Multiphase/Multidomain Computations Using Continuum and Lattice–Boltzmann Methods
Publication: Journal of Aerospace Engineering
Volume 19, Issue 4
Abstract
Multiphase and multidomain fluid flows associated with interfacial dynamics, steep jump in fluid properties, and moving boundaries between different phases and materials pose substantial computational challenges. In this paper, recent progresses made in numerical simulation using continuum and lattice–Boltzmann methods are highlighted, with special attention paid to issues related to time varying geometries, adaptive grid refinement, interfacial and geometric tracking, topological changes, and reduced numerical dispersion and dissipation. Illustrative physical applications including: (1) multiple rising bubbles interacting with carrier phase and with each other; (2) wave reflected on an inclined wall; and (3) the Rayleigh–Taylor instability problem, are presented to highlight the various aspects of the techniques developed.
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Acknowledgments
The present effort has been supported by the NASA Constellation University Institute Program (CUIP), Ms. Claudia Meyer program monitor.
References
Al-Rawahi, N., and Tryggvason, G. (2004). “Numerical simulation of dendritic solidification with convection: Three-dimensional flow.” J. Comput. Phys., 194(2), 677–696.
Annaland, M. V. S., Deen, N. G., and Kuipers, J. A. M. (2005). “Numerical simulation of gas bubbles behavior using a three-dimensional volume of fluid method.” Chem. Eng. Sci., 60(10), 2999–3011.
Aparajith, H. S., Dhir, V. K., Warrier, G. R., and Son, G. (2003). “Numerical simulation and experimental validation of the dynamics of multiple bubble merger during pool boiling under microgravity conditions.” Proc., Microgravity Transport Processes in Fluid, Thermal, Biological, and Material Sciences III, Davos, Switzerland.
Aulisa, E., Manservisi, S., and Scardovelli, R. (2004). “A surface marker algorithm coupled to an area-preserving marker redistribution method for three-dimensional interface tracking.” J. Comput. Phys., 197(2), 555–584.
Brereton, G., and Korotney, D. (1991). “Coaxial and oblique coalescence of two rising bubbles.” Dynamics of bubbles and vortices near a free surface, I. Sahin and G. Tryggvason, eds., Vol. 119, ASME, New York.
Carnahan, N. F., and Starling, K. E. (1969). “Equation of state for non-attracting rigid spheres.” J. Chem. Phys., 51(2), 635–636.
Carnahan, N. F., and Starling, K. E. (1972). “Intermolecular repulsions and the equation of state for fluids.” AIChE J., 18(6), 1184–1189.
Chandrasekhar, S. (1981). Hydrodynamic and hydromagnetic stability, Dover, New York.
Chen, Y., Teng, S. L., Shukuwa, S., and Ohashi, H. (1998). “Lattice Boltzmann simulation of two-phase fluid flows.” Int. J. Mod. Phys. C, 9(8), 1383–1391.
Enright, D., Fedkiw, R. P., Ferziger, J., and Mitchell, I. (2002). “A hybrid particle level set method for improved interface capturing.” J. Comput. Phys., 183(1), 83–116.
Esmaeeli, A., and Tryggvason, G. (1998). “Direct numerical simulations of bubbly flows. Part I: Low Reynolds number arrays.” J. Fluid Mech., 377, 313–345.
Esmaeeli, A., and Tryggvason, G. (1999). “Direct numerical simulations of bubbly flows. Part II: Moderate Reynolds number arrays.” J. Fluid Mech., 385, 325–358.
Francois, M., and Shyy, W. (2003a). “Computations of drop dynamics with the immersed boundary method. Part 1—Numerical algorithm and buoyancy induced effect.” Numer. Heat Transfer, Part B, 44(2), 101–118.
Francois, M., and Shyy, W. (2003b). “Computations of drop dynamics with the immersed boundary method. Part 2—Drop impact and heat transfer.” Numer. Heat Transfer, Part B, 44(2), 119–143.
Francois, M., Shyy, W., and Chung, J. (2002). “Analysis of micro-scale, multiphase device for enhanced thermal management.” Progress Computational Fluid Dynamics, 2, 59–71.
He, X. Y., Chen, S., and Zhang, R. Y. (1999). “A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh–Taylor instability.” J. Comput. Phys., 152(2), 642–663.
Inamuro, T., Ogata, T., Tajima, S., and Konishi, N. (2004). “A lattice Boltzmann method for incompressible two-phase flows with large density differences.” J. Comput. Phys., 198(2), 628–644.
Lee, T., and Lin, C. L. (2005a). “A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio.” J. Comput. Phys., 206(1), 16–47.
Lee, T., and Lin, C.-L. (2005b). “Rarefaction and compressibility effects of the lattice Boltzmann equation method in a gas microchannel.” Phys. Rev. E, 71, 046706.
Marella, S., Krishan, S., Liu, H., and Udaykumar, H. S. (2005). “Sharp interface Cartesian grid method I: An easily implemented technique for 3D moving boundary computations.” J. Comput. Phys., 210(1), 1–31.
Nie, X. S., and Chen, W. E. (2004). “A continuum and molecular dynamics hybrid method for micro- and nano-fluid flow.” J. Fluid Mech., 500, 55–64.
Osher, S., and Fedkiw, R. P. (2001). “Level set methods: An overview and some recent results.” J. Comput. Phys., 169(2), 463–502.
Peskin, C. S. (1977). “Numerical analysis of blood flow in the heart.” J. Comput. Phys., 25(3), 220–252.
Popescu, M., and Shyy, W. (2005). “Finite volume treatment of dispersion-relation-preserving and optimized prefactored compact schemes for wave equations.” J. Comput. Phys., 210(2), 705–729.
Popescu, M., Tai, C., and Shyy, W. (2005). “A finite volume-based high order Cartesian cut-cell method for computational aeroacoustics.” Proc., 11th AIAA/CEAS Aeroacoustics Conf., Monterey, Calif.
Rider, W. J., and Kothe, D. B. (1998). “Reconstructing volume tracking.” J. Comput. Phys., 141(2), 112–152.
Rowlinson, J. S., and Widom, B. (1982). Molecular theory of capillarity, Oxford University Press, New York.
Scardovelli, R., and Zaleski, S. (2002). “Interface reconstruction with least-square fit and split Lagrangian-Eulerian advection.” Int. J. Numer. Methods Fluids, 41, 251–274.
Shan, X. W., and Chen, H. (1993). “Lattice Boltzmann model for simulating flows with multiple phases and components.” Phys. Rev. E, 47, 1815.
Shin, S., and Juric, D. (2002). “Modeling three-dimensional multiphase flow using a level contour reconstruction method for front tracking without connectivity.” J. Comput. Phys., 180(2), 427–470.
Shyy, W. (2004). “Multiphase computations using sharp and continuous interface techniques for micro-gravity applications.” Computes Rendus Mecanique, 332, 375–386.
Shyy, W., Udaykumar, H. S., Rao, M. M., and Smith, R. W. (1996). Computational fluid dynamics with moving boundaries, Taylor & Francis, Washington, D.C.
Singh, R. K., N’Dri, N., Uzgoren, E., Shyy, W., and Garbey, M. (2005). “Three-dimensional adaptive, Cartesian grid method for multiphase flow computations.” Proc., 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nev., AIAA paper-1390.
Singh, R. K., and Shyy, W. (2006). “Three-dimensional adaptive grid computation with conservative, marker-based tracking for interfacial fluid dynamics.” Proc., 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nev., AIAA paper-1523.
Succi, S. (2001). The lattice Boltzmann equation for fluid dynamics and beyond, Oxford University Press, New York.
Sussman, M. (2003). “A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles.” J. Comput. Phys., 187(1), 110–136.
Tam, C. K. W., and Webb, J. C. (1994). “Radiation boundary condition and anisotropy correction for finite difference solutions of the Helmholtz equation.” J. Comput. Phys., 113(1), 122–133.
Torres, D. J., and Brackbill, J. U. (2000). “The point-set method: Front-tracking without connectivity.” J. Comput. Phys., 165(2), 620–644.
Tryggvason, G., et al. (2001). “A front-tracking method for the computations of multiphase flow.” J. Comput. Phys., 169(2), 708–759.
Udaykumar, H. S., Mittal, R., and Shyy, W. (1999). “Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids.” J. Comput. Phys., 153(2), 535–574.
Ye, T., Mittal, R., Udaykumar, H. S., and Shyy, W. (1999). “An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries.” J. Comput. Phys., 156(2), 209–240.
Ye, T., Shyy, W., and Chung, J. C. (2001). “A fixed-grid, sharp-interface method for bubble dynamics and phase change.” J. Comput. Phys., 174(2), 781–815.
Ye, T., Shyy, W., Tai, C.-F., and Chung, J. N. (2004). “Assessment of sharp- and continuous-interface methods for drop in static equilibrium.” Comput. Fluids, 33(7), 917–926.
Youngs, D. L. (1982). “Time-dependent multi-material flows with large fluid distortion.” Numerical methods for fluid dynamics, K. W. Morton and M. J. Baines, eds., Academic, New York.
Yu, D., Mei, R., Luo, L.-S., and Shyy, W. (2003). “Viscous flow computations with the method of lattice Boltzmann equation.” Prog. Aerosp. Sci., 39(5), 329–367.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 19 • Issue 4 • October 2006
Pages: 288 - 295
Copyright
© 2006 ASCE.
History
Received: Apr 27, 2005
Accepted: Apr 11, 2006
Published online: Oct 1, 2006
Published in print: Oct 2006
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