CIRCUMFERENTIAL NONUNIFORMITY OF WAVES ON LIQUID FILM IN ANNULAR FLOW WITHOUT LIQUID ENTRAINMENT

Interfacial Phenomena and Heat Transfer, 1 (2): 139 151 (2013) CIRCUMFERENTIAL NONUNIFORMITY OF WAVES ON LIQUID FILM IN ANNULAR FLOW WITHOUT LIQUID ENTRAINMENT S. V. Alekseenko, 1,2 A. V. Cherdantsev, 1,2, S. V. Isaenkov, 1,2 & D. M. Markovich 1,2 1 Novosibirsk State University, 2, Pirogov St., Novosibirsk 630090, Russia 2 Kutateladze Institute of Thermophysics, 1, Lavrentiev Ave., Novosibirsk 630090, Russia Address all correspondence to A. V. Cherdantsev, E-mail: cherdantsev@itp.nsc.ru The wavy structure of liquid film in downward annular flow without liquid entrainment is studied. Temporal evolution of instantaneous distributions of local film thickness over longitudinal and circumferential coordinates is studied using high-speed laser-induced fluorescence technique. Wavy structure in such flow consists of fast long-living primary waves and slow short-living secondary waves that are generated at the back slopes of primary waves. An automatic algorithm of identification of characteristic lines of primary waves is applied to data obtained in a number of circumferential positions. Contours of waves in each time frame are identified to obtain temporal evolution of the shape of each wave in longitudinal and circumferential coordinates. Circumferential size of primary waves is estimated based on frequency of different kinds of waves. It is shown that variation of primary waves height along circumferential coordinate is most likely caused by absorption and generation of secondary waves. KEY WORDS: annular flow, gas shear, laser-induced fluorescence, wavy structure 1. INTRODUCTION The term annular flow is applied to the flow of liquid film along pipe walls together with high-velocity gas stream along pipe center. Interaction of the gas stream and liquid film leads to the appearance of complicated wavy structure on film surface. Wavy processes substantially change heat and mass transfer and pressure drop in flow. At high liquid flow rates, liquid droplets are entrained from film surface into the gas core. The entrainment phenomenon also exerts essential influence on integral characteristics of the flow. Wavy structure in annular flow is different in cases of the presence or absence of liquid entrainment. In regimes with entrainment, large-amplitude disturbance waves appear on the film surface. Disturbance waves coexist with small-scale ripples. The ripples can travel either on the base film layer between disturbance waves, or on the disturbance waves themselves. Ripples on disturbance waves can be disrupted by the gas shear into droplets (Woodmansee and Hanratty, 1969). This phenomenon is regarded as one of the main sources of entrainment. For flow regimes without entrainment, it was considered earlier that only the ripples are present on the film surface. A large amount of experimental work is devoted to studying amplitude, velocity, and frequency of disturbance waves (e.g., Chu and Dukler, 1975; Azzopardi, 1986; Han et al., 2006; Sawant et al., 2008). Ripples in regimes without entrainment are less studied: Asali and Hanratty (1993) measured ripples wavelength, Hagiwara et al. (1985) measured ripples frequency and amplitude. Recently, Alekseenko et al. (2009) have shown that there exists similarity between flow regimes with and without liquid entrainment. Using the high-speed laser-induced fluorescence (LIF) technique, they studied temporal and spatial evolution of waves with high resolution in space and time. It was found that in flow with entrainment, all the ripples are 2169 2785/13/$35.00 c 2013 by Begell House, Inc. 139

140 Alekseenko et al. NOMENCLATURE A amplitude of primary waves h p peak height of primary waves d pipe diameter L circumferential size of the area F c frequency of primary waves, occupying of measurements the whole visible area L p circumferential size of primary waves F e frequency of edges of primary waves L s circumferential size of secondary waves F tot frequency of all primary waves Re liquid film Reynolds number, Re = 4q/πdν F y frequency of primary waves at q volumetric liquid flow rate circumferential position y t time h film thickness ν kinematic viscosity of liquid h b thickness of the base film between V g superficial gas velocity primary waves x longitudinal coordinate h T threshold value of film thickness y circumferential coordinate generated at the back slopes of disturbance waves and travel either faster or slower than the disturbance waves. In flow without entrainment, two types of waves exist on the film surface: primary waves with larger velocity, amplitude, and lifetime; and small-scale secondary waves that are generated at the back slopes of primary waves. Thus, the behavior of primary and secondary waves in flow without entrainment is similar to the behavior of, respectively, disturbance waves and ripples in flow with entrainment. The main difference consists in the absence of secondary waves that would move faster than primary waves. Crests of primary waves are not covered by smaller waves that could be disrupted by the gas shear and contribute to entrainment. In most experimental works, measurements were performed in one circumferential position of the pipe. Such approach might provide incorrect information on waves behavior and characteristics due to possible circumferential nonuniformity of waves. The problem of circumferential nonuniformity was investigated in a relatively small number of papers. Circumferential coherence of disturbance waves was studied by Hewitt and Lovegrove (1969), Azzopardi and Gibbons (1983), Martin and Azzopardi (1985), and Sekoguchi et al. (1985). According to these papers, disturbance waves form full rings in small (less than 3 cm) diameter pipes, though the height of waves is not uniform around the circumference of the pipe. An increase of pipe diameter leads to the appearance of circumferentially localized disturbance waves; the fraction of localized waves increases with pipe diameter. The same is true for the growth of gas velocity. Circumferential profiles of disturbance waves height, obtained by Belt et al. (2010), show that variation of disturbance waves height is of the same order of magnitude as a wave s height. Photographs of film surface, presented by Asali and Hanratty (1993), show that waves in regimes without entrainment are circumferentially localized. Ohba and Nagae (1993) found two types of waves in flow without entrainment. The waves were different by many parameters, including circumferential size. Waves with larger circumferential size were named ring waves, since they occupied all the visible part of the pipe, and it was considered that they form full rings around pipe circumference. The other type of wave was identified as ripples. Comparison of waves velocity, measured by Ohba and Nagae, to velocity of waves, observed by Alekseenko et al. (2009), leads to the conclusion that ring waves and ripples correspond to primary and secondary waves, respectively. In Alekseenko et al. (2012), the LIF method was applied to study evolution of waves in three dimensions (longitudinal and circumferential coordinates and time). For flow with entrainment, it was found that circumferential nonuniformity of disturbance waves exerts influence on the generation of ripples. For flow without entrainment, it was found that primary waves do not form full rings around pipe circumference, since edges of primary waves are often encountered. Thus, the term ring waves, used by Ohba and Nagae, is not correct. The circumferential size of Interfacial Phenomena and Heat Transfer

Circumferential Nonuniformity of Waves 141 secondary waves is smaller than that of primary waves; generation of secondary waves occurs either at the central parts or at the edges of primary waves. The present paper is a continuation of Alekseenko et al. (2012). The scope of the present paper is to provide quantitative information on circumferential nonuniformity of waves in annular flow without entrainment. For this purpose, a new automatic algorithm of identification and processing of waves is developed. 2. EXPERIMENTAL SETUP AND MEASUREMENT TECHNIQUE Downward annular flow is studied in two vertical Plexiglas pipes with inner diameters d = 15 mm and d = 11.7 mm and length 1 m. Each pipe has a flat outer section to avoid optical distortions at the outer surface of the pipe. Gas stream entered the working section through coaxial pipe of smaller diameter. Working liquid was introduced through a ringshaped slot between the inner surface of the pipe and the outer surface of gas-feeding tube; the slot thickness is 0.5 mm. Two water-glycerol solutions were used as working liquids. Flow parameters used for each pipe are given in Table 1. Liquid Reynolds number Re is defined as 4q/πdν, where q is volumetric flow rate of liquid, ν is kinematic viscosity of liquid. For these flow conditions no liquid entrainment occurs at any gas velocity. The absence of entrainment was also validated directly using the standard sampling probe technique: no liquid flow through the probe was observed during long-time runs. LIF technique was used for film thickness measurements. Fluorescent dye (Rhodamine 6G) was dissolved in liquid in low (30 mg/l) concentration. A continuous 2W laser with wavelength of 532 nm was used for excitation of fluorescence. Brightness of fluorescent light was measured by high-speed digital camera, equipped with an orange filter. Brightness is then converted into local film thickness using a calibration curve. Details of the calibration procedure are given in Alekseenko et al. (2012). A fragment of the visible part of the tube was used as the area of measurement (which is marked by the dashed line in Fig. 1). Its longitudinal size is 12 cm; the circumferential size of the area of measurements L is equal to 1/4 of the pipe perimeter. Laser beam was spread to enlighten the area of measurements using scattering length. The spatial resolution is 0.2 mm in both the longitudinal and circumferential directions. The sampling frequency is relatively low TABLE 1: Flow parameters Pipe diameter, mm 15 11.7 Viscosity of working liquid, m 2 /s 3 10 6 2 10 6 Liquid Reynolds number 72,172 60,140 Superficial gas velocity, m/s 18-27 18-44 Sampling frequency, khz 0.5 2 Spatial resolution, mm 0.1 0.2 FIG. 1: Area of measurements Volume 1, Number 2, 2013

142 Alekseenko et al. (0.5 and 2 khz), since the large size of the area of measurements makes high demands on the local illumination of the film surface. Measurements were performed at the distances equal to 40 pipe diameters below the inlet. For flow regimes without liquid entrainment this distance is sufficient for stabilization of waves properties (see, e.g., Hagiwara et al., 1985). 3. DATA REPRESENTATION AND PROCESSING Obtained data represent evolution of film thickness h in three dimensions: longitudinal coordinate x, circumferential coordinate y, and time t. Two kinds of data representation will be used for further data processing. 3.1 Processing of x t Representation of Data Surface h(x, t) at fixed y enables one to study the spatial and temporal evolution of waves in one longitudinal section of the pipe. This approach was applied for a single longitudinal section in Alekseenko et al. (2009). An example of such surface is given in Fig. 2. In this image brightness is directly proportional to film thickness. The vertical axis corresponds to time, and horizontal axis to longitudinal distance. The flow direction is from left to right. Waves are visible in this image as brighter bands crossing this surface along their characteristic lines. The slope of a characteristic line to the t axis is proportional to the wave s velocity. Primary waves can be distinguished by larger values of velocity, amplitude, and lifetime. Secondary waves appear at the back slopes of primary ones; they travel along the base film between primary waves with lower velocity until the following primary waves absorb them. An automatic technique of identification of characteristic lines of primary waves was developed recently by Alekseenko et al. (2013). The technique is based on the Canny method of edges detection, which is often applied in image analysis. The Canny method consists of searching for local maxima in the response of the signal to the Gaussian filter. As a result, it marks the areas of maximum gradient of image brightness (Canny, 1986). When this method is applied to the matrix h(x, t) h x (x, t) =, (1) x it marks crests of waves. The marked positions of a wave s crest in different time moments are then concatenated into the characteristic line of the wave. Primary waves are characterized by larger values of velocity and lifetime in comparison to secondary waves. The product of velocity and lifetime gives longitudinal distance, over which the wave is observed. This distance is used as a criterion to separate primary and secondary waves. After that, velocity, amplitude, and frequency of primary waves are measured. At relatively low gas velocities the technique almost does FIG. 2: Fragment of h(x, t) surface with marked crests of primary waves. d = 11.7 mm, Re = 60, V g = 18 m/s. Interfacial Phenomena and Heat Transfer

Circumferential Nonuniformity of Waves 143 not miss primary waves, so it can be used for measuring the frequency of primary waves as well. Crests of primary waves are marked by white dots in Fig. 2. A number of longitudinal sections with step 1 mm are investigated (12 sections for d = 15 mm and 9 sections for d = 11.7 mm). Figure 3 shows the passing frequency (a), velocity (b), and height (c) of primary waves in different longitudinal sections for d = 15 mm. Frequency and velocity tend to be the same at different circumferential positions; this behavior is consistent with the basic assumption that the time-averaged characteristics of the flow are circumferentially uniform. The waves height is evidently overestimated far from the centerline of the area of measurements. This is related to deviation of the optical path from the normal to film surface. Estimation of the ratio h/h 0 at different circumferential positions was calculated earlier (see Fig. 4 in Alekseenko et al., 2012); behavior of this ratio is similar to that of waves height. FIG. 3: Average frequency (a), velocity (b), and height (c) of primary waves in different circumferential positions. d = 15 mm, Re = 72. (1) V g = 18 m/s, (2) V g = 22 m/s, (3) V g = 27 m/s. For (c), numbers 4 6 denote values of base film thickness. Volume 1, Number 2, 2013

144 Alekseenko et al. FIG. 4: Comparison of the average frequency (a), velocity (b), and height (c) of primary waves in different pipes. (1) d = 11.7 mm, Re = 60; (2) d = 11.7 mm, Re = 140; (3) d = 15 mm, Re = 72; (4) d = 15 mm, Re = 172. To minimize the influence of this distortion on further processing, the data were compensated as follows: h (x, y, t) = h b (y 0 ) + [h(x, y, t) h b(y)] [h p (y 0 ) h b (y 0 )] h p (y) h b (y) (2) Here, h p is average height of primary waves, observed in given longitudinal section; h b is thickness of the base film between primary waves (defined as the most probable value of film thickness); y 0 corresponds to the central longitudinal section, where the distortion is expected to be minimal. Figure 4 presents comparison of frequency (a), velocity (b), and height (c) of primary waves for different experimental conditions. Each point in this image is the result of averaging by all processed longitudinal sections. Frequency and velocity of primary waves grow almost linearly when gas velocity increases; the height of primary waves decreases with the growth of gas velocity. All three characteristics are growing with liquid flow rate. Unfortunately, data for different pipe diameters are also different in liquid viscosity, so it is not always clear which parameter defines the difference in waves properties. According to our earlier experiments, performed in a two-dimensional approach, Interfacial Phenomena and Heat Transfer

Circumferential Nonuniformity of Waves 145 an increase of liquid viscosity leads to an increase of primary waves velocity and height and almost does not change the frequency of waves. Thus, we suppose that the main source of difference in waves properties, observed in Fig. 4, is the viscosity of liquid. 3.2 Processing of x y Representation of Data Surface h(x, y) represents the real instantaneous shape of the film surface in the area of measurements [Fig. 5(a)]. As it was mentioned above, the circumferential size of primary waves is always larger than the circumferential size of the area of measurements L. At the same time, edges of primary waves are often encountered in the area of measurements. This means that the circumferential size of primary waves is smaller than the pipe perimeter. The circumferential size of secondary waves is normally smaller than L, and the secondary waves can be generated by either central parts or edges of primary waves. To study the shape of a primary wave in longitudinal and circumferential dimensions, contours of primary waves were identified. Contours were defined as lines in h(x, y) surface where the surface crosses the threshold value of film thickness ht. When searching for primary waves, ht was defined as < h > + (< h > - hb ) in order to exceed the height of secondary waves. Here, < h > denotes average film thickness. An example of h(x, y) surface with marked contours of two primary waves is shown in Fig. 5(b). The contours were related to primary waves if they enclosed crests of primary waves, marked at the previous stage in any longitudinal section passing through the contour. After that, contours obtained in different time moments were related to certain primary wave if they enclosed the same characteristic lines, obtained earlier. As the result, for each primary wave, contour on x y surface at each time moment of its life was obtained. For the secondary waves, there is no information on their characteristic lines in the x t approach, since the automatic method, described in the previous subsection, fails to identify them reliably. Thus, the algorithm is slightly different for secondary waves. At the first stage, areas of the base film between primary waves were selected for further processing. At the base film, the same searching for contours is performed with ht = < h >. After that, for each contour, the nearest contour in the neighboring frame was found. The two contours are considered to belong to the same secondary wave if the longitudinal shift between them roughly corresponds to the velocity of secondary waves, and the circumferential sizes are close enough to each other. In this case, the next frame is analyzed. (a) (b) FIG. 5: Fragment of h(x, y) surface. (a) Edges of primary waves; (b) Contours of primary waves. d = 15 mm, Re = 72, V g = 18 m/s. Volume 1, Number 2, 2013

146 Alekseenko et al. Figure 6 shows an example of the evolution of a contour of a single secondary wave in six subsequent time moments. 4. RESULTS AND DISCUSSION The goal of the present paper is to study the circumferential nonuniformity of liquid film wavy structure. The degree of nonuniformity of waves is characterized by their typical circumferential size and variation of their amplitude by the circumferential coordinate. 4.1 Circumferential Size of Primary and Secondary Waves It is impossible to measure the circumferential size of primary waves directly, since it is always larger than that of the area of measurements L. Nonetheless, it can be estimated using relative frequencies of waves, occupying the whole area of measurements ( centers ) and waves, occupying only part of the area ( edges ). Estimation is based on two assumptions: (1) circumferential distribution of waves position is uniform; (2) distribution of primary waves by the circumferential size is symmetric around the average circumferential size L p. In this case, relative frequencies F c (frequency of centers) and F e (frequency of edges) are defined by L p and L. The idea is illustrated in Fig. 7. Waves with the left border located within the area S c will be seen as centers in the area of measurements (left-hand part of Fig. 7). The length of this area is defined as S c = L p L. Waves with either the left or right border located within the area of measurements will be seen as edges (middle part of Fig. 7). The length of such areas for left and right edges is defined as S le = S re = L. Thus, the ratio of frequencies is defined as the ratio of lengths of these areas: F c S c = = L p L F e S le + S re 2L (3) Hence, circumferential size L p is defined as ( L p = L 1 + 2F ) c. (4) F e FIG. 6: Example of evolution of contour of a secondary wave. d = 15 mm, Re = 72, V g = 18 m/s. Interfacial Phenomena and Heat Transfer

Circumferential Nonuniformity of Waves 147 FIG. 7: Possible position of primary waves, visible as centers (top) and edges (bottom) For the case when L p is larger than πd L, the situation is more complicated, since both edges might appear in the area of measurements (which corresponds to the position of the left edge within S lre region in the right-hand part of Fig. 7). The length of this area is defined as S lre = L (πd L p ). The appearance of only one edge corresponds to the position of the left edge in the regions S le or S re (the right-hand part of Fig. 7). The length of each of these two regions in this case is defined as S le = S re = πd L p. The expression for S c remains the same; the ratio of frequencies is then defined as F c F e = S c = L p L S le + S re + 2 S lre 2L S lre is multiplied by 2, since in this case two edges appear in the working area. Thus, the result coincides with that of relation (3), and relation (4) is applicable for the case of large L p as well. Two methods are used to measure F c and F e. The first one is to measure sizes of contours of waves directly. The second one is to estimate these values on the basis of two quantities: passing frequency of primary waves in any longitudinal section F y (see Section 3.1) and total number of primary waves obtained in h(x, y, t) coordinates F tot (see Section 3.2). These quantities are expected to be related to F c and F e as F tot = F c + F e, F y = F c + F e /2 (6) The latter equation is derived as follows: (1) All the centers pass through each longitudinal section; (2) Frequency of either the left or right edges linearly changes with y between 0 on one side and F e /2 on the other (since we assume that circumferential distribution of waves position is uniform). The sum frequency of the left and right edges for given y is F e /2 [since F y does not depend on y; see Fig. 3(a)]. Thus, F e = 2(F tot F y ), F c = 2F y F tot. (7) Substituting (7) into (4), the following relation for L p as a function of L, F tot and F y is obtained: F y L p = L (8) F tot F y Both methods of measuring F c and F e are quite sensitive to the threshold value h T. Several additional tests were performed in order to validate that h T satisfies the following requirements: (1) h T should be large enough so that contours of primary waves would not merge with contours of adjacent primary or secondary waves; (2) h T should be small enough so that contours of primary waves would not split into smaller ones. In most cases, there was no big difference between initial and improved values of h T. The second method was found to be slightly more reliable, since it is less sensitive to the threshold value. Results are given in Fig. 8 in (5) Volume 1, Number 2, 2013

148 Alekseenko et al. FIG. 8: Estimation of circumferential size of primary waves. (1) d = 15 mm, Re = 72, ν = 3 10 6 m 2 /s. (2) d = 11.7 mm, Re = 60, ν = 2 10 6 m 2 /s. dimensionless form L p /d, along with uncertainty range. Estimated values of L p slightly decrease with V g. The circumferential size is much smaller for lesser diameter. We suppose that this difference is mainly defined by the difference in liquid viscosity and liquid flow rate, normalized by pipe perimeter (defined as Re ν). For the secondary waves, circumferential size L s can be measured directly, as time-averaged circumferential size of obtained contours (see Fig. 6). To increase the reliability of measurements, only the waves with long enough lifetime (three time instants or more), lying inside the area of measurements, were selected. Distribution of secondary FIG. 9: Distribution of secondary waves by circumferential size at different gas velocities, normalized by the total number of waves. (a) d = 15 mm, Re = 72, ν = 3 10 6 m 2 /s. (b) d = 11.7 mm, Re = 60, ν = 2 10 6 m 2 /s. (1) V g = 18 m/s; (2) V g = 22 m/s; (3) V g = 27 m/s; (4) V g = 36 m/s; (5) V g = 44 m/s. Interfacial Phenomena and Heat Transfer

Circumferential Nonuniformity of Waves 149 waves on circumferential size is nearly the same for different values of gas velocity (Fig. 9). The most probable value of L s lies around 3 mm for d = 15 mm and 2 mm for d = 11.7 mm. 4.2 Variation of Primary Waves Height Figure 10(a) shows example of wave s height variation along the circumferential coordinate at a fixed moment of time. Although the wave s height oscillates along this direction, we should note that peak height is also not stable in the longitudinal direction: it oscillates with time [Fig. 10(b)]. One possible reason for such oscillations is interaction of the primary wave to secondary waves. Due to such interactions, the height of the wave grows when it absorbs secondary waves, and diminishes when it generates secondary waves. Such behavior is clearly seen for wave II in Fig. 6 in Alekseenko et al. (2009). Since secondary waves are characterized by a relatively small circumferential size, the temporal change of a primary wave s amplitude is expected to be localized by the circumferential coordinate. Thus, we suppose that the circumferential variation is caused by such localized interactions. Circumferential and longitudinal variation of primary waves amplitude and amplitude of secondary waves are compared in Fig. 11. Variation is defined as δa(y) = std (A(y)) std (A(t)), δa(t) = < A > < A >, where A = h p h b (9) The average amplitude of secondary waves is also normalized by < A >. It can be seen that circumferential variation is of the same order of magnitude, as longitudinal variation and both variations are smaller than the amplitude of secondary waves. This observation supports the hypothesis described above. 5. CONCLUSIONS Three-dimensional structure of waves on the surface of gas-sheared liquid film is studied using a high-speed laserinduced fluorescence technique. Wavy structure in such flow regime consists of fast long-living primary waves and slow short-living secondary waves. Secondary waves are generated at the back slopes of primary waves. FIG. 10: Example of change of height of a primary wave with circumferential coordinate in fixed time moment (a) and with time at fixed circumferential position (b) Volume 1, Number 2, 2013

150 Alekseenko et al. FIG. 11: Variation of primary waves amplitude. (a) d = 15 mm, Re = 72, ν = 3 10 6 m 2 /s. (b) d = 11.7 mm, Re = 60, ν = 2 10 6 m 2 /s. (1) Variation with time; (2) Variation with circumferential coordinate; (3) Relative amplitude of secondary waves. Velocity, frequency, and height of primary waves are measured. A way to compensate circumferential distortion of film thickness data for further investigation is developed. An automatic algorithm that enables one to get the temporal evolution of either primary or secondary waves in both longitudinal and circumferential coordinates is developed. The circumferential size of primary waves is estimated based on primary waves frequency in different longitudinal sections, and the circumferential size of secondary waves is measured directly. The circumferential size of primary waves decreases with gas velocity; the influence of gas velocity on average circumferential size of secondary waves is weak. It is shown that variation of amplitude of primary waves by circumferential coordinate is most likely caused by the absorption and generation of secondary waves. ACKNOWLEDGMENTS The work was supported by Russian Foundation for Basic Research (grants 13-08-01400 and 12-01-00778); and President of Russian Federation (grants MK-115.2011.8 and NSh-6686.2012.8); Government of Russian Federation (project 11.G34.31.0035). REFERENCES Alekseenko, S. V., Antipin, V. A., Cherdantsev, A. V., Kharlamov, S. M., and Markovich, D. M., Two-wave structure of liquid film and waves interrelation in annular gas-liquid flow with and without entrainment, Phys. Fluids, vol. 21, pp. 061701 061704, 2009. Alekseenko, S., Cherdantsev, A., Cherdantsev, M., Isaenkov, S., Kharlamov, S., and Markovich, D., Application of a high-speed laser-induced fluorescence technique for studying three-dimensional structure of annular gas-liquid flows, Exp. Fluids, vol. 53, no. 1, pp. 77 89, 2012. Alekseenko, S. V., Cherdantsev, A. V., Heinz, O. M., Kharlamov, S. M., and Markovich, D. M., Application of the image-analysis method to studies of the space-time wave evolution in an annular gas-liquid flow, Patt. Recogn. Image Anal., vol. 23, no. 1, pp. 35 43, 2013. Interfacial Phenomena and Heat Transfer

Circumferential Nonuniformity of Waves 151 Asali, J. C. and Hanratty, T. J., Ripples generated on a liquid film at high gas velocities, Int. J. Multiphase Flow, vol. 19, pp. 229 243, 1993. Azzopardi, B. J., Disturbance wave frequencies, velocities and spacing in vertical annular two-phase flow, Nucl. Eng. Design, vol. 92, pp. 121 133, 1986. Azzopardi, B. J. and Gibbons, D. B., Annular two-phase flow in a large diameter tube, Chem. Eng., vol. 398, pp. 19 31, 1983. Belt, R. J., Van t Westende, J. M. C., Prasser, H. M., and Portela, L. M., Time and spatially resolved measurements of interfacial waves in vertical annular flow, Int. J. Multiphase Flow, vol. 36, pp. 570 587, 2010. Canny, J., A computational approach to edge detection, IEEE Trans. Pattern Anal. Mach. Intell., vol. PAMI-8, no. 6, pp. 679 698, 1986. Chu, K. J. and Dukler, A. E., Statistical characteristics of thin, wavy films: Part III. Structure of the large waves and their resistance to gas flow, AIChE J., vol. 21, pp. 583 593, 1975. Hagiwara, Y., Miwada, T., and Suzuki, K., Heat transfer and wave structure in the developing region of two-component two-phase annular flow, Phys. Chem. Hydrodyn., vol. 6, pp. 141 156, 1985. Han, H., Zhu, Z., and Gabriel, K., A study on the effect of gas flow rate on the wave characteristics in two-phase gas liquid annular flow, Nucl. Eng. Des., vol. 236, pp. 2580 2588, 2006. Hewitt, G. F. and Lovegrove, P. C., Frequency and velocity measurements of disturbance waves in annular two-phase flow, UKAEA Report AERE-R4304, 1969. Martin, C. J. and Azzopardi, B. J., Waves in vertical annular flow, Phys. Chem. Hydrodyn., vol. 6, pp. 257 265, 1985. Ohba, K. and Nagae, K., Characteristics and behavior of the interfacial wave on the liquid film in a vertically upward air-water two-phase annular flow, Nucl. Eng. Des., vol. 141, pp. 17 27, 1993. Sawant, P., Ishii, M., Hazuku, T., Takamasa, T., and Mori, M., Properties of disturbance waves in vertical annular two-phase flow, Nucl. Eng. Des., vol. 238, pp. 3528 3541, 2008. Sekoguchi, K., Takeishi, M., and Ishimatsu, T., Interfacial structure in vertical upward annular flow, Phys. Chem. Hydrodyn., vol. 6, pp. 239 255, 1985. Woodmansee, D. E. and Hanratty, T. J., Mechanism for the removal of droplets from a liquid surface by a parallel air flow, Chem. Eng. Sci., vol. 24, pp. 299 307, 1969. Volume 1, Number 2, 2013