Energy Cascade in Water - Air Bubble Grid Turbulence
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1 11th Workshop on Two-Phase Flow Predictions Merseburg, April 5-8, 5 Energy Cascade in Water - Air Bubble Grid Turbulence Thrassos Panidis, Demos Papailiou Laboratory of Applied Thermodynamics, Department of Mechanical Engineering & Aeronautics, University of Patras, Rio-Patras, Greece, panidis@mech.upatras.gr Keywords: Bubble Flow, Grid Turbulence, Energy Cascade Abstract Experimental findings regarding the turbulence energy budget in water - air bubble grid turbulence are presented. This work is part of an extensive experimental study of the development of the mean and turbulent structure of an initially nearly isotropic grid turbulent field in the presence of a dispersed phase at low void fractions. The turbulent structure of the two-phase flow has been monitored in relation to the influence of the dispersed phase on the transport processes and particularly the energy transfer mechanism between the two phases. The key result of this work is based on autocorrelation and power spectra measurements, which provide information regarding the evolution of the flow structure and turbulence scales as the flow develops. Close to the grid the influence of the bubble injection is evident. Further downstream the scales of the flow are influenced by the void fraction. For low void fraction the scales of the flow are reduced as related to single-phase flow values. Higher void fractions result to the re-increase of the turbulent scales. Introduction The turbulence energy budget and the associated issue of flow scales is an open research topic since the times of pioneer researchers such as Taylor and Kolmogorof. Today a significant amount of information has been accumulated and highly sophisticated tools analytical, experimental or numerical are utilized to enhance our knowledge on the topic. Defying all these efforts only the simplest flows such as isotropic turbulence or two-dimensional turbulence have been granted with pieces of successful and mature results. Two phase flow theory and especially bubble flow theory is lagging considerably behind. Bubble motion is influenced by several effects such as deformation and oscillation of bubble surface, buoyancy forces, forces resulting from bubble-continuous phase flow field and bubble-bubble interactions. Besides, the relative significance of these effects may vary considerably within the same flow field. The consequent complexity of the motion of a swarm of bubbles, although deterministic, defies our analytical or numerical capabilities and has to be faced most of the time as a random turbulent or pseudo-turbulent process. The physical and technological significance of two phase flows along with significant advances in the computational and experimental tools now available have been the basis for the significant growth of two-phase flow research during the last decades. Computational fluid dynamics and especially Direct Numerical Simulation are now capable, based on simple flow analysis, to provide information on the physical aspects of the flow as well as on the influence of specific parameters hardly obtainable by other means. Instrumentation such as hot wire anemometry, Laser Doppler and Phase Doppler anemometry as well as particle image and particle tracking velocimetry supported by highly developed equipment and sophisticated data processing is now available for providing information on complex bubble flows. Several investigators have performed measurements in liquid-gas bubble two-phase flows. The patterns of these studies follow closely the corresponding
2 Table 1 Experiments in Bubbly Flows Flow type Work Test section Void fraction Bubble diameter Water velocity Pipe flow Serizawa (1974), Serizawa 60.mm, L=2.10 m 5-70 % 4 mm m/s et al. (1975) Nakoryakov et al. (1981) 86 mm, L=6.5 m % Bubble to slug m/s Theofanous and Sullivan 57 mm 30% 3-4 mm m/s (1982) Michiyoshi and Serizawa 60 mm, L=2.15 m 47 % 3 mm m/s (1986) Wang et al. (1987) 57.mm % Bubble to slug m/s Liu (1997) 57mm, L=8 m 38 % 10 mm -3.0 m/s Triangular conduit Sim and Lahey (1986) Lopez de Bertodano et al (1994) Boundary layer Moursali et al. (1995), Marie et al. (1997) Grid turbulence Lance and Bataille (1982, 1991), Marie (1983) Panidis and Papailiou (1993, 0) Present Work L=91 cm, base 50.8 mm, % m/s height 98.4 mm L=70 D, base 50.8 mm, % - m/s height mm 2.5x0.4x0.4 m % mm <1.5 m/s 2x0.45x0.45 mm 3 M=40 mm, rods 8 mm 1.2x0.3x0.3 mm 3 M=30 mm, rods 5 mm 0-5% 5 mm <1.2 m/s 0-5% 3 mm 0.25 m/s investigations on single phase flows. Most of the conducted experiments pertain to up - flows in vertical tubes as indicated in Table 1 in which those experiments and their measured experimental parameters are summarized. Prerequisite for the effective use of such measurements is the detailed monitoring of the initial and boundary conditions of the flow domain including phase distribution, the turbulence structure and the developing wall shear. Despite all these efforts today there is limited information regarding the energy budget and the scales developing in bubble flows. 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 1 mm long with a square cross section of width, B = mm. It is positioned vertically with the mean flow of water directed upwards. Two transparent facing walls allow Laser Doppler Velocimetry (LDV), and visualization techniques to be used. Probes can be inserted in the flow through openings at 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 Optoflow fiber optics probe. 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. Extensive reference to the experimental apparatus, instrumentation and the measuring and data interpretation techniques used in this work can be found in Panidis and Papailiou (0). The water flow rate was kept constant during all the experiments. The corresponding single phase Reynolds number based on grid mesh was low (7,000) so that the turbulence energy introduced to the flow due to buoyancy was significant as compared to the single phase flow
3 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 Fig. 1. Side view of the experimental facility. turbulence. Measured quantities comprise local void fraction as well as water mean velocity, turbulence intensity, skewness, and flatness factors profiles at six locations downstream of the grid for varying void fraction (Panidis & Papailiou 1). All the evidence support the notion that two distinct ranges one close to the wall and one at the central part of the channel are developing downstream. The corresponding boundary layer thickness is a function of the downstream distance and the void fraction. The key result of this work is based on autocorrelation and power spectra measurements, which provide information regarding the evolution of the flow structure and turbulence scales as the flow develops. Results and discussion Close to grid the void fraction distribution is dictated by the bubble injection pattern as it is clearly indicated by the peak values measured above the injectors locations (Fig. 2, H = 2.3 M). At a distance of 7 M from the grid, a pattern of two distinct regions prevails in the void distribution. At this location one region extending over the central part of the channel can be identified, where the influence of the injector's location is still present and a second region develops close to the wall where the void appears redistributed to the effect that the initially two peaks close to the wall have been merged to form a wider peak. Further downstream the void distribution exhibits two separate regions forming two peaks located between the wall and the central line of the channel. At larger distance from the grid a one peak distribution is observed which appears to prevail thereafter. The mean velocity distribution appears to be closely related to that of the void fraction as they follow the same pattern. As shown in Fig. 3 close to the grid the influence of the injectors is obvious and a similar to the void distribution merging pattern evolves in the following stages although in a less pronounced way. The influence of the bubble-wall interaction is strong in all stages extending to considerable distance from the wall, which increases further from the grid and for higher void fraction. These findings are in agreement with the results in Panidis and Papailiou (0) complementing and clarifying the evolution of the flow mean structure in the channel. The related experiments of Lance and Bataille (1991) were deliberately designed to avoid these effects. The length of the test section does not allow a final conclusion regarding attainment of full development
4 and establishment of self preservation in the flow structure. However, for low void fraction there is some indication that convergence to a fully developed state might have been reached at the end of the test section. The characteristic pattern of the phase distribution evolution and the accompanying velocity distribution are closely related to the sensitivity of the lift force to the local shear and the shape of the bubbles as well as to the development of large 40 M eddies entraining the bubbles. Moreover it is plausible to suggest that the final result of the above 2 described phenomena is the development of a two distinct regions flow pattern downstream of the grid namely, one close to the wall region strongly 0 33 M 2 40 M 0 27 M M LOCAL VOID FRACTION M 13 M 7 M 2.3 M LONGITUDINAL MEAN VELOCITY / (mm/s) 20 M 13 M 7.5 M z/B Fig. 2. Development of the local void fraction e profile along the channel for varying gas flow rate ratios, (see Fig. 3 for legend) z/B Fig. 3. Distribution of the longitudinal mean velocity along the channel for varying gas flow rate ratios,
5 =0 =17 =21 (sec) 0.4 (sec) 0.4 (sec) 0.4 =24 =28 =32 (sec) 0.4 (sec) 0.4 (sec) 0.4 =36 Figure 4. Longitudinal autocorrelation for varying gas flow rate ratios, at different distances H from the grid (thin lines represent the corresponding single auto- correlation) (sec) 0.4
6 =0 =17 =21 =24 =28 =32 =36 Figure 5. Longitudinal power spectra for varying gas flow rate ratios, at different distances H from the grid (thin lines represent the corresponding single phase spectrum)
7 Figure 6. Integral timescale based on the longitudinal auto-correlation for varying gas flow rate ratios, at different distances H from the grid affected by the dispersed phase and a second region extending over the central part of the channel in which the effect of the dispersed phase is less pronounced as already has been discussed by Panidis and Papailiou (0). Autocorrelation and spectra measurements at the center of the channel provide information on the energy transfer processes and the scales of the turbulent field (Figs. 4, 5). A general remark for the autocorrelation diagrams at all locations is that for low void fraction the autocorrelation is decreasing much faster than the corresponding single phase curve. This behavior consistent with the findings of Lance and Bataille (1982, 1991) and Panidis and Papailiou (0) indicates that even for the lowest void fraction the integral scale and the microscale are significantly decreased as related to the single phase magnitudes. This trend is reversed as the air flow rate ratio increases, more notably at the further downstream locations, a feature not present in Lance and Bataille flow. A small secondary hump at low void fraction indicative of a double turbulence structure is also present in most of the low void fraction autocorrelation diagrams. Complimentary information about the structure of the flow can be obtained from the spectra measurements. The reduction of the turbulence scales for low void fraction is manifested in the low frequency part of the spectrum while there is no visible difference in the higher frequency part where a 2 power form is retained for all the measurements. As the void fraction increases the low frequency part of the spectrum is increased indicating the development of larger turbulent structures in the flow more notable at the locations close to the end of the test section. All two phase flow spectra present small peaks in a rather large region around 10 Hz. These peaks, which were also present in the previous work measurements, may be indicative of the bubble-turbulence interaction scales. This notion is compatible with the development of an inverse cascade as proposed Panidis and Papailiou (0). As related to Lance and Bataille (1982, 1991) measurements the differences in the autocorrelation evolution and the corresponding 8/3 power form found in this work should be attributed to the different scales of turbulence and bubble forcing in the two experiments. The integral timescales derived from the autocorrelation diagrams provide quantitative
8 information on the evolution of scales (figure 6). In single phase flow(β = 0) the scales increase downstream almost linearly. Two phase flow scales are significantly reduced in the vicinity of the grid and remain rather low downstream for most of the cases. For the higher air flow rate ratio values the scales increase downstream attaining even larger values than the single phase flow as mentioned in the discussion of the autocorrelation. It is interesting to observe that the lowest scales do not correspond to the minimum gas flow rate ratio, but the scales are diminishing gradually and then increase again with β depending on the distance from the grid. The evolution of the turbulent kinetic energy (figure 7) derived from the flow velocity statistics (Panidis & Papailiou 1) characterizes the development of the flow. Single phase turbulence decays steadily downstream while even for the lowest gas flow rate ratios turbulence generation due to the bubbles' presence results to higher turbulent kinetic energy values in accordance with β. Downstream, the flow restructuring along with bubble turbulence generation compete with the grid turbulence decay leading to the increase of the kinetic energy, most notably for the higher values of β. Acknowledgement The authors would like to express their thanks to Dr. Ziping Feng for his help to accomplish most of the measurements in this work. References Figure 7. Longitudinal Turbulent kinetic energy for varying gas flow rate ratios, at different distances H from the grid Chen, R.C.,Resse, J.,Fan,L.-S.,1994. Flow structure in a three-dimensional bubble column and three-phase fluidized bed, A.I.Ch.E. Journal 40, pp Cui Z., Fan L.S., 4, Turbulence energy distributions in bubbling gas-liquid and gas-liquid-solid flow systems, Chem Eng Sci 59 (8-9), pp
9 Lance, M. and Bataille, J., Turbulence in the liquid phase of a bubbly air-water flow. Nato Workshop, Shliersee. Lance, M. and Bataille, J., Turbulence in the liquid phase of a uniform bubbly air-water flow. J. Fluid Mech. 222, Liu, T. J., Investigation of the wall shear stress in vertical bubbly flow under different bubble size conditions. Int. J. Multiphase Flow 23, 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, Marie, J. L., Investigation of two-phase bubbly flows using laser Doppler anemometry. PCH J. 4, Marie, J. L. and Lance, M., Turbulence measurements in two-phase bubbly flows using laser Doppler anemometry. In Measuring Techniques In Gas-Liquid Two-Phase Flows, pp Springer. 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, Michiyoshi, I. and Serizawa, A., Turbulence in two-phase bubbly flow. Nuc. Eng. Design 95, Moursali, E., Marie, J. L. and Bataille, J., An upward turbulent bubbly boundary layer along a vertical flat plate. Int. J. Multiphase Flow 21, Nakoryakov, V. E., Kashinsky, O. N., Burdukov, A. P. and Odnoral, V. P., Local characteristics of upward gas liquid flows. Int. J. Multiphase Flow 7, Panidis, Th. and Papailiou, D. D., The Structure of Water-Air Bubble Grid Turbulence in a Square Duct. Applied Scientific Research 51, Panidis Th., and Papailiou, D. D., 0, The structure of two-phase grid turbulence in a rectangular channel: An experimental study, Int. J. Multiphase Flow, Vol. 26 (8), pp Panidis, Th, and D. D. Papailiou, D. D., 1, Development of water - air bubble grid turbulence, 4th International Conference on Multiphase Flow, New Orleans, Paper 814, pp Papailiou, D. D., Statistical characteristics of a turbulent free convection flow in the absence and presence of a magnetic field. Int. J. Heat and Mass Transfer 23, Serizawa, A., Fluid-dynamic characteristics of two-phase flow. Thesis, Institute of Atomic Energy, Kyoto. Serizawa, A., Kataoka, I. and Michiyoshi, I., Turbulence structure of air-water bubbly flow. Parts I-III. Int. J. Multiphase Flow 2, Sim, S. K. and Lahey, R. T. Jr., Measurement of phase distribution in a triangular conduit. Int. J. Multiphase Flow 12, Theofanous, T. G. and Sullivan, J., Turbulence in two-phase dispersed flows. J. Fluid Mech. 116, Tomiyama, A., Sou, A., Zun, I., Kanami, N. and Sakaguchi, T., Effects of Eotvos number and dimensionless liquid volumetric flux on lateral motion of a bubble in a laminar duct flow. In Proc. of the 2nd Int. Conf. On Multiphase Flow, pp. PD , Kyoto. Townsend, A. A., The structure of turbulent shear flow, Cambridge University Press, Cambridge. Wang, S. K., Lee, S. J., Jones, O. C. Jr. and Lahey, R. T. Jr., D turbulence structure and phase distribution measurements in bubbly two-phase flows. Int. J. Multiphase Flow 13,
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