the identification of gas-liquid co-current two phase flow

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: [email protected]; [email protected]

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.

www.ccsenet.org/mas Modern Applied Science Vol. 6, No. 9; 2012

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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)


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)


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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Reference

Cai, S., HIdentihttp:/

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Haluk, T., Jiaification in Air//dx.doi.org/10

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anhung, Q., &r-Water Two P

0.1002/cjce.545

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Drahos, J., Tihon, J., Serio, C., & Liibbert, A. (1996). Deterministic chaos analysis of pressure fluctuations in a horizontal pipe at intermittent flow regime. The Chemical Engineering Journal, 64, 149-156. http://dx.doi.org/10.1016/S0923-0467(96)03128-4

Drahos, J., Zahradnik, J., Puncochar, M., Fialova, M., & Bradka, F. (1991). Effect of operating conditions on the characteristics of pressure fluctuations in a bubble column. Chemical Engineering and Processing, 29, 107-115. http://dx.doi.org/10.1016/0255-2701(91)87019-Y

Ding, H., Zhiyao, H., Zhihuan, S., & Yong, Y. (2007). Hilbert–Huang transform based signal analysis for the characterization of gas–liquid two-phase flow. Flow Measurement and Instrumentation, 18, 37-46. http://dx.doi.org/10.1016/j.flowmeasinst.2006.12.004

Fausett, L. (1994). Fundamental of Neural Networks. Prentice Hill, New Jersy .

Jia, Z., Niu, G., & Wang, J. (2005). Identification of flow regimes in a horizontal flow using neural network. Journal of Hydrodynamics, Ser. B, 17(1), 66-73, China Ocean Press.

Matsui, G., Fujino, G., & Suzuki, M. (2007). Two Phase Flow sensing using differential pressure fluctuations. Jurnal of JSEM, 7, 50-55.

Wu, H., Zhou, F., & Wu, Y. (2001). Intelligent identification system of flow regime of oil-gas-water multiphase flow. International Journal of Multiphase Flow, 27(3), 459-475. http://dx.doi.org/10.1016/S0301-9322(00)00022-7

Xie, T., Ghiaasiaan, S. M., & Karrila, S. (2004). Artificial neural network approach for flow regime classification in gas-liquid-fiber flows based on frequency domain analysis of pressure signals. Chemical Engineering Science, 59(11), 2241-2251. http://dx.doi.org/10.1016/j.ces.2004.02.017

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


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


67

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)

the identification of gas-liquid co-current two phase flow

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