Examination of Existing Correlation for Wave Velocity in Horizontal Annular Flow

Examination of Existing Correlation for Wave Velocity in Horizontal Annular Flow Andriyanto Setyawan 1, Indarto 2, Deendarlianto 2, Prasetyo 3, Agus Suandi 4 Department of Refrigeration and Air Conditioning Engineering, Politeknik Negeri Bandung, Bandung 40012 1 andriyanto@polban.ac.id Department of Mechanical Engineering, Gadjah Mada University, Yogyakarta 55281 2 Department of Mechanical Engineering, Politeknik Negeri Bandung, Bandung 40012 3 Department of Mechanical Engineering, Universitas Bengkulu, Bengkulu 38371 4 Abstract Annular flow is one of the most important flow regimes in two-phase flow and it is easily found in many industrial applications. To study the characteristics of such flow, a deep examination of disturbance wave velocity is necessary. In this paper, examination of the existing correlations concerning to the wave velocity in horizontal annular flow has been carried out. Eight correlations were tested using experimental results in 16 mm and 26 mm pipes. A range of superficial liquid velocity of 0.05 m/s to 0.2 m/s and superficial gas velocity of 12 m/s to 40 m/s were used. In addition, liquid with different surface tension and viscosity were also employed in this experiment. The performance of wave velocity correlations in some cases are in a good agreement with experimental data, especially for the experiment with air-water. However, if the liquid viscosity and surface tension were changed, the correlations are no longer in accordance with the experimental data. The large errors for both experiment with different liquid viscosity and surface tension are attributed to the neglected effect of both liquid properties in these correlations. Keywords: annular flow, wave velocity, surface tension, viscosity 1. Introduction As an important regime in two-phase flow, annular flow has been investigated for years concerning to its pressure drop, void fraction, liquid holdup, film thickness, droplet entrainment, wave velocity, wave frequency, and other wave parameters. For horizontal orientation, however, the investigation of annular flow is more complicated than that of vertical flows (Rodriguez, 2009). The gravity effect creates asymmetry of circumferential film thickness distribution over the pipe wall. In addition, the droplet concentration is also influenced by gravity effect. Consequently, the modeling of horizontal annular flow is less successful than that of vertical flow (Weidong, 1999). In annular flow, two kinds of wave structure are found, disturbance waves and ripple waves. Disturbance waves are responsible for transfer of mass, momentum, and energy along the tube (Sawant, 2008). With a higher amplitude and relatively long-lived structures along the pipe (Shedd, 2001), disturbance waves are also responsible for the entrainment of liquid droplets into the gas core when high velocity gas flows and shears the wave. Ripple waves, with the low amplitude surface waves, create interfacial roughness and, therefore, are responsible for the pressure drop. To investigate the effect of disturbance waves on annular flow, the knowledge of wave velocity, frequency, and spacing are required (Schubring and Shedd, 2008). In analyzing annular flow, one of the most important parameter is disturbance wave velocity. This parameter affects the characteristics and mechanism of annular flow, especially in horizontal orientation. Based on his experiment using 25.2 mm and 95.3 mm diameter pipes, Andritsos (1992) showed that the relative wave velocity (ratio of wave velocity to the actual liquid velocity, C/U L ) tends to unity if the gas flow rate increases. The actual liquid velocity is defined as the ratio of superficial liquid velocity to the liquid holdup, η. The correlation of Ousaka et al. (1992) related the wave velocity as a function of superficial liquid velocity and gas and liquid Reynolds numbers. The effect of superficial velocity is, however, compensated by the liquid Reynolds number. Paras et al. (1994) proposed a correlation for wave velocity in terms of gas superficial gas velocity, film thickness at the bottom, and pipe diameter. The correlation of wave velocity, expressed merely in terms of liquid and gas superficial velocities and Reynolds numbers, has been proposed by Kumar et al. (2002). The correlation was obtained by equating the friction factor at the gas-liquid interfacial. To improve the performance of this correlation, Mantilla (2008) involved the effect of liquid viscosity in the correlation. Correlation of wave velocity involving the modified Reynolds number has been proposed by Schubring and Shedd (2008). The effects of surface tension and viscosity are, however, not Sekolah Tinggi Teknologi Nasional (STTNAS) Yogyakarta 365

taken into account in this correlation. Using the results of experiment in various pipe inclinations, Al-Sarkhi et al. (2012) proposed a correlation for wave velocity in term of modified Lockhart-Martinelli parameter. This parameter is modified as the ratio of liquid and gas Froude number. To improve this correlation, Gawas et al. (2014) used 9 different data banks and proposed a correlation based on two different conditions depending on the value of the modified Lockhart- Martinelli parameter. The paper is aimed to compare the existing correlations for wave velocity in annular flows. The correlations are tested using experimental data using 16 mm and 26 mm pipes and liquids with different surface tension and viscosity. 2. Methodology To analyze the existing correlations for wave velocity, a series of experiment were been conducted in Fluids Laboratory, Department of Mechanical Engineering, Gadjah Mada University. The obtained wave velocity from the experiment was then compared with the existing correlations and analyzed. The rig for the experimental purpose is given in Figure 1. The rig consists of piping section, water supply, air supply, test section, and visual observation section. The piping was constructed from 26 mm and 16 mm transparent acrylic pipes to facilitate visual observation. Before entering the test and visualization sections, air and water were passed through a mixer to guarantee the fully developed annular flow in both sections. The experiment use a range of superficial liquid velocity of 0.05 m/s to 0.2 m/s and superficial gas velocity of 12 m/s to 40 m/s. In Mandhane map (1974), most of the experimental runs are located in the annular flow region (Figure 2). In addition to air-water, liquids with different surface tension and viscosity were also employed in this experiment. To vary the surface tension, water with surface tension of 71 mn/m and 2% and 5% butanol solutions with surface tensions of 47 mn/m and 34 mn/m were used. The liquid viscosity was varied using water, 30%-glycerin solution, and 50%- glycerin solution. They give viscosity of 1.0 mpa.s, 2.6 mpa.s, and 5.2 mpa.s, respectively. Figure 1. Experimental rig. To obtain the wave velocity, a cross-correlation function was employed. This tool calculates the delay time of wave that pass through the upstream and downstream sensors. Based on the delay time, the wave velocity was calculated as the ratio of the distance between the sensors and the delay time. The resulted wave velocity was then compared with the correlations from previous publications. The difference between the experimental result and the correlations are expressed in the mean absolute error (MAE). J L [m/s] 10 1 0.1 0.01 PLUG STRATIFIED BUBBLY SLUG WAVY 0.001 0.1 1 J G [m/s] 10 100 Figure 2. Experimental matrix. ANNULAR In the test section, the liquid holdup data were measured using constant-electric current method (CECM) sensors developed by Fukano (1998). These sensors measure the holdup signal (that is the fraction of pipe cross sectional area occupied by liquid) based on the voltage drop caused by the change of the amount of each phase of fluid passing through the sensors. The visual observation was carried out using high speed video camera to trace the dynamics of the fluid flows along the visualization section. Detail of the experimental rig could be found in Setyawan et al. (2014). 3. Results and Discussion Based on statistical analysis of waves in 25.2 and 95.3 mm pipes, Andritsos (1992) showed that relative wave velocity trend to unity when the gas velocity is high and increases with the increase in liquid viscosity. The relative velocity is defined as 366 Sekolah Tinggi Teknologi Nasional (STTNAS) Yogyakarta

the ratio of wave velocity to the actual liquid velocity, C/U L, and the actual liquid velocity is the ratio of liquid superficial velocity to the liquid holdup, η. (1) Ousaka et al. (1992) carried out an experiment in 26 mm horizontal/near horizontal orientation using airwater and correlated the wave velocity with superficial liquid velocity and gas and liquid Reynolds numbers as follows (2) Experiment on the measurement of film thickness and wave velocity in vertical duct has been reported by Kumar et al. (2002). By calculating the interfacial friction factor based on the gas and liquid velocity, they proposed a model for predicting the wave velocity. The interfacial velocity (or wave velocity) is obtained by equating the friction factor at the interfacial where (4) (5) In this correlation, the effect of liquid superficial velocity is compensated by the liquid Reynolds number and the gas superficial velocity significantly affects the wave velocity. Comparison of experimental data with the correlation of Ousaka et al. (1992) gives a mean absolute error (MAE) of about 12% for experiment with water with a surface tension of 71 mn/m and viscosity of 1.0 mpa.s in 26 mm pipe. For 16 mm pipe, the MAE is 24% (Figure 3). Figure 3. Performance of wave velocity prediction by Ousaka et al. (1992). This correlation has a fairly good prediction for wave velocity in the case of experiment with airwater. However, when compared to experimental data with liquid surface tensions of 47 mn/m (S1) and 34 mn/m (S2), the MAEs increase to 31% and 34%, respectively. Increasing liquid viscosity to 2.6 mpa.s (V1) and 5.2 mpa.s (V2) results in the MAEs of 90% and 250%, respectively. Therefore, this correlation is not suitable for different surface tension and viscosity. Paras et al. (1994), using pipe diameters of 26 mm, 50 mm, and 95 mm, correlated the wave velocity with the gas superficial gas velocity, film thickness at the bottom, h 0, and pipe diameter, expressed as (3) C fi G and C fi L represent the friction coefficient at gas and liquid phase, respectively. If the gas-liquid interface is fully rough as in the case of two-phase flow with disturbance waves, then C fi is a function of wave roughness and the ratio of friction coefficient could be expressed in the ratio of Reynolds number as shown in the following equation (6) The wave velocity can, therefore, be expressed merely in terms of liquid and gas superficial velocities and Reynolds numbers. A comparison between this correlation and the experimental data is given in Figure 4. Wave velocity from equation (4) is normalized by liquid superficial velocity and plotted against. The MAEs for this correlation are 43% and 69% for experiment with water in 26 mm and 16 mm pipes, respectively. Experiment using S1 and S2 give MAEs of 79% and 103%, respectively. Using V1 and V2, the correlation gives MAEs of 39% and 42.8%, respectively. In general, the correlation underpredicts the normalized velocity for lower surface tension and overpredicts for higher viscosity. The difference between the prediction and the experimental data increases as the liquid surface tension decreases and viscosity increases. To improve this correlation, Mantilla (2008) proposed a modification of ψ, in which the effect of viscosity is taken into account, (7) where ( L / W ) is the viscosity ratio of liquid to that of water. The modification results in improvement of errors to 24.8% and 18.3% for experiment with V1 and V2, respectively. The errors for experiment with lower liquid surface tension are still large as the effect of surface tension is not included in this correlation. The performance of the correlation is given in Figure 5. Sekolah Tinggi Teknologi Nasional (STTNAS) Yogyakarta 367

Figure 4. Performance of correlation for relative wave velocity by Kumar et al. (2002) Figure 6. Performance of correlation for wave velocity by Schubring and Shedd (2008) Figure 5. Performance of correlation for relative wave velocity by Mantilla (2008) Based on the experimental results using 8.8 mm, 15.1 mm, and 26.3 mm ID pipes, Schubring and Shedd (2008) proposed a correlation of wave velocity involving the flow quality, x, and modified liquid Reynolds number, Re lm, as follows (8) The modified Reynolds number is expressed as (9) where G is the mass flux and μ L is liquid viscosity. In this correlation, the wave velocity is strongly affected by gas superficial velocity, but is compensated by the modified liquid Reynolds number. The flow quality is also considered as an important factor affecting the wave velocity. Figure 6 shows the performance of this correlation. Compared to the experimental data, this correlation gives MAEs of 15% and 25% for experiment with water in 26 mm and 16 mm pipes, respectively. Smaller errors are obtained by experiment with V1 and V2 that give MAEs of 12 and 10%, while experiment with S1 and S2 result in larger errors with MAEs of 32% and 35%. Again, as the effect of surface tension is not taken into consideration in this correlation, larger errors are resulted. Experimental investigation on wave characteristics with various pipe inclinations has been carried out by Al-Sarkhi et al. (2012) using 76.2 mm ID pipe. To predict the wave velocity, they proposed a correlation between the normalized wave velocity with the modified Lockhart-Martinelli parameter X* or the Froude number ratio based on liquid and gas superficial velocity. It is defined as where and (10) The idea of using X* in this analysis results in a single parameter that accounts for the ratio of liquid and gas velocities and densities. For horizontal pipe, the proposed correlation is (11) This correlation gives MAEs of 47.8% and 55.2% if it is compared to the experimental data with airwater of 26 mm and 16 mm pipe, respectively. The similar errors for experiment with different liquid viscosity are 45.3% and 40.2% for V1 and V2, respectively. The larger errors are resulted with the experimental data using reduced liquid surface tension, with MAEs of 50.1% and 54.5% for experiment with S1 and S2, respectively. In general, this correlation underpredicts the normalized wave velocity for all cases of experiment. The large errors for both experiment with different liquid viscosity and surface tension are resulted from the neglected effect of both liquid properties in this correlation. Performance of this correlation is shown in Figure 7. 368 Sekolah Tinggi Teknologi Nasional (STTNAS) Yogyakarta

Figure 7. Performance of correlation for relative wave velocity by Al-Sarkhi et al. (2012) Figure 8. Performance of correlation for relative wave velocity by Gawas et al. (2014) To improve the model of Al-Sarkhi et al. (2012), Gawas et al. (2014) analyzed 9 different data series and proposed two different correlations for predicting the wave velocity, depending on the value of X*, as follows and (12) (13) The performance of this correlation compared to the experimental data is presented in Figure 8. Although could slightly improve the error, as could be seen, this correlation still underpredicts the normalized wave velocity in all experimental cases, with a total MAE of 38.4%. 4. Conclusion An examination and analysis of the existing correlations on the wave velocity have been carried out. In many correlations, the wave velocity is normalized using superficial liquid or gas velocities. The performance of wave velocity correlations in some cases are in a good agreement with experimental data, especially for the experiment with water. If the liquid viscosity and surface tension were changed, the correlations are no longer in accordance with the experimental data. The large errors for both experiment with different liquid viscosity and surface tension are presumed to be the result of the neglected effect of both liquid properties in these correlations. In general, there is no standard formula in developing correlations for wave velocity. The kinds of parameters used for correlation development are also not well defined. As a result, the accuracy of the prediction of wave velocity is generally only valid for certain cases of experiment and producing large error for the other cases. Acknowledgement The authors wish to thank Mr. Ade Indra Wijaya, Mr. Anam Bahrul, and Mr. Guntur Purnama, the former student of the Department of Mechanical and Industrial Engineering, Gadjah Mada University, Indonesia, for their helpful support during the experiment in the Fluid Laboratory, Department of Mechanical and Industrial Engineering, Gadjah Mada University. Financial support from the Directorate General of Higher Education, the Ministry of Education and Culture of the Republic of Indonesia is also gratefully acknowledged. Reference Al-Sarkhi, A., Sarica, C., Magrini, K. (2012). Inclination effects on wave characteristics in annular gas liquid flows. AIChE J. 58, 1018 1029. Andritsos, N. (1992). Statistical analysis of waves in horizontal stratified gas liquid flow. Int. J. Multiphase Flow 18, 465 473. Fukano, T. (1998). Measurement of time varying thickness of liquid film flowing with high speed gas flow by CECM, Nuclear Engineering & Design, 184, 363 377. http://dx.doi.org/10.1016/s0029-5493(98)00209-x. Gawas, K., Karami, H., Pereyra, E., Al-Sarkhi, A., Sarica, C. (2014). Wave characteristics in gas oil two phase flow and large pipe diameter. International Journal of Multiphase Flow 63 (2014) 93 104. http://dx.doi.org/10.1016/ j.ijmultiphaseflow. 2014.04.001. Mandhane, J.M., G.A. Gregory, K. Aziz (1974). A Flow Pattern Map for Gas-Liquid Flow in Horizontal Pipes, Int. J. Multiphase Flow, Vol. 1, pp. 537-553. Mantilla, I. (2008). Mechanistic Modeling of Liquid Entrainment in Gas in Horizontal Pipes. Dissertation for Doctor of Philosophy in Petroleum Engineering, the University of Tulsa. Sekolah Tinggi Teknologi Nasional (STTNAS) Yogyakarta 369

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