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E-proceedings of the 36th IAHR World Congress 28 June – 3 July, 2015, The Hague, the Netherlands
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LABORATORY INVESTIGATION ON THE HYDRODYNAMIC CHARACTERIZATION OF ARTIFICIAL GRASS
A.VARGAS-LUNA (1) (2), A. CROSATO (1) (3), L. COLLOT (4) & W.S.J. UIJTTEWAAL (1) (1) Faculty of Civil Engineering and Geoscience, Delft University of Technology, Delft, The Netherlands,
e-mail [email protected]; [email protected] (2) Department of Civil Engineering, Pontificia Universidad Javeriana, Bogotá D.C., Colombia,
e-mail [email protected] (3) Department of Water Engineering, UNESCO-IHE, PO Box 3015, 2601 DA Delft, The Netherlands,
e-mail [email protected] (4) ENGEES, Strasbourg, France,
e-mail [email protected]
ABSTRACT
The morphological evolution of river systems is strongly influenced by the presence of vegetation. On vegetated beds, velocity fields are spatially heterogeneous at different scales according to vegetation density and hydraulic conditions. Plants affect velocity profiles that deviate from those commonly found in non-vegetated flows, changing the local sediment transport rates and the morphodynamic trends. To simulate the effects of vegetation on hydrodynamics and sediment transport, plants are often treated as uniform arrays of rigid cylinders characterized by diameter, height, density and drag coefficient. Given the vast variety of plant shapes and considering that plants may be flexible, it is important to define the key parameters that characterize plants in rigid-cylinder representations. In this work, artificial grass is characterized in a laboratory setup considering emergent and submerged conditions, three densities, and two sediment types. The same flow discharges are used in all the tests in order to be able to compare the cases. The results show the effectiveness of a selected rigid-cylinder representation in reproducing the measured vegetation effects. The results suggest a non-linear relationship between the total shear stress, the bed-shear stress and the drag exerted by plants.
Keywords: Grass-type vegetation, rigid cylinders, Baptist method, laboratory experiments, morphodynamics
1. INTRODUCTION
Flow velocity, sediment transport and local morphodynamics are all strongly affected by the presence of plants (e.g. Hickin, 1984; Nepf, 2012; Yager and Schmeeckle, 2013), and the importance of including the effects of vegetation in morphodynamic studies is now widely recognized (e.g. Crosato and Samir-Saleh, 2011). However, plants are often treated in numerical models and experimental set ups as rigid cylinders characterized by diameter, height, density and drag coefficient (e.g. Li and Shen, 1973; Dittrich et al., 2012; Stone and Shen, 2002; Baptist, 2005). It is therefore relevant to define the characteristics of the array of cylinders that better represents the effects of a selected vegetation type (Vargas-Luna et al., 2014).
The method developed by Baptist (2005) has shown to be in good agreement with observations for the prediction of global flow resistance of vegetated beds (Vargas-Luna et al., 2015). This method requires knowing the drag coefficient of vegetation in advance. This parameter generally varies with flow and vegetation properties. However, in practical applications the vegetation drag coefficient is assumed to be constant, and constant is also assumed to be the roughness coefficient for the bare soil. In this work, we combine experimental measurements and the Baptist method to characterize artificial grass. The experiments were carried out on non-erodible beds maintaining uniform flow conditions under the same flow discharges and energy gradients in order to compare the effects of different vegetation densities and bed roughness's. The tests consider emergent and submerged vegetation, three different plant densities, and two sediment sizes. The properties of the array of cylinders that describe each vegetation configuration are derived by applying Baptist’s method on the basis of two assumptions: 1) the roughness coefficient of the bare soil can be obtained from non-vegetated conditions, and 2) the drag coefficient assigned to each configuration is calculated with the properties of the assumed array of cylinders.
2. MATERIALS AND METHODS
2.1 Baptist's method
Baptist (2005) derived an expression for the hydraulic resistance to a flow over (submerged) and through (emergent) vegetation from the momentum balance, based on the following assumption:
E-proceedings of the 36th IAHR World Congress, 28 June – 3 July, 2015, The Hague, the Netherlands
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b vghi [1]
where is the mass density of water (kg/m3); g is the acceleration due to gravity (m/s2); h is the water depth (m); i is the longitudinal water surface slope (m/m); b is the bed shear stress (N/m2) and v is the extra shear stress caused by vegetation (N/m2). The averaged flow velocity, ,u in this method is expressed as:
ru C hi [2]
in which Cr represents the total friction coefficient expressed in terms of Chézy coefficient (m1/2/s). For the submerged case (h > hv) Cr is given by:
2
1 ln1 2
r v
b D v
gC h h
C C ah g
[3]
where Cb is the Chézy coefficient of the bare soil (m1/2/s); CD is the drag coefficient of the plants (-); a is the projected cylinders area per unit of volume (m-1) (Nepf, 2012) = mD (m being the number of stems, N, per bed surface area in m-2 and D the reference cylinder diameter in m).
For emergent vegetation: h ≤ hv. The water depth is equivalent to the vegetation height in the flow, so h=hv and Eq. [3] is reduced to:
2
11 2
r
b D
CC C ah g
[4]
2.2 Laboratory setup
Both emergent and submerged conditions were tested with flow discharges between 0.4 l/s and 40 l/s and bed slopes and longitudinal energy gradients between 0.03 and 0.30 % by using two bed materials (gravel and sand), in a 0.40 m wide and 15 m long flume at the Delft University of Technology, see Figure 1 and Table 1. A downstream weir was used to ensure uniform flow conditions, maintaining the same discharges, bed slope and energy gradient for all of the vegetation configurations. Bed and water levels were made parallel by adjusting the downstream weir to assure uniform flow conditions. The sediment (sand or gravel) was glued to metallic plates placed on the bottom of the flume, creating hydraulic roughness, but preventing sediment transport and bed level changes. Sand and gravel had median diameter, D50, equal to 1.0×10-3 and 5.3×10-3 m, respectively, as shown in Figure 2a. In addition to the non-vegetated conditions three different staggered plant configurations were tested (D1=31 plants/m2, D2=112 plants/m2 and D3=422 plants/m2), see Figure 2c. The plastic grass was also glued on the plates after testing the case without vegetation. Each plastic plant is composed by 69 elements with diameter of 1 mm, see Figure 2b. Flow discharges and water depths were measured. Vertical velocity profiles were measured for the submerged conditions.
2.3 Data processing
From the measurements carried out for the non-vegetated conditions, the characteristics of the granular bed materials were obtained. Sidewall corrections were included by applying the method of Vanoni and Brooks (1957) in order to estimate the bed roughness. Functions of the friction coefficients for the sediments were obtained by means of a regression procedure. The variation of drag coefficient as a function of flow is derived by characterizing vegetation as a uniform array of rigid cylinders. The array of cylinders considered in each configuration is described by the same diameter (0.001 m) and height (0.03 m) of the plastic grass elements. In this way, the parameter to be obtained from the laboratory experiments is the cylinder density that provides the best fit with the measured water depths (equivalent cylinder density).
2.4 Drag coefficients
The drag coefficient is calculated for emergent conditions with the method proposed by Cheng (2013). Cheng’s method is based on a characteristic hydraulic radius defined in terms of the geometrical properties (m and D) of the cylinders array and the energy gradient. For submerged conditions, the drag coefficient is calculated with the method proposed by Ghisalberti and Nepf (2004). Ghisalberti and Nepf proposed a representative bulk drag coefficient for submerged arrays of cylinders as a function of the bulk drag coefficient for emergent conditions as
D DhC C [5]
E-proceedings of the 36th IAHR World Congress
28 June – 3 July, 2015, The Hague, the Netherlands
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where is a parameter that represents the effects on the drag coefficient due to the vegetation free end in submerged conditions, and CDh is the value of the drag coefficient at the top of the canopy estimated for emergent conditions (see Ghisalberti and Nepf, 2004). As is obtained by considering turbulent vertical gradients that were not measured in the experiments, this parameter is treated in this work as a calibration parameter.
PG4
Metallic plates with glued sediment/vegetation
Weir
Flowstraightener
10.0 m14.0 m
40 cm
EMS PG3PG1 PG2
EMS : Electronic flow velocimeter.P.G. : Point gauge.
a b
Figure 1. Laboratory setup: (a) Schematic side view, (b) Perspective view of the vegetated bed from upstream.
Table 1. Flow regime conditions for the tests carried out
Test No. Q (x10-3 m³/s) i (m/m) EMERGENT 0.4 0.0030 1 0.4 0.0030 2 1.4 0.0030 3 1.3 0.0020 4 0.9 0.0005 5 0.7 0.0010 6 0.7 0.0020 7 0.4 0.0020 8 0.4 0.0005 9 1.2 0.0020 10 0.9 0.0020
SUBMERGED 11 3.1 0.0010 12 4.3 0.0003 13 4.3 0.0020 14 9.1 0.0020 15 9.1 0.0005 16 14.5 0.0012 17 18.9 0.0010 18 22.6 0.0012 19 27.2 0.0012 20 32.8 0.0008 21 38.3 0.0006
E-proceedings of the 36th IAHR World Congress, 28 June – 3 July, 2015, The Hague, the Netherlands
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0102030405060708090
100Cu
mul
ativ
e pa
ssin
g (%
)
0.1 1 100.2 0.3 0.5 2 3 5 200.05Particle size (mm)
SandGravel
D50 = 5.3 mmD50 = 1.0 mm
a b
c
Figure 2. Description of bed roughness elements. (a) Grain size distribution of the granular materials, (b)
Plastic vegetation element, (c) Vegetation densities considered in the study.
3. Results
3.1 Friction coefficients of the bed materials
From the tests conducted for non-vegetated conditions the values of the Chézy coefficient for the bare sediment, Cb, were obtained. Sidewall corrections were included by applying the method of Vanoni and Brooks (1957). From these Chézy coefficient values an expression was obtained by means of a multiple lineal regression procedure, given by
321 Re xx
bC x i [6]
where Re=uh/ is the Reynolds number, u is the mean flow velocity (m/s), h is the water depth (m), is the cinematic viscosity (m2/s), i is the longitudinal water surface slope (m/m), and x1, x2, x3, are regression coefficients for each bed material. The regression coefficients and the goodness of fit are summarized in Table 2.
Table 2. Regression coefficients (with 95% confidence bounds) for the friction coefficients described by Eq. [6]
x1 (m1/2/s) x2 x3 R2 RMSE (m1/2/s) SAND 1.313 0.2097 -0.2243 0.9833 2.405
GRAVEL 0.1439 0.3587 -0.2575 0.9925 1.607
3.2 Velocity profiles and water levels
Figure 3 shows the water depths and velocity profiles for the Test No. 21 (Table 1), relative to submerged conditions, with three different vegetation densities and including the case without vegetation. The figure shows how water depths and velocity profiles are affected by the presence of vegetation. Water levels increase and vertical flow velocities decrease as vegetation density increase. Similar effects were observed for all the experiments conducted for submerged conditions.
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Flow velocity (m/s)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35z (
m)
D3D2D1NV
hv
NV
D1
D2
D3 b a
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Flow velocity (m/s)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
z (m
)
D3D2D1NV
hv
NV
D1
D2
D3
Figure 3. Velocity profiles for Test No. 21 of the submerged conditions for bed with no vegetation (NV) and bed with the three considered
vegetation densities (D1, D2, and D3) for: (a) Sand bed, and (b) Gravel bed. The canopy height, hv, is 0.03 m.
The measured water levels for selected slopes are shown as a function of the discharge in Figures 4 and 5 for the emergent and submerged conditions, respectively. Figure 4 shows that emergent conditions were obtained only for the smallest vegetation density. Figures 3 to 5 show also that the differences in water levels are more noticeable for the sand bed than for the gravel bed, especially for the highest densities D2, and D3.
0 0.2 0.4 0.6 0.8 1 1.2
Q (x10-3 m3/s)
0.00
0.01
0.02
0.03
0.04
0.05
0.06
h (m
) D3D2
0 0.2 0.4 0.6 0.8 1 1.2
Q (x10-3 m3/s)
0.00
0.01
0.02
0.03
0.04
0.05
0.06
h (m
)
D1NV
(a) (b)
Figure 4. Water levels for the tests in emergent conditions with i=0.0020 m/m for bed with no vegetation (NV) and bed with the three considered
vegetation densities (D1, D2, and D3) for: (a) Sand bed, and (b) Gravel bed. The canopy height, hv, is 0.03 m.
10 15 20 25 30 35
Q (x10-3 m3/s)
0.05
0.10
0.15
0.20
0.25
h (m
) D3D2
10 15 20 25 30 35
Q (x10-3 m3/s)
0.05
0.10
0.15
0.20
0.25
h (m
)
D1NV
(a) (b)
Figure 5. Water levels for the tests in submerged conditions with i=0.0012 m/m for bed with no vegetation (NV) and bed with the three
considered vegetation densities (D1, D2, and D3) for: (a) Sand bed, and (b) Gravel bed. The canopy height, hv, is 0.03 m.
E-proceedings of the 36th IAHR World Congress, 28 June – 3 July, 2015, The Hague, the Netherlands
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3.3 Equivalent cylinder densities
The equivalent densities were derived by applying the Baptist method. The results for emergent conditions (lowest density, D1) are listed in Table 3 together with the range of the computed drag coefficients.
Table 3. Equivalent cylinder density, m, and ranges of drag coefficient, CD, at emergent conditions
m (m-2) CD (a)
SAND 2440 1.3 – 1.6 GRAVEL 1739 1.5 – 2.0
(a) Calculated with Cheng’s (2013) method Values in Table 3 show that for the same flow regimes and vegetation configurations but different bed composition, the response obtained by using the Baptist method is substantially different. Sand bed configurations exhibit higher densities and lower values of the drag coefficient when compared to the values obtained for the gravel bed configurations. The calculated values of the drag coefficient under these assumptions are within the expected order of magnitude.
The densities that were found by using the Baptist method and the calculated drag coefficients for submerged conditions are presented in Table 4 for each vegetation type. Parameter in Table 4 represents the ratio of the drag coefficients for the submerged case and the drag coefficient at the top of the vegetation canopy assuming emergent conditions, as suggested by Ghisalberti and Nepf (2004), see Eq. [5]. As well as for the emergent case, the calculated values of the drag coefficient under these assumptions are within the expected ranges, however, the values of parameter are higher than the obtained in detailed investigations. Ghisalberti and Nepf (2004), for instance, found depth-averaged values of between 0.65 and 0.74.
Table 4. Equivalent cylinder density, m, and ranges of drag coefficient, CD, at submerged conditions
m (m-2) CD (a)
SAND D1 1199 1.3 1.5 – 1.8 D2 2708 1.2 1.4 – 2.1 D3 3997 1.4 1.6 – 2.5
GRAVEL D1 1644 1.1 1.2 – 2.0 D2 3695 1.3 1.5 – 2.4 D3 3965 1.1 1.2 – 2.0 (a) Calculated with Ghisalberti and Nepf’s (2004) method
Tables 3 and 4 show that different bed roughness result in different combinations of equivalent cylinder densities and drag coefficients even if flow and vegetation configurations are the same.
4. CONCLUSIONS
A laboratory-based study analysing the influence of grass on water depth and flow velocity was carried out in order to obtain the characteristics of the array of cylinders that best reproduce the effects of vegetation if adopting Baptist's method. The variability of the bed roughness and the drag coefficient is considered as a function of flow regime. The equivalent cylinder density was found to vary according to bed roughness, even for the same flow regime and vegetation density. This finding shows that the contributions of bed-shear stress and vegetation drag to form the total shear stress (global flow resistance) depend on the combination of vegetation density - bed material. This suggests that the linear distribution of bed shear stress and vegetation drag, described by Eq. [1], might not be valid for all conditions, thus more research in this field is required. A better understanding of the bed shear stress contribution will improve the description of water and sediment fluxes in vegetated areas, thus progressing on estimating the morphological evolution of natural systems.
ACKNOWLEDGMENTS
Andrés Vargas-Luna is grateful to COLCIENCIAS (Colombian Institute for the development of Science and Technology), and to Pontificia Universidad Javeriana, the institutions that support financially his studies in the Netherlands.
E-proceedings of the 36th IAHR World Congress
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REFERENCES
Baptist M.J. (2005). Modelling Floodplain Biogeomorphology. Ph.D. Thesis, Delft University, Delft, The Netherlands. ISBN 90-407-2582-9.
Cheng N. (2013). Calculation of Drag Coefficient for Arrays of Emergent Circular Cylinders with Pseudofluid Model. Journal of Hydraulic Engineering, 139, 602-611.
Crosato A., and Samir Saleh M. (2011). Numerical study on the effects of floodplain vegetation on river planform style, Earth Surface Processes and Landforms, 36(6), 711-720.
Dittrich A., Aberle J. and Schoneboom T. (2012). Environmental Fluid Mechanics: Memorial colloquium on environmental fluid mechanics in honour of Prof. Gerhard H. Jirka, IAHR Monographs, CRC Press, Ch. Drag forces and flow resistance of flexible riparian vegetation, 195-215.
Ghisalberti M. and Nepf H.M. (2004). The limited growth of vegetated shear layers. Water Resources Research, 40, W07502.
Hickin E.J. (1984). Vegetation and river channel dynamics. The Canadian Geographer/Le Géographe Canadien, 28(2), 111-126.
Li R. and Shen H.T. (1973). Effect of tall vegetations on flow and sediment, Journal of the Hydraulics Division, ASCE, 99(5), 793-813.
Nepf H.M. (2012). Flow and transport in regions with aquatic vegetation. Annual Review of Fluid Mechanics, 44, 123-142.
Stone B.M. and Shen H.T. (2002). Hydraulic resistance of flow in channels with cylindrical roughness, Journal of Hydraulic Engineering, 128(5), 500-506.
Vanoni V.A. and Brooks N.H. (1957). Laboratory studies of the roughness and suspended load of alluvial streams. California Institute of Technology Sedimentation Laboratory.
Vargas-Luna A., Crosato A., Calvani G., and Uijttewaal W.S.J. (2014). Mimicking the effects of vegetation in laboratory setups. 10th International Symposium on Ecohydraulics 2014 Proceedings. Paper No. 288, Vegetation and fluvial processes. Norwegian University of Technology, Trondheim, Norway, June 23rd-27th.
Vargas-Luna A., Crosato A., and Uijttewaal W.S.J. (2015), Effects of vegetation on flow and sediment transport: comparative analyses and validation of predicting models. Earth Surface Processes and Landforms, 40(2), 157-176.
Yager E.M., and Schmeeckle M.W. (2013). The influence of vegetation on turbulence and bed load transport, Journal of Geophysical Research: Earth Surface, 118(3), 1585-1601.
