Problem

During a transient simulation in HAMMER, how do transient waves reflect off different boundary conditions, such as demands, reservoirs or dead ends?

How can I decide what type of boundary condition to assume at the cut-off point to an un-modeled part of the system?

Solution

A transient wave will reflect differently against an open boundary such as a reservoir or tank, versus a closed boundary such as a dead end or demand.

When a wave, defined by a head pulse ΔHo and traveling in a pipe, comes to a node, it transmits itself with a head value ΔHs to all other connected pipes and reflects in the initial pipe with a head value ΔHR. The wave reflection occurring at a node changes the head and flow conditions in each of the pipes connected to the node. Hf represents final head—the head after wave transmission/reflection.

• Reservoir or tank: A wave reaching a reservoir or tank reflects with the opposite sign.
  
  
• Dead-end or closed valve: A wave reflects at a closed extremity of a pipe with the same sign, and therefore, head amplification occurs at that extremity. If a flow control operation causes a negative pressure wave that reaches a closed valve, the wave’s reflection causes a further reduction in pressure. This transient flow condition can cause liquid column separation and in low head systems, potential pipeline collapse. The figure below shows that at a dead end, the wave is reflected with twice the pressure head of the incident wave.
  
  Note: to model a dead end (or cap at end of pipe), simply use a junction node. When only one pipe connects to a junction and there is no demand entered in that junction, is it considered a closed end and transient waves will reflect off it accordingly.
  
  
• Pipe diameter reduces: In this case head that is transmitted is amplified. The larger pipeline will also be subjected to this head change after the wave partially reflects at the node. The effect of a contraction is illustrated in the Figure below.
  
  
• Pipe diameter increases: In this case, an attenuation of the incident head occurs at a pipeline diameter increase. The smaller pressure wave is transmitted to the larger pipeline, and after the reflection, the smaller pipeline is subjected to the lower final head. The Figure below shows that at an expansion, only some of the wave is reflected.

Choosing a Boundary Condition at a Connection to an Unmodeled System

It is important to understand the differences in how a wave reflects at different boundary conditions especially when preparing a hydraulic model if you are not modeling the entire system and need to "cut off" at an assumed boundary condition. Here are the primary boundary conditions:

1. Junction with demand - may represent one demand, or multiple demands in a downstream un-modeled system. Pressure waves will reflect.
2. Reservoir - an assumed, fixed hydraulic grade which could represent the HGL at the connection to an un-modeled downstream system. Pressure waves will reflect.
3. Endless pipe - fictitious long pipe with tiny wave speed, such that a pressure wave does not bounce back.

The third approach mentioned above would not reflect the wave, so it may be appropriate if an un-modeled downstream system is long and the pressure waves would mostly dissipate downstream. This is sometimes known as an "endless pipe", "pipe to eternity" or "infinite pipe". In HAMMER this can be modeled with a pipe connected to a junction, with a very long user-defined length and/or a very small wave speed. If you need to have flow out of this pipe (into the unmodeled system), enter a demand or reservoir at the terminating junction (depending on how you would like the hydraulics to behave with the initial conditions solver) and adjust the wave speed to a very small number, so that the wave never returns.

If unsure, try modeling it all three ways (scenarios and alternatives can be used for this, namely with the active topology alternative) and compare the transient results. Animate profile paths to understand how the waves interact.

Ideally, it is best to model a simplified version of the system all the way back the source and all the way to the farthest point in the network, even if it is a simplified version of it.

See Also

Preparing an existing model for a transient analysis in HAMMER

Advanced Water Distribution Modeling and Management book, Chapter 13