CFD Simulation of isothermal upward two-phase flow in a vertical annulus using interfacial area transport equation
Simulação Computacional de fluxo bifásico ascendente isotérmico em um anel vertical usando a equação de transporte de área interfacial
DOI:
https://doi.org/10.53660/CLM-1617-23I17Palavras-chave:
Bubble column, Two-phase flow, Annular channel, CFD, Interfacial area concentrationResumo
This work presents a numerical simulation of a vertical, upward, isothermal two-phase flow of air bubbles and water in an annular channel applying a Computational Fluid Dynamics (CFD) code. For this, the Two-Fluid model is applied considering interfacial force correlations, namely: drag, lift, wall lubrication, turbulent dispersion, and virtual mass. The turbulence k-ε model effects and the influence of One-group Interfacial Area Transport Equation (IATE) are taken into account, in this case, the influence of two source term correlations for the bubble breakup and coalescence IATE is analysed. The work assesses whether the code properly represents the physical phenomenon by comparing the simulation results with experimental data obtained from the literature. Six flow conditions are evaluated based on two superficial liquid velocities and three void fractions in the bubbly flow regimen. The annular channel adopted has an outer pipe with an internal diameter of 38.1 mm and an inner cylinder of 19.1 mm. To represent this geometry, a three-dimensional mesh was generated with 160,000 elements, after a mesh sensitivity study. The void fraction distribution, taken radially to the flow section, is the main parameter analysed as well as interfacial area concentration, interfacial gas velocity, and bubble sizes distribution. The CFD model implemented in this work demonstrates satisfactory agreement with the reference experimental data but indicates the need for further improvement in the phase interaction models.
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Referências
Ansys. (2013). ANSYS Fluent Theory Guide (ANSYS (ed.); Release 15). ANSYS. http://www.ansys.com
Antal, S. P., JR, R. T. L., & Flaherty, J. E. (1991). Analysis of Phase Distribution in Fully Developed Laminar Bubbly Two-Phase Flow. International Journal of Multiphase Flow, 17(No.5), 635–652
Colombo, M., & Fairweather, M. (2019). Influence of multiphase turbulence modelling on interfacial momentum transfer in two-fluid Eulerian-Eulerian CFD models of bubbly flows. Chemical Engineering Science, 195, 968–984. https://doi.org/10.1016/j.ces.2018.10.043
Drew, D. A., & Lahey, R. T. (1990). Some supplemental analysis concerning the virtual mass and lift force on a sphere in a rotating and straining flow. International Journal of Multiphase Flow, 16(6), 1127–1130. https://doi.org/10.1016/0301-9322(90)90110-5
Drew, D. A., & Lahey, R. T. (1993). Particulate Two-Phase Flow. In Butterworth-Heinemann Series in Chemical Engineering. Butterworth-Heinemann (January 18, 1993)
Feng, J., & Bolotnov, I. A. (2017). Interfacial force study on a single bubble in laminar and turbulent flows. Nuclear Engineering and Design, 313, 345–360. https://doi.org/10.1016/j.nucengdes.2016.12.034
Hibiki, T., & Ishii, M. (2000). One-group Interfacial Area Transport of Bubbly Flows in Vertical Round Tubes. International Journal of Heat and Mass Transfer, 43(15), 2711–2726. https://doi.org/10.1016/S0017-9310(99)00325-7
Hibiki, T., Mi, Y., Situ, R., & Ishii, M. (2003). Interfacial area transport of vertical upward bubbly two-phase flow in an annulus. International Journal of Heat and Mass Transfer, 46(25), 4949–4962. https://doi.org/10.1016/S0017-9310(03)00318-1
Ishii, M., & Hibiki, T. (2011). Thermo-Fluid Dynamics of Two-Phase Flow. In Intergovernmental Panel on Climate Change (Ed.), Climate Change 2013 - The Physical Science Basis. Springer New York. https://doi.org/10.1007/978-1-4419-7985-8
Ishii, M., & Kim, S. (2001). Micro four-sensor probe measurement of interfacial area transport for bubbly flow in round pipes. Nuclear Engineering and Design, 205(1–2), 123–131. https://doi.org/10.1016/S0029-5493(00)00350-2
Kelessidis, V. C., & Dukler, A. E. (1989). Modeling flow pattern transitions for upward gas-liquid flow in vertical concentric and eccentric annuli. International Journal of Multiphase Flow, 15(2), 173–191. https://doi.org/10.1016/0301-9322(89)90069-4
Kocamustafaogullari, G., & Ishii, M. (1995). Foundation of the interfacial area transport equation and its closure relations. International Journal of Heat and Mass Transfer, 38(3), 481–493. https://doi.org/10.1016/0017-9310(94)00183-V
Krepper, E., Reddy Vanga, B. N., Zaruba, A., Prasser, H. M., & Lopez de Bertodano, M. A. (2007). Experimental and numerical studies of void fraction distribution in rectangular bubble columns. Nuclear Engineering and Design, 237(4), 399–408. https://doi.org/10.1016/j.nucengdes.2006.07.009
Lahey, R. T., & Drew, D. A. (2001). The analysis of two-phase flow and heat transfer using a multidimensional, four field, two-fluid model. Nuclear Engineering and Design, 204(1–3), 29–44. https://doi.org/10.1016/S0029-5493(00)00337-X
Launder, B. E., & Spalding, D. B. (1972). Lectures in Mathematical Modeling of Turbulence (London (ed.))
Lee, D. Y., Liu, Y., Hibiki, T., Ishii, M., & Buchanan, J. R. (2013). A study of adiabatic two-phase flows using the two-group interfacial area transport equations with a modified two-fluid model. International Journal of Multiphase Flow, 57, 115–130. https://doi.org/10.1016/j.ijmultiphaseflow.2013.07.008
Lopez de Bertodano, M. (1991). Turbulent Bubbly Flow in a Triangular Duct. Rensselaer Polytechnic Institute, Troy, New York
Lopez de Bertodano, M., Lahey, R. T., & Jones, O. C. (1994). Development of a k-ɛ Model for Bubbly Two-Phase Flow. Journal of Fluids Engineering, 116(1), 128. https://doi.org/10.1115/1.2910220
Lopez de Bertodano, M., Sun, X., Ishii, M., & Ulke, A. (2006). Phase Distribution in the Cap Bubble Regime in a Duct. Journal of Fluids Engineering, 128(4), 811. https://doi.org/10.1115/1.2201626
Lubchenko, N., Magolan, B., Sugrue, R., & Baglietto, E. (2018). A more fundamental wall lubrication force from turbulent dispersion regularization for multiphase CFD applications. International Journal of Multiphase Flow, 98, 36–44. https://doi.org/10.1016/j.ijmultiphaseflow.2017.09.003
Marfaing, O., Guingo, M., Laviéville, J., Mimouni, S., Baglietto, E., Lubchenko, N., Magolan, B., Sugrue, R., & Nadiga, B. T. (2018). Comparison and uncertainty quantification of two-fluid models for bubbly flows with NEPTUNE_CFD and STAR-CCM+. Nuclear Engineering and Design, 337(December 2017), 1–16. https://doi.org/10.1016/j.nucengdes.2018.05.028
Prabhudharwadkar, D., Vaidheeswaran, A., de Bertodano, M. L., Buchanan, J., & Guilbert, P. (2012). Two-Fluid CFD Simulations of Cap Bubble Flow Using the Two-Group Interfacial Area Transport Equations. The Journal of Computational Multiphase Flows, 4(4), 363–374. https://doi.org/10.1260/1757-482x.4.4.363
Rzehak, R., & Krepper, E. (2013). CFD modeling of bubble-induced turbulence. International Journal of Multiphase Flow, 55, 138–155. https://doi.org/10.1016/j.ijmultiphaseflow.2013.04.007
Sato, Y., & Sekoguchi, K. (1975). Liquid velocity distribution in two-phase bubble flow. International Journal of Multiphase Flow, 2(1), 79–95. https://doi.org/10.1016/0301-9322(75)90030-0
Schiller, L., & Naumann, Z. (1935). A drag coefficient correlation. Z.Ver.Deutsch.Ing, 77(13–14), 318–320. https://doi.org/10.1016/j.ijheatmasstransfer.2009.02.006
Serizawa, A., & Kataoka, I. (1988). Phase distribution in two-phase flow, Transient Phenomena in Multiphase Flow. Transient Phenomena in Multiphase Flow, 179–224
Sharma, S. L., Hibiki, T., Ishii, M., Brooks, C. S., Schlegel, J. P., Liu, Y., & Buchanan, J. R. (2017). Turbulence-induced bubble collision force modeling and validation in adiabatic two-phase flow using CFD. Nuclear Engineering and Design, 312, 399–409. https://doi.org/10.1016/j.nucengdes.2016.05.006
Sharma, S. L., Ishii, M., Hibiki, T., Schlegel, J. P., Liu, Y., & Buchanan, J. R. (2019). Beyond bubbly two-phase flow investigation using a CFD three-field two-fluid model. International Journal of Multiphase Flow, 113, 1–15. https://doi.org/10.1016/j.ijmultiphaseflow.2018.12.010
Shaver, D. R., & Podowski, M. Z. (2015). Modeling of Interfacial Forces for Bubbly Flows in Subcooled Boiling Conditions. Transactions of the American Nuclear Society, 113(10), 1368–1371
Stern, F., Wilson, R. V., Coleman, H. W., & Paterson, E. G. (2001). Comprehensive Approach to Verification and Validation of CFD Simulations—Part 1: Methodology and Procedures. Journal of Fluids Engineering, 123(4), 793. https://doi.org/10.1115/1.1412235
Sugrue, R., Magolan, B., Lubchenko, N., & Baglietto, E. (2017). Assessment of a simplified set of momentum closure relations for low volume fraction regimes in STAR-CCM+ and OpenFOAM. Annals of Nuclear Energy, 110, 79–87. https://doi.org/10.1016/j.anucene.2017.05.059
Tomiyama, A., Tamai, H., Zun, I., & Hosokawa, S. (2002). Transverse migration of single bubble in simple shear flows. Chemical Engineering Science, 57, 1849–1858
van Wachem, B. G. M. M., & Almstedt, A. E. (2003). Methods for multiphase computational fluid dynamics. Chemical Engineering Journal, 96(1–3), 81–98. https://doi.org/10.1016/j.cej.2003.08.025
Wu, Q., Kim, S., & Ishii, M. (1998). One-group interfacial area transport in vertical bubbly flow. Int. J. Heat Mass Transfer., 41(8–9), 1103–1112. https://doi.org/10.1016/S0017-9310(97)00167-1
Yeoh, G. H., & Tu, J. (2010). Future Trends in Handling Turbulent Multi-Phase Flows. In Computational Techniques for Multiphase Flows (pp. 567–601). Elsevier. https://doi.org/10.1016/B978-0-08-046733-7.00010-2
