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Impacts of vegetation configuration on flow structure and resistance in a rectangular open channel
Available online at www.sciencedirect.com
ScienceDirect Journal of Hydro-environment Research 9 (2015) 295e303 www.elsevier.com/locate/jher
Impacts of vegetation configuration on flow structure and resistance in a rectangular open channel Satoshi Yokojima a,*, Yoshihisa Kawahara b, Takuya Yamamoto b b
a Department of Mathematical and Systems Engineering, Shizuoka University, Hamamatsu 432-8561, Japan Department of Civil and Environmental Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan
Available online 19 December 2014
Abstract Riparian vegetation exerts significant effects on the flow structure and the geomorphology of rivers. While it provides a rich wildlife habitat as well as a protection from bank erosion, vegetation can increase the risk of flood inundation by reducing the carrying capacity of flood. A proper balance between flood control and riparian eco-diversity is therefore indispensable for better riparian management. In the present study, the effect of vegetation configuration on turbulent flows in a rectangular open channel, especially on the resulting flow resistance, has been investigated both experimentally and numerically. The laboratory experiments are conducted for two types of vegetation configurations, where vegetation is established either continuously or in a discrete way along the centerline of the flume. A regular array of emergent circular cylinders of diameter 3 mm with the stem-to-stem centerline spacing of 3 cm is used as a laboratory model for vegetation. The applicability of a basic large-eddy simulation (LES) method together with a canopy model is critically examined against the experimental data. A great agreement between the present three-dimensional LES results and the experimental data is achieved in the continuous case. On the other hand, the LES is found to fail in reproducing the streamwise variation of the mean flow structures accurately in the discrete case. This failure is mainly due to the arrangement of a uniform distribution of the drag coefficient required in the canopy model. The LES is applied to flows with a wide variety of vegetation configurations to examine the relationship between the presence of vegetation and the resulting flow resistance. It is found that, in most cases, the flow resistance solely depends on the total volume of vegetation, irrespective of the configuration details in the streamwise direction. However, shifting vegetation toward the side wall achieves a considerable drag reduction. This is partly because the primary velocity is decreased with approaching the side wall and partly because the lateral mixing is suppressed by the presence of the side wall. © 2014 International Association for Hydro-environment Engineering and Research, Asia Pacific Division. Published by Elsevier B.V. All rights reserved.
Keywords: Vegetated open-channel flow; Large-eddy simulation; Large-scale vortices; Drag reduction
1. Introduction Flow through vegetation has been a key research topic in hydraulics, since riparian vegetation is ubiquitous in a wide variety of aquatic environments and plays a crucial role in both physical and biological aspects (Nepf, 1999; Neary et al., 2012). In one sense vegetation provides a rich wildlife habitat as well as a protection from bank erosion. On the other * Corresponding author. Tel./fax: þ81 53 478 1258. E-mail addresses: [email protected] (S. Yokojima), [email protected] (Y. Kawahara).
hand it can increase the risk of flood inundation since it increases drag to the flow and hence reduces the carrying capacity of flood. A proper balance between flood control and riparian eco-diversity is therefore indispensable for better riparian management, which requires a deep understanding about the effect of vegetation configuration on the flow behaviors. In the present study, the effect of vegetation configuration on turbulent flows in a rectangular open channel, especially on the resulting flow resistance is investigated both experimentally and numerically. Most of the numerical studies performed in the past have relied on the Reynolds-averaged
http://dx.doi.org/10.1016/j.jher.2014.07.008 1570-6443/© 2014 International Association for Hydro-environment Engineering and Research, Asia Pacific Division. Published by Elsevier B.V. All rights reserved.
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NaviereStokes (RANS) turbulence models (Shimizu and Tsujimoto, 1994; L opez and García, 2001; Fischer-Antze et al., 2001; Choi and Kang, 2004; Jahra et al., 2011). While these models have been compared favorably against laboratory test cases, their analyses were restricted inherently to timeaveraged flows. We employ a large-eddy simulation (LES) method to explicitly resolve unsteady large-scale horizontal vortices evolving along the interface between vegetation and non-vegetated zones. Since the large eddies induce significant momentum exchanges in the lateral direction and hence strongly characterize the flow, LES is expected to be more plausible in reproducing the flows and to provide detailed information about the three-dimensional flow field not just at time-averaged level but also at instantaneous level. Although a few application examples of LES to vegetated open-channel flows have been reported for both submerged and emergent cases (Xiaohui and Li, 2001; Cui and Neary, 2008), their attention is limited to the cases where vegetation exists continuously in the streamwise direction. The present study covers the cases where vegetation is distributed in patches. This is more common in natural rivers and makes the flowvegetation interaction more complicated. This is an extension of the study of Yokojima et al. (2013). Several improvements in the numerical strategies enable a more critical comparison between the present LES results and the corresponding experimental data, and the effect of vegetation configuration on the flow is examined in greater detail. 2. Experimental and numerical details 2.1. Experimental details Laboratory experiments are performed in a 24 m long by 80 cm wide flume with a bed slope of 1/555. The bottom and side walls are hydraulically smooth. Cylindrical bamboo stems of diameter d ¼ 0.3 cm are used as laboratory models for vegetation. The stems are arranged on 99 cm 9 cm aluminum sheets in a lattice-type square pattern of stem-tostem centerline spacing 3 cm. The use of the sheets can provide a variety of vegetation configurations in the experimental flume easily. Two specific vegetation configurations focused in the present study, Case 1 and Case 2, are shown in Fig. 1. The
Fig. 1. Schematic plan views of vegetation configurations in Cases 1 and 2.
vegetation density l is 1/30 cm1 and the ratio of the stem diameter to the spacing d/s is 0.1, which are in accordance with actual stem populations typically observed in real rivers (Fukuoka et al., 1992) as well as in marsh and marine grasses (Luhar et al., 2008). The flow discharge is set to be 9000 cm3/s in the two cases. The mean water depth in Case 1 and Case 2 is 4.78 cm and 4.71 cm, respectively. Under these conditions, the model plants are always emergent. Three velocity components are measured by using two-component electromagnetic current meters of both L type and I type, and water depth is measured by using water level gages. Two-minute records are collected at 10 Hz for both the velocity and water-depth measurements. Aniline blue (blue dye) is introduced on the free surface to visualize the behaviors of the large horizontal vortices evolving along the edge of vegetation zone. 2.2. Numerical details The governing equations for LES are obtained by the application of a spatial filter to the three-dimensional, incompressible NaviereStokes equations. The resulting unclosed correlations, the subgrid-scale stresses, are parameterized by the Smagorinky model. In the present LES, the effect of vegetation on flows is macroscopically modeled by introducing a drag-force term into the filtered momentum equation. The drag-force term is expressed as ! 1 ! f ¼ CD l ! u u ; 2
ð1Þ
u is the filtered velocity. where CD is the drag coefficient and ! There is no standard way to find an appropriate CD for arbitrary vegetation configurations. In the test flows, the stem Reynolds number based on the cylinder diameter and the bulk mean velocity is around 700, where the drag coefficient of an isolated circular cylinder is about 1.0. Since a certain amount of drag reduction on downstream cylinders can be expected, the value of CD ¼ 0.8 is employed within the vegetation zones in the present study. This way of setting the model parameter CD is similar to that of Xiaohui and Li (2001), where an empirical function was introduced as the shading factor. The drag-force term is employed at all the velocity allocation points within the vegetation zones. It should be borne in mind that we do not claim it is an optimal CD. Rather it will be presented later that the choice of CD does not affect the simulation results significantly by a sensitivity test, as far as CD is set to be uniform in the vegetation zones. The equations are discretized in time with a semi-implicit method that uses a low-storage third-order Runge-Kutta method (Spalart et al., 1991) for the convective terms and the Crank-Nicholson method for the viscous diffusion terms. Spatial derivatives are discretized with fully-conservative second-order central differences (Kajishima, 1999). The discretized equations are solved with a fractional step method. In the present simulations, the flow is assumed to be periodic in the streamwise direction. The length of the domain in the periodic direction L1 is set to be 594 cm, which is 50%
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Table 1 Simulation parameters for Cases 1 and 2. Reb
Case 1 Case 2
11,250 11,250
Domain size (cm)
Number of grid points
Grid spacing (cm)
L1
L2
L3
n1
n2
n3
Dx1
Dx2
Dx3
594 594
4.78 4.71
80 80
480 480
37 36
194 194
1.238 1.238
0.0130.314 0.0140.317
0.0140.504 0.0140.504
larger than that of Yokojima et al. (2013). It is much longer than the width of the flume and, in Case 2, is three times as large as the geometrical minimal unit. The bottom and side walls of the flume are hydraulically smooth so that the no-slip condition is imposed. The free surface is set as a friction-less rigid lid. As we will see later, the unsteady deformation of the free surface can be estimated fairy well by applying the hydrostatic approximation to the surface pressure. While Yokojima et al. (2013) fixed the mean pressure gradient in time, the mass flow rate is fixed in the present LES. It enables a closer comparison between LES results and experimental data, since the laboratory experiments have been conducted at a constant flow discharge of 9000 cm3/s. The flow depth is set at that observed in the experiments. The Reynolds number based on the bulk mean velocity and the water depth, Reb, is 11,250 in both cases. The simulation parameters introduced above are listed in Table 1. The number of grid points (n1, n2, n3) employed in each simulation is also included. The grid spacing (Dx1, Dx2, Dx3) is uniform in the streamwise x1 direction, while nonuniform spacing concentrated near the bottom/side walls and free surface is used in the vertical x2 and lateral x3 directions. Once the flow reaches the statistically-steady state, the simulation is continued for a data accumulation time Ta of about 120 s with a time increment of Dt ¼ 1/112.5 s to obtain wellconverged flow statistics. 3. Results and discussion 3.1. Instantaneous flows Fig. 2(a) shows a visualized flow pattern obtained from the experiment in Case 1, and Fig. 2(b) shows the free-surface velocity vectors reproduced by the present LES. In both experimental and LES results, two staggered rows of largescale horizontal vortices arising from shear instabilities can be observed along both sides of the vegetation-zone interfaces. The length scale of the large horizontal vortices in the streamwise direction is about 90 cm in both experiment and LES. The vortices are found also in Case 2 (see Fig. 3), where
Ta (s)
Dt (s)
120.9 120.9
1/112.5 1/112.5
vegetation patches of size 99 cm 27 cm are installed discretely in the streamwise direction. The size of the vortices is 80100 cm in the streamwise direction, which is comparable to that in Case 1. In this case, the horizontal vortices developed at the vegetation interface start to fluctuate in the transverse direction and deform in the non-vegetation zones. The deformed vortices encounter the next vegetation patch before they attain to disintegration. Although not shown here, it is confirmed that this behavior of the vortices does not change essentially by increasing the distance between neighboring vegetation patches up to 300 cm. Fig. 4 shows the time series of the velocity fluctuations u1 and u3 in Case 1. These data are sampled at point A1 presented in Fig. 1, i.e., on the edge of the vegetation belt at a depth of x2 ¼ 2.5 cm. These two velocity components are clearly in phase and well correlated. It can be seen that the present LES accurately reproduces the time series obtained from the experiment in waveshape as well as amplitude. Note that the temporal resolution of the electro-magnetic velocimetry used in the experiment is at most 5 Hz, much lower than that of the present LES. Fig. 5(a) shows the time series of the water-depth fluctuations obtained from the experiment in Case 1 sampled at both sides of the vegetation edge, A1 and A2 presented in Fig. 1. The surface fluctuations at these two points are clearly in antiphase. It physically means that the water bodies in two main-stream zones located on both sides of the vegetation belt fluctuate alternatively. Fig. 5(b) shows the LES results, where the surface fluctuations are estimated by applying the hydrostatic approximation on the surface pressure. It is demonstrated that the present LES can reproduce not just the oscillation frequency but the asymmetric fluctuations of the time series as well. Fig. 6 displays the velocity fluctuations u1 and u3 in Case 2 at point B1, located in a gap between two vegetation patches. Since the large-scale horizontal vortices occupying both sides of the flume interact with each other in the gap, the two time series obtained from the experiment become less correlated than those of Case 1, and the fluctuations of the lateral component u3 are enhanced, revealing the active momentum
Fig. 2. Visualized instantaneous flow pattern on the free surface in Case 1.
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Fig. 3. Visualized instantaneous flow pattern on the free surface in Case 2.
Fig. 4. Time series of velocity fluctuations u1 and u3 in Case 1, sampled at point A1: blue, u1; red, u3. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
transfer in the absence of vegetation. The present LES is found to fail in reproducing these properties well and give results similar to those from Case 1. Fig. 7 shows the surface fluctuations at points B1 and B2. Because of no flow resistance due to vegetation, the amplitude measured at these points tends to be smaller than that at the vegetation interface. As has been found in the time series of velocity fluctuations given in Fig. 6, the two-point surface
fluctuations are less correlated in the experimental data while the present LES does not reproduce the behavior well. In summary, a great agreement between the LES results and the corresponding experimental data is confirmed in the continuous case, Case 1. It is also found that the present LES does not seem to be very good at predicting the flow passing a series of discrete vegetation patches aligned in the streamwise direction. This point is discussed further in Section 3.2, where
Fig. 5. Time series of free-surface fluctuations in Case 1, sampled at points A1 (blue) and A2 (red). The fluctuations in LES are estimated by applying the hydrostatic approximation to the surface pressure. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. Time series of velocity fluctuations u1 and u3 in Case 2, sampled at point B1: blue, u1; red, u3. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 7. Time series of free-surface fluctuations in Case 2, sampled at points B1 (blue) and B2 (red). The fluctuations in LES are estimated by applying the hydrostatic approximation to the surface pressure. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 8. Streamwise mean velocity profiles in Case 1, normalized by the bulk mean velocity. The secondary flow pattern is also shown in the LES results by the velocity vectors.
Fig. 9. Streamwise mean velocity profiles in Case 2, normalized by the bulk mean velocity. The secondary flow pattern is also shown in the LES results by the velocity vectors.
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Fig. 10. Streamwise mean velocity profiles in Case 1 obtained by LES with CD ¼ 0.6 and 1.0. Fig. 8 is the counterpart.
Fig. 11. Streamwise mean velocity profiles in Case 2 obtained by LES with CD ¼ 0.6 and 1.0. Fig. 9 is the counterpart.
the mean velocity profiles at several cross sections are presented. 3.2. Mean flows Fig. 8 shows the streamwise meanevelocity profiles normalized by the bulk mean velocity Ub in Case 1. Inside the vegetation belt, the velocity substantially decreases due to the vegetation drag. Near the edges of the belt, the velocity increases with large velocity gradient in the lateral direction. The velocity takes the maximum value away from the vegetation and near the side banks. The present LES is found to reproduce the mean flow structures observed in the corresponding experiment fairly well. In Fig. 9, the normalized mean velocity profiles for Case 2 at five cross-Sections S1 through S5 marked in Fig. 1 are shown. When the fluid flow impinges on an isolated vegetation patch, deceleration of the fluid within the vegetation and acceleration in the two mainstream zones occur (Sections S1 through S4). After passing the vegetation patch, the inhomogeneous velocity distribution is gradually relaxed (Sections S4 and S5). It is found that the
predicted flow field by the present LES seems to require slightly longer relaxation time to fit with continual appearance and disappearance of the vegetation patches. This trend is in accordance with the findings obtained from Figs. 6 and 7. This failure is primarily because the model parameter CD of the canopy model (1) is set to be uniform within the vegetation zones in the present study. One may easily suppose that CD gets a maximum at the leading edge and tends to decrease with proceeding downstream. In Section 3.3 a sensitivity analysis with respect to CD presents that the failure cannot be overcome by simply shifting the level of the uniform drag coefficient. A proper estimation methodology of the model parameter CD is therefore essential for a better prediction of flows past vegetation patches, however, it is beyond the scope of the present paper. 3.3. Effect of model drag coefficient on flow prediction The simulation results presented so far are based on the uniform CD distribution of 0.8 within the vegetation zones. Here additional computations with CD ¼ 0.6 and 1.0 are
Fig. 12. Time series of velocity fluctuations in Case 1 obtained by LES with CD ¼ 0.6 and 1.0. Fig. 4 is the counterpart.
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Fig. 13. Time series of velocity fluctuations in Case 2 obtained by LES with CD ¼ 0.6 and 1.0. Fig. 6 is the counterpart.
Fig. 14. Schematic diagram of vegetation configuration examined by LES. Vegetation cover fraction fV is the ratio of the volume occupied by vegetation to the whole flow domain.
carried out to examine the effect of the value on the simulation results. Figs. 10 and 11 show the streamwise mean velocity profiles in Cases 1 and 2, corresponding to Figs. 8 and 9, respectively. In Case 1, CD ¼ 1.0 as well as 0.8 are found to give a reasonable prediction of the flow, while CD ¼ 0.6 reproduces drag a little bit lower than that of the experimental results within the vegetation belt. In Case 2, as has been mentioned in Section 3.2, the experimental data show that large velocity difference between the inside and the outside of a vegetation patch is quickly weakened after passing it. Fig. 11(c and d) demonstrate that neither CD ¼ 0.6 nor 1.0 can reproduce the feature. Time series of velocity fluctuations presented in Figs. 12 and 13 indicate that the choice of CD does not affect the simulation results significantly in both Cases 1 and 2.
vegetation belt: 27 cm in Cases 1 and 2, and 26.7 cm (¼(1/3) L3) in Runs 1a and 2a. Note that there is another small difference between Case 2 and Run 2a in flow depth. In a series of Runs 1, vegetation belt continuous in the streamwise direction is set in three different locations in the lateral direction, i.e., along the centerline of the flume (Run 1a), along the side wall (Run 1c), and at the middle of these two (Run 1b). The influence of the space between the vegetation patches aligned in the streamwise direction is examined in Runs 2. In Runs 3, the vegetation volume fraction fV is changed by decreasing the width of the vegetation belt. Note that, between Runs 2 and Runs 3, there is an obvious
4. Effect of vegetation configuration on flow resistance In this section, we apply the LES method whose basic capabilities have been well demonstrated in Section 3 to flows with a wide variety of vegetation configurations, to explore the relationship between the configuration and the resulting flow resistance. Here we simulate flows in the same flume employed in the previous section and assume the same water depth (4.78 cm) and flow discharge (9000 cm3/s) imposed in Case 1 for all the cases. Fig. 14 shows the schematic diagram of the vegetation configuration studied here. Vegetation cover fraction, fV, denoting the ratio of the volume occupied by vegetation to the whole flow domain, is introduced as a parameter. Runs 1a and 2a are quite similar to Cases 1 and 2, respectively, and the slight difference lies in the width of the
Fig. 15. Mean pressure gradient required to maintain the constant flow rate of 9000 cm3/s as a function of the vegetation cover fraction fV.
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difference in the vegetation layout but mutual correspondence in fV. LES is applied also to flows with fV ¼ 0 (Run 0a) and 1 (Run 0b) for reference. Fig. 15 shows the absolute value of the time-averaged pressure gradient in the streamwise direction DP/L1 required to maintain the constant flow rate, as a function of the vegetation cover fraction fV. By comparing the results of Runs 2 and Runs 3, it is found that the mean pressure gradient and hence the flow resistance are decreased with decreasing fV and that the flow resistance solely depends on the value of fV, irrespective of the details of the vegetation configuration. A desirable finding in terms of enhancement of the carrying capacity of flood obtained from Runs 1 is that the flow resistance can be reduced by shifting the vegetation belt toward the side wall. Conceivable explanations for the excessive drag reduction are: (i) arranging vegetation zones on regions with lower fluid velocity leads to lower drag to the flow, and (ii) the presence of the side wall, especially the impermeability to the normal direction, damps lateral mixing of the flow. Fig. 16 shows visualized flow patterns on the free surface. It is clear from Runs 1 that the size of the large horizontal vortices becomes large as the continuous vegetation belt is shifted toward a side wall. It is seen in Runs 2 that a pair of vortices shed from a vegetation patch interacts with each other and becomes obscure as it moves downstream. However, the vortices do not dissipate completely as far as examined in the present study. In Runs 3, the vortices arranged along both side
of the vegetation belt become weakened as the width of the vegetation belt is decreased. It is noteworthy that the characteristic length scale of the horizontal vortices in the streamwise direction remains to be about 100 cm in all the cases examined in Runs 2 and 3. It suggests that not only the size but the strength of the horizontal vortices affect the flow resistance. 5. Conclusions The effect of vegetation configuration on turbulent flows in a rectangular open channel has been investigated both experimentally and numerically. A basic LES method and a classical canopy model were employed in the numerical simulations. The applicability of the method was critically examined against the corresponding experimental data. The relationship between vegetation configuration and the resulting flow resistance were investigated by the LES. While a great agreement is obtained between the present LES results and the corresponding experimental data in the case where vegetation is established continuously in the streamwise direction, the present method is found to fail in reproducing the streamwise variation of the mean flow structures accurately in the discrete case. This is mainly due to the arrangement of a uniform distribution of the drag coefficient, CD, required in the canopy model. Application of the LES to flows with a wide variety of vegetation configuration reveals that, in most cases, the flow
Fig. 16. Visualized instantaneous flow pattern on the free surface for a wide variety of vegetation configurations.
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resistance solely depends on the total volume of vegetation, irrespective of the configuration details in the streamwise direction, and that shifting vegetation toward the side wall achieves a considerable drag reduction. This is partly because the primary velocity is decreased with approaching the side wall and partly because the lateral mixing is suppressed by the presence of the side wall. Acknowledgment The study was partially supported by Grant-in-Aid for Scientific Research No. 23360215 (YK) and for Young Scientists No. 23760456 (SY), from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, and a financial support from the Takahashi Industrial and Economic Research Foundation (SY). References Choi, S.-U., Kang, H., 2004. Reynolds stress modelling of vegetated openchannel flows. J. Hydr. Res. 42 (1), 3e11. Cui, J., Neary, V.S., 2008. LES study of turbulent flows with submerged vegetation. J. Hydr. Res. 46 (3), 307e316. Fischer-Antze, T., Stoesser, T., Bates, P., Olsen, N.R.B., 2001. 3D numerical modelling of open-channel flow with submerged vegetation. J. Hydr. Res. 39 (3), 303e310.
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Fukuoka, S., Fujita, K., Niida, H., 1992. Prediction in flood water level of river courses with vegetation. Proc. JSCE II-19 447, 17e24 (in Japanese). Jahra, F., Kawahara, Y., Hasegawa, F., Yamamoto, H., 2011. Flow-vegetation interaction in a compound open channel with emergent vegetation. Int. J. River Basin Manag. 9 (3e4), 247e256. Kajishima, T., 1999. Finite-difference method for convective terms using nonuniform grid. Trans. JSME 65B (633), 1607e1612 (in Japanese). Lopez, F., García, M.H., 2001. Mean flow and turbulence structure of openchannel flow through non-emergent vegetation. J. Hydr. Eng. 127 (5), 392e402. Luhar, M., Rominger, J., Nepf, H., 2008. Interaction between flow, transport and vegetation spatial structure. Environ. Fluid Mech. 8, 423e439. Neary, V.S., Constantinescu, S.G., Bennett, S.J., Diplas, P., 2012. Effects of vegetation on turbulence, sediment transport, and stream morphology. J. Hydr. Eng. 138 (9), 765e776. Nepf, H.M., 1999. Drag, turbulence, and diffusion in flow through emergent vegetation. Water Resour. Res. 35 (2), 479e489. Shimizu, Y., Tsujimoto, T., 1994. Numerical analysis of turbulent openchannel flow over a vegetation layer using a kε turbulence model. J. Hydrosci. Hydr. Eng. 11 (2), 57e67. Spalart, P.R., Moser, R.D., Rogers, M.M., 1991. Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96, 297e324. Xiaohui, S., Li, C.W., 2001. Large eddy simulation of free surface turbulent flow in partly vegetated open channels. Int. J. Numer. Meth. Fluids 39, 919e937. Yokojima, S., Kawahara, Y., Yamamoto, T., 2013. Effect of vegetation configuration on turbulent flows in a rectangular open channel. In: Proc. Of 35th IAHR World Congress, Chengdu, China, p. A11875.
ScienceDirect Journal of Hydro-environment Research 9 (2015) 295e303 www.elsevier.com/locate/jher
Impacts of vegetation configuration on flow structure and resistance in a rectangular open channel Satoshi Yokojima a,*, Yoshihisa Kawahara b, Takuya Yamamoto b b
a Department of Mathematical and Systems Engineering, Shizuoka University, Hamamatsu 432-8561, Japan Department of Civil and Environmental Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan
Available online 19 December 2014
Abstract Riparian vegetation exerts significant effects on the flow structure and the geomorphology of rivers. While it provides a rich wildlife habitat as well as a protection from bank erosion, vegetation can increase the risk of flood inundation by reducing the carrying capacity of flood. A proper balance between flood control and riparian eco-diversity is therefore indispensable for better riparian management. In the present study, the effect of vegetation configuration on turbulent flows in a rectangular open channel, especially on the resulting flow resistance, has been investigated both experimentally and numerically. The laboratory experiments are conducted for two types of vegetation configurations, where vegetation is established either continuously or in a discrete way along the centerline of the flume. A regular array of emergent circular cylinders of diameter 3 mm with the stem-to-stem centerline spacing of 3 cm is used as a laboratory model for vegetation. The applicability of a basic large-eddy simulation (LES) method together with a canopy model is critically examined against the experimental data. A great agreement between the present three-dimensional LES results and the experimental data is achieved in the continuous case. On the other hand, the LES is found to fail in reproducing the streamwise variation of the mean flow structures accurately in the discrete case. This failure is mainly due to the arrangement of a uniform distribution of the drag coefficient required in the canopy model. The LES is applied to flows with a wide variety of vegetation configurations to examine the relationship between the presence of vegetation and the resulting flow resistance. It is found that, in most cases, the flow resistance solely depends on the total volume of vegetation, irrespective of the configuration details in the streamwise direction. However, shifting vegetation toward the side wall achieves a considerable drag reduction. This is partly because the primary velocity is decreased with approaching the side wall and partly because the lateral mixing is suppressed by the presence of the side wall. © 2014 International Association for Hydro-environment Engineering and Research, Asia Pacific Division. Published by Elsevier B.V. All rights reserved.
Keywords: Vegetated open-channel flow; Large-eddy simulation; Large-scale vortices; Drag reduction
1. Introduction Flow through vegetation has been a key research topic in hydraulics, since riparian vegetation is ubiquitous in a wide variety of aquatic environments and plays a crucial role in both physical and biological aspects (Nepf, 1999; Neary et al., 2012). In one sense vegetation provides a rich wildlife habitat as well as a protection from bank erosion. On the other * Corresponding author. Tel./fax: þ81 53 478 1258. E-mail addresses: [email protected] (S. Yokojima), [email protected] (Y. Kawahara).
hand it can increase the risk of flood inundation since it increases drag to the flow and hence reduces the carrying capacity of flood. A proper balance between flood control and riparian eco-diversity is therefore indispensable for better riparian management, which requires a deep understanding about the effect of vegetation configuration on the flow behaviors. In the present study, the effect of vegetation configuration on turbulent flows in a rectangular open channel, especially on the resulting flow resistance is investigated both experimentally and numerically. Most of the numerical studies performed in the past have relied on the Reynolds-averaged
http://dx.doi.org/10.1016/j.jher.2014.07.008 1570-6443/© 2014 International Association for Hydro-environment Engineering and Research, Asia Pacific Division. Published by Elsevier B.V. All rights reserved.
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NaviereStokes (RANS) turbulence models (Shimizu and Tsujimoto, 1994; L opez and García, 2001; Fischer-Antze et al., 2001; Choi and Kang, 2004; Jahra et al., 2011). While these models have been compared favorably against laboratory test cases, their analyses were restricted inherently to timeaveraged flows. We employ a large-eddy simulation (LES) method to explicitly resolve unsteady large-scale horizontal vortices evolving along the interface between vegetation and non-vegetated zones. Since the large eddies induce significant momentum exchanges in the lateral direction and hence strongly characterize the flow, LES is expected to be more plausible in reproducing the flows and to provide detailed information about the three-dimensional flow field not just at time-averaged level but also at instantaneous level. Although a few application examples of LES to vegetated open-channel flows have been reported for both submerged and emergent cases (Xiaohui and Li, 2001; Cui and Neary, 2008), their attention is limited to the cases where vegetation exists continuously in the streamwise direction. The present study covers the cases where vegetation is distributed in patches. This is more common in natural rivers and makes the flowvegetation interaction more complicated. This is an extension of the study of Yokojima et al. (2013). Several improvements in the numerical strategies enable a more critical comparison between the present LES results and the corresponding experimental data, and the effect of vegetation configuration on the flow is examined in greater detail. 2. Experimental and numerical details 2.1. Experimental details Laboratory experiments are performed in a 24 m long by 80 cm wide flume with a bed slope of 1/555. The bottom and side walls are hydraulically smooth. Cylindrical bamboo stems of diameter d ¼ 0.3 cm are used as laboratory models for vegetation. The stems are arranged on 99 cm 9 cm aluminum sheets in a lattice-type square pattern of stem-tostem centerline spacing 3 cm. The use of the sheets can provide a variety of vegetation configurations in the experimental flume easily. Two specific vegetation configurations focused in the present study, Case 1 and Case 2, are shown in Fig. 1. The
Fig. 1. Schematic plan views of vegetation configurations in Cases 1 and 2.
vegetation density l is 1/30 cm1 and the ratio of the stem diameter to the spacing d/s is 0.1, which are in accordance with actual stem populations typically observed in real rivers (Fukuoka et al., 1992) as well as in marsh and marine grasses (Luhar et al., 2008). The flow discharge is set to be 9000 cm3/s in the two cases. The mean water depth in Case 1 and Case 2 is 4.78 cm and 4.71 cm, respectively. Under these conditions, the model plants are always emergent. Three velocity components are measured by using two-component electromagnetic current meters of both L type and I type, and water depth is measured by using water level gages. Two-minute records are collected at 10 Hz for both the velocity and water-depth measurements. Aniline blue (blue dye) is introduced on the free surface to visualize the behaviors of the large horizontal vortices evolving along the edge of vegetation zone. 2.2. Numerical details The governing equations for LES are obtained by the application of a spatial filter to the three-dimensional, incompressible NaviereStokes equations. The resulting unclosed correlations, the subgrid-scale stresses, are parameterized by the Smagorinky model. In the present LES, the effect of vegetation on flows is macroscopically modeled by introducing a drag-force term into the filtered momentum equation. The drag-force term is expressed as ! 1 ! f ¼ CD l ! u u ; 2
ð1Þ
u is the filtered velocity. where CD is the drag coefficient and ! There is no standard way to find an appropriate CD for arbitrary vegetation configurations. In the test flows, the stem Reynolds number based on the cylinder diameter and the bulk mean velocity is around 700, where the drag coefficient of an isolated circular cylinder is about 1.0. Since a certain amount of drag reduction on downstream cylinders can be expected, the value of CD ¼ 0.8 is employed within the vegetation zones in the present study. This way of setting the model parameter CD is similar to that of Xiaohui and Li (2001), where an empirical function was introduced as the shading factor. The drag-force term is employed at all the velocity allocation points within the vegetation zones. It should be borne in mind that we do not claim it is an optimal CD. Rather it will be presented later that the choice of CD does not affect the simulation results significantly by a sensitivity test, as far as CD is set to be uniform in the vegetation zones. The equations are discretized in time with a semi-implicit method that uses a low-storage third-order Runge-Kutta method (Spalart et al., 1991) for the convective terms and the Crank-Nicholson method for the viscous diffusion terms. Spatial derivatives are discretized with fully-conservative second-order central differences (Kajishima, 1999). The discretized equations are solved with a fractional step method. In the present simulations, the flow is assumed to be periodic in the streamwise direction. The length of the domain in the periodic direction L1 is set to be 594 cm, which is 50%
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Table 1 Simulation parameters for Cases 1 and 2. Reb
Case 1 Case 2
11,250 11,250
Domain size (cm)
Number of grid points
Grid spacing (cm)
L1
L2
L3
n1
n2
n3
Dx1
Dx2
Dx3
594 594
4.78 4.71
80 80
480 480
37 36
194 194
1.238 1.238
0.0130.314 0.0140.317
0.0140.504 0.0140.504
larger than that of Yokojima et al. (2013). It is much longer than the width of the flume and, in Case 2, is three times as large as the geometrical minimal unit. The bottom and side walls of the flume are hydraulically smooth so that the no-slip condition is imposed. The free surface is set as a friction-less rigid lid. As we will see later, the unsteady deformation of the free surface can be estimated fairy well by applying the hydrostatic approximation to the surface pressure. While Yokojima et al. (2013) fixed the mean pressure gradient in time, the mass flow rate is fixed in the present LES. It enables a closer comparison between LES results and experimental data, since the laboratory experiments have been conducted at a constant flow discharge of 9000 cm3/s. The flow depth is set at that observed in the experiments. The Reynolds number based on the bulk mean velocity and the water depth, Reb, is 11,250 in both cases. The simulation parameters introduced above are listed in Table 1. The number of grid points (n1, n2, n3) employed in each simulation is also included. The grid spacing (Dx1, Dx2, Dx3) is uniform in the streamwise x1 direction, while nonuniform spacing concentrated near the bottom/side walls and free surface is used in the vertical x2 and lateral x3 directions. Once the flow reaches the statistically-steady state, the simulation is continued for a data accumulation time Ta of about 120 s with a time increment of Dt ¼ 1/112.5 s to obtain wellconverged flow statistics. 3. Results and discussion 3.1. Instantaneous flows Fig. 2(a) shows a visualized flow pattern obtained from the experiment in Case 1, and Fig. 2(b) shows the free-surface velocity vectors reproduced by the present LES. In both experimental and LES results, two staggered rows of largescale horizontal vortices arising from shear instabilities can be observed along both sides of the vegetation-zone interfaces. The length scale of the large horizontal vortices in the streamwise direction is about 90 cm in both experiment and LES. The vortices are found also in Case 2 (see Fig. 3), where
Ta (s)
Dt (s)
120.9 120.9
1/112.5 1/112.5
vegetation patches of size 99 cm 27 cm are installed discretely in the streamwise direction. The size of the vortices is 80100 cm in the streamwise direction, which is comparable to that in Case 1. In this case, the horizontal vortices developed at the vegetation interface start to fluctuate in the transverse direction and deform in the non-vegetation zones. The deformed vortices encounter the next vegetation patch before they attain to disintegration. Although not shown here, it is confirmed that this behavior of the vortices does not change essentially by increasing the distance between neighboring vegetation patches up to 300 cm. Fig. 4 shows the time series of the velocity fluctuations u1 and u3 in Case 1. These data are sampled at point A1 presented in Fig. 1, i.e., on the edge of the vegetation belt at a depth of x2 ¼ 2.5 cm. These two velocity components are clearly in phase and well correlated. It can be seen that the present LES accurately reproduces the time series obtained from the experiment in waveshape as well as amplitude. Note that the temporal resolution of the electro-magnetic velocimetry used in the experiment is at most 5 Hz, much lower than that of the present LES. Fig. 5(a) shows the time series of the water-depth fluctuations obtained from the experiment in Case 1 sampled at both sides of the vegetation edge, A1 and A2 presented in Fig. 1. The surface fluctuations at these two points are clearly in antiphase. It physically means that the water bodies in two main-stream zones located on both sides of the vegetation belt fluctuate alternatively. Fig. 5(b) shows the LES results, where the surface fluctuations are estimated by applying the hydrostatic approximation on the surface pressure. It is demonstrated that the present LES can reproduce not just the oscillation frequency but the asymmetric fluctuations of the time series as well. Fig. 6 displays the velocity fluctuations u1 and u3 in Case 2 at point B1, located in a gap between two vegetation patches. Since the large-scale horizontal vortices occupying both sides of the flume interact with each other in the gap, the two time series obtained from the experiment become less correlated than those of Case 1, and the fluctuations of the lateral component u3 are enhanced, revealing the active momentum
Fig. 2. Visualized instantaneous flow pattern on the free surface in Case 1.
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Fig. 3. Visualized instantaneous flow pattern on the free surface in Case 2.
Fig. 4. Time series of velocity fluctuations u1 and u3 in Case 1, sampled at point A1: blue, u1; red, u3. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
transfer in the absence of vegetation. The present LES is found to fail in reproducing these properties well and give results similar to those from Case 1. Fig. 7 shows the surface fluctuations at points B1 and B2. Because of no flow resistance due to vegetation, the amplitude measured at these points tends to be smaller than that at the vegetation interface. As has been found in the time series of velocity fluctuations given in Fig. 6, the two-point surface
fluctuations are less correlated in the experimental data while the present LES does not reproduce the behavior well. In summary, a great agreement between the LES results and the corresponding experimental data is confirmed in the continuous case, Case 1. It is also found that the present LES does not seem to be very good at predicting the flow passing a series of discrete vegetation patches aligned in the streamwise direction. This point is discussed further in Section 3.2, where
Fig. 5. Time series of free-surface fluctuations in Case 1, sampled at points A1 (blue) and A2 (red). The fluctuations in LES are estimated by applying the hydrostatic approximation to the surface pressure. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. Time series of velocity fluctuations u1 and u3 in Case 2, sampled at point B1: blue, u1; red, u3. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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299
Fig. 7. Time series of free-surface fluctuations in Case 2, sampled at points B1 (blue) and B2 (red). The fluctuations in LES are estimated by applying the hydrostatic approximation to the surface pressure. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 8. Streamwise mean velocity profiles in Case 1, normalized by the bulk mean velocity. The secondary flow pattern is also shown in the LES results by the velocity vectors.
Fig. 9. Streamwise mean velocity profiles in Case 2, normalized by the bulk mean velocity. The secondary flow pattern is also shown in the LES results by the velocity vectors.
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Fig. 10. Streamwise mean velocity profiles in Case 1 obtained by LES with CD ¼ 0.6 and 1.0. Fig. 8 is the counterpart.
Fig. 11. Streamwise mean velocity profiles in Case 2 obtained by LES with CD ¼ 0.6 and 1.0. Fig. 9 is the counterpart.
the mean velocity profiles at several cross sections are presented. 3.2. Mean flows Fig. 8 shows the streamwise meanevelocity profiles normalized by the bulk mean velocity Ub in Case 1. Inside the vegetation belt, the velocity substantially decreases due to the vegetation drag. Near the edges of the belt, the velocity increases with large velocity gradient in the lateral direction. The velocity takes the maximum value away from the vegetation and near the side banks. The present LES is found to reproduce the mean flow structures observed in the corresponding experiment fairly well. In Fig. 9, the normalized mean velocity profiles for Case 2 at five cross-Sections S1 through S5 marked in Fig. 1 are shown. When the fluid flow impinges on an isolated vegetation patch, deceleration of the fluid within the vegetation and acceleration in the two mainstream zones occur (Sections S1 through S4). After passing the vegetation patch, the inhomogeneous velocity distribution is gradually relaxed (Sections S4 and S5). It is found that the
predicted flow field by the present LES seems to require slightly longer relaxation time to fit with continual appearance and disappearance of the vegetation patches. This trend is in accordance with the findings obtained from Figs. 6 and 7. This failure is primarily because the model parameter CD of the canopy model (1) is set to be uniform within the vegetation zones in the present study. One may easily suppose that CD gets a maximum at the leading edge and tends to decrease with proceeding downstream. In Section 3.3 a sensitivity analysis with respect to CD presents that the failure cannot be overcome by simply shifting the level of the uniform drag coefficient. A proper estimation methodology of the model parameter CD is therefore essential for a better prediction of flows past vegetation patches, however, it is beyond the scope of the present paper. 3.3. Effect of model drag coefficient on flow prediction The simulation results presented so far are based on the uniform CD distribution of 0.8 within the vegetation zones. Here additional computations with CD ¼ 0.6 and 1.0 are
Fig. 12. Time series of velocity fluctuations in Case 1 obtained by LES with CD ¼ 0.6 and 1.0. Fig. 4 is the counterpart.
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Fig. 13. Time series of velocity fluctuations in Case 2 obtained by LES with CD ¼ 0.6 and 1.0. Fig. 6 is the counterpart.
Fig. 14. Schematic diagram of vegetation configuration examined by LES. Vegetation cover fraction fV is the ratio of the volume occupied by vegetation to the whole flow domain.
carried out to examine the effect of the value on the simulation results. Figs. 10 and 11 show the streamwise mean velocity profiles in Cases 1 and 2, corresponding to Figs. 8 and 9, respectively. In Case 1, CD ¼ 1.0 as well as 0.8 are found to give a reasonable prediction of the flow, while CD ¼ 0.6 reproduces drag a little bit lower than that of the experimental results within the vegetation belt. In Case 2, as has been mentioned in Section 3.2, the experimental data show that large velocity difference between the inside and the outside of a vegetation patch is quickly weakened after passing it. Fig. 11(c and d) demonstrate that neither CD ¼ 0.6 nor 1.0 can reproduce the feature. Time series of velocity fluctuations presented in Figs. 12 and 13 indicate that the choice of CD does not affect the simulation results significantly in both Cases 1 and 2.
vegetation belt: 27 cm in Cases 1 and 2, and 26.7 cm (¼(1/3) L3) in Runs 1a and 2a. Note that there is another small difference between Case 2 and Run 2a in flow depth. In a series of Runs 1, vegetation belt continuous in the streamwise direction is set in three different locations in the lateral direction, i.e., along the centerline of the flume (Run 1a), along the side wall (Run 1c), and at the middle of these two (Run 1b). The influence of the space between the vegetation patches aligned in the streamwise direction is examined in Runs 2. In Runs 3, the vegetation volume fraction fV is changed by decreasing the width of the vegetation belt. Note that, between Runs 2 and Runs 3, there is an obvious
4. Effect of vegetation configuration on flow resistance In this section, we apply the LES method whose basic capabilities have been well demonstrated in Section 3 to flows with a wide variety of vegetation configurations, to explore the relationship between the configuration and the resulting flow resistance. Here we simulate flows in the same flume employed in the previous section and assume the same water depth (4.78 cm) and flow discharge (9000 cm3/s) imposed in Case 1 for all the cases. Fig. 14 shows the schematic diagram of the vegetation configuration studied here. Vegetation cover fraction, fV, denoting the ratio of the volume occupied by vegetation to the whole flow domain, is introduced as a parameter. Runs 1a and 2a are quite similar to Cases 1 and 2, respectively, and the slight difference lies in the width of the
Fig. 15. Mean pressure gradient required to maintain the constant flow rate of 9000 cm3/s as a function of the vegetation cover fraction fV.
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difference in the vegetation layout but mutual correspondence in fV. LES is applied also to flows with fV ¼ 0 (Run 0a) and 1 (Run 0b) for reference. Fig. 15 shows the absolute value of the time-averaged pressure gradient in the streamwise direction DP/L1 required to maintain the constant flow rate, as a function of the vegetation cover fraction fV. By comparing the results of Runs 2 and Runs 3, it is found that the mean pressure gradient and hence the flow resistance are decreased with decreasing fV and that the flow resistance solely depends on the value of fV, irrespective of the details of the vegetation configuration. A desirable finding in terms of enhancement of the carrying capacity of flood obtained from Runs 1 is that the flow resistance can be reduced by shifting the vegetation belt toward the side wall. Conceivable explanations for the excessive drag reduction are: (i) arranging vegetation zones on regions with lower fluid velocity leads to lower drag to the flow, and (ii) the presence of the side wall, especially the impermeability to the normal direction, damps lateral mixing of the flow. Fig. 16 shows visualized flow patterns on the free surface. It is clear from Runs 1 that the size of the large horizontal vortices becomes large as the continuous vegetation belt is shifted toward a side wall. It is seen in Runs 2 that a pair of vortices shed from a vegetation patch interacts with each other and becomes obscure as it moves downstream. However, the vortices do not dissipate completely as far as examined in the present study. In Runs 3, the vortices arranged along both side
of the vegetation belt become weakened as the width of the vegetation belt is decreased. It is noteworthy that the characteristic length scale of the horizontal vortices in the streamwise direction remains to be about 100 cm in all the cases examined in Runs 2 and 3. It suggests that not only the size but the strength of the horizontal vortices affect the flow resistance. 5. Conclusions The effect of vegetation configuration on turbulent flows in a rectangular open channel has been investigated both experimentally and numerically. A basic LES method and a classical canopy model were employed in the numerical simulations. The applicability of the method was critically examined against the corresponding experimental data. The relationship between vegetation configuration and the resulting flow resistance were investigated by the LES. While a great agreement is obtained between the present LES results and the corresponding experimental data in the case where vegetation is established continuously in the streamwise direction, the present method is found to fail in reproducing the streamwise variation of the mean flow structures accurately in the discrete case. This is mainly due to the arrangement of a uniform distribution of the drag coefficient, CD, required in the canopy model. Application of the LES to flows with a wide variety of vegetation configuration reveals that, in most cases, the flow
Fig. 16. Visualized instantaneous flow pattern on the free surface for a wide variety of vegetation configurations.
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resistance solely depends on the total volume of vegetation, irrespective of the configuration details in the streamwise direction, and that shifting vegetation toward the side wall achieves a considerable drag reduction. This is partly because the primary velocity is decreased with approaching the side wall and partly because the lateral mixing is suppressed by the presence of the side wall. Acknowledgment The study was partially supported by Grant-in-Aid for Scientific Research No. 23360215 (YK) and for Young Scientists No. 23760456 (SY), from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, and a financial support from the Takahashi Industrial and Economic Research Foundation (SY). References Choi, S.-U., Kang, H., 2004. Reynolds stress modelling of vegetated openchannel flows. J. Hydr. Res. 42 (1), 3e11. Cui, J., Neary, V.S., 2008. LES study of turbulent flows with submerged vegetation. J. Hydr. Res. 46 (3), 307e316. Fischer-Antze, T., Stoesser, T., Bates, P., Olsen, N.R.B., 2001. 3D numerical modelling of open-channel flow with submerged vegetation. J. Hydr. Res. 39 (3), 303e310.
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Fukuoka, S., Fujita, K., Niida, H., 1992. Prediction in flood water level of river courses with vegetation. Proc. JSCE II-19 447, 17e24 (in Japanese). Jahra, F., Kawahara, Y., Hasegawa, F., Yamamoto, H., 2011. Flow-vegetation interaction in a compound open channel with emergent vegetation. Int. J. River Basin Manag. 9 (3e4), 247e256. Kajishima, T., 1999. Finite-difference method for convective terms using nonuniform grid. Trans. JSME 65B (633), 1607e1612 (in Japanese). Lopez, F., García, M.H., 2001. Mean flow and turbulence structure of openchannel flow through non-emergent vegetation. J. Hydr. Eng. 127 (5), 392e402. Luhar, M., Rominger, J., Nepf, H., 2008. Interaction between flow, transport and vegetation spatial structure. Environ. Fluid Mech. 8, 423e439. Neary, V.S., Constantinescu, S.G., Bennett, S.J., Diplas, P., 2012. Effects of vegetation on turbulence, sediment transport, and stream morphology. J. Hydr. Eng. 138 (9), 765e776. Nepf, H.M., 1999. Drag, turbulence, and diffusion in flow through emergent vegetation. Water Resour. Res. 35 (2), 479e489. Shimizu, Y., Tsujimoto, T., 1994. Numerical analysis of turbulent openchannel flow over a vegetation layer using a kε turbulence model. J. Hydrosci. Hydr. Eng. 11 (2), 57e67. Spalart, P.R., Moser, R.D., Rogers, M.M., 1991. Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96, 297e324. Xiaohui, S., Li, C.W., 2001. Large eddy simulation of free surface turbulent flow in partly vegetated open channels. Int. J. Numer. Meth. Fluids 39, 919e937. Yokojima, S., Kawahara, Y., Yamamoto, T., 2013. Effect of vegetation configuration on turbulent flows in a rectangular open channel. In: Proc. Of 35th IAHR World Congress, Chengdu, China, p. A11875.