1. INTRODUCTION The junctio

1. INTRODUCTION

The junction of two open channels is a common occurrence in many hydraulic structures ranging from wastewater treatment facilities to ?sh passage conveyance structures. Conduit outlets into open channels are common hydraulic structures. They are necessarily encountered at the end of urban sewage or agricultural subsurface drainage networks, where they release water. Their construction generally aims at a maximum efficiency discharge and a protection of the channel bottom and banks against erosion processes. Their behavior and design have been considered of interest concerning channel bed erosion that could result from the flow convergence or jet impingement. There are numerous factors that in?uence ?ow characteristics at the junction of two open channels. One set of variables can be described as geometry variables, such as the size, shape, slope, and angle between the combining channels. Many combinations of these four variables are possible. A second set are ?ow variables, such as the Froude number in the downstream ?ow, the channel roughness, the ratio of discharge between the two tributary channels, and the variation of ?uid properties.
Concerning discharge efficiency, pipe outlets have been less thoroughly studied in terms of purely hydraulic processes, or have generally been considered as free ended in several detailed studies. The hydraulic processes involved in these structures are similar to those of a junction. It depends on flow coming from upstream (discharge from subsurface network and concomitant discharge from open channel) and on possible tail water effects from downstream. Tail water effects from downstream may occur if flood control structures store water by means of a rise of the free-surface level. Field experiments by Nedelec (2005) have shown that such a practice in an arterial drainage ditch could dramatically change subsurface drainage flow hydrographs. Observations show that this system can behave either as a weir, a classical junction, or a deflected jet. In all cases, water levels are changed by the flow junction. But the most specific consequence, in the pipe, is a transition of flow from free surface to pressurized, controlled by the combination of several geometric parameters and experimental variables.
In this paper a comparison of flow patterns at the junction of two channels and at the junction of a channel and pipe is done. The experimental study done by Nedelac and Gay (2008) of a junction between a closed conduit and an open channel and an experimental study by Weber et al. (2001) of a junction of two channels are reviewed here.

2. CHANNEL FLOW AT JUNCTIONS

The distinctive characteristics of a junction of closed conduit and channel as well as that of a sharp-edged, open-channel junction ?ow, as illustrated in Figs.1 and 2 respectively, are a zone of separation immediately downstream of the junction branch channel, a contracted ?ow region in the main channel due to the separation zone, a stagnation point immediately upstream of the junction, a shear plane developed between the two combining ?ows, and an increase in depth from the downstream channel to the upstream contributing channels. The zone of separation results due to the momentum of the lateral branch ?ow causing the main ?ow to detach at the downstream corner of the junction

Fig.1 Junction between a pipe and an open channel

(Source: Webber et al; 2001)
Fig.2 Flow Characteristics in Open-Channel Junction

3. EXPERIMENTAL STUDY ON A JUNCTION BETWEEN CLOSED CONDUIT AND OPEN CHANNEL
(Nedelac and Gay. 2008)

In order to study the flow patterns at a junction between a pipe and an open channel an experimental study published by Nedelac and Gay (2008) is reviewed. The experimental set up used by them and the important results are discussed in the following sections.

3.1 EXPERIMENTAL SETUP

The experimental apparatus was built at the Cemagref Research Center in Antony, near Paris. Fig. 3 shows a simplified view of the model. A detailed description of the experiment, and the instrument used is as follows:

(Source: Nedelac et al; 2008)
Fig. 3. Experimental setup overview

The main part of the model was a rectangular glass flume, 6 m long, 0.3 m wide, and 0.3 m in depth. Its downstream end was closed by a gate sliding vertically, acting as a horizontally crested weir. The channel bed slope was adjustable and the bottom wall was covered with rough PVC lining in order to increase the friction slope. One of the flume’s sidewalls was equipped with a 0.2 m wide opening in its middle, so that a rectangular plate with a circular hole could be inserted, and ensure wall continuation. This plate connected a lateral circular pipe positioned at a right angle. The pipe connection to the channel allowed small vertical angular deviations. It was designed so that the pipe slope could be adjusted. The pipe length was 1.20 m and its interior diameter was 0.08 m. The pipe invert was concordant with the channel bed. After the setup of the installation, the channel slope was initially measured as 0.324%, and the pipe slope as 0.23%. They were kept unchanged because of their being typical of values in actual subsurface drainage systems.
Supply water came into the channel and pipe from a constant head tank through circular PVC conduits. Both input flow rates could be independently controlled by butterfly gate valves.
Both approach flows were improved using transition structures within stilling zones, 0.8 m long for the channel, and 0.2 m long for the pipe. The channel’s input flow fell from the pipe through a vertical perforated cylinder before being guided and stilled by plastic grids. The pipe’s flow was introduced upstream using a T-junction and guided by a deflecting grid followed by a bundle of 0.2 m long and 0.025 m diameter parallel perforated tubes. The length left for flow development before the test section was equivalent to 12 diameters for the pipe. It was at least 25 times the hydraulic radius of the channel.
Both discharge flow rates were measured by electromagnetic flow meters with an accuracy of 0.66L/s for the maximum input of 12 L/s. Flow depths were measured in the channel by a point gauge and a spanning bridge. Flow depths in the pipe were estimated from pressure values, when a free-surface could be observed. Twenty capillaries connected to a single pressure transducer were used to measure the static pressure at five cross sections. Each cross section comprised the four ends of one vertical and one horizontal diameter.

3.2 Experimental Variables and Test Procedures

The results presented here concern steady-state flows, in response to experimental variables. The limits were chosen to encompass real observations made in an arterial drainage ditch and discharging drainage collector drain, by an application of Froude similitude. The Reynolds similitude could not be simultaneously satisfied because of a limited space for the apparatus. The Froude similitude was preferred because of its applicability to open channel flow. Its application at the scale of 1:6 resulted in prototype values of maximum flow rates up to 1,060 L/s for a 1.8 m wide channel, and 280 L/s for a 0.48 m diameter pipe. These limits, combined with a downstream gate level ranging from 0 to a little more than one pipe diameter, allowed the observation of various flow patterns and of the transitions between them. Two realistic combinations between upstream flow rates were chosen:
(1) Sets of upstream flow linked by a given constant sum downstream
(2) Sets of upstream flow rates linked by a given constant ratio.
The first kind of combination simulated the influence on junction behavior of one given downstream control structure or channel flow capacity. The sum of the two flow rates together with one gate level became a single and invariable downstream constraint condition.
The second kind simulated the junction’s typical behavior in case of concomitant floods coming from similar catchments. In this case, at any time during one flood event, both upstream flows (yet considered here as constant) were set proportional to a common specific flow rate. The ratio between flow rates represented the ratio between watershed areas. Because of a head loss due to the flow guides at the pipe’s inlet, an undesirable pressurized flow could be introduced upstream. The installation of a small air vent upstream of the conduit could change the depth-discharge curve beyond a given nondimensional discharge. In order to check for possible air presence influence on flow patterns, a tiny hole (0.005 m in diameter) was drilled through the pipe upstream wall 1 m away from the junction point. Along with visual flow observations, quantitative data sets for each test comprise results from variables listed in Table 1.

Table 1 Model variables
Variable name Definition Range of values Q Channel flow rate 0-12 L/s q Pipe flow rate 0-3.3 L/s q* Nondimensional pipe flow rate 0-0.58 Hd Downstream gate level above channel bottom 0-85m h / d nondimensional surface elevation above channel bottom 0-1.5 p / ƒgd Nondimensional wall static pressure in pipe 0-1.4
The open channel junction water level above the channel bottom was measured at two cross-sections: two channel widths upstream (hu) and three channel widths downstream (hd). A few complementary sets of water levels above the channel bottom were collected on a regular grid of 5 cm between these two cross sections.

3.3 RESULTS AND DISCUSSIONS

3.3.1 FLOW PATTERNS

The flow at channel or pipe junctions could be separated into several regions and show a strong dissymmetry. Alterations of the free-surface elevation and of the pipe wall pressure could be linked to these flow regions and to the flow dissymmetry.
A typical example of channel free-surface shape is presented in Fig. 4, in the form of elevation profiles. Non dimensional free surface elevation above the channel bottom h/d (h=free surface elevation above channel bottom or pipe invert, d=pipe diameter) is shown at locations regularly spaced along the channel axis, for a channel flow rate Q of 0.006 m3 s-1 and a pipe flow rate q of 0.002 m3 s-1 . Two cases are shown, corresponding to a downstream gate level above the channel bottom Hd of (a) 0.025 m (in this case the pipe flows with a free surface along its hole length) and (b) 0.030 m (in this case the pipe flows entirely pressurized).
Dotted lines are drawn to indicate the channel bed slope, so that they would represent a theoretical horizontal surface. These profiles show the final decrease in free-surface elevation between upstream and downstream, observed similarly in other kinds of junctions. An additional elevation decrease was also apparent in front of the pipe outlet, and could be linked to the separation zone and the contracted cross section previously known in right-angled channel junctions. Fig. 4(b) shows that the flow may be entirely pressurized in the pipe despite a free surface in the channel lower than the pipe soffit at the outlet. In this particular case the pipe flow pattern is directly controlled by the channel state and cannot be deducted from the pipe flow rate alone, or from an intuitive hypothesis on free-surface continuity between upstream branches.

Fig.4. Longitudinal profiles of nondimensional free-surface elevation above the channel bottom, along three transversal abscissas Y. (o) Close to the bank connected to the pipe. (x) Along channel center line. (+) Close to the bank opposite to pipe outlet, Q=6 L/s, q=2 L/s: (a) Hd =0.025 m; (b) Hd =0.030 m. The dashed lines denote profiles corresponding to a theoretical horizontal free surface. The pipe outlet is represented by an ellipse.
The free surface at the very front of the pipe outlet may fall almost against the channel bottom, in response to a completely lowered downstream gate.
Pipe wall pressure longitudinal profiles showed flow dissymmetry, which increased as water approached the pipe outlet. Fig. 4 shows an example of such profiles. An inclined dotted line was drawn to locate the conduit top. The observed hydraulic grade line tended to become almost horizontal toward the upstream end of the pipe, until the initiation of flow development introduced a slight dissymmetry.
Three pressure measurement points on a cross section were not sufficient to precisely convert pressure differences into forces deflecting the pipe flow toward the channel axis, because the pressure distribution may have been somewhat more complex than in a rectangular lateral channel or conduit (Ramamurthy and Zhu 1997). These observations nevertheless gave an estimation of the upstream scope of the influence of the channel entrance, set to a maximum length of two pipe diameters.
Fig.5. Longitudinal profiles of nondimensional wall static pressure in pipe, along three transversal abscissas X. (o) At pipe axis level, on the channel downstream side. (x) At pipe invert level. (+) At pipe axis level on the channel upstream side of the pipe. Q=6 L/s, q=2 L/s, Hd =0.030 m; The dashed line is the pressurized flow limit.

Figures 6 (a and d), and Fig. 7(a) show ordinary free-surface junctions. Fig. 6(a) is listed separately because the problem depends on only two variables at its boundaries. Figs. 6(b) and 7(b) show a pipe outlet entirely submerged, making the junction similar to a deflected jet. Fig. 7(c) shows a free surface at the end of a pressurized pipe, similar to a free fall at pipe outlet.

Fig.6. Channel flow patterns (the channel free surface is represented in dark gray, the pipe free surface is represented when necessary in light gray). (a)No upstream channel flow (b) drowned flow, similar to a jet deflection; (c) weir effect; (d) free-surface; and (e) partial lateral circular weir.

Two additional channel flow patterns are considered here as interesting, because their characteristics are specifically related to the present system. The flow pattern defined as “weir effect” [Fig. 6(c)] refers to pressurized flow in pipe, which leads channel water to flow above pipe water but fall lower than the level of the pipe crown, reproducing the fall of water above a physical weir. The flow pattern defined as “partial lateral circular weir” [Fig. 6(e)] refers to a strongly curved free surface, which falls from one half of the pipe edge as if it fell from a circular weir. In this particular case, the free-surface locally faces downward [location is shown by an arrow in Fig. 6(e)].
The last two pipe flow patterns [Figs. 7(d and e)] are introduced because of a possibly inclined pipe, in which the hydraulic grade line may be less inclined than the pipe, or parallel to it in the last case.
This last case is generally a transitional and quite unstable state, though the air pockets may remain trapped at stationary locations. The cavities in Figs. 7(d and e) may
Fig.7. Pipe flow patterns (the pipe free surface is represented when necessary in dark gray, the channel free surface is represented in light gray). (a) Free-surface (b) pressurized (c)downstream cavity flow (d) upstream cavity flow and (e) transitional.

result from trapped air after an increase in water level in the channel, or equilibrium with atmospheric pressure through the upstream air vent in the pipe. In test conditions trapped air slowly bubbles downstream until a stationary state is reached.

3.3.2 INFLUENCE OF JUNCTION ON WATER LEVEL

A drop of channel free-surface level occurred between the upstream and downstream sections. This drop was measured in various sets of interdependent experimental variables. The flow patterns observed here were those found in Fig. 6(a, d, and e) for low downstream water levels, and Fig. 6(b and c) for high downstream water levels.
Fig.8 compares the non dimensional free-surface level above the channel bottom between the upstream and downstream sections, for a given total flow rate for each data series. The remaining free variable is the downstream gate level above the channel bottom. The Froude number here ranged from 0.12 to 0.75. The lowest downstream water levels were limited because a critical section was formed when the downstream gate level decreased sufficiently.
Fig.8. Nondimensional free-surface level above channel bottom: Upstream level as a function of downstream level, for various Hd (steps of 0.005 m) and flow rates with q+Q=8L/s [(q+Q)/ (gd5)1/2 =1.41] (?) q*=0; (*) q*=0.176; (+) q*=0.353; (x) q*=0.529. The dashed line denotes the horizontal free surface.
The water level difference tended to align to that of a nearly horizontal free surface at high gate levels. The difference increased as the gate was lowered, and at an increased rate as the pipe’s flow rate was higher. Thus the influence of a conduit outlet may not be negligible in case of a high discharge into a channel with a high discharge capacity. Conversely, a channel management policy of keeping water at high levels will reduce the pipe discharge influence on upstream channel levels compared to an improvement of channel discharge capacity.
3.3.3 INFLUENCE OF JUNCTION ON ENERGY LOSS

The energy loss resulting from the junction of two flows of the same kind was thoroughly studied and modeled and considering that the portions of the channel free surface in both the upstream and downstream directions were nearly horizontal (as in Fig. 4), we may define the energy loss coefficient Ke as

= Ke —————————– (1)

where A and a = correction coefficients for energy, considered from hereon as equal to 1; Z= vertical free-surface or piezometric level;
Zu in the channel and in the pipe are supposed to be nearly equal, for open channels;
?= angular variable representative of free-surface elevation above the pipe invert, defined as the angle between a radius extending from the pipe’s bottom to the central axis, and a radius extending from the central axis to the point of contact between the free
surface and pipe:

?= ?- 2 Arccos (v h/d) ——————— (2)

Serre et al. (1997) introduced 2 coefficients defined by
——- (3)
Neglecting the friction energy loss in Eq (3), the combination of Eqs. (1) and (3) yields

Ke= ———– (4)
Fig.9 Comparison of energy loss coefficients Ke, computed from experimental data versus those computed from Serre. formulas. (x) Computation with observed upstream and downstream water levels. (?) Computation considering only downstream (Zu=Zd) water level. The dashed line is the line of perfect agreement

The values of Ke calculated from experimental data and those computed from Serre et al. formulas are shown in fig 9.
Considering that friction energy loss was neglected in the application of Eq. (3), the comparison shows a rather good correspondence between a model developed for circular conduit junction and the system studied here.

4. EXPERIMENTAL STUDY ON JUNCTION BETWEEN
TWO OPEN CHANELS
[WEBER et al. (2001)]

4.1 EXPERIMENTAL DETAILS

The experiments were performed in a 900 combining flow flume Head tanks on both the main and branch channels supplied the discharge. To ensure properly developed flow entering into the junction branches, perforated plates and 100 mm thick honeycomb were placed at the main and branch channel inlets. Volumetric measurements were made with manometer readings. The tailwater depth in the downstream channel was controlled by an adjustable tailgate.
The coordinate system defined for this testing had the positive x-axis oriented in the upstream direction of the main channel. The positive y-direction points to the main channel wall opposite of the channel junction. Thus the positive z-axis is upward in the vertical direction. The origin from which all points are measured was the bed at the upstream corner of the channel junction. All distances were normalized by the channel width. All test sections in this study were denoted by the distance in channel widths measured positive in the x-direction for upstream main channel measurements, negative in the x-direction for combined tailwater flow measurements, or negative in the y-direction for measurements in the branch channel.

4.2 RESULS AND DISCUSSIONS

4.2.1 VELOCITY PATTERN

The longitudinal velocity u* is the dimensionless velocity in the x-axis direction. Plate 1 displays u*-velocity contours near the water surface for q* = 0.250 {q* or ?ow ratio is de?ned as the ratio of the upstream main channel ?ow (Qm) to the total ?ow (Qt)}. The separation zone can be seen as the area of low velocity along the junction adjacent wall immediately downstream of the channel junction. Recirculation inside the separation zone is shown as the region of positive velocity, indicating upstream motion. The largest velocities occur just downstream of the junction, in the main channel ?ow region contracted by the zone of separation.
All longitudinal velocity contours near the bed are distinctly different from the near surface velocity patterns. The separation zone is larger near the surface (both in length and width) its size varies from top to bottom because of the angle of entrance of the branch channel ?ow. There is also more recirculation inside the separation zone near the surface. In the constricted reach immediately downstream of the junction, higher velocities occur near the bed. This effect is also attributed to the entrance angle of the lateral ?ow. Once the contracted region is passed, velocities readjust to the typical open- channel condition of higher velocities near the surface.
.

(Source: Weber et al; 2001)
Fig.10. Schematic of Flow Structure
As more discharge enters from the main channel the separation zone decreases in width and length. This can be justi?ed by considering the limiting condition of all ?ow entering the junction from the main channel which would likely exhibit no separation at the downstream corner of the junction. Lower velocities in the junction region result from the reduced contraction of the main channel ?ow due to a smaller zone of separation

Fig.11 Plate1. Surface Velocity Pattern

Fig. 12 Plate2. Cross-Sectional Velocity Pattern.
Plate 2(a) displays a cross-sectional view of the u*-velocity downstream of the junction for q* = 0.250. The separation zone is clearly depicted along the junction adjacent wall, y*= 0.00. It is apparent that the constricted ?ow has been de?ected to the outer half of the main channel.
Plate 2(b) contrasts the ?ow downstream of the channel junction with q* = 0.750. The separation zone, at the same cross section, immediately downstream of the channel junction, extends much further into the main channel for q* = 0.250 [Plate 2(a)] than for q* = 0.750 [Plate 2(b)].
This is caused by the decreased momentum of lateral channel ?ow as q* increases. The higher momentum for the low q* condition allows the branch channel ?ow to extend further into the main channel before being de?ected downstream, therefore causing a wider zone of separation.

4.2.2 FLOW PATTERN

Water surface mappings allow visualization of the dynamics of the water surface through the channel junction region. A depth decrease from the flow upstream of the junction to the tailwater flow is generally observed.

Fig 13. Water Surface Mapping- Flow Level

Fig.14 Flow Pattern Graph at Junction of Two Channels (Along Wall Side)

For all ?ow conditions the water surface generally displays a drawdown longitudinal pro?le, Fig.14, as the ?ow enters the contracted region and then exhibits a depth increase as the ?ow expands to the entire channel width downstream of the separation zone. This pattern is more distinctive for lower q* ?ow conditions where the water surface depression within the separation, adjacent and downstream of the lateral branch, is deeper and more extensive.

5. COMPARISON BETWEEN FLOW PATTERNS OF JUNCTION OF TWO CHANNELS AND JUNCTION OF A CHANNEL AND PIPE

The experiment indicates that the maximum difference in the average upstream depths is very small and decreases with increasing q*. The main channel upstream cross-section profile is horizontal; however, the branch channel depth decreases as x* approaches 1.00. For low q* flow conditions this decrease is substantial but for high q* the cross-section profiles show smaller cross-channel variations. This trough exhibited at low q* is attributed to the drawdown feature evident in the junction flow. From fig 11, it can be seen that the flow has not completely recovered from junction effect until beyond x*=-6.00. This complicates the design of successive junctions. Figure 13 indicates that as main channel flow reaches the junction more decrease in surface elevation is caused and only after reasonable flow, does the main channel regains its original characteristics.
While in the case of a junction between a channel and pipe, the decrease in surface elevation is less compared to former. The effect of flow patterns in pipe vary from free-surface flow to pressurized pipe flow depending on the discharge and carrying capacity of pipe.

6. CONCLUSIONS

The results raised the following important effects resulting from particular combinations of experimental variables or geometrical parameters:
(1) The conduit outlet may cause non-negligible tail water effects upstream in case of high pipe flow combined with high channel discharge capacity.
(2) The channel tail water effect upstream due to pipe outlet flow may increase with flow rates in both the pipe and channel, which could occur through the simultaneous flow from both the upstream catchments of the channel and pipe.
(3) The influence of combined pipe slope and downstream tail water effects may cause a change in pipe flow from free surface to pressurized. The present observations extend available knowledge on free-pipe outlet flow. This influence may lead to two forms of transitional cavity flow, with possible different behaviors in transient conditions.
(4) The velocity dip in open channel flow is responsible for the following:
4.1 A reduction in main channel longitudinal velocities as flow passes through the junction.
4.2 No main-channel recirculation at the free surface.
4.3 Lower through flow and recirculating velocities in the branch channel.
(5) The surface elevation of main channel flow decreases more in the case of junction of two channels rather than a junction between a channel and closed conduit. This theory should be considered in the construction of drainage ditch or underground drainage systems.
REFERENCES

1. Barkdoll, B. D., Hagen, B. L., and Odgaard, A. J. (1998). “Experimental comparison of dividing open-channel with duct flow in a T-junction.” Journal of Hydraulic Engineering, ASCE Vol-124-1, pp. 92-95.

2. Ramamurthy, A. S., and Zhu, W. M. (1997). “Combining flows in 90° junctions of rectangular closed conduits.” Journal of Hydraulic Engineering, ASCE Vol-123-11, pp. 1012-1019.

3. Weber, L. J., Schumate, E. D., and Mawer, N. (2001). “Experiments on flow at a 90° open-channel junction.” Journal of Hydraulic Engineering, ASCE Vol-127-5, pp 340-350.

4. Y.Nedelec., and B.Gay. (2008). “Experimental study of a right-angled end junction between a pipe and an open channel.” Journal of Hydraulic Engineering, ASCE Vol-134-5-, pp 616-625.

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