基于三频点声速测量的气体压强合成算法

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

计算物理 ›› 2022, Vol. 39 ›› Issue (4): 411-417.DOI: 10.19596/j.cnki.1001-246x.8459

基于三频点声速测量的气体压强合成算法

张向群¹(), 杜根远¹^,*(), 刘婷婷²

1. 许昌学院信息工程学院, 河南许昌 461000
2. 湖北第二师范学院物理与电子信息学院, 河南许昌 461000

收稿日期:2021-10-08 出版日期:2022-07-25 发布日期:2022-11-17
通讯作者: 杜根远
作者简介:
张向群(1978-), 女, 博士, 副教授, 从事声学气体检测和信号处理研究, E-mail: dzzxq18@163.com
基金资助:
国家自然科学基金(62071189); 国家自然科学基金(61901164); 河南省科技厅科技攻关项目(212102310906); 许昌学院省级创新团队培育项目(2022CXTD004); 贵州省科学技术基金项目(黔科合基础-ZK[2021]一般318)

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

Xiang-qun ZHANG¹(), Gen-yuan DU¹^,*(), Ting-ting LIU²

1. School of Information Engineering, Xuchang University, Xuchang, Henan 461000, China
2. School of Physics&Electronics Information, Hubei University of Education, Wuhan, Hubei 430205, China

Received:2021-10-08 Online:2022-07-25 Published:2022-11-17
Contact: Gen-yuan DU

摘要/Abstract

摘要：

利用声速测量精度高, 测量方法简单的特点, 提出一种基于三个频率点测量声速合成气体压强的算法。首先在三个频率点测量声速, 然后计算得到声速频散谱拐点的弛豫频率, 最后根据弛豫频率与压强成线性正比的关系得到气体压强, 仿真结果验证了该算法的可行性。为在线实时检测气体腔体压强提供了一种技术简单、精度高的超声方法。

关键词: 声学测量, 声弛豫频率, 气体压强, 超声检测

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

张向群, 杜根远, 刘婷婷. 基于三频点声速测量的气体压强合成算法[J]. 计算物理, 2022, 39(4): 411-417.

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.

图/表 6

图1 温度为304.2 K，不同压强下(从左到右压强分别为0.04、0.2、1、5、25 atm)100%CO2重建的声速频散谱

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]

表1 100%CO2在不同压强下，三个频率点上的测量声速、计算声弛豫频率和气体压强

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

图2 温度为303.15 K，不同压强下(从左到右分别为0.05、0.25、1、4、20 atm)混合气体86.9%CO2-13.1%N2重建的声速频散谱，“+”为实验数据来自文献[19]

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]

表2 混合气体86.9%CO2-13.1%N2在不同压强下三个频率点上测量的声速、计算声弛豫频率和气体压强

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

表3 86.9%CO2-13.1%N2三个频率点的声速测量误差对探测压强的影响

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

表4 图 1中f3=200 kHz的声速测量误差对探测压强参数的影响

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

参考文献 20

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[1]	张克声, 张世功, 张向群, 周正达. 基于声弛豫频率的可激发气体压强合成算法[J]. 计算物理, 2019, 36(6): 699-706.
[2]	张克声, 张向群, 邵芳, 唐文勇. 多元可激发气体声弛豫频率的环境影响分析[J]. 计算物理, 2019, 36(1): 89-98.
[3]	宋文栋, 刘祖黎, 李再光. 低气压下辉光放电等离子体参量对二次电离系数的影响[J]. 计算物理, 1992, 9(1): 53-58.

基于三频点声速测量的气体压强合成算法

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

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