Dear,
We are doing a waterhammer calculation with time history for the first time. And we see that as we raise the cutoff frequency the stresses grow linearly. What is the criterion for setting the cutting frequency? We reached 800 HZ and the tensions are very high. Thank you very much.
Is there a frequency of convergence?
Or is a cutting frequency defined?
Thank you very much.

Rodrigo Vicente

Please share your model so we can see what's causing it. Seems unusual. What is the longest pipe length elbow to elbow distance?. Usually for water hammer the axial mode is being excited. Is it Time history analysis? Usually 100 to 300 Hz would be enough for cut-off frequency. Is it long km pipeline?

What you can do if you have a Time History of WaterHammer Forces you can convert using DLF Spectrum Generator in Caesar II and check at what frequency the highest force will occur. Run a modal analysis of your piping system and check the natural frequency. Then from there you can compare what is the nearest frequency the piping system will be excited by your peak waterhammer frequency. Then you can use this as your basis for your frequency cut-off. Maybe add +50Hz?

Anyway, I'm also new to water hammer calc.

Any other opinion is highly appreciated.

Cheers!!!

If you have chosen to "include missing mass components" in the control parameter tab, the maximum calculated stresses should not change at all! you just won't be able to see what mode is problematic in your calculation in the stress output.

Thanks Pooria for that very good idea. That's also a good approach.

Cheers!!!

The problem is that if I keep increasing the cutoff frequency the stresses continue to increase. The time history has very high frequency components, but this frequency has a very low amplitude. As if it was an electrical signal with a lot of noise. The pipe is not large, the longest section is 6 meters.

Something unusual in the system. What is the magnitude of stress in MPa? Usually waterhammer will not excite shell modes of vibration. If the frequency is very high then, beam models will not be a valid approach to check the stresses. If the frequency is very high it will be just like AIV where the frequency ranges from 500Hz to 2000 Hz.

Anyway, I'm also confused with the physics in this case. Please correct my statement if I have made wrong ones.

Any other opinion is highly appreciated.

Cheers!!!

Let's take it step by step, then.

• Imagine a very long run of pipe with an expansion loop in the center.
• You have 5 elements of pipe, split by nodes 10, 20, 30, 40, 50 and 60.
• The flow of liquid was from 60 to 10 and the system is closed suddenly at 10 and 60.
• As the fluid momentum is attempted to suddenly halt, a fluid obeying Bernoulli's correlation P+1/2*rho*v² has to swap all kinetic energy into static energy, or pressure.
• As the fluid is nearly incompressible, the amount of energy that doesn't cause the pipe to expand locally is backed down the pipe at the speed of sound.
• When it does so, it is not unlike a rocket. Force 1 acts on element 10-20 axially, up until the pressure wave gets to the elbow. Direction of force at this point in time is opposite of what was the flow, because the high pressure side is coming from node 10.
• When it passes node 20, loads on 10-20 cease, but aren't reversed, and are now on nodes 20-30, again, opposite in direction of original flow. (In reality, the energy is split. Some portion will travel back to node 10, but the majority will go to node 30. For simplicity, we'll assume it all goes to node 30 for now.)
• The pressure wave continues through the system, self canceling, but not reversing, up until it gets to node 60. If the pipe had no elasticity to "bounce" back into place, then nodes 10 and 20 would still be deflected, because the forces were cancelled, but not reversed to push the pipe back into place.
• Now, repeat the above steps, except in reverse, as the pressure wave reflects back from node 60 to node 10. If the pipe had no elasticity to "bounce" back into place, then this pressure wave will put it back into place, minus the losses exhibited as the pressure wave travels down the line.

Observations:

• Elements 10-20 and 50-60 will have loads switching on/off on them far less frequently than elements 20-30, 30-40, and 40-50.
• Elements between 20-50 will have loads switching on/off at a higher frequency, but frequency of turning on is a function of overall length.
• Worst case with back-refracted waves is if they are able to achieve resonance.

See attached graph from Aft-Impulse Documentation depicting this behavior.
Original file located here:
http://www.aft.com/documents/AFT-Evaluat...-02-2013-SI.pdf

Looking at the far right end, you can get an idea of what kind of frequencies they get. I suggest adapting this for your model.

Hi Michael,

Thanks for that detailed reply.

Hi Rodrigo,

Please share your stress results for different frequency say 100Hz, 200 Hz, 300 Hz, 400 Hz, 500 Hz....etc. I'm curious about the system, as usually my cut off for waterhammer is usually from 100Hz to 300Hz depending on the peak frequency of the unbalanced force. Based from the Michael's attachment the transient amplitude at the far right are small compared to the peak surge.

Maybe I'm also missing something in my surge/waterhammer analysis.

Thanks & Warm Regards,