Experimental Investigation on Disturbance Wave Velocity and Frequency in Air-Water Horizontal Annular Flow

The wave characteristics of horizontal air-water annular two-phase flow in 16 and 26-mm-diameter pipe were investigated experimentally using flush-mounted constant electric current method (CECM) sensors and visual observations. The air and water superficial velocities were varied from 12 to 40 m/s and 0.05 to 0.2 m/s, respectively. The flow morphology of annular flow such as the disturbance wave, ripple, wave coalescence, wave development, entrainment, and breakup could be observed. Using cross correlation and power spectral density functions of liquid holdup signals, the wave velocity and frequency were determined. The effect of superficial liquid velocity on the wave velocity and frequency was found to be less significant compared to that of superficial gas velocity. Simple correlations for wave velocity and frequency were also developed.


Introduction
Annular two-phase flow is easily found in many industrial applications involving phase-change.This flow regime is quite complex, and it is characterized by liquid film on the wall and a gas core containing liquid droplets.For horizontal orientation, due to gravity effect, annular flow is more complicated and it is characterized by the asymmetric distribution of liquid film with thicker liquid flows along the bottom of a tube than on the sides and the top (Shedd, 2001).It also causes the higher droplets concentration in the bottom part than in the other circumferential locations.
Researches for horizontal annular two-phase flow have been carried out over decades.Many aspects have been investigated, including the circumferential liquid film thickness distribution, droplet concentration, secondary flow, pressure drop, and annular flow mechanism.Few theoretical models of such flow have also been developed.However, due to its complexity, it is generally less successful than in those of vertical flow.As a result, the mechanism by which the liquid film is transported to the upper parts of the pipe remains unanswered (Rodriguez, 2009).Sawant et al. (2008) noted that two types of wave structures are found in annular flow.The first is small ripple wave located on the base film that moves at low velocities, does not have a continuous life, and is considered as not to carry the liquid mass.The second structure, called disturbance wave, has a larger film thickness, usually forming complete rings in the pipe, and travels at a higher velocity.It is 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 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 & Shedd, 2008).

Experi
The range respectivel the given superficial experimen   For smaller pipes (8.8 and 15.1 mm), the wave velocities are in the range of 1.97 to 8.37 m/s when the superficial liquid velocity is set from 0.05 to 0.2 m/s.The correlation for the wave velocity of the three pipe diameters used in their experiment is expressed as follows:

Flow T
, 0.42 √ . (1) The similar correlation from Ousaka et al. (1992) is given by , 3.0 . (2) In the last correlation, the effect of liquid velocity on wave velocity is noticed as a proportionally linear.
In comparison to the present work, Equation ( 1) results in mean absolute errors (MAE) of 14.8% for 16 mm pipe and 29.6% for 26 mm pipe.Equation ( 2) gives MAE of 20.7% and 23.3% for 16 mm and 26 mm pipe, respectively.
Using similar form of Schubring and Shedd (2008), the best correlation for the present work for wave velocity for 16 mm and 26 mm pipes, judged by the smallest MAE, is given by , 0.34 √ . (3) Here, the effects of superficial gas velocity and flow quality on the wave velocity are similar to those of Schubring and Shedd (2008).The gas Reynolds number, however, is considered less significant in the developed correlation.
For the inner pipe diameters of 16 mm and 26 mm, this correlation gives MAE of 13.4% and 9.4%, respectively, and the overall MAE for both diameters is 11.4%, as shown clearly in Figure 9.To investigate the effect of diameter on the wave velocity, the results of the present work are combined with the results of Fukano et al. (1983), Paras and Karabelas (1991), and the correlations from Schubring and Shedd (2008) and Ousaka et al. (1992).Figure 10 presents the wave velocity variation for 6 different pipe diameters.It is obvious that the larger diameter results in the smaller wave velocity.The present results are in fairly good agreement with those resulted by Schubring and Shedd (2008) for the similar diameters.For 26 mm pipe, the mean absolute errors of this experiment are 11.8%, 11.3%, and 10.4% for superficial liquid velocity of 0.05, 0.1, and 0.2 m/s, respectively.It gives an overall MAE of 11.2%.The comparison with the correlation of Ousaka et al. (1992) gives larger MAE: 12.9%, 13.6%, and 14.5% for the three superficial liquid velocities used in this experiment, or an overall MAE of 13.7%.

Wave Frequency
The wave frequency can be determined from the frequency corresponding to the largest peak of power spectral density function.Figure 11 shows the wave frequency plotted against superficial gas velocity for various superficial liquid velocities.It is obvious that the wave frequency decreases with the increase of the inner pipe diameter.In addition, the wave frequency increases with the increase of superficial gas velocity.It is in accordance with the experiment of Paras and Karabelas (1991), Jayanti et al., (1990), Fukano et al. (1983), and Schubring and Shedd (2008).
a. Inner diameter = 16 mm b.Inner diameter = 26 mm Figure 11.Wave frequency As in the wave velocity, the effect of superficial liquid velocity on the wave frequency is also less significant compared to those of superficial gas velocity.In the present experimental study, multiplying the superficial gas velocity by a factor of 3.33 results in the increase of wave frequency by a factor of 2.69.Meanwhile, multiplying the superficial liquid velocity by a factor of 4 only results in the increase of frequency by a factor of 1.25.The experiment of Schubring (2009) show that an increase of superficial gas velocity by a factor of 2.29 results in the increase of frequency by a factor of 1.83 for 15.1 mm pipe.For 26.3 mm pipe, increasing the superficial gas velocity by a factor of 1.99 results in the increase of frequency by a factor of 2.91.This emphasizes the importance of superficial gas velocity on the wave frequency.
The insignificance of superficial liquid velocity could be seen by its little effect on the wave frequency.Increasing the superficial liquid velocity from 0.05 to 0.2 m/s (400% from its original value) only gives an increase of wave frequency by a factor of 1.25 (or 25% increase in wave frequency).The previous work of Paras and Karabelas (1991), however, showed that the wave number decreases with the increase of superficial liquid velocity.The similar trend has also been proposed by Mantilla (2008) for low superficial gas velocity.To explain the difference of the results, he argued that as the superficial liquid velocity increase, the wave amplitude will also increase, thus more energy is required from the gas to keep the waves moving.Since the wave velocity is higher for higher superficial liquid velocity, then for constant gas velocity fewer waves or lower frequency are resulted due to energy conservation.
The correlations for the wave frequency have been developed by Schubring and Shedd (2008), in which the frequency is directly proportional to the superficial gas velocity.For experiment with 8.8 mm and 15.1 mm pipes, the correlation is where f w is the wave frequency, J G is superficial gas velocity, D is pipe diameter, and x is the flow quality.For 26.3 mm pipe, the correlation is expressed as where the modified Froude number, Fr mod , is defined by The similar correlation from Ousaka et al. (1992) is expressed as Here, the effect of superficial gas and liquid velocities are expressed directly by J L and indirectly by the gas and liquid Reynolds numbers, Re G and Re L .In comparison to the correlation of Schubring and Shedd (2008) for 16 mm pipe, the results of the present work give the mean absolute errors of of 22.2%, 10.2%, and 11.9% for superficial liquid velocities of 0.05, 0.1, and 0.2 m/s, respectively.For 26 mm pipe, comparison to equation ( 5) for the given superficial liquid velocities gives larger errors: 28.4%, 28.9%, and 31.5%,respectively.The comparison with the correlation from Ousaka et al. (1992) for the given superficial liquid velocity gives MAE of 26.3%, 14.0%, and 21.7% for 16 mm pipe and 14.3%, 20.6%, and 35.1% for 26 mm pipe.
To improve the performance of the prediction of wave frequency, a new correlation is developed following the model of Schubring and Shedd (2008).The best correlation resulted in this experiment for both pipe diameters, evaluated by the smallest MAE, is given by Here, superficial liquid velocity is involved in the correlation, although the effect is almost negligible.Using these correlations, the MAE for 16 mm pipe for the given superficial liquid velocities are 9.2%, 9.6%, and 3.6%.For 26 mm pipe, the mean absolute errors are 6.4%, 8.7%, and 14.0%.The performance of the developed correlation for wave frequency is presented in Figure 12.The effect of pipe diameter on the wave frequency is described in Figure 13 with a diameter range from 8.8 mm to 50.8 mm.The wave frequencies for pipe diameters of 8.8 mm and 15.1 mm are obtained from the correlation of equation ( 4) and the frequency for 26.3 mm pipe is resulted from equation ( 5).From figure 13, it is apparent that the larger diameter gives the lower wave frequency.From equations ( 4) and ( 7), it is clearly shown that the dependence of wave frequency to the pipe diameter is inversely proportional.The involvement of the modified Froude number in Equation ( 5), however, shows that the effect of the pipe diameter is no longer inversely proportional for 26.3 mm pipe.This emphasizes that there is no agreement among the researchers in determining the effect of pipe diameter on the wave frequency.
Figure 13.The effect of diameter on wave frequency The ratio of velocity and length scales could be used for dimensional analysis of wave frequency, as suggested by Schubring (2009).In this case, the velocity scale is superficial gas velocity and the length scale is pipe diameter.From the experiment, the wave frequency tends to be approximately 1.1% of J G /D.It means that this simple correlation is equivalent to assume a constant Strouhal number of 0.011.This is slightly different to those of Schubring (2009), in which he suggested a value of J G /D = 1%.The mean absolute errors resulted from this correlation are 10% for 16 mm pipe and 22.9% for 26 mm pipe.Plot of wave frequency against J G /D is presented in Figure 14.As shown in Figure 15, the proportionality of the wave frequency to superficial gas velocity could not be found in the present work and the proportionality of 16 mm pipe is better than that of 26 mm pipe.In general, the plot shows that the dependence of frequency on superficial gas velocity is non-linear, indicating that the effect of superficial gas velocity is not correctly predicted using velocity and length scales, as clearly shown in Figure 14.

Conclusion
Experiment of air-water horizontal annular flow have been carried out using 16 and 26 mm pipe and both the transition of wavy-annular and fully developed annular flow have been successfully established.The common phenomena of annular flow such as ripple waves, disturbance waves, wave development and entrainment, coalescence, and breakup could be observed both visually and using liquid holdup signal.The effects of superficial gas velocity on wave velocity and frequency are clearly seen.The superficial liquid velocity, however, has a less significant effect on both wave characteristics.Correlations for wave velocity and frequency have been developed and both give reasonably good agreement with the experimental data.
Analysis using wave scale shows that the wave frequency tends to be approximately 1.1% of the ratio gas velocity to pipe diameter.The examination of the dependence of wave frequency on superficial gas velocity using plot of Strouhal number against liquid film Reynolds number, however, fail to show the linear proportionality of frequency to gas velocity.

Figure 9 .
Figure 9. Performance of the developed correlation for wave velocity

Figure 10 .
Figure10.The effect of diameter on wave velocity

Figure 12 .
Figure 12.Performance of developed correlation for wave frequency diameter = 26 mm Figure14.Wave frequency vs wave scale To examine the proportionality of frequency to superficial gas velocity for constant diameter and liquid Reynolds number, a plot of Strouhal number, Sr, against liquid film Reynolds number, Re L,film , is used.If frequency is proportional to superficial gas velocity, the plot of Sr against Re L,film would result in a line.Strouhal number and liquid film Reynolds number are defined as (flow rate and μ L is liquid viscosity.
Figure 15.Wave Strouhal number vs liquid film Reynolds number