化工学报 ›› 2024, Vol. 75 ›› Issue (2): 484-492.DOI: 10.11949/0438-1157.20231089
收稿日期:
2023-10-24
修回日期:
2023-12-13
出版日期:
2024-02-25
发布日期:
2024-04-10
通讯作者:
张一帆
作者简介:
李乃良(1983—),男,博士,讲师,linailiang@cumt.edu.cn
基金资助:
Nailiang LI(), Changsong LIU, Xueping DU, Yifan ZHANG(), Dongtai HAN
Received:
2023-10-24
Revised:
2023-12-13
Online:
2024-02-25
Published:
2024-04-10
Contact:
Yifan ZHANG
摘要:
基于多尺度方法和Hurst分析方法,分析了严重段塞流的多尺度结构及其非线性特征。以空气、水两相混合物作为实验介质,利用高速数据采集板获得了集输立管内气液两相严重段塞流的压差波动信号。使用db4小波在1~8尺度下对压差信号进行分解和重构,提取不同尺度的系统动力学特征,发现严重段塞流气液喷发和液体回落的瞬态过程主要体现在d5~d8尺度的细节信号上。通过对压差波动信号不同尺度下的分解信号进行Hurst指数分析,发现严重段塞流存在显著的双分形特征,同时受正持久性和反持久性两种动力学因素的制约,但概貌分量和细节分量表现出截然相反的分形结构,概貌分量具有正持久性,而细节分量具有反持久性。d1尺度下的细节分量描述了微尺度的气泡与气泡之间的相互作用;d2~d5尺度下的细节分量描述了微尺度的液体与气泡之间的相互作用;d6~d8尺度下的细节分量描述了宏尺度的气液两相与管壁之间的相互作用。压差波动信号的能量主要分布于宏尺度上。
中图分类号:
李乃良, 刘常松, 杜雪平, 张一帆, 韩东太. 基于Hurst指数的严重段塞流多尺度分形特性[J]. 化工学报, 2024, 75(2): 484-492.
Nailiang LI, Changsong LIU, Xueping DU, Yifan ZHANG, Dongtai HAN. Analysis of multi-scale fractal characteristics of severe slugging based on Hurst exponent[J]. CIESC Journal, 2024, 75(2): 484-492.
No. | Wavelet | Scale | |||||||
---|---|---|---|---|---|---|---|---|---|
2 | 3 | 4 | 5 | 6 | 7 | 8 | Mean | ||
1 | db2 | 2.686 | 2.605 | 2.667 | 2.667 | 2.734 | 2.405 | 2.277 | 2.572 |
2 | db3 | 2.836 | 1.919 | 2.025 | 1.961 | 2.234 | 1.366 | 1.244 | 1.949 |
3 | db4 | 2.299 | 1.885 | 1.778 | 1.647 | 1.675 | 1.105 | 1.031 | 1.631 |
4 | db5 | 2.541 | 1.905 | 1.969 | 1.739 | 1.454 | 1.266 | 1.188 | 1.723 |
5 | db6 | 3.143 | 2.060 | 1.957 | 1.869 | 1.892 | 1.426 | 1.297 | 1.949 |
6 | db7 | 2.301 | 1.877 | 1.802 | 1.619 | 2.071 | 1.282 | 1.168 | 1.732 |
7 | db8 | 2.342 | 1.918 | 1.962 | 1.671 | 1.552 | 1.183 | 1.081 | 1.678 |
8 | db9 | 2.943 | 1.924 | 1.929 | 1.887 | 1.492 | 1.267 | 1.153 | 1.793 |
9 | db10 | 2.556 | 1.976 | 1.859 | 1.634 | 1.965 | 1.341 | 1.211 | 1.932 |
表1 不同紧支集的Daubechies小波对压差波动信号的分解误差(×10-9)
Table 1 Decomposition error of Daubechies wavelet with different compact supports for pressure difference fluctuation signals(×10-9)
No. | Wavelet | Scale | |||||||
---|---|---|---|---|---|---|---|---|---|
2 | 3 | 4 | 5 | 6 | 7 | 8 | Mean | ||
1 | db2 | 2.686 | 2.605 | 2.667 | 2.667 | 2.734 | 2.405 | 2.277 | 2.572 |
2 | db3 | 2.836 | 1.919 | 2.025 | 1.961 | 2.234 | 1.366 | 1.244 | 1.949 |
3 | db4 | 2.299 | 1.885 | 1.778 | 1.647 | 1.675 | 1.105 | 1.031 | 1.631 |
4 | db5 | 2.541 | 1.905 | 1.969 | 1.739 | 1.454 | 1.266 | 1.188 | 1.723 |
5 | db6 | 3.143 | 2.060 | 1.957 | 1.869 | 1.892 | 1.426 | 1.297 | 1.949 |
6 | db7 | 2.301 | 1.877 | 1.802 | 1.619 | 2.071 | 1.282 | 1.168 | 1.732 |
7 | db8 | 2.342 | 1.918 | 1.962 | 1.671 | 1.552 | 1.183 | 1.081 | 1.678 |
8 | db9 | 2.943 | 1.924 | 1.929 | 1.887 | 1.492 | 1.267 | 1.153 | 1.793 |
9 | db10 | 2.556 | 1.976 | 1.859 | 1.634 | 1.965 | 1.341 | 1.211 | 1.932 |
图5 压差信号概貌分量8尺度分解结果(UGS = 0.25 m/s, ULS = 0.09 m/s)
Fig.5 Approximate components decomposed using Daubechies fourth order wavelet on differential pressure of severe slug flow for 8 scales (UGS = 0.25 m/s, ULS = 0.15 m/s)
图6 压差信号细节分量8尺度分解结果(UGS = 0.25 m/s, ULS = 0.09 m/s)
Fig.6 Detail components decomposed using Daubechies fourth order wavelet on differential pressure of severe slug flow for 8 scales (UGS = 0.25 m/s, ULS = 0.09 m/s)
No. | UGS/(m/s) | ULS/(m/s) | Micro-scale/% | Meso-scale/% | Macro-scale/% |
---|---|---|---|---|---|
1 | 0.07 | 0.09 | 5.34 | 21.37 | 73.29 |
2 | 0.25 | 0.09 | 3.42 | 25.92 | 70.66 |
3 | 0.7 | 0.09 | 1.52 | 28.91 | 69.57 |
4 | 0.11 | 0.06 | 4.66 | 22.35 | 72.99 |
5 | 0.23 | 0.07 | 3.51 | 21.37 | 75.12 |
6 | 0.31 | 0.07 | 2.81 | 20.66 | 76.53 |
7 | 0.56 | 0.08 | 6.82 | 23.67 | 69.51 |
8 | 0.62 | 0.11 | 5.19 | 21.26 | 73.55 |
9 | 0.91 | 0.12 | 4.29 | 24.16 | 71.55 |
10 | 1.17 | 0.12 | 3.47 | 27.91 | 68.62 |
表2 压差波动信号的三尺度能量分布
Table 2 Three scales energy distribution of pressure difference fluctuation signals
No. | UGS/(m/s) | ULS/(m/s) | Micro-scale/% | Meso-scale/% | Macro-scale/% |
---|---|---|---|---|---|
1 | 0.07 | 0.09 | 5.34 | 21.37 | 73.29 |
2 | 0.25 | 0.09 | 3.42 | 25.92 | 70.66 |
3 | 0.7 | 0.09 | 1.52 | 28.91 | 69.57 |
4 | 0.11 | 0.06 | 4.66 | 22.35 | 72.99 |
5 | 0.23 | 0.07 | 3.51 | 21.37 | 75.12 |
6 | 0.31 | 0.07 | 2.81 | 20.66 | 76.53 |
7 | 0.56 | 0.08 | 6.82 | 23.67 | 69.51 |
8 | 0.62 | 0.11 | 5.19 | 21.26 | 73.55 |
9 | 0.91 | 0.12 | 4.29 | 24.16 | 71.55 |
10 | 1.17 | 0.12 | 3.47 | 27.91 | 68.62 |
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