## Abstract

Determining the proper installation location of flow meters is important for accurate measurement of discharge in sewer systems. In this study, flow field and flow regimes in two types of manholes under surcharged flow were investigated using a commercial computational fluid dynamics (CFD) code. The error in measuring the flow discharge using a Doppler flow meter (based on the velocity in a Doppler beam) was then estimated. The values of the corrective coefficient were obtained for the Doppler flow meter at different locations under various conditions. Suggestions for selecting installation positions are provided.

## INTRODUCTION

Real-time flow monitoring plays an important role in sewer networks (Mingkai *et al.* 2017). Acoustic Doppler flow meters, as one of the most commonly used instruments, are easy to set up and can be applied under various circumstances. Installation guidance (e.g. Sigma Flow Meter Models 950 User Manual 2014) usually suggests that flow meters should be arranged at a minimum distance of 10 times the pipe diameter from manholes and joints, where flow is fully developed. However, physical constraints often limit the accessibility of installation positions in the field. In a recent field study in the city of Wuxi, Jiangsu Province, China, sensors could only be placed near manholes due to limited operating space where flow fields were quite complicated. There is a practical need to access the impact of the installation location in the flow rate measurement.

As it is known, Doppler flow meters obtain velocity information using Doppler effects and are built on a ‘flow-area’ approach. Flow rate is calculated from the flow area and the cross-sectional averaged flow velocity. While the flow area can be calculated from the sectional shape and the water level, the average velocity is much more difficult to obtain. Sensors collect information through a cone-like shape volume, which is defined by emission angle and beam width (Larrarte *et al.* 2008). In this process, partial flow field data are relied to represent cross-sectional averaged velocities, which leads to the deviation of the measured values from the true values. Therefore, the corrective coefficient is needed and can be defined as follows (Bonakdari & Zinatizadeh 2011): K_{c} = V/V_{m}, where V is the true mean velocity of the cross section in the pipe, and V_{m} is the measured velocity in the cone-shaped signal beam area. In practice, this coefficient is usually considered as a constant value because accurate evaluations of K_{c} value from field calibrations can be very difficult and expensive. However, previous studies have pointed out that the coefficient is affected by a number of factors, including geometries (Sharifipour *et al.* 2015), sensor locations (Mignot *et al.* 2012) and sensor types (Larrarte *et al.* 2008) with changing hydraulic conditions.

Commercial computational fluid dynamics (CFD) code has become a commonly used tool in hydraulics research and engineering. Previous studies like Zhao *et al.* (2008), Schmidtke & Lucas (2009), Bonakdari *et al.* (2011), Bennett *et al.* (2011), and Stovin *et al.* (2013) have demonstrated the advantages of CFD ability. Compared to traditional physical model studies, it is cost-effective, especially in predicting detailed flow distributions. Additionally, it can simulate the real sizes, thus avoid scale effect, which usually is the bottleneck in laboratory experiments (e.g. pipe diameter, flow rate). However, carefully validating is needed to ensure the results are reliable.

Hilgenstock & Ernst (1996) focused on pipes with bends and concluded that numerical model is a powerful tool to investigate installation effects, and standard turbulence models can provide reasonable agreement with experimental results. Bonakdari & Zinatizadeh (2011) applied CFD to calculate the corrective coefficients in open straight pipes and compared three types of sensors with different locations. Mignot *et al.* (2012) studied flow structures in open channel junctions and evaluated the typical error of flow rate measurement by 3D numerical model and suggested that installation location should be in the upstream branch or in the downstream branch at a minimum distance of x/b = 8 from the junction, where x is the distance between the flow meter and the junction, and b is the channel width. Sharifipour *et al.* (2015) studied the impact of confluence angles to the open channel junctions and estimated the error of measurement of flow meter devices using CFD models, with a maximum error of about 40% at a confluence angle of 90°. Most of the earlier studies focused on the pipe with bends or junctions (e.g. Mignot *et al.* 2012; Sharifipour *et al.* 2015), K_{c} in manhole structures under surcharged flow conditions is still not clear. Ideally, at proper locations, the values acquired by sensors are close to real mean velocities, which means the corrective coefficient is close to 1. At the same time, the value of coefficient is stable and less affected by hydraulic conditions (water level, water velocity). However, due to the irregularity and complexity of the boundaries and geometries, the coefficient can vary significantly from 1 (e.g. 0.7–1 by Bonakdari 2012, and 0.66–0.88 by Mignot *et al.* 2012). The objectives of this study are: to investigate flow regimes under surcharged conditions, to evaluate the K_{c} values for the Doppler flow meters at different positions, and to provide suggestions for proper installation. Additionally, the flow measurement in the reversed flow condition is also studied.

## NUMERICAL MODEL

The numerical model was constructed based on the conditions of the authors' recent field study. Hach submerged area-velocity AV9000 flow meter was used in the study. The Doppler sensor has 15 ° and 17 ° for the emission angle and the beam width, respectively, see Figure 1(a), and the signal range is over 3.5 m (Hach AV900 User Manual 2016; Larrarte *et al.* 2008). The field geometry of the manholes is shown by Figure 1(b). Both the inlet and outlet pipes have a diameter of 500 mm and a slope of 0.002. There is a straight-through junction with a circular manhole of a diameter of 1,250 mm. The origin of the horizontal axis x is defined at the end of the inlet pipe (or the beginning of the junction) and the bottom of pipes was set as z = 0. In order to estimate the influence of the bottom shape of the manholes on Doppler flow meters, two types of manholes are studied: type 1 represents manholes with flat bottoms, whereas type 2 are manholes with full benching, see Figure 1(c).

*ε*model was chosen, which is able to provide satisfactory predictions of the 3D behavior when flow passes manhole junctions (Zhao

*et al.*2008; Motlagh

*et al.*2013). The Reynolds averaging governing equations can be written as follows (Ferziger & Peric 1996): In these equations,

*x*represents the Cartesian coordinates where are the mean velocities, and are the fluctuating velocities. Besides, are components of average viscous stress tensor and

_{i}*p*is the pressure. Volume of Fluid method was used to handle multi-phase conditions. The air entrainment is relatively small in this study and has very little impact on the water flow field. It was assumed that the air and water phases in this study share a common turbulence field, which is referred to as a homogeneous model in CFX. Upstream and downstream boundary distances were set as 50 times the pipe diameter from the manholes to ensure the flow is fully developed. The inlet boundary condition is set as uniform velocity, and the outlet boundary condition is specified as hydrostatic pressure distribution. No-slip walls with a roughness height of 0.5 mm were set and the scalable wall functions were applied here, which allowed the use of coarser meshes near the wall. Besides, top boundaries of manholes were defined as opening type with atmospheric pressure, where it allows air phase to go in and out.

Meshes were generated by Ansys-Mesh. To save computational resources, structured meshes were used in the long straight structure. To apply it, the geometry was divided into several parts with structured grid parts connected by a region with unstructured grids in the middle, see Figure 2. Structured inflation near the walls was built as well.

To determine mesh density required for the simulations, five groups of mesh sizes with various densities were tested. Figure 3 shows the sensitivity of the simulation results to the number of nodes in the computational domain: H is the water surface height inside the junction, and K is the head loss coefficient. K is defined as ΔE = K V^{2}/2 g where ΔE is the junction head loss, V is the mean velocity in the inlet pipe and g is the gravitational acceleration. As shown in Figure 3, values of K and H show little variation when the node number is larger than 1.20 × 10^{6}. Thus, the mesh size with 1.20 × 10^{6} nodes was used in this study. The selected mesh size had 15 layers of near-wall structured inflation. The convergence targets were selected as 10^{−4} for momentum and mass residual, and the mass imbalance is less than 1%.

Proper modeling of the velocity distribution in cross sections is important for the predictions of flow discharge. Due to the absence of detailed measurement in the field work, the numerical model was validated using Bonakdari *et al.*'s (2007) measurement data from an open channel flow. In this study, the vertical cross section was discretized into sampling points, and a two dimensional remote-controlled device called ‘Cerbère’ was applied to obtain a velocity distribution in the field experiment. Two typical conditions were selected to compare the velocity distributions obtained from experiment and CFD predictions.

Figure 4(a) and 4(b) show velocity distributions from the experimental measurements where Figure 4(c) and 4(d) are the CFD predictions. The contours are the local velocity ratio of U/U_{max}. It is clear that CFD model predictions show satisfactory agreement with the experimental data. The differences between the CFD predictions and the measurements were found to be less than 2% of the measured values. In addition, the CFD predictions properly show the ‘dip phenomenon’ in the experiments, i.e. the velocity maximum region lies below the water surface. Thus, the CFD model is able to provide accurate predictions of velocity distributions in cross sections.

## FLOW REGIMES

For two benching type manholes, the flow patterns are shown in Figure 5 with the top view of the velocity vector and contour under a surcharged height S = D. Within type 1 manholes, the flow cross-sectional area increases significantly at the junction. As a result, the recirculation eddies are observed at both sides of the main flow. The velocity in the main jet decreases in the junction and increases again when the flow enters into the outlet pipe. In the type 2 manhole, the velocity vector shows that the full benching structure avoids the large recirculation eddies with only slight flow expansion at both sides of the main flow. As it effectively reduces the flow, sudden expansion and contraction, type 2 structures are found to be effective in reducing energy losses in junctions, as reported by Marsalek (1984) and Mrowiec (2007).

Furthermore, flow patterns under two surcharged levels are examined in Figure 6 at the middle plane of type 1 manhole. When the surcharged level is small, as shown in Figure 6(a), incoming flow only expands slightly within the junction. With a large submergence level, however, the incoming flow turns weaker, and a large recirculation zone with low velocities is developed above the pipe level, see Figure 6(b). The appearance of recirculation zone is considered to affect the local head losses factor, which was reported by Stovin *et al.* (2010). Previous laboratory studies also showed that the local head loss coefficient K became larger with the rise of water level until some certain value is attained when the recirculation is formed (Lindvall 1984, 1987; Marsalek 1984; Mrowiec 2007). Meanwhile, in both cases, the local flow velocity inside the outlet pipe (at about 0.65 m/s) is larger than the mean velocity of 0.5 m/s due to flow contraction at the outlet pipe.

## EFFECTS OF INSTALATION POSITION ON FLOW DISCHARGE

As flow sensors send the beam at a certain angle against the flow direction, they rely on partial flow field data to obtain the measurement. In this study, the difference in the sensor measurement from the true cross-sectional average velocity (which is used in flow rate calculation) is assessed from CFD model results by comparing corrective factor K_{c}. Since velocity fields are known from CFD simulations, the cone-like volume average velocity can be calculated with knowing the emission angle, the range and the beam width, and it is regarded as V_{m.} Besides installation positions, several factors, including manhole shape, water level, and water velocity are believed to affect flow meter measurements and are taken into considerations as well. To investigate the influence, corrective factors in various positions were compared where positions are present as x/D, see Figure 7.

In Figure 7, locations are shown by x/D and the region from x = 0 to x = 2.5D is the manhole junction where sensors should not be placed. Upstream branches are shown in the left half while downstream branches are shown in right half starting from x = 2.5D. Additionally, (a) and (c) show the situation in type 1 manholes where (b) and (d) represent the manhole 2.

As shown, K_{c} values experience a similar variation trend under various conditions in two types of manholes. When the site is arranged at the upstream branch, K_{c} keeps a relatively stable level even when the sensor is very close to the manhole, because the emission signal points at the upstream direction and effects of sudden expansion have only a small role in affecting sensors. When the site moves to the downstream branch, K_{c} experiences drastic fluctuation due to multiple factors. If a flow meter is arranged near the manhole at the downstream direction (x = 2.5D − 6.5D, i.e. the distance from the manhole is less than 4D), the error in the Doppler measurements increases when the signal's conical beam cuts into the manhole volume. The maximum error can reach up to 40% when the installation site is around x = 4.5D − 5.5D downstream of the manhole. With farther distances from manholes (more than 4D or x > 6.5D), the sensor is affected mainly by sudden flow contraction effect in the outlet pipe, and K_{c} falls to its lowest point. Eventually, K_{c} goes back to normal value with flow development at a distance not less than 10D (x > 12.5D).

The variation of flow regimes related to water depth is also contributing to affect flow meters. Specifically, the corrective coefficient in a shallow surcharged depth (S = 0.5D) is lower than that in deeper conditions where the large recirculation is formed. Two deeper conditions (S = 1D and S = 3D) show little difference, see Figure 7(a) and 7(b). From Figure 7(c) and 7(d), it is found that K_{c} rises with reduction of flow velocity in both types of manholes. Additionally, the geometry characteristics of manhole benching also exert an influence. At a distance of around 5D downstream (or x ≈ 7.5D), the velocity field is closer to a fully developed flow field in a type 2 manhole than a type 1 manhole due to the effect of the contraction.

Compared to the downstream branch, K_{c} in the upstream branch does not vary much, which means the measurement is more reliable. However, sometimes the sensor has to be arranged in the downstream pipe, for example, to acquire total flow rate when there is additional inflow. In the circumstances, aiming the signal at the downstream direction rather than the normal is considered as an alternative choice and was also suggested by Sigma insight user's guide. This installation effect was investigated and the results are shown in Figure 8.

Figure 8(a) shows the emitted beam with regular and the reverse direction, where Figure 8(b) shows the effect of reverse installation at downstream branch and the annotation of B represents the situation with adjusted beam direction. As shown, with reversed installation, the beam will no longer enter the manhole region and the sensor is only influenced by the sudden contraction effect, which reduces the error from over 40% to around 5% at a distance of 0–5D (x = 2.5 − 7.5D). With a greater distance (x > 12.5D), the K_{c} shows little difference with two installation methods.

## SUMMARY AND CONCLUSIONS

In this study, three-dimensional air-water two-phase computational simulations were carried out for discharge measurement, and the homogeneous free surface model was employed with standard k-ɛ model. Installation positions of the flow meters, manhole geometries, water depth and velocities were considered as variables. From the current study, the following results are obtained. Firstly, manholes of different benching style present their distinct characteristics in flow regimes. Large recirculation eddies along the boundaries are found in type 1 manhole, where type 2 manhole effectively reduces the effect of sudden expansion and contraction. Flow patterns influenced by water depth were investigated and compared as well. Secondly, less interference is brought to flow meters at the upstream branch, as the corrective coefficient K_{c} only varies slightly. Therefore, the upstream branch is recommended for installation. In the downstream outlet pipe, sensors are mainly influenced by the sudden flow contraction effects. However, if sensors are not far enough from manholes (less than 4D in the downstream pipe), part of beam would enter the manhole region, causing additional errors. Up to 40% of errors were found at a distance of 3D inside the downstream pipe. To avoid this influence, aiming the signal at the downstream direction rather than the normal is recommend and the error will be reduced to around 5%. In addition, upstream branch and at least 10D from manholes in the downstream branch is suggested to guarantee the reliability of values of corrective coefficients. This study also confirms the capability of CFD as a powerful tool to predict flow regime in manholes and to investigate installation effects in flow measurements.

## ACKNOWLEDGEMENTS

This research was supported by the National Natural Science Foundation of China (No. 51678337) and the Tsinghua University Initiative Scientific Research Program (No. 2014z21028, No. 20173080016), and Natural Sciences and Engineering Research Council (NSERC) of Canada. The first author acknowledges the support from China Scholarship Council (CSC).

## REFERENCES

*.*