应用于低温流体两相流测量的修正电容层析成像线性反演算法

doi:10.11949/0438-1157.20190313

摘要/Abstract

摘要：

针对低温流体液、气两相的介电特性，通过向传统的电容-介电分布函数关系的线性近似方程中引入修正偏量，得到了修正的电容层析成像线性反演算法。以8电极电容层析成像传感器作为几何模型，对液氧-氧气管内两相流进行了模拟，对比了4种不同流型下原始线性算法、修正的线性算法及以全变分1范数正则化为代表的非线性算法的反演结果。采用相关性系数及图像误差定量衡量了反演结果的质量，结果表明，修正线性反演算法显著提升了反演结果的质量，全变分1范数正则化的求解耗时是修正线性算法的10倍以上。当赋以3%测量噪声时，非线性算法表现出对噪声极强的敏感性，修正线性算法具备更好的抗噪能力和反演结果准确性。

关键词: 两相流, 测量, 低温流体, 成像, 线性反演算法

Abstract:

Based on the dielectric properties of liquid and vapor phases of cryogenic fluids, the modified linear inversion algorithms of electrical capacitance tomography (ECT) are obtained by introducing a correcting deviation into the linear approximate equation of the traditional capacitance-permittivity distribution function. The 8-electrode capacitance tomography sensor was used as the geometric model to simulate the two-phase flow in the liquid oxygen-oxygen tube. The original linear algorithm, the modified linear algorithm and the total variation 1 norm regularity were compared under four different flow patterns. The inversion results of four different flow patterns of original linear algorithms, modified linear algorithms and non-linear algorithms represented by total variation L ¹-norm regularization (TV L ¹-norm) are compared. The correlation coefficient and image error are taken to measure the quality of the inversion results. The results of numerical experiments show that compared with the original linear algorithms, the quality of the inversion results is greatly improved by the modified linear inversion algorithm. The TV L ¹-norm takes more than 10 times as much time as the modified linear inversion algorithm. And when 3% measurement noise is applied, the non-linear algorithm shows strong sensitivity to measurement noise. The modified linear algorithms have better anti-noise ability and accuracy of inversion results.

Key words: two-phase flow, measurement, cryogenic fluids, tomography, linear inversion algorithm

中图分类号:

O 359.1

谢黄骏, 陈虹, 高旭, 郑旭东, 张小斌. 应用于低温流体两相流测量的修正电容层析成像线性反演算法[J]. 化工学报, 2019, 70(9): 3320-3328.

Huangjun XIE, Hong CHEN, Xu GAO, Xudong ZHENG, Xiaobin ZHANG. Modified electrical capacitance tomography linear inversion algorithms for cryogenic fluids two-phase flow measurement[J]. CIESC Journal, 2019, 70(9): 3320-3328.

图/表 13

图1 8极片ECT传感器几何机构

Fig.1 Geometric structure of eight-electrode ECT sensor

图2 反问题计算域网格划分

Fig.2 Mesh scheme of computational domain for inversion problem

表1 1 atm（101325 Pa）下不同流体介质的相对介电常数[28]

Table 1 Relative permittivity of different fluids at 1 atm（101325 Pa）[28]

流体介质	相对介电常数
水/空气 (300 K温度下)	77.747/1.0005
液氮/氮气(77 K温度下)	1.4337/1.0021
液氧/氧气 (90 K温度下)	1.4877/1.0016
液化/气态甲烷 (112 K温度下)	1.6299/1.0020

图3 预设相分布

Fig.3 Pre-set phase distribution

图4 相关性系数随正则化参数的变化

Fig.4 Variation of Rxy with regularization parameter

图5 图像误差（%）随正则化参数的变化

Fig.5 Variation of IE (%) with regularization parameter

图6 原始线性算法、修正线性算法及全变分1范数正则化算法反演结果对比

Fig.6 Comparisons of inversion results calculated by original linear algorithms, modified linear algorithms and TV L 1-norm algorithm

图7 反演结果的相关性系数

Fig.7 Rxy of inversion results

图8 反演结果的图像误差

Fig.8 IE of inversion results

表2 不同算法的求解耗时/s

Table 2 Computational time of inversion algorithms/s

Algorithms	Case 1	Case 2	Case 3	Case 4
TR	0.395	0.388	0.398	0.399
MTR	0.420	0.402	0.427	0.400
ITR	0.613	0.605	0.649	0.614
MITR	0.680	0.704	0.734	0.728
SIRT	0.487	0.425	0.525	0.411
MSIRT	0.570	0.549	0.580	0.515
TV L ¹-norm	7.999	7.954	7.925	7.978

图9 噪声干扰条件下原始线性算法、修正线性算法及全变分1范数正则化算法反演结果对比

Fig.9 Comparisons of inversion results calculated by original linear algorithms, modified linear algorithms and TV L 1-norm algorithm under noise interference

图10 有噪声和无噪声反演结果相关性系数对比

Fig.10 Comparisons of Rxy for inversion results of noise-contaminated and noise-free

图11 有噪声和无噪声反演结果图像误差对比

Fig.11 Comparisons of IE for inversion results of noise-contaminated and noise-free

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