Experimental study on influence of boundary on location of maximum velocity in open channel flows

Jing YAN, Hong-wu TANG*, Yang XIAO, Kai-jie LI, Zhi-Jun TIAN

1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, P. R. China

2. National Engineering Research Center of Water Resources Efficient Utilization and Engineering Safety, Nanjing 210098, P. R. China

3. College of Water Conservancy and Hydropower, Hohai University, Nanjing 210098, P. R. China

Experimental study on influence of boundary on location of maximum velocity in open channel flows

Jing YAN1,2,3, Hong-wu TANG*1,2,3, Yang XIAO1,2,3, Kai-jie LI3, Zhi-Jun TIAN1,2,3

1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, P. R. China

2. National Engineering Research Center of Water Resources Efficient Utilization and Engineering Safety, Nanjing 210098, P. R. China

3. College of Water Conservancy and Hydropower, Hohai University, Nanjing 210098, P. R. China

The velocity dip phenomenon may occur in a part of or in the whole flow field of open channel flows due to the secondary flow effect. Based on rectangular flume experiments and the laser Doppler velocimetry, the influence of the distance to the sidewall and the aspect ratio on the velocity dip is investigated. Through application of statistical methods to the experimental results, it is proposed that the flow field may be divided into two regions, the relatively strong sidewall region and the relatively weak sidewall region. In the former region, the distance to the sidewall greatly affects the location of maximum velocity, and, in the latter region, both the distance to the sidewall and the aspect ratio influence the location of the maximum velocity.

velocity dip; open channel flow; location of maximum velocity; sidewall effect; aspect ratio

1 Introduction

The velocity dip is an intrinsic feature of open channel flows, and it describes the phenomenon that the maximum streamwise velocity occurs below the flow surface. It was first identified in a flume experiment in 1883, and further experimental studies showed that the velocity dip was caused by the presence of secondary flow structures. Based on these studies, a double-spiral flow model was proposed to describe the secondary flow (Wang et al. 1988). The occurrence of the secondary flow structure was also confirmed by other research work (Nezu and Nakagawa 1993).

Based on a wide range of experimental studies, Nezu and Nakagawa (1993) demonstratedthe essential processes governing the velocity dip: low momentum fluid parcels are transported by the secondary motion from the near-bank to the center, while high momentum fluid parcels are moved by this motion from the free surface toward the bed, as shown in Fig. 1, whereBis the width of the flume,His the water depth,dis the distance of a measurement section to the sidewall,yis the vertical distance from the flume bottom,zis the distance of a measurement section to the flume centerline,Umaxis the maximum flow velocity; anddbis the maximum width of the region that is affected by the sidewall.

Fig. 1 Velocity dip in open channel flows

The essential processes of the velocity dip indicate that the influencing factors of the location of the maximum velocityy′with respect to the water depth include the sidewall roughness (the absolute sidewall effect), the distance to the sidewall (the absolute sidewall effect), the aspect ratio (the relative sidewall effect), the bed roughness, and free surface atmospheric conditions. As the Froude numberFr＜ 1.0, the impact of the free surface can be ignored (Nezu and Nakagawa 1993). The velocity dip phenomenon makes the velocity profile complex, and the log-law and parabola models cannot describe the velocity distribution effectively (Yang et al. 2004; Luo and Lü 2006; Hu et al. 2008). Yang et al. (2004) proposed a dip-modified log law that was capable of describing the velocity dip phenomenon and was applicable over the whole water depth. However, the location of the velocity dip, where the maximum velocity occurs, is still poorly understood. Wang et al. (1998, 2001) and Sun et al. (2004) proposed empirical expressions ofas the function of. Hu and Ni (1988) suggested that, for smooth open channels with the same roughness of the sidewall as that of the bed,in the centerline is the function of.

Based on flume experiments, this study investigatedfrom different distances to the sidewallat different aspect ratiosand analyzed the influence ofandon. A relatively strong sidewall region and a relatively weak sidewall region were proposed as definable regions.

2 Experimental setup and flow conditions

All experiments were conducted in a 12 m-long and 0.42 m-wide recirculating rectangularflume with glass sidewalls and a plastic bed. The slope was adjusted as necessary to obtain uniform flow conditions. The discharge was measured by an acoustic flowmeter. The water level was controlled by a tail gate weir and measured by a point gauge meter. The TSI laser Doppler velocimeter was utilized to obtain the velocity distribution. The experiments were performed in five cases:H= 6 cm, 9 cm, 12 cm, 15 cm, and 18 cm, and in each case, velocities were measured at different profiles from the sidewall. The experimental parameters are given in Table 1, where,Ais the area of the cross-section;,vis the kinematic viscosity;; andgis the gravitational acceleration.

Table 1 Experimental conditions for five cases

3 Experimental results

3.1 Velocity distribution

The mean velocity distributions for five cases are shown in Fig. 2, whereu?is the friction velocity, andis the dimensionless velocity.

Nezu and Rodi (1985) proposed that the open channel flows could be classified into two categories according to the aspect ratio:

(1) For narrow open channels where≤5, the flow withis three-dimensional over the whole flow field.

(2) For wide open channels where, in the central zone with, the sidewall effect occurs and the flow has two-dimensional flow properties; in the region, the flow is affected by the sidewall.

Fig. 2(a) shows that when=7.0, three velocity profiles forz= 0 cm, 3 cm, and 6 cm are close to each other and the velocity dip does not occur, which indicates that the region withz≤ 6 cm is not effected by the sidewall. In these cases, the range ofzmeets the central zone () proposed by Nezu and Rodi (1985). Whenz≥ 12 cm, the velocity profiles are distinguishable from each other and the values ofy′ for each profile are below the free surface. ForH=9 cm, 12 cm, 15 cm, and 18 cm, Figs. 2(b) through (e) show thatover the whole flow field, and (2) from the flume center to the sidewall,y′becomes lower. Near the sidewall, the velocity profiles are close to vertical lines, which indicates that the restriction of the sidewall to the fluid is comparable to the flow intensity,making the velocity approach a constant value.

Fig. 2 Vertical profiles of streamwise velocityUfor all cases

3.2in different cases

In this study, the roughness of the bed and sidewall was invariable and their effects were not examined. We focused on the influence of the aspect ratioand the distance from the sidewalldon. The relationship betweenis presented in Fig. 3.

Fig. 3 Relationship betweenandfor five cases

Fig. 3 shows that, for a given value of,generally decreases with. The data for Case 1 and Case 2 have relatively largerratios, and those of Case 3, Case 4, and Case 5 are close to one another. In the central zone whereis closely related with, anddecreases withfor a given value ofdecreases, this relationship becomes weaker and has even been observed to vanish.

4 Discussion on relationship betweeny′HanddHorBH

Wang et al. (1998) presented an empirical expression, provided as Eq. (1) based on the experimental data obtained in flumes withvarying over a large range, which shows thatis related to the lateral position.

The relationships betweenandin the present study as well as Eq. (1) are plotted in Fig. 4. Just as predicted, for all five cases,increases with, as shown in Fig. 4, which means that the sidewall effect decreases with the increase of. Moreover, whendecreases, the data are more concentrated and converge to Eq. (1). This characteristic is consistent with the figure plotted by Wang et al. (1998) using the data from ten different investigators.

Fig. 4 Relationship betweenandfor five cases

The concentration degreeηof all the experimental data to Eq. (1) is defined as

The functionnummeans the number of the data that meet the condition in the brackets.is the experimental datum, andis the value computed by Eq. (1).Nis the deviation limit between the experimental data and the computed values from Eq. (1). The concentration degreeηis the percentage of experimental data with their deviation to the computed results from Eq. (1) less thanNin the rangeGenerally, the deviation is considered to be small whenN= 0.05. Here, we setN= 0.03. The relationship ofη-Kis shown in Fig. 5.

Fig. 5 shows thatη＞ 50% whenK＜ 0.5, and the shorter the distance to the sidewall is, the larger the value ofηis. WhenK＞ 1.0, the value ofηis less than 40%. This indicates that in the near-wall region,fits Eq. (1) well, i.e.,is closely related with. Combing Fig. 3 with Fig. 5, we can find that, near the central zone (), the correlation betweenandweakens, while the correlation betweenandstrengthens.

Thus, according to the sidewall effect on the velocity distribution, the flow area of the open channel can be partitioned into a relatively strong sidewall region and a relatively weak sidewall region, as shown in Fig. 6.dcis the border location of the two regions, which is defined as the location wherevaries rapidly, i.e.,. In the relatively strong sidewall region where,is significantly affected by, while in a relatively weak sidewall region wheredc＜d＜db,is jointly influencedbyand.

Fig. 6 Partition of flow area for open channel according to sidewall effect on velocity distribution

5 Conclusions

The flume experiments have validated the classification of wide and narrow open channel flows presented by Nezu and Rodi (1985) and shown that the velocity dip phenomenon is characteristic of three-dimensional open channel flow area.

With the experimental data, the relationships betweenandandwere discussed. For a given value ofB H,decreases within general. In the central zone wheredecreases withfor a given value of. Asdecreases, this relationship becomes weaker. Based on the literature and analysisof the experimental results, the characteristics of a relatively strong sidewall region and a relatively weak sidewall region are proposed. In the former region,y′His greatly affected bydH, and in the latter region, bothdHandBHhave impacts ony′H.

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This work was supported by the National Natural Science Foundation of China (Grants No. 50879019, 50909036, and 50879020), the Research Fund for the Doctoral Program of Higher Education (Grants No. 200802940001 and 200802941028), the Fundamental Research Funds for the Central Universities (Grants No. 2010B02214, 2009B08014, and 2010B14214), the Natural Science Foundation of Hohai University (Grant No. 2008426411), and the Jiangsu “333” Program for High Level Talents (Grant No. 2017-B08038), and the National Undergraduate Innovation Training Plan (Grant No. G20101106).

*Corresponding author (e-mail:hwtang@hhu.edu.cn)

Received Oct. 20, 2010; accepted May 27, 2011