In this paper, we observe the over-weir flow pattern and drainage capacity of the piano key weir through physical model tests, and analyze the advantages of the piano key weir in terms of drainage compared to traditional thin-walled weirs (Jiang et al. 2019). Due to the complex flow pattern of the weir, the model test alone cannot fully analyze its superior drainage efficiency mechanism. numerical simulation is used as a supplement to study the drainage characteristics in terms of flow pattern and flow velocity, and research the mechanism for improving the drainage of the weir, so as to provide a reference for the optimization of the weir body shape and parameter sensitivity analysis.

#### 2 Physics Model Experiment

#### 2.1 Experimental Setup

The experimental device was built in the hall of Tiexinqiao test base of Nanjing Hydraulic Research Institute, and the experimental device consisted of water measuring weir and water tank, as shown in Fig. 2 below. During the experiment, the water from the groundwater reservoir is pumped to the upstream water measuring weir, and the water flow is stabilized by the water measuring weir free overflow sink, and finally the water flow is stabilized again by the elimination wall to the downstream sink, and the water flows through the sink to reach the model of the piano key weir, and then the overflow flows through the model and finally flows into the groundwater reservoir through the sink, forming a circulatory system throughout.

Fig. 2. Experiment layout

The model of the piano key weir is made of 3 mm organic plastic board, and the specific parameters are shown in Table 1. The model is 6 inlet chambers and 5 outlet chambers with inverted A-type inverted structure upstream and downstream, and the model is installed in the middle of the 16 m-long downstream flume, and the model centerline coincides with the flume centerline in the incoming flow direction, and the model is spaced 0.81 m from both ends of the flume to the left and right. The experiments were conducted to study the hydraulic characteristics of the weir and to compare the discharge capacity with that of the traditional thin-walled weir, and reasonable body parameters were selected according to the conclusions of previous studies by experts and scholars (Lemperiere and Guo 2005): the spreading ratio L/W = 5.34, the tangent of the upstream and downstream inversion angle Tan Si = 0.53, and the tangent of the upstream and downstream inversion angle Tan So = 0.53. Tan So = 0.53, upstream/downstream inversion ratio Bi/Bo = 1.06, inlet/outlet width ratio Wi/Wo = 1.23, and weir height to weir width ratio P/W = 0.16.

Table 1. Dimensions of the piano key weir model (Unit: m)

#### 2.2 Experimental Results

In order to observe the flow pattern and discharge capacity of the piano weir through physical model tests and to compare it with the traditional thin-walled weir, 12 sets of water crossing experiments were conducted throughout the experiment, and data such as flow rate, syringe reading, and travel velocity were measured and recorded, and the head on the weir was obtained from the water level syringe reading, and the total head on the weir was calculated from the measured travel velocity. The ratio of the total head on the weir to the weir height can be obtained by combining the total head on the weir with the weir height, which is known from the previous measurements of piano key weir. The specific data are shown in Table 2 below.

Table 2. Experimental data table

In order to compare the overflow capacity of the piano key weir and the traditional linear weir, it is assumed that the position of the piano key weir in the flume is replaced by a thin-walled weir of equal width and height (Qi et al. 2018), and the overflow flow of the thin wall is projected with the same total head on the weir, and the ratio of the flow of the piano key weir to the flow of the thin-walled weir is expressed as the overdischarge ratio: r, r ¼ QPKW QS and the over-discharge ratio of the two is shown in Table 3 below.

The discharge expression of the piano key weir is similar to the thin-walled weir flow equation through the dimensional analysis, and the flow equation of both is as follows.

$$Q\_{PKW} = C\_d W \sqrt{2g} H^{3/2} \tag{1}$$

$$\mathcal{Q}\_{\mathcal{S}} = m\_0 W \sqrt{2g} H^{3/2} \tag{2}$$

where: Cd is the piano key weir flow coefficient, W is the piano key weir width, H is the total head on the piano key weir, H ¼ h0 þ V2 2g, h0 is the head on the piano key weir, V is the traveling flow rate, m0 is the thin walled weir flow coefficient, m0 ¼ 0:4034 þ 0:0534 H P1 þ 0:0007 H , P1 is the sum of the weir height and the base height, P1 ¼ P þ Pd.

Table 3. Over-discharge ratio of piano key weir and thin-walled weir

#### 2.3 Analysis of Drainage Capacity

In order to compare the discharge capacity of the piano key weir and the traditional thin-walled weir, the flow rate of the piano key weir and the thin-walled weir at the same head on the weir, and the flow coefficient of the piano key weir and the thinwalled weir at the same head on the weir are made as follows, and the relationship between the over-discharge ratio and the head on the weir and the weir height ratio is made as follows (Barcouda et al. 2006) which can visually show the comparative relationship between the discharge of the piano weir and the thin-walled weir.

Fig. 3. The relationship between the piano key weir and thin-walled weir flow coefficient, flow rate and total water head on the weir

Fig. 4. The relationship between over-discharge ratio and H/P

As can be seen from Fig. 3, the flow coefficient and discharge volume of the piano key weir are significantly higher than those of the thin-walled weir at the same total head on the weir, and the piano key weir has a better discharge capacity than the thinwalled weir. As can be seen from Fig. 4, the piano key weir has a high discharge efficiency than the thin-walled weir, and the overflow ratio is basically maintained at 3– 4 times, with the increase of upstream flow, the overflow ratio of the piano key weir shows a decreasing trend, the decrease of the piano key weir discharge capacity is because the overflow effect of the outlet chamber and the side weir of the inlet chamber receives a weakening when the upstream flow increases, but overall the piano key weir has a better overflow capacity compared with the thin-walled weir.

### 3 Mathematical Model Setup and Result Analysis

#### 3.1 Model Building and Numerical Processing Methods

#### 3.1.1 Model Setup

In order to study the hydraulic characteristics of the discharge of the piano key weir in more detail, the above physical model was used as a prototype and modeled 1:1 using software, and finally imported into numerical simulation software for simulation calculations. The simulated calculation model of the piano key weir is as follows, which consists of upstream channel, weir body and downstream channel (Li et al. 2015). The length of the piano key weir body in the direction of water flow is 630 mm, the inlet court is 135 mm, the outlet court is 110 mm, and the width of the weir body is 785 mm. In order to ensure the smooth flow over the weir and better simulate the water tongue as well as the actual situation, the length of the upstream channel is 800 mm and the length of the downstream channel is 800 mm in the calculation model 2000 mm.

The grid quality, quantity and division method have an important influence on the accuracy of the simulation results. In the numerical simulation of pian key weir, the total area grid number is 387.7946 million, the calculation file size asks 12 GB, the finish time is 50 s, and the calculation time is about 60 h, among which the grid number of PKW area is 107.2537 million and the grid size is 0.005 m.

The simulated area is divided into the upstream channel area, the pian key weir area and the downstream channel area according to the overall area and the piano key parts. The upstream channel area and the downstream channel area have relatively regular flow patterns, so the grid is relatively sparse. The weir area and the area behind the weir are the piano key parts of the study, so a denser grid is generated to ensure the accuracy of the simulation (Li et al. 2016).

Fig. 5. The mathematical model setting of the piano key weir

#### 3.1.2 Turbulent Flow Equation and VOF

Combined with the flow characteristics of the experimental piano key weir, the turbulent flow mathematical model is selected as the RNG k-e equation model (Jiang 2020). The RNG k-e equation is a mathematical model derived using the statistical method of reformed group theory for the instantaneous N–S equation, compared with the standard k-e model, the RNG k-e model adds a term to the e equation that reflects the mainstream time-averaged strain rate and improves the accuracy of high-speed motion (Zhao et al. 2020). In addition, the RNG k-e model takes into account the effect of vortices on turbulent flow and eliminates the singularity of the standard k-e model, which combined makes the RNG k-e equation more accurate and reliable in simulating jet diffusion, etc. The k and e equations are as follows.

$$\frac{\partial(\rho k)}{\partial t} + \frac{\partial(\rho k u\_i)}{\partial \mathbf{x}\_i} = \frac{\partial}{\partial \mathbf{x}\_i} \left[ \frac{\mu\_r}{\sigma\_k} \frac{\partial k}{\partial \mathbf{x}\_i} + \mu \right] + G\_k - \rho \varepsilon \tag{3}$$

$$\frac{\partial(\rho\varepsilon)}{\partial t} + \frac{\partial(\rho\varepsilon u\_i)}{\partial \mathbf{x}\_i} = \frac{\partial}{\partial \mathbf{x}\_j} \left[ \frac{\mu\_t}{\sigma\_\varepsilon} \frac{\partial \varepsilon}{\partial \mathbf{x}\_j} + \mu \right] + \rho C\_1 \mathbf{S} \varepsilon - \rho C\_2 \frac{\varepsilon^2}{k + \sqrt{\mathbf{v}\varepsilon}} \tag{4}$$

where: q is the fluid density, t is time, k is the turbulent kinetic energy, e is the turbulent kinetic energy dissipation rate, ui is the velocity component, xi, xj are the coordinate components, m is the viscosity, m ¼ l q, l is the coefficient of viscosity, rk ¼ 1:0, re ¼ 1:2, Gk is the turbulent kinetic energy generation term due to the average velocity gradient, Gk ¼ ltS2, S ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2EijEij q , Eij ¼ 1 2 @ui @xj þ @uj @xi , the coefficient C1 ¼ max 0:43; g g þ 5 h i, g ¼ Sk e , C2 ¼ 1:9, lt is the turbulent viscosity, lt ¼ qCl k2 e , Cl ¼ 1 A0 þ AsUk e , A0 = 4.0, As ¼ ffiffiffi 6 p cos/, / ¼ cos1 ffiffiffi 6 p x , / ¼ EijEjkEik ffiffiffiffiffiffiffiffiffiffiffi ð Þ EijEij p , U ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi EijEij þ Xij Xij q , Xij ¼ Xij 2eijkxk, Xij ¼ Xij eijkxk.

The flow pattern is complex during the release of the piano key weir, and the method VOF (Fan et al. 2022) is used in the capture of the free liquid surface, which is constructed using the volume ratio function F xi ð Þ ; t , and the F xi ð Þ ; t function is as follows.

$$\frac{\partial F}{\partial t} + \mu\_i \frac{\partial F}{\partial \mathbf{x}\_i} = \mathbf{0} \tag{5}$$

When: F xi ð Þ¼ ; t 0, it means the place is water phase; when 0\F xi ð Þ ; t \1, it means the place is water-gas phase intersection; when F xi ð Þ¼ ; t 1, it means the place is gas phase.

#### 3.1.3 Model Boundary Settings

Set the boundary conditions of the model before simulation, set the specified pressure at the upstream inlet, and set the fluid elevation; set the outflow at the outlet: the two walls and the bottom are set as non-sliding wall; the top is set as atmospheric pressure inlet boundary condition, see Fig. 5 above for the specific settings (Li 2020).

#### 3.2 Numerical Simulation Results and Analysis

#### 3.2.1 Drainage Capacity Model Validation

In order to verify the numerical simulation of the discharge capacity of the piano key weir, by giving different working conditions of the head on the weir, the respective discharge volume was calculated by simulation, and the error between the simulated and experimental values was calculated, the experimental data and the data derived from the simulation are shown in Table 4 below, and Fig. 6 can more visually reflect the error between the experimental and simulated values.

Table 4. Data table of experimental and simulated values

By comparing the flow value and simulation value of this model experiment, it can be found that the flow value calculated by numerical simulation of head on the same weir is basically linearly distributed with the experimental value and the values of the two curves are very close, and the error values of both are distributed around the straight line with slope k = 1, and the error values are between the two straight lines of −5% and +5%, and the results of numerical simulation are more reliable and meet the requirements of numerical simulation of hydraulics.

### 3.2.2 Flow Analysis

The following figure shows the profiles of the inlet chamber and outlet chamber of the weir and four profiles in the direction of the incoming flow of the weir. The flow pattern has the characteristics of ternary flow. When the water flows through the piano key weir, the water flows partly from the inlet, and the water flows downstream along the bottom plate in the inlet chamber and freely overflows to the downstream sink at the outlet, and the water flows in the inlet chamber also overflows from the side weir to the outlet chamber. Some of the water flows in from the exit overflow, collide and mix with the water flowing down the side weir of the incoming palace chamber, flow downstream along the bottom plate of the outgoing palace chamber, and are ejected at the exit. The overall flow over the weir is a mixture of forward and lateral flow, the flow pattern is complex, and the water flows collide and mix with each other, the flow pattern of the whole process can be seen in Fig. 7 below.

(c)Profile in the direction n of water flo ow

Fig. 7. Schematic diagram of the flow pattern of water over the weir of the piano key weir

During the simulation, it was found that when the flow rate of water over the weir was small, the water surface line upstream of the piano key weir was basically the same as the water surface line of the flume, and the water flowed smoothly through the piano key weir, producing only a small drop in water level at the entrance and exit of the palace, and it could be found from the profile feature map in the direction of incoming flow that the water tongue overflowing from the side weir to the exit palace chamber was detached from the side wall, and the lateral water flow was free to flow out, and the lateral water tongue was thin, and the adjacent side walls were free to flow out Tongue of water does not interfere with each other into the exit palace room, in the middle of the front of the exit palace room to stimulate the final convergence of water outflow. The flow pattern at the exit of the exit chamber is more complex, the water jet at the exit while the water will spread down and left and right, and again collide and mix with the water flowing down from the overflow of the incoming palace, the water diffusion at the exit of the exit chamber is intense, and the flow pattern is chaotic.

### 3.2.3 Flow Rate Distribution

The flow pattern of the water over the weir is complex, and the velocity of the water will change when passing the weir. The velocity contour clouds of the inlet and outlet chambers are derived from the numerical simulation, which can reflect the magnitude of the fluid velocity visually. From the simulation results, it can be seen that the upstream of the weir is smooth and the velocity is small. The water flows into the inlet chamber first and the velocity starts to increase, and then picks up at the end of the inlet chamber in the form of a water tongue (Fig. 8).

Fig. 8. Schematic diagram of the inlet and outlet speed of the water head on different weirs

From the above figure, it can be seen that the overall flow velocity of the piano key weir is small at low head, and the water can flow smoothly and evenly along the palace chamber and side walls, and finally overflows out from the weir at the outlet, with good overall flow. With the increase of the head on the weir, the flow velocity of the water over the weir also increases, indicating that the increase of the head on the weir can increase the flow velocity of the water over the weir. However, while the head on the weir increases, some areas with lower flow velocity appear at the entrance and exit of the palace, and these areas obstruct the water flow under the action of the inertia of the water flow, which reduces the drainage capacity of the piano key weir, which is the reason why the head on the piano key weir increases and the flow velocity increases but the drainage capacity decreases.

### 4 Conclusion

As a new type of labyrinth weir, the piano key weir has a good application prospect in flood control and drainage. In this paper, the flow pattern and discharge capacity of the piano key weir are studied through physical model tests, and the discharge capacity of the piano key weir is compared with that of the thin-walled weir and the over-discharge ratio of the piano key weir. The numerical simulations of the discharge capacity of the piano key weir were compared with the physical simulations, and the flow patterns matched with the experimental flow patterns, which verified the reliability of the simulations. The simulation analysis of the flow velocity of the piano key weir shows that the increase of head on the weir can increase the flow velocity of the water over the weir, but the increase of head on the weir also decreases the discharge efficiency, which provides a reference for the optimization of the piano key weir shape to improve the discharge efficiency in the future.

Acknowledgements. This study is supported by Central-level Public Welfare Research Institutes Basic Research Business Expenses Special Funds (Y121005).

### References

Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# Analysis on Throughput Capacity of Water-Saving Ship Lock in Simulation Method

Ying Tang(&) , Chunze Liu, Fengshuai Cao, and Jianping Shang

CCCC Water Transportation Consultants Co., Ltd., Beijing, China<EMAIL_ADDRESS>
Abstract. When the double-line water-saving ship locks operate in the mode of filling and emptying mutually, the filling water process of one lock chamber and emptying water process of the other one are carried out at the same time, thus the situation of chambers waiting for each other is inevitable. Besides, the variation of ship navigating speed and safety interval time between two adjacent ships may have a more significant impact on the operation efficiency of the ship lock, which cannot be ignored. Combined with the actual condition of a planned lock on a canal in China, the throughput capacity and operation efficiency of the double-line water-saving ship locks under the mode of filling and emptying mutually are studied. A coupled operation simulation model of double-line locks is established, in which the mode of filling and emptying water mutually or independently is adopted. In the model, the whole operation processes of the locks are simulated. The simulation results show that the throughput capacity of the planned ship lock is reduced by 5.6%–7.8%, and the average lockage time is increased by about 10.8%, when comparing the mode of filling and emptying water mutually with independently. Besides, using average value of speed and safety interval time of ships is acceptable when doing research on the throughput capacity and operation efficiency of ship locks. The achievements can provide technical support for the analysis of the throughput capacity and operation efficiency of the water-saving ship lock.

Keywords: Water-saving ship lock Throughput capacity Operation process of ship lock System simulation

### 1 Introduction

The operation of ship locks on the inland river and canal in China is often restricted by the shortage of water resources, so it is necessary to build water-saving ship locks in some places. There are four main types of water-saving ship locks: the ship lock with a water-saving pool, the multi-level ship lock without waiting for navigation, the doubleline ship locks filling and emptying water mutually, and the ship lock with an intermediate channel (Chen et al. 2021). At present, the water-saving ship locks that have been put into operation in China mainly include the third and fourth line ship locks in Changzhou and the second and third lines in Feilaixia. A number of new water-saving ship locks are under planning and construction (Dongle et al. 2020).

The operation experience of the third and fourth line ship locks in Changzhou shows that the throughput capacity and operation efficiency of water-saving ship locks are affected by filling and emptying water mutually.

When the double-line water-saving ship locks operate in the mode of filling and emptying mutually, the filling water process of one lock chamber and emptying water process of the other one are carried out at the same time. On the premise that other operating parameters of locks are the same, because the number of ships passing through the two locks may be different in one lockage, the situation of chambers waiting for each other is inevitable, which affects the operation efficiency of the two locks. In addition, in the mode of filling and emptying mutually, the operation of the double-line water-saving ship locks are coupled with each other. Compared with the mode of filling and emptying independently, the fluctuation of ship navigating speed and interval time may have a more significant impact on the operation efficiency of the ship lock, which cannot be ignored.

The current research of water-saving ship locks focuses on the hydraulics of water conveyance system (Chen et al. 2021), the calculation of water-saving rate (Dongle et al. 2020) and benefit analysis about water-saving (Yang and Chen 2013). But there is almost no research on the impact of water-saving mode on the throughput capacity and operation efficiency of ship lock.

Combined with the condition of a planned lock on a canal in China, the throughput capacity and operation efficiency of the double-line water-saving ship locks under the mode of filling and emptying mutually are studied. Based on the simulation model of double-line locks which filling and emptying independently, a coupled operation simulation model of double-line locks is established, in which the mode of filling and emptying mutually is adopted. The whole operation processes of the locks are simulated, under two set of ship types and proportions. Indexes such as throughput capacity, chamber occupy rate and one lockage time are collected in the model, statistic data are compared and analyzed.

### 2 Building, Verifying and Validating Simulation Model

#### 2.1 Model Scope and Boundary

The model includes the anchorage, connecting section, approach channel, berthing structure, lock head at the upstream and downstream and lock chamber of the doubleline locks. The upper and lower boundaries of the model are the upstream and downstream anchorages of the ship lock.

#### 2.2 Lockage Process

Lockage process in the mode of filling and emptying water independently and mutually are shown separately in Fig. 1 and Fig. 2.

Fig. 1. Lockage process in the mode of filling and emptying water independently

Fig. 2. Lockage process in the mode of filling and emptying water mutually

#### 2.3 Main Algorithms and Basic Assumptions

The model specifies the ship lock for a ship, according to the state of the double-line ship locks (upgoing or downgoing). When the ship lock allows ship to wait at waiting section, the position of the ship in the lock chamber and order in the queue are determined according to the ship arrangement algorithm, and then ships of one same lockage are sent to the waiting section. After that, the whole process of ships passing through lock are simulated. The ship arrangement algorithm is shown in Fig. 3, which is based on the two-dimension packing algorithm. For details, please refer to the ship arrangement algorithm for single lock adopted by Shang et al. (2011) and Liu et al. (2020).

Fig. 3. Ship arrangement algorithm

The basic assumptions of model are listed below:

(1) The target of the model is to calculate the capacity of the ship lock. In order to ensure the full load operation of the ship lock, there should be enough ships waiting for lock in the anchorage.

#### 2.4 Statistic Data and Key Performance Indicators

These data are collected: total number of ships passing through single lock upstream or downstream, total number of lockages, total number of bulk ships, total number of container ships, total DWT of bulk ships, total container capacity of container ships, average DWT of one lockage, the occupy rate of chamber, average number of ships per lockage, average lockage time, and average number of lockages per day.

These key performance indicators are calculated: total DWT of ships passing through one-line lock upstream or downstream per year (A TEU is treated as 15 ton), one-way annual capacity of one-line ship lock, which equals to the total DWT of ships passing through one-lock upstream or downstream per year ship loading coefficient/ unbalanced coefficient of traffic volume, and one-way capacity of double-line ship locks.

### 2.5 Model Verification and Validation

The model is verified and validated using the upgoing data of the Three Gorges doubleline five-level locks in 2013. The plane dimension of lock chamber of each level in Three Gorges is 280 m 34 m (length width). The length of lock head is 50 m. The locks operate in one-way and ships wait at waiting section just before the lock head. Assume that ships enter and exit chamber in turn one by one, and the entering speed is set to 0.4 m/s, the exiting speed is set to 1.0 m/s. The safety interval time between two ships is set to 2 min. Ships are arranged in chamber according to the firstcome-first-serve rule, and ships are generated randomly following the same rule within a year. The unbalanced coefficient of traffic volume is 1.1, which is used to amend the total one-direction cargo ton or the total DWT of ships passing through one-line lock collected in the model.

The results of model verification and validation show that the simulation model has correct logic and can get reasonable results, which can be used for the next research.

#### 3 Simulation Experiment

#### 3.1 Experiment Scheme

The model does not simulate the process that the ship lock cannot operate (accident, maintenance, flood and dry season, etc.), so the simulation model runs 340 days per year and 22 h per day. The warmup period of the model is 10 days. The experiment scheme is shown in Table 1 below.

Table 1. Experiment scheme

In Table 1, "no variation" means that the ship enters and exits the lock at the base value of speed and safety interval time. And "variation ±30%" "variation ±50%" means that ship speed and safety interval time are randomly sampled from 70%–130% of the input basic value and 50%–150%, which are decided when ships are generated. Those random values are input in the model, but can only be treated as expected, because the actual speed and safety interval time of a ship will be affected by the speed of the front ship. When this ship has speed less than the speed of the front ship, or is more than 1.5 m away from the front ship, it will move at the preset speed. When this ship has higher speed than the front ship, and is within 1.5 m away from the stern of the front ship, it moves at the same speed as the front ship.

As a result, if input the same entering and leaving speeds in "variation" experiments as in "no variation" experiments, the average speeds of those two type of experiments are not the same for sure. To study the influence of variation, the average value of entering and leaving speeds are adjusted to be the same among all experiments, thus the input value is a little higher in "variation" experiment schemes.

#### 3.2 Input Parameters

#### 3.2.1 Plane Layout

The lock chamber is 300 m in length and 34 m in width. Considering the safe distance between the ship in chamber and the chamber wall and between ships, the length and width of the lock chamber for arranging ships are 280 m and 32.8 m (Fig. 4).

Fig. 4. Ship lock layout in the model

#### 3.2.2 Ship Type and Proportion

According to the history statistic data, length and width of ships of each type are ranges. As input in the model, each level of tonnage and container capacity are subdivided into three grades: ship length and width taking the lower limit of its range, taking the average value and taking the upper limit, and the corresponding proportion of each grade are 33%, 34% and 33% in its tonnage level or container capacity level. Besides, the DWT value of bulk ships is equal to its tonnage, the DWT value of container ships is equal to the container capacity (in TEU) 15t.

Some parameters of ships in the model are not considered, such as the height above the waterline and the loading rate (Table 2).

Table 2. Ship type and proportion input in the model

#### 3.2.3 Time Related Parameters and Other Inputs

The time of opening and closing gate are all 4 min. And the time of filling and emptying water are all 14 min.

The basic values of ship speed entering and leaving locks are 0.8 m/s and 1.2 m/s in "variation" experiments, 1.0 m/s and 1.4 m/s in "no variation" experiments. The actual speed of the ship entering and leaving the lock is randomly determined by the basic value and variation range. The basic value of the safety interval time between two adjacent ships entering and leaving the lock is 2 min. The actual value of a ship entering and leaving the lock are the same, and are also randomly determined by the basic value and variation range.

According to the ship lock design code in China, the ship loading coefficient is taken as 0.8 when there is no relevant statistic. The unbalanced coefficient of traffic volume is taken as 1.1.

### 4 Simulation Experiment Results and Analysis

In this study, the speed of the ship entering and leaving the lock and the safety interval time between two adjacent ships are the two main factors that may influence the throughput capacity and operation efficiency of ship locks, under the condition of filling and emptying water mutually or independently.

After preliminary analysis, the above factors mainly have impact on total number of ships passing through one-line lock upstream or downstream, total number of lockages, one-way annual capacity of one-line ship lock, one-way capacity of double-line ship locks and average lockage time, but have no impact on average DWT of one lockage, the occupy rate of chamber, average number of ships per lockage. The one-way capacity of double-line ship locks and the average lockage time can fully reflect the influence, so the two indexes are mainly analyzed. See Table 3 and Table 4 for simulation results.

Table 3. Simulation results of the one-way capacity of double-line ship locks

Table 4. Simulation results of the average lockage time in "no variation" experiments

### 5 Conclusions

(1) On the premise of the same time of filling and emptying water, the throughput capacity will be reduced if the double-line ship locks operate in the mode of filling and emptying water mutually compared with independently. The range of capacity reduction is related to the composition of ships, and the variation amplitude of ship speeds entering and leaving locks and safety interval time between two adjacent ships.

Acknowledgements. We appreciate the support from China Communications Construction Company (CCCC), which is our superior company. The CCCC pays great attention to scientific research and application, and try his best to support young research staffs in the company.

### References

Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# Applicability of the Blue Wave to the Canal from Villiers to Beaulieu

J. M. Deplaix(&)

AFTM, Paris, France<EMAIL_ADDRESS>
Abstract. The Blue Wave is a locking structure that allows simultaneous navigation in both directions of navigation, without stopping in most cases, and at a speed depending on the local topography.

Its principle has been described in an issue of PIANC Bulletin, N°108, september 2001.

It could be used, in lieu of a set of locks, on a Canal which is presently being improved to CEMT Class Va, far upstream from Paris, the Canal from Villiers to Beaulieu (Petite Seine, France).

It is possible to form 10 reaches of 1,000 m each, separated by doors (mitre or valve). The depth available in the existing borrow pits is sufficient for the navigation of the project boats, which have 31.9 m2 of wetted section.

By using the existing pits, which were dug in advance for improvement of this waterway, the structure very faithfully respects the current levels of these bodies of water, which avoids costly measures to restore the water table. In addition, the 2 upstream gates being non-overtopping, the non-overtopping dykes only total 2 km, instead of 16 km in the lock option.

These two points confirm that the proposed solution is more respectful of the environment and landscapes than the lock option. Thus, since the set speed of the concept is practically the optimum speed permitted by the cross-section of the canal, it can be said that the site of the Canal from Villiers to Beaulieu is optimal for the application of the Blue Wave principle.

Keywords: Blue-Wave Canal Lock Seine River Speed

### 1 Introduction

The Blue Wave is a locking structure that allows simultaneous navigation in both directions of navigation, without stopping in most cases, and at a speed depending on the local topography.

Its principle has been described in an issue of PIANC Bulletin, N°108, september 2001.

It could be used, in lieu of a set of locks, on a Canal which is presently being improved to CEMT Class Va, far upstream from Paris, the Canal from Villiers to Beaulieu (Petite Seine, France).

This paper will show that the proposed solution is more respectful of the environment and landscapes than the lock option. Thus, since the set speed of the concept is practically the optimum speed permitted by the cross-section of the canal, it can be said that the site of the Canal from Villiers to Beaulieu is optimal for the application of the Blue Wave principle.

### 2 The Blue Wave Concept

In cities, traffic lights are synchronised, so as to allow vehicles, running at a set speed, to travel without finding a red light. This is called Green Wave.

Similarly, on a canal, the Blue Wave concept enables craft to never stop, while encountering differences of elevation. If the Lock is akin to an elevator, the Blue Wave is an escalator. The difference of elevation is broken in a number of steps, each usually some 1 m high, and the reach varies up or down while the craft is moving, albeit at slow speed. In contrast, the craft does not move in a lock, and needs to have, between 2 locks, a large canal to ply sufficiently fast to compensate for this stop.

As can be seen on the figure, boats can navigate up and down at the same time, provided sufficient passing space is provided. Locks cannot do that. Another advantage, on shallow terrain, is that the Blue Wave can stick to the slope of the natural terrain, while, for a lock, there must be deep trenches or high embankments which, apart from being costly, are very conspicuous in the landscape. This is less and less accepted.

In natural rivers with rapids (less than 5 m fall), a Blue Wave can enable to navigate on a parallel canal across the rapids. This will be of use on African, South American, and Asian rivers, where there are many shallow rapids.

Similarly, where a bend is short-circuited, for hydraulics reasons the main flow has to continue to use the bend, and there is a slight difference of level between the two ends of the by-pass. With a set of Blue Wave gates at each end that alternatively open, it is possible to compensate for this slight fall, while the natural hydraulics of the river remain unchanged.

In canals, the cross section of the canal can be smaller with a Blue Wave than with a set of locks, and yet retain the same average speed on the whole voyage. A canal designed for 6.7 km/h is much cheaper to excavate than the one designed for 10 km/h.

Let us assume a 10 km canal designed for 10 km/h, with a 10 m high lock at the end. It takes roughly 1.5 h to cross both. 6.7 km/h on average, or 1.85 m/s.

A Blue Wave needs 10 km to overcome 10 m. At 1.85 m/s, this is 5400 s or 1.5 h, with a canal designed for 6.7 km/h only, thus a much smaller cross-section.

If the 12 gates needed for a Blue Wave are not more expensive than a 10 m lock, with all its concrete, then a Blue Wave is cheaper than a classical waterway.

The design speed depends on the local topography and the length of the craft.

### 3 Application to Bray-Nogent Project

#### 3.1 The Bray-Nogent Project History

In the eighties, the improvement of the Bray-Nogent waterway was already planned. It was thought possible to seize an opportunity and excavate a large gauge canal parallel to the existing Villiers-Beaulieu canal, the excavated material being needed to create the platform of a Nuclear Power Plant nearby. There was actually 8 borrow pits, so that the water table would not be impaired, but the Bray-Nogent waterway was deferred, and the borrow pits were left unused.

40 years later, the project is on the verge to be implemented, and a classical canal with one lock has been designed parallel to the Villiers-Beaulieu canal. This project is using the borrow pits, but the 4.44 m fall at the lock obliges to raise the banks of the new canal over 12 km (2 6 km), to deepen some borrow pits (4 km) and to take the actions necessary to stabilise the water table, a very touchy problem in this area.

#### 3.2 The Blue Wave Solution

It was thought possible to fruitfully apply the Blue Wave technique there:

By using the borrow pits, the structure very faithfully respects the current levels of these bodies of water, which avoids costly measures to restore the water table. In addition, only the banks of the 2 upstream cells need to be raised, and by 1 m only, against 16 km in the lock option, by up to 4 m!

These two points confirm that the proposed solution is more respectful of the environment and landscapes than the lock option.

Here, the set speed may be 2 m/s, i.e. 7.6 km/h, very close to the commercial speed permitted by the wet section of the canal.

It is possible to form 10 reaches of 1,000 m each, separated by collapsible doors (mitre or valve) with a feeding system from one reach to the other. The depth available in the borrow pits is sufficient for the navigation of the project boats (31.9 m2 of wetted section). For the economy of the system, it would be preferable, but not essential, for the width of the different reaches to be identical, and not to exceed 50 m at the water surface. In this case, the volume exchanged from reach to reach will be 25,000 m3 , since it is on average a section of 0.5 m that thus passes from one reach to the other.

The first two reaches are used to dampen level variations of the Seine in the reach of Beaulieu, between 60.60 (Normal Pond Level-RN/NPL) and 61.57 (Reference Water Level-LER/RWL). The following figures, extrapolated from VNF documents, show the kinematics for a downhill boat.

#### 3.2.1 Downstream Movement at Normal Pond Level

At NPL, at the green light, the boat (or the group of boats) enters reach 1 towards reach 2, both being at the upstream pond level, and while it travels in it at 2 m/s, the door pk0 closes. It then enters reach 2, since gate pk1 has remained open, and, as soon as it enters, this gate pk1 closes, while in synchronization (as soon as it is completely closed) reach 2 begins to empty into reach 3 with a flow rate between 50 and 100 m3 /s.

When the equality of levels is reached (duration approximately 360 s) the gate pk2 opens, and the boat passes into reach 3 which is then at elevation 60.10.

If a rising boat were in this reach, it can enter reach 2 before gate pk2 closes. This crossing operation can be carried out simultaneously, if the doors are wide enough (30 m), or in succession, under the control of lights, if they are narrower (18 m).

For the downstream boat, the gate pk2 closes as soon as any rising boat has crossed it, reach 3 empties into reach 4 until the levels are equal (59.60), at which time the gate pk3 opens to allow the passage of the boat in reach 4.

The operations are repeated step by step, with 5 crossing possibilities over the entire route.

#### 3.2.2 Downstream Movement in Flood Condition

If the Beaulieu reach is higher than the NPL, up to the RWL (or the Highest High Water), the first reach is used to dampen this variation:

At RWL, at the green light, the boat (or the group of boats) enters reach 1, and while it travels through it at 2 m/s, the gate pk0 closes, while in synchronization (as soon as it is completely closed) reach 1 begins to empty into reach 2 with a flow between 50 and 100 m3 /s. The excess volume is rejected downstream by dumping in the reach 3 above or around the gate pk2.

When the equality of levels is reached (duration approximately 360 s) the door pk1 opens, and the boat passes in the reach 2 which is then at the elevation 60.60. We are then in the same situation as before, see above the NPL conditions.

#### 3.2.3 Upstream Movement at Normal Pond Level

For rising boats, the principle is similar, and is explained within the figure for NPL conditions, see below:

If the Seine is at RWL or in full flood, gates pk10 and pk9 are open or anyway already at the same flood level, since the level in reach 9 is practically identical to that of the Seine RWL (56.58). In extreme flood, both reaches will be at flood level, possibly even reach 8.

At the green light, reach 10 and reach 9 are travelled at set speed by the upbound boat. As soon as gate pk9 is crossed, it closes and while the boat travels along reach 9, reach 8 empties into reach 9 until the levels are equal (57, 10, or higher), which then allows the gate pk8 to be opened in front of the rising boat, which can enter reach 8, and so step by step until pk0.

### 4 Conclusion

We can see that the site of the Canal de Villiers in Beaulieu is optimal for the application of the Blue Wave principle, since the set speed is practically the commercial speed allowed by the wet section of the canal.

The structure would be crossed in 5,000 s (1 h 23), while crossing the same canal with passing through a lock would last at best 5,400 s (1 h 30).

Regarding the waiting time in front of the structure, the maximum duration of a possible red light before entering the structure would only be 1,000 s (16 min 40 s), while the mathematical expectation of waiting in front of the lock would be 30 min (duration of ½ cycle), according to the Operation Programme.

By integrating the average of a possible wait, the passage with lock would last 2 h, and only 1 h 39 with the Blue Wave.

Thus, using a Blue Wave in Canal de Beaulieu would seem to be a better proposition than a Lock.

### Reference

Deplaix JM (2001) The Blue Wave, a new concept of waterways enabling to increase velocity or to reduce impact on environment. PIANC Bulletin, 108, Autumn 2001. French version. http:// aftm.free.fr/PromoL.htm

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# Benchmark of Turning Basin Options for the ECMT Class V Network of Nord-Pas-de-Calais (France)

Sebastien Page1(&) , Marc Mansuy2 , Katrien Eloot3 , Maxim Candries2 , and Roeland Adams1

1 International Marine and Dredging Consultants (IMDC) NV, Antwerp, Belgium<EMAIL_ADDRESS>2 Maritime Technology Division, Ghent University, Ghent, Belgium<EMAIL_ADDRESS>3 Flanders Hydraulics, Antwerp, Belgium<EMAIL_ADDRESS>
Abstract. The Nord-Pas-de-Calais Division of Voies navigables de France (VNF), the French Waterways authority, is preparing a master plan for the development of turning basins for its ECMT class V network. In this frame, IMDC has been asked to carry out a comparative analysis (benchmark) of the different designs of turning basins in France and elsewhere in the world and to propose design criteria adapted for future developments (for ships of 110 m and 135 m) on the Nord-Pas-de-Calais network. The first part of the study consisted in a desktop review of available national and international guidelines or recommendations on the subject of turning basins design. This helped building a better understanding of the needs in terms of geometry for safe and/or comfortable turning maneuvers. Technical studies of built or projected turning basins on the Nord-Pas-de-Calais network were also analyzed to refine the knowledge on local conditions. Based on the findings of the desktop analysis, interviews of European waterways authorities, international experts and skippers were carried out to further improve the understanding of the problem, both from the infrastructure side as well as from the users' side. On top of geometry concerns, the interviews tackled hydrometeorological constraints, operational and environmental aspects, auxiliary equipment, etc. From this, a draft technical reference system was proposed for future turning basins on the Nord-Pas-de-Calais network. It proposes two options, depending on whether the basin is located on two banks or on one bank only, and aims at offering each option in two safety and ease levels: a comfort level version, on which the turn must always be relatively easy, and a safety level version, on which the turn must always be possible, but with less ease. The designs were then tested using real time navigation simulations. Optimizations of some of the designs were also proposed to adapt to severe hydro-meteorological conditions. Finally, a decision tree has been developed to facilitate the selection of a design solution according to the local characteristics of the projected basin location on the network. This tool allows the selection of the geometry allowing the easiest turn possible according to the available space and the hydrometeorological conditions present on the envisaged site.

Keywords: Waterway infrastructure Turning basins Navigation Hydraulics Ship simulator

### 1 Introduction

The Nord-Pas-de-Calais ECMT Class V network will play a major role in linking the Canal Seine-Nord Europe to the ports of Dunkirk and the inland navigation network of Flanders and Wallonia (Belgium), and connected ports in the Scheldt-Rhine delta such as Ghent, Antwerp or Rotterdam.

The future commissioning of the Seine Nord-Europe Canal and the prospect of 24 h navigation should result in a significant increase in traffic, particularly of vessels of 110 m and 135 m.

The Nord-Pas-de-Calais Division of Voies navigables de France (VNF), the French waterways manager, is therefore preparing a master plan for the development of turning basins for ships of up to 135 m on the ECMT class V network. Within this masterplan, VNF has hired IMDC and its subcontractors Flanders Hydraulics (FH) and Ghent University to propose well suited geometries that can be applied in all locations and conditions on the network (Fig. 1).

Fig. 1. The ECMT class V Nord-Pas-de-Calais network (circled in red) in the Seine-Scheldt environment (source: VNF)

The network has a total length of 240 km and, on most of its length, has a width of 34 m at 3.5 m depth. It is situated in a rather highly urbanized environment. From a hydrometeorological point of view, the canalized rivers of the network (Deûle, Lys and Scheldt Rivers) can be host to significant currents while strong wind conditions (5 Bf and above) are more frequent at the coast (Dunkerque area) than more inland.

The proposed turning basin geometries shall be suited to all envisaged locations, with varying hydrometeorological conditions (current and wind), availability of (both or only one) banks for construction, environmental or land use constraints while guaranteeing satisfactory operational conditions and for limited costs. For each of the proposed designs, the study aims to define a minimum safety geometry allowing safe turning considered and a geometry with larger dimensions, allowing turning under better comfort conditions, always whatever the location and conditions considered on the ECMT class V network of Nord-Pas-de-Calais.

In a first phase, a desktop review of available national and international guidelines on the subject of turning basins design as well as of technical studies of built or projected turning basins on the Nord-Pas-de-Calais network is performed. Based on the findings of the desktop analysis, interviews of European waterways managers, international experts and skippers are carried out to refine the understanding of the constraints at stake. From this, propositions of well-suited geometries of turning basins are made. Finally, these geometries are tested on real-time navigation simulators and, in some cases, optimized.

### 2 Design Ships

The study focuses on ECMT Va class vessels of 110 m and 135 m (the latter is named "Va+" below). The vessels studied are container ships since this type of vessel is the most constraining when turning in windy conditions. The draft in loaded condition is taken equal to that of a loaded bulk carrier (2.5 m) in order to guarantee the validity of the simulations for loaded bulk carriers as well (since container ships generally have smaller drafts) (Table 1 and Fig. 2).

Table 1. Main dimensions of the design ships

Fig. 2. A 110 m-long ship on the ECMT class V Nord-Pas-de-Calais network

It should be noted here that on canals or canalized rivers with relatively weak current (which is the case of the study area), a ship can always turn empty except in exceptional cases. Exceptions are either rare (diversion of deliveries, unexpected and prolonged closures of the channel or of a lock) or limited to bulk carriers and avoidable (bulk loading generating dust settling in the deckhouse).

In terms of steering aids, both design ships are equipped with bow thrusters. On European waterways, this type of equipment is mandatory on any vessel longer than 110 m (Va+ class in this case) and it is present on the majority of current Va units.

### 3 Literature Review

The first step of the literature review consisted in studying recommendations related to turning basin design in national and international guidelines and recommendations.

The sections related to turning basins in the Dutch (RWS 2017), German (BMVBS 2011), French (Ministère de l'Équipement 1995), Chinese (PIANC 2019), Russian (PIANC 2019) and American (USACE 2006) guidelines were studied as well as in the PIANC InCom WG 141 recommendations for the design of inland waterways (PIANC 2019). It is worth noting that the main features of national guidelines in relation to turning basins design are recapitulated (and translated) in the annexes to the WG 141 report.

The guidelines which are more applicable to the studied case are the Dutch and the German guidelines as they both target the design ships of the study. The French directive, which is of application in the present case, does not make recommendations pertaining to turning basins. Other consulted guidelines are less applicable in the present case as, for instance, some consider sea going ships only (US guidelines) or ships with much lower maneuverability or sailing on rivers with much stronger current (Chinese guidelines).

For waterways of medium traffic density, which is the case of the studied network, the Dutch guidelines recommends circular geometries with a diameter of 1.2 L (L = length of the ship). It must be noted that this is applicable to canals or rivers with a current lower than 0.5 m/s which is the case in more than 95% of the time in the study area.

On the other hand, the German guidelines recommend using basins of trapezoidal shapes. The case of 110 m and 135 m inland ships is specifically addressed in the guidelines. For both ships, a distance from the waterway axis to the small base of the trapeze equal to the length of the ship (1 L) is proposed (see Fig. 3). No indication is given for the dimension of the larger base or for the angles of the trapeze.

Fig. 3. Turning basins dimension for 110 m and 135 m ships in the German guidelines (L: length of ship)

The PIANC recommendations build on the above-mentioned guidelines and propose a dimension of 1.2 L (for a quality of driving C1 ) with no indication on the shape of the basin (circular or trapezoidal) (see Table 2). The size of the basins should be chosen according to the targeted level of accessibility (quality of driving). The report however acknowledges the presence of turning basins of 1.15 L (and less) in Europe.

Table 2. Minimum width of turning basins (including safety allowances) as a factor of ship dimension from existing guidelines (PIANC 2019). Minimum widths for sheltered water and canals are circled in red.

The PIANC recommendations (PIANC 2019) also indicate that hydrometeorological conditions (wind and current) must be taken into account. A formula is suggested for lengthening the basins of rivers with significant current. This formula is based on the hypothesis of a drift not compensated by the pilot, which is generally not the case during a turning maneuver in a confined environment such as a canal or river.

1 Quality of driving C corresponds to a strongly constricted drive, as opposed to quality of driving A (nearly unrestricted drive) or B (moderate to strongly restricted drive) (PIANC, 2019).

The formula is therefore not applicable in the context of the study as it would lead to excessive basins lengths.

In a second phase, existing or studied turning basins on the ECMT class V network of Nord-Pas-de-Calais were studied. This helped better understand the constraints to be taken into account for the design of turning basins in the study area (wind, current and lack of available space, mainly). In the reviewed studies, the proposed geometries were either circular or trapezoidal with dimensions ranging from 1.1 L to 1.3 L.

It is worth noting that, although most studies acknowledge the interest of keeping the turning basins outside of the navigation channel as much as possible, all proposed designs integrate the entire channel (in order to limit the excavation costs, and to avoid additional expropriation costs). This is also true for most of the existing turning basins on the Nord-Pas-de-Calais network.

Amongst the reviewed turning basins studies, the report of a turning basin project in Arques (FH & Ghent University 2017) for ships of 135 m and 143 m on either circular or trapezoidal geometries supported by navigation simulations helped better evaluate safety and ease level of the turns on such geometries and under the hydrometeorological conditions of Nord-Pas-de-Calais.

Finally, a short analysis of the existing turning basins (geometries, dimensions, etc.) was also carried out, to serve as input when considering upgrades (enlargement) of existing turning basins.

### 4 Interviews of Skippers, Waterway Managers and Experts

With the knowledge acquired in the previous phase, a questionnaire was drafted to refine the understanding of the problem by means of interviews of waterways authorities, international experts, and skippers. In total, seven employees of waterways authorities (VNF in France, DVW and SPW in Belgium and RWS in the Netherlands), six international experts and six skippers, from various countries have been interviewed. This enabled a better understanding of the problem from both the side of the user as well as the side of the infrastructure provider. Information related to bank protection for turning basins, equipment (signaling, lighting, mooring, etc.), waterway maintenance and management (dredging, impact from and on traffic, etc.) was also collected.

Most experts or waterway managers referred to Dutch, German or PIANC guidelines and to circular or trapezoidal geometries with dimensions of 1.2 L to 1.3 L being the most commonly cited options. Many also pointed to the fact that ship maneuvering simulations are recommended by most guidelines in case of strong current or wind. There was a wide consensus on having a depth equal to the depths of the waterway, with many pointing to the fact that large under keel clearances (UKC) have a positive impact on the ease of the turn.

Skippers tend to prefer circular geometries for ease of maneuvering but confirm that trapezoidal geometries are also interesting options. Moreover, they are often obliged to turn in much narrower basins and mention that basins of 1.1 L width or less are not uncommon.

### 5 Proposition of Geometries Suited for the ECMT Class V Network of Nord-Pas-de-Calais

From the information collected above, two main designs have been proposed: a circular shape for situations where both banks of the canal or canalized river can be used and a trapezoidal shape when the turning basin can only be built on one bank of the waterway. For both options, two sizes are proposed based on information collected in the previous phases of the study: a larger one which is expected to allow comfortable turns in all conditions and a smaller one, which is designed to be sufficient to allow turns, though with less ease.

#### 5.1 Option N°1: Circular Geometry, Using Both Banks of the Waterway

A circular geometry has the advantages of allowing simpler (circular) maneuvers while keeping excavation volumes limited. It also is the most commonly encountered geometry on the Nord-Pas-de-Calais network and its users are therefore very well accustomed to it. The main disadvantage of this solution is the total interruption of traffic when a turn is performed, regardless of the size of the turning ship. If such interruption is deemed unacceptable, a single bank solution (trapezoidal) should be considered.

Both small and large sizes of the proposed circular geometry are shown in Fig. 4.

Fig. 4. Proposed circular geometry for 110 m ships using both banks of the waterway, small size (left) and large size (right). The channel is shown in blue and the area to be excavated in hatching

#### 5.2 Option N°2: Trapezoidal Geometry, Using Only One Bank of the Waterway

The advantages of this option are mainly land use (and budget) related. Indeed, it is the solution that requires the least amount of space when the basin must be located on a single bank and therefore potentially minimizes excavations and land acquisitions. Also, by being positioned off-center, this geometry does not imply a systematic interruption of the traffic during turns, at least not during the turns of ships of smaller dimensions than those of the design ship.

On the downside, the two-stage maneuver, which must be carried out on this type of basin, is more complex and more time-consuming than the one-stage circular maneuver, but it is nevertheless commonly practiced by all skippers. Finally, this trapezoidal solution is not yet widely used on the Nord-Pas-de-Calais network and the services in charge of waterway maintenance might have to get accustomed to this new design. The skippers should not encounter major difficulties in using such basin, since they are already used to turning in various types of geometries (wide portions of the waterway, junctions, etc.).

Both small and large sizes of this geometry are shown in Fig. 5.

Fig. 5. Proposed trapezoidal geometry for 110 m ships using only one bank of the waterway, small size (left) and large size (right). The channel is shown in blue and the area to be excavated in hatching

The base angles of the trapezoid are chosen based on results of navigation simulations on ships of 135 m on similar geometries in the study of the turning basin in Arques cited above (FH & Ghent University 2017).

### 6 Check of Accessibility and Optimization of the Proposed Geometries by Means of Real-Time Navigation Simulations

All proposed geometries have then been tested on the real-time navigation simulators of Flanders Hydraulics (FH) in Antwerp, Belgium.

The parameters of the study (ship classes, geometries, hydrometeorological conditions, basin positioning, etc.) are numerous and the number of possible scenarios (several thousands) greatly exceeded the material possibilities of the study. A twophased approach was therefore used for the real-time simulations: a first phase of exploratory simulations, during which the impacts of the different criteria were analyzed, and a second phase, during which the most relevant scenarios (key scenarios) were studied.

#### 6.1 Results of the Exploratory Phase

#### 6.1.1 Analysis of the Impact of the Simulation Parameters (Current, Wind, Ship Draft, etc.)

#### <IP_ADDRESS> Impact of the Hydrometeorological Conditions

The selected current velocities and wind speeds for the simulations correspond to strong but not extreme conditions (values not exceeded 95% of the time). Currents up to 0.4 m/s and wind speed up to 5 Bf depending on locations were computed and introduced in the simulators.

In the case of trapezoidal basins, turning in the upstream direction is more difficult than turning in the downstream direction. This is because the stern of the ship is in a current that opposes the rotation of the ship, causing it to drift toward the edge of the basin. On the other hand, turning after approaching in the downstream direction is easier because the current drags the stern of the ship and makes it turn in the desired direction. The result is a smooth and centered maneuver in the basin (Fig. 6).

Fig. 6. Large trapezoid for a 110 m ship, sailing downstream (left) and upstream (right), with a current of 0.4 m/s. In the case of the upstream turn (right), the shorter distance to the banks and the lower fluidity are clearly visible.

In the case of circular basins, the direction of the current has no influence because of the symmetry of the layout.

Transverse wind was identified as the most unfavorable regardless of the type of basin (circular or trapezoidal).

The unfavorable effect of the wind is further illustrated in Fig. 7 where the maneuver is performed very close to the side opposite to the wind direction for instance.

Fig. 7. Influence of the wind in a circular basin. Condition without wind (left) and with crosswind (blue arrow) 5 Bf (right)

#### <IP_ADDRESS> Impact of Ship Draft

In the case of the circular basins, empty ships (i.e. ships with empty containers) are the more critical ships in windy situations, as shown in Fig. 8. Indeed, empty ships lead to an increased effect of the wind which is not counterbalanced by the better underwater maneuverability.

Fig. 8. Impact of the draft on turns on circular basins in unfavorable wind condition (5 Bf transverse), empty ship (left) and loaded ship (right). Note: the contact in the empty ship maneuver (left) is due to reduced visibility on the simulator and could have been avoided.

In the absence of wind, the loaded condition is the most critical, as shown in Fig. 9, since maneuverability is reduced by the high draft.

Fig. 9. Influence of loading on turns on circular basins in the absence of wind. Empty ship (left) and loaded ship (right).

In the case of trapezoidal basins, the loaded condition is more critical even in the presence of wind, as shown in Fig. 10. Indeed, in a trapezoidal basin, the ship makes a turn to enter the basin. This maneuver is more difficult in the loaded condition since the reduction in maneuverability of a loaded ship compared to a light ship outweighs the difficulty associated with the increase in windage area of an empty ship (empty containers) during the turn.

Fig. 10. Influence of draft on trapezoidal basins, empty ship (left) and loaded ship (right) in wind condition (5 Bf transverse)

The impact of other parameters, such as basin positioning (left or right bank, in a straight line or a curve, etc.) were studied but are not described here.

#### 6.1.2 Optimization of Certain Geometries

The tests performed in the exploratory phase revealed a too constrained space in the small trapezoids and optimizations of this geometry were proposed, the objective remaining to guarantee the turns in unfavorable hydrometeorological conditions in a geometry of reduced size.

Two optimized geometries have been proposed depending on whether the solution is limited to a single bank or whether it can occupy both banks (e.g. the case of the enlargement of a circular basin occupying both banks) The optimizations were performed using an overlay of the simulation trajectories and are shown at Fig. 11.

Fig. 11. Principle of the optimization of the small trapezoid (in red), optimized geometry on one bank only (left): rounded top and opening from the channel following the approach paths and optimized geometry using both banks (right): widening of the channel on the opposite bank

#### 6.2 Results of the Second Phase of Simulations

Over both phases of simulations, 97 simulations were performed, and 85 results were deduced directly from simulations results.

Results showed that the proposed large circle allows for an unconstrained turn (of empty ships) while the small circle allows for a constrained turn (of the same ships). These geometries therefore meet the desired high and low quality of driving objectives as defined in the introduction. It is also worth noting here that turns of loaded ships are possible in all hydrometeorological conditions, though with less ease, on these basins.

Results for the trapezoidal geometries (large trapezoid and small optimized trapezoid) showed similar results for empty ships at the exception of the case of a construction on a river (with current) and when the smaller base would be oriented towards the direction of the prevailing winds. In such case, turns proved to be impossible for all trapezoidal basins. Tests on optimized geometries showed the improved ease of driving compared to that of the original small trapezoid. It must be noted here that on the numerous stretches with no current on the Nord-Pas-de-Calais network (canals), the large and small optimized trapezoids can be used regardless of the orientation and meet the desired high and low quality of driving objectives.

To facilitate the decision making of VNF, a decision tree was proposed. It allows to determine the most appropriate geometry (the one that allows the easiest turn) according to the availability banks (both or only one), the available space, the presence or absence of current and the possibility of arranging the basin so that the top of the trapezoid is not oriented in the direction of the prevailing winds.

### 7 Conclusion

A study was performed to identify turning basin geometries which allow turns of ships up to 135 m in any location of the Nord-Pas-de-Calais network, with varying hydrometeorological conditions (current and wind), availability of (both or only one) banks for construction, environmental or land ownership constraints while guaranteeing satisfactory operational conditions and for limited costs.

The first phase of the study consisted in the review of national and international guidelines in relation to turning basins design as well as the analysis of past turning basins studies and existing turning basins on the Nord-Pas-de-Calais network. In a second phase, interviews of waterways authorities' staff, international experts, and skippers were performed to better understand how the information collected in the first phase should be applied to the case of the studied network.

From this, geometries were proposed for the future turning basins of the Nord-Pasde-Calais. Two options were proposed, depending on whether the basin can be located on two banks (circular geometry) or on one bank only (trapezoidal geometry), and are given in a comfort level version, for which the maneuver must always be relatively easy, and a safety level version, for which the turn must always be possible, potentially with less ease.

These draft geometries were then tested on real-time navigation simulators in order to demonstrate their accessibility and to potentially propose improvements. Optimizations of the trapezoidal geometries were proposed to adapt to severe hydrometeorological conditions, for a single or double bank implementation.

The results show that circular geometries allow the turn in all circumstances and can be retained according to the available space between a comfort level (diameter 1.3 L) and a safety level (diameter 1.2 L). Optimized trapezoids allow for easier turns but are not suitable when the small base is oriented in prevailing wind direction when applied on rivers (with current). On the canals sections of the network however, the proposed trapezoidal geometries did give the desired results, in other words: comfortable turns on the large trapezoid and safe turns on the small (optimized) geometries.

Finally, the results have been compiled in a decision tree which will facilitate the selection of a design solution according to the local characteristics of the projected basin location, keeping in mind that a certain flexibility will be required in the application of the proposed designs since local constraints often complicate the application of generic solutions.

Acknowledgements. The study was commissioned by Voies navigables de France (VNF) The study was coordinated by International Marine and Dredging Consultants (IMDC) in collaboration with its subcontractors: Ghent University and Flanders Hydraulics. The results of the analysis were discussed on several occasions with representatives of the inland navigation sector, whose valuable input is acknowledged.

#### References

BMVBS (2011) Richtlinien für Regelquerschnitte von Binnenschifffahrtskanälen

PIANC (2019) Design Guidelines for Inland Waterway Dimensions. InCom WG 141 Rijkswaterstaat (2017) Richtlijnen Vaarwegen RVW 2017

USACE (2006) EM 1110-2-2602. Hydraulic design of deep-draft navigation projects

Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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# Comparative Study of the Hydraulic Characteristics of Stratified Energy Dissipators in In-Chamber Longitudinal Culvert Systems

Xin Ma1,2(&) , Yaan Hu1 , and Zhonghua Li1

1 State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Nanjing Hydraulic Research Institute, Nanjing 210029, China<EMAIL_ADDRESS>2 State Key Laboratory of Hydraulics and Mountain River Engineering,

Sichuan University, Chengdu 610065, China

Abstract. The study of energy dissipation characteristics of stratified energy dissipators in the lock chamber is carried out by numerical simulation. Discussed the hydraulic characteristics of different energy dissipators in the lock chamber and open channel area (e.g., flow field in the lock chamber, flow distribution in the branch holes and energy dissipation mechanism). The results show that the stratified energy dissipation makes the water flow in the open ditch area more fully mixed; the flow distribution in the branch holes is more balanced; the maximum flow velocity into the bottom of the lock chamber is reduced. The in-chamber longitudinal culvert system with open channel + cover has the best flow conditions, followed by open channel + grating, both of the above are better than the traditional open ditch energy dissipator.

Keywords: Numerical simulation Locks Filling and emptying system Energy dissipator

### 1 Introduction

With the rapid development of China's economy, a large number of world-class highhead water conservancy projects have been completed and put into use one after another. The establishment of high headlocks to enable ships to travel unimpeded on the rivers has become another new national strategy. However, high headlocks are required to meet two conditions at the same time - cargo capacity and protection of locks and ship safety. The instantaneous large flow rate will endanger the safety of ships moored in the lock. To meet the safety of ships mooring in the lock, it is necessary to set up the energy dissipator in the filling and emptying system, so as to reduce the energy of the water around the ship and enhance the uniformity of water flow to achieve the purpose of reducing the mooring ship bollard force (Zong and Yang 1989).

In the 1930s, the United States in some locks used the open ditch energy dissipator type: Lower Granite, Bay Spring, New Bankhead and other locks had been applied. In addition, in the 1960s, the U.S. Army Corps of Engineers had also placed open ditch energy dissipators at ship locks experiment stations on the Columbia River and Snake River, and many experiments and studies had been done for this purpose. (Perkins and Chanda 1975; Richardson 1969; Richardson and Webster 1960). Similarly, Marmet Lock (Hite 1999) with the open ditch energy dissipator on both sides of the increased in force dissipation threshold to increase the smoothness of the flow to optimize mooring conditions. In China, the open ditch energy dissipation type was first used in Gezhouba 2 locks, after which the energy dissipation type has been widely used, such as Sichuan Fuzhou River Lotus Temple, Santai locks, Xijiang River Guiping a line of locks. Recently, China's researchers on the basis of single ditch research, for this reason, the domestic energy dissipation on the basis of single ditch, proposed a double ditch, three ditch arrangement type (Li et al. 2021).

For higher heads, such as a 60 m single-stage ship lock, the open ditch energy dissipator will be difficult to reach the lock design requirements. By adding grilles or covers, the single layer open trench energy dissipator, is changed to a "double layer energy dissipator". Whether the innovative types of ditch + grille and ditch + cover are better than single layer is to be demonstrated. This study investigates the hydraulic characteristics of single-layer open ditch energy dissipator and layered open ditch energy dissipation (ditch + grille and ditch + cover form) by numerical simulation, aiming to understand the effect of different energy dissipation arrangements on the flow regime of the lock chamber, the flow distribution of branch holes and energy dissipation effect.

### 2 Numerical Simulation

#### 2.1 Calculation Area and Grid

Without affecting the calculation accuracy, reduce the calculation volume and improve the calculation efficiency. According to the characteristics of the arrangement of the outlet water transmission system in the second section of the open channel, half of the entire lock chamber area was selected for the simulation study in the calculation area. At the same time, to ensure that the flow velocity and flow direction on the inlet boundary is relatively smooth, the corridor inlet was extended horizontally, and the calculation model is shown in Fig. 1.

Fig. 1. Calculation area schematic

The calculation area has meshed with a hexahedral structure. Mesh encryption is applied to the side branch holes, open trenches and their nearby areas. The total number of grid cells is about 2.54 million and the total number of nodes is about 1.65 million. The grid division diagram is shown in Fig. 2.

Fig. 2. Grid profile diagram

#### 2.2 Control Equations and Boundary Conditions

In terms of model selection, the volume of fluid method (VOF) was chosen for the free surface tracking (Hirt and Nichols 1981); the renormalization group (RNG) k - e turbulence model was used for the turbulence model (Yakhot and Orszag 1986). According to the actual lock gate opening-closing flow variation under the lock chamber inlet, the inlet flow rate is adopted as variable flow rate that is, the incoming flow is non-constant. The highest head, the lowest initial head and the shortest opening time in the physical model test were selected (Design water head H = 60 m, Initial lock chamber water level h0 = 6 m, Gate opening time tv = 8 min, and the inlet flow velocity variation is shown in the following figure (Fig. 3).

Fig. 3. Variation of inlet flow rate and inlet flow rate

The boundary settings are shown below:

#### 2.3 Model Validation

In the physical model experiments, the pressure measurement points of the side branch holes and the monitoring points of the water level change in the lock chamber are compared respectively (Fig. 4).

Fig. 4. Comparison of numerical simulation results with physical experimental data: a. Water level change in the lock chamber; b. Pressure change at the top of the main corridor.

According to the change of water level in the lock chamber and the change of pressure in the branch hole, we could get that the simulation was validated against the experimental data which were within a reasonable range.

#### 3 Results and Analysis

#### 3.1 Lock Chamber Flow Field

It can be seen from Fig. 5, at the maximum flow rate of Q = 330 m3 /s (T = 400 s), the jet velocity of the traditional open channel branch hole reaches 12.21 m/s; the flow velocity of the open channel + grille branch hole is 9.42 m/s; the flow velocity of the open channel + cover plate branch hole is 11.32 m/s. From the Fig. 5, it can be seen that after the water flows through the open ditch, there is still a high-speed water flow of more than 3 m/s into the lock chamber. And no larger flow velocity is found in the open ditch + grille and open ditch + cover. It means that the open ditch cannot fully kill the energy of water flow in the branch hole.

Fig. 5. Three different energy dissipator transverse flow velocity diagram and vector diagram

From the vector distribution diagram (Fig. 6), it can be seen that, compared with the conventional open channel energy dissipators, the addition of the grille makes the water in the open ditch dissipator area mixed more strongly, the spin roll is enhanced, energy dissipation is more adequate. In addition, the addition of the grille also adjusts the direction of the main jet of the lock chamber flow, so that the speed into the lock chamber is further reduced, and the lateral diffusion is more rapid. The upper branch hole and the addition of the cover plate (ditch + cover energy dissipator), so that the bright ditch area whirlpool intensity more and more intense and in the cover plate out of the flow formed after the second spin roll, into the lock chamber inside the maximum flow velocity of about 2.24 m/s, only 47% of the traditional bright ditch energy dissipators, bright ditch + cover plate layered energy dissipation water transfer system.

Fig. 6. Longitudinal chamber flow velocity distribution at the moment of maximum water transfer (with ditch energy dissipator)

From the longitudinal flow field diagram at the time of the maximum flow rate (x = 6.75 m cross section), it can be seen that the maximum inclination of the water flow in the vertical direction at the time of the maximum flow rate is about 45°, of which the inclination of the upstream side is about 52°, that is, part of the jet is shot obliquely to the water body of the lock chamber and the maximum flow velocity into the lock chamber is 4.97 m/s. This makes the whole lock chamber form a huge transverse vortex, and the main jet decays along the course to maintain a certain velocity near the water surface. The flow velocity is maintained near the water surface. This indicates that when the design head reaches 60 m, the dissipation effect in the open channel area slows down significantly, and more energy needs to be dissipated by mixing and diffusion in the water body of the lock chamber (Fig. 7).

Fig. 7. Longitudinal chamber flow velocity distribution at the moment of maximum water transfer (with ditch + grille energy dissipator)

The velocity of water entering the lock chamber on the upstream side is obviously reduced, but at the end, there is still a large flow velocity (maximum velocity out of the lock chamber is 2.64 m/s) due to the blockage at the end of the branch corridor and the inertia of the water. However, after the water flows through the grille, the water flows make a local impact due to the sudden narrowing of the outlet aperture, which restrains the flow direction, and the flow direction after the lock chamber is almost vertical into the lock chamber. This leads to the lock chamber without a wide range of vortex, and because of the grille barrier, the water flows out of the lock chamber and the water body inside the lock chamber through the role of volume suction, rapid mixing and elimination of energy, combined with a faster reduction in velocity (Fig. 8).

Fig. 8. Longitudinal chamber flow velocity distribution at the moment of maximum water transfer (with ditch + cover energy dissipator)

At the time of the maximum water transfer of the open channel + cover, there is still a lower velocity water body around the branch hole outflow in the middle section for absorption and mixing. It means that the setting of the open channel + cover plate has caused some influence on the outflow of the branch hole. It can be found that, due to the value-added cover plate, the dissipation caused by the impact of water flow on the cover plate is very large, plus the skirt of the cover plate to increase the outflow length, adjust the uniformity, the outflow are more uniform and flow velocity is not large (maximum velocity out of the lock chamber is 1.67 m/s). The middle main shot in the low water depth for the emergence of convergence, increasing the respective lateral diffusion space, while the upstream and downstream ends on both sides also bear a certain dissipation. Resulting in the entire flow is very uniform, near the surface combined velocity does not exceed 0.28 m/s.

#### 3.2 Branch Hole Flow Distribution

The energy dissipator are different, but the outflow law is roughly similar: at the beginning of the lock transmission, the outflow velocity of each branch hole is decreasingly distributed along the flow direction of the branch corridor, that is, the flow velocity of the branch hole near the inlet of the branch corridor is large (4#, 10#), and the flow velocity of the branch hole at the end of the branch corridor is small (16#, 19#); over time, the outflow velocity of each branch hole is increasingly distributed along the branch corridor, that is, the flow velocity of the branch hole near the inlet of the branch corridor is small, and the flow velocity of the branch hole at the end of the branch corridor is large. The flow velocity of each branch is increasing along the branch corridor (Fig. 9).

Fig. 9. Three different energy dissipators side branch hole flow velocity distribution: a) ditch dissipator; b) ditch + grille dissipator; c) ditch + cover dissipator.

The difference is that, when the flow rate is larger, the uniformity of the traditional open channel energy dissipator branch hole outflow is poor (Q = 330 m3 /s moment each branch hole flow rate statistics standard deviation r is 0.75). Adding the equal spacing grille, the maximum flow rate moment (Q = 330 m3 /s) standard deviation r reduced to 0.47, the flow peak is obviously reduced. The addition of the cover, the water flow can be more fully in the open ditch energy dissipation area mixing, so that the water pressure near each branch hole to get re-equilibrium, resulting in the flow of water outflow flow rate does not appear large differences, regardless of the initial filling or maximum water transfer time, branch hole outflow uniformity is the best among the three (the maximum flow time standard deviation r only 0.44).

#### 3.3 Energy Dissipation Analysis

The magnitude of turbulence energy can reflect the dissipation state of the open ditch area:

Fig. 10. Turbulent energy values corresponding to the internal flow structures of the three body types (T = 400 s, cross-section at the longitudinal symmetry center of the lock chamber)

From the Fig. 10, the turbulence is most intense in the open trench area of the open ditch + cover, with large turbulence energy values near the orifice, in the middle of the open trench and near the cover. The addition of the grille allows the more turbulent flow to be concentrated in the middle of the orifice and open trench. The turbulent energy values in the ditch energy dissipator are relatively discrete except at the orifice, and there is still some mixing at the bottom of the lock chamber (marked in red). It shows that the effect of energy dissipation by stratified-energy dissipation is obvious, and the energy dissipation is concentrated in the open ditch area.

### 4 Conclusions

In this study, the hydraulic characteristics of the stratified energy dissipator open channel + grate and open channel + cover are studied by numerical simulation. The flow characteristics, branch hole flow distribution and energy dissipation mechanism of the two new energy dissipators are discussed in detail. Based on these studies, the following conclusions were obtained.

grille, the water in the open ditch mixes more fully and adjust the flow of water into the lock chamber flow pattern, so that with the surrounding water diffusion more fully, the main jet to the bottom of the lock chamber near the energy is lower.

3 Ditch + cover because the upper branch hole area is smaller so that the entire branch corridor side branch hole inlet pressure distribution is more uniform. The cover greatly enhances the strength of the water turbulence in the open ditch area. The flow pattern of water entering the lock chamber is the best among the three.

In summary, for 60 m head, stratified energy dissipators is more superior than traditional energy dissipators.

Acknowledgements. The research reported herein is funded by the China National Key R&D Plan (Grant No.: 2016YFC0402001).

### References

Richardson GC (1969) Filling system for lower granite lock. J Waterways Harbors Div 95:275–289

Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# Corridor Scale Planning of Bunker Infrastructure for Zero-Emission Energy Sources in Inland Waterway Transport

Man Jiang1(&) , Fedor Baart1,2, Klaas Visser1 , Robert Hekkenberg1 , and Mark Van Koningsveld1,3

1 Delft University of Technology, Delft, The Netherlands<EMAIL_ADDRESS>2 Deltares, Delft, The Netherlands<EMAIL_ADDRESS>3 Van Oord Dredging and Marine Contractors B.V., Rotterdam, The Netherlands

Abstract. The availability of supporting bunker infrastructure for zeroemission energy sources will be key to accommodate zero-emission inland waterway transport (IWT). However, it remains unclear which (mix of) zeroemission energy sources to prepare for, and how to plan the bunker infrastructure in relative positions and required capacity at corridor scale. To provide insight into the positioning and dimensions of bunkering infrastructure we propose a bottom-up energy consumption method combined with agent based network simulation. In the method, we first produce a two-way traffic energy consumption map, aggregated from the energy footprint of individual vessels on the transport network. Next we investigate the potential sailing range of the vessels on the network if they would sail the same routes, but with alternative energy carriers. Based on the sailing range of the vessels for different energy carriers, the maximum inter-distance between refuelling points can be estimated. By aggregating the energy consumptions of all the vessels on the network, we can estimate the required capacity of a given refuelling point. To demonstrate the basic functionality we implement the method to four representative corridor scale inland shipping examples using zero-emission energy sources including hydrogen, batteries, e-NH3, e-methanol and e-LNG. The application in this paper is limited to four abstract cases. A recommended next step is to apply this approach to a more realistic network.

Keywords: Inland waterway transport Zero-emission Bunkering infrastructure Sustainable energy sources Energy consumption

### 1 Introduction

The world's economy relies heavily on waterborne supply chains. Approx. 80% of all global trade is shipped by marine transport; according to UNCTAD (2021) subdivided into tanker trade (2020: 2,918 106 tons loaded), main bulk (2020: 3,181 106 tons loaded) and other dry cargo (2020: 4,549 106 tons loaded, of which a little over 40% is attributed to container transport). Overall efficiency of global supply chains is to a great extent determined by the inland transport networks they are connected with. Approximately one third of the operating cost of vessels is related to energy use.

The Paris Climate Agreement, and its subsequent implementation, a.o. by the International Maritime Organization (IMO), requires significant changes in power systems on board (engine room, energy storage). These changes will not only affect the performance of individual vessels (e.g. loading capacity, range, velocity), but also the performance of ports and waterway networks (e.g. allocation of bunker stations, development of the new fuel supply network, potential modal shift, network intercompetitiveness).

A major challenge that is currently hindering the energy transition is the lack of insight in how alternative power source strategies on board of individual vessels cascade through a ports and waterways system, ultimately impacting its overall competitive performance. A recent first step was the development of a method enabling corridor scale estimation of inland shipping related energy consumption, fuel use and emission patterns (Jiang et al. 2022b). A logical next step is to develop a method that builds on these energy consumption and fuel use patterns to support the rational design of bunkering networks (per energy carrier estimate a logical maximum inter-distance between bunkering stations and their respective required total capacity).

### 2 Method

When the transport demand (volumes, origins, destinations), the state of the waterway network (e.g., water depths, currents), and the state of the fleet (composition, engine ages, etc.) are known, the associated energy demand for transport can be estimated using vessel resistance algorithms (Bolt 2003; Hekkenberg 2013; Vehmeijer 2019; Segers 2021; Van Koningsveld et al. 2021, Rijkswaterstaat 2022a; Rijkswaterstaat 2022b).

Fig. 1. Methodology for estimating emissions for IWT vessels (image modified from Segers 2021, by TU Delft Ports and Waterways is licenced under CC BY-NC-SA 4.0)

Figure 1 describes the methodology for estimating emissions for IWT vessels. Starting point of the analysis are the ship dimensions (length at the waterline (Ls), beam (Bs) and actual draught (Ts)), the vessel sailing speed (Vs) relative to the water, and the waterway characteristics (water depth (h0), waterway width (W), current (Uc)). With this information, based on Holtrop and Mennen's method (1982) with Zeng et al.'s (2018) shallow water effect correction, we can estimate the total resistance a vessel experiences while sailing at a given velocity with respect to the water. Once the total resistance (kN) is calculated we estimate the total power (kW) that is required to overcome this resistance, which includes the power for propulsion and hotel system. Next we calculate the energy (kWh) that is consumed by multiplying this total power with the duration of its application. The energy consumption estimate can then be translated to fuel use and emissions.

Segers (2021), showed how this approach can be used to estimate corridor scale energy consumption, fuel use and emission patterns; both to estimate current patterns, using position information from the Automatic Identification System (AIS) that vessels need to have on board, and future patterns under various scenarios and policies. Jiang et al. (2022b) further generalized the approach by Segers (2021) to come to an approach that in principle is world-wide applicable (provided the required input data can be provided of course). A logical next step is to use this method to estimate energy consumption and fuel use to inform decision making on bunker infrastructure, both placement and capacity. Figure 2 displays the method we propose in this paper to plan a corridor scale bunkering infrastructure in terms of relative positions and required capacity for IWT.

The relative position of a refueling point is related to the sailing range (m) of the fleet, which depends on the total amount of energy storage (kWh) on board and the energy consumption per meter (kWh/m). The required capacity of the refueling points can be estimated based on the total energy consumption (kWh) of the ships between the refueling points.

As a fundamental step, the energy consumption calculation algorithm for a single ship and the whole corridor network has been written into the Python package Open source Transport Network Simulation (OpenTNSim) version v1.1.2 (Jiang et al. 2022a), which enables the further determination of the relative position and required capacity of refueling points in corridor scale.

The following sections describe (1) OpenTNSim simulation with an energy module and how the energy consumption algorithm can be applied using OpenTNSim, (2) how energy consumption maps can be used to rationalize the relative positions of bunker stations, and (3) how energy distribution over the shipping network can be used to define the required capacity of bunker stations.

Fig. 2. Schematic diagram of the method

#### 2.1 Energy Consumption

#### 2.1.1 OpenTNSim

OpenTNSim is a python package for the investigation of traffic behaviour on networks. It can be used to investigate how water transport chains interact with the waterway network and its infrastructure. Simulations can be used to compare the consequences of traffic scenarios and network configurations (Van Koningsveld and Den Uijl 2020). In this paper we use OpenTNSim version v1.1.2 (Jiang et al. 2022a) (which includes an energy module) to perform energy consumption estimation and determine the relative positions and required capacity of refueling points. The energy module contains 'resistance, power and energy consumption estimation' algorithm, that can be applied to consecutive dx/dt events from either actual position data (AIS data, trip logs, etc.) or simulated position data (e.g. discrete event simulation output). This enables us to resolve footprints as a function of space and time. The model simulation mainly includes three components:

#### 2.1.2 Energy Consumption Estimation in OpenTNSim

The general steps for the energy consumption estimation for a single vessel in OpenTNSim are as follows. First we create a vessel with its vessel properties, mainly include vessel dimensions, vessel sailing speed relative to the water, vessel installed engine power, etc. Then we create a graph with nodes linked by edges composing a network. We use nodes position to represent the geo-locations (longitude and latitude) of waterways. The waterway characteristics which cover the water depth, waterway width, and current speed are contained on each linking edge as edge information. Then we define the route (which is 'path' in the graph) that the vessel will sail. The path is defined by providing the origin and destination nodes in Dijkstra's path algorithm to find the shortest paths. Next we make an environment and add the created graph to the environment. Then we add the created vessel, to which we will append the environment and the route. Lastly, we give the vessel the process of moving from the origin to the destination of the defined path. We incorporate the energy module to this moving vessel, and via this energy module, the resistance, power and energy consumption of the moving vessel are successively calculated per edge along the path. Summing up the energy consumption of all the edges, the total energy consumption along the route can be obtained. Energy consumption in time and space of the vessel can also be mapped via displaying the energy consumption of all the edges along the route together.

The energy consumption of the corridor network can be mapped by aggregating the results of multiple vessels that together represent the corridor's traffic. The corridor energy consumption map is composed of the geographic waterway network, the energy consumption of ships per sailing edge aggregated in space along the waterways, the energy consumption directions according to the ship sailing directions, and the energy consumption in different time scales such as daily, weekly, monthly, seasonally and yearly (for the determination of required capacity for refueling points in different time scales).

### 2.2 Relative Position

The refueling points are positioned according to the minimum sailing range of the representative fleet (PROMINENT 2016; MOT 2022) in the corridor. The minimum sailing range provides an indicator for the maximum inter-distance between two refueling points, as this minimum value allows all types of ships in the corridor to arrive at the next refueling point. For the minimum sailing range determination, in OpenTNSim, we define vessels with a 'fuel volume', each discrete event we calculate how much energy is consumed and how much fuel. This volume can then be subtracted from the fuel volume. The fuel tank slowly depletes along with the sailing. When a certain 'buffer' is reached this can be defined as the sailing range by that vessel for the given fuel and given the volume of the fuel tank. Then by doing this for various vessels we can find the minimum range. The inter-distance between bunker points should not be larger than this minimum range. It should be noted that the maximum allowable energy use amount is smaller than the total amount of energy storage on board, since we set a residual energy margin which is 5–10% of the total energy storage on board, to prevent the ships running out of all the fuels on board before reaching the next refueling point. The total amount of energy storage can be determined by knowing the mass or volume of zero-emission energy sources on board, energy density and energy conversion system efficiency.

#### 2.3 Required Capacity

Once refueling points are positioned on the corridor energy consumption map, the required capacity of each refueling point can be estimated based on the total energy consumption at various time scales. As shown in Fig. 2(c), the waterway network is divided into waterway segments by the refueling points. As a first scenario we put one refueling station is 'in charge' of all the waterway segments it directly connects. However, to prevent overlapping energy supply for the same segment by the two refueling points at both ends, we allocate the required energy supply amount according to the energy consumption direction, as shown in the refueling points capacity table in Fig. 2(c).

### 3 Results

Zero-emission energy sources in this paper refers to (green) hydrogen, e-fuels, and batteries. Among which, e-fuels are produced from electricity, water and carbon dioxide or nitrogen. When using electricity from renewable sources and circular carbon dioxide (e.g. from biomass or direct capture from the air), net emissions are near zero (Van Kranenburg et al. 2020). The e-fuels analyzed here include e-NH3, e-methanol and e-LNG.

Although there are increasing number of vessels powered by zero-emission energy sources in recent years (Arief and Fathalah 2022), the energy storage and conversion systems for zero-emission energy sources on board for wide use are still in designing stages (de Vos et al. 2018; de Vos 2020; van Kranenburg et al. 2020; Huang et al. 2021). Therefore, there is no certain value of the total storage amount for zero-emission energy sources on board to refer to. This forms an obstacle to get the sailing range of a zero-emission energy source powered vessel, which in turn hinders the determination of the relative positions and required capacities of the refuelling points. However, with the method implemented in OpenTNSim, we could calculate the required amount of energy (in kWh) and zero- emission energy sources (in kg and m3 ) of a vessel sailing on a route to give some insight on designing the energy storage volume on board and preparing the energy amount for the whole route and corridor network.

Via the investigation of inland waterway characteristics (MOT 2022; RVW 2020; CCNR 2021), we have simulated the energy consumption of a motor vessel (M8 type (RVM 2020)) sailing in the corridor network along four distinct routes using Open-TNSim. The vessel properties and waterway network with characteristics are shown in Fig. 3. With the same total sailing distance of 450 km, Route 1 starts from Node 0, through Nodes 1, 2, 3 to Node 4, representing an 'unrestricted waterway' from sea port to the hinterland. Route 2 starts from Node 0 through Nodes 1, 2, 5 to Node 6, representing a route from sea port to the hinterland that includes a 'shallower section (150 km)'. Route 3 starts from Node 0 through Nodes 1, 2, 7 to Node 8, representing a route from sea port to the hinterland that includes a 'very shallow section (150 km)'. Route 4 starts from Node 0, through Nodes 1, 2, 9 to Node 10, representing a route from sea port to the hinterland that includes a 'very shallow section (25 km)'. At routes 1 and 2, the M8 vessel is able to sail with its maximum draught. However, at routes 3 and 4, the M8 vessel has to reduce cargo to gain a smaller draught to pass the limited water depth waterway sections.

Fig. 3. OpenTNSim input: vessel properties and graph information.

Knowing the net energy gravimetric density (kWh/kg) and net energy volumetric (kWh/m3 ) density for zero emission energy sources and the corresponding energy conversion system efficiency, the amount of energy consumption on board can be translated to the amount of zero emission energy sources consumption in mass and volume on board.

The required amount of energy and zero-emission energy sources (in mass and volume) along the route of the M8 vessel estimated via OpenTNSim, are shown in Table 1.

Table 1. The required amount of energy and zero emission energy sources (in mass and volume) along the route

As shown in Table 1, with the same sailing distance (450 km (Fig. 3)) and same payload (2628 ton), the required energy amount and the required amount of each zeroemission energy source for Route 1 and Route 2 are different. The required energy amount for Route 2 with a shallower section is 0.23 MWh higher than it for Route 1, as more energy is needed to overcome higher sailing resistance in the shallower section. Similarly, the required energy amount for Route 3 is 1.82 MWh higher than Route 4 though with the same sailing distance (450 km) and reduced payload (1056 ton), which is due to the longer 'very shallow section' in Route 3.

In general, for each route, the required mass of zero-emission energy sources in order from smallest to largest are: hydrogen (liquid, −253 °C), E–LNG (liquid), Emethanol (liquid), E–NH3 (liquid, −34 °C), battery with 2 MWh capacity (20ft Containers). The required volume of zero-emission energy sources in order from smallest to largest are: E–LNG (liquid), E- methanol (liquid), E–NH3 (liquid, −34 °C), hydrogen (liquid, −253 °C), battery with 2 MWh capacity (20ft Containers).

For Route 1, it requires 1.02 ton of hydrogen (liquid, −253 °C), which is the lowest mass among other zero emission energy sources. However, the practical constraints on board of a ship are not so much mass, but volume. The required volume of hydrogen (liquid, −253 °C) is the highest among others, 13.26 m3 , which is 2.78 times than required diesel volume. Considering its packing factor, 2, on a ship, the actual required space would be 26.52 m3 , 7.7 times higher than diesel (Van Kranenburg et al. 2020). If its storage space is designed to be of the same size as a diesel tank, with the consideration of 10% residual energy margin on board, then at least 9 bunker points along Route 1 are needed for the vessel to refuel. If its storage space is designed the double size as diesel tank (meanwhile less cargo on board can be taken), with the consideration of 10% residual energy margin on board, then at least 5 bunker points along Route 1 are needed for the vessel to refuel.

The required amount of E–NH3 (liquid, −34 °C) and E- methanol (liquid) are similar both in mass and volume, with E–NH3 is slightly higher. Considering the packing factors, which are 1.1 and 1 respectively, for Route 1, the actual required storage space on board of E–NH3 (liquid, −34 °C) and E- methanol (liquid) are 9.51 m3 and 7.72 m3 , respectively.

There is only a small difference between the required fuel amount of E–LNG (liquid) and diesel. The required fuel amount of E–LNG (liquid) for Route 1 in mass is 1.13 ton less than diesel, in volume is 1.07 m3 more than diesel. The packing factor of E– LNG (liquid) is 2 times higher than diesel, which leads to 2.14 m3 of extra required storage space than diesel on board.

For Route 1, the required number of battery containers with 2 MWh capacity (in 20ft container), considering 10% residual energy margin, is 12. If the M8 vessel takes 2 battery containers on board, at least 6 docking stations along the route are needed; if the M8 vessel takes 4 battery containers on board, then at least 3 docking stations along the route are needed. It should also be noted that the payload capacity onboard is reduced due to more battery containers.

### 4 Discussion

To estimate the energy amount for the whole route and corridor network, the reliable quantification of energy demand (kWh) is needed. It should be observed that even the same vessel type with the same payload (ton) and sailing distance (km) oftentimes results in different energy consumption patterns along the route due to different sailing situations such as water depth variation as shown in the Results. Therefore, it is essential to consider waterway characteristics along the route to get reliable quantification of energy demand of an individual vessel and the whole corridor.

The data availability may hinder the wider use of the method, as it requires quite some input data: on the state of the IWT network (water depth, ambient currents, waterway classes, available routes), on the state of the vessel fleet (vessel speeds to the water, vessel dimensions, payload levels, actual draughts, installed engine power), origin - destination information, etc. However, recently much of this information is gathered and disseminated by authorities, which greatly enhances the data availability. Changjiang Waterway Bureau (China), for example, provides Changjiang Waterway electronic map including a comprehensive description of waterway characteristics for public free use. Pearl River Administration of Navigational Affairs (China) publishes daily number of ships passing through locks in Pearl River with sailing directions and payload information. Rijkswaterstaat (The Netherlands) hosts Vaarweginformatie.nl, where a lot of crucial information on the water transport network is disseminated and kept up to date. Other countries undertake similar efforts, a.o. in European projects. Realistic vessel speeds (relative to the ground), for the sailing events, can be obtained from AIS data (ship geographic position time series). Combined with data on ambient currents, vessels speeds relative to the water can be estimated. When detailed information is hard to come by, averages or probability distributions may be useful to provide insight.

As this method implemented in OpenTNSim is able to quantify the required energy amount of both an individual vessel and the whole corridor network with various water depths, current, payload, and sailing speed, vessel types and amount, etc., it can be used for designing bunker infrastructure with various scenarios including extreme discharge scenarios, concerning environment and economy changes. However, as the bunker locations in practice is selected not merely based on energy demand but also other societal considerations, this method should not be used to really find the exact locations of bunker points, but rather to make sure that the bunker points are located at a reasonable spacing given the vessels, their fuel tanks and energy carriers.

### 5 Conclusions and Recommendations

This paper proposes a bottom-up method implemented in the agent-based transport simulation, OpenTNSim, for corridor scale planning of bunker infrastructure for zeroemission energy sources (hydrogen, batteries, e-NH3, e-methanol and e-LNG) in IWT. It focuses on the positioning and dimensions of bunkering points based on vessel energy consumption in the corridor.

Taking vessel properties and waterway characteristics into account for energy consumption estimation, the method is applied to four distinct IWT routing examples, in which the variation of the energy demand (MWh) for an individual M8 vessel sailing at routes with same sailing distance (km) and payload (ton) conditions is revealed. The total required amount for each zero-emission energy source in mass and volume (number of containers for batteries) is also calculated and analysed. The application examples provide insight into designing the energy storage volume on board, preparing the number of bunkering points and total energy amount for the whole route and corridor network.

The method is recommended to be applied to map corridor two-way traffic energy consumption in time and space with actual data such as AIS data, trip log and the depth, width, and current information of waterway network. Then with the value of suitable energy storage space on board for different vessel types as input, derive the sailing range via OpenTNSim for the determination of relative positions of bunkering points, and finally estimate the required capacity in various time scales of bunkering points in the corridor network.

Acknowledgements. This paper is part of Man Jiang's PhD project "Greenpower – Assessing the Consequences of the Energy Transition on Waterborne Supply Chains", that is funded by SmartPort. This project is supervised a.o. by Klaas Visser, Robert Hekkenberg and Mark van Koningsveld. The work done in this paper is assisted by Fedor Baart. Finally we thank Nanjing Hydraulic Research Institute for organizing the PIANC Smart Rivers 2022 Conference.

### References

Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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# Design of Longitudinal Air Bubbler System Inside Ship Lock

Iqbal Singh Biln1(&) and Chandler Engel2(&)

1 St. Lawrence Seaway Management Corporation, St. Catharines, ON, Canada<EMAIL_ADDRESS>2 US Army Cold Regions Research and Engineering Laboratory, Hanover, NH, USA<EMAIL_ADDRESS>
Abstract. This study investigated the expected behavior of installing a longitudinal air bubbler system in the St Lambert Lock, Quebec, Canada to bring "warm" water from the depths of the lock chamber and reduce ice buildup on the lock walls during the winter navigation. The bubbler manifold would be installed near the bottom of the lock chamber and extend along the entire wall of the lock chamber. Compressed air would be provided to the manifold and the air would be released through a series of holes (orifices) installed along the length of the manifold. A vertical water current would be induced in the lock chamber by the rising air bubbles. The continuous supply of water to the surface should reduce ice formation along the wall of the chamber. This use of a longitudinal air bubbler system to reduce ice buildup along lock walls during the winter season is a novel use of an air bubbler system in North America in a navigation lock.

Keywords: Ice Air screen Bubbler Lock

### 1 Introduction

The St Lawrence Seaway Management Corporation (SLSMC) contemplates installing a pilot-level longitudinal air bubbler system in the St. Lambert Lock to bring "warm" water from the depths of the lock chamber and reduce ice buildup during the winter season. Figure 1 below shows the ice buildup on the lock walls which can become significant enough to impede the clear passage of vessels without intervention. Figures 2 and 3 show the current methods of ice removal from the lock walls with a customized ice scraper tug and a long arm excavator.

Fig. 1. Ice buildup on the lock wall surface

Fig. 2. Ice removal with a customized ice scraper tug

Fig. 3. Ice removal with long arm excavator

The bubbler manifold would be installed near the bottom of the lock chamber and extend along the entire south wall of the chamber where ice buildup is most pronounced due to reduced solar exposure. Compressed air would be provided to the manifold and the air would be released through a series of holes (orifices) installed along the length of the manifold. A vertical water current would be induced in the lock chamber by the rising air bubbles. The continuous supply of water to the surface should reduce ice formation along the walls of the chamber.

This use of a longitudinal air bubbler system to reduce ice buildup along lock walls during the winter season is a novel use of an air bubbler system in North America at a navigation lock. In all other cases known to the authors, air bubbler systems have been installed at locks primarily to create horizontal flow velocities at the water surface to move or deflect floating surface ice. Those systems are relatively high flow bubblers that require large air flow rates (see for example Rand 1988; Haehnel 2016). The SLSMC became aware of an application of a longitudinal air bubbler system to create vertical currents in Finland at locks located along the Saimaa Canal.

The proposed longitudinal air bubbler system would not be required to create substantial horizontal flow velocities at the water surface. Rather the goal of the proposed system would be to provide a constant supply of relatively "warm" water to the surface in order to suppress or a least reduce ice formation on the lock wall surface. Here, "warm" refers to the temperature of water that is greater than 0 °C with no specification of an actual temperature.

Unfortunately, nothing is known about the vertical temperature structure of the water contained in the St. Lambert Lock during the winter, and little is known about the environmental conditions in the lock at the water surface during the winter season. Therefore it is not possible to determine the required supply of water that must be brought to the surface. This conceptual design will estimate the longitudinal air bubbler performance over a range of practical orifice diameters, orifice spacings, manifold sizes, and air compressor sizes. A best design will then be selected based on the estimated performance, practicality of installation, likelihood of success, and potential for future modification, if required.

#### 2 Background

There are many publications describing the mechanics of air bubble plumes that are relevant to the use of air bubbler systems at navigation structures (See for example, Kobus (1968), Ashton (1974), Tuthill and Stockstill (2005), and Haehnel (2016)). Ashton (1974) specifically addresses the use of air bubblers systems to suppress surface ice. These authors address the use of "high flow" bubblers. The proposed longitudinal air bubbler system that is the focus of this study would be used to suppress ice formation using a "low flow" bubbler. The basis of this approach rests on the change of density of water with temperature. Fresh water is an unusual substance in that its maximum density occurs at 4 °C (approximately 39 °F). Because of this, during the winter season, the water in the lock is likely to be stratified with the coldest water at the surface. The air bubbler is used to induce an upward vertical current to move the "warm" water from the depths of the lock chamber to the surface. This continuous supply of warmer water should suppress the formation of ice.

As mentioned above, a longitudinal air bubbler system in Finland has been applied in locks located along the Saimaa Canal. (Private communication from Tero Sikiö, Head of Unit, Finnish Transport Infrastructure Agency, Inland Waterways) The manifold is located about 3 ft above the bottom of the lock and attached directly to the wall of the lock chamber. The manifold diameter is 20 mm (3/4″ in.), the orifice diameter is quite small, only 0.7 mm (0.02756 in.) and the orifice spacing is 2.0 m.

#### 3 Air Bubbler System Design

The air bubbler system is required to provide sufficient vertical upward water flow to effectively suppress ice formation along the length of the lock wall. Given that the water temperature structure of the lock is not known it is not possible to calculate the ice suppression based on heat transfer calculations. Rather a range of possible designs was determined based on the estimated performance, practicality of installation, likelihood of success, and potential for future modification, if required. The of the longitudinal bubbler system for the St Lambert Lock was investigated using the computer program BUB300 (USACE 2006). The input data for BUB300 include: manifold length and diameter, supply line length and diameter, orifice diameter and spacing, nominal compressor pressure, and submergence depth.

#### 3.1 Bubbler System Dimensions

The relevant system dimensions used in the analysis are described here.

Manifold Length: The required length of the manifold is 768 ft to provide coverage along the entire length of the south wall of the lock.

Supply Line Length and Diameter: The air supply line length was estimated to be 100 ft and the supply line diameter was assumed to match the manifold diameters, discussed below.

Manifold Submergence Depth: The submergence depth varied between 25 ft and 50 ft depending on the operation of the lock and the upstream and downstream water levels (Fig. 4). This compares to the maximum possible depth of the lock, from the bottom of the lock to the top of the wall, which is 60 ft.

Sizing Manifold Diameter to Provide Uniform Flow Out of All Orifices. The first step in the manifold design is to compare the orifice sizes and manifold size to ensure that the flow rates out of the orifices are as nearly uniform as possible along the length of the manifold. A commonly used rule of thumb is that the flow rates out of the orifices will be nearly uniform if the sum of the area of all the orifices is less than 25% of the cross-sectional area of the manifold. Flow rates through each orifice will be calculated directly with BUB300 and the actual uniformity of a proposed system geometry can be assessed for various input flow rates.

Fig. 4. Estimated Submergence depth of manifold in feet for three winter seasons

A manifold diameter of 3″ was selected as the best choice to provide practicality of installation, likelihood of success, and potential for future modification. The number of orifices required is equal to the total length of the manifold, 768 ft., divided by the orifice spacing. Table 1 shows the required manifold diameter, calculated using the 25% area criteria discussed above, for various orifice spacings (4, 8, 12, 16 foot) and various orifice diameters (0.7 mm, 1.0 mm, and 1/16″, 1/8″, 3/16″, 1/4″, 5/16″, 3/8″, 7/16″, 1/2″). The orifice diameters of 0.7 mm and 1.0 mm are included to match the orifice diameters used in the Finnish locks. A 3″ diameter manifold will provide sufficient flow capacity to maintain uniform flow across the manifold only for the cases shaded in yellow in Table 1. The detailed analysis of the 3″ manifold was limited to these cases.

#### 3.2 Bubbler System Performance

The manifold and supply line dimensions used in the analysis are shown in Table 2. The range of manifold depths, orifice spacings, and orifice diameters analyzed are listed in Table 3. The largest orifice analyzed was 3/16″ (4.76 mm) because it was found that uniform flow could not be maintained out of all orifices at a larger orifice diameter and 8′ orifice spacing. BUB300 estimated the required air discharge through each of the orifices based on the air pressure supplied by the compressor. The sum of the individual orifice flow rates represents the total airflow to operate the bubbler at the specified pressure. The characteristics of the vertical plume created by the air bubbles were analyzed using the description provided by Ashton (1974) using the calculated air flow rate from each orifice and the depth of submergence of the manifold.

The vertical plume carries a volume of water to the surface. The vertical water discharge carried by the plume increases with depth of submergence of the manifold due to flow entrainment and the plume expands as it rises. An important point is the length of the lock wall protected by the plume reaching the surface.

Protection requires that the plume expands enough to cover the spacing between the orifices. The ratio of the plume width at the surface to orifice spacing was calculated to provide insight into portion of the wall that would be reached by the plume. It must be noted that the equations of Ashton assume that the bubbler orifices are located far from any vertical wall. In the case of the St Lambert Lock application, the bubbler will be located immediately next to the lock wall. It is not thought that this will make a significant difference in the results.