Looking for explanation into resonance seen in pressure measurement

[akalmand]

I am trying to get dynamic pressure measurement using a strain based pressure transducer (good upto 5000 Hz). I have used 2 different lengths of plumbing (hose) to mount my sensor. While using 12 inches hose, I see a resonance of 228 Hz in my data. While using 7 inches hose, I see a resonance of 375 Hz. Static pressure varies between 200 - 300 KPa and the inner dia of the hose is 6 mm (approx). I am trying to figure out the phenomenon causing it.

Resonance in pipes is given by :-

f = speed of sound in air/(2*length of pipe + (8/3pi)diameter)

This equation gives a very big number (more than 2000 Hz)

Then, I looked into Helmholtz Resonator natural frequency

f = SQRT ((gamma*static pressure* area) / (density*volume*Length))

This equation gives me natural frequencies 4 times I get in my data.

I am trying to figure out what is causing this resonance and how to better explain it.

Any inputs will be welcomed

Thanks,

aki

 

[Strong]

If your pressure sensor is at the end of a tube that is either 7" or 12" long that connects to the wall of the pipe where you want the pressure, then resonance in the connecting tube is at 1/4 wavelength. Say sound speed is roughly 1100 ft/sec, the 12" tube frequency is 275 Hz and 7" tube is 642 Hz. There may be other issues (such as non rigid tube) to match these rough calcs. to your measurements.

Walt

 

[MikeyP]

I get 476 Hz for the 7" tube and 276 Hz for the 12" tube based purely on 1/4 wave resonance of a rigid circular pipe with squared-off open end and dry air at 20 degC

M

--
Dr Michael F Platten

 

[GregLocock]

As they've said, temperature affects the speed of sound, not the pressure.

If you posted a diagram of your setup we'd probably be even more helpful.



Cheers

Greg Locock


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[electricpete]

The flexibility of the pipe (tube) reduces the speed of sound in fluid (and therefore the resonant frequency).

According to PRACTICAL DESIGN AGAINST PUMP PULSATIONS by Corbo and Stearns. 22ND International Pump Users Symposium Proceedings (Turbolab TAMU), this effect can be considered by adjusting the acoustic velocity of the fluid to account for effects of pipe wall flexing as follows:
C = Crigid / sqrt{1 + Kbulk * d/(E*t)}
where
c = Actual acoustic velocity
Crigid = Acoustic velocity calculated using rigid pipe assumption
KBULK = Fluid bulk modulus
d = Pipe diameter
E = Pipe elastic modulus
t = Pipe wall thickness


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[akalmand]

Gentlemen,

Thanks a lot for your replies so far. I have attached a picture showing differnt measurement setups along with the fft's.

Temperature - increases from 130 - 200 C during the runs
Mean Pressure - increases from 200 - 350 KPa
Resonance is seen through out the run.

Can you please also indicate what explanation will best describe this. Is this a Helmholtz resonance example ? I have only seen it if I measure air at such a low pressure. I have not seen it in High Oil pressure measurements (in the range of 100's psi). What can explain the this difference ?

Thanks for your help

 

[akalmand]

One correction - Oil pressure measures is in 1000's psi and I do not see any resonance after using 1ft long hose.

 

[Strong]

I assume you are accurately measuring distance from inner wall of test pipe to pressure sensor diaphram on the connecting hose. When measuring with oil in the system, then be sure to purge all air from pressure sensor and connecting hose. Whay not mout pressure sensor much closer to test pipe?

Walt

 

[akalmand]

Strong,

Well, with oil, the pressure is 5000 psi and I do not see any resonance with the same length of hose. I have mounted another sensor right at the test piece and that does not show any resonance. I just want to identify what is causing it and how to better explain it. Then later on I can decide on the length of the hose looking at the frequency of interest.

PS:- how did u come up with 275 Hz freq for 12 in tube? Can you explain

Thanks

 

[GregLocock]

speed of sound in oil is probably 3 or 4 times that in air.

I doubt it is helmholtz.


Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[MikeyP]

275 Hz comes from assuming that the pipe is closed at one end of the tube and open to atmosphere at the other. The first natural frequency of the fluid has a mode shape with maximium pressure at the closed end and minimum pressure at the open end (plus end correction). The shape with the lowest frequency that fits these boundary conditions is a 1/4 wavelength. 275 comes from speed of sound / 4 / (length of tube plus end correction).

That is the lowest resonance you can get from a tube on its own and based on your original post we had very little information to go on so we gave you an example of a situation where you could get a resonance at a lower frequency than the one you measured.

M

--
Dr Michael F Platten

 

[SomptingGuy]

...there was also a not unreasonable assumption of air being the medium.

- Steve

 

[akalmand]

Gentlemen,

Thanks a lot for your inputs. In the attached picture, I have attached the cross-sectional schematic of the hoses that I used for taking air pressure measurements. The cross-section of the fitting going into the hose is smaller comparatively. I have calculated the resonance considering both quarter wave and helmholtz, and they both are close to the test data. Looking at the schematic, what you think is the reason - Helmholtz or Quarter Wave ?

Thanks

aki

 

[akalmand]

Moving on,

The next one is a little more complicated for me. I also measured water pressure in the same setup. All details on the attached picture. I used 2 sensors for each line (water in and water out). One mounted right on the water line and the other one using 12 inch hose. For 12 inch hose sensors, I am seeing at 77ish and 200ish hz resonance for inlet and 83is hz resonance for outlet. Another factor is that air was not bled from the lines after filling the system with water. So, I am thinking that part of the hose will have air filled and part water filled.If there are 2 fluids in the hose, How can the frequencies be explained ? Attached picture has all the details.

Thanks

aki

 

[GregLocock]

The usual approach can be found in any exhaust design literature. The fundamental resonance is a quarter wave I suspect, the proportions are wrong for a Helmholtz.


If you haven't bled the air out when you fill it with water again you have created a level of complexity beyond what we have been discussing. That would be more like a helmholtz, the mass of water and the springiness of the air dominating.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?