NUMERICAL STUDY OF FLOW AND TURBULENCE THROUGH SUBMERGED VEGETATION

NUMERICAL STUDY OF FLOW AND TURBULENCE THROUGH SUBMERGED VEGETATION HYUNG SUK KIM (1), MOONHYEONG PARK (2), MOHAMED NABI (3) & ICHIRO KIMURA (4) (1) Korea Institute of Civil Engineering and Building Technology, Goyang, Korea, e-mail: Hskim0824@kict.re.kr (2) Korea Institute of Civil Engineering and Building Technology, Goyang, Korea, e-mail: moon@kict.re.kr (3) Deltares, Delft, Netherlands, e-mail: Mohamed.Nabi@deltares.nl (4) Hokkaido University, Sapporo, Japan, e-mail: i-kimu2@eng.hokudai.ac.jp ABSTRACT In this paper, we perform LES (large eddy simulation) for open channel flows through submerged matrix cylinders which are regarded as rigid vegetation. The computational model solves the filtered Navier-stokes equations on a Cartesian grid with local refinement and employs the ghost-cell immersed boundary method to deal with solid boundary. The cylinders are explicitly treated by computational grids. The model is validated through comparison with experimental data of the streamwise velocity profile. The effects of submergence ratio (water depth to vegetation height) on flow and turbulence structure are investigated. The coherent structures are produced above and behind the cylinders and those intensities amplified with decreasing submergence ratio. The large scale vortices, which are a main mechanism of momentum exchange between the vegetation layer and the out of vegetation, are generated above the vegetation and these penetration depths decrease with an increases in the submergence ratio. It is demonstrated that LES can capture large scale vortices originating at the top of vegetation and account for detailed instantaneous flow field through submerged vegetation. Keywords: LES, vegetation, submergence ratio, turbulence 1. INTRODUCTION Aquatic vegetation in streams is common and plays important roles in physical and ecological processes. It reduces the mean velocities in vegetation zone. The additional form drag exerted by vegetation significantly impacts the mean and instantaneous velocities, Reynolds stresses and turbulence quantities (Choi and Kang, 2004; Lopez and Garcia, 2001; Shimizu and Tsujimoto,1994; Stoesser et al., 2010). In particular, the submerged vegetation produces the velocity gradient above the top of vegetation and thus generates shear layer formation (Nepf and Vivoni, 2000; Nezu and Sanjou, 2008; Stoesser et al., 2009). Due to such complex flow structures, vegetation affects the transport of sediment and solutes. Several computational models have been developed to solve the 3D steady or unsteady Reynolds-averaged Navier- Stokes equations (RANS), which are capable of accurately predicting the time-averaged flows. In order to consider vegetation effects, additional source terms have been employed in momentum and transport equations with coarse grids. This approach is the most suitable method for providing reasonable accuracy of time-averaged flow fields (Choi and Kang, 2004; Fischer-Antze et al., 2001; Shimizu and Tsujimoto,1994;). However, RANS is not able to reproduce the large-scale unsteadiness induced by turbulent flow instabilities because of unsteady shear layer. When the vegetation is submerged, the inflection of the velocity profile at the top of vegetation occurs and thus the strong shear layer is generated. The 3D vortices are produced at the top of vegetation. The coherent structures above the vegetation are important roles in momentum exchanges with sweep and ejection (Ghisalberti and Nepf, 2002 and 2006; Nezu and Sanjou, 2008). Recently, LES (large eddy simulation) model have been developed to solve the unsteady filtered Navier-Stokes equations. LES offers better understanding of the instantaneous unsteady 3D turbulent flow field originated by large-scale unsteadiness. Relatively few studies using LES on open channel flows through vegetation have been conducted by Cui and Neary (2002), Stoesser et al. (2009) and Stoesser et al. (2010) who elucidate the large scale coherent structures. In this paper, we present LES of turbulent open channel flows over and through submerged cylinders which are regarded as rigid vegetation. Individual cylinders are explicitly resolved by computational grid, so that form drag is directly accounted for. Firstly, the present model is validated through comparison with measured data conducted by Liu et al. (2008). The flow and turbulence structures are described and the distance of flow penetration into vegetation canopy is analyzed. 2. Numerical framework The present computational model solves the filtered Navier-Stokes equations on a Cartesian grid. The advection and diffusion terms in the momentum equations are discretized in space on a staggered grid using a second-order finite 1

, volume method. A second-order Adams Bashforth scheme is used for the time integration of the advection term, while the Crank Nicolson method is applied for the diffusion term. A ghost-cell immersed boundary method based on a Cartesian grid is used for the bed surface and solid object boundaries. In the Cartesian grid system, uniform grids provide a low efficiency in 3D numerical simulations because a huge number of grids are essential to capture small scale turbulence eddies. In order to resolve this issue, an adaptive multilevel-structure Cartesian grid with local refinement is utilized around high gradients (i.e., near solid boundaries). For more details, we refer to Nabi et al. (2012) 3. Boundary conditions and model setup The setup for first simulations is selected to compare the experiments conducted by Liu et al. (2008). Liu et al. (2008) carried out flume experiments in rectangular open channel placed rigid cylinders with a staggered array and measured the flow using laser Doppler velocimeter (LDV) at the six locations as shown in Fig. 1. The distance between two cylinder is 10D where D (= 6.35 mm) is the cylinder diameter. The ratio of water depth h to cylinder height h v (= 76mm) is h/h v = 1.5 and 2 cylinders are included in the computational box as shown in Fig. 1. The computational domain spans 10D in both streamwise and lateral directions. In addition to the submergence ratio (h/h v = 1.5) of Liu et al. (2008), numerical simulations are performed for the submergence ratio of h/h v = 1.25 and 3.0. Periodic boundary conditions are applied in the streamwise and lateral directions. At the cylinders and channel bed, the no-slip boundary condition is applied and the free surface is treated as rigid lid without a friction. 4. Results Figure 1. Computational domain and the measured locations (left) and computational box including 2 cylinders (right). Fig. 2 shows the comparison of the LES with the measured data at the six locations for time-averaged streamwise velocities which is normalized by bulk velocity. Figure 2. Comparison of time-averaged streamwise velocities of the LES with measured data at the six selected locations. 2

Overall, the computed results are in good agreement with measured data. Streamwise velocities decrease within the canopy and accelerate above the canopy. As shown in the results, the profiles of streamwise velocities are similar regardless of the locations of the profile, which indicates that the flow is affected by the canopy in the entire region, even though the distance of the canopy is large enough. At location 1, which is just downstream of the cylinder, the computed velocity within the canopy is under-predicted whereas it is in agreement with measurement above the canopy. The region where the LES predicts lower velocity is characterized by high turbulence due to vortex shedding. At location 6, which is further downstream of the cylinder, the comparison shows good agreement between computed and measured data. At the results of the other locations (2~5), the computed profiles of the streamwise velocities match well with measured ones. There is almost constant velocity within the canopy and the high velocity gradients are found above the canopy. Fig. 3 presents the time-averaged streamwise velocity in two longitudinal planes where the upper part is a slice through the cylinder and the lower part is a slice of the center between cylinders. In this figure, the time-averaged flow fields for the submergence ratio of 1.25 and 3.0 are displayed. The flow is significantly decelerated within the vegetation layer. In particular, the retardation of the flow is obviously observed behind the cylinder irrespective of the submergence ratio, which is corresponded to recirculation zone. The flow is accelerated above the cylinders and its acceleration increases with a decrease in the submergence ratio, which indicates that a strong shear layer is produced. On the other hand, the time-averaged flow fields in plane where there are no cylinders are not appreciably different from those of a slice through the cylinder except for the downstream of the cylinder. It indicates that high fluid momentum from the vegetation layer is ejected to the out of the vegetation layer. The inflection of the velocity profile at the top of the vegetation layer induced by the suppression of the streamwise velocity in the vegetation zone generates unsteady shear layer and thus it causes large-scale vortices such as trailing vortices or tip vortices. Figure 3. Time-averaged streamwise velocities in two selected longitudinal planes: The upper part presents a slice through the cylinder and the lower part presents a slice of the center between cylinders. The left part is the submergence ratio is 1.5, the middle part is the submergence ratio is 3.0, the right part is the submergence ratio is 1.25. Fig. 4 presents the instantaneous vorticity in longitudinal plane where the slice is through the cylinder axis for the submergence ratio of 1.5, 1.25 and 3.0. There are two distinct regions of high vorticity. The high value of the vorticity 3

, occurs behind the cylinder which is recirculation zone. The vortices are observed by vortex shedding due to Kelvin Helmholtz instability. These vortices occur along the entire cylinder height and the magnitude of vortices is amplified as a decrease in the submergence ratio. The second region of high vorticity is the interface region. The trailing vortices are produced at the top of the cylinders and these are transferred to downstream region. The trailing vortices are interfered with those resulting from vortex shedding, which indicates that high level of turbulence occurs in the rear and the top of the cylinder due to tip vortices penetrating into the canopy. In the interface between the canopy and free flow, fluctuations in the vertical direction that is attributed to the vertical exchange processes are generated in the streamwise direction. The magnitude of the vortices occurring at the canopy increases with decreasing in the submergence ratio. The LES captures the instantaneous vortex structures resulting from the vegetation element. Figure 4. The instantaneous vorticity in longitudinal plane where the slice is through the cylinder: The left part is the submergence ratio is 1.5, the middle part is the submergence ratio is 3.0, the right part is the submergence ratio is 1.25. Fig. 5 shows the distributions of the turbulence intensity against the vertical direction at the location 3 for three submergence ratio and the comparison of penetration depth according to the submergence ratio. For the emergent vegetation, the turbulence intensity is significantly smaller than those of the submerged vegetation (Nepf and Vivoni, 2000; Nezu and Sanjou, 2008). This is due to fact that there is no vertical transport of momentum. The highest turbulence intensities are found at the top of canopy layers and the highest value of turbulence intensity occurs when the submergence ratio is 1.5. Several researches suggested that the penetration depth of turbulence stress is influenced by the mixing-layer vortices where the penetration depth is defined by the distance from the top of the canopy to the level where the Reynolds stress, normal stress or total kinetic energy decay 10% of the maximum value (Nepf and Vivoni, 2000; Nikora and Nikora, 2010; Nezu and Sanjou, 2008; Wilson et al., 2003). In this paper, the penetration depth is defined by the turbulence intensity. In Fig. 5 (right), the variations of the penetration depth are displayed against the submergence ratio. For comparison, the value of the penetration depth for the flexible vegetation conducted by Nepf and Vivoni, 2000, Wilson et al., 2003 and its value for rigid vegetation of Nezu and Sanjou (2008) are included. The value of the submergence ratio decreases rapidly from 1.0 (emergent vegetation) to 1.5, after which it decreases slowly. The value of the penetration depth for the rigid vegetation is higher than the value of the flexible vegetation which means that the higher momentum exchange occurs for the rigid vegetation. In addition, the penetration depth increases with an increase in the vegetation density. Figure 5. Streamwise turbulence intensities at the location 3 (right) and comparison of penetration depth (left) 4

5. Conclusions In this paper, we have presented the LES results for open channel flows with the submerged vegetation. For validation of the model, the computed time-averaged velocity at six locations is compared with measurement and the comparison showed good agreement between computed and measured data. The time-averaged velocity, vorticity and turbulence intensity are significantly influenced by the submergence ratio. The presence of the inflection in velocity profile produces a shear layer and the maximum value of turbulence stress near the top of the canopy. The strong shear is highly associated with development of coherent flow structures. The LES reproduces the trailing vortices originating near the top of the canopy and vortex structures behind the cylinder. The penetration depth of large-scale turbulence into the canopy is assessed using the turbulence intensity. The penetration depth increases with increasing the vegetation density or decreasing the submergence ratio. ACKNOWLEDGMENTS This research was financially supported by the Korea Institute of Civil Engineering and Building Technology (project: Development of Floodplain Maintenance Technology for Enhancement of Waterfront Values) REFERENCES Choi, S. U., and Kang, H. (2004). Reynolds stress modeling of vegetated open channel flows. J. Hydraul. Res., 42 (1), 3-11. Cui, J., and Neary, V. S. (2008). LES study of turbulent flows with submerged vegetation. J. Hydraul. Res., 46 (3), 307-316. Fischer-Antze, T., Stoesser, T., Bates, P. B., and Olsen, N. R. (2001). 3D numerical modelling of open channel flow with submerged vegetation. J. Hydraul. Res., 39, 303-310. Ghisalberti, M., and Nepf, H. (2002). Mixing layers and coherent structures in vegetated aquatic flows. J. Geophys. Res., 107(C2), 3-1-3-11. Ghisalberti, M., and Nepf, H. (2006). The structure of shear layer in flow over rigid and flexible canopy. Environ. Fluid Mech., 6, 277-301. Liu, D., Diplas, P., Fairbanks, J. D., and Hodges, C. C. (2008). An experimental study of flow through rigid vegetation. J. Geophys. Res., 113, 1-16. Lopez, F., and Garcia, M. (2001). Mean flow and turbulence structure of open channel flow through non-emergent vegetation. J. Hydraul. Eng., 127(5), 392-402. Nabi, M., H. J. de Vriend, Mosselman, E., Sloff, C. J., and Shimizu, Y. (2012). Detailed simulation of morphodynamics: 1. Hydrodynamics model, Water Resour. Res., 48, W12523 Nepf, H., and Vivoni, E. R. (2000). Flow structure in depth-limited, vegetated flow. J. Geophys. Res., 105(C12), 28457-28557. Nezu, I., and Sanjou, M. (2008). Turbulence structure and coherent motion in vegetated canopy open channel flows. J. Hydro-environ. Res., 2, 62-90. Nikora, N., and Nikora, V. (2010). Flow penetration into the canopy of the submerged vegetation: definitions and quantitative estimates. Proc., River Flow 2010, 437-444. Shimizu, Y., and Tsujimoto, T. (1994). Numerical analysis of turbulent open channel flow over vegetation layer using k-eps turbulence model. J. Hydrosci. Hydr. Eng., 11(2), 57-67. Stoesser, T., Palau, G., Rodi, W., and Diplas, P. (2009). Large eddy simulation of turbulent flow through submerged vegetation. Transp Porous Med., 78, 347-365. Stoesser, T., Kim, S. J., and Diplas, P. (2010). Turbulent flow through idealized emergent vegetation. J. Hydraul. Eng. 136(12), 1003-1016. Wilson, C. A. M. E., Stoesser, T., Bates, P. D., Batemann-Prinzen, A. (2009). Open channel flow through different forms of submerged flexible vegetation. J. Hydraul. Eng. 129, 847-853. 5