Two-dimensional velocity-field measurement on a sharp open-channel right-angle junction by LDV

Transcription

1 Two-dimensional velocity-field measurement on a sharp open-channel right-angle junction by LDV M. Shaban Eissa, J. Ignacio Garcia, E. Calvo, J. Antonio Garcia & L.A. Aisa Fluid Mechanics Area, Centro Politkcnico Superior, Zaragoza University, Spain. Abstract The velocity field on a sharp right-angle channel junction, with zero slope angle, has been studied. A Laser Doppler Velocirnetry system for 2-D velocity data acquisition has been used at many measurement points. The two-dimensional velocity distribution, at the junction zone, has been measured for a mesh in four horizontal planes to acheve a detailed description of the flow division mechanism at the channel junction area. For the present work, a particular flow condition has been fixed when a hydraulic jump was formed at both channel parts. The channel has been made of Perspex to allow full optical measurement techniques access. Both channel arms are identical. The cross section is 240 mm wide by 160 mm hgh. The channel allows continuous modification of the slope and a zero slope condition has been selected for this research. The dimensional description can be seen in Figure (1). Some different flow rates and depths have been measured in order to obtain a relation between the arms flow rate and the main channel Froude number. The results show the evolution of the flow ratio between both channel arms versus the Froude number value of the main waterway. This ratio is related to the Froude number, up to a certain value. 1 Introduction Channel junctions are founds in many engineering applications, with different shapes, width values, and angles of intersection, with different upstream and downstream conditions. Taylor [l] presented the relevance of channel junction

2 368 Fluid Structure Interaction 11 problem for a combining and dividing flow type, applying the principles of momentum preservation on the flow stream at frictionless equal width channels, with zero bottom slope, for 45" and 135" intersection angles. The dividing flow, as presented by Taylor, is more difficult to analyze than the combining flow because for ths type of flow it is not possible to assume that the water depth after the junction will be the same for both arms, which adds an unknown term to the momentum equations. The proposed equations were consistent with experimental measurements at low discharge and angle, but at the 135" angle showed bad agreement. Lately, Harold K. Palmer proposed that the problem of channel junctions should be better approached from the stand point of loss of energy rather than from momentum equations. Webber [2] studied with different intersection angles and curved channel sidewall, the agreement of Taylor equations and found that there was good agreement only at low discharge and small angles. Amruthur[3] considered the effect of lateral channel discharge, on the channel flow depth, for a 90" combining flow sharp-edged junction, and verified the proposed relationshp with experimental results. He found that the side channel momentum transfer is linearly proportional to the discharge in the branch channel and to the mean velocity in the main channel for critical flow at the downstream branch and values accomplishmg that 0.23 (QSide/Qtotal) 0.6 Chung Chieh Hsu [4] presented an analytical approach for solving both the upstream and downstream depth ratio, and the energy loss through junctions of equal width with subcritical flows at horizontal bed for combining flow type. A one-dimensional approach, proposed by Hager [5] to predict the upstream water level for a combining flow, is considered for transitions from subcritical to supercritical flow. It is found that the transitional flow can only exist if the lateral discharge is more than the 15% of the total discharge, and also Hager [6] analyzed theoretically and experimentally the flow in the channel junction with supercritical flow. Barkdoll [7] experimentally described the dividing flow by measuring the velocity and water surface elevation, it is found that, the main channel longitudinal velocities reduce as flow passes through the channel, no main channel recirculation at the free surface, and velocity deviation of up to 0.36 Ux/Uo and 0.7 Ux/Uo in the main and side channels respectively. A study on subcritical equal width open channel dividing flow junction by Chung Chieh Hsu [8] found that, the contraction coefficient at the maximum width contracted section is almost inversely related to the main channel upstream to downstream discharge ratio. He presented a different equation for solving main channel upstream to downstream depth ratio and the limitations of branch channel downstream to main channel upstream discharge ratio at a given main channel upstream discharge with prescribed downstream Froude Number. 2 Experimental setup The goal of this research is to obtain, with a good accuracy, the velocity pattern at the junction zone for a dividing flow, and study the relation between Froude

3 Fluid Structure Interaction I1 369 number and lateral channel to total discharge ratio for a fixed aspect ratio and channels with the same downstream conditions. The experiments were performed in a close loop channel. Fig (l), show a schematic layout of the experimental channel and the measurement locations. The main and lateral channels are 6. m and 1.6 m long respectively, the junction was located at the middle of the main channel, and has a sharp angled edge with 90" of interaction angle. Both channels are 240 mm width and 160 mm height, and made fi-om Perspex, to enable the measurement by LDV, and reduce the wall friction effects. Both channels are in free discharge, slide weirs at the end of each arms are use to control the initial channels downstream conditions. LDV have been used to measure 2D velocity distributions at the junction, with sample rates fi-om 40 to 120 Hz, about 6000 samples at each measured point have been acquired. The grid of measurement points is shown in fig. (1). 2D velocities had been measured at each point of the grid points, at depth (Z= 5mm) from the channel bottom, while at Z= lomm, 17mm, and 20mm, the velocities had measured at each grid point at the grid points in the main channel only. A flow condition when observed jumps in both channel arms downstream the junction has been fixed for velocities measurements. In which main channel Froude number was 0.754, and a discharge ratio (QL/Q3 was 0.23, S= 0.179, corresponds to this condition. The occurrence of the jump in both channels is very sensitive to the side channel downstream condition; the jump at the lateral channel disappears for a small increasing of its water depth. The measurements of water head have been made using custom made devices. Its measure the electrical resistance between two vertical parallel wires of lmm diameter and have been calibrated to measure water level with a sample rate of about 3KHz. The flow discharges have been measured by mean of the time to fill a fixed known volume. Head Tmk 1.6 tn Sink Tank l Figure (1) Channel schematic layout and grid point measurements

4 370 Fluid Structure Interaction 11 3 Discussion of results Starting from the velocity profile at many location fig. (2), it could be see that at x=o until x=230 mm, a depression for the point of maximum velocity on the horizontal velocity profile at the main channel was predicted. Research made by Baarkdoll [7] found a depression point at the position of maximum velocity at the vertical velocity profile for a channel of aspect ratio of 2. At planes of measurement with vertical coordinate values of Z= lomm and 17mm from the channel bottom, the velocity profile at each cross section, was nearly the same over the junction in the main channel, while for Z= 5mm (near the channel bottom) and Z=20mm (near the channel free surface), it can be say that, the profile at the half channel opposite to the junction side, is the same for each cross section. It could be noticed that the velocity at the main channel increased through the junction, until the flow reaches the zone of stagnation at the intersection between the main and lateral channel sidewall or the jump of the main channel. As shown in fig. (4), the plot of the difference of absolute velocity at each point (X) and the initial absolute velocity (at x=o) normalized by the initial absolute velocity for Z=5mm, and at four distances of y = 10, 60, 120, and 230 mm from the junction side. It could be observed that at y= 120, and 230 the velocity increases linearly, about the 32% of its initial velocity at the starting section, until X= 260 mm, and decreases after that. For y= lomm, the velocity increases quickly a 35% from its initial velocity at X= 140 mm and decreases rapidly after that by effect of the stagnation zone, reducing the 70% of its initial value at x=280 mm. For the lateral channel, as shown in fig (3), it could be noted that, zones of contracted flow and recirculation flow are generated at the branch channel. The maximum contraction happened a distance of about 0.5 of the channel width, and have a width about half the channel width. As plotted in fig. (5), the ratio between lateral channel discharge and the main channel upstream discharge could be correlate with the main channel upstream Froude number. For the present aspect ratios of S = ,0.158,0.167, and 0.179; there was a lineal trend, until Froude number reaches a value of about On the other hand the discharge ratio value was different for each aspect ratio: 0.3 for S= and 0.35 at S= , which indicates that the discharge ratio at the point of maximum Froude number decreases when increasing the aspect ratio. The energy head upstream and downstream at the main channel H,,= h, +~,2/2 have been measured for two sections 1 m away from the junction at each side. The assumption of preservation of energy head, have been proposed by Chung- Chieh Hsu [8] for supercritical flow, to predict an analytical solution. Plots showing the acquired data are presented at fig. (6). The confidence interval was about 0.97 %, for all points that had been measured.

5 Fluid Structure Interaction I1 371 Channel width mnfor X= 0 m Channel width mm for^ 30 mm Channel width m for X=80 m Channel W idth mnfor X= 140 mn Channel width mnfor X=200 mn Channel width mnfor X=230 mn Channel width mnfor X= 250 mn Channel width mnfor X=270 mn Figure (2) Axial velocity distributions at the Junction for the main channel

6 372 Fluid Structure Interaction I1 Figure (3) Velocity vector distribution through the Junction and lateral channel Junction hnath at the main channel Figure (4) Main channel dimensionless velocity evolution at the Junction for Z=Smm

7 Fluid Structure Interaction Froude No Figure (5) Discharge Ratio vs. main channel upstream Froude number Ho upstream Figure (6) Upstream vs. Downstream total Energy 4 Conclusions Accurate 2D velocity measurements at a the channel junction of 90" for a specific flow condition and at four horizontal planes, which provide benchmark

8 374 Fluid Structure Interaction 11 experimental data intended for the validation of numerical studies, have been made. The assumption of equal total head upstream and down stream at the main channel gives values differing less that 3 % with the corresponding measured values. The lateral channel flow to total flow ratio (QL/Qt) had a lineal trend with the main channel upstream Froude number until a Froude number value of The flow ratio at the point of maximum Froude number increases by decreasing the aspect ratio for thls range of measurements. References [l] Edward H. Taylor, Flow Characteristics at Rectangular open Channel Junction. Trans. ASCI 109,PP ,1944. [2] Webber N.B., &Greated C. A., An Investigation of Flow Behavior at the Junction of rectangular Channels. Proc. ICE, 34, pp , [3] Arnruthur S. Ramamurthy, Luis B. Carballada, & Duc Mlnh Tran, Combining Open Channel Flow At Right Angled Junctions. j. Of Hydraulic Engineering, 114(12), pp , [4] Chung Chieh Hsu, Feng Shuai Wu, & Wen Jung Lee, Flow at 900 Equal Width Open Channel Junction. j. Of Hydraulic Engineering, 124(2), pp ,1998. [5] Willi H. Hage, Transitional Flow In channel Junctions, j. of Hydraulic Engineering, 115(2), pp , [6] Willi H. Hage, Supercritical Flow In channel Junctions. j. Of Hydraulic Engineering, 115(5), pp , [7] Brian D. Barkdoll, Brad L. Hagen, & A. Jacob Odgaard, Experimental Comparison of Dividing Open Channel With Duct Flow in T- Junction. j. Of Hydraulic Engineering, 124(1), pp ,1998. [S] Chung Chieh Hsu, Chii Jau Tang, Wen Jung Lee, & Mon Yi Shieh, Subcritical 900 Equal Width Open Channel Dividing Flow. j. Of Hydraulic Engineering, 128(7), pp ,2002.