CFD modelling of bubble-driven flow

• Autorzy: Laux H. , Bech L. R. , Hellevik L. R. , Johansen S.T.
• Języki publikacji: EN

Abstrakty

EN

Bubble-driven flows, which belong to the large group of bubbly multiphase flows, are important in many industrial processes. Relevant examples are metal refining operations such as tapping of steel furnaces, gas-stirred lades, and aluminum electrolysis. Over the last 15 years, numerical solutions of mathematical models for bubble-driven flows have contributed to a better understanding of the governing physical mechanisms, and thus allowed optimization of existing or aided the design of new industrial processes. The first part of this paper gives a short, although not complete, introduction to CFD modeling of bubbly flows (Computational Bubble Dynamics, CBD). The other presents examples of modeling of bubble-driven flows: (1) bubble-driven flow in aluminum electrolysis cells; (2) flow pattern in steel ladles during tapping of steel furnaces; (3) flow pattern in a gas-stirred ladle. The mathematical models are described but only modifications to standard models that were necessary to study above-mentioned flows are discussed in greater detail. Some simulation results of these industrial relevant cases are presented. Improvements to the present modeling that seem necessary in the future are addressed.

Słowa kluczowe

EN

bubble-driven flow; computational fluid dynamics CFD; mathematical modeling; industrial applications

PL

modelowanie matematyczne; dynamika płynów; zastosowania przemysłowe

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2002
• Tom: Vol. 7, no 1
• Strony: 329--359
• Opis fizyczny: Bibliogr. 63 poz., rys., wykr.

Twórcy

autor

Laux H.

• SINTEF Materials technology Process Metallurgy and Ceramics Flow technology Alfred Getz vei 2B N-7465 Trondheim, Norway

autor

Bech L. R.

• SINTEF Materials technology Process Metallurgy and Ceramics Flow technology Alfred Getz vei 2B N-7465 Trondheim, Norway

autor

Hellevik L. R.

• SINTEF Materials technology Process Metallurgy and Ceramics Flow technology Alfred Getz vei 2B N-7465 Trondheim, Norway

autor

Johansen S.T.

• SINTEF Materials technology Process Metallurgy and Ceramics Flow technology Alfred Getz vei 2B N-7465 Trondheim, Norway

Bibliografia

• [1] Bech K.H., Solheim A.S., Johansen S.T. and Haarberg T. (2001): Coupled current distribution and convection simulator for electrolysis cells. - In: Light Metals 2001 (J.L. Anjier, Ed.), The Minerals, Metals and Materials Society, Annual TMS Meeting 2001, New Orleans, pp.463-468.
• [2] Berg H., Laux H., Johansen S.T. and Kievan O.S. (1999): Flow pattern and alloy dissolution during tapping of steel furnaces. - Ironmaking and Steelmaking, vol.26, pp.127-139.
• [3] Bin A.K. (1993): Gas entrainment by plunging jets. - Chem. Eng. Sci., vol.48, pp.3585- 3630.
• [4] Calderbank P.H. (1958): Physical rate processes in industrial fermentation. Part I: The interfacial area in gas-liquid contacting with mechanical agitation. - Trans. Instn. Chem. Engrs., vol.36, pp.443-463.
• [5] Chapman S. and Cowling T.G. (1970): The Mathematical Theory of Non-Uniform Gases. - Cambridge: Cambridge University Press.
• [6] Chen S. and Doolen G.D. (1998): Lattice Boltzmann method for fluid flows. - Ann. Rev. Fluid Mech., vol.30, pp.329-364.
• [7] Choh T., Iwata K. and Inouye M. (1983): Estimation of oxygen and nitrogen absorption of liquid steel during tapping from converter. - Transactions ISIJ, vol.23, pp.680-689.
• [8] Clift R., Grace J.R. and Weber M.E. (1978): Bubbles, Drops, and Particles. - New York: Academic Press Inc.
• [9] Delnoij E. (1998): Fluid Dynamics of Gas-liquid Bubble Columns. - Ph.D. Thesis, Twente University, The Netherlands.
• [10] Elgobashi S.E. and Abou-Arab T.W. (1983): A two-equation turbulence model for two- phase flows. - Phys. Fluids, vol.26, pp.931-938.
• [11] Esmaeeli A. and Tryggvason G. (1996): An inverse energy cascade in two-dimensional low Reynolds number bubbly flows. - J. Fluid Mech., vol.314, pp.315-330.
• [12] Esmaeeli A. and Tryggvason G. (1998): Direct numerical simulations of bubbly flows. Part 1: Low Reynolds number arrays. - J. Fluid Mech., vol.377, pp.313-345.
• [13] Esmaeeli A. and Tryggvason G. (1999): Direct numerical simulations of bubbly flows Part 2: Moderate Reynolds number arrays. - J. Fluid Mech., vol.385, pp.325-358.
• [14] Fluent (1997): User's Guide Version 4.4 May 1997. - Lebanon New Hampshire: Fluent Inc.
• [15] Gore R.A. and Crowe C.T. (1989): Effect of particulate size on modulating turbulent intensity. - Int. J. Multiphase Flow, vol. 15, No.2, pp.279-285.
• [16] Hashimoto Y. and Ohashi H. (1997): Droplet dynamics using the lattice gas method. - Int. J. Modern Physics, vol.8, No.4, pp.977-983.
• [17] Hellevik L.R. and Laux H. (2000): Modellering av gassdriven str0m i ei oval ause. - SINTEF Report, No.STF24 F00615 (in Norwegian).
• [18] Hetsroni G. (1989): Particles turbulence interaction. - Int. J. Multiphase Flow, vol. 15, No.5, pp.735-746.
• [19] Hibiki T. and Ishii M. (1999): Experimental study on interfacial area transport in bubbly two-phase flows. - Int. J. Heat Mass Transfer, vol.42, pp.3019-3035.
• [20] Hibiki T. and Ishii M. (2000): One-group interfacial area transport of bubbly flows in vertical round tubes. - Int. J. Heat Mass Transfer, vol.43, pp.2711-2726.
• [21] Hinze J.O. (1959): Turbulence. - New York: McGraw-Hill.
• [22] Hoomans B.P.B., Kuipers J.A.M., Briels W.J. and van Swaaij W.P.M. (1996): Discrete particle simulation of bubble and slug formation in a two-dimensional gasfluidized bed: A hard-sphere approach. - Chem. Eng. Sci., vol.51, pp.99-118.
• [23] Hop B.I., Johansen S.T. and Rasch B. (1996): A 3-D numerical model for removal of inclusions to gas bubbles. - EPD Congress 1996 (G.W. Warren, Ed.), The Minerals, Metals and Materials Society, Annual TMS Meeting 1996, Anaheim, pp.647-656.
• [24] Iguchi M., Tani J., Uemura T., Kawabata H., Takeuchi H. and Morita Z. (1989): The characteristics of water and bubbling jets in a cylindrical vessel with bottom blowing. - Transactions ISIJ, vol.29, pp.309-317.
• [25] Iguchi M., Okita K. and Yamamoto F. (1998): Mean velocity and turbulence characteristics of water flow in the bubble dispersion region induced by plunging water jet. - Int. J. Multiphase Flow, vol.24, No.4, pp.523-537.
• [26] Jakobsen H.A., Sannaes B.H., Grevskott S. and Svendsen H.F. (1997): Modelling of vertical bubble-driven flows. - Ind. Eng. Chem. Research, vol.36, pp.4052-4074.
• [27] Johansen S.T. (1990): On the Modelling of Disperse Two-Phase Flows. - Ph.D. thesis, Norwegian University of Science and Technology, Norway.
• [28] Johansen S.T. (1998): Large-scale simulation of separated multiphase flows. - In: Proceedings of 3rd Int. Conf. Multiphase Flow, Lyon June 8-12, 1998, CD-ROM.
• [29] Johansen S.T. (2001): Multiphase flow modeling in metallurgical flows. - In: Proceedings of 4th Int. Conf. Multiphase Flow, New Orleans May 27 - June 1 2001, CD-ROM.
• [30] Johansen S.T. and Boysan F. (1988): Fluid dynamics in bubble-stirred ladles. Part II: Mathematical modeling. - Metallurgical Transactions B, vol.l9B, pp.755-764.
• [31] Johansen S.T. and Engh T.A. (1985): Combined surface injection and gas-stirring in ladles studied in water models. - Scand. J. Metallurgy, vol. 14, No.4, pp.214-223.
• [32] Johansen S.T., Fredriksen A. and Rasch B. (1995): Particle flotation to bubbles in rotor-stirred reactors for melt treatment. - In: Light Metals 1995 (J.W. Evans, Ed.), The Minerals, Metals and Materials Society, Annual TMS Meeting 1995, Las Vegas, pp.1203-1206.
• [33] Johansen S.T., Robertson D.G.C., Woje K. and Engh T.A. (1988): Fluid dynamics in bubble-stirred ladles. Part I: Experiments. - Metallurgical Transactions B, vol.l9B, pp.745-754.
• [34] Krishna R., Urseanu M.I., van Baten J.M. and Ellenberger J. (1999): Rise velocity of a swarm of large gas bubbles in liquids. - Chem. Eng. Sci., vol.54, pp. 171-183.
• [35] Kuipers J.A.M. and van Swaaij W.P.M. (1997): Application of computational fluid dynamics to chemical reaction engineering. - Rev. Chem. Eng., vol. 13, No.3, pp. 1-118.
• [36] Lahey R.T., Lopez de Bertodano M. and Jones Jr O.C. (1993): Phase distribution in complex geometry conduits. - Nuclear Engineering and Design, vol. 141, pp. 177-201.
• [37] Laux H. (1997): Fluid flow analysis of a multiphase mixer. - SINTEF Report, No. STF24 F97586.
• [38] Laux H. (1998): Modeling of Dilute and Dense Dispersed Fluid-Particle Flow. - Ph.D. thesis, No. 1998/71, Norwegian University of Science and Technology, Norway.
• [39] Laux H. and Johansen S.T. (1999): A CFD analysis of the air entrainment rate due to a plunging steel jet combining mathematical models for dispersed and separated multiphase flows. - In: Fluid Flow Phenomena in Metals Processing (N. El-Kaddah, G.C. Robertson, S.T. Johansen and V.R. Voller, Eds.), The Minerals Metals and Materials Society, 1999 Annual TMS Meeting, San Diego, pp.21-30.
• [40] Laux H., Johansen S.T., Berg H. and Kievan O.S. (2000): CFD analysis of the turbulent flow in ladles and the alloying process during tapping of steel furnaces. - Scand. J. Metallurgy, vol.29, pp.71-80.
• [41] Laux H., Johansen S.T., Berg H. and Kievan O.S. (2001): Gas-induced motion in metallurgical ladles due to gas entrainment during tapping of steel furnaces. - SINTEF Report, No.STF24 A01605.
• [42] Laux H. and Ytrehus T. (1997): Computer simulation and experiments on two-phase flow in an inclined sedimentation vessel. - Pow. Tech., vol.94, pp.35-49.
• [43] Lo S. (1999): Some redent developments and applications of CFD to multiphaseflows in stirred reactors. - In: Proceedings of AMIF-ESF Workshop on Computing Methods for Two-phase Flow, Aussios, France, January 12-14, 2000, CD-ROM.
• [44] Lopez de Bertodano M. (1992): Turbulent Bubbly Two-Phase Flow in a Triangular Duct. - Ph.D. thesis, Rensselaer Polytechnic Institute, USA.
• [45] Lun C.K.K., Savage S.B., Jeffrey D.J. and Chepurniy N. (1984): Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in general flow field. - J.Fluid Mech., vol. 140, pp.223-256.
• [46] Luo H. and Svenden H.F. (1996): Theoretical model for drop and bubble coalescence in turbulent dispersions. - AIChE J., vol.42, No.5, 1225-1233.
• [47] McKeogh E.J. and Ervine D.A. (1981): Air entrainment rate and diffusion pattern of plunging liquid jets. - Chem. Eng. Sci., vol.36, pp. 1161-1172.
• [48] Milles M. and Mewes D. (1999): Interfacial area in bubbly flow. - Chem. Eng. Processing, vol.38, pp.307-319.
• [49] Morsi S. A. and Alexander A.J. (1972): An investigation of particle trajectories in two- phase flow systems. - J. Fluid Mech., vol.55, pp. 193-208.
• [50] Rudman M. (1996): Volume-tracking methods for interfacial flow calculations. - Int. J. Numerical Methods in Fluids, vol.24, pp.671-691.
• [51] Russo G. and Smereka P. (1996a): Kinetic theory for bubbly flow: Collisionless case. - SISM J. Appl. Math., vol.56, No.2, pp.327-357.
• [52] Russo G. and Smereka P. (1996b): Kinetic theory for bubbly flow: Fluid dynamic limit. - SISM J. Appl. Math., vol.56, No.2, pp.358-371.
• [53] Scardovelli R. and Zaleski S. (1999): Direct numerical simulation of free-surface and interfacial flow. - Ann. Rev. Fluid Mech., vol.31, pp.567-603.
• [54] Serizawa A. and Kataoka I. (1987): Phase distribution in two-phase flow. - In: Proceedings of ICMHT Int. Seminar on Transient Phenomenon in Multiphase Flow, Dubrovnik.
• [55] Simonin O. and Viollet P.L. (1990): Predictions of an oxygen droplet pulverization in a compressible subsonic coflowing hydrogen flow. - In: Numerical Methods for Multiphase Flows, ASME FED, vol.91, pp.65-82.
• [56] Smagorinsky J. (1963): General circulation experiments with the primitive equations. Part I: The basic experiment. - Mon Weather Rev., vol. 100, pp.99-164.
• [57] Solheim A., Johansen S.T., Rolseth S. and Thonstad J. (1989): Gas-induced bath circulation in aluminium reduction cells. - J. Appl. Electrochemistry, vol. 19, pp.703-712.
• [58] Tennekes H. and Lumley J.L. (1990): A First Course in Turbulence. - Cambridge: MIT Press.
• [59] Tomiyama A. (1998): Struggle with computational bubble dynamics. - In: Proceedings of 3rd Int. Conf. Multiphase Flow, Lyon June 8-12 1998, CD-ROM.
• [60] Tomiyama A. and Shimada N. (1998): Numerical simulation of bubble columns using a 3-D multi-fluid model. - In: Proceedings of 3rd Int. Conf. Multiphase Flow, Lyon June 8-12, 1998, CD-ROM.
• [61] Tomiyama A., Zun I., Sou A. and Sakaguchi T. (1993): Numerical analysis of bubble motion with the VOF method. - Nucl. Eng. Des., vol. 141, No.l, pp.69-82.
• [62] Univerdi O.S. and Tryggvason G. (1992): A front-tracking method for viscous, incompressible, multi-fluid flows. - J. Comput. Phys., vol. 100, pp.25-37.
• [63] White F.M. (1991): Viscous fluid flow. - New York: McGraw-Hill.