3D numerical simulation of the separation zone at the channel–pipe junction

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.

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.

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.

There were four types of channel discharge (Q_u), four types of discharge ratio of the lateral pipe to channel (q_r) and three types of the height of tailgate (H_d). 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_wp) ranged from −0.4r to 5r (r was the pipe radius and equaled to 0.025 m) under the different H_d. When d_wp < 0, the water surface was below the pipe center and when d_wp = r, the water surface just submerged the pipe. Besides, the channel flow was subcritical and the Froude number (F_r) ranged from 0.16 to 0.82.

All the experiment variables are shown in Table 1.

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).

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.

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).

where h_i represents the results attained from simulations using the grid of G_i and h_D represents the water-surface height observed by the experiment.

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).

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.

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_r = 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 q_r. 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 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.

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.

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 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.

Basing the Equation (8), the increase of the q_r and the height of the h_u both lead to the increase of the M_r and the impact of M_r 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 M_r and the separation zone gradually is extended driven by the circulation flow. According to this conclusion, in addition to the q_r and h_u, the pipe flow area and width of the channel may also be two important elements affecting the volume of the separation zone.

Besides, to verify the relationship between the V_s and M_r, the correlation analysis is used based on 48 sets of data. The results of the bivariate Pearson test show that V_s was positively correlated with M_r (r = 0.79, P < 0.05).

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.

On the one hand, V_s discussed in this research is an absolute value instead of a relative value of V_s and channel flow area. With the increased h_d, both the flow area and V_s increase but the relative value of the V_s and flow area may decrease, which needs to be determined. On the other hand, the Froude number (F_r) of the channel flow becomes smaller when h_d increases. The smaller F_r 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 F_r. The result of the correlation analysis between F_r and h_r also confirms that there is a positive relationship between F_r and h_r (p < 0.01, R = 0.97).

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_s 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.

• (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_d. 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.

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.

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).

All authors contributed equally to this work.

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

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

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

The authors declare there is no conflict.