3rd Workshop on Transport Phenomena in Two-Phase Flow Nessebar, Bulgaria, 2-7 September 1998, p.p. 133-138 INTERACTION OF AN AIR-BUBBLE DISPERSED PHASE WITH AN INITIALLY ISOTROPIC TURBULENT FLOW FIELD TH. PANIDIS, Z. FENG AND D. D. PAPAILIOU Lab. of Applied Thermodynamics, University of Patras, GR-265 00 Patras, Greece, e-mail: papailiu@thermo.mech.upatras.gr Keywords: Two phase flow, bubbly flow, grid turbulence ABSTRACT Measurements in two-phase, water-air bubble, grid turbulence have been conducted in a vertical water channel, of square cross section. The measured flow characteristics included local void fraction, mean velocity and statistical quantities such as turbulence intensity, probability distribution function, skewness and flatness factors, as well as autocorrelation and power spectra, for both the longitudinal and transverse velocity components. Based on the obtained experimental results, the influence of the dispersed phase on the initially isotropic turbulence field is identified and the physical processes responsible for the observed changes are discussed. INTRODUCTION It has been recognised during the last few decades that available knowledge on multiphase flows has been inadequate to cover demands resulting from an increasing number of applications this field finds in science and engineering. Especially turbulent multiphase flows and the effect of a dispersed phase on turbulence transport processes is considerably lacking behind the presently existing level of understanding on single phase turbulence. Several investigators have performed measurements in liquid-gas bubble two-phase flows. The main topics addressed are the phase distribution, the turbulence structure and the developing wall shear. In Table 1 a summary of the reported in the literature up-flows in vertical passages experiments is presented while particular cases will be discussed in the following when it will be found necessary. The laboratory of Applied Thermodynamics has been involved in the last ten years in an experimental effort aiming at investigating the structure and related transport phenomena of turbulence as influenced by the presence of a dispersed phase. In this context following the development of research on single phase turbulence an investigation regarding the influence of a second dispersed phase on the structure of a simple well investigated flow that is, the nearly isotropic turbulence field created behind a grid was initiated. The main findings of this research effort on water-air bubble grid turbulence are summarised in the present paper.
Table 1. Experiments in Bubbly Flows Flow type Work Test section Void fraction Bubble dia. Water velocity Serizawa et al. [1] 1974 60.mm, L=2.10 m 5-70 % 4 mm 0.3-1.03 m/s Nakoryakov et al. [2] 1981 86 mm, L=6.5 m 50-80 % bubble to slug 0.22-2.05 m/s pipe flow Theofanous and Sullivan [3] 1982 57 mm 3-20% 3-4 mm 0.23-0.62 m/s Michiyoshi and Serizawa [4] 1986 60 mm, L=2.15 m 4-27 % 3 mm 0.45-0.77 m/s Wang et al. [5] 1987 57.mm 10-50 % bubble to slug 0.43-0.94 m/s Liu [6] 1997 57mm, L=8 m 3-28 % 1-20 mm -3.0 m/s Sim and Lahey [7] 1986 triangular L=91 cm, base 50.8 mm, height 98.4 mm 66-90 % 0.65-1.0 m/s conduit L=70 D, base 50.8 mm, Lopez de Bertodano et al [8] 1994 height 100 mm 10-35 % -1.0 m/s boundary Marie et al. [9] 1997 layer 2.5x0.4x0.4 m 3 0-5.5 % 3.5-6.0 mm <1.5 m/s 2x0.45x0.45 mm Lance & Bataille [10] 1991 grid M=40 mm, rods 8 mm 0-5% 5 mm <1.2 m/s turbulence 1.2x0.3x0.3 mm 3 Present Work [12] M=30 mm, rods 5 mm 0-5% 3 mm 0.25 m/s EXPERIMENTAL APPARATUS AND EQUIPMENT The experiments have been conducted in the two-phase water channel operating in the Laboratory of Thermodynamics shown in Fig. 1. The test section is 1200 mm long with a square cross section of width, B = 300 mm. It is positioned vertically with the mean flow of water directed upwards. Two transparent facing walls allow Laser Doppler Velocimetry (LDV), and visualisation techniques to be used. Probes can be inserted in the flow through openings at 100 mm intervals on the third wall. The grid placed at the test section entrance forms a biplane square, consisting of copper tubes with outside diameter of 5 mm, crossed at mesh spacing M = 30 mm. It is also used for the injection of the bubbles, through hypodermic needles of inside diameter 0.2 mm, located at the copper tube crossings. The volumetric air flow rate is regulated by a pressure reducer and measured with a variable area flowmeter. The water velocity field is monitored with a dual beam forward scatter LDV system, the transmitting and the receiving optics of which were mounted on a carrying table capable of moving in three directions. Local void fraction measurements were conducted with an 1 Test section 2 Turbulence generating grid 3 Nozzle 4 Grids 5 Honeycomb 6 Curved fins 7 Diffuser 8 Orifice plate-floating meter 9 Pump 10 Water tank 11 Curved fins 12 Air vessel 13 Pressure reducer 14 Floating meter 15 Laser source 16 Transmitting optics 17 Receiving optics 18 3D table y x z Figure 1. Side view of the experimental facility.
Optoflow fiber optics probe as well as with hot film anemometry by using a TSI 1050 anemometer with a cylindrical probe (TSI 1210-60W). Bubble measurements were conducted with double-exposure photography. Bubble mean diameter was found to be 3 mm and bubble mean slip velocity, at low void fraction, was approximately 250 mm/s. EXPERIMENTAL RESULTS - DISCUSSION The conducted measurements of the present work (except of these for the development of the void distribution along the channel) were obtained at a distance of 900 mm from the turbulence generating grid equivalent to 30 mesh, M. The water volume rate was maintained constant in these experiments at a corresponding single phase Reynolds number, based on mesh length, equal to Re M =8000. Measurements of the mean and statistical characteristics of the single phase grid turbulence presented in Fig. 2 and 3 indicate that the structure of the turbulent field in the central part of the channel's cross section is nearly isotropic exhibiting statistical characteristics comparable to well established similar measurements in the literature. Figure 2. Measurements of single phase flow ( Longitudinal, Transverse components). The Two-Phase Turbulence Field Fig. 3. Single phase autocorrelation Besides the main body of measurements at distance 30 M from the grid for Re=8000 the development of the local void fraction, L, distribution along the channel has been exclusively studied for Re=7000 (Fig. 4). Very close to the grid the void distribution is dictated by the bubble injection pattern as clearly indicated by the peak values of void fraction attained at close distance above the injector locations. Starting at the height of 7 M, a drastic change develops in the void fraction distribution with the elimination of the peaks corresponding to the second injector from the wall. This development continues upwards terminating to a final distribution of void fraction consisting of two distinct areas located at the central part L 40 M and close to the wall of the channel respectively. This two-peak void fraction distribution persists farther up to 27 M where the distribution is characterised by only one 27 M peak located between the centre and the wall of the channel, which is preserved thereafter. Consistent with this behaviour local void fraction L, measurements at 30 M (Fig. 5) indicate significant lateral migration of the bubbles for higher volumetric gas flow rate ratio with the peak value located approximately at midpoint between the wall and the centre of the channel. 4 13 M 7 M 2.3 M 1 4 8 32 0.1 0.2 0.3 0.4 z/b Figure 4. The development of the void distribution along the channel
L L 15 15 10 5 0 z/b 1.0 0 7 13 3 9 10 5 0 Figure 5. Evolution of local void fraction. 4 6 z/b.033 0.10 0.30 0 400 U x (mm/s) 200 ) I x 0.2 0.1 0 y/b 1.0 4 6 Figure 6. Longitudinal mean velocity (legend as Fig. 5) y/b 1.0 4 6 Figure 7. Longitudinal turbulence intensity (legend as Fig. 5) 0.2 0.2 I z I z 0.1 0.1 y/b 1.0 4 6 Figure 8 Transverse turbulence intensity along y-axis (legend as Fig. 5) z/b 1.0 4 6 Figure 9 Transverse turbulence intensity along z- axis (legend as Fig. 5) s x 0.8 k x 6.0 0.4 4.0 2.0-0.4 y/b 1.0 4 6 Figure 10 Longitudinal skewness (legend as Fig. 5) y/b 1.0 4 6 Figure 11 Longitudinal flatness (legend as Fig. 5) As shown in Fig. 6 similar peaks are observed in the profiles of the longitudinal mean velocity, U x, along the y axis that is, in the direction perpendicular to that of the void fraction profiles. Thus it is plausible to assume that peaks in the channel develop in a peripheral pattern. This phenomenon should not be confused with the wall peaking reported by several
y/b=00 z/b=00 y/b=00 z/b=00 y/b=00 z/b=00 1.0 R 11 7 13 (sec) 0.4 3 9 50 43 36 56 E 11 10-4 10-6 10-8 -2 43 36 9 3 13 7 10 0 10 1 10 2 10 3 f (sec) -1 1.0 R 33 7 13 (sec) 0.4 3 9 50 43 36 56 y/b=00 z/b=00-2 investigators [1, 3, 5, 9]. It has a resemblance to the Segre-Sielberberg effect [11] as modified for deformable bubbles in the strong presence of buoyancy and should be attributed mainly to the lift force due to the interaction of the particle with the local shear. The resulting void distribution is the outcome of equilibrium attained between interdependent forces such as the restricting effect of the walls, the lift, the drag and the buoyancy force. In the present case the phenomenon is probably dominated by the low water velocity and the relatively large channel cross section and is representative of the stage of flow development. In conclusion it can be stated, that the bubble motion establishes in the central part of the channel a free turbulence flow pattern, while a boundary layer of considerable thickness develops near the walls as a result of bubble-wall interaction. Measurements of the turbulent intensity, I, in three directions (Fig. 7-9) as well as of skewness, s, and flatness, f, factors (Fig. 10,11) provide information about the isotropy of the resulting field and the mechanisms responsible for its destruction Focusing attention mostly at the central part of the channel it can be concluded that the interfacial drag and the high bubble velocities have a direct effect on the water velocity field increasing significantly the mean velocities with gas flow rate. At low gas flow rate the bubble influence is intermittent leading to significant departure of the skewness and flatness values from these corresponding to a normal velocity distribution. At high gas flow rate the bubble influence dominate the flow and the velocity probability distribution function returns to a form close to that of a normal distribution. Fluctuations in the longitudinal direction are bounded at the low end by the single phase velocity and at the high end by the total velocity of the bubbles which increase interactively with the mean velocity as the gas flow rate increases. Thus the turbulence intensity in the longitudinal direction is constantly increasing with gas flow rate ratio. In the transverse directions the water velocity fluctuations are due to the bubble wakes and remain almost proportional to the mean flow keeping the transverse turbulence intensities almost constant with gas flow rate after a jump from single phase flow. Due to this fact the isotropy of the flow field is inevitably destroyed. Finally as an assessment of the overall effect of the dispersed phase on the mean flow characteristics (Fig. 5-11) it can be stated, that two distinct regions corresponding to low and higher gas flow rate ratios have been identified. These regions which are clearly distinguished in the measurements of both the mean and statistical flow characteristics, are apparently associated with the existence of two different modes of interaction between the two phases, at low and high bubble concentration, related to changes in the balance among the acting forces. Further information pertaining to the nature of the energy transfer processes, occurring
between the turbulence field and the dispersed phase, can be obtained from the measured temporal autocorrelation and frequency spectra for different gas flow rate ratios,, presented in figures 12. The introduction of the bubbles at low gas flow rates results in a significant fragmentation of the original single phase flow eddies due to the presence of small eddies associated with the bubble wakes. This trend is reversed after a specific gas flow rate ratio value is attained. For higher gas flow rate the bubble forcing that is, the energy transferred from the bubbles to the mean flow becomes significant relatively to the mean flow energy content. This energy transfer at intermediate scales corresponding to the bubble motion can not be entirely dissipated towards smaller scales but is redistributed to larger scales thus activating an inverse energy cascade process. B I E k M s T U channel's width (300 mm) turbulence intensity nondimensional power spectrum flatness factor grid mesh (30 mm) skewness factor turbulence macroscale mean water velocity NOMENCLATURE L local void fraction volumetric gas flow rate ratio Coordinates x axial direction y, z transverse directions (see Fig. 1) Subscripts 11 longitudinal autocorrelation or spectrum 33 transverse autocorrelation or spectrum REFERENCES 1. Serizawa, A., Kataoka, I. and Michiyoshi, I., Turbulence structure of air-water bubbly flow, Parts I-III, Int. J. Multiphase Flow 2 (1975) 221-259 2. Nakoryakov, V. E., Kashinsky, O. N., Burdukov, A. P. and Odnoral, V. P. (1981) Local characteristics of upward gas liquid flows. Int. J. Multiphase Flow 7, 63-81. 3. Theofanous, T. and Sullivan, J., Turbulence in two-phase dispersed ws, J. Fluid Mech. 116 (1982) 343-362. 4. Michiyoshi, I. and Serizawa, A., Turbulence in two-phase bubbly flow, Nuc. Eng. Design 95 (1986) 253-267. 5. Wang, S. K., Lee, S. J., Jones, O. C. Jr. and Lahey, R. T. Jr., 3-D turbulence structure and phase distribution measurements in bubbly two-phase flows, Int. J. Multiphase Flow 13 (1987) 327-343. 6 Liu, T. J., Investigation of the wall shear stress in vertical bubbly flow under different bubble size conditions, Int. J. Multiphase Flow 23 (1997) 1085-1109. 7. Sim, S. K. and Lahey, R. T. Jr., Measurement of phase distribution in a triangular conduit, Int. J. Multiphase Flow 12 (1986) 105-425. 8. Lopez de Bertodano, M., Lahey, R. T. Jr. and Jones, O. C., Phase distribution in bubbly two-phase flow in vertical ducts, Int. J. Multiphase Flow 20 (1994) 805-818. 9. Marie, J. L., Moursali, E. and Tran-Cong, S., Similarity law and turbulence intensity profiles in a bubbly boundary layer at low void fractions Int. J. Multiphase Flow 23 (1997) 227-247. 10. Lance, M. and Bataille, J., Turbulence in the liquid phase of a uniform bubbly air-water flow, J. Fluid Mech. 222 (1991) 95-118. 11. Segre, G. and Silberberg, A., Behaviour of macroscopic rigid spheres in Poiseuille flow. Parts 1-2, J. Fluid Mech. 14 (1962) 115-157. 12. Panidis, Th. and Papailiou, D.D. The structure of water - air bubble grid turbulence in a square duct. Appl. Sci. Res. 51 (1993) 269-273.