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Prototype-scale flume experiments on hydraulic roughness of
submerged vegetation
D.G. MEIJER1 and E.H. VAN VELZEN2
1 HKV consultants, Lelystad, The Netherlands
2 Ministry of Transport, Public Works and Water Management, Institute for Inland Water Management and Waste Water Treatment (RIZA), Arnhem, The Netherlands
In 1996, a new analytical model of the vertical flow velocity profile and the hydraulic roughness of submerged vegetation was developed (Klopstra et al, 1997). The model is physically based with only one empirical parameter. Different shear-stress descriptions are applied for the vegetation layer and the surface layer. Calculated flow profiles and roughness values correspond well with results from scale model studies reported in literature. This paper discusses new flume experiments on prototype scale, conducted in 1997 and 1998. These confirm the applicability of the analytical model for field conditions. The tests were done by using vertical steel bars and natural reed. The prediction of the empirical parameter has been improved on the basis of the experiments. The results imply a considerable improvement of roughness predictions of submerged vegetation, compared to traditional methods. The new method will be applied for nature rehabilitation projects, to be implemented in river floodplains in the Netherlands.
In the last decade, nature rehabilitation of river floodplains has become an important aspect of river management world wide. It is important to assess how the hydraulic roughness of the flood plains will be affected in order to maintain the level of safety against floods. In 1996, a new, physically based model that predicts the vertical flow velocity profile and the hydraulic roughness of submerged tall vegetation was developed (Klopstra et al, 1997). The set of explicit analytical expressions can be easily incorporated in numerical hydraulic software packages. This paper discusses an extensive set of flume tests, carried out in 1997 and 1998, which confirm the applicability of the analytical expressions.
The analytical model (Klopstra et al, 1997) describes the flow velocity profile in the vegetation layer and the surface layer separately. The turbulent shear stress in the vegetation layer is described by a Boussinesq-type equation:
(1)
with: a = characteristic turbulence length scale (m)
r = density of water (kg/m3)
t = shear stress (kg/ms2)
u(z) = flow velocity (m/s)
z = vertical co-ordinate (m)
The term r×a×u(z) represents the turbulent eddy viscosity. The characteristic length scale a is an empirical constant, assumed to be independent of z. Below, the model is described briefly. For a detailed derivation of the equations reference is made to the source above. The flow velocity profile in the vegetation layer reads:
(0 < z < k) (2)
with: 
= resistance
term (m-2)
C1, C2 = integration constants (m2/s2)
CD = drag coefficient (-)
g = acceleration due to gravity (m/s2)
i = energy gradient (-)
k = vegetation height (m)
m = vegetation density (m-2)
= undisturbed
flow velocity in vegetation (m/s)
For the surface layer, Prandtl's mixing length concept is adopted resulting in the well known logarithmic flow velocity profile:
(k < z < h) (3)
with: k = Von Kármán's constant (-)
hs = vertical shift of the virtual zero-level of the logarithmic profile (m)
= virtual shear-stress velocity of the surface
layer (m/s)
z0 = length scale for virtual bed roughness of the surface layer (m)
Three conditions at the interface (continuity of the shear stress, the velocity and its vertical gradient) and one at the bottom (shear stress neglected) determine the constants C1, C2, hs and z0, which result in explicit equations for these parameters. The only unknown parameter is the characteristic turbulence length scale a.
The hydraulic roughness expressed as the value of Chézy (m0.5/s) can be obtained using the depth-averaged flow velocity:
(4)
Substitution of equations (2) and (3) in (4) results in a complex explicit expression for the Chézy coefficient, which is independent on the energy gradient. The hydraulic roughness thus can be calculated analytically when the vegetation characteristics m, D, CD and k, the water depth h and the characteristic turbulence length scale a are known. The only unknown parameter a is to be determined by physical model tests. The analytical model was validated by results from literature (Tsujimoto et al, 1990 and 1993; Shimizu, 1994), based on scale model tests. An empirical relation for a was found. However, the model had not been validated for field conditions yet, due to lack of data.
In 1997, an extensive series of tests was carried out in a large flume facility. The facility measures a length of over 100 m, a width of 3 m and a depth of 3 m. The primary aim of the model investigation was the calibration and verification of the analytical model. Steel bars were used to simulate the vegetation layer in order to approximate the theoretical schematisation. The use of steel bars enabled a precise manipulation of the model parameters, and ensured the best possible circumstances to verify calculated flow profiles. Over 15,000 vertical round bars with a diameter of 8 mm were placed into prepared holes in a double wooden floor on the flume bottom over a length of 20.5 m. Near the downstream end, an empty space was reserved for flow-velocity measurements (see figure 1).
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Figure 1 Length profile of test site in the flume (definition sketch)
In total, 56 tests were carried out, in which the height of the steel bars, their density and the energy gradient were systematically varied. Vegetation heights of 0.45 m, 0.90 m and 1.50 m were simulated in densities of 256 and 64 bars per m2, respectively. Each of these six set-ups was run under eight flow conditions: energy gradients of 1·10-3 and 2·10-3 were combined with four depths. A complete combination of these conditions gives a total of 48 tests, and enables systematic analysis of the results. In order to find the drag coefficient of the bars, eight separate tests were carried out with the bars not submerged, under different conditions of depth, density and flow velocity. The measured CD-values varied between 0.91 and 1.18.
In each of the tests water levels were measured using point gauges at three locations in the length profile: near the upstream boundary of the test site, in the middle and near the end. The energy gradient was defined by using the latter two measurements, whereas the first point gauge allows the detection of a second-order derivative in the water level, which enables to judge the adaptation of the flow conditions over the length of the site. Flow measurements were conducted by using an acoustic flow meter, which measures flow velocities in three dimensions with a frequency of 25 Hz. These measurements were carried out in the cross section shown in figure 1: in the centre of the flume and at a distance of 0.5 m from one of the walls (left or right, sometimes both). The vertical measurement interval was 0.10 m. Each measurement lasted 100 s. Occasionally, measurements were done at other locations in order to check the adaptation of the flow profile.
The tests were analysed almost simultaneously, using a computer near the test site.
The analysis procedure was as follows:
· The flume discharge is determined by integration of the flow profile.
· The calculated discharge is matched to this discharge by fitting the a-value.
· The calculated flow profile, based on this a-value, is plotted together with the measured values (figure 2: solid line).
Figure 2 shows the results of the flow measurements of one of the tests.
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Figure 2 Measured and calculated flow profile (test 22)
The analytical model describes the measured flow profiles quite well. However, they were indirectly matched (via the discharge) by fitting the empirical a-value. After collecting all 48 empirical a-values, the search for a relation between a and one or more of the model parameters could begin. In spite of Tsujimoto's assumption (Tsujimoto et al, 1990) the a-value proved to be independent of the vegetation density (i.e. the distance between the steel bars). Flow conditions (velocity, energy gradient) did not affect its value either. As the bar diameter was not varied, its influence on a could not be analysed. A significant dependence of a on the height of the vegetation elements and the water depth was found. Several hypothetical relations were tried and judged by their correlation coefficient. Previous model studies were involved in the analysis (Tsujimoto et al, 1990 and 1993; Shimizu, 1994).
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Figure 3 Relation between a, h and k |
Figure 4 Correlation between measured and calculated Chézy coefficients |
The best relation, so far found, is (figure 3):
(5)
Incorporation of formula (5) in the analytical model
completes the procedure of predicting vegetation roughness. The Chézy
coefficients were calculated using the analytical model with this relation, and
compared to the 'measured' values (i.e. those, which follow directly from the
flume tests by
). The high correlation (figure 4) is due to the fact that
the Chézy coefficients are relatively insensitive to deviations in the a-value. This is good news, as the a-parameter is still the only empirical
element in the analytical model, with the highest uncertainty. The figure shows
also Chézy coefficients based on the White-Colebrook formula, which is
traditionally used for roughness predictions in the Netherlands. The
substantial gap indicates that the White-Colebrook formula strongly
underestimates vegetation roughness.
An additional set of tests was performed in 1998, in order to verify the applicability of the analytical method for reed-type vegetation. Whereas the tests with the steel bars can be considered as fundamental research, the tests with the natural reed should be regarded as a verification in a more realistic situation. In the flume the steel bars were removed and natural reed was placed in a high density (256 per m2) into the holes of the wooden floor (figure 5). The reed parameters height and diameter were not constant and had average values of 1.58 m and 5.7 mm, respectively. Half of the reed stalks had a tuft, the average number of leaves was two.
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Figure 5 Placing reed stalks in the flume facility, overview over the test site with a movable measurement bridge
In two preliminary tests the reed was not submerged and the drag coefficient was determined. Its significantly higher value (CD = 1.8) can be explained by the leaves. Eight tests were performed in the same way as described above. The mentioned energy gradients were applied, although those in the Dutch rivers have another order of magnitude (i »10-4). Figure 6 shows the measured and calculated flow profile of one of the tests. In this case the profile was not matched by fitting the a-factor, but relation (5) was used.
The figure shows a fair description of the flow profile. Near the surface the velocities seem to be somewhat underestimated. The other tests show similar results. It should be noticed that the a-function, validated for steel bars, is not necessarily valid for the reed. Besides, the average stalk height (1.58 m) may not represent the reed field well, as heights vary roughly between 1 and 2 m.
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Figure 6 Measured and calculated flow profile (test R6)
Although there are still unresolved questions, the flume experiments seem to confirm the applicability of the new method for the prediction of hydraulic roughness of reed-type vegetation. Further analysis is expected to bring more answers. The analytical equations are currently implemented in the 2D-modelling system Waqua, used by the Netherlands Ministry of Transport, Public Works and Water Management for assessment studies.
As the a-value is the only empirical model parameter, the analysis of the steel-bar tests was very much focused on finding a proper relation that predicts its value. This has been done in an empirical way, without questioning the physical background of the dependence shown in formula (5). From academic point of view, it is still interesting to improve the a-relation in a more fundamental way, involving the turbulence characteristics. There are still a lot of unused data available. Each measurement of 100 s contains 7500 measured velocities (25 Hz in three dimensions). In these studies only the average flow velocity in one dimension was involved. It is obvious that these data could tell us much more about the turbulence near the interface between the vegetation layer and the top layer, which could bring the final solution closer. However, the practical need for this is limited as the Chézy coefficient, calculated by the analytical model, proves to give satisfying results when empirical relations are used.
The analytical model does not incorporate the effects of variable diameters and heights, tufts and the bending of the reed stalks. Despite these shortcomings, the results confirm the applicability of the analytical model for reed-type vegetation.
Klopstra D., H.J. Barneveld, J.M. van Noortwijk and E.H. van Velzen, 1997: Analytical model for hydraulic roughness of submerged vegetation. In: Managing Water: Coping with Scarcity and Abundance. Proceedings of the 27th IAHR Congress in San Fransisco, USA, August 1997
Meijer D.G., 1998: Model tests submerged vegetation, physical model investigation (in Dutch). HKVconsultants, commissioned by Rijkswaterstaat/RIZA, The Netherlands
Shimizu Y. and T. Tsujimoto, 1994: Numerical analysis of turbulent open-channel flow over a vegetation layer using a k-e turbulence model. Journal of hydroscience and hydraulic engineering. Vol. 11, no 2. January 1994.
Tsujimoto T. and T. Kitamura, 1990: Velocity profile of flow in vegetate bed channels. Progressive Report June 1990. Hydraulic Laboratory Kanazawa University
Tsujimoto T, T. Okada and K. Kontani, 1993: Turbulent structure of open-channel flow over flexible vegetation. Progressive Report. December 1993. Hydr. Lab., Kanazawa University
