Available online at www.sciencedirect.com ScienceDirect Aquatic Procedia 4 (2015) 805 – 811 INTERNATIONAL CONFERENCE ON WATER RESOURCES, COASTAL AND OCEAN ENGINEERING (ICWRCOE 2015) Distribution of Depth-Averaged Velocity along a Highly Sinuous Channel Arpan Pradhan, Kishanjit K. Khatua, Saine S. Dash* Civil Engineering Dept., N.I.T Rourkela, Rourkela, Sundergardh, Odisha, India-769008 Abstract Precise measurement of depth-averaged velocity is essential for governing the total discharge in an open channel. In this paper, an experimental investigation has been carried out to compute depth-averaged velocity at different cross-sections along a meandering path. The meander path is divided into 13 sections, ranging from one bend apex to the next bend apex. The meander path changes its course at the cross-over section. Bend apex is the section at which maximum curvature of the meander path occurs while cross-over represents the section at which the sinuous channel straightens and changes course. Depth-averaged velocity is considered to be the average velocity at any vertical section of a channel cross-section. The occurrence of this velocity is generally trusted to be found at 0.4H from the bed of the channel. H is the flow depth of water at the particular section. In this paper the depth averaged velocity is explored at different sections throughout the meander path. The study also assists in understanding the movement of localized maximum averaged velocity while traversing along a meander path. These investigations aid in researches in the field of sediment transport and depositional patterns, bank protection, navigation, etc. © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license © 2015 The Authors. Published by Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of organizing committee of ICWRCOE 2015. Peer-review under responsibility of organizing committee of ICWRCOE 2015 Keywords: depth-averaged velocity; bend apex; meandering channel; cross-over. * Corresponding author. Tel.: 0661-246-2307; fax: 0661-247-2926. E-mail address: kkkhatua@nitrkl.ac.in 2214-241X © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of organizing committee of ICWRCOE 2015 doi:10.1016/j.aqpro.2015.02.100 806 Arpan Pradhan et al. / Aquatic Procedia 4 (2015) 805 – 811 1. Introduction Flow in meandering channel is quite ambiguous for natural flow systems such as rivers. Rivers generally follow this pattern for minimization of energy loss. Despite substantial research on various aspects of velocity distribution in curved meandering rivers, no systematic effort has been made to analyze the variation of velocity profile along a meander path. Flow characteristics in channel bends are much more complicated than those in straight channels. Some researchers have carried out extensive studies on flow characteristics in channels with different bend angels by using the experimental and numerical models. Shino (1999) developed turbulence models and studied the behaviour of secondary flows and centrifugal forces for straight and meandering channels. Blanckaert and Graf (2001) investigated channel bed level changes at a 120º sharp bend with a movable bed using an experimental setup. They reported a minor secondary rotating flow cell at the outer wall of the bend. As numerical hydraulic models can significantly reduce costs associated with the experimental models, their use has been rapidly expanded in recent decades. Booij (2003) and VanBalen et al. (2009) modelled the flow pattern at a mildly-curved 180º bend and assessed the secondary flow structure using large eddy simulation (LES). Zhou et al. (2009) using the two-dimensional depth-averaged model, simulated the flow pattern in 180° sharp bend and 270° mild bend, with and without consideration of the secondary flow and claimed that, given the effect of the secondary flow, the simulation results in the first state has a better agreement with the experimental results. Khatua et al. (2012) studied evaluation of roughness coefficients in meandering channels. Dash and Khatua (2013) formulated the roughness coefficient for meandering channels. Naji Abhari et al. (2010) studied the flow pattern in a 90° mild bend numerically and experimentally. In this study, they focused on the velocity distributions, the streamlines at different water levels and the distribution of shear stresses and they did not study water surface profiles. The results showed that the flow pattern in a channel bend is heavily influenced by the secondary flow and centrifugal force. Bonakdari et al. (2011) investigated the flow pattern at a 90º mild bend using numerical model, artificial neural network and genetic algorithm. In this paper, the depth-averaged profile is studied throughout a meander path of a highly sinuous meandering channel of sinuosity 4.11. The depth-averaged velocity data are studied to find the flow pattern and movement of the localized maximum averaged velocity at each section along the meander path. The study is carried out on a 120° meandering path from the cross-over to the corresponding bend apex. 2. Methodology 2.1. Experimental Setup For carrying out research in meandering channels, experimental setup was built in Fluid Mechanics and Hydraulics Laboratory of NIT Rourkela. A meandering channel is built inside a steel tilting flume of around 15m length as shown in Fig. 1. The bed and wall of channel was made with Perspex sheet (6 to 10 mm thick), having Manning’s n value=0.01. The detailed geometric parameters of the meandering channel are illustrated in the following tabulation. Arpan Pradhan et al. / Aquatic Procedia 4 (2015) 805 – 811 807 Fig. 1. Photographs of the Experimental Channel Table 1. The details of Geometrical Parameters of the Experimental Meandering Channel. Sl. No Parameters Description 1 Type of Channel Simple Meandering 2 Flume Dimension 4.0m×0.5m×15m Long 3 Meandering Channel Geometry Trapezoidal with side slopes 1:1 4 Type of Bed Surface Rigid and Smooth Bed 5 Section of Channel 0.33m at Bottom and 0.46 m at Top 6 Bank Full Depth 0.065m 7 Bed Slope of the Channel 0.00040146 8 Sinuosity of the Channel 4.11 9 Amplitude of the Meandering Channel 1.555 m 10 Wave length of the Meandering Channel 2.162 m 2.2. Position of Measurement All the measurements are observed from the second bend apex to the next corresponding bend apex passing through the cross-over of the experimental meandering channel from the upstream end. Observations are recorded under steady and uniform conditions. A moving bridge arrangement is provided along the width of the channel of around 1.2m width by 4m length across the channel. The measuring instruments such as point gauges and Pitot tubes are arranged on the bridge such that each section along the meander path is accessible for measurements. A section at crossover perpendicular to both the inner and outer curves of the meandering channel is drawn and extended unto the extended bend apex line, as shown in Fig. 2. An angle of 120⁰ is formed for both the curves. This is the crossover angle or the arc angle. The curves are divided into 6 equal sections of 20⁰ each to the centreline of the meandering channel. Channel sections are drawn along the width i.e. perpendicular lines drawn to both the curves from these points. Sections A and M are the bend apex sections while section G is the cross-over section. The sections A through M are considered for measurement of the boundary shear stress. A constant discharge of 5.2 x 10-3 m3/s is maintained while taking the readings for the entire meandering path with the help of a rectangular notch incorporated at the start of the flume. Series of Pitot-tubes with moving bridge arrangement are made to measure the pressure difference at different grid points of the flow passage of the channel as shown in Fig. 3. The Pitot tube is used as Preston tube to find the shear stress at the channel bed and side slopes. The measurements are taken at different reaches along the meander path for every section. The lateral spacing of the grid points has been taken as 4cm on either side of the centreline. The measurements are taken at the bed of the channel and the side slopes at by 0.4H, 0.6H, and 0.8H from the bed. H here is the average depth of water at the every corresponding section along the meander path. Depth-averaged velocity is considered to be the average velocity at any vertical section of a channel cross-section. The occurrence of this velocity is generally trusted to be 808 Arpan Pradhan et al. / Aquatic Procedia 4 (2015) 805 – 811 found at 0.4H from the bed of the channel. The depth-averaged velocity is hence considered at 0.4H above the bed from the above experimental investigation. Fig. 2. Plan Geometry of the Meandering Path. Fig. 3. Grid Arrangement of Points for Shear Stress Measurement across the Channel Section. 3. Discussion and Result 3.1. Depth-Averaged Velocity The following Fig. 4.1. to Fig. 4.13. represent the horizontal velocity profile at 0.4H from the bed of the channel, where H is the average flow depth of water at the corresponding section. The graphs represent all the sections along meandering path. The depth-averaged velocity is usually found to be higher around the centre of the channel section in case of a simple straight channel, but in the present experimental observation higher depth-averaged velocity is found closer towards the inner wall of the simple meandering channel. The depth-averaged velocity remains higher towards the right of the channel section which is the inner wall in the initial sections of the meander path. At the cross-over section the higher depth-averaged velocity moves towards the centre of the channel, as observation usually seen in straight channels. This observation depicts that a meandering channel behaves as a straight channel at around the cross-over section. At sections subsequent to the cross-over, the higher depth-averaged velocity moves towards the left of the channel section, this is now the inner wall for the channel section. Fig. 5. represents the contour plot of depth-averaged velocity distribution of the meander path. Here it is observed that the maximum depth-averaged velocity occurs somewhere at sections C, D, J and K. The velocity is higher at these intermediate sections due to the curvature of the meander path moving towards the cross-over. Arpan Pradhan et al. / Aquatic Procedia 4 (2015) 805 – 811 Fig. 4.1. Fig. 4.7. Fig. 4.2. Fig. 4.8. Fig. 4.3. Fig. 4.9. Fig. 4.4. Fig. 4.10. Fig. 4.5. Fig. 4.11. 809 810 Arpan Pradhan et al. / Aquatic Procedia 4 (2015) 805 – 811 Fig. 4.7. Fig. 4.12. Fig. 4.13. Fig. 4.1. to Fig. 4.13. Horizontal Velocity Profile at 0.4H from the bed of the Channel Section along the Meander Path Fig. 5. Horizontal Velocity Profile at 0.4H from the bed of the Channel Section along the Meander Path 3.2. Occurrence of Maximum Depth-Averaged Velocity The readings of depth averaged velocity at different vertical sections of a cross-section are taken. The process is repeated for thirteen cross-sections along the meander path. At every cross-section the occurrence of maximum depth averaged velocity along the meander path are found and plotted. Fig. 6. demonstrates the movement of local maximum depth averaged velocity at every section along the meander path of the meandering channel. It is observed from the figure that the maximum depth-average velocity remains at the inner wall throughout the meander path. The velocity is also found to remain closer towards the inner wall at sections nearer to the cross-over region. The maximum depth averaged velocity moves towards the centre of the cross-over section. There is a direct movement of local maximum depth averaged velocity from the inner wall of the section F towards inner wall of section H passing through the centre of the cross-over section G. Arpan Pradhan et al. / Aquatic Procedia 4 (2015) 805 – 811 811 Fig. 6. Occurrence of Maximum Depth Averaged Velocity along the Meander Path 4. Conclusions The following conclusions can be represented in this 1. The results of Horizontal velocity profile shows higher velocity results at the inner wall of the channel section than outer wall and gradually decreases towards the outer wall. 2. Horizontal velocity profile of a highly sinuous meandering channel remains higher at the inner wall of the channel section and decreases towards the outer wall. 3. At the bed of the cross-over section, the local maximum velocity is found to move towards the centre of the section, with gradual variations towards the inner and outer walls. 4. Maximum longitudinal velocity from the inner bank of the bend apex sections are found to move toward the central region sections. The maximum local velocity initially moves close to the surface, which later moves towards the bed. 5. Sections C and K (intermediate sections) have the highest maximum velocity throughout the meander path as seen in the longitudinal velocity contour plots for the entire path. Such observations are due to the curvature of the meander path moving towards the cross-over. 6. From the occurrence of maximum depth averaged velocity, It is observed, that the maximum velocity always remains towards the inner wall and moves even closer to the inner wall while approaching the crossover. 7. The maximum depth averaged velocity is found to move through the center of the cross-over section from the inner wall of one curvature to the inner wall of the other inverse curvature of the meandering channel. Acknowledgment The authors wish to acknowledge thankfully the support received by the fourth author from DST India, under grant no. SR/S3/MERC/066/2008 for conducting experimental research works. References Abhari, M.N., Ghodsian, M., Vaghefi, M., Panahpur, N., 2010. Experimental and numerical simulation of flow in a 90 bend. Flow Measurement and Instrumentation, 21(3), 292-298. Blanckaert, K., Graf, W.H., 2001. Mean flow and turbulence in open-channel bend. 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