Water Hammer Analysis: Comparing Wave Method and Method of Characteristics

These methods have both been shown to produce solutions identical to an exact solution for cases where line function is not considered (this is the only situation for which an exact solution can be attained).

Both the Method of Characteristics (MOC) and Wave Method (WM) obtain solutions at intervals of (change in t) at all junctions and components.  However, the MOC also requires solutions at all interior points for each time step.  This basically handles the effects of function and the wave characteristics of the solutions.  The WM handles these effects by using pressure waves.  The waves are modified for the effects of function by a single calculation.

For most systems the WM approach requires fewer calculations while producing virtually identical results.  For example, for a 2517-pipe water distribution system the MOC requires 323,995 calculations per time step.  The WM requires 4267 calculations per time step while producing virtually identical solutions.  This comparison depends on the accuracy of the model pipe lengths.

Over the past 30 years we at KYPipe, LLC have developed the extremely efficient and accurate WM (aka Wave Characteristic Method or Wave Plan Method) for analyzing transients in piping systems. This significant development not only provides the capability to handle distribution systems, but because it is based on the movement of pressure waves it gives the engineer an immediate intuitive understanding of transient flow in all piping systems. The traditional MOC approach requires complex mathematical manipulations and provides no insight into the phenomena of pressure wave action. However, the really serious difficulty with the MOC approach is that the requirement for calculations at many interior locations results in orders of magnitude more calculations.  Numerous examples are available in journals showing that solutions obtained by the MOC and the WM are virtually identical (as, of course, they should be). This requirement to make internal calculations essentially limits the use of the MOC approach to transmission pipelines and relatively simple pipe networks. Analyzing extensive distribution systems using existing MOC modeling software is not an option.

There are ongoing attempts to turn the enormous computational disadvantage of the MOC into an advantage by saying the thousands of required internal calculations somehow assure the modeler that important results will not be missed. It is also said that the Wave Method only computes results at junctions. Let us be clear on this point – with the Wave Method internal nodes can be inserted at any desired location. We recommend that modelers do this at local high and low points and in very long stretches of pipelines. This could result in adding 10% more nodes – not 20 times as many nodes (or more) and the results are comprehensive – nothing of significance is missed. We are proud of our very significant development of the Wave Method which opens the door to transient modeling of distribution systems. Low pressure transients in drinking water systems pose a real health hazard (pathogen intrusion) and it is imperative that engineers have the tools to address this and other pressure surge problems in these systems, no matter how simple or complex the networks are.

WPC