Synthesizing Gas Pressure Based on Acoustic Relaxation Frequency of Sound Speed Dispersion Measured at Three-frequency Point

doi:10.19596/j.cnki.1001-246x.8459

Abstract

Abstract:

We present a method of synthesizing gas pressure based on acoustic velocity at three-frequency point with high accuracy and simple measurement. Firstly, acoustic velocity at three frequency points is measured. Then, relaxation frequency of acoustic velocity dispersion is calculated. Finally, gas pressure is obtained according to the linear proportional relation between relaxational frequency and gas pressure. Simulation results verify feasibility of the algorithm. The method is simple and of high precision for ultrasonic online real-time pressure detection of gas chambers.

Key words: acoustic measurement, acoustic relaxation frequency, gas pressure, ultrasonic detection

Xiang-qun ZHANG, Gen-yuan DU, Ting-ting LIU. Synthesizing Gas Pressure Based on Acoustic Relaxation Frequency of Sound Speed Dispersion Measured at Three-frequency Point[J]. Chinese Journal of Computational Physics, 2022, 39(4): 411-417.

Figures/Tables 6

Fig.1 Acoustic velocity dispersion for 100%CO2 at T=304.2 K under different pressures (0.04, 0.2, 1, 5, 25 atm from left to right); "+": Experimental data from Shields[18]

Table 1 Acoustic velocity of 100%CO2 at three selected frequencies (0.6, 20, 200 kHz) under different pressures (T = 304.2 K), synthesized acoustic relaxation frequencies and gas pressures

c₁/(m·s^-1)	c₂/(m·s^-1)	c₃/(m·s^-1)	f_m/Hz	测量P/atm	探测P/atm
272.0	283.5	283.7	1 766	0.04	0.04
270.8	281.6	283.7	8 871	0.2	0.20
270.8	273.0	283.2	43.5 × 10³	1	1.00
270.4	270.8	276.6	218.3 × 10³	5	5.01
270.2	270.6	271.1	1.1 × 10⁶	25	25.01

Fig.2 Acoustic velocity dispersion of gas mixtures 86.9%CO2- 13.1%N2 at T = 303.15 K under different pressures (0.05, 0.25, 1, 4, 20 atm from left to right); "+": Experimental data from Zhang[19]

Table 2 Acoustic velocity of gas mixtures 86.9%CO2-13.1%N2 at three selected frequencies (0.6, 40, 200 kHz) under different pressures (T = 303.15 K), synthesized acoustic relaxation frequencies and gas pressures

c₁/(m·s^-1)	c₂/(m·s^-1)	c₃/(m·s^-1)	f_m/Hz	测量P/atm	探测P/atm
279.7	290.1	290.2	1 836	0.05	0.05
278.5	289.5	290.1	9 350	0.25	0.26
278.4	284.7	289.8	36.5 × 10³	1	1.00
270.4	279.2	286.0	147.4 × 10³	4	4.04
270.3	278.5	279.2	738.5 × 10³	20	20.2

Table 3 Effects of acoustic velocity measurement error at three selected frequencies for gas mixtures 86.9%CO2-13.1%N2 on synthesized gas pressure

V(f₁)误差/%	V(f₂)误差/%	V(f₃)误差/%	测量P/atm	探测P/atm	压强误差/%
+1	0	0	1	1.001	+0.1
-1	0	0	1	0.998	-0.2
0	+1	0	1	0.997	-0.3
0	-1	0	1	1.002	+0.2
0	0	+1	1	1.002	+0.2
0	0	-1	1	0.999	-0.1
+1.5	0	-1.5	2	2.0	0
+1.5	0	+1.5	2	1.99	+0.5
-1.5	0	+1.5	2	2.0	0
-1.5	0	-1.5	2	2.01	-0.5

Table 4 Effects of acoustic velocity measurement error on detected gas pressure at f3 = 200 kHz in Fig. 1

V(f₃)误差/%	f_m/kHz	探测P/atm	P误差/%
2.5	226	1.005	+0.5
-2.5	164	0.996	-0.4

References 20

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