Flow characteristics in open channels with aquatic rigid vegetation ＊

Yan-jie Wu , He-fang Jing, , Chun-guang Li, Ying-ting Song

1. College of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei 230009, China

2. School of Civil Engineering, North Minzu University, Yinchuan 750021, China

3.Key Laboratory of Intelligent Information and Big Data Processing of Ningxia Province, Yinchuan 750021,China

4. Research Institute of Numerical Computation and Engineering Applications, North Minzu University, Yinchuan 750021, China

5. State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300350,China

Abstract: In order to study the flow characteristics in water bodies with rigid aquatic vegetation, series of laboratory experiments are carried out in an open channel, in which glass rods are used as plants with diameters of 6mm, 8mm and 10mm, respectively. For each diameter of glass rods, four typical cases are considered with various densities and arrangements of glass rods. The flow velocities in the four cases are measured by the 3-D laser Doppler velocimeter (LDV). The water surface slope, the flow velocity, the water head loss, the vegetation drag force and the hydraulic slope are calculated, analyzed and discussed. The horizontal, vertical and total vegetation densities in the vegetation area are defined and the relationship between these physical parameters and the water surface slope are studied. The head loss and the hydraulic slope in the vegetation area are also calculated, compared and analyzed. It is indicated that the water surface slope and velocity, the head loss and the hydraulic slope in the vegetation area have a close relationship with the arrangement, the density, and the plant diameter of the vegetation.

Key words: Aquatic rigid vegetation, flow velocity, laser Doppler velocimeter (LDV), head loss, hydraulic slope

Introduction

The aquatic rigid vegetation, such as the reed, the lotus, and the cortaderia selloana., can be found in natural rivers, lakes, reservoirs, seas, or open channels,and play an important role in the sediment transportation, the water purification, the bank protection works,among others. The aquatic rigid vegetation affects the flow structure, increases the flow resistance, and decreases the flow capacity, to cause flood disasters in the water bodies[1-2]. Therefore, the study of the flow with vegetation is important not only in the management of rivers, lakes, reservoirs, etc., but also is in the water environment protection and the water ecology construction. In recent years, the hydraulic problems in water bodies with vegetation were extensively studied, including the field measurement,the flume experiment, and the numerical simulation.

The field measurement, directly measuring the natural water bodies with vegetation, can acquire original data about vegetated water bodies. Therefore,it is relatively of high accuracy. Since the 1980’s, the spatial and temporal distributions and the growth of the aquatic vegetation were monitored by using the technology of remote sensing. Zhang[3]investigated the biomass of the submerged plant in the Honghu Lake in China using the landsat thermatic mapper(TM). Jakubauskas et al.[4]measured the spectrum reflectivity of the lotus in a lake in America and studied the relationship between the reflectivity and the coverage of the lotus. Dekker et al.[5], Gullstrom et al.[6]surveyed the spatial and temporal distributions of the submerged water grass and macroalgae along the sea bank in Australia and Tanzania. Yuan and Zhang[7]investigated the spectral responses of several common submerged aquatic plants in Shanghai using a field portable spectroradiometer.

However, the field measurement is time consuming, economically expensive, and difficult to conduct because of the limits of instruments, and the complex water and weather conditions. Therefore,most researches focus on the flume experiment and the numerical simulation, as well as, occasionally, the theoretical analysis.

The flume experiment is relatively cheaper and easier to perform than the field measurements, and as such, quite an amount of data was accumulated.Carollo et al.[8]measured the local flow velocities for different vegetation concentrations, discharges, and flume bed slopes by using the 2-D acoustic Doppler velocimeter (ADV). Yang et al.[9]used the 3-D ADV to measure the local flow velocities for different types of vegetations on the floodplain in a movable bed flume in the State Key Laboratory of Hydraulics and Mountain River Engineering of Sichuan University. It was found that the flow velocity follows an S-shaped profile, with three zones in the floodplains with vegetation. Wu and Yang[10]measured and studied the effects of flow conditions and characteristics of vegetation on the bending rigidity of the submerged vegetation in a laboratory flume. Ricardo et al.[11]calculated the time and space averaged flow variables in a flume with non-uniform emergent vegetation from the instantaneous velocity maps obtained with the particle image velocimetry (PIV). Liu et al.[12]investigated the flow features in a meandering compound channel with grass on the floodplain.Recently, Liu and Nepf[13]investigated the effect of vegetation on the sediment transport and deposition in an open channel. Song et al.[14]studied the characteristics of open channel flows with submerged rigid vegetation by laboratory experiments.

The numerical simulation is another efficient method to study the problems of flow with aquatic vegetation with the development of computer science and technology. Li et al.[15]investigated the effects of vegetation patch density on flow velocity characteristics in an open channel.

Wilson et al.[16]used a 3-D k-ε turbulence model to simulate the impact of willow stands on the velocity distribution. Huai et al.[17]proposed a new three-layer model , and showed that it can be used to predict the velocity distribution of the open channel flow with submerged rigid vegetation in numerical simulations. After that, Huai et al.[18]proposed an analytical model for predicting the vertical distribution of the mean streamwise velocity in an open channel with double-layered rigid vegetation. Kim et al.[19]simulated the flow with rigid emergent cylinders by using the 3-D large eddy simulation (LES). Cai et al.[20]studied the effect of rigid unsubmerged vegetation on the flow in a flume with various arrangements of vegetation by employing 2-D lattice Boltzmann methods (LBM). Liu et al.[21]proposed a model for estimating the flow direction in the meandering compound channels, and the results were in good agreement with the measurements. Shan et al.[22]proposed an effective model for predicting the depth-averaged two-dimensional flow direction along a smooth and vegetated meandering compound channels. Huai et al.[23]investigated open channel flows with non-submerged vegetation using the LES.Jing et al.[24]investigated the open channel flow with unsubmerged rigid vegetation by the lattice Boltzmann method.

Above results may serve as a foundation for studying the flow with aquatic vegetation. Because of the complexity of flows with aquatic vegetation,further extensive studies are desirable. For example,most measuring instruments of the velocity in the laboratory flume in the available literature are the ADV, including, occasionally, the PIV. However, the LDV is seldom used in these cases.

The 3-D laser Doppler velocimeter (LDV)produced by the TSI cooperation in the United States has many advantages, such as the high precision,without disturbance of the velocity field, the wide range and the high frequency of measured velocities.It can measure not only the velocity field, but also other flow physical quantities such as the turbulence intensity, the Reynolds stress, and the particle diameter.

In this study, the 3-D LDV is employed to measure the vegetated flow in a flume of North Minzu University, China. The glass rods are used as the rigid plants, and series of measurements are made to study the effect of vegetation on the flow.

1. Experiments

1.1 Description and procedure of experiments

Experiments are carried out in a flume of North Minzu University, China. The flume is self-circulated,with a fixed bed slope, and consists of an intake tower,a glass flume and a circulation pool. The glass flume is 15.00 m in length, 0.49 m in width, and 0.50 m in depth, as shown in Fig. 1.

Fig. 1 (Color online) The flume and the LDV

Table 1 Summary parameters of experiments

The LDV is used to measure the velocity pointto-point in the vegetation area. At each point, the measuring time is set as 30 s to ensure the accuracy of the measured data. The water level and the discharge are measured by the water level gauge and the magnetic flow meter. The flow rate is kept constant throughout the test. The flow velocity is measured using the LDV, ranging from -300 m/s to 700 m/s.The measured relative error is less than 1%.

1.2 Experimental conditions

In order to study the flow characteristics with the aquatic rigid vegetation, four cases (cases 1-4) are designed in terms of the rod distributions. Parameters of the experiments are shown in Table 1.

In cases 1, 2, the glass rods are staggered distributed, while in Cases 3, 4, the glass rods are parallel distributed, as shown in Fig. 2. In cases 1, 3,the distances between two adjacent rods along both the transverse and longitudinal directions are 82 mm,while in cases 2, 4, the distances are 41 mm.

Fig. 2 The distribution of glass rods and measured positions

2. Results and discussions

2.1 Water level

Because of the resistance of the vegetation, the water level at the upstream of the vegetation area will be raised, and after the water passes through the vegetation area, the water level is lowered. Therefore,in the vegetation areas, a large water surface slope is produced. In this experiment, the aquatic vegetation is represented by cylindrical glass rods with height of 50 mm and diameters of 6 mm, 8 mm and 10 mm,respectively. Because the height of the glass rods is higher than the highest water level, the unsubmerged vegetation is simulated. With the same flow rate(=0.054 m3/s), the distribution of the water level varies with the arrangement of the glass rods, as shown in Fig. 3.

As can be seen from Fig. 3, the arrangement of vegetation has a great influence on the water level and the water surface slope in the vegetation area. In general, both the water level and the water surface slope are the largest in the dense and staggered case(case 2), followed by the dense and parallel case (case 4), with the sparse and staggered case (case 1) in the third place, and the sparse and parallel case (case 3) in the last place. Therefore, it is concluded that both the water level and the water surface slope are larger when the vegetation is arranged more densely and when the vegetation is in the staggered arrangement(as compared with the parallel arrangement).

By comparing the water level and the water surface slope in the same case with different diameters of the glass rod, it can be found that the larger the diameter of glass rods, the higher the water level and the water surface slope.

where Asvis the total projection area of the vegetation group on the flume bed, Asis the area of the flume bed in the studied area, Auvis the total projected area of the vegetation on the cross-section along the flow direction.

Fig. 3 Comparison of water level distribution in vegetation area in four typical cases

When the glass rod is used for the vegetation, the diameter of the glass rod is D, and the number of glass rods is N,hρ can be expressed as Let H be the water depth at the first row of the rods, and m be the number of effective rods on the upwind direction (i.e., rods that can produce projections on the cross-section along the flow direction),then

Eqations (2) and (4) can be employed to calculate the horizontal and vertical densities of the vegetation in the four typical cases in this study, as shown in Table 1. It can be seen that the total number of vegetation and the number of effective vegetation on the upwind direction are different in different cases. The total numbers of vegetation in cases 1, 3 are close, and the horizontal vegetation densities in cases 1, 3 are close, too. However, the number of the effective vegetation on the upwind direction in case 1 is about twice as that in case 3, and the vertical vegetation density in case 1 is twice as that in case 3.

Similarly, both the numbers of vegetation and the horizontal vegetation densities in cases 2, 4 are close,but both the vertical effective vegetation number and the vertical vegetation density in case 2 are near twice as those in case 4. In addition, it can also be found from Table 2 that both the horizontal and vertical vegetation densities increase with the increase of the vegetation diameter.

In order to study the relationship between the water surface slope and the vegetation density, the measured water levels at the inlet (z1) and the outlet(z2) of the vegetation area, and the water surface slope in four typical cases for three different diameters of vegetation are shown in Table 3. The water surface raise (Hr) can be calculated as

In Fig. 4, the fitted curve I shows the relationship between the water surface slope (S) and the horizontal vegetation density as fitted from the measured data, while the fitted curve II shows the relationship between the water surface slope and the vertical density as fitted from the measured data. It can be seen that the water surface slope not only increases with the increase of the horizontal vegetation density, but also increases with the increase of the vertical vegetation density. Comparatively speaking,the growth rate of the water surface slope with the horizontal vegetation density is larger than that with the vertical vegetation density. Therefore, both the horizontal and vertical vegetation densities have a great influence on the water surface slope, so they should generally be considered.

Table 2 Horizontal and vertical vegetation densities in four typical cases

Table 3 Water levels at the inlet of the vegetation area, water surface slopes in four typical cases

Fig. 4 Relationship between the water surface slope and the horizontal, vertical vegetation densities

The integrated vegetation densityiρ is defined as the weighted average of the horizontal and vertical vegetation densities, which can be expressed as

where w1and w2are the weighted factors of the horizontal and vertical vegetation densities, respectively, and can be set as the following empirical values to reflect the fact that the horizontal density is the main factor for the water surface slope:

The relationship between the integrated vegetation density and the water surface slope is shown in Fig. 5. Let JSbe the water surface slope, then the curve for the water surface slope and the integrated vegetation density can be obtained by using a polynomial fitting, as shown by Fig. 5, and the fitted quadratic polynomial is as follows

Fig. 5 Relationship between integrated vegetation density and water surface slope

2.2 Measurement and analysis of flow velocity

The measured flow field distributions are different in the four typical cases because of the different vegetation arrangements. It is shown that the measured flow fields of the same case with three vegetation diameters are very similar. Therefore, only the results of four cases with the vegetation diameter of 6mm are presented, as shown by Fig. 6.

The velocity is measured by the LDV point by point. Along the longitudinal direction, the measured points are set in the centerlines between two rows of adjacent rods, along the transverse direction, the measured points are set behind of each rod or in the centerline of two columns of rods, and along the vertical direction, the measured points are set every 20 mm from the flume bed. In Fig. 6，the flow field is represented by the averaged velocity and only the velocities in the longitudinal and transverse directions are considered. The flow velocity along the longitudinal direction is larger than that in the transverse direction, and the flow directions are basically parallel to the wall of the flume, as shown by Fig. 6. When the vegetation is parallel (Figs. 6(c), 6(d)), the velocity varies greatly along the transverse direction. Due to the resistance of the vegetation, the flow velocity is smaller at the measured point behind a rod than that at the measured point behind the gap of rods. When the vegetation is staggered (Figs. 6(a), 6(b)), all measured points are behind the rods, and the velocity changes slowly along the transverse direction.

Fig. 6 (Color online) Measured flow field in the vegetation area(D=6mm)

Fig. 7 (Color online) Velocity distribution along the transverse direction in the vegetation area (D=6mm)

Table 4 Average velocity at the inlet and the outlet of vegetation area in the four typical cases

In order to show the velocity variations against the vegetation clearly, the velocity distributions along the transverse direction in cases 2, 4 are presented, as shown in Fig. 7, in which the diameter of the vegetation is 6 mm. Three typical cross sections are chosen to compare, and they are located near the inlet, the middle and the outlet of the vegetation area. The distances between these sections and the inlet of the vegetation area in case 2 are 0.118 m, 0.278 m and 0.438 m, respectively, and the distances in case 4 are 0.065 m, 0.263 m and 0 .463 m, respectively.

In Fig. 7, it can be found that no matter the vegetation in the flow is staggered or parallel, the measured flow velocity distribution along the transverse direction is indented. However, the fluctuation amplitude of the flow velocity is larger when the vegetation is parallel (case 4) than when it is staggered(case 2). When the glass rods are parallel distributed,the flow velocities near these rods are small, while they are large between two neighbor rods along the transverse direction. While in the staggered cases, all glass rods have influence for the flow field. As a result,the amplitude of the flow velocity is larger when the vegetation is parallel than when the vegetation is staggered. In other words, when the vegetation is arranged in the staggered manner in the water flow,the flow velocity is nearly homogeneous along the transverse direction.

In order to compare the effects of the vegetation on the flow, the average velocities at the inlet and the outlet of the vegetation area in four typical cases are compared, as shown in Table 4. It can be seen that the velocity is larger at the outlet than at the inlet in the vegetation area in the same case and when the vegetation diameters are the same. The reason is that the water level at the inlet is raised due to the resistance of the vegetation area, and the water level decreases gradually in the vegetation area. The water level is much lower at the outlet than at the inlet of the vegetation area. Therefore, the discharge area is larger at the inlet than at the outlet.

From Table 4, it can also be found that the upstream velocities in the vegetation area are significantly different in different cases with the same diameter of the vegetation, but the differences of the downstream velocities are much smaller in different cases with the same diameter of the vegetation. In addition, the velocities at the inlet of the vegetation area are larger when the vegetation is sparsely distributed (cases 1, 3) than when the vegetation is densely distributed (cases 2, 4) if the vegetation diameter is the same.

2.3 Head loss and hydraulic slope in the vegetation area

Because of the resistance of the vegetation, the flow energy will decrease after passing the vegetation area. The head loss can be calculated according to the following energy equation of the flow

where p1and p2are the pressures at the inlet and the outlet, ρ is the density of the water, g is the gravity acceleration and hwis the total head loss. In the study, the pressures at both the inlet and the outlet are the same, so the total head loss can be calculated as follows

The total head losses in the four typical cases are calculated, as shown in Table 5. It can be found that the head losses are different in different cases.Generally speaking, if the diameter of the vegetation remains the same, the head losses are larger when the vegetation is densely arranged (cases 2, 4) than when the vegetation is sparsely arranged (cases 1, 3), they are larger when the vegetation is staggered (cases 1, 2)than when the vegetation is parallel (cases 2, 4). In addition, if the vegetation arrangement is the same,the head loss decreases with the decrease of the diameter of the vegetation.

Table 5 Head loss and hydraulic slope in the vegetation area under four cases

In fact, the head loss reflects the resistance of the vegetation to the water flow. According to the Newton’s Third Law, the resistance of the vegetation to a flow is equal to the drag force of the water to the vegetation, but in the opposite direction. Therefore, if the diameter of the vegetation is the same, the drag forces are larger when the vegetation is dense and staggered than when the vegetation is sparse and parallel. And the drag force of the water flow decreases with the decrease of the diameter of the vegetation.

The hydraulic slope is another parameter that reflects the resistance of the flow, and it can be defined as follows

where J is the hydraulic slope, L is the length of the vegetation area. Because the length of the vegetation area is the same in the four cases, both the hydraulic slope and the head loss vary with the same trend in the four cases with the same diameter of the vegetation, and in the same case with different diameters of the vegetation. In Table 4, the hydraulic slopes of the four cases with three diameters of the vegetation are also presented.

In addition, it can be found that the values of the hydraulic slope and the water surface slope are completely different by comparing Tables 2, 4. However,in the flow with vegetation, both the water surface slope and the hydraulic slope obey the following same rules: they are larger when the vegetation is staggered or dense than when the vegetation is parallel or sparse,with the same diameter of the vegetation, they increase with the increase of the diameter of the vegetation in the same case.

3. Conclusions

In this study, the 3-D LDV is employed to measure the 3-D flow velocity in a flume with aquatic vegetation, and the measured results are analyzed and compared. Glass rods with three diameters (6 mm,8 mm and 10 mm) are used to represent the aquatic rigid vegetation. Four typical cases are designed according to the density and the arrangement of the glass rods, and the relationship between the density of the comprehensive vegetation and the water surface slope, the head loss and the hydraulic slope in the vegetation area are studied. The main results are as follows:

(1) The water surface slope increases with both the horizontal and vertical vegetation densities, the water surface slopes are larger when the glass rods are staggered than when the glass rods are parallel arranged with the same diameter and number.

(2) The relationship between the water surface slope and the vegetation density can be obtained by fitting with a parabolic function, as shown in Eq. (8).

(3) The velocity distribution is indented along the transverse direction in the vegetation area in all four cases. However, the flow velocity fluctuates more significantly when the glass rods are parallel than when the glass rods are staggered.

(4) The water level rises and the flow velocity is relatively small in the upstream of the vegetation area.However, the water level falls and the flow velocity increases in the downstream of the vegetation area.

(5) The averaged flow velocity is larger when the glass rods are sparse than when the glass rods are dense in the upstream of the vegetation area; the average velocity is larger when the vegetation is parallel than when the vegetation is staggered.

(6) Both the head loss and the drag force of the vegetation are larger when the glass rods are dense than when the glass rods are sparse; both the head loss and the drag force of the vegetation are larger when the glass rods are staggered than when the glass rods are sparsely.

(7) The hydraulic slope varies with the same trend as the head loss in the vegetation area. However,the hydraulic slope varies with the different trend as the water surface slope.

Acknowledgments

This work was supported by the Key Project of North Minzu University in China (Grant No.2019KJ125, 2018XYZSX04), the Project of Key Research and Development Planned by Science and Technology Department of Ningxia, China (Grant No.2019BEG03048), the Science and Technology Research Projects in Ningxia Higher Education Institutions (Grang No. NGY2018-140). The authors declare that the manuscript does not contain clinical studies or patient data. Reviewers’ comments have greatly improved the quality of the paper.