This paper deals with wall shear stress in an upward gas-liquid slug flow inside a vertical tube. Local characteristics were measured by the electrodiffusion ...
Thermophysics and Aeromechanics, 2006, Vol. 13, No. 3
WALL SHEAR STRESS IN AN UPWARD SLUG FLOW IN A VERTICAL TUBE* O.N. KASHINSKY, A.S. KURDYUMOV, and V.V. RANDIN
Kutateladze Institute of Thermophysics SB RAS, Novosibirsk, Russia (Received May 12, 2006) This paper deals with wall shear stress in an upward gas-liquid slug flow inside a vertical tube. Local characteristics were measured by the electrodiffusion method. The method of conditional averaging over realization ensemble was used, and this allows distinguishing large-scale structures on the background of turbulent pulsation of liquid. While averaging, each slug velocity measured by a double probe of electric conductivity was taken into account. Averaged distributions of shear stress over the wall under a gas slug were obtained for different mode parameters. INTRODUCTION
The gas-liquid slug flow takes place in tubes in a wide range of superficial velocities of gas and liquid. Gas slugs, often called Taylor bubbles, characterize the feature of this flow mode. A gas slug occupies almost the whole cross section of a tube. The slug flow mode is characterized by quazi-periodic alternation of gas slugs and liquid plugs. In vertical tubes, gas slugs have a rounded nose, whereas their sterns are almost flat. They are separated by liquid plugs, where the gas phase is met as bubbles. The flow structure in a liquid plug differs significantly both from a single-phase flow in a tube and from a two-phase bubble flow. Many papers dealt with the slug flow mode. It was shown in [1] that the velocity of gas slug rise does not depend on its length, and it can be determined on the basis of the known velocity of slug motion in motionless liquid. A calculation model for determination of the main characteristics of the slug flow was presented in [2]. This model was based on a simplified scheme of the flow. Statistic parameters of the upward slug flow were studied in [3]. It is necessary to note that most researches dealt with gas phase characteristics (slug length and velocity, frequency of their passing). Simultaneously, characteristics of the liquid phase are also of a significant interest. Liquid motion in the slug flow was studied in [4] by the method of flow visualization. The PIV method was used in [5, 6]. But the above works did not study the near-wall flow zone. To study the shear stress on the wall, the electrodiffusion method was used in [7−9]. The structure of the slug flow was studied in [8] by the method of specific averaging by the length of a gas slug and liquid plug, however, data on the average velocity of gas slugs (for this mode) were used there. It was shown in some papers, particularly in [3, 5],
*
The work was financially supported by the Russian Foundation for Basic Research (Grant No. 04-0100328) and the Russian Science Support Foundation (Grant “The Best Post-Graduate of RAS-2006”). O.N. Kasinsky, A.S. Kurdyumov, and V.V. Randin, 2006
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that there is a positive deviation in velocity of separate slugs from the average value. Specific velocity profiles in a liquid plug behind a gas slug were studied in [10]. This work is aimed at investigation of the wall shear stress behavior in the upward slug flow. We used the methods, which consider the velocity of each slug during averaging by ensemble. 1. MEASUREMENT METHODS
Experiments were carried out on the setup described in [10]. This setup is a closed liquid flow loop. A vertical stainless steel tube with the inner diameter of 20 mm and length of 4.5 m acted as the test section. A centrifugal pump fed liquid from a tank into the test section through regulating valves; the flow rate was measured by rotameters. Air was fed into the liquid flow at the inlet to the test section through a nozzle of the 8-mm diameter. The air flow rate was determined by the pressure drop on a flow-meter diaphragm. Measurements were carried out in the range of superficial liquid velocities from 0.5 to 1.0 m/s and volumetric gas flow rates from 0.2 to 0.5. The electrodiffusion (electrochemical) method was used for measurements [7, 10]. To determine the velocity and length of gas inclusions, two probes of electric conductivity were mounted on the tube axis. These probes were made as platinum electrodes of the 50-µm diameter, welded into a glass capillary of the 100-µm diameter. The ends of these probes were polished to make them conic. A distance between the probes was 5.75 mm. A double shear stress probe was mounted in the same cross section as the first probe of electric conductivity [7, 8]. This probe measured the alternating wall shear stress and determined the time moments of the flow direction change. This probe was made of thin platinum plates of 0.07×0.9 mm separated by a thin dielectric film. For simultaneous switching-on of both probe electrodes, the signal for the second electrode is slightly lower than that for independent switching-on, since it is located within the diffusion wake of the first electrode. Thus, comparison of electrode signals allows determination of the flow direction. To determine the value of the shear stress on a wall, we used the signal of the first sensor electrode. We applied a relative version of electrochemical method with sensor calibration in a single-phase flow. The line coupling of primary electronic equipment is shown in Fig. 1. The signals of conductivity probes (1, 2) were sent to amplifiers (3, 4) and after rectification (5, 6) they were fed to analogue-digital converter (7). Shear stress probe (8) was connected to twochannel amplifier (9), after this amplifier signals were also fed to ADC (7). Then, signals
Fig. 1. The scheme of test section. 382
Fig. 2. Recording the signals of shear stress and conductivity probes.
were digitally treated by a PC. The probes were interrogated with a frequency of 100 kHz along each channel during 100–200 s (depending on the mode parameters), the volume of primary data was 200–400 Mb per each point. Statistics from 400 to 600 slugs was accumulated for every mode. All obtained implementations were recorded on a hard disc for the following processing. The following methods were used for conditional averaging. The first stage was determination of a threshold level for the signal of electric conductivity probe corresponding to the gas-liquid transition. The velocity of gas inclusion motion was determined by the time of gas-liquid interface propagation (Fig. 2). The following indications are used in the figure: 1 shear stress probes, 2 probes of electric conductivity; dashed lines indicate the probes, which are first along the flow, and solid lines indicate the second probes. The length of a gas inclusion was calculated from the velocity and gas-stay-time of a conductivity probe. Gas inclusions with a length higher than the tube diameter were considered as the slugs. 2. EXPERIMENTAL RESULTS
Data on the slug velocities under different modes were obtained via the treatment of implementations of the double electric-conductivity probe. Dependency between the average slug velocity and velocity of mixture motion is shown in Fig. 3. The average slug velocity was lower than the dependency shown in Collins paper [12]. Under one mode (with constant values of superficial velocities of liquid and gas), velocities of separate slugs differed significantly. The typical histogram of slug velocity distributions for the mode of VL = 0.5 m/s, β = 0.4 is shown in Fig. 4. Dispersion of slug velocity is shown in Fig. 5 for values of superficial velocity of liquid. Apparently, the values of dispersion increase significantly with a rise of volumetric gas flow rate. This proves the fact that for high gas flow rates, the slug flow becomes less regular. Measurement results on time-average wall shear stress are shown in Fig. 6. For the superficial liquid velocity of 0.5 m/s, there is some deviation of experimental results from calculations by the Armand dependency [13] at high volumetric gas flow rates (β = 0.5). Similar behavior of shear stress in the slug flow was noted in [7]. For lower superficial velocities of liquid, the time-average shear stress can become negative. Distribution of instantaneous shear stress on a wall obtained via the treatment of currents recording from the doubled shear stress probe, is shown in Fig. 7. It is clear that there are large-scale pulsations of shear stress caused by passing a gas slug and a liquid plug. When a gas slug passes by, the shear stress value decreases drastically, then it becomes negative, and the flow near the wall is directed downward. The region of a negative flow corresponds to the downward flow of a liquid film, streamlining a gas slug. Small pulsations caused by intrinsic turbulence of liquid are superimposed on the large-scale structure of wall shear stress distribution.
Fig. 3. Velocity of slugs vs. velocity of mixture. 383
Fig. 5. Dispersion of slug velocities. Fig. 4. Distribution histogram for slug velocities.
To obtain the averaged distribution of wall shear stress at time moments of gas slug passing, the method of specific averaging by implementation ensemble was used. Previously, this method was used for studying the slug flow in [8, 10]. In signal recordings they have chosen regions corresponding to passing slugs with similar lengths. The averaged values of wall shear stress under a gas slug for different slug lengths are shown in Fig. 8 for VL = 0.5 and β = 0.4. It is clear that shear stress decreases with a distance from a slug nose and can take negative values for large slug lengths. An increase in the volumetric gas flow rate provides a rise of wall shear stress under the slug. For slugs with different lengths and gas flow rates, the character of wall shear stress alteration stays almost constant with a distance from the slug beginning. It is necessary to note that in the zone of negative wall shear stress, there is no wall shear stress stabilization along the length, which, perhaps, is related to insufficient length of gas slugs.
Fig. 6. Average wall shear stress. 384
Fig. 7. Instantaneous wall shear stress.
Fig. 8. Wall shear stress averaged by the ensemble.
At the beginning of a liquid plug following a gas slug, shear stress increases drastically because of breaking the near-wall liquid jet flowing from under a gas slug. As a result, a circulation flow is formed (toroidal vortex), which significantly deforms the velocity profile along a liquid plug mentioned in [10]. CONCLUSION
Experimental data on wall shear stress distribution in an upward slug flow were obtained. These results demonstrate the averaged local structure of the slug flow. Data of the present work can be used for development and test of new methods of slug flow calculation based on the real structure of a liquid-gas flow. A.S. Kurdyumov acknowledges the Russian Science Support Foundation for the provided grant for the Best Post-Graduates of RAS-2006. NOMENCLATURE VL superficial velocity of liquid, m/s, β volumetric gas flow rate, σ dispersion of slug velocities, m/s,
τ instantaneous wall shear stress, N/m , τm average wall shear stress for the whole 2 implementation array, N/m , 2 τa wall shear stress averaged over ensemble, N/m . 2
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