What Is the Frequency Response of a Pressure Tube System in an Air Duct?

[Ron D]

A high-frequency response pressure transducer at one end of a 7 inch long (approx. 0.6 inch ID) tube will be used to measure static pressure pulsations in a duct of flowing air. Interest is for air at 70 F and at 460 F. The transducer end of the measurement tube has no appreciable volume. What is the frequency response of the measurement system? In other words, what is the highest duct frequency that can be measured with reasonable engineering accuracy?

Are there references that outline the relevant acoustics theory?

Thanks. ...Ron

 

[FredGarvin]

If you can wing it, it is always best to flush mount dynamic pressure transducers to the flowpath. However, if that is not possible, you will want to shorten the interface tube as much as possible. The Helmholtz resonator natural frequencies can be calculated from

$$f_n=\frac{c}{4 \pi} \left[\frac{\pi d^2}{V(L+.85d)} \right]^{.5}}$$

where
V= volume under sensing diaphragm
c = speed of sound
d = diameter of the tube
L = length of tube

If the volume of the tube can be reduced to about half of that of the resonator chamber, then the wave equation form can be used which is a bit simpler:

$$f_n = \frac{(2n-1)c}{4L}$$

 

[Ron D]

First, a correction: The tube ID is about 0.06 inch, not 0.6 inch.

Comments to FredGarvin's response:

(1) Cannot flush mount x-ducer. Need to keep transducer away from 460 F air stream in the final test run, the real objective of test. The tube will be cooled over more than half its length to eliminate conduction as well as to cool the air column within.

(2) There is no appreciable resonator chamber. Transducer end of tube terminates in a free space of about 0.25" diameter by 0.008-0.010 inches from transducer diaphragm. Therefore Helmholtz freq. calculation is not appropriate.

It seems to me that this measurement tube system is more of an organ pipe (one end closed) analysis. If so, the natural frequency can be determined by calculation or recognized in the data. We should be able to "trust" pressure variation data (i.e., profile stucture) corresponding to frequencies below and above the region of that natural frequency, and perhaps even do some digital "notch filtering" to eliminate natural frequency content (please confirm). Am I expecting too much in this approach?