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global maximum and minimum pressures in the system. An investigation of the Clare. Valley network identified that tanks and sometimes pumping stations act to ...
Development of network simplification techniques for water hammer modelling by Cantone, J., Furness, B., Nicholls, T., Staniford, P. and Simpson, A.R.

OzWater Conference 2005

Citation: Cantone, J., Furness, B., Nicholls, T., Staniford, P. and Simpson, A.R. (2005). “Development of network simplification techniques for water hammer modelling”, OzWater Conference 2005, Australian Water Association, Brisbane, Australia, 8-12 May. [CD–ROM]. For further information about this paper please email Angus Simpson at [email protected]

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Development of Network Simplification Techniques for Water Hammer Modeling Joshua Cantone, University of Adelaide, [email protected] Benjamin Furness, University of Adelaide, [email protected] Timothy Nicholls, University of Adelaide, [email protected] Phillip Staniford, University of Adelaide, [email protected] Angus Simpson, University of Adelaide, [email protected]

EXECUTIVE SUMMARY Behaviour of water distribution systems under transient conditions is complex, making them inherently difficult to model. By developing ways of simplifying a pipe network model, the time taken to create an efficient and accurate transient model can be reduced. Interviews conducted with water hammer modellers from around the world, both academics and consultants, identified a number of simplification techniques currently employed. Such techniques are often applied without appropriate justification, with their effectiveness assessed solely on maximum and minimum pressures. Using the transient analysis program, TransAM, a number of case studies were conducted to determine the validity and effectiveness of such simplifications. Experimental tests were performed on the single pipe network in the Robin Hydraulics Laboratory at The University of Adelaide, to investigate the effects of truncating sub-networks. These tests validated the TransAM model developed and strengthened the conclusion that it is better to truncate subnetworks partially rather than back to the main pipeline. Effects of network skeletonisation were investigated on the Willunga water distribution network, identifying that it is possible to reduce the number of pipes in the system by half without significantly affecting the global maximum and minimum pressures in the system. An investigation of the Clare Valley network identified that tanks and sometimes pumping stations act to segregate networks, allowing them to be split-up into a number of smaller sub -systems. INTRODUCTION The simulation of transient events is a field of water engineering receiving increasing attention in research and consultancy. The development of the Method of Characteristics (MOC) formulation has been accompanied by the creation of an unprecedented number of water hammer simulation packages for the modern transient analyst. However, no matter which computer package is chosen, limitations often exist on the degree of network detail that can be included in the model. The research presented in this paper focused on developing a series of valid network simplification techniques that could provide an efficient and accurate means of predicting surge pressures in pipe networks. Accordingly, it centres on the effects that network simplifications have on the behaviour of transients in networks. In addition, the applicability and effectiveness of the simplification techniques has been investigated. The research was divided into three principal stages. Stage I of the research involved identifying the simplification techniques currently being employed, via a review of literature and interviews with water hammer modellers. Stage II involved developing a number of TransAM models to assess whether or not the simplifications identified in Stage I were valid. Integrated into Stage II was a laboratory investigation, which involved the set-up and

testing of a model to assess TransAM’s ability to model transients as well as the validity of one simplification technique. Also, the modelling of two complex systems, the Willunga and Clare Valley networks, focused on assessing the applicability of particular simplifications when used on complex systems. Finally, Stage III involved evaluating the effectiveness and applicability of the techniques to generic water distribution systems. PRELIMINARY RESEARCH A study of the literature revealed a wide variety of methods exist that can be used to analyse transient events (Greco and Carravetta 1999; Karney and McInnis 1990; Priddin 1980). However, the literature provided little insight into the simplification techniques available and the application of these techniques to networks for water hammer modelling. One method that has been documented and used extensively is skeletonisation. McInnis and Karney (1995) described a method of obtaining a good indication of the sensitivity of the results to the skeletonisation process. By beginning with the biggest and most dominant pipes in the system and then progressively adding details to refine their initially crude representation, they were able to grasp the sensitivity of the system with respect to transient pressures. Haestad Methods (2002) have gone a step further and developed the Skelebrator to automate the skeletonisation process. The scarce documentation on network simplification techniques in the literature prompted interviews to be conducted with transient analysts from around the world. The aim of the interviews was to identify some of the simplification techniques currently used by leading water hammer modellers. These interviews served to identify commonly employed techniques, which then formed the focus of the research undertaken. Initially, these simplification techniques were applied to simple pipe networks, consisting of usually less than ten pipes, to identify the effect of such simplifications. These then formed the basis for the laboratory and complex network investigations that followed. LABORATORY INVESTIGATION The objectives of the laboratory investigation were to verify the ability of TransAM to accurately model transient events and to verify the process of ‘truncation’ as a valid simplification technique. A simple network was designed and constructed in the Robin Hydraulics Laboratory at The University of Adelaide. The network was originally made up of a single pipeline connecting two tanks. The network was modified to include a subnetwork branching off the main pipeline at its quarter point (see Figure 1 for network schematic). A solenoid valve, at the downstream end of the system, was used to initiate a transient corresponding to an instantaneous valve closure in 0.004 seconds. Initially, the full network was tested, followed by two truncated models. Truncation 1 reduced the subsystem to a single branch, lumping the demands at Node A. Truncation 2 removed this branch with the demands lumped at Node B on the pipe-main (as seen in Figure 1). In each case, the outflow through the solenoid valve was kept as constant as possible to ensure that the magnitude of the transient event remained approximately the same. For each stage of truncation, a plot of pressure head against time was developed for the downstream pressure transducer at the solenoid (Node 1) and the internal transducer (Node 2) for a demand and no demand case.

Pressure transducer Orifice demand point Solenoid valve

B 2

1

A

Full Network includes entire sub network (all pipes shown)

B 2

Truncation 1 removes pipes back to Node A

1

Truncation 2 removes pipes back to Node B

1

A B 2

Figure 1 Single pipe-main with branched sub-network

Verification of TransAM Model The recorded pressure variations in the laboratory were compared to the results from the model developed in TransAM. Table 1 summarises the maximum observed pressures in all three systems for the demand and no demand cases for both the TransAM model and the laboratory data. This table highlights TransAM’s ability to accurately predict maximum pressures. Figure 2 describes the variation in transient pressure over time for pressure transducer 1. This figure shows that TransAM not only accurately predicts the maximum transient pressures but also produces a transient almost identical in shape to that observed in the laboratory. These two conclusions offer assurance that the TransAM model is both reliable and accurate. 60 Slower rate of dissipation in TransAM

Pressure (m)

50

Table 1 Maximum pressures for the Loading Full Model Case Network Laboratory 57.5 Demands TransAM 58.1 No Laboratory 62.5 Demands TransAM 63.0

40 30

20

loading cases Truncation 1 2 53.0 52.0 51.3 51.4 60.0 52.0 65.3 51.8

Small errors develop in timing

10 0.00

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0.20

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0.50

0.60

0.70

Time (sec) Transducer 1 - Laboratory

Transducer 1 - TransAM

Figure 2 Pressure traces recorded in the laboratory and predicted by TransAM for the full network

Although the TransAM model provides an acceptable representation of the true transient behaviour, Figure 2 identifies a number of discrepancies between the TransAM and laboratory results, namely: § The inability of TransAM to predict the observed levels of transient energy dissipation over time in the laboratory network. This can be explained by TransAM’s failure to incorporate unsteady friction (and possibly entrapped air and inadequate restraint), which is prevalent in real distribution networks; and § The errors in timing produced by the process of wave speed adjustment adopted in TransAM. In order to ensure an integer number of reach lengths are present in each pipe, TransAM adjusts the wave speed.

Verification of Simplification Technique Of critical importance to the validity and effectiveness of this technique is how well the two truncated TransAM models predict the global maximum pressures as well as the overall transient response of the system (see Figure 3). Consider the no demand case where the maximum pressure in the Full Network was found to be 62.5 m in the laboratory (see Table 1). Using TransAM, the maximum pressures observed for Truncation 1 and Truncation 2 were 65.3 m and 51.8 m respectively. Clearly, Truncation 1 provides a much better representation of the maximum pressures observed in the Full Network. When comparing the laboratory results for the no demand case the maximum pressures were 60 m and 52 m for Truncation 1 and Truncation 2 respectively. Therefore, the laboratory results confirm the findings from the TransAM model identifying that Truncation 1 is the better simplification technique. 70

SUPERPOSITION: higher pressure is produced due to the interaction between transient waves.

Pressure (m)

60 50 40 30 20 10 0 0.00

0.10

0.20

0.30

0.40

Time (sec) Complete Network

Truncation #1

Truncation #2

Figure 3 Laboratory transient responses for the two-stage truncation process

When considering the variation in pressure over time it was identified that the truncation does influence the transient response of the network. Figure 3 clearly shows that both truncated models predict a similar timing of transient propagation, however, give slightly different magnitudes of pressures due to different superposition events caused by the truncation process. The Full Network developed the largest pressures surges after one transient period, with Truncation 1 giving similar magnitudes. However, the complete removal of the sub-network in Truncation 2 in turn removes the effects of superposition of pressures since the there are no rebounding pressures re-entering the pipe-main. Effectively, the laboratory results support the conclusions made from the TransAM simulations developing confidence in TransAM for subsequent investigations. The laboratory investigation led to one key research conclusion; specifically, sub-networks can be truncated to the connecting branch with demands lumped at the end node. However, it is not recommended to truncate a sub-network right back to a node on the pipe-main. WILLUNGA NETWORK The Willunga water distribution network, shown in Figure 4, supplies water to the town of Willunga and surrounding settlements south of Adelaide, South Australia. The transient modelling investigations focused on identifying the extent to which the network could be skeletonised while still providing an acceptable representation of the transient pressures. A secondary goal was to investigate the variation in transient response at particular locations during the different stages of network simplification. Initially, a simple network was developed consisting of only a single pipe from the tank to Node 9 with two truncated branches leaving this main (Network 1 in Figure 5). Additional pipes and loops were then

added to this initial network facilitating the gradual build up of the network from 10 pipes to the full network with 60 pipes. This network build up took place over six stages as depicted in Figure 5.

Node 13 Network 1 11 Nodes 10 Pipes

Node 20 Node 9

Network 3 23 Nodes 25 Pipes

Network 2 17 Nodes 18 Pipes

Network 4 30 Nodes 32 Pipes

Node 58 Pumping main from Node 9 to Tank

Water supply from an external source, delivered to Node 9

513m

Tank/Reservoir Node 1

430m Network 5 34 Nodes 36 Pipes

Figure 4 Schematic of Willunga Network

Network 6, 58 Nodes, 60 Pipes

Figure 5 The stages of skeletonisation

The total system demand was limited to 100 L/s leaving the tank at Node 1. The demand was kept constant to allow the comparison of the global maximum and minimum pressures occurring in each network. The results presented here are for transient events initiated by the instantaneous closure of valves at Nodes 13, 20 and 58 in 0.1 seconds (see Figure 4). Where these valves are not present in the network, transient simulation was not performed (e.g. Network 1 was not modelled for these transient events as these nodes do not exist). Skeletonisation Investigation Figure 6 displays the global maximum and minimum pressures plotted against the number of pipes in the netwo rk as the system was built up. Figure 6 clearly shows the convergence to approximately constant values after the inclusion of 32 pipes in the network (Network 4, Figure 5). This 32 pipe network comprises the full network with the majority of branches truncated back to the central two loops and pumping main, leaving a short branch of pipe at each point. It can be concluded from this investigation that it is reasonable to truncate the Willunga network back to a branched system provided the major network components (such as loops and larger diameter pipes) are included. In contrast too much skeletonisation leads to a poorer prediction of transient pressures as seen on the left hand portion of Figure 6. 150

300

Pressure Head (m)

Pressure Head (m)

400

200 100 0

POOR

GOOD

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Timing of second transient peak varies significantly

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Number of Pipes Node 13 (Max)

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Node 58 (Min)

Figure 6 Global pressures for Node 13, 20 and 58

0.5

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Time (seconds) Network 4

Network 5

Network 6

Figure 7 Node 20 transient traces for instantaneous valve closure at Node 20

Nodal traces of transient pressures were recorded at different network nodes and for different transient events. Networks 4, 5 and 6 were considered, as it has already been established that there are only slight differences in the global maximum and minimum pressures for these networks. Investigation focused on the similarities and differences in the recorded nodal traces for these three networks. Three locations were considered to investigate the effect of network truncation on the nodal trace. Figure 7 displays the nodal traces at Node 20 for the Node 20 transient event. While the other results are not presented here, similar conclusions and observations were recorded. A significant phase shift can be observed in Figure 7, resulting in the peak pressures occurring at different times suggesting that the nodal trace is changed significantly as a result of skeletonisation. The maximum and minimum pressures remain approximately the same but there are small fluctuations as a result of network skeletonisation. These small variations in the transient pressures between the networks can be attributed to corresponding changes in superposition of the water hammer waves induced by skeletonisation. It is therefore recommended that caution be taken when skeletonising a network if the accuracy of the nodal trace is important, such as for leak detection using inverse transient analysis. CLARE VALLEY NETWORK Interviews conducted with Chris Hewitson, David Murchland and Tim Rowan, from ARUP, focused on the investigation of the transient behaviour of the Clare Valley Water Supply Scheme (CVWSS). It was identified that TransAM was used to model the system and that the network was split into three sub -systems, which could then be analysed individually. Segregation of the system was based on two underlying assumptions: 1. A tank acts to segregate the system, implying that a transient event occurring upstream of the tank has no effect on the downstream component of the system and vice-versa; and 2. Pumps act to segregate the system due to the presence of the non-return valve on the discharge side of the pump. In order to assess the validity and effectiveness of segregating the system, TransAM models were developed for the four networks shown in Figure 9 and compared to a model of the full network (Figure 8). The aim here was not to determine whether the system was able to withstand the transient pressures generated but rather how the different subsystems responded under transient conditions. Valve C

Valve C

To Clare Booster Pumping Station

Supply Reservoir from Hanson Pumping Station

NETWORK 3 4.6 km

11.6 km Trillians Hill Tank

Valve B Mintaro Pumping Station

Valve B

NETWORK 2

NETWORK 1

6.26 km 10.4 km

Valve A NETWORK 4

10 km To Upper Wakefield Storage

Valve A

Figure 8 Schematic of full Clare Valley system

Valve A

Figure 9 Simplified network configurations

Instantaneous closure of Valve A Valve A (see Figure 9) was closed in 0.001 seconds causing a high-pressure wave to propagate upstream in the system. Table 2 indicates the magnitude of the global maximum and minimum pressures in the system for the networks considered. There is little difference between the magnitudes of the pressures (Table 2) or the overall transient response of the system with time (Figure 10) when comparing Network 4 to the Full Network. These two observations validate the assumption that a tank acts to segregate the system and implies that this is an effective simplification technique. Table 2 Global pressures for Valve A closure

Pressure Head (m)

600 500

Network

400

1 4 Full

300

Global Pressure (m) Maximum Minimum 444.3 -53.5 500.2 -100.1 500.6 -101.5

200 100 0 -100

0

20

40

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Time (seconds) Full Network

Network 4

Network 1

Figure 10 Transient behaviour recorded at Valve A

Table 2 shows that the global maximum and minimum pressures obtained using the simplified system in Network 1 underestimate the pressures predicted using a model of the full system. It can thus be concluded that it would be unsuitable to ignore the pump-tank section of the Clare Valley system when assessing the transient behaviour for the instantaneous closure of Valve A.

Pressure Head (m)

Power failure at Mintaro Pumping Station In this case, a power failure at Mintaro pumping station was simulated causing a lowpressure wave to propagate downstream on the discharge side and a high-pressure wave to propagate upstream on the suction side of the pump. Figure 11 and Table 3, summarise the results and again identify that there is little difference in the transient behaviour when the network upstream of the tank is included. The results also indicate that the global maximum and minimum pressures and the transient response over time are overestimated when the system upstream of the pump is ignored. These observations make it clear that to ignore components of the system downstream of the tank and upstream of the pumping station in the Clare Valley system is a valid simplification for a power failure in the Mintaro 200 pumping station. However, the preferred and 180 more accurate simplification would include 160 components of the system upstream of the 140 pumping station (i.e. Network 4). 120 100

Table 3 Global pressures for pump failure

80 60 40

Network

20 0 0

50

100

150

Time (seconds) Full Network

Network 4

2 4 Full

Global Pressure (m) Maximum Minimum 183.1 -28.6 164 -21.9 162.1 -21.6

Network 2

Figure 11 Transient behaviour on discharge side at Mintaro Pumping Station for pump failure

CONCLUSION This paper has focused on several different network simplification techniques commonly employed when modelling transient events. Several principal conclusions have been identified and are detailed below. The tests performed in the Robin Hydraulics Laboratory at The University of Adelaide confirmed the ability of TransAM to accurately predict transient behaviour. It was shown that TransAM provides an effective model, identifying similar maximum and minimum pressures to those observed in the laboratory. However, it struggles to accurately predict the degree of transient dissipation over time and its adopted wave speed adjustment method introduces errors in timing. It was also identified that the preferred truncation process involves reducing the sub-network back to a single branching arm rather than back to the main pipeline. For the Willunga network, the 60-pipe full network model could be reduced to a 32-pipe skeletonised network without significantly affecting the global maximum and minimum pressures. However, when applying such a technique in applications such as inverse transient analysis, where the variation in pressure over time is important, caution must be exercised as skeletonisation does change the transient response of a network over time. Generally, it is recommended that the model be built up slowly but include major components of the system, suc h as loops and larger pipes. Tanks can be used to segregate the network into portions without causing a significant change to the global maximum and minimum pressures or the pressure variation over time. They act as a break point in the network facilitati ng the development of several smaller networks simplifying the modelling process. Pumping stations can also be used to segregate networks in certain instances but such a simplification should not be applied without appropriate investigation. Each of the techniques investigated reduces the number of pipes required in a transient model, sometimes by up to half. This makes these simplification techniques an efficient means of reducing the time taken to set up the model and run a transient simulation. Although the transient behaviour of any water distribution system is unique, in complex networks simplifications must inevitably be made. The authors are therefore confident that the simplification techniques presented here can be applied in both design and in research. REFERENCES Greco, M. and Carravetta, A. (1999) "Water Hammer in Branched Networks", 28th Biannual Congress, IAHR. Haestad Methods Incorporated. (2002) "Automated Skeletonisation Techniques", Haestad Methods Incorporated, White Paper Series No.2, Rev. 1, Document Number 020022. Karney, B. W. and McInnis, D. (1990) "Analysis of Transient Flow in Pipe Networks", Proc. CSCE Annual Conference - 1st Bi-Annual Environmental Speciality Conference, Hamilton, Ontario, 1-18. McInnis, D. and Karney, B. W. (1995) "Transients in Distribution Networks - Field-Tests and Demand Models", Journal of Hydraulic Engineering, ASCE, 121, 3, 218-231. Priddin, K. G. (1980) "The calculation of pressure surge in complex networks", Third International Conference on Pressure Surges, 63-72.