## Abstract

At the confluence zone, the separation zone affects the flow, pollutant transport, and damages the bed and sidewalls of the channel. In this research, the geometric characteristics of the separation zone and the tailwater effect at the 90° channel–pipe junction are investigated using experiments and numerical simulations. These characteristics are different from the previous study in the channel or river junctions. (1) The separation zone is not attached to the sidewall of the channel. The shape of the separation zone is close to an ellipse but there is depression at the inside of the separation zone. (2) There is a pair of helical cells with opposite flow directions near the sidewall, which affects the shape of the separation zone and results in the differences. (3) The volume of the separation zone is proportional to the discharge ratio and the water-surface height. Furthermore, it's found that the momentum ratio is the basic reason affecting the volume of the separation zone. (4) The tailwater effect is affected by the discharge ratio and the water-surface height. And there is a significant positive correlation between the volume of separation zone and tailwater effect.

## HIGHLIGHTS

The characteristics of separation zones at channel–pipe junction are researched, which are rarely studied.

The shape of the separation zone and circulation flow is totally different from the previous studies.

The correlation between the separation zone and the tailwater effect is verified in this research.

## INTRODUCTION

*et al.*1992; Gurram

*et al.*1997). According to the hydraulic characteristics, Best (1987) divided the confluence zone into six zones, such as flow stagnation (a zone of relative flow stagnation near the upstream junction comer), flow deflection (an area of flow deflection where each stream enters the confluence), flow separation (a zone of separated flow below the downstream junction corner), flow acceleration (an area of flow acceleration), flow recovery (an area of gradual flow recovery downstream from the flow separation zone), and shear layer (several distinct shear layers with associated vortex generation) (Biron

*et al.*1996a; Serres

*et al.*1999). The confluence zone is shown in Figure 1.

At the interval zone between the deflected tributary flow and sidewalls, there is a low-velocity, low-pressure and low-vorticity zone that is the separation zone. The existence of the separation zone would occupy a part of the channel capacity, so it would affect the flow capacity of the channels and rivers. Also, because of the hydraulic characteristics, the separation zone also would affect the pollutant transport, riverbed morphology, flow capacity and sidewall erosion (Ashmore 1993; Dinh Thanh *et al.* 2010).

For a better understanding of the nature of the separation zone, researchers concentrated on the geometric and hydraulic features of the separation zone carrying out a lot of study. Taylor (1944), who was the first one to focus on the confluence zone, studied the flow characteristics at open channel junctions at junction angles of 45° and 135°. Modi *et al.* (1981) established a mathematical model by conformal transformation method and used the model to predict the shape of the separation zone. Best & Reid (1984) defined a coefficient about the shape of the separation zone and found that the coefficient was close to a constant. Rhoads & Kenworthy (1995) found the existence of the separation zone in the natural rivers for the first time, and before that, the separation zone only was observed in the laboratory experiments. Biron *et al.* (1996b) focused on the effect of the discordance of bed in the junctions, finding the mixing layer was distorted to a shallower channel and the shallower bed did not appear in the separation zone. Shin *et al.* (2021) investigated the influence of the separation zone on pollutant transport by numerical simulation. It was found that the separation zone accumulated the solute and there was a negative relationship between the volume of the separation zone and the transverse dispersion.

However, there is less research concerning the separation zone at the channel–pipe junction. On the one hand, for the channel–pipe junction, the separation zone is inevitable to be met at the man-made canals and has an obvious influence on the flow capacity and stability of the channel. On the other hand, comparing the channel or river junctions, the hydraulic features of the separation zone at the channel–pipe junction are more complex because of the relatively large number of parameters involved (United States Army Corps of Engineers Los Angeles District 1975). Based on the above two points, there is still a need to investigate the separation zone at the channel–pipe junction.

This research mainly concentrated on the separation zone in the channel–pipe confluence zone. The discharge ratio and water-surface height were chosen as the control variables. Through laboratory experiments and 3D numerical simulation, the geometric features of the separation zone and tailwater effect were investigated.

## EXPERIMENT

In previous studies, the extensive research confirmed that the intersection angle, bed discordance, discharge ratio, and Froude number were the main factors affecting the geometric and hydraulic features of the separation zone (Hsu *et al.* 1998; Guillén-Ludeña *et al.* 2016; Zhang & Lin 2021). Also, Nédélec & Gay (2008) presented that the increased water-surface height caused a change in pipe flow from non-pressure to pressure. So, in this paper, we refer to the previous studies and design the experiment to research the flow features at the channel–pipe junction.

### Experimental setup

There were two main experiment elements, a rectangular flume and a closed circular pipe, which was connected to a channel with 90°. One tank was set below the outlet of the open channel, collecting the water from the outlet of the channel. The open channel, lateral pipe and tank, all linked with pipes, composed a water recirculation device.

The open channel was 8 m long, 0.5 m wide, and 0.5 m in depth and the bottom of the whole open channel was smooth. There is a grill set at the connection between the channel inlet and tank for that the channel inlet flow was closed to a steady flow. Besides, the distance between the channel inlet and lateral pipe equaled 2 m (4 times the channel width). An adjustable tailgate was set at the channel downstream to control the height of the channel water surface, which was 4.5 m (9 times the channel width) away from the lateral pipe. The lateral pipe had a diameter of 0.05 m and a length of 2 m. Additionally, the center of the pipe was 0.075 m from the bottom of the channel. There is a vertical pipe that was connected to the lateral pipe and supplied water to it as same as a constant head tank. Due to that the channel was surrounded and supported by metal brackets, the slope of the open channel is also adjustable by the hydraulic jack and it was horizontal in this research.

Both the channel and the lateral pipe were equipped with independent valves and electromagnetic flow meters to facilitate controlling and monitoring of their discharges, respectively. Also, using Acoustic Doppler Velocimeter (ADV) to measure the 3D flow velocity in the channel.

### Control variables

There were four types of channel discharge (*Q _{u}*), four types of discharge ratio of the lateral pipe to channel (

*q*) and three types of the height of tailgate (

_{r}*H*). Also, all the experimental cases were 48 groups (4 × 4 × 3). In the experiments, the distance from the channel water surface above the pipe to the pipe center (

_{d}*d*) ranged from −0.4

_{wp}*r*to 5

*r*(

*r*was the pipe radius and equaled to 0.025 m) under the different

*H*. When

_{d}*d*< 0, the water surface was below the pipe center and when

_{wp}*d*=

_{wp}*r*, the water surface just submerged the pipe. Besides, the channel flow was subcritical and the Froude number (

*F*) ranged from 0.16 to 0.82.

_{r}All the experiment variables are shown in Table 1.

Q (L/s)
. _{u} | q (%)
. _{r} | H (m)
. _{d} | d
. _{wp} | F
. _{r} |
---|---|---|---|---|

15, 20, 25,30 | 2.5, 5, 7.5,10 | 0 | −0.4r–0.4r | 0.72–0.82 |

…… | …… | 0.05 | 1.5r–2.5r | 0.28–0.37 |

…… | …… | 0.1 | 4r–5r | 0.16–0.24 |

Q (L/s)
. _{u} | q (%)
. _{r} | H (m)
. _{d} | d
. _{wp} | F
. _{r} |
---|---|---|---|---|

15, 20, 25,30 | 2.5, 5, 7.5,10 | 0 | −0.4r–0.4r | 0.72–0.82 |

…… | …… | 0.05 | 1.5r–2.5r | 0.28–0.37 |

…… | …… | 0.1 | 4r–5r | 0.16–0.24 |

## NUMERICAL SIMULATION

The flow structures and the shape of the separation zone evidently have 3D characteristics resulting from the vertical nonuniformity of the mean-flow quantities (Mignot *et al.* 2012). There was a need to complement experiments and capture data in more detail by the 3D numerical simulation. The 3D numerical simulation has been used in studying the confluence zone for a long time, and validated that it is capable to simulate the flow in the confluence zone (Huang *et al.* 2002; Zeng & Li 2010; Brito *et al.* 2014).

### Numerical method

*ANSYS FLUENT*, which is the most powerful, well-validated physical and CFD modeling software tool (Zou

*et al.*2018). The Reynold-averaged Naviers–Stokes (RANS) equations are capable of the research. Also, RNG

*k*–

*ε*model was chosen to close the RANS equations. The RNG

*k*–

*ε*model was proposed by Yakhot

*et al.*(1992), and gradually applied in studying the confluence zone (Bradbrook

*et al.*1998; Biron

*et al.*2004). Numerous studies confirmed the advantage of the RNG

*k*–

*ε*model simulating the flow separation (Lien & Leschziner 1994; Shakibainia

*et al.*2010). The RANS equations and the RNG

*k*–

*ε*model equations are shown as follows:where represents the

*x, y, z*coordinate, respectively; is the mean velocity component; is fluctuating velocity components; is the fluid density;

*p*is pressure;

*t*represents time; is viscosity coefficient.where

*k*is the turbulent kinetic energy; is turbulent kinetic energy dissipation rate; is effective viscosity coefficient, , is the eddy viscosity coefficient of the fluid; represents the generation of turbulence kinetic energy due to the mean velocity gradients, ; is the turbulent kinetic energy due to buoyancy, ; represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate, , is the turbulent Mach number, ; , ; , , .

### Volume of fluid

*et al.*2021). The volume of fluid (VOF) was chosen in this research because of great conservation and accuracy. The VOF method, belonging to multi-model, was proposed by Hirt & Nichols (1981). In this model, all fluids, which commonly refer to two or more immiscible fluids, have their own volume fraction and solve a single set of momentum functions shared by all fluids. The tracking of the interface(s) between the phases is accomplished by the solution of a continuity equation for the volume fraction of one (or more) of the phases. This method has great conservation and accuracy as well as its expenditure is affordable, so choosing it to treat the water surface. For the q

^{th}phase, the volume fraction equation is shown as follows:where the

*m*is the mass transfer from phase

_{pq}*p*to phase

*q*, conversely, the

*m*is the mass transfer from phase

_{qp}*q*to phase

*p*;

*S*is the source term of the mass of

_{αq}*q*phase.

^{th}### Boundary conditions and wall functions

The channel-inlet concludes a water inlet and an air inlet as well as the pipe inlet only has a water-inlet. Both the water-inlets adopt the velocity inlets and the air inlet adopts the pressure inlets with an atmospheric pressure. The pressure outlets are adopted in the outlet and top. The outlet boundary location is set enough far away from the confluence to ensure that all variables have zero gradients at the outlet.

Because of the capability of partly accounting for the effects of pressure gradients and departure from equilibrium, the non-equilibrium wall functions (Kim & Choudhury 1995) are recommended for use in complex flows involving separation, reattachment and impingement where the mean flow and turbulence are subjected to severe pressure gradients and change rapidly. In such flows, improvements can be made, particularly in the prediction of wall shear (skin-friction coefficient). So in this article, the non-equilibrium wall function is adopted.

The key elements in the non-equilibrium wall functions are as follows: Launder and Spalding's log-law for mean velocity is sensitized to pressure-gradient effects; the two-layer-based concept is adopted to compute the budget of turbulence kinetic energy in the wall-neighboring cells; the law-of-the-wall for mean temperature or species mass fraction remains the same as in the standard wall functions.

### Meshing

The flow direction of the open channel is the *X*-axis, the flow direction of the lateral pipe is the *Z*-axis and the direction of height is the *Y*-axis.

Because the geometry of the model is simple, the structured grid is used for better accuracy. In addition, the fluid domain is divided into three zones, which are the pre-confluence zone, post-confluence zone and confluence zone (as shown in Figure 3). In the confluence zone, the hydraulic elements such as velocity, pressure and water-surface, change acutely and the separation zone appears. So, the finer grids are used in the confluence zone to improve the simulation accuracy (as shown in Figure 4).

^{−7}m

^{3}), G2 (grid numbers = 2,310,270 and minimum grid volume = 7 × 10

^{−8}m

^{3}) and G3 (grid numbers = 2,939,010 and minimum grid volume = 6 × 10

^{−8}m

^{3}). For choosing the appropriate grids, the water-surface at the junction attained from numerical simulations using different grids and experiments were compared (

*Q*= 25 L/s,

_{u}*H*= 0 m). The result is shown in Figure 5:

_{d}*δ*was used to be as a coefficient for the errors. The equation and result as shown in Table 2.

ID . | Q = 25 L/s_{u}. | H = 0 m_{d}. | ||||||
---|---|---|---|---|---|---|---|---|

q = 2.5%_{r}. | q = 5.0%_{r}. | q = 7.5%_{r}. | q = 10.0%_{r}. | |||||

δ_{max}
. | δ_{mean}
. | δ_{max}
. | δ_{mean}
. | δ_{max}
. | δ_{mean}
. | δ_{max}
. | δ_{mean}
. | |

G1 | 8.84% | 4.55% | 7.54% | 3.51% | 13.43% | 4.17% | 15.33% | 10.25% |

G2 | 4.62% | 1.79% | 6.96% | 2.26% | 4.53% | 1.73% | 8.06% | 3.81% |

G3 | 3.09% | 1.60% | 4.16% | 1.94% | 3.09% | 1.49% | 5.73% | 2.54% |

ID . | Q = 25 L/s_{u}. | H = 0 m_{d}. | ||||||
---|---|---|---|---|---|---|---|---|

q = 2.5%_{r}. | q = 5.0%_{r}. | q = 7.5%_{r}. | q = 10.0%_{r}. | |||||

δ_{max}
. | δ_{mean}
. | δ_{max}
. | δ_{mean}
. | δ_{max}
. | δ_{mean}
. | δ_{max}
. | δ_{mean}
. | |

G1 | 8.84% | 4.55% | 7.54% | 3.51% | 13.43% | 4.17% | 15.33% | 10.25% |

G2 | 4.62% | 1.79% | 6.96% | 2.26% | 4.53% | 1.73% | 8.06% | 3.81% |

G3 | 3.09% | 1.60% | 4.16% | 1.94% | 3.09% | 1.49% | 5.73% | 2.54% |

where *h _{i}* represents the results attained from simulations using the grid of

*G*and

_{i}*h*represents the water-surface height observed by the experiment.

_{D}In all hydraulic situations, *δ*_{max} of G2 and G3 were less than 10% and *δ*_{mean} of them was less than 5%. It meant that choosing the grids of G2 or G3 hardly affected the results of numerical simulations. So in this paper, we chose the grids of G2 (the numbers of 2,310,270).

### Model validation

*x*-direction) and circulation flow velocity (the direction of

*y*–

*z*) of the same cross-section from the downstream of the pipe (

*x*= 2.04 m), which are attained from the same case (

*Q*= 25 L/s,

_{u}*q*= 5.0%,

_{r}*H*= 0.05 m).

_{d}From the main flow velocity distribution, the result of the simulation is close to the experiment data. Both of them catch the negative velocity zone and the shapes of this zone are similar (*z* = 0–0.04 m), which will be analyzed in the following. As for the high-velocity zone that appeared in the experiment (*z* = 0.04–0.1 m), it would be related to the fluctuations of channel or pipe discharge or the disturbance of measuring equipment (ADV). Besides, in the simulations (Figure 6(c)), the helical cells are caught clearly but it's not obvious in the experiments (Figure 6(d)). However, basing the upwelling and downwelling near the sidewall (*z* = 0 m) as well as the lateral movement of flow at the middle of the channel (*y* = 0.06 m), it can also prove the existence of helical cells.

Based on the comparison between the experiments and simulations, it can be considered that the simulation is believable and accurate, which can be used for extracting the separation zone and flow field in the subsequent analysis.

## RESULTS AND DISCUSSION

### The shape of the separation zone

*et al.*2008), the geometric boundary of the separation zone is defined by the isoline of the flow velocity along the mainstream (

*X*-direction flow velocity), in which the flow velocity of the mainstream is equal to 0 m/s. According to the method, the separation zone is extracted from the numerical simulations (as shown in Figures 7 and 8).

Observing the shape of the separation zone in the channel–pipe confluence, there are conspicuously some obvious characteristics when *H _{d}* = 0.05 and 0.1 m. First, whether

*q*= 2.5%, 5.0%, 7.5% or 10.0%, the separation zone is not attached to the sidewall near the tributary. The separation zone is gradually far away from the sidewall near the tributary with the increase of the

_{r}*q*. Second, the overall shape of separation is close to an ellipse but there is a depression at the inside of the separation zone near the sidewall. However, in the previous studies, the shapes of separation zones in river junctions are different (Xiaoping & Wenqi 1993; Mao

_{r}*et al.*2005). For example, the separation zone is small near the bed and gradually increases when approaching the water surface. The separation zone is always attached to the sidewall under the squeeze of deflected tributary flow. The differences may be due to the form of the channel–pipe junction and worth further studying the impact in other aspects.

### Circulation flow

In the previous study, it has been confirmed that the shape of the separation zone is affected by the circulation flow in the river and channel confluence zone (Xiaoping & Wenqi 1993). To explain the differences in the shape of the separation zone, this relationship also is discussed.

*H*= 0.05 and 0.1 m. Observing the vectors at cross sections, it is clear that there are a pair of helical cells with opposite flow directions near the sidewall. The helical cell at the upper part is clockwise and the helical cell at the lower part is anti-clockwise. Furthermore, based on the form of helical cells and the shape of separation, it's certain that there is an obvious relationship between the separation zone and helical cells. The separation zone is away from the sidewall driven by the helical cells. Also, the encounter of two helical cells results in the flow in the separation zone moving toward the outside. So, this causes depression inside the separation zone.

_{d}According to the analyses about the form, it could be concluded that the shape of the separation zone is strongly affected by the circulation flow, which results in the differences in the shape of the separation zone. As for the generation of circulation flow, it would be related to the deflected lateral pipe flow. Because when the pressured pipe flow bends, there is a pair of helical cells with opposite flow velocity. In the channel–pipe junction, the water-surface is higher than the pipe, so the pipe flow is pressured when it flows out from the pipe and into the channel. The pressure condition and deflected direction of pipe flow result in the generation of circulation flow.

### The volume of separation zone

The volume of the separation zone (*V _{s}*) is the key to deciding the affection of the separation zone to the pollution transport and channel flow capacity. Because the geometric boundary of the separation zone had been extracted in section 4.1, the volume of the separation zone could be calculated by the volume integration in post-processing.

*H*and the

_{d}*q*between the channel and pipe also affect the

_{r}*V*. Figure 10(a) shows the positive relationship that the

_{s}*V*increased with the increase of

_{s}*q*. For instance, when the

_{r}*Q*= 30 L/s,

_{u}*H*= 0.05 m and

_{d}*q*= 2.5%, the

_{r}*V*equals to 0.020 m

_{s}^{3}and when only the

*q*increases to 10%, the

_{r}*V*also increases to 0.087 m

_{s}^{3}. Figure 10(b) shows that the higher water level resulted in a bigger

*V*. Choosing the situation that the

_{s}*Q*= 30 L/s and the

_{u}*q*= 2.5%, when the

_{r}*H*= 0 m, the

_{d}*V*equals to 0.002 m

_{s}^{3}and when the

*H*= 0.1 m, the volume equals to 0.022 m

_{d}^{3}.

*V*in the above hydraulic situations could be explained by the momentum ratio between the channel flow and the lateral pipe flow (the equation is shown as follows). The results about the

_{s}*M*are shown as follows:where the subscript

_{r}*u, lp*signify the flow from the upstream channel and the lateral pipe, respectively. The

*m*is the mass of the flow, the

_{i}*v*is the mean velocity of the flow, the

_{i}*w*is the width of the channel and the

*A*is the flow area

_{i}Basing the Equation (8), the increase of the *q _{r}* and the height of the

*h*both lead to the increase of the

_{u}*M*and the impact of

_{r}*M*increase can be explained from two aspects: (1) the lateral pipe flow is more difficult to deflect under the influence of channel flow, which means there is a larger area between the deflected pipe flow and the sidewall; (2) the deflected pipe flow results in a stronger circulation flow with the increased

_{r}*M*and the separation zone gradually is extended driven by the circulation flow. According to this conclusion, in addition to the

_{r}*q*and

_{r}*h*, the pipe flow area and width of the channel may also be two important elements affecting the volume of the separation zone.

_{u}Besides, to verify the relationship between the *V _{s}* and

*M*, the correlation analysis is used based on 48 sets of data. The results of the bivariate Pearson test show that

_{r}*V*was positively correlated with

_{s}*M*(

_{r}*r*= 0.79,

*P*< 0.05).

### Tailwater effect

*q*and

_{r}*H*were chosen as the controlled variables and the relationships between these variables and the tailwater effect were researched. At first, the

_{d}*h*is defined as the dimensionless coefficient about the tailwater height (the equation is shown as follows):in which, the

_{r}*h*is the max water level height at the junction upstream and the

_{m}*h*is the water level height at the junction downstream when the flow recovers to steady.

_{d}*q*,

_{r}*h*increases similarly. For instance, under the fixed

_{r}*Q*and

_{u}*H*(

_{d}*Q*= 15 L/s,

_{u}*H*= 0 m), when the

_{d}*q*= 2.5%, the

_{r}*h*= 1.25. However, when the

_{r}*q*increases to 10%, the

_{r}*h*also increases to 1.32. Another evident tendency is that at the fixed

_{r}*q*and

_{r}*Q*, the

_{u}*h*would be bigger when the

_{r}*H*is smaller. Such as, when the

_{d}*Q*= 15 L/s,

_{u}*H*= 0 m,

_{d}*q*= 10%, the

_{r}*h*= 1.32 and when the

_{r}*H*increases to 0.05 and 0.1 m, the

_{d}*A*, respectively, is 1.05 and 1.01. Based on the above instances, it could be concluded that the

_{c}*h*is in direct ratio with the

_{r}*q*and was in inverse ratio with the

_{r}*H*. The results are corresponded with the research of Nazari-Sharabian

_{d}*et al.*(2020).

In addition to the mutual extrusion between the channel and pipe flow, the volume of the separation zone is also an important reason for the tailwater effect. Because the flow velocity in the separation zone is less than or equal to 0, the existence of the separation zone would have a block effect on channel flow and affect the tailwater effect. In this research, the relationship between the tailwater effect and the volume of the separation zone is discussed by correlation analysis.

*h*and

_{r}*V*at different

_{s}*h*are shown clearly and it also could be concluded that there is a block effect of separation on the tailwater effect. There is a significant positive correlation such as when

_{r}*H*= 0 m (

_{d}*p*< 0.01,

*R*= 0.825) or

*H*= 0.05 m (

_{d}*p*< 0.05, R = 0.612). However, when

*h*increases to 0.1 m, the significance and relevance of the correlation both decrease (

_{d}*p*> 0.05,

*R*= 0.452). The reasons for this change are shown as follows.

On the one hand, *V _{s}* discussed in this research is an absolute value instead of a relative value of

*V*and channel flow area. With the increased

_{s}*h*, both the flow area and

_{d}*V*increase but the relative value of the

_{s}*V*and flow area may decrease, which needs to be determined. On the other hand, the Froude number (

_{s}*F*) of the channel flow becomes smaller when

_{r}*h*increases. The smaller

_{d}*F*means that the gravity potential energy is greater than kinetic energy and when the kinetic energy is converted into gravitational potential energy (the channel flow collides with the separation zone), this energy conversion and increase of water-surface (tailwater effect) is not obvious compared with high

_{r}*F*. The result of the correlation analysis between

_{r}*F*and

_{r}*h*also confirms that there is a positive relationship between

_{r}*F*and

_{r}*h*(

_{r}*p*< 0.01, R = 0.97).

## CONCLUSION

This paper investigates the separation zone in the channel–pipe junction by numerical simulations and experiments. The results show the geometric shape of separation zone and form of circulation flow at the channel–pipe junction are special when the channel water level is higher than the pipe and the tailwater effect is related to the separation zone. Besides, the variations in the volume of the separation zone and tailwater height under the tailgate height and discharge ratio also are discussed. The results are shown in detail as follows:

- (1)
When the water level is higher than the pipe, the separation zone is not attached to the sidewall near the tributary flow and the overall shape of the separation zone is close to an ellipse, but there is an obvious depression in the middle of the separation zone inner side (near the sidewall).

- (2)
When the water level is higher than the pipe, there is a pair of helical flows in opposite directions affecting the shape of the separation zone. From the form of helical flows, it is very close to the secondary flow generated by the pressured and deflected pipe flow.

- (3)
The volume of the separation zone is in direct ratio with the discharge ratio and the tailgate height. Besides, the momentum ratio is a basic reason affecting

*V*by theoretical analysis and correlation analysis. The tailwater height is in direct ratio with the discharge ratio but in reverse ratio with the tailgate height._{s} - (4)
There is a positive correlation between the volume of separation zone and tailwater height. However, the significance and relevance of the correlation gradually become unobvious with the increased

*H*. That means the block effect of the separation zone must be considered when the channel water surface is low and provides a new direction for controlling the tailwater effect._{d}

This paper proves the differences in separation zone between channel–pipe junction and channel junction when the water level is higher than the pipe. The paper will be a foundation for further studies about the channel–pipe junction.

## ACKNOWLEDGEMENTS

This work was supported by the National Key Research and Development Program of China (No. 2022YFC3801002), National Natural Science Foundation of China (No. 51978630), Program for Innovative Research Team (in Science and Technology) in University of Henan Province (No. 23IRTSTHN004), Key Scientific Research Projects of Colleges and Universities in Henan Province (22A570009), Open Research Fund of Key Laboratory of Water-saving Irrigation Engineering of the Ministry of Agriculture and Rural Affairs (MARA) (FIRI2021020201), Yellow River Laboratory (Zhengzhou University) first-class project special fund project (YRL221R11), Open Research Fund of MWR Key Laboratory of Lower Yellow River Channel and Estuary Regulation (LYRCER202202), Fundamental Research and Cultivation of Young Teachers (JC22550027), and Special Scientific Research Project of Yellow River Water Resources Protection Institute (KYY-KYZX-2022-01).

## AUTHORS’ CONTRIBUTIONS

All authors contributed equally to this work.

## ETHICAL APPROVAL

This article does not contain any studies with human participants or animals performed by any of the authors.

## INFORMED CONSENT

Informed consent was obtained from all individual participants included in the study.

## DATA AVAILABILITY STATEMENT

Data cannot be made publicly available; readers should contact the corresponding author for details.

## CONFLICT OF INTEREST

The authors declare there is no conflict.

Recent Developments in Fluvial Sedimentology. https://doi.org/10.2110/pec.87.39.0027