Liquid Dangers... aka pressure surge (part 2) - 5 minute read

by the way, a google search of "liquid dangers" predominantly refers to vaping / e-cigarettes / juul none of which are referred to in this article. I# haven't seen any reports of pressure surges occurring on those devices...

So here is my part 2 on this topic, if you missed the first part "click here".

still feel free to educate me further on this vast subject, comments appreciated!

Background

Most of the commercially available software used in liquid hydraulic analysis for closed conduit cylindrical systems either use a Eulerian or Langrangian approach to solve the hydraulic calculations. 

Discuss - Major Calculation Methodologies

The Eulerian (fixed grid) approach is more popular and uses the MOC (Method of Characteristics). It is the basis of calculation methodology for a majority of the commercially available surge analysis software. Examples of software tools using this approach include: 

• AFT-Impulse (https://www.aft.com/products/impulse);
• SPS (https://www.dnvgl.com/services/pipeline-simulator-and-surge-analysis-software-analyse-pipeline-design-and-performance-synergi-pipeline-simulator-5376);
• BOSFluids (https://www.dynaflow.com/software/bosfluids/);
• FloMaster (https://www.mentor.com/products/mechanical/flomaster/flomaster/). 

The less popular (arguably), Langrangian approach uses the WCM (Wave Characteristic Method), examples of software tools using this approach include; 

• KYPIPE (https://kypipe.com/);
• InfoSurge (https://www.innovyze.com/en-us/products/infowater/infosurge).

The Eulerian approach via the MOC is much more computationally intensive as it solves the hydraulic equations at both the nodes (like WCM) but also at all interior grid points per time to satisfy Courants stability criteria. 

The Langrangian approach via the WCM on the other hand solves the equations at the nodes, dramatically reducing the amount of computations, especially for massive pipeline networks. However, the flipside being that short pipes are not considered, dependent on their location, the size and the configuration of your system this may not be a big issue.

On my part I'm not sure, how faithfully, phenomena such as vapour cavitation is modelled via the Langrangian approach. 

Dependent on software used (especially if based on MOC), it is advisable to analyse via a few quick simulations, the most suitable value for the minimum time step and calculation interval in order not to dramatically slow down the simulation or miss out on surge events. 

It is also worth verifying the actual worst-case scenario via an appropriate genetic (or other) optimisation algorithm. This is a useful step and a more quantitative methodology to justify the design case selected.

However, I haven’t seen many examples of this. Typically, the worst case surge scenario is assumed to be simultaneous pump power failure.

Back to Basics – Simple Calculations

The Joukowsky equation can be used to obtain a relatively conservative estimate of surge pressure (especially if effective valve closure is less than wave period).

It’s a quick and dirty means of estimating the “maximum” surge pressure within the system prior to using a more complicated hydraulic software (remember its drawbacks re: cavitation et al.). It involves the following steps, where valve closing time is unavailable / assumed instantaneous:

Note that Joukousky equation does not account for column separation which may exceed the initial surge conditions, or reflected waves from branches.

If the effective valve closure time is longer than the wave period (i.e. valve closing time is longer than the wave reflection time/period [2L/a] – slow closing valve), the Vensano equation or Wood and Jones chart may be used to give an indication of pressure spikes.

The Wood and Jones chart displays the relationship between valve closure time and maximum transient pressure change whilst the Vensano equation assumes that the change in liquid velocity on valve closure is linear (however valve characteristic curve may not be). The Vensano equation is displayed below:

Note that both the Vensano equation and the Wood and Jones charts tend to under-predict the pressure spikes to varying extents, and from a practical point of view, extending valve closure time only really becomes significant if the closure time exceeds the wave period by around 10x.

Relationships to Remember

The size of the pressure increase caused by valve closure (or other disturbance) depends on: 

• the magnitude of velocity reduction; 
• the rate of velocity reduction; 
• the length of the pipeline (tank to tank); 
• the compressibility of liquid (and degree of air entrainment to an extent); 
• the elasticity of the pipe;
• long pipelines + cascading design pressures potentially leads to line packing;
• the valve closure time may differ from the effective closure time (this is what you need).

Being over-conservative with design is the easy part!

Just remember that it can have a huge impact during construction, on project CAPEX / OPEX and future operational flexibility. 

References:

1. Systematic Surge Protection for Worst-Case Transient Loadings in Water Distribution Systems” 2009 – Bong Seog Jung and Bryan W. Karney
2. https://www.ksb.com/centrifugal-pump-lexicon/surge-pressure/328136/