the identification of gas-liquid co-current two phase flow
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Modern Applied Science; Vol. 6, No. 9; 2012 ISSN 1913-1844 E-ISSN 1913-1852
Published by Canadian Center of Science and Education
56
The Identification of Gas-liquid Co-current Two Phase Flow Pattern in a Horizontal Pipe Using the Power Spectral Density and the
Artificial Neural Network (ANN)
Budi Santoso1,4, Indarto2, Deendarlianto2 & Thomas S. W.3 1 Graduate Program of Mechanical and Industrial Engineering, Faculty of Engineering, GadjahMada University, Indonesia 2 Department of Mechanical and Industrial Engineering, Faculty of Engineering, GadjahMada University, Indonesia 3 Departmen of Electrical Engineering and Information Technology, Faculty of Engineering, GadjahMada University, Indonesia 4 Department of Mechanical Engineering, Faculty of Engineering, SebelasMaret University, Indonesia
Correspondence: Budi Santoso, Department of Mechanical Engineering, Faculty of Engineering, SebelasMaret University, Jl. Sutarmi 36A Surakarta 57126, Indonesia. E-mail: msbudis@yahoo.co.id; budisant@mail.uns.ac.id
Received: July 23, 2012 Accepted: August 18, 2012 Online Published: August 29, 2012
doi:10.5539/mas.v6n9p56 URL: http://dx.doi.org/10.5539/mas.v6n9p56
Abstract This paper presents a new method of the flow pattern identification on the basis of the analysis of Power Spectral Density (PSD) from the pressure difference data of horizontal flow. Seven parameters of PSD curve such as mean (K1), variance (K2), mean at 1-3 Hz (K3), mean at 3-8 Hz (K4), mean at 8-13 Hz (K5), mean at 13-25 Hz (K6) and mean at 25-30 Hz (K7) were used as training vector input of Artificial Neural Networks (ANN) in order to identify the flow patterns. From the obtained experimental of 123 operating conditions consisting of stratified flow, plug and slug, ANN was trained by using 100 data operation and 23 tested data. The results showed that the new method has a capability to identify the flow patterns of gas-liquid two phase flow with a high accuracy.
Keywords: flow pattern identification, power spectral density (PSD), artificial neural network (ANN), two phase flow
1. Introduction The knowledge of two phase flow is of important in engineering process, such as oil industry, chemical process, power generation, and phase change heat exchanger apparatus. The common characteristics of parameter related to the flow pattern are the pressure gradient and the void fraction. The main issue in two phase flow researches is the relationship between the pressure fluctuation and flow pattern. In general, the pressure fluctuations resulted from the liquid-gas flow and their statistical characteristics are very interest for the objective characterization of the flow patterns because the required sensors are robust, inexpensive and relatively well established, and therefore more likely to be implemented in the industrial systems (Drahos et al., 1991).
Drahos et al. (1996) has already conducted the study of the wall pressure fluctuations in a horizontal gas-liquid flow by using the methodology of chaotic time series analysis in order to obtain a new insight of the dynamics of the intermittent flow patterns. Next, Franca et al. (1991) presented the fractal techniques for flow pattern identification and classification. They observed that PSD and PDF could not easily be used for the flow pattern identification and the objective discrimination between separated and intermittent regimes. Ding et al. (2007) reported the application of the Hilbert-Huang Transform (HHT) to the dynamic characterization of transportation of the gas-liquid two-phase flow in a horizontal pipe. Matsui et al. (2007) studied the sensing method of gas-liquid two phase flow in horizontal pipe on the basis of statistical processing of differential pressure fluctuation. The flow pattern, the void fraction and the velocity of gas phase were measured by PDF and cross correlation. From the view point of engineering, the above method’s are subjective in nature, therefore a newly scientific based method is needed.
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Artificial Neural Network (ANN) provides an alternative method for either modeling phenomena which are too difficult to model from fundamental principles, or reduce the computational time for predicting expected behavior. Artificial neural network is based on the important rules for classifying the flow pattern. Neural network stimulate human mind and demonstrate high intelligence and it can be trained to study the correct output and classify training exercises. Here, neural network needs knowledge input for training. After the training, the neural network can classify the similar flow pattern with a high accuracy.
Cai et al. (1994) applied the Kohonen self-organizing neural network in order to identify the flow pattern in a horizontal air-water flow. In their work, the neural network was trained with stochastic features derived from the turbulent absolute pressure signals obtained across a range of the flow regimes. The feature map succeeded in classifying samples into distinctive flow regime classes consistent with the visual flow regime observation. Next, Wu et al. (2001) recorded the pressure difference signal in pipe flow and used the fractal analysis to analyze them for identification of flow pattern. By using the ANN, the good result was obtained but it is only considered stratified, intermittent and annular flows. For this reason, Jia et al. (2005) proposed a new flow pattern identification method based on PDF and neural network at the horizontal flow in pipe.
Xie et al. (2004) examined the feasibility of the implementation of the artificial neural network (ANN) technique for the classification of flow regimes in three phase gas/liquid/pulp fiber systems by using the pressure signals as input. For this purpose, the flow behavior by using the power spectral density function is needed to implement the parameterization of the information contained in the spectral patterns.
Table1. The experiment conditions using pressure sensor
Authors System Diameter/ Orientation
Measurement technique Method and finding
Franca et al. (1991)
Water-air (wavy, plug, slug and annular)
D=19 mm; horizontal
Pressure drop, XDP=8D, N=5 000
Using fractal techniques for flow pattern identification and classification.
Cai et al. (1994)
Water-air (stratified, slug, intermittent transition, and bubble)
D= 50 mm; horizontal
Two absolute pressure, XDP=1D, SR=40Hz, N=40 000
Kohonen self-organizing neural network to identify flow regimes.
Drahos et al. (1996)
Water-air (plug and slug)
D=50 mm; horizontal
wall pressure fluctuations, XDP=8D, SR=500Hz, N=60 000
Chaotic time series analysis to obtain a new insight into the dynamics of the intermittent flow pattern.
Wu et al. (2001)
Oil-gas-water, (stratified, intermittent and annular)
D= 40 mm; horizontal
Differential pressure, XDP=5D,
The fractal analysis to analyze the signal for identification of flow pattern.
Jia et al. (2005)
Water-air (stratified, churn, slug, annular)
D= 32 mm; horizontal
Differential pressure, XDP=10D, SR=200Hz, N=6 000
Flow pattern identification method based on PDF and neural network.
Matsui et al. (2007)
Water and nitrogen gas (small bubble train, plug and slug)
D= 7 mm; horizontal
Differential pressure, XDP=1D, XDP=7D SR=100Hz, N=2 000
The flow pattern, the void fraction and the velocity of gas phase were measured by PDF and cross correlation.
Hao et al. (2007)
Water-air, (wavy, bubble, plug and slug)
D=15 mm, 25 mm, 40 mm; horizontal
Differential pressure, XDP=250mm, SR=200Hz, N=30 000
The application of the Hilbert–Huang Transform (HHT) to identify flow regimes.
Xie et al. (2004)
Gas-liquid-pulp fiber (churn, slug)
D= 50.8mm, vertical
Local pressure fluctuations, SR=200Hz, N=2 000
To characterize the hydrodynamics of the flow based on the power spectral density function.
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AcknowleThis workof Higher “Hibah Pa
Reference
Cai, S., HIdentihttp:/
Demuth, H
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art of test exam
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fication ability
Result of identi
f flow pattern
f correct identi
of identificatio
sion r uses a differeural network cteristics of thas the merits his method hatificial interve
ature tificial neural n
erential pressur
erage different
rmalized press
superficial ve
uperficial veloc
wer spectral de
edgments k was supporte
Education) Mascasarjana UG
e
Haluk, T., Jiaification in Air//dx.doi.org/10
H., & Beale, M
mples and iden
conditions of e selected as te
of the neural n
fication use Ba
ification
on rating
rential pressurintelligently id
he differentialsuch as easy as a advantagntion.
network
re (Pa)
tial pressure (P
ure different s
elocity (m/s)
city (m/s)
ensity
ed by DP2M DMinistry of EduGM 2012”.
anhung, Q., &r-Water Two P
0.1002/cjce.545
M. (2000). Neur
Modern
ntification resu
f experiment aest samples. Tanetwork is very
ack Propagatio
Stratif
10
re transducer tdentifies the fll pressure sign
computation ge method for
Pa)
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DIKTI (Directoucation and Cu
& John, S. A.Phase Flow. Th50720308
ral Network To
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ults
are selected asable 3 and Taby good.
on Artificial N
fied flow 5
5
00%
to measure thflow pattern. Stnals at differeand easily quthe industrial
orate of Reseaulture Indonesi
. (1994). NeuThe Canadian J
oolbox for Use
ce
s training modble 4 show the
Neural Network
Plug flow9
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100%
he differential tatistical analyent flow conduantifying the l application s
arch and Publiia through the
ural Network Journal of Che
e with MATLAB
dels to train thresult of iden
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9
pressure of twysis of PSD wditions. Result
characteristicsuch as high
ic Service of DCompetitive G
Based Objectemical Enginee
B. The MathW
Vol. 6, No. 9;
he network anntification, in w
ug flow 9
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98%
wo phase flowas used to quats showed thacs of the measaccuracy, fast
Directorate GeGrant Research
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Works, Inc.
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nd 23 which
w and antify at the sured t and
neral h and
gime -445.
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Appendix The PSD Theory
The goal of spectral analysis is to describe the distribution of the power contained in a signal over a frequency, based on a finite set of data. It converts information available in the time-domain into the frequency-domain. The averaged modified periodogram method was adopted to diminish the distortion of the spectrum due to a finite length of data record. If x(n) (n=0, 1, ... , N−1) is only measured over a finite interval, the power spectral density may be computed using the periodogram method:
k
fsfkiekxRfPx 2ˆ)(
(2)
Where: N is finite length of a discrete time signal, k is discrete time shift, f is frequency,fs is the sampling frequency and the autocorrelation is given as
kN
Nn
nxknxN
kxR1
)()(1
)(ˆ
(3)
The Statistical Theory
The statistical analysis methods mentioned clustered PSD data are mean and variance. These features are used as inputs to the neural network.
The mean is given by,
N
iix
N 1
1
(4)
The variance is given as,
N
iix
N 1
2
1
1
(5)
The Back Propagation ANN
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66
These networks usually contain three types of layers:
1. An input layer
2. A hidden layer sigmoid bipolar and
3. An output layer linear transfer/ramp
Training process:
Step 1. Design the structure of neural network and input parameters of the network
Step 2. Get initial weights W and initial θ values from randomizing.
Step 3. Input training data matrix X and output matrix T.
Step 4. Compute the output vector of each neural unit.
(a) Compute the output vector H of the hidden layer
kiikk XWnet
(6)
kk netfH (7)
(b) Compute the output vector Y of the output layer
jikjj HWnet
(8)
jj netfY
(9)
Step 5. Compute the distances
(a) Compute the distances d of the output layer
jjjj netfYT '
(10)
(b) Compute the distances of the hidden layer
jkkjjk netfW '
(11)
Step 6. Compute the modification of W and θ (η is the learning rate)
(a) Compute the modification of W and θ of the output layer
kjkj HW
(12)
jj
(13)
(b) Compute the modification of W and θ of the hidden layer
ikik XW (14)
kk (15)
Step 7. Renew W and θ
(a) Renew W and θ of the output layer
kjkjkj WWW
(16)
jjj
(17)
(b) Renew W and θ of the hidden layer
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ikikik WWW (18)
kkk (19)
Step 8. Repeat step 3 to step7 until convergence.
Testing process:
Step 1. Input the parameters of the network.
Step 2. Input the W and θ
Step 3. Input an unknown data matrix X
Step 4. Compute the output vector
(a) Compute the output vector H of hidden layer
kiikk XWnet
(20)
kk netfH (21)
(b) Compute the output vector Y of the output layer
jikjj HWnet
(22)
jj netfY
(23)
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