Surge analysis is one of our core competences. We have many years’ experience of doing pipeline surge analysis for clients in the water, wastewater, fuel systems, oil and gas and renewable sectors. From preliminary review and concept design to finial design and safety case studies. We can help our clients find safe and cost effective solutions to any surge issues they may have.

#### What is Surge?

When the velocity of a fluid in a pipe changes, such as when a pumps stops or starts there is a change in the fluid momentum. In accordance with Newton’s second law if there is a change in fluid momentum the fluid must be subject to an external force. In a pipeline this external force is provided by a change in pressure or a pressure transient.

For steady state flow calculations it is usual to assume the fluid is incompressible however for unsteady flow this assumption is not so valid, particularly if the change in fluid velocity is very rapid. This compressibility means it takes a finite amount of time for a velocity change in one part of the pipe to propagate along it. A velocity change propagates along the pipeline as a wave at the sonic speed. Alongside this velocity wave there is also a pressure wave which forces the fluid velocity (momentum) to change. The movement of these pressure and velocity waves along a pipeline can lead to very high and low pressure transients which is why it is called surge.

Surge waves are reflected and modified where there are changes in the pipe such as at the ends, changes in pipe diameter, branch connections, valves and other connected equipment such as accumulators which may have been added to control the surge. These surge wave reflections can induce very complex surge flows and pressures in the pipeline.

Surge can induce sub atmospheric or negative pressure transients which cause cavitation and out gassing of air from the fluid which complicates the situation further because when the negative pressure transient has passed, a cavitation collapse occurs which induces additional surge waves. Also any gas that is released in a negative pressure transient is not instantaneously re-absorbed into the fluid, but can remain as very small air bubbles dispersed in the fluid. These air bubbles reduce the bulk modulus of the fluid which then reduces the sonic speed.

#### Methods used for Surge Analysis.

Because of the various phenomena that can occur in a pipeline or pipe network following a transient flow event. Predicting how the surge waves progress over time can become very complex. These days surge problems are often solved using computer programs which split the pipeline or network into a number of small sections and then analyse what happens in each section over a small increment of time. Then by stepping forward in small time increments it is possible to predict what happens over an extended period throughout the whole system.

Usually in a surge analysis you start at some predefined steady state condition. Then an event or events occurs which cause a flow transient. The analysis is then continued until the flow and pressure transient has died down and you approach some new steady state condition.

There are two main computer methods used to solve surge problems both methods split the pipeline or network into small sections and then investigate what happens over small increments of time as described above. At Fluid Mechanics we have software tools which allow us to use either method and we would choose the most appropriate for the surge analysis required.

The most popular method and usually most accurate for longer pipelines particularly where there is rapidly changing flow conditions is called the “method of characteristics”. In this method a fix step time solver is used. With this method the split length of each section and the time step are chosen, so that the length divided by the sonic velocity equals the solver time step. So after each time step the surge wave will have moved along the pipeline by one section. Using this method the pressures and flows are calculated at the ends of each section after each time step. The method of characteristics is used by many software packages such as Wanda and Flowmaster which we use at Fluid Mechanics but there are many other software tools which also use this method.

The other computer method used to model transient flow and surge does not have a universally recognized name to describe it. It is usually used with a variable time step solver, and with complex multi domain systems but the pipe lengths are not so long. For example modelling aircraft landing gear or vehicle hydraulics. We call this method the variable time step method.

With the variable time step method each section of pipe is treated as a spring mass type system. With the spring being the fluid compressibility and pipeline expansion and the mass being the fluid inertia. Then the whole system is compiled into a set of simultaneous equations which are solved at each time step. The drawback with this method of modelling hydraulics is a step change in conditions at one end of a pipeline will have a small instantaneous influence at the other end so when dealing with step changes in conditions this will result in a roll off or damping down of the peak pressures. The advantage of this method is it allows a complete set of simultaneous equations for a multi domain (hydraulic, mechanical, electrical, control etc.) to be made and solved for the complete system. If the pipeline is split into small enough sections then this method does give similar results to the method of characteristics but there may be some roll off or smoothing when there is a step change in flow and pressure conditions.

SimulationX and Sim Hydraulics (which is part of Matlab Simulink suite of programmes) use the variable time step solver method. We can use both of these software tools but where we are primarily dealing with a surge analysis problem we would tend to use Wanda or Flowmaster for the improved accuracy.

SimulationX is built on an open source modelling language call Modelica, and there are a number of other commercial programs built using this language. All the Modelica programmes would usually use a variable time step solver.