Dynamic Calibration (B.T model)

Dynamic Calibration

A general recursion formula has been derived by Bergh &Tijdeman [1] which relates the sinusoidal pressure disturbance in volume j to the pressure disturbances in the preceding volume j-1 and the next volume j+1. The recursion formula estimates a complex ratio of the pressure fluctuation of each volume j to the input pressure p0. 

Figure 1.Single pressure measuring system [1]. 

General solution: 

The following parameters have been assumed in this model-

• Tube diameter : 1.27 mm 

• Tube length : 0.2413 m 

• Transducer Volume: 1.324e-8 m3 

• Cp : 1007 J/Kg.K

Results: 

Figure 2 shows the comparison between the model and the experimental data. It has been observed that the model over predicted amplification at similar frequency. In addition, the model under predicted phase lag at similar frequency. Several factors could be responsible for this deviation. In the model, the non-dimensional transducer volume increase term (σ) was assumed as zero. But in reality, the volume of the transducer will change with pressure. Moreover, the measured uncertainty of tube diameter and length are also responsible for this deviation.

MATLAB Code

Reference 

[1] Berg. H., and Tijdeman, H., “Theoretical and Experimental Results for the Dynamic Response of Pressure Measuring Systems,” National Aerospace Lab., NLR-TR F.238, Amsterdam, Jan. 1965.