Hi there

I have a few questions concerning the correct procedure for performing water hammer analysis using Caesar II. The model I created consisted of a fairly short section of FRP line (roughly 250m) containing many changes in direction. Being on the discharge side of the pump I calculated the magnitude of the pressure wave using the difference of the design pressure and the water vapour pressure (as described in the technical manual). The velocity of the pressure wave was also calculated using the formulas specified in the technical manual. I then calculated the unbalanced force using the calculated magnitude of the pressure wave and the internal area of the pipe.

(1) My first question is this. Was I correct in using the difference between the design pressure and the vapour pressure for the maximum magnitude of the pressure wave? My concern is that this magnitude was approximately half the magnitude of the supply side pressure wave (based on the fluid density, the wave velocity and the change in the fluid velocity). Also, the manual states that if the pressure drops below the vapour pressure, vapour bubbles can form which can cause extremely high local pressures when they collapse. Can this be taken into account in Caesar II.

(2) What is the correct procedure for applying the unbalanced forces to the elbow-elbow pairs? I used the following method as I understood from the Caesar II manual. I identified all the elbow-elbow pairs in the model. I then calculated the time taken for the pressure wave to pass between successive runs of pipe between elbow-elbow pairs.
I then created the force spectrums for each of the elbow-elbow pairs using the times that I had calculated. The remainder of the steps were performed as specified in the aplications guide. Is this method correct, as from what I can understand all the unbalanced forces are applied in isolation to each of the elbow-elbow pairs and there is no interaction between successive unbalanced forces which may reflect off the elbows and act on opposite elbows in opposite direction (possibly at the same time as another force further down the line)?

Lastly, should the forces be applied in the direction of flow, as well as in the opposite direction to the flow?

I really appreaciate your time to read through my concerns.

Best regards

Jason de Beer

There are two separate aspects of a water hammer analysis.
1- The calculation of pressure variation history at different points of the system.
2- Mechanical impacts of the dynamic forces resulting from the unbalanced pressure as calculated in step 1 above.

Caesar can calculate, with reasonable accuracy, the mechanical impacts on piping due to dynamic forces caused by the unbalanced pressure in the line. The calculation of magnitude of the dynamic force or unbalanced pressure is the user responsibility. Caesar given relation to calculate the unbalanced pressure force is just guidance. In hydraulic vibrating systems, similar to mechanical vibrating systems, pressure can magnify depending upon the characteristics of the hydraulic system. In orer to estimate the pressure history and thus the dynamic force, proper analysis is required for which specialize software are available. Once dynamic force is estimated, its impacts on piping system should simulated using Caesar II.
This is my opinion regarding point 1.

Yes, the difference between the design and vapor pressures will give you the delta P for the system that you want to analyze with. For this analysis, you really don't care about the pressure on the other side of the pump.

As to the collapse of vapor bubbles, no CAESAR II won't address this. CAESAR II doesn't address hydraulics or two phase flow. CAESAR II just works with the loads specified by the analyst.

Your pulses and force sets are correctly described for each individual leg for spectrum analysis. True, there will not be any interaction between these loads or the legs.

If you want to consider this interaction, you must use the time history method of analysis. Just ensure that your time pulses are "timed" properly. Note, even this will not address wave reflection - which must be also be defined by you.

Yes the forces should be applied in the direction of flow, unless you are attempting to address reflection. However, to address this, you'll probably need to run a hydraulics program to determne the force/time relations throughout the system, so you can then input the proper data into CAESAR II.

The first step in water hammer analysis is to find out the surge pressure. The pressure surge can occur in a piping system due to valve closure, pump trip, pump start up etc. It is better to use commercially avalilabe hydraulics softwares like Flowmaster, Pipenet, etc to find out the surge pressure (peak pressure- operating pressure)at various sections of the piping.

The second step is to impose the surge force( surge pressure * pipe flow area) in Caesar model at all elbow pairs. This can be done either as quasi static analysis or dynamic analysis.

In quasi static analysis, the caesar static analysis is ued.The surge forces are applied at all elbows one at a time, so that we have to perform load cases as many number of elbows in the system. This is the most conservative approach, but it takes less time and generally followed by many consultants.

In dynamic analysis, the surge forces are applied at elbows as force spectrum, or Time history using dynamic analysis of the caesar software. This is the most accurate method but it takes more time.

So we have to decide the type of analysis depending upon the system.Also care shall be taken to input the surge forces resolved suitably in x,y,z directions at elbows depending on the angle of elbow.