choi (2010) proposed a velocity relationship to predict the velocity distribution in two-layer flow in vegetation. Also, field
Corresponding author. E-mail address: [email protected] (I.W. Seo).
https://doi.org/10.1016/j.ecoleng.2020.105721 Received 5 September 2019; Received in revised form 27 December 2019; Accepted 7 January 2020 0925-8574/ © 2020 Elsevier B.V. All rights reserved.
Ecological Engineering 145 (2020) 105721
J. Shin, et al.
Fig. 1. Schematic diagram of flow characteristics of submerged vegetation flow: a) Streamwise velocity, b) Turbulent shear stress, c) Turbulent diffusion coefficient; Solid line means flow characteristics in case of vegetated flow and dotted line indicates the case of non-vegetated flow. (Adapted from Raupach et al., 1996)
vegetation. Hamidifar et al. (2015) calculated the longitudinal mixing using image processing to estimate the tracer concentration in compound open channels in smooth and vegetated floodplains to find out that vegetation can delay peak concentration up to 500%. Since these research efforts used only the tracer tests to calculate the longitudinal dispersion coefficients, they did not use the velocity measurements directly so the effects of vertical shear contributions from the velocity deviations over fast and slow zones were not fully addressed. With the advancement of velocity measurement equipment velocity profiles could be easily obtained, and 2D dispersion coefficients could be calculated effectively using the equation by Fischer et al. (1979). The equations assumed that the shear dispersion were more dependent on the vertical deviation of velocity than molecular diffusion, and calculated the two-dimensional coefficients using triple integration to the deviation of 2D vertical velocities. Although this method had been applied to open channels (Carr and Rehmann, 2007) or laboratory experiments (Lee and Seo, 2013) the application to vegetated channels have not been conducted previously. Also, the former studies related to analysis of velocity characteristics in vegetated channels did not find its effects to mixing in channels. Thus, direct calculation of the longitudinal dispersion coefficients from the detailed velocity measurements (Fischer et al., 1979), where both the effects of the vertical velocity deviation and the vertical distribution of the turbulent diffusion coefficient were considered, needs to be compared with the results by the concentration-based method. The objective of this study is to analyze the effect of submerged aquatic plants on longitudinal mixing in waterways by observation of the vertical velocity profile in vegetated channels. The experiments were conducted with different vegetation submergence ratio, and canopy density, and the detailed velocity profile was measured using a micro acoustic Doppler velocimeter (ADV) for each cases. The calculation of the longitudinal dispersion coefficient based on the velocity profile data was compared with the concentration-based method from the tracer experiment data.
experimental surveys of vegetation affect to flow velocity in natural rivers (Errico et al., 2019) or in a large fluvial lake (Bulat et al., 2019) have been conducted previously. These studies showed that vegetation and canopy drag would reduce velocities in these open channels. Other studies conducted additional mixing experiments in vegetated channels to show that the reduced velocities could cause particulates and contaminants to settle out of the water body. Various approaches have been proposed to analyze these effects, and the analyses were based on the two-layer method to describe flow through submerged vegetation. Fig. 1 shows that in these methods, the flow domain was usually divided into three layers: one through the vegetation called the “vegetation layer”, the “surface layer” above the vegetation, and the “shear layer” in between. In the case of canopy density, dense submerged canopies caused an inflection point of the velocity profile at the top of the canopy between the two layers due to the shear layer effect (Ghisalberti and Nepf, 2002; Nepf and Ghisalberti, 2008). The density of the vegetation would affect the position of the inflection point and the velocity difference of the vegetation layer and the surface layer (Ghisalberti and Nepf, 2004). Therefore, to find the characteristics of vegetation effect on flow and contaminant mixing, careful research of the changes of vertical velocity profile by vegetation and canopy density should be undertaken. Fig. 1 shows that in addition to the canopy density, the submergence ratio of vegetation also significantly affects the vertical profile of stream-wise velocity, in which the stream-wise velocity decreases in the vegetated zone and increases sharply in the upper water body above the vegetation. This causes increase of the vertical shear, and pollutant particles to spread faster than in non-vegetated channels. Because the velocity profile in submerged vegetation is different from a logarithmic form over the full depth, as plotted by a dotted line in Fig. 1, the traditional treatment of longitudinal dispersion in open channels without vegetation cannot be directly applied to vegetated ones. The longitudinal dispersion in flows with emergent and submerged vegetation has been studied by several researchers based on tracer tests in which they calculated longitudinal dispersion coefficients using either the moment-based method (Aris, 1956), or the routing method (Fischer, 1968; Fischer et al., 1979). The studies for mixing in vegetation included studies such as Nepf et al. (1997) which showed the increase of vertical shear in vegetation would also increase the longitudinal dispersion. White and Nepf (2003) showed that the unsteady recirculation zone close to vegetation cylinders, and velocity defect behind each cylinders affected the longitudinal mixing in tracer experiments. Lightbody and Nepf (2006) maintained that the size of the vertical velocity will vary inversely with canopy drag in vegetated channels. Later, Shucksmith et al. (2011) developed a mathematical model to predict the longitudinal mixing in real vegetation and found the mixing layer size to be related with the growing
2. Theoretical backgrounds 2.1. Flow and mixing characteristics in vegetated flows Fig. 1 shows that in submerged vegetated flows, as aforementioned, the flow field can be split into three distinct zones: a slow-moving zone through the vegetation (vegetation layer), a faster free-flow zone over the top of the canopy (surface layer), and a shear layer zone in-between (shear layer). The flow above the vegetation behaves as a turbulent shear layer, while the vegetation compared within the non-vegetated channels retards the flow within the vegetated or wake zone. A logarithmic law (Kouwen et al., 1969) can describe the velocity profile in 2
Ecological Engineering 145 (2020) 105721
J. Shin, et al.
the layer above the vegetation. The shear layer in-between has the maximum turbulent shear stress among the three layers as the velocities rapidly increase. Studies showed that this shear layer transported the mass pollutant more efficiently than momentum transport (Ghisalberti and Nepf, 2002). In addition, vortices dominated the vertical transport between the surface layer and vegetation layer (Ghisalberti and Nepf, 2009), which led to faster vertical transport of pollutants in the shear layer. The submergence ratio of the vegetation, Sr, in open channels in which Sr is defined as the ratio of water depth divided by the vegetation height, affects the vertical velocity profile. If the submergence ratio is small, i.e. the depth of the vegetation layer is large compared to the total depth of the channel, the retardation of the velocity profile becomes more prominent. In the cases where the submergence ratio is larger, the stem height would be smaller compared to the water depth, therefore the surface layer in Fig. 1a) would be larger compared to the vegetation layer, and the vertical velocity shear gets smaller. Former research showed that as the submergence ratio increased, the effects of retardation decreased (Shucksmith et al., 2010). The vertical velocity profile in flows with submerged vegetation is also dependent on the canopy density (Ghisalberti and Nepf, 2002). There are two types of behavior according to the canopy density: if bed drag is larger than canopy drag, then the mean velocity profile follows a turbulent logarithmic velocity profile in sparse density. If the bed drag is smaller than canopy drag, then the discontinuity in drag generates a region of shear resembling a free shear layer causing an inflection point at the top of the canopy in dense submerged canopies (Ghisalberti and Nepf, 2002; Nepf and Ghisalberti, 2008). In vegetated channels, the main source of velocity shear is between the vegetated and surface layers (Shucksmith et al., 2011). In the case of sparse vegetation, the velocity difference between the vegetated and surface layers is lower than for the case of dense vegetation. Also, the less dense and deeply submerged canopies' turbulent motions of vortices in the mixing layer penetrate the entire canopy height, and transfer mass and momentum between the main channel and the canopy; the vertical velocity profiles with the inflection point in vegetated channels makes the flow susceptible to instability leading to the generation of vortices within the layers. Thus, in the case of sparse density canopy, the vertical velocity profile shows a boundary-layer form without the inflection point. The submerged vegetation also produces difference in normalized turbulent stress in the channels (Raupach et al., 1996) where the vegetated layer and surface layer is generated as depicted in Fig. 1b). Nepf and Ghisalberti (2008) and Shucksmith et al. (2010) showed in their experiments that the maximum Reynolds turbulent stress occurred at the vegetation top; but without vegetation, the peak is located near the bottom of the channel, as plotted by the dotted line in Fig. 1b), typically shown for the turbulent stress for fully developed flow. For vegetated flows, as shown in Fig. 1b), the highest point of Reynolds turbulent stress is located at the shear layer along with the inflection point in the vertical velocity profile. Since the estimated Reynolds turbulent stress can be used as the numerator, and the velocity gradient as the denominator to calculate the turbulent diffusivity coefficient, using the Reynolds analogy that the mixing coefficients for mass transport and momentum transport are the same for the fully turbulent flow (Fischer, 1966). A solid line in Fig. 1c) can depict the typical profile of the turbulent diffusion coefficient. Thus, the vertical profile of the turbulent diffusion coefficient for vegetated flows is different from that for nonvegetated flows, since the maximum point of the turbulent diffusion coefficient is located in the middle of the depth without vegetation, while the profile of the turbulent stress with vegetation has two peak values as shown in Fig. 1c) due to the velocity gradient of the flow. Mixing in vegetated flows is caused by a combination of diffusion and dispersion processes by velocity shear with contribution from trapping mechanisms by the vegetation. The vegetation layer would create a relatively low velocity field where a fraction of the contaminant would be trapped in the vegetation, and released after the
main cloud has passed (Nepf et al., 1997). Due to these characteristics of vegetated flow, the range of dispersion coefficients related to longitudinal mixing has a wide range, which reflects the large influence that different hydraulic and physical parameters have on the mixing processes (Shucksmith et al., 2011). In the case of dense vegetation, the vortices generated in the flow did not penetrate to the channel bed so the longitudinal mixing was comparatively higher than for the sparsely vegetated channels (Shucksmith et al., 2010), while some submerged cases did not show a clear trend in the changes to the longitudinal mixing coefficient (Nepf et al., 2007). An experimental study with the model vegetation by Murphy et al. (2007) showed that when the submerged ratio was higher than 2.0, the non-dimensionalized longitudinal mixing coefficient became approximately constant with depth, while in the experiment by Shucksmith et al. (2010), when Sr is lower than 2.0, longitudinal dispersion coefficient monotonically increased with increasing Sr. The relative importance of the shear dispersion could outweigh the importance of dispersion due to exchange between the vegetated layer and surface layer, with higher submergence ratio. 2.2. Calculation of dispersion coefficients 2.2.1. Mixing in open channel flows Mixing in open channel flows is caused by a combination of diffusion and dispersion processes with additional contribution from the effect of dead zones. Shear dispersion is the spreading of solute due to the spatial variation of primary velocities in the channel. For the modeling of solute dispersion in the intermediate region in the open channel flow, the two-dimensional (2D) depth-averaged advectiondispersion equation (ADE) has frequently been used (Rutherford, 1994). The 2D advection-dispersion equation derived by depth-averaging the three-dimensional transport equation for natural channels could be shown in the curvilinear coordinate system as the following (Lee and Seo, 2013):
C C C 1 C 1 C + us + un = hDL + hDT t s n h s s h n n
(1)
where C is the depth-averaged concentration; us and un are the depthaveraged velocities in the streamwise and span-wise directions, respectively; DL is the longitudinal dispersion coefficient; DT is the transverse dispersion coefficient; h is the local depth; s is the streamwise direction; n is the spanwise direction; and t is time. The depth-averaged velocities are the following:
us =
1 h
0
un =
1 h
0
h
us dz
(2a)
un dz
(2b)
h
where us and un are the point velocities in the streamwise and span-wise directions, respectively; and z is the vertical distance from the channel bottom as shown in Fig. 1. 2.2.2. Velocity-based dispersion coefficient To use the 2D ADE for the analysis of contaminant transport in the shallow flows of rivers, the appropriate dispersion coefficients should be provided. The analysis undertaken by Taylor, 1954 remains the most commonly used method to describe mixing using dispersion coefficients in turbulent open channel flow. Assuming that the shear dispersion is more dependent on the vertical deviation of velocity than molecular diffusion, the two-dimensional coefficients could be derived as follows (Fischer et al., 1979):
3
DL =
1 h
0
DT =
1 h
0
h
h
us
un
z 0
z
z
z 0
1 0
1 z
z 0
us dzdzdz
un dzdzdz
(3a) (3b)
Ecological Engineering 145 (2020) 105721
J. Shin, et al.
where εz is the vertical turbulent diffusion coefficient; us and un are the deviation of the local velocity from the depth-averaged velocities, us and u¯n in the s and n directions respectively as shown in Fig. 1a). The deviation of velocities is the following:
us = us
us
(4a)
un = un
un
(4b)
2.2.3. Concentration-based dispersion coefficients When concentration data from tracer tests are available, the dispersion coefficients can be calculated by either applying moment-based methods (Seo et al., 2006) or routing procedures (Fischer et al., 1979). For the calculation of both longitudinal and transverse dispersion coefficients from concentration curves of 2D tracer tests, the 2D steamtube routing procedure (2D STRP) is more viable than moment methods because it can calculate the dispersion coefficients based on the dosage profile, which is converted from the concentration-time curves obtained from tracer tests (Baek and Seo, 2010). In this method, the stream-tube method was used with a fixed value of discharge attached to a fixed streamline, by moving the coordinate system back and forth across the cross-section along with the flow; thus, it could efficiently deal with the lateral migration of the water flow in irregularly curved rivers and the tracer cloud in meandering rivers (Seo et al., 2016). The equation for 2D STRP is shown below:
The turbulent diffusion coefficients εz were derived from the equations of vertical shear stress based on the Reynolds analogy that the mixing coefficients for mass transport and momentum transport are the same for the fully turbulent flow (Fischer, 1966). z
ux uz
=
dus dz
(5)
where
u x uz =
1 T
T 0
ux uz dt
(6a)
ux = ux
us
(6b)
uz = u z
w
(6c)
us =
1 T
0
w=
1 T
0
T
T
u x dt
(6d)
uz dt
(6e)
C (s2 , , t ) =
exp
{
4 BC (s2
0
·exp
( 4BC (s2
)2 s1 )
d
U2 (t¯2 t¯1 4DL (t¯2
t + )2 t¯1 )
}d
s1 ) (8)
where C(s2, η, t) is a temporal profile of the predicted concentration at the downstream section, s2; C(s1, ω, τ) is the temporal profile of measured concentration at the upstream section, s1; τ is the dummy time variable of integration; and t1 , t2 are the mean times of passage in sections s1 and s2, respectively. ω is the normalized dummy variable of integration; and η is the dimensionless discharge, U is the averaged velocity for each stream-tube, and Bc is the bulk dispersion coefficient, which is defined as:
where ux and uz are the instantaneous velocities and us and w are the time-averaged velocities in the steamwise and vertical direction, respectively. Using the Reynolds analogy, Elder (1959) derived expressions for longitudinal mixing for boundary layer flow based on the logarithmic profile of velocity and diffusivity in an infinitely wide channel as below:
DL = 5.93HU
C (s1 , , )U t¯1 )
4 DL (t¯2
1
Bc =
Hs 2Us DT Qs 2
(9)
where Qs is the span-averaged value of the flow discharge, Hs is the span-averaged value of the cross-sectional average depth of the river H, Us is the span-averaged value of the cross-sectional averaged velocity, and ψ is the normalized shape factor with the range 1.0–3.6 (Beltaos, 1980). Multiple regression techniques were used to fit the predicted concentration to the measured concentration since the two parameters are determined simultaneously through only one equation Eq. (8). Since this method used the actual contaminant dispersion data, the irregularities of the channel and storage effects due to the submerged vegetation were reflected in the dispersion coefficient results.
(7)
where H shows the cross-section averaged flow depth, and U∗ represents the boundary shear velocity. Although this value has many assumptions in its calculation, it had been widely used in many modeling applications due to its simplicity and applicability. However, in vegetated channels, the effect of aquatic plants changes the logarithmic form of the velocity as shown in Fig. 1a). Hence, other experimental values must be used for the longitudinal dispersion coefficient. In recent years, since with the advancement of velocity measurement equipment such as the Acoustic Doppler velocimeter (ADV) and Acoustic Doppler current profiler (ADCP), velocity profiles can be easily obtained, and 2D dispersion coefficients can be calculated more effectively using Eq. (3). However, the dispersion research using this method was usually focused on the calculation of the longitudinal dispersion coefficient of the one-dimensional mixing assuming the contaminants have gone through full lateral mixing in the far field. (Bogle, 1997; Carr and Rehmann, 2007; Shen et al., 2010; Kim, 2012). They used the acoustic Doppler current profilers to measure the longitudinal velocity in order to estimate the longitudinal dispersion coefficient as an alternative to the tracer test approach. Lee and Seo (2013) conducted the utilization of ADV for the laboratory experiment, which used the data from laboratory flume experiments on a meandering channel to use the vertical velocity profiles to predict the longitudinal and transverse dispersion coefficients. Other research efforts by Launay et al. (2015) and Zhu et al. (2017) were based on the measured velocity of longitudinal flow, and its shear dispersion due to the longitudinal flow distribution. In the case for transverse dispersion coefficients, Jung et al. (2019) measured large rivers in an experiment without considering vegetation. Since these research efforts were conducted under non-vegetated flows, the present research compared the velocity-based method and the concentration-based method in vegetated channels.
3. Experiments 3.1. Experimental set-up The experiments were carried out in a re-circulating flume of 12 m length, 0.3 m width, and with a fixed slope of 0.004 as shown in Fig. 2a). At the head tank, five honeycomb sheets were utilized to eliminate the swirl and provide a stable and uniform flow to the channel with similar setup with previous experiments (Ghisalberti and Nepf, 2002). The water discharge was supplied using the pump that has a capacity of (0.6 to 7.5) L/s, and the water depth was controlled by the tailgate. Artificial vegetation was installed between (5 and 7) m downstream from the head tank. This initial reach prevented the occurrence of large-scale disturbances due to vegetation, and allowed the development of a constant flow in the test section. Fig. 2b) shows that to study the velocity profiles and pollutant mixing in the vegetated flows, the model plants made of acrylic cylinders with a diameter of 6 mm and 0.1 m height were mounted onto acrylic boards of 2 m length, 0.3 m width, and 0.01 m height. The spacing of the acrylic cylinders was different between the lateral and 4
Ecological Engineering 145 (2020) 105721
J. Shin, et al.
Fig. 2. Schematic diagram, photos and results of experiments: a) Schematic diagram of experiment, b) Photo of installed vegetation, c) Photo of tracer cloud (NaCl solution with potassium permanganate).
stream-wise directions depending on the stem density. To analyze the effect of the vegetation on the characteristics of flow and pollutant mixing, the stem density was selected as (0.40, 0.85, 1.53, 2.97 and 5.94) m−1, in which the stem density is defined as
M = ad
Table 1 Summary of experimental conditions and results.
(10)
where a(m−2) is the number of cylinders per unit area, in stems per square meter; and d(m) is the cylinder diameter. Besides the stem density, the submergence ratio, Sr, the ratio of the water depth to the stem height, H/hV, was also selected as a significant parameter in the analysis of the velocity structure and mixing mechanism of the vegetated flow. Here, hV is the height of the model vegetation, and H is the water depth. In this experiment, four different conditions of the submergence ratio were tested in the range (2.0 to 3.5). Sr in this study was set to higher values than 2.0 in order to validate the results of Murphy et al. (2007), in which when Sr > 2.0, the longitudinal dispersion coefficient approached a constant value. Table 1 summarizes these experimental conditions, along with the results of the longitudinal dispersion coefficient calculated from the velocity profile data.
5
Case
Sr
M (m−1)
U (m/s)
IVD (m/s)
DLV (m2/s)
DLV/HU∗
S120 S121 S122 S123 S124 S131 S132 S133 S140 S141 S142 S143 S144 S151 S152 S153
2.0
0.40 0.85 1.53 2.97 5.94 0.85 1.53 2.97 0.40 0.85 1.53 2.97 5.94 0.85 1.53 2.97
0.119 0.118 0.114 0.110 0.114 0.099 0.103 0.102 0.082 0.082 0.085 0.084 0.086 0.069 0.069 0.070
0.0191 0.0234 0.0271 0.0327 0.0330 0.0113 0.0150 0.0210 0.0064 0.0097 0.0119 0.0168 0.0184 0.0075 0.0094 0.0124
0.0059 0.0124 0.0197 0.0256 0.0318 0.0149 0.0248 0.0335 0.0173 0.0205 0.0268 0.0417 0.0490 0.0371 0.0382 0.0430
3.77 6.02 8.63 7.66 8.98 7.16 10.4 10.6 11.5 12.0 10.9 15.5 15.0 21.7 17.0 16.9
2.5 3.0
3.5
Ecological Engineering 145 (2020) 105721
J. Shin, et al.
3.2. Velocity measurements
Table 2 Summary of dispersion study.
To collect the data of the stream-wise velocity at a number of vertical points in the cross sections of the vegetated reach of the channel, an acoustic Doppler velocity meter (SONTEK; 16 MHz Micro ADV) with down-looking probes was used as shown in Fig. 2a). The figure shows that the velocity profiles were measured at the centerline in six cross sections. The velocities were measured from the water surface down to the point at 1 cm above the bottom with (2 or 3) cm intervals, and more densely inside the vegetation zone with 1 cm intervals. At each point of the velocity measurement, the velocity was sampled for 120 s at the sampling rate of 25 Hz (Velasco et al., 2003) to make a total of 3000 samples at each point. This sampling duration of 120 s was selected through time scale analysis for the mean velocity. Later from the 3000 instantaneous values of the three-dimensional velocities, the turbulence-averaged velocities and turbulence shear stress were calculated using Eqs. 5 and 6. Fig. 2a) also shows that the velocities in the upper zone from the water surface to the water depth of 6 cm could not be measured, because the distance to the sampling point of Micro ADV was 5 cm away from the sensor. The unmeasured velocities near the water surface were extrapolated by applying the logarithmic law since the surface layer of vegetated flow follows the logarithmic form (White and Nepf, 2003).
Cp (ppm)
tp (sec)
tc (sec)
σ2 (ppm)2
DLC (m2/s)
DLC/HU∗
S120
C1 C2 C1 C2 C1 C2 C1 C2 C1 C2
30.62 17.27 23.03 12.32 27.90 18.99 30.01 19.96 35.79 16.85
41.25 54.75 41.50 56.25 41.50 56.50 47.50 59.25 42.25 56.00
43.44 57.87 43.38 59.02 43.17 58.07 50.68 61.81 43.57 57.73
23.66 31.09 13.49 43.03 16.38 27.20 31.81 46.17 11.41 52.46
0.0104
6.65
0.0109
5.29
0.0202
8.85
0.0293
8.76
0.0337
9.52
S122 S123 S124
Cp: peak concentration (ppm) of the tracer curve. tp: peak time of tracer. tc: centroid time of tracer. σ2: variance of C-T curve. a Same NaCl solution input with mixture of water, potassium permanganate, and ethanol used for all cases.
submergence ratio were carried out in order to analyze their effects on the velocity profiles in the submerged vegetated flows. The velocity profiles for four different submergence ratios and up to five different stem density cases were collected. Fig. 3 plots the vertical distributions of the normalized velocity versus the dimensionless depth for different submergence ratio and stem density. This figure shows that the vertical distributions of the normalized velocity were similar for different submergence ratio and stem density in which the stream-wise velocity was retarded by the vegetation stem while the velocity in the surface layer increased with increasing vertical coordinate Z/H, taking the logarithmic profile. In the interface between the two layers, the velocity increased very sharply; and this large velocity gradient was closely related to the velocity fluctuations that induced the high turbulent shear stresses at the shear layer as shown in Fig. 5. Fig. 3 also demonstrates that as the submergence ratio increased, the slope of the velocity profile, dus , got steeper. The variation of the dz vertical profile of the stream-wise velocity with the stem density change showed the same trend as the submergence ratio. As the submergence ratio increased, the deviation of the normalized velocity from the depth-averaged value became smaller, which means that stem height was the significant factor for the vertical deviation of the stream-wise velocity. As the stem density increased, the velocity deviation got larger, which means that the stem density was also the essential factor for the vertical deviation of the stream-wise velocity, as was the stem height. To quantify the variation of the velocity deviation, the amount of velocity deviation over the whole flow depth was analyzed using the intensity of velocity deviation (IVD), as defined by the equation given below (Fischer et al., 1979):
The tracer study was conducted to obtain the concentration-time curves, which were used to calculate the concentration-based longitudinal dispersion coefficient in which the 2D stream tube routing method was applied. Tracer experiments were carried out by releasing a dye with an instantaneous injection as a vertical line source at the upstream point of the vegetated section. As the tracer, NaCl solution was used, and it consisted of a mixture of water, potassium permanganate, and ethanol, with the later added to render the solute neutrally buoyant in the channel. At two downstream sections, the NaCl cloud was measured using the electrical conductivity meter (KENEK; MKTS2–50-04) with a sampling rate of 15 Hz. The conductivities provide voltage through the voltage amplification system, and then the voltage was converted to concentration (ppm) from a data acquisition system that was logged on a computer, as shown in Fig. 2a). The two sets of five conductivity sensors were positioned at the upstream and downstream sections of the test area, Sec. C1 and Sec. C2. The NaCl concentration was measured at mid-depth of the vegetation layer and surface layer at Sec. C1 and C2. These sections were located at (7 and 9) m downstream from the injection point respectively, ensuring the complete vertical mixing of the injected tracer. The criteria for the complete vertical mixing of the tracer cloud were checked using the equation given below:
IVD =
¯ 2 UH z
Section
S121
3.3. Concentration measurements
L = 0.1
Casea
(11)
1 H
H 0
us 2dz
1/2
(12)
Fig. 4 plots the variation of IVD against the submergence ratio and the stem density. Fig. 4a) shows that as Sr increased, IVD was decreasing exponentially, which was already found in the variation of the vertical velocity profiles shown in Fig. 3. Fig. 4b) also shows that with increasing stem density, IVD was increasing. In this case, the rate of increase of IVD was rather gradual or linear, compared to the rapid decrease of IVD with increasing Sr.
where εz is the vertical turbulent diffusion coefficient, H is the water depth, U¯ is the depth-averaged streamwise velocity, L is the length required for complete vertical mixing. Fig. 2c) indicates that the tracer cloud was moving downstream, maintaining full mixture over the entire water depth. Table 2 summarizes the experimental conditions of the tracer experiment, along with the statistical parameters and longitudinal dispersion coefficients calculated from the concentration curves.
4.2. Calculation of the dispersion coefficient using the vertical velocity profile
4. Results and discussions
The measured vertical velocity distribution were used to calculate the longitudinal dispersion coefficient by Eq. (3a)), and this coefficient was named the velocity-based dispersion coefficient, DLV. To complete the calculation of the triple integration of Eq. (3a)), the vertical
4.1. Analysis of the velocity profile As listed in Table 1, 16 runs with different stem density and 6
Ecological Engineering 145 (2020) 105721
J. Shin, et al.
Fig. 3. Variation of vertical velocity distributions with stem density for different submergence ratio.
turbulent diffusion coefficient, εz needed to be determined. In the vegetated flows of this study, assuming that the turbulent transport of mass and momentum is equivalent, Eq. (5) was incorporated into Eq. (3a)) to calculate the longitudinal dispersion coefficient considering the vertical variations of both velocity and turbulent diffusion coefficient as sketched in Fig. 1. Fig. 5 represents vertical distributions of the Reynolds turbulent stress for different submergence ratio and stem density cases. In this figure, the vertical profile of the turbulent shear stress showed the Gaussian distribution in which the maximum turbulent shear stress z occurred at the top of the canopy which is the shear layer, i.e., h = 1,
and decreased exponentially with increasing vertical coordinate. This profile is completely different from the linear one as maintained by previous researchers, including Righetti and Armanini (2002), that the distribution of shear stress above vegetation followed a linear trend between the vegetation top and the free surface. In the vegetation zone, the turbulent shear stress showed almost zero near the flume wall, and with increasing vertical coordinate, it increased exponentially. Fig. 5 shows that with decreasing submergence ratio and increasing stem density, the Reynolds turbulent stress increased. The turbulent diffusion coefficient was calculated using Eq. (5), and plotted against z/H in Fig. 6. This figure shows that, unlike the vertical distribution of the Reynolds turbulent stress shown in Fig. 5, maximum
v
7
Ecological Engineering 145 (2020) 105721
J. Shin, et al.
Fig. 4. Variation of IVD with stem density and submergence ratio.
Fig. 5. Vertical distributions of Reynolds turbulent stress along with stem density. 8
Ecological Engineering 145 (2020) 105721
J. Shin, et al.
Fig. 6. Vertical distributions of turbulent diffusion coefficient along with stem density.
values of εz occurred near the water surface of the surface layer not at z the top of the canopy, h = 1. At the shear layer, as shown in Fig. 3, the v slope of the velocity profile, which is the denominator in Eq. (5), was the largest even though the Reynolds turbulent stress had the maximum z value, which produced the small values of εz at h = 1. v Table 1 lists the longitudinal dispersion coefficients calculated by Eq. (3a)), and Fig. 7 plots them against the stem density and the
submergence ratio. Table 1 also shows the dimensionless values of DLV that were calculated using the shear velocity given as:
U =
max
=
(
u x uz )max (13)
where τmax is the maximum Reynolds stress which is located at the top of the vegetation (Murphy et al., 2007). Fig. 7a) reveals that, unlike the
Fig. 7. Variation of velocity-based longitudinal dispersion coefficient with stem density and submergence ratio. 9
Ecological Engineering 145 (2020) 105721
J. Shin, et al.
Fig. 9. Time concentration curves for Case S123. a) Upstream section C1, b) Downstream section C2.
turbulent diffusion coefficient and turbulent shear stress in the calculation of the velocity-based longitudinal dispersion coefficient had greater effect in higher submergence ratio, which caused the difference from the former result of the longitudinal dispersion coefficients calculated by the moment method (Murphy et al., 2007) applied to the concentration data, while for higher density the results remained similar. 4.3. Calculation of the dispersion coefficient using concentration curves
Fig. 8. Comparison of longitudinal dispersion coefficients calculated from velocity and concentration data.
In the dispersion study, the concentration-time curves were obtained at five lateral points in two sections, C1 and C2, as shown in Fig. 2. Fig. 9 plots the typical concentration-time curves measured at Sections C1 and C2 for Case S123, in which the concentration-time curves were smoothed by applying the moving average method. This figure shows that the concentration-time curves represent an asymmetric distribution, and the peak concentration was found in the center of the channel. As the tracer cloud moved downstream, the variance of the concentration-time curves increased, and showed a longer tail of concentration due to submerged vegetation, as shown in Fig. 9. Table 2 lists the statistical parameters of the concentration-time curves at the channel center for each case, along with the longitudinal dispersion coefficient calculated by Eq. (8). Table 2 also shows that as M increases, the variance increment between Sec. C1 and Sec. C2 increases, which meant that the longitudinal dispersion was also increasing. In this study, the stream-tube routing procedure (STRP) was used to calculate the longitudinal dispersion coefficient based on the dosage profiles, which were converted from the two-dimensional concentration-time curves shown in Fig. 9 (Seo et al., 2016). In the calculation of the dispersion coefficient by Eq. (8), the time-concentration curve at the downstream section was calculated with the input of the measured time-concentration curves at the upstream section. The predicted curve was repeatedly fitted with the measured curve at Section C2 (downstream), until the optimal value of the dispersion coefficients was found with nonlinear multiple regression technique, to find the longitudinal and transverse dispersion coefficient at the same time. The results of the longitudinal dispersion coefficients calculated from the concentration data, named the concentration-based
intensity of the velocity deviation, DLV was increasing as the submergence ratio, Sr, increased for all cases of the stem density. The reason for this increase of DLV was considered to be that as Sr increased, the turbulent diffusion coefficient, εz, which is a denominator in Eq. (3a)), increased more rapidly than the velocity deviation, us′. Fig. 7b) shows that in the case of stem density, DLV was increasing with increasing stem density, M, which is also true for the intensity of the velocity deviations IVD. Thus, in this case of the stem density change, the intensity of the velocity deviation was increasing more rapidly than the turbulent diffusion coefficient. This was similar to former research (Murphy et al., 2007) that maintained that for higher density canopies, the dispersion coefficients were higher. These results clearly illustrated that in the vegetated flow, the roles of the turbulent diffusion coeffiux uz , were as significant as cient, εz, and the turbulent shear stress, the effect of the velocity deviation, us′, in the calculation of the longitudinal dispersion coefficient from the vertical profiles of the streamwise velocity. The results of Fig. 7a) were plotted with the experimental results from former research (Murphy et al., 2007) in Fig. 8a). The vegetation densities for the former experiments were comparable as the values ranged (1.5 to 4.8), while this research had values of (0.85 to 2.97). The comparison result showed that in the former experiment, the dimensionless longitudinal dispersion coefficient values approached a constant value in higher submergence ratio Sr > 2, while the current research using velocity-based calculation results showed a linear increase with higher submergence ratio. This shows that the role of the 10
Ecological Engineering 145 (2020) 105721
J. Shin, et al.
coefficient, DLC, were listed in in Table 2, and plotted in Fig. 8b) along with the velocity-based dispersion coefficient, DLV. The results show a linear relation between the velocity-based dispersion coefficient, DLV, and the concentration based coefficient DLC, even though the DLC values were somewhat larger than those of DLV. The larger values of the longitudinal dispersion coefficients driven by the concentration curves could be due to the additional mixing effect by storage zones of the submerged vegetation, while the velocity driven coefficients only accounted for the shear flow effects which was shown in open channel experiments without considering vegetation (Jung et al., 2019). Although the former research (Jung et al., 2019) compared transverse dispersion coefficients, a similar result was shown with longitudinal dispersion, but with the introduction of vegetation the reason for storage zones was more evident in these experiment results. Former studies (Nepf et al., 1997) have also maintained that the storage zones of the submerged vegetation could be generated from physical obstruction associated with plant stems, and this study showed the effects of the vegetation to storage zones and mixing using both velocity-based and concentration-based methods. Since results from both methods are comparable to each other, it shows the feasibility for using the velocity driven method as an alternative to the traditional high-cost concentration driven method in vegetated channels.
concentration-based coefficients, DLC, had higher values than the velocity-based dispersion coefficients, DLV. These differences could be explained by the fact that concentration-driven dispersion coefficient included the additional mixing mainly by storage effects due to the submerged vegetation, while the velocity-based coefficient only accounts for shear flow effects. This finding suggests that the velocitybased method can be used to obtain the longitudinal dispersion coefficient in vegetated open channel flows, without performing the highcost tracer test. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement This research is supported by the BK21 PLUS research program of the National Research Foundation of Korea and also supported by the Korea Ministry of Environment (MOE) as “Chemical Accident Response R&D Program (2018001960001).” This research work was conducted at the Institute of Engineering Research and Institute of Construction and Environmental Engineering in Seoul National University, Seoul, Korea.
5. Conclusions
References
The mixing characteristics of pollutants in open channel flows with submerged vegetation were investigated through velocity measurements and tracer experiments. The effects of the submergence ratio and stem density on the vertical distribution of the stream-wise velocity and the turbulent shear stress were analyzed, and the longitudinal dispersion coefficients calculated from both the velocity and concentration data were compared. The experimental results show that the vertical distributions of the stream-wise velocity were similar for different submergence ratio and stem density in which the velocity was retarded by the vegetation stem while the velocity in the surface layer increased with water depth taking the logarithmic profile. At the shear layer, the velocity increased very sharply, and this large velocity gradient was closely related to the velocity fluctuations that induced the large turbulent shear stresses at the interface between vegetation and surface layers. Both the intensity of velocity deviation and the turbulent shear stress tended to increase with increasing submergence ratio and with increasing stem density. The longitudinal dispersion coefficient was calculated using two different methods: the first one, named the velocity-based dispersion coefficient, DLV, was calculated from the velocity profile data, and the second one, named the concentration-based dispersion coefficient, DLC, was calculated from the concentration-time data. The results of the velocity-based dispersion coefficient show that, unlike the intensity of the velocity deviation, DLV was increasing as the submergence ratio, Sr, increased for all cases of the stem density. Compared to former research, this monotonic increase of the velocity-based dispersion coefficient was different from the concentration-based dispersion coefficients, where the values approached a constant value in higher submergence ratio over 2.0. The reason for this increase of DLV was considered to be the turbulent diffusion coefficient, εz, which is a denominator in the dispersion equation, decreased more rapidly than the velocity deviation, us′, as Sr increased. Also, DLV was increasing with increasing stem density, M, which is also true for the intensity of the velocity deviations IVD. These results indicate that in the vegetated flow, variation of the turbulent diffusion coefficient needs to be adequately considered, as well as the distribution of the velocity deviation, in the calculation of the longitudinal dispersion coefficient from the vertical profiles of the stream-wise velocity. As the stem density increased, the concentration-based longitudinal dispersion coefficients, DLC, also increased. The comparison of the two dispersion coefficients shows a linear relation between DLC and DLV. The
Aris, R., 1956. On the dispersion of a solute in a fluid flowing through a tube. Proceed. Royal Soc. A. 235 (1200), 67–77. Baek, K.O., Seo, I.W., 2010. Routing procedures for observed dispersion coefficients in two-dimensional river mixing. Adv. Water Resour. 33 (12), 1551–1559. Baptist, M.J., Babovic, V., Rodriguez, U.J., Uittenbogaard, R.E., Mynett, A., Verwey, A., 2007. On inducing equations for vegetation resistance. J. Hydraul. Res. 45 (4), 435–450. Beltaos, S., 1980. Transverse mixing tests in natural streams. J. Hydraul. Div. 106 (10), 1607–1625. Bogle, G.V., 1997. Stream velocity profiles and longitudinal dispersion. J. Hydraul. Eng. 123 (9), 816–820. Bulat, M., Biron, P.M., Lacey, J.R., Botrel, M., Hudon, C., Maranger, R., 2019. A three‐dimensional numerical model investigation of the impact of submerged macrophytes on flow dynamics in a large fluvial lake. Freshw. Biol. 64 (9), 1627–1642. Carr, M.L., Rehmann, C.R., 2007. Measuring the dispersion coefficient with acoustic doppler current profilers. J. Hydraul. Eng. 133 (8) 997–982. Elder, J.W., 1959. The dispersion of marked fluid in turbulent shear flow. 5, 544–560. Errico, A., Lama, G.F.C., Francalanci, S., Chirico, G.B., Solari, L., Preti, F., 2019. Flow dynamics and turbulence patterns in a drainage channel colonized by common reed (Phragmites australis) under different scenarios of vegetation management. Ecol. Eng. 133, 39–52. Fischer, H.B., 1966. Longitudinal dispersion in laboratory and natural streams. In: W M Keck Laboratory of Hydraulics and Water Resources Report, https://doi.org/10. 7907/Z9F769HC. Fischer, H.B., 1968. Dispersion predictions in natural streams. J Sanit Eng 94 (SA5), 927–943. Fischer, H.B., List, E.J., Koh, R.C.Y., Imberger, J., Brooks, N.H., 1979. Mixing in Inland and Coastal Waters. Academic Press, New York. Ghisalberti, M., Nepf, H., 2002. Mixing layers and coherent structures in vegetated aquatic flows. J. Geophys. Res. 107 (C2), 3011. Ghisalberti, M., Nepf, H., 2004. The limited growth of vegetated shear layers. In: Water Resour. Res, doi:tp10.1029/2003WR002776. Ghisalberti, M., Nepf, H., 2009. Shallow flows over a permeable medium: the hydrodynamics of submerged aquatic canopies. Transp. Porous Media 78, 309–326. Hamidifar, H., Omid, M.H., Keshavarzi, A., 2015. Longitudinal dispersion in waterways with vegetated floodplain. Ecol. Eng. 84, 398–407. Jung, S.H., Seo, I.W., Kim, Y.D., Park, I., 2019. Feasibility of Velocity-based Method for Transverse Mixing Coefficients in River Mixing Analysis. J. Hydraul. Eng. 145 (11), 04019040. Kadlec, R., Knight, R., 1966. Treatment wetlands. Lewis publishers, FL. Kim, D., 2012. Assessment of longitudinal dispersion coefficients using acoustic Doppler current profilers in large river. J. Hydro-environment Res. 6 (1), 29–39. Klopstra, D., Barneveld, H.J., Noortwijk, J.M., Velzen, E.H., 1997. Analytical model for hydraulic roughness of submerged vegetation. In: Proc 27th IAHR Congress, pp. 775–780. Kouwen, N., Unny, T., Hill, H., 1969. Flow retardance in vegetated channels. J. Irrig. Drain. 95 (2), 329–342. Launay, M., Le Coz, J., Camenen, B., Walter, C., Angot, H., Dramais, G., Faure, J.B., Coquery, M., 2015. Calibrating pollutant dispersion in 1-D hydraulic models of river networks. J. Hydro Environ. Res. 9 (1), 120–132.
11
Ecological Engineering 145 (2020) 105721
J. Shin, et al. Lee, M.E., Seo, I.W., 2013. Spatially variable dispersion coefficients in meandering channels. J. Hyraul. Eng. 139 (2), 141–153. Lightbody, A., Nepf, H., 2006. Prediction of velocity profiles and longitudinal dispersion in emergent salt marsh vegetation. Limnol. Oceanogr. 51 (1), 218–228. MacDonald, L., 1994. Water pollution solution: build a marsh. Am. For. 100 (7), 26–29. Murphy, E., Ghisalberti, M., Nepf, H.M., 2007. Model and laboratory study of dispersion in flows with submerged vegetation. Water Resour. Res. 43 (5). Nepf, H.M., Ghisalberti, M., 2008. Flow and transport in channels with submerged vegetation. Acta. Geophysica. 56 (3), 753–777. Nepf, H., Mugnier, C., Zavistoski, R., 1997. The effects of vegetation on longitudinal dispersion. Estuar. Coast. Shelf Sci. 44, 675–684. Nepf, H., Ghisalberti, M., White, B., Murphy, E., 2007. Retention time and dispersion associated with submerged aquatic canopies. Water Resour. Res. 43 (4). Palmer, M., Nepf, H., Petterson, T., Ackerman, J., 2004. Observations of particle capture on a cylindrical collector: Implications for particle accumulation and removal in aquatic systems. Limnol. Oceanogr. 49, 76–85. Raupach, M., Finnigan, J.J., Brunet, Y., 1996. Coherent eddies and turbulence in vegetation canopies: the mixing-layer analogy. In Boundary-layer meteorology 25th anniversary volume, Springer. Dordrecht. 1970–1995, 351–382. Righetti, M., Armanini, A., 2002. Flow resistance in open channel flows with sparsely distributed bushes. J. Hydrol. 269 (1–2), 55–64. Rutherford, J.C., 1994. River Mixing. Wiley, Chichester, UK. Schultz, M., Kozerski, H.P., Pluntke, T., Rinke, K., 2002. The influence of macrophytes on sedimentation and nutrient retention in the lower river spree. Water Res. 37, 569–578. Seo, I.W., Baek, K.O., Jeon, T.M., 2006. Analysis of transverse mixing in natural streams under slug tests. J. Hydraul. Res. 44 (3), 350–362.
Seo, I.W., Choi, H.J., Kim, Y.D., Han, E.J., 2016. Analysis of two-dimensional mixing in natural streams based on transient tracer tests. J. Hydraul. Eng. 142 (8). Shen, C., Niu, J., Anderson, E.J., Phanikumar, M.S., 2010. Estimating longitudinal dispersion in rivers using acoustic Doppler current profilers. Adv. Water Resour. 33 (6), 615–623. Shimizu, Y., Tsujimoto, T., 1994. Numerical analysis of turbulent open-channel flow over a vegetation layer using a k-ɛ turbulence model. J. Hydrosci. Hydraul. Eng. 11 (2), 57–67. Shucksmith, J.D., Boxall, J.B., Guymer, I., 2010. Effects of emergent and submerged natural vegetation on longitudinal mixing in open channel flow. Water Resour. Res. 46 (4). Shucksmith, J.D., Boxall, J.B., Guymer, I., 2011. Determining longitudinal dispersion coefficients for submerged vegetated flow. Water Resour. Res. 47 (10). Taylor, G., 1954. The dispersion of matter in turbulent flow through a pipe. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 223 (1155), 446–468. Velasco, D., Bateman, A., Redondo, J.M., Demedina, V., 2003. An open channel flow experimental and theoretical study of resistance and turbulent characterization over flexible vegetated linings. Flow Turbul Combust 70 (1–4), 69–88. White, B.L., Nepf, H.M., 2003. Scalar transport in random cylinder arrays at moderate Reynolds number. J. Fluid Mech. 487, 43–79. Yang, W., Choi, S., 2010. A two-layer approach for depth-limited open-channel flows with submerged vegetation. J. Hydraul. Res. 48 (4), 466–475. Zhu, Z., Motta, D., Jackson, P.R., Garcia, M.H., 2017. Numerical modeling of simultaneous tracer release and piscicide treatment for invasive species control in the Chicago Sanitary and Ship Canal. Environ. Fluid Mech. 17 (2), 211–229.
12