Analysis of multi-scale fractal characteristics of severe slugging based on Hurst exponent

doi:10.11949/0438-1157.20231089

Abstract

Abstract:

Based on the multi-scale method and Hurst analysis, the multi-scale structure and nonlinear characteristics of severe slugging flow were studied in the present work. Experimental investigation on severe slugging were performed in pipeline-riser system using air and water and the signal of pressure difference was recorded. Based on db4 wavelet, the signal of pressure difference was decomposed and reconstructed at 1—8 scales. The dynamics characteristics of gas-liquid two-phase flow at each individual scale were extracted. It was found that the transient process of gas blowout and liquid fallback in severe slug flow was mainly reflected in the detail signals at d5—d8 scales. The result of Hurst exponent analysis on the decomposed signals of pressure difference fluctuation shows that severe slug flow has significant bi-fractal characteristics, which are constrained by two dynamic factors, i.e. positive persistence and anti-persistence. However, the approximate component and the detail component exhibit completely opposite fractal structures. The approximate component has positive persistence, while the detail component has anti persistence. The detail component at scale d1 describes the interaction between micro-scale bubbles. The meso-scale interaction between liquid phase and gas bubbles was reflected by the detail components at the d2—d5 scales. The macro-scale interaction between gas-liquid phase and the pipe wall was described by the detail components at the d6—d8 scales. The energy of the pressure difference fluctuation signal is mainly distributed at the macro-scale.

Key words: severe slugging, differential pressure, multi-scale, fractal, gas-liquid flow, Hurst exponent

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。

关键词: 严重段塞流, 压差, 多尺度, 分形, 气液两相流, Hurst指数

CLC Number:

O 359.1

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.

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.

Figures/Tables 12

Fig.1 Gas-liquid two-phase flow experimental system

Fig.2 Schematic diagram of three-scale decomposition based on wavelet transform

Fig.3 Flow pattern map

Fig.4 Pressure difference curves of severe slug flow under different gas and liquid flow rates

Table 1 Decomposition error of Daubechies wavelet with different compact supports for pressure difference fluctuation signals（×10-9）

No.	Wavelet	Scale
No.	Wavelet	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

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)

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)

Fig.7 R/S analysis of 8-scale approximate signals of severe slug flow

Fig.8 R/S analysis of 8-scale detail signals of severe slug flow

Fig.9 Hurst exponent H of the approximate component and detail component at each scale

Fig.10 Resolution of differential pressure fluctuation signal into micro-scale, meso-scale and macro-scale

Table 2 Three scales energy distribution of pressure difference fluctuation signals

No.	U_GS/(m/s)	U_LS/(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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