CURVED OPEN CHANNEL FLOW ON VEGETATION ROUGHENED

124

2012,24(1):124-129

DOI: 10.1016/S1001-6058(11)60226-6

CURV ED OPEN CHANNEL FLOW ON V EGETATION ROUGHENED INNER BANK*

HUAI Wen-xin, LI Cheng-guang, ZENG Yu-hong, QIAN Zhong-dong, YANG Zhong-hua

State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China, E-mail: wxhuai@https://www.sodocs.net/doc/4e994102.html,

(Received October 5, 2011, Revised December 14, 2011)

Abstract: A RNG kε?numerical model together with a laboratory measurement with Micro ADV are adopted to investigate the flow through a 180o curved open channel (a 4 m straight inflow section, a 180o curved section, and a 4m straight outflow section) partially covered with rigid vegetations on its inner bank. Under the combined action of the vegetation and the bend flow, the flow structure is complex. The stream-wise velocities in the vegetation region are much smaller than those in the non-vegetation region due to the retardation caused by the vegetation. For the same reason, no clear circulation is found in the vegetated region, while in the non-vegetation region, a slight counter-rotating circulation is found near the outer bank at both 90o and downstream curved cross-sections. A comparison between the numerical prediction and the laboratory measurement shows that the RNG kε? model can well predict the flow structure of the bend flow with vegetation. Furthermore, the shear stress is analyzed based on the numerical prediction. The much smaller value in the inner vegetated region indicates that the vegetation can effectively protect the river bank from scouring and erosion, in other words, the sediment is more likely to be deposited in the vegetation region.

Key words: RNG kε?numerical model, non-submerged rigid vegetation, bend flow, stream-wise velocities, shear stress

Introduction

Aquatic vegetations usually exist in natural cha- nnels, and they can retard the flow and change the internal flow structure to a certain extent. For this rea- son, the vegetation revetment has now frequently been adopted as an important ecological measure in the river regulation and ecological restoration works.

The flow structures in straight open channels with vegetation were much studied[1-4]. Stone and Shen[5], Li and Shen[6] experimentally studied the flow in straight rectangular channels with vegetation on the whole bed, and found that the vegetation density and arrangement can both affect the velocity distribution. Nezu and Onltsuka[7] investigated flow structures in an open channel partially covered with vegetation by *Project supported by the Natural National Science Foun- dation of China (Grant Nos. 11172218, 10972163, 51079102 and 50979078).

Biography: HUAI Wen-xin (1963-), Male, Ph. D., Professor Corresponding author: ZENG Yu-hong,

E-mail: yhzeng@https://www.sodocs.net/doc/4e994102.html, theoretical analysis and experimental measurement. Huai et al.[8] adopted large eddy simulation to investi- gate the flow characteristics in vegetated open cha- nnels, and they concluded that the vegetation can homogenize the mainstream flow structures both in supercritical and subcritical flow conditions. Kang and Choi[9] used a Reynolds stress model to simulate com- pound open-channel flows through vegetation. Naot et al.[10,11] used an algebra stress model to simulate seve- ral kinds of vegetation flows both in rectangular and compound open channels. Hui et al.[12], Chen and Kao[13], Nehal et al.[14], Pasche and Rouve[15] studied various aspects of flows through vegetation.

Up to now, the straight open channel flows with vegetation have obtained enough research attentions. However, little attention has been paid on the curved ones. This article applies a RNG kε

? turbulence model to simulate the curved open channel flows through partial non-submerged rigid vegetation, and the impacts of the non-submerged rigid vegetation both on the flow structures and the wall shear stresses are investigated in detail. To validate the model, the calculated results are compared with the experimental data.

125

1. Model description 1.1 Physical experiment

The experiment was conducted in a 180o curved Plexiglas flume, 1 m wide, 0.25 m deep, and consi- sting of a 4 m straight inflow section, a 180o curved section, and a 4 m straight outflow section. The discha- rge is 0.03 m 3/s and the water depth measured at the end of the channel is 0.148 m. Reinforcing steel bars were used to simulate the natural vegetation, and its diameter and height are 0.006 m and 0.15 m, respe- ctively. A 0.25 m wide band along the inner bank was planted perpendicularly with the artificial vegetation, and the interval size is 0.05 m. The sketch of this experiment is shown in Fig.1.

Fig.1 Sketch of experimental arrangement

Table 1 Radial layout of measuring lines on each cross-

section

Number of measuring lines

Radius (m)

a 1.55

b 1.65

c 1.75

d 1.85

e 2

f 2.15

g 2.3

h 2.45

Fig.2 Grid arrangement

The 3-D Doppler ultrasound anemometer was used to measure the flow velocities on 5 typical cross-

sections (0o , 45o , 90o , 135o , 180o °cross-section, res- pectively), and 8 vertical measuring lines (Table 1) were arranged on each cross-section. The experi- mental data are derived from detailed high-resolution measurements of the three velocity components on each measuring line. The sampling time is 60 s at each measuring point, and the sampling rate is as high as 50 Hz to ensure the measurement accuracy. 1.2 Mathematical model

The RNG k ε? turbulence model is obtained from the Navier-Stokes equations, using a statistical RNG methods. The main governing equations are as follows:

Continuity equation

=0i

i

u x ?? (1)

Momentum equation +=+i j i i i j j i j

j u u u u 1p

u u t x ?x x x ν§·

?????′′??¨?¨???????1

(2)

k ε? equation

+=+t i

i i j i i

k i j u k k k u u u ?t x x ?x x ννao§·????

?′′????¨?

????????1??(3)

+=+t i i i

?i u t x x ?x νεεενao§·???

?????¨????????1??

2

12

i i j j

u c u u c k x k ε

ε?′′?? (4) where ρ is the density of the fluid, u is the temporal average velocity, p is the pressure, ν is the kinematic viscosity, k and ε are the turbulent

kinetic energy and the dissipation rate, respectively.

i j u u ′′? stands for the Reynolds stress tensor, 2=+

3j

i i j t ij j i u u u u k?x

x ν§·??′′??¨?¨????1

,2=?t c k νε,=0.0845c μ,==0.07179k εσσ,2=1.68c ,

013

1=1.421+c ηηβη§

·

?

¨??

1

?

,=Sk ηε,()12=2ij ij S S S ,

1=

+2j

i ij j i u u S x x §·

??¨?¨????1

,0=4.38η, =0.012

β

126

Fig.3 Comparison between the calculated and measured vertical distributions of the stream-wise velocity

127 Fig.4 Comparison of secondary flow structures between the measured and calculated results on 5 cross-sections

1.3 Calculation method

The calculation domain is the same as the experi- mental one in length and width, while the calculation height is 0.2 m. In the vegetation region, unstructured grids are used. The interval dimensions are about 0.004 m in longitude and latitude, and 0.0125 m in the vertical direction and the cylinder is meshed into regu- lar hexagons (Fig.2). In the non-vegetation region, structured grids are used, with the interval dimensions of 0.01 m in longitude and latitude, and 0.0125 m in the vertical direction. The total grid number is about 7.5×106.

The Volume Of Fluid (VOF) model is used to solve the free surface. The mass flow inlet condition is imposed on the inflow boundary, and the pressure out- let condition is imposed on the outlet and the upper boundary. For sidewall, bed wall and cylinder wall, no-slip wall boundary condition is used. Finite volume method is used to discretize and solve the governing equations. The SIMPLE-Consistent (SIMPLEC) algo- rithm is used for the pressure-velocity coupling at each time step/iteration. When the residuals are less than 1×10–4 for the continuity equation and 1×10–6 for other equations, the convergence is assumed to be rea- ched.

2. Results and discussions

2.1 Distribution of stream-wise velocity

The calculated and measured vertical distribu- tions of the stream-wise velocity on five typical cross-

sections are shown in Fig.3. For each cross-section,

128

the velocity profiles for four lateral locations, one in the vegetated region (b), and the other three in the nonvegetated region ((d), (e), (g)) are compared.

In Fig.3, it can be seen that, under the retard effect of vegetation, the velocities on line (b) (in the vegetation region) are much smaller than those on lines ((d), (e), (g)) (in the non-vegetation region). Along the stream-wise direction, the velocities in the vegetation region decrease while heading downstream, reach the minimum at the 135o cross-section. There appears a small bounce at the 180o cross-section, which can be ascribed to the fact that the weakening of the transverse circulation in the non-vegetation region makes the transverse distribution a bit more homogeneous (see Fig.3). In the non-vegetation region, the vertical distributions of velocity at the entrance of the curve are “J” shaped approximately, while heading downstream, the maximal velocity is gradually shifted to the flume bed. The reason may be that the main circulation in the curve changes the inte- rnal flow structures, and the velocity distribution varies accordingly.

2.2 Secondary flow structures

Figure 4 shows a comparison of secondary flow structures between measured and calculated results on these five typical cross-sections. The dotted line repre- sents the interface between the vegetation region and the non-vegetation region. The predictions in the cur- ved reach agree well with the measured data, while in the inlet and outlet reaches of the curve, there are some discrepancies. The possible reason may be that the flow conditions are very complex and varying rapidly at the interface of the straight and curved rea- ches.

In the vegetation region, no clear circulation is found in the whole region, while in the non-vegetation region, under the combined effect of the centrifugal force, and the pull of gravity and vegetation, lateral flows toward the outer bank are generated at the entra- nce of the curve (0o), but no circulation forms. At the 45o cross-section, a circulation is fully formed and reaches the maximum in the transverse range. Then the scale gradually decreases and finally disappears at the outlet of the curve. Besides the primary circulation, a small counter-rotating circulation is generated near the outer bank of the 90o cross-section, and reaches the maximum both in length and scale at the 135o cross-section and remains at the outlet of the curve. These phenomena can not be clearly seen in the experiment for it is difficult to decide adequate mea- suring points. The existence of the outer bank circula- tion may partly explain why the primary circulation is downscaled in the downstream part of the 45o cross-section.

2.3 Wall shear stresses

The wall shear stresses play an important role in the process of sediment transport and erosion. Distri- butions of sidewall shear stresses and bed wall shear stresses on 5 cross-sections based on the RNG predi- ction are shown in Fig.5 and Fig.6, respectively.

Fig.5 Wall shear stresses on the inner on 5 cross-sections

Fig.6 Bed wall shear stresses on 5 cross-sections

In Fig.5, it can be seen that the wall shear stre- sses reach a local minimum both at the channel bed and the water surface. In the straight reach, influenced by the vegetation, the inner bank shear stresses are smaller than the outer ones, while according to Van Balen et al.[16], in the straight reach of a curved open channel without vegetation, the distribution and the magnitude of the bank shear stresses are quite the same for the inner bank and the outer bank . In the curved reach, the outer bank shear stresses increase gradually, while the inner bank shear stresses decrease gradually and a small bounce appears at the outlet (the 180o

cross-section) of the curve, which is similar to

129

the variation trend of the stream-wise velocity distri- bution. The inner bank shear stresses reach approxi- mately 0.1 times of the outer bank ones in the down- stream part of the curve, while for the non-vegetated channel, according to Van Balen et al.[16], the inner bank shear stresses reach about 0.4 times of the outer bank ones in the downstream part of the curve. So it is concluded that the vegetation can effectively protect the river bank from scour and erosion.

In Fig.6, the bed shear stresses in the vegetation region are much smaller than those in the non-vege- tation region, since velocities in the vegetation region are very small under the retard effect of vegetation. It can be concluded that the sediment is more likely to be deposited in this region. The variation trend in this region is similar to that of the stream-wise velocities along the curve. In the outer bank, the bed shear stre- sses are greatly increased in the downstream reach due to curvature.

3. Conclusions

A RNG kε

?numerical model together with a laboratory measurement with Micro ADV are adopted to investigate the curved open channel flow through partial non-submerged rigid vegetation. The effects of vegetation and bend curvature on the flow structures and the wall shear stresses are analyzed. Main findings are as follows:

(1) The RNG kε

?model can well predict the structure of the curved open channel flow through partial non-submerged rigid vegetation.

(2) Under the combined effect of vegetation and bend curvature, the stream-wise velocities in the vege- tation region are much smaller than those in the non- vegetation region, and a slight counter-rotating circu- lation is found near the outer bank at both 90o and downstream curved cross-sections in the non-vegeta- tion region.

(3) The result about the wall shear stresses indi- cates that the vegetation can effectively protect the river bank from scour and erosion. Nevertheless, since the bed shear stresses in the vegetation region are much smaller than those in the non-vegetation region, the sediment is more likely to be deposited in the vegetation region.

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《可可.香奈儿的传奇一生》笔记

《可可.香奈儿的传奇一生》 香奈儿（1883-1971，88岁）传记——（英）贾斯迪尼.皮卡蒂著（郭昌京等译） 南宁〈广西科学技术〉2011.11（硬皮精装16开/共335页/68元） 作者简介：（英）贾斯迪尼.皮卡蒂：英国著名传记作家。本书为应香奈儿公司之邀，特地为纪念香奈儿女士诞辰128周年而写。为香奈儿公司唯一官方授权传记，纪念诞辰128周年珍藏版，近200张照片。英国国家图书馆奖提名作品。 作为享誉全球的时尚女性，20世纪最杰出的时装大师之一，小黑裙的设计师，5号香水的缔造者，简约中透出奢华的香奈儿品牌的创始人，可可.香奈儿，这位时尚领袖对世人始终像个谜。

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