Flow noise characterization of gas–liquid two-phase flow ...or.nsfc.gov.cn/bitstream/00001903-5/96690/1/1000007213444.pdfFlow noise characterization of gas–liquid two-phase

Measurement 46 (2013) 3887–3897

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Measurement

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Flow noise characterization of gas–liquid two-phase flow basedon acoustic emission

0263-2241/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.measurement.2013.07.032

⇑ Corresponding author. Tel.: +86 0312 5079330; fax: +86 03125092717.

E-mail addresses: [email protected] (L. Fang), [email protected](Y. liang), [email protected] (Q. Lu), [email protected] (X. Li),[email protected] (R. Liu), [email protected] (X. Wang).

Lide Fang ⇑, Yujiao liang, Qinghua Lu, Xiaoting Li, Ran Liu, Xiaojie WangCollege of Quality and Technical Supervision of Hebei University, No. 180 Wusi East Road, 071000 Baoding, Hebei, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 2 November 2012Received in revised form 17 July 2013Accepted 24 July 2013Available online 17 August 2013

Keywords:Wavelet transformChaosCorrelation planeFlow noiseAcoustic emissionFlow transition

Flow noise of gas–liquid two-phase flow in horizontal pipeline was detected by using theacoustic emission technique (AE); signals were processed by wavelet transform and cha-otic analysis. Conclusions were drawn that stratified flow, annular flow and their transitioncan be divided clearly through multi-scale energy distribution of flow noise, and thatdynamic characteristic of flow pattern transition from stratified flow to annular flow,which is described via correlation dimension, acts in accordance with that of annular flow.The dynamic characteristic of the transition condition has already been consistent withthat of the annular flow, but due to the low gas flow rate, the energy of the hydrodynamicnoise was not enough to reach the complete annular flow pattern. Results were in accor-dance with experimental facts. Flow noise reflects the complexity of gas–liquid two-phaseflow by means of multi-scale energy distribution and chaotic features. Consequently, flownoise based on acoustic emission is a novel and promising point for researching gas–liquidtwo-phase flow.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Two-phase flow exists widely in petroleum, chemical,metallurgy, transportation, refrigeration and other fields;so it has a very important significance to discuss the mech-anism of two-phase flow for the research and developmentof modern industrial equipment. Due to the complexity ofgas–liquid two-phase flow, experiment is often ahead oftheory, which is to explain experimental phenomena byusing various theories and then gradually forming theoret-ical results. Therefore, plenty of research areas of gas–li-quid two-phase flow still need to explored andconsummated. And because of this, more and moreresearchers have attempted to apply a variety of sensingtechnologies, including numerous detection methods inother researching fields, to measure two-phase flow in

order to obtain an experimental and theoreticalbreakthrough.

Zheng et al. [1] used the combination instrument of tur-bine flowmeter and conductance sensor with petal typeconcentrating flow diverter to solve the flow rate measure-ment problem of gas–liquid two-phase flow. Shi and Geng[2] from differential pressure signal’s perspective exploredhow to better characterize flow characteristics. Marco et al.[3] employed capacitance signal to determine the phaseholdup of cross section. César et al. [4] applied the gammaray to identify flow regimes and predict volume fraction.Roitberg et al. [5] used a wire-mesh sensor and a digitalcamera to measure the instantaneous phase distributionon the pipe cross section. Mena et al. [6] applied a monofi-ber optical probe on three-phase flow to investigate thegas phase velocity and gas phase flow residence time.

This article, from the view of flow noise, explored char-acteristics of gas–liquid two-phase flow. In gas–liquid twophase flow, hydrodynamic noise exists objectively; how-ever, there have been few reports about it. The gas–liquidtwo-phase flow is a typical fluid–solid coupling system,

3888 L. Fang et al. / Measurement 46 (2013) 3887–3897

and the impact between liquids and pipe mainly comprisesa fluid–solid coupling and Poisson coupling. Flow noise ofgas–liquid two-phase flow caused by coupling effect is re-ceived in the form of elastic wave by four acoustic emissionprobes coupled to the pipe wall. The noise signal will beamplified, processed and displayed. Then, the mechanismof gas–liquid two-phase flow can be investigated fromthe microscopic view. Flow noise is easy to obtain, and sig-nal collection is non-invasive, having no influence on flowpattern of gas–liquid two-phase flow; and the flow mediadoes not harm the probe as well. Therefore, this paper usesthe acoustic emission technique to research flow noise ofgas–water two-phase flow in horizontal pipeline, whichis a new point to reveal features of two-phase flow.

2. Experimental setup

2.1. Acoustic emission principle

The material or structure under stress deformation canform elastic waves internally to release strain energy, andthe acoustic emission technique uses piezoelectric probecoupled on the surface of material or component to detectthese elastic waves and convert them into electrical sig-nals, from which the internal situation of material or com-ponent can be obtained. Therefore, flow noise is obtainedmore easily than pressure and differential pressure signal;from microcosmic angle, flow noise reflects the complexityof gas–liquid two-phase flow. Fig. 1 just with one probesymbolically shows a schematic diagram of flow noiseacquisition.

As shown in Fig. 1, Probe is a piezoelectric probe cou-pled on the surface of pipe through high vacuum grease.The signal of flow noise detected by probe is processedby AMSY-5, an acoustic emission system manufacturedby Vallen-System GmbH. Then, the voltage signal is sent

Fig. 1. Flow noise acquisition principle diagram.

Fig. 2. Experimental s

to a computer for recording and displaying. These recordswill be exported to a text for further data processing suchas wavelet transform and chaotic analysis.

2.2. Experimental structure

The experiment was conducted in Low-pressure andMoisture Laboratory of Tianjin University. Flow noiseacquisition was completed through AMSY-5, with sam-pling rate 5 MHz and sampling points 524288. Experimen-tal structure is shown in Fig. 2.

In Fig. 2, the arrow indicates the direction of fluid flow,E is a transparent pipe made of organic glass, which facili-tates watching flow regime; B is a flange; C is a metal pipe;experimental pipe diameter D is 50 mm; A–A is on which 4probes is fixed, and fixing detail is shown in Fig. 3.

As shown in Fig. 3, the black point shows the directionin which fluid flows; C1, C2, C3, and C4 is short for probe 1,probe 2, probe 3, and probe 4, respectively. These fourprobes through the system displayed in Fig. 1 acquire sig-nals of flow noise which are sent to AMSY-5 in the nextstep.

2.3. Experimental parameters

Three experimental pressure points are 0.05, 0.1,0.15 MPa, taking 0, 0.05, 0.15, 0.25, 0.35, 0.45, and0.55 m3/h to be liquid phase points, with 0, 20, 30, 40,50, 60, 70, 80, 90, 120, 150, and 180 m3/h as gas phasepoints. With the combination of these working conditions,stratified flow, annular flow and their transition are

ystem structure.

Fig. 3. Probe position.

Table 1Experimental parameters.

Pressure(MPa)

Liquid flowrate (m3/h)

Gas flow rate (m3/h)

0.05 0 0, 30, 60, 90, 120, 150, 180, 0, 20, 30, 40,50, 60, 70, 80, 90, 120, 150, 1800.05

0.150.250.350.450.55

0.1 0 0, 30, 60, 90, 120, 150, 1800.05 0, 20, 30, 40, 50, 60, 70, 80, 90, 120, 150,

1800.150.250.350.450.55

0.15 0 0, 30, 60, 90, 120, 150, 1800.05 0, 20, 30, 40,50, 60, 70, 80, 90, 120, 150,

1800.150.250.350.450.55

Table 2Frequency analysis data.

Signal Pressure(MPa)

Liquid flow rate(m3/h)

Gas flow rate(m3/h)

Probe

1 0.05 0 0 C22 0.05 0.25 60 C33 0.05 0.55 210 C44 0.1 0 0 C25 0.1 0.25 60 C36 0.1 0.55 180 C47 0.15 0.05 20 C28 0.15 0.25 60 C39 0.15 0.55 90 C4

Fig. 4. Flow noise spectrum under 0.05 MPa. (a) Flow noise spectrum of the seconoise spectrum of the third probe—C3 when water flow is 0.25 m3/h and gas floflow is 0.55 m3/h and gas flow is 210 m3/h.

L. Fang et al. / Measurement 46 (2013) 3887–3897 3889

generated to investigate flow noise characterization ofgas–liquid two-phase flow. Configuration details of exper-imental parameters are listed in Table 1.

Experimental media are air and water. In the pipeline,water flow rate is fixed, and gas flow rate increased gradu-ally. After observing flow regime, water flow rate is in-creased, starting next experiment. Individual gas phasepoint extends to 210 m3/h.

3. Data processing

Acoustic emission signal measured in this study is aflow noise signal of gas–liquid two-phase flow, which be-longs to the continuous high-frequency signal. Cite refer-ences have explored various high frequency signalprocessing methods for gas–liquid two-phase flow. Vanet al. [7] used the method of wavelet transform in verticalupward pipe of gas–liquid two-phase flow to research voidratio. Sun et al. [8], directing at the differential pressuresignal of gas–liquid two-phase flow, employed empiricalmode decomposition (EMD) and independent componentanalysis (ICA) to establish characteristic vectors for un-known flow patterns, a better characterization of flow pat-tern. Sun et al. [9] applied wavelet transform to denoisesignals, used chaos and fractal technology to research thegas–liquid two-phase flow differential pressure signal,and achieved the result that attractor can characterizethe kinetic behavior of gas–liquid two-phase flow system.Langford et al. [10], using chaotic analysis method, dealtwith pressure signal of air–water two-phase flow in theheat rising pipe to prove that correlation dimension andK entropy can deeply explain nonlinear dynamic character-istics of system. Letel et al. [11], applying chaos, analyzedpressure signal in a gas–liquid reactor to point out thatthe relation between K entropy and superficial gas velocitycan determine the flow pattern transition point. Jin et al.,

nd probe—C2 when water flow is 0 m3/h and gas flow is 0 m3/h; (b) floww is 60 m3/h; (c) flow noise spectrum of the forth probe—C4 when water

3890 L. Fang et al. / Measurement 46 (2013) 3887–3897

using the differential pressure densimeter to analyze theflow pattern of oil–gas–water three-phase flow, thoughtits three-phase flow is a low dimensional chaotic system,attractor dimension ranging from 4.16 to 5.87, fractaldimension ranging from 1.18 to 1.46. Bai et al. [12] consid-ered that fractal dimension of differential pressure fluctu-ation in the upward section of U type tube in annularflow is greater than 1.5 at a high gas velocity, within otherflow patterns it is less than 1.5, and that superficial liquid

Fig. 5. Flow noise spectrum under 0.1 MPa. (a) flow noise spectrum of the seconoise spectrum of the third probe—C3 when water flow is 0.25 m3/h and gas floflow is 0.55 m3/h and gas flow is 210 m3/h.

Fig. 6. Flow noise spectrum under 0.15 MPa. (a) Flow noise spectrum of the seconoise spectrum of the third probe—C3 when water flow is 0.25 m3/h and gas floflow is 0.55 m3/h and gas flow is 210 m3/h.

velocity strongly affects the chaotic characteristic of pres-sure difference fluctuation.

Based on previous researches, in order to reduce theamount of data and extract effective noise characteristicparameters, this paper calculated energy of the corre-sponding scale coefficients under wavelet transform, andgiven the strong nonlinearity of two-phase flow, in themeantime, the selection of correlation dimension is

nd probe—C2 when water flow is 0 m3/h and gas flow is 0 m3/h; (b) floww is 60 m3/h; (c) flow noise spectrum of the forth probe—C4 when water

nd probe—C2 when water flow is 0 m3/h and gas flow is 0 m3/h; (b) floww is 60 m3/h; (c) flow noise spectrum of the forth probe—C4 when water

Table 5Information entropy ratio of each decomposition scale.

Informationentropy (%)

P0L055G0C3 P50L055G80C3 P50L055G150C3

cD1 62.07 64.21 66.65cD2 44.26 42.97 44.38cD3 30.86 28.47 29.46cD4 21.24 18.93 19.5cD5 13.95 13.05 12.8cD6 9.56 9.17 8.34cD7 6.32 5.84 5.44cD8 4.1 3.55 3.51cD9 2.63 2.21 2.21cD10 1.66 1.54 1.4cD11 0.98 0.82 0.8811cD12 0.62 0.62 0.54

Table 6Energy proportion at each scale of wavelet decomposition.

Energy (%) P50L055G0C3 P50L055G80C3 P50L055G150C3

cD1 20.1002 0.9357 0.9759cD2 21.7307 3.5534 3.8135cD3 14.4465 12.8538 13.927cD4 5.5161 35.2227 39.3639cD5 2.5328 40.1653 37.8648cD6 0.7741 5.4627 2.7025cD7 0.3532 1.1673 0.9172cD8 0.19 0.4617 0.3421cD9 0.0885 0.0963 0.0712cD10 0.0408 0.0199 0.0164cD11 0.0253 0.0084 0.0039cD12 0.024 0.0014 9.45E�04

L. Fang et al. / Measurement 46 (2013) 3887–3897 3891

necessary for analyzing dynamic characteristics of two-phase flow noise.

3.1. Frequency domain analysis

Nine groups of data shown in Table 2 are adopted toanalyze the frequency-domain feature of flow noise.Results are drawn in Figs. 4–6.

Although the transition from stratified flow to annularflow in the experiment under working conditions as shownin Figs. 4(b), 5(b) and 6(b) has been observed, respectively,meanwhile, the annular flow is observed under shownworking conditions in Figs. 4(c) and 5(c), respectively, itcan be seen from Figs. 4–6 that regardless of different li-quid flow rates, gas flow rates, and distinct flow patternsobserved, the main band of signal is similar and overlap-ping, mainly concentrating between 50 and 150 kHz.Therefore, it is not rational from the spectrum of flow noiseto identify flow regimes and their transitions, and wavelettransform and chaotic analysis are necessary.

3.2. Wavelet analysis

Wavelet transform, which has been applied widely insignal analysis, speech synthesis, image recognition, com-puter vision, data compression, seismic surveys, and atmo-spheric and ocean wave analysis [13], is mainly used intwo ways in the field of multiphase flow: first, it is aboutsignal pretreatment for removing noise; second, it is aboutdata compression to extract feature parameters.

Different wavelet bases applied in signal analysis willyield different results, sometimes drawing opposite con-clusion. Therefore, the choice of wavelet basis should takeinto account wavelet basis properties, including orthogo-nality, compact support, symmetry and regularity, etc.[14]. However, for how to choose a proper and reasonablewavelet basis, academia has no unified theory and

Table 3Wavelet base comparison.

Wavelet base Haar DaubechiesAbbreviation in MATLAB haar db

Orthogonalityp p

Biorthogonalityp p

Compact supportp p

Symmetryp �

Regularity � —CWT

p p

DWTp p

Table 4Signal reconstruction error.

Waveletbase

1 2 3

Haar 1.1153E�17 — —Daubechies — 3.5936E�14 3.9819E�13Biorthogonal 1.2042E�17

(bior1.3)1.22E�17(bior1.5)

1.5209E�17(bior2.2)

Coiflets 5.3237E�14 6.7071E�13 3.0460E�14Symlets 1.1153E�17 3.5936E�14 3.98E�13

understanding. Most scholars will link the wavelet basisselection criteria with the original signal characteristics.Consequently, sifting of wavelet basis based on signal char-acteristics and research purpose is essential. For this rea-son, this paper applies signal reconstruction error and

Biorthogonal Coiflets Symletsbior coif sym

� p pp p pp p pp

— —� � �p p pp p p

4 5 6

— — —7.5481E�14 1.1492E�13 5.3889E�142.2338E�17(bior3.1)

1.4999E�17(bior3.9)

8.7796E�18(bior2.4)

1.4017E�12 3.2205E�10 —2.9440E�14 1.0095E�14 4.7361E�14

3892 L. Fang et al. / Measurement 46 (2013) 3887–3897

properties of wavelet basis to determine the wavelet basis,information entropy and energy of each scale to determinethe decomposition scale [14]. This article utilizes wave-dec() in MATLAB to decompose flow noise and calculateenergy logarithm of scale coefficients.

3.2.1. Selection of wavelet base and decomposition scaleFive kinds of wavelet families (Haar, Daubechies, Bior-

thogonal, Coiflets and Symlets) in MATLAB are selected tocompare their properties, including orthogonality, bior-thogonality, compact support, symmetry, regularity, con-tinuous wavelet transform (CWT) and discrete wavelettransform (DWT), shown in Table 3.

In Table 3,p

indicates having this property, � does nothaving this property, and — shows that some wavelet basisin a wavelet family have this property, some do not. FromTable 3, all of these wavelet bases property of CWT and

Fig. 7. Energy logarithm of scale coefficients u

Fig. 8. Energy logarithm of scale coefficients un

DWT. Haar, the simplest wavelet base, is not continuous.Biorthogonal does not have property of orthogonality.

Table 4 displays signal reconstruction error of flownoise collected by C3 probe under the condition of liquid0.55 m3/h and gas 80 m3/h. The signal decomposition levelequals 5.

In Table 4, bior1.3 bior1.5, bior2.2, bior3.1, bior3.9, andbior2.4 in a biorthogonal wavelet family, are used to calcu-late the corresponding reconstruction error. From Table 4,Haar, Biorthogonal and Symlets, three kinds of wavelet ba-sis, are suitable to treat flow noise. Therefore, combiningTables 3 and 4, the best choose is Haar (the simplest wave-let base).

Information entropy reflects the average uncertainty ofsystem before outputting signal. The greater the entropy,the greater the uncertainty of information is. It is generallybelieved that when the entropy of detail coefficient ac-counts for less than 5% of the original signal entropy, the

nder 0.1 MPa, liquid flow rate: 0 m3/h.

der 0.1 MPa, liquid flow rate: 0.25 m3/h.

Fig. 9. Energy logarithm of scale coefficients under 0.1 MPa, liquid flow rate: 0.55 m3/h.

L. Fang et al. / Measurement 46 (2013) 3887–3897 3893

analysis should be stopped [14]. The entropy analysis offlow noise acquired by C3 probe under 0.05 MPa, liquidphase point 0.55 m3/h, and gas phase point 0, 80 and150 m3/h is shown in Table 5.

In Table 5, cDi (i = 1, 2, . . . , 12) is the detail coefficientunder corresponding decomposition scale. It can be seenfrom Table 5 that the entropy ratio of the detail coefficient,cD8, is less than 5% of the original signal information en-tropy, and that decomposition is no longer necessary.

Fig. 10. Comparison of c

Therefore, from the perspective of information entropy,signal should be decomposed into 7th scale.

Three signals shown in Table 5 are analyzed to calculateenergy proportion, which is listed in Table 6.

In Table 6, P50 is a simplified form of 0.05 MPa, L055 asimplified form of liquid 0.05 m3/h, G80 a simplified formof gas 80 m3/h. C3 is C3 probe shown in Fig. 3. (In the fol-lowing figures, the similar symbols have the same mean-ing.) From the view of energy, scale 6 is appropriate for

orrelation planes.

Fig. 11. Correlation plane of P100L025G180C3.

3894 L. Fang et al. / Measurement 46 (2013) 3887–3897

decomposition. Considering above analysis, Haar waveletbase and scale 6 are rational to choose for decomposingflow noise.

3.2.2. Wavelet decompositionFig. 9 indicates the energy logarithm of scale coeffi-

cients under wavelet decomposition on flow noise de-tected by C2 probe under 0.1 MPa, liquid phase point0 m3/h, and gas liquid points ranging from 0 m3/h to

Fig. 12. Evolution of c

180 m3/h. Figs. 10 and 11 shows the energy logarithm offlow noise acquired by C2 probe under 0.1 MPa, gas liquidpoints ranging from 0 m3/h to 180 m3/h. X-axes, Y-axes ofboth Figs. 9–11 are scale coefficients and energy logarithm,respectively.

From Fig. 7, wavelet decomposition scale energy distri-bution of pure gas flow noise is analogous, and the acous-tic emission energy of flow noise is very low, only the gas180 m3/h having a greater change, which is in accordancewith the following correlation dimension analysis. G0–G30, G40–G90, and G120–G180 under each liquid pointmaintain a similar energy distribution, respectively,which can be seen from Figs. 8 and 9 indicating that inthe case of liquid existing, G0–G30 belong to the sameflow pattern, stratified flow, G120, G150 and G180belonging to the same flow regime, annular flow, G40–G90 belonging to the transition state. And the interactionbetween gas and liquid contribute to noise energy greatly.Wavelet decomposition scale energy distribution of flownoise shows the flow division and transition preciselyand distinctly.

3.3. Chaos analysis

Literatures [15–17] studied correlation plane, and con-sidered that the correlation plane can distinguish chaosand noise signals better. For chaotic signal, if parametersand initial condition randomly change, correlation planes

orrelation plane.

L. Fang et al. / Measurement 46 (2013) 3887–3897 3895

have a similar shape, varying in a certain range and per-forming stability on the whole. The intricacy of phasetrajectory in the correlation plane points the local instabil-ity, indicating a certain sequence association. When thetrajectory fills the entire plane and loses locality, the se-quence association does not exist, and signal analyzed ex-presses randomness. Therefore, correlation planes aredrawn to compare the deterministic signal, random signal,Logist chaotic signal and flow noise signal based on acous-tic emission, and then calculated correlation dimension offlow noise.

In 1983, Grassberger and Procaccia basing on theembedding theory and the phase space reconstruction pro-posed G–P algorithm [18,19]. From G–P algorithm, correla-tion dimension (Dc) can be directly calculated according tothe time series. Using G–P algorithm, this paper calculatedthe correlation dimension of flow noise in MATLAB envi-ronment, determining delay time s through the first inflec-tion point of the autocorrelation function. Vector Xi (i = 1,2, . . . , Nm) in the phase space reconstruction was derivedfrom Eq. (1).

rij ¼ ðXi;XjÞ ¼ sumXm�1

i¼0

absðXiþls � XjþlsÞ" #

ð1Þ

where Xi, Xj, are vectors in the phase space reconstruction,sum() function for summation, abs() function for absolutevalue. The correlation integral function C(r) under given

Fig. 13. Evolution of co

m is obtained by repeating this process for all Xi (i = 1,2, . . . , Nm). And the slope of log2 C(r)–log2 r in a non-scalerange equals Dc. Then m is increased to calculate Dc in thesame way until Dc saturation.

3.3.1. Correlation planeThe deterministic signal is taken by 2000 numbers of

y = x2; rand() in MATLAB generates the random signal;l = 4 in Logist equation xn+1 = lxn(1 � xn), the initial valueof xn equals 0.9, taking the final 2000 numbers of 10,000iterations as the chaos signal; flow noise is acquired byC4 probe under 0.05 MPa shown in Fig. 10.

The deterministic signal displays in the correlationplane just as a line in Fig. 10(a), expressing the determi-nacy; the random signal occupies the whole correlationplane in Fig. 10(b), losing the sequence association; the Lo-gist chaotic signal exists in the local of Fig. 10(c), with anunstable interior displaying the local instability and globalstability; Fig. 10(d) has a similar correlation plane with asimilar correlation plane with (c), showing analogical cha-otic features.

Fig. 11 shows the correlation plane of flow noise under0.1 MPa collected by C3 probe.

Unlike Fig. 10(b), full of correlation plane, the sequenceassociation does exist in signal amplitude of flow noise,which can be seen from Figs. 10(d) and 11. Flow noisebased on acoustic emission with property of correlationplane is globally bounded, but instable in the local. From

rrelation plane.

Fig. 14. Evolution of correlation plane.

Fig. 15. Correlation dimension of flow noise under 0.1 MPa.

3896 L. Fang et al. / Measurement 46 (2013) 3887–3897

flow noise, chaotic features of two-phase flow dynamicsystem can be revealed, which is consistent with Baiet al. [12,20] and Yang et al. [21].

To reveal the evolution of correlation plane of flownoise, signals collected by C2 probe under 0.1 MPa areadopted, as shown in Figs. 12–14.

L. Fang et al. / Measurement 46 (2013) 3887–3897 3897

It can be seen from Figs. 12–14 that gas 0, 20, 30 m3/hshare similar planes, gas 60, 70, 80, 90, 120, 150, 180 m3/h having resemble planes, gas 40, 50 m3/h showing a tran-sition state.

3.3.2. Correlation dimensionFig. 15 shows correlation dimension of flow noise under

0.1 MPa. Data displayed in Fig. 15(a) is processing result ofsignals collected by C2 probe, (b) by C3 probe, (c) by C4probe. The horizontal axis is gas flow rate in Fig. 15; thelongitudinal axis is correlation dimension.

The correlation dimension of gas flow rate 180 m3/h inpure gas is low, compared to other gas points, which is dis-played in Fig. 15 and related to higher energy of G180 inFig. 7. From Fig. 15(a)–(c), it can be concluded that in gasphase points 0, 20, 30 m3/h, correlation dimension main-tains a high value, about 6.5; in gas points ranging from60 m3/h to 180 m3/h, it holds a lower value, about 4; how-ever, correlation dimension of gas points 40 and 50 m3/hkeeps a transition condition. Three states of correlationdimension described above demonstrate that gas 0, 20and 30 m3/h have a similar system dynamic characteristic,gas 60–180 m3/h keeping a alike system dynamic charac-teristic, gas 40 and 50 m3/h being in a transition state,according with the analysis of correlation plane evolutionshown in Figs. 12–14. Combined with scale energy distri-bution of wavelet decomposition, in experiment of gasG60–G90, a stable annular flow does not appear due tothe low gas velocity, the energy of flow noise having notyet reached a certain degree, but from the stability of cor-relation dimension, system dynamic characteristics ofG60–G90 keep the same as G120–G180, consisting withthe state of correlation plane reflected by the correlationplane of flow noise. The correlation plane of G0–G30 andG60–G180 under per liquid point maintains similar shapes,respectively, while G40–G50 is in the transition state,which is also consistent with flow patterns observed inthe experiment.

4. Conclusion

1. The main energy of flow noise of gas–liquid two-phaseflow concentrates on two bands, cD4 and cD5, with themain spectrum ranging from 50 to 150 kHz.

2. The energy distribution of flow noise decomposed bywavelet accurately reflects characteristics of flow pat-terns and transition.

3. Correlation dimension of flow noise in horizontal pipeflow essentially displays system dynamic characteris-tics, revealing characteristics of flow regime transition.

Limited to experimental conditions, this paper onlyconsiders stratified flow, annular flow, and their transitionstate in a horizontal pipe. Other flow regimes need a fur-ther research. Flow noise based on the acoustic emissiontechnique in gas–liquid two-phase flow reflects the com-plexity of two-phase flow system from the microscopicpoint of view. With the development of theory and methodabout high-frequency signal processing, the nature of two-phase flow can be revealed from flow noise.

Acknowledgements

This study is funded by National Natural Science Foun-dation 61074174, Natural Science Foundation of HebeiProvince F2011201040, and Key project of the Ministry ofEducation, Hebei Province ZH2012064 and supported byLow-pressure Moisture Device Laboratory of TianjinUniversity.

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