The article linked below seems to be a very comprehensive article on various causes of piping pressure pulsations
http://turbolab.tamu.edu/pubs/Pump22/P22pg137.pdf

If you saw abnormally high blade pass frequency vibration on the piping associated with a centrifugal pump, you might consider the possibility of an acoustic resonance (in addition to improper pump gaps and operating point causing excessive excitation)

The length of pipe which will be acoustically resonant at a given frequency depends primarily on the speed of sound in the fluid. To a lesser extent, it also depends on the pipe diameter and thickness.

I made a simple spreadsheet to compute the acoustical resonant lengths using the equations from the link above. You have to input the the fluid density, the fluid bulk modulus (there is some info in separate tabs to help with those), the suspected resonant frequency, the pipe I.D. and wall thickness, pipe modulus of elasticity (E=30E6 for steel). The spreadsheet computes the legnths of the various possible acoustic resonances and displays them at the bottom.

Let me know if you have any comments on the spreadsheet. There is a macro which displays the formulas....the spreadhseet will still work if you don't enable macros.

Has anyone seen acoustic resonances excited by pumps?
Would acoustic resonance typically increase the associated vibration on the pump (for example blade pass)? Or just the piping?

AcousticPipeResonance.xls (32 Kb, 71 downloads)

Yes, I've seen it excited with pumps. Nuclear main heat transport system. Big time problem. Led to replacement of 5-vane with 7-vane impellers. Very water-temperature dependent (sound speed decreases with increasing temperature). Also flow dependent, as you move away from BEP.
You don't necessarily see dramatic mechanical pump vibration. Some of the unsteady flow / pressure pulsation acts on the pump - some is radiated out into the circuit. You'll probably see relatively more pump vibration at low flow, and relatively more circuit effects at high flow. (I made a posting on the old board explaining why).

I had a case where the pressure pulsations resonated not only the piping but also the room in which the pumps were located and caused the windows to rattle on a house 1km away across an open field.
Best Regards,
Tom Murphy

General comments on the excel sheet, I’m not qualified to evaluate it technically:
1. You usually reserve a tab for instructions. Not sure why you did not do it here.
2. A graphical representation of the case could make it easier for the user to visualize the input and output.
3. Luck some of the cells to avoid missing up with the results.
4. Give an explanatory example in writing, something like this, a pipe made of steel XXX, with ID=ID and a thickness of th. The pipe experiences a severe vibration of 2 ips at the following frequencies: 100, 230 and 490 Hz. Pump (7 vanes, 5 diffusers) is running at 1790 rpm. The discharge isolation v/v is 3 ft from the pump discharge nozzle. An anchor is located 40 downstream the v/v. calculate the expected freq etc.
5. Counter check the results using known software like cesar II.

Just my humble opinion.

This message has been edited. Last edited by: Shurafa,

quote:

Originally posted by Tom Murphy:
I had a case where the pressure pulsations resonated not only the piping but also the room in which the pumps were located and caused the windows to rattle on a house 1km away across an open field.
Best Regards,
Tom Murphy

Tom,
Interesting case. Presumably these were large low-RPM pumps, with relatively low vane-pass frequency, in a low- pressure system with relatively thin-walled piping.
Was that the case, or not?

Hi Ron,
large pumps, yes. 590 rpm was the rotational speed and 10Hz was my problem. Very high pressure, roughly 1m diameter suction and discharge pipes.
The pipework was substantial but it was not stiff enough for the job and so was sucked and blown close to resonance. Furthermore there were three of these pumps in the same room with each of the 6 pipes located in an antinode of a room which was unfortunately perfectly tuned to the same 10Hz!
An absolutely wonderful example of how not to design or build for a specific purpose.

quote:

Originally posted by Tom Murphy:
Hi Ron,
large pumps, yes. 590 rpm was the rotational speed and 10Hz was my problem.

Tom,
Thanks very much for the follow up info.
So... this one was at 1X, not vane-pass frequency!.
Good educational value here folks! (ie, although not as strong and well known as the vane-pass effects, there's always some hydraulic unsteadiness at 1X also; not everyone knows this). Seems that in this case, the resonances were able to crank it up into a problem.

El Pete has provided something for nothinhg. We don't find this everyday.

I skimmed the paper (a lot to go through, because the authors have done what we used to call a "core dump" - ask somebody a question, and they'll proceed to say, or write down, absolutely everything they know about the subject).
However, I found one passage that needs a comment. On page 162, the authors say that "piping mechanical frequencies can only be calculated to an accuracy of +/- 20%. And then quote "Tison and Atkins" (2001) to the effect that frequencies could be off by +/- 50%.
This does not match my experience. Haven't done a lot of this, but, late in my career, we modelled four or five systems. (Two nuclear main steam systems, gas recycle compressor / bottle / piping, and a gorator / cold water loop of some kind in a tissue plant I was actually astonished at how accurate they were - and this was in comparison with careful and thorough field measurements.
It would be useful if the authors, or somebody, could clarify just how broadly their claim applies. It wouldn't surprise me if some complex, higher-frequency, short wavelength modes might be off. But not everything.

I should mention that the article indicates that the simple formulas in that spreadsheet are approximate and (as usual), the best solution can only be obtained with detailed modeling.

In a tab of my spreadsheet I incorrectly indicated that an elbow acts like a closed end condition. But according to the article, an elbow represents no change in acousic impedance and is therefore no different than a straight run of pipe.

Ron - interesting that the conclusion that piping vibration analysis is inexact leads to the author's recommended approach to perform detailed acoustic analysis rather than detailed piping vibration analysis ("Because of the accuracies that the two analyses can be performed to, the first approach is highly preferable to the second").

I just wanted to mention some interesting aspects of acoustic resonance as it relates to musical instruments.

In the above excercize we were considering a fixed frequency and asking what are the possible resonant lengths.

A similar question is examining a fixed length pipe (such as musical instrument) and asking what are the resonant frequencies.

From simple consideration of the mode shapes and the equation c=f*lambda where c is constant, we can determine the series of resonant frequencies for a given pipe:

• If the boundary conditions are the same at each end (open/open or closed/closed)
  then the possible resonant frequencies are a series f1, 2*f1, 3*f1, 4*f1...
  
• If the boundary conditions are opposite at each end (open/closed or closed/open)
  then the possible resonant frequencies are a series f1, 3*f1, 5*f1, 7*f1...

Now, anyone who has played a brass instrument knows the series of notes you can play without changing the valves. Start with the pedal tone low B-flat for bass instruments or low C for treble. For example
C, C', G', C'', E'', G'' etc (where the single quote indicates pitch raised by an octave)

The intervals between above are octave, fifth, fourth, major third, minor third

These correspond to frequency ratio's: 2/1 (octave), 3/2 (fifth), 4/3 (fourth), 5/4 (major third), 6/5 (minor third) etc.

So it is a series of the form f1, 2*f1, 3*f1, 4*f1, 5*f1, 6*f1 etc

It seems to fit the open/open and closed/closed pattern. We know the bell is open, so the mouthpiece must be open, right? (I always used to think so).

Wrong! The mouthpiece acts as a closed boundary condition because the lips are closed except for bursts of air that puff out when they vibrate. The pressure pulse cannot continue back past the persons lips into their mouth, so it acts as a closed boundary condition.

So how can a closed/open pipe (horn) gives a series that seems to match the open/open pattern?

It is not a constant diameter pipe. All of these equations apply to constant diameter pipe. The diameter of the horn increases in a precisely-calculated manner to give that particular harmonic series. It is a lot more complicated than the simple constant-diameter pipes.

A flute and a clarinet are true closed/open pipes with constant diameter over most of their length, and I'm pretty sure they give the resonant series 1f1, 3f1, 5f1, etc (for a given fingering position) which a horn would give if it had constant diameter. For example on clarinet, the fingering for low F is almost the same as for C' (an octave and a fifth above).

This message has been edited. Last edited by: electricpete,

electricpete, should you ever want a career change the Blue Man group could sure use your expertise in tuning their plastic tubing!

John

Thanks, I'll keep that in mind.

I'll confess I had to look up Blue Man group:

http://en.wikipedia.org/wiki/Blue_Man_Group

Under musical instruments is a discussion of their tube-type instruments.. sounds pretty interesting

I also saw this on youtube. Apparently the sound is really coming from that tube and they are altering the pitch by changing the length. Pretty cool.

http://www.youtube.com/watch?v=Q1K0_JWwi0k

I have attended a live performance of Blueman Group in Boston and found the acoustics and music entertaining. Now I have to study your SS.

Walt

"Has anyone seen acoustic resonances excited by pumps?"

I think so, Any time grounded piping a long way from the pump makes audible noise and has larger measureable vibration at blade pass than it did closer to the pump. I continue to think the escape mechanism and problem causer is less often what can get right thru round pipe walls, and more often the lateral motion that results from the increased amplitude pressure pulses straightening out the elbows as they roll on through.
http://symtym.com/images/party_favor.gif

I am more sure that I saw a strong acoustic resonance in some air compressor inlet piping at the Glad Bag plant in Connecticut. The inlet pulse frequency was measureable on a distant neghbor's stud framed walls, at levels that Shook that neighbor's dishes when the comps unloaded, and regularly busted the reed valves in the compressors. I wanted them to let me cut some tuning holes in the inlet piping, like a piccolo, but they moved the inlets back indoors.

The compressor manual advised against long inlet ducts, warning that "supercharging" might result if the lengths were right/wrong.