Physical modelling of energy losses at surcharged three-way junction manholes in drainage system

With global warming and the acceleration of urbanization, existing storm sewer systems in urban areas are frequently overloaded due to insufficient drainage capacity (Chang et al. 2013). This may cause serious problems such as sewer pipe rupture, blown-off manhole covers, soil erosion, and urban flooding (Jo et al. 2018; Crispino et al. 2019b; Crispino et al. 2021). For instance, the cover of a three-way junction manhole was blown off during the storm 2016 in the city of Wuhan, China. The precise indication of the places where water spills over through manholes of the storm sewer networks is necessary to reduce urban flood risk. Therefore, it is crucial to study drainage capacity for preventing urban flooding (Ruggaber et al. 2007; Borsányi et al. 2008; Granata et al. 2014).

In urban areas, manholes connecting sewer pipes at pipe joints are essential parts in the drainage system, especially during urban flooding due to their importance in sewer maintenance, sewer connection, and diversion function (Crispino et al. 2015; Zhang et al. 2018, 2020). It has been found that manhole energy loss plays a significant role in drainage capacity (Stovin et al. 2013). The increased energy loss at a surcharged junction manhole reduces the capacity of the drainage system (Wang et al. 1998; Tavakol et al. 2016). Over the past few decades, many efforts have been made to study energy loss at the surcharged junction manholes based on physical models (Del Giudice et al. 2000; Pfister & Gisonni 2014; Zhu et al. 2016; Rubinato et al. 2017, 2018a, 2018b; Jo et al. 2018; Crispino et al. 2019a, 2019b, 2021; Lin et al. 2020). Study on head loss coefficient calculation and head loss reduction in surcharged manholes with different manhole shapes and benching floor configurations was conducted by (Marsalek 1984). Energy losses at a surcharged two-way junction manhole with a main inflow pipe and a lateral inflow pipe were measured by Lindvall (1984). A comprehensive experiment was conducted to investigate the local head losses of combining flows at junction manholes for free surface flows in circular conduits, with various diameters and in the presence of sub- and super-critical approaching flows (Pfister & Gisonni 2014). Wave configurations of supercritical junction manholes were investigated by Del Giudice et al. (2000) and Gisonni & Hager (2002). A series of laboratory experiments were conducted by (Zhang et al. 2020) to study the hydraulic properties of three-way manhole junctions. Study of energy dissipation in a circular drop manhole with different flow patterns and drop heights was conducted by Granata et al. (2014) and Zheng et al. (2017). Results show that various parameters affect the hydraulic performance of the drop manhole. Kim et al. (2018) used a physical model to derive efficient benching designs that can reduce head loss. Results indicate that the installation of full rectangular benching reduced the head loss coefficients and can be installed to improve the drainage capacity of urban stormwater conduit facilities. Based on the experimental datasets, several types of theoretical formulae for energy loss coefficients have been proposed. One representative head loss coefficient formula guideline was proposed in the urban drainage design manual (UDDM) by the federal highway administration (FHWA 2009). Following this guideline, an alternative formula was proposed for three-way manholes under surcharged conditions by considering more variables of structural elements for the pipes and the manholes (Arao et al. 2016). In the proposed formula, the effect of diameter ratios between inflow and outflow pipes, flow rate ratios between inflow pipes, connected angle between inflow pipes, and drop gaps between inflow pipes and outflow pipe were included.

Currently, there is limited existing work investigating the flow structure and the influence of hydrodynamic force on energy loss in the surcharged three-way manhole system. Moreover, it is also observed that the head loss coefficient at manholes is usually neglected in floods analysis model due to the lack of validated theoretical formulae. To improve the reliability of the flood modelling, it is necessary to evaluate the risk of manhole failure quantitatively with efficient and accurate theoretical formulae of energy loss coefficients in the manhole. Therefore, more validations are needed to examine the existing empirical formulae.

The objective of this study is to use a physical model to investigate the influencing factors of local energy loss at the surcharged three-way junction manhole not only by calculating the energy loss coefficients, but also by calculating hydrodynamics and identifying flow structures in the manhole. In addition, two representative empirical formulae for energy loss coefficients were examined based on the experimental datasets. The paper is organized as follows: In section 2, an introduction of the physical model is given. In section 3, theoretical background of energy loss coefficients and hydrodynamic force are presented. Results and discussion are demonstrated in section 4. Finally, conclusions and future works are summarized in section 5.

The physical model (Figure 1(a)) was operated at the Ujigawa Open Laboratory, Disaster Prevention Research Institute of Kyoto University. The three-way junction manhole is sketched in Figure 1(b). It consists of two upstream pipes including a straight inflow pipe and a lateral inflow pipe, all having circular cross-section of diameters ⁠. The connected angle between two inflow pipes can be adjusted. There is a downstream outflow pipe with a circular cross-section of diameter ⁠. The manhole diameter B is 0.15 m. Discharge of the straight inlet flow ⁠, lateral inlet flow ⁠, and outlet flow pipes are recorded by three electro-magnetic flow meters (Yokogawa Electric ADMAG AXF) located in the upstream of the inlet pipes and the downstream of the outlet pipe, respectively. is the water depth in the manhole and is the water depth in the downstream tank. The piezometric heads at representative locations in the pipes are measured with a sequence of customized piezometers as shown in Figure 1(b). In the upstream of the pipeline system, there are two tanks which supply water to the straight and lateral inlet pipes, respectively. At the downstream of the outlet pipe, there is a tank and a reservoir. Water is pumped from the downstream reservoir to the upstream tanks. The flow discharge is adjustable through a pump-valve system. The pipe flow is pressurized flow and the flow in the manhole is free surface flow. The manhole, the sewer pipes, the tanks, and the reservoir are made from transparent acrylic materials. The sewer pipes are arranged horizontally in the experiments.

Flow features in the manhole were investigated by a Particle Image Velocimetry (PIV) system as shown in Figure 2. A laser (DPGL-2 W, Japan Laser, Co., Ltd) and a high-speed camera (FASTCAM Mini UX50, Photron Limited) were used to record the flow motion in horizontal and vertical cross-sections of the manhole as shown in Figure 2(a) and 2(b), respectively. The position of the high-speed camera and the laser are perpendicular to each other. When measuring the horizontal cross-section, the high-speed camera is placed at the vertical position of the section, that is, directly under the manhole model as shown in Figure 2(a). For vertical cross-section measurement, the PIV laser is located directly below the manhole model as shown in Figure 2(b). Measurements were recorded for a period of 3 min for each test. The obtained images were analyzed using the commercial PIV software (Flow Expert 2D2C, Katokoken Co., Ltd) and an adaptive correlation was performed to determine the velocity field for each time adjacent image pair.

For this physical model, the flow discharge in the inlet pipes varied from 0 to 3 ⁠, while the flow discharge in the outlet pipe was kept as a constant of ⁠. The ratio of flow discharge was set from 0 to 1.0. Downstream flow height varies from to ⁠. The connected angle between two inflow pipes can be adjusted. Square and circular cross-section manholes were compared. Detailed experimental conditions of the model are outlined in Table 1.

The relationships between head loss coefficients (⁠⁠, ⁠, and ⁠) and the downstream water depth (⁠⁠) in different flow discharge ratio (⁠⁠) conditions are shown in Figure 3. Results show that there is a slight variance of the total energy loss coefficients at the junction manhole with the change of downstream water depth, especially for K and ⁠. Overall, the effect of downstream water depth on manhole local energy loss is not obvious.

Figure 4 shows the manhole head loss coefficients K, ⁠, and with flow discharge ratio for ⁠, ⁠, and ⁠, respectively. It is found that K and are consistently increased with the increase of ⁠. When 2:3, the inlet flow rate ratio was dominated by the lateral inlet pipe, and the total head loss coefficient K increases significantly. However, it is observed that the trend of is different compared to that of K and ⁠. When and ⁠, increases continuously with the increase of ⁠. However, when ⁠, varies between peak and valley values.

Figure 5 shows the dynamic force F and manhole water depth with a flow discharge ratio for ⁠, ⁠, and ⁠, respectively. It is found that both of F and are consistently increased with the increase of the flow discharge ratio. This trend is consistent with the total head loss coefficients K. With the increase of the velocity in the lateral pipe, the water depth in the junction manhole was increased due to the increased velocity head transfers to the pressure head.

To further investigate the flow details in the junction manhole, Figures 6 and 7 present the velocity distribution and flow streamline in horizontal and vertical cross-sections at the junction manhole. It is observed that when the flow discharge ratio is increased from 1/3 to 1/2, the velocity distribution in horizontal and vertical cross-sections expanded with increased values and the vortex structure (streamline in ellipse dotted line) is also enhanced. Therefore, the total energy loss at the manhole significantly increases with the increase of ⁠. When increases, the flow velocity distribution and vortex structure are both enhanced thus leading to an increased energy loss at the manhole.

In this section, the influence of the connected angle between inflow pipes on total energy loss coefficient K at the manhole is discussed. Figure 8(a) shows the trend of the local energy loss with flow discharge ratio under different connected angles (⁠⁠, ⁠, ⁠). It is observed that the local energy loss coefficient K increases with the increase of ⁠. Moreover, there is a critical flow discharge ratio for the effect of connected angle on manhole local energy loss. When ⁠, the total head loss coefficient K of the connected angle is larger than that of and ⁠. Conversely, when ⁠, K of is smaller than that of and ⁠. Figure 8(b) shows the trend of the hydrodynamic force F along the main flow direction with flow discharge ratio under different connected angles (⁠⁠, ⁠, ⁠). It is found that the F decreases when is increased from to ⁠. This trend is not fully consistent with the trend of the total head loss coefficient. To further analyze the phenomenon, Figure 9 shows the flow structure in the manhole by comparing the velocity distribution and streamline in horizontal cross-section with two different connected angles and ⁠, respectively.

When the flow discharge ratio ⁠, vortex flow structure area (streamline in the ellipse dotted line) at the manhole of is larger than that of ⁠. Therefore, in this case, the local energy loss of is bigger than that of ⁠. However, when the flow discharge ratio increasing from to 2:3, the local energy loss of is bigger than that of ⁠. This is because vortex flow structure at the manhole of is enhanced and becomes stronger than that of ⁠, which dominates the local energy loss even though the hydrodynamic force term of is larger than that of ⁠. Overall, the effect of connected angle on manhole local energy loss is influenced by the flow discharge ratio ⁠. When is smaller than 0.5, the local energy loss of the connected angle is larger than that of and ⁠. Conversely, if is larger than 0.5, the local energy loss of is smaller than that of and ⁠. It is noted that the enhanced vortex structure increases the local energy loss at the junction manhole.

In this section, the influence of the manhole cross-section shapes (square and circle) on total energy loss at the three-way junction manhole is discussed. Figure 10 displays the trend of the local energy loss coefficient K with flow discharge ratio at circular and square cross-section manholes, respectively. It is found that the local energy loss at the circular manhole is smaller than that of the square manhole. This is due to the boundary condition of the square manhole being sharper than that of the circular manhole, which will enhance the generation of turbulence and lead to the increase of the local energy loss. Manhole cross-section shape has an effect on the local energy loss; energy loss at the circular manhole is smaller than that of the square manhole.

The expression of the head loss coefficients provides an important tool for the design of urban drainage system and flood modelling. To validate the existing empirical head loss coefficient formulae, the head loss coefficients of a surcharged three-way junction manhole obtained from experiments were used to examine two empirical formulae by FHWA (2009) and Arao et al. (2016). Results in Figure 11 show that the tendencies of the total head loss coefficients were in a relatively good agreement for both empirical formulae. It was observed that the formula proposed by ARAO et al. (2016) performs better than the formula of UDDM for K and ⁠. However, the formula of UDDM has better accuracy than ARAO et al. (2016) in terms of calculating ⁠.

To further examine the applicability of these two empirical formulae, the correlation between experimental and theoretical values were analyzed. Pearson correlation coefficients (⁠ and ⁠) were calculated to represent the correlation magnitudes. Figure 12 shows the scatter plot of correlation analysis between the experimental and theoretical results according to head loss coefficients K, ⁠, and ⁠, respectively. It is observed that both empirical formulae showed positive correlations. Correlation coefficients for K by UDDM and ARAO et al. are and 0.9739, respectively. Correlation coefficients for by UCDM and ARAO et al. are and ⁠, respectively. This indicates that the accuracy of ARAO et al. is higher than that of UDDM in terms of calculating K and ⁠. However, it is also found that both formulae cannot fit well with the calculation of ⁠. Correlation coefficients for by UDDM and ARAO et al. are and ⁠, respectively. The accuracy of UDDM is higher than that of ARAO et al. in terms of calculating ⁠.

This paper presents an experimental study on local energy loss and flow structures at the surcharged three-way junction manhole according to the changes in the downstream water depth, the inlet flow rate ratio, the connected angle between two inlet pipes, and the manhole shape. Head loss coefficients K, ⁠, and at the surcharged three-way manholes were quantified and used to validate two empirical formulae.

The present work demonstrates that total head loss coefficient at the three-way junction manhole increases as the flow rate ratio was increased. There exists a critical flow discharge ratio for the effect of connected angle on the manhole local energy loss. Specifically, when ⁠, the local energy loss value of the connected angle is larger than that of and ⁠. When ⁠, the local energy loss value of the connected angle is smaller than that of and ⁠. In addition, it is also observed that the effect of downstream water depth on manhole local energy loss is insignificant for the studied cases.

Vortex structure was evident in the energy loss at the surcharged three-way manhole due to changes of hydraulic and geometrical parameters, including: (1) the increased flow discharge for junction manholes by the lateral inlet pipe; (2) the flow directional change of the inlet lateral pipe; and (3) the cross-sectional change of the manhole from circular to square. It is demonstrated that with the increase of the lateral inflow discharge, the flow velocity distribution and vortex structure are both enhanced and lead to obvious increased energy loss at the manhole. The enhanced vortex flow structure for different connected angles has a significant effect on the local energy loss with the increased flow discharge ratio. It is also found that a circular manhole can reduce local energy loss compared to the square manhole due to a less-sharp and smoother boundary, which reduces the effect of turbulent flow leading to a decrease in local energy loss.

Two empirical head loss coefficient equations were tested at the three-way surcharged manhole model. The equation of ARAO et al. (2016) performs better than the equation of UDDM in terms of calculating K and ⁠. However, the accuracy of UDDM is higher than ARAO et al. (2016) for calculating ⁠. Overall, these two empirical formulae fit well with the data measured on the physical model for the basic trend of the total head loss coefficients at the three-way surcharged manhole. The present results may potentially be useful to develop the design and validation of novel theoretical formulae for head loss coefficients.

Further investigations are expected to study other important aspects in the evaluation of the flow behavior of vortex flow structure and to develop efficient and accurate formulae for the calculation of energy loss coefficients. It is noted that the specific manhole configuration considered in this work is simpler than the practical manhole system, which may include benching. The study of energy loss in benched manhole system and future research to test the reliability of the empirical formulae will be desirable especially for practical engineering conditions.

This research work was supported by the National Natural Science Foundation of China (Grant Nos. 41890823, 51725902); the Newton Advanced Fellowships from the NSFC and the UK Royal Society (Grant Nos. 52061130219; NAF\R1\201156); and the Royal Academy of Engineering through the Urban Flooding Research Policy Impact Programme (Grant No. UUFRIP\100031). This research was also supported by the JSPS KAKENHI Grants-in-Aid for Young Scientists (A) (Grant No. 16H06100) and the DPRI Collaborative Research Fund of Kyoto University (Grant No. 2019G-05). The authors thank the linguistic suggestions from Dr Syazana Omar. The authors would like to express their sincere thanks to the editor and anonymous referees for their valuable comments and suggestions.

All relevant data are included in the paper or its Supplementary Information.