A Two-Phase Flow Interface Tracking Algorithm Using a Fully Coupled Pressure-Based Finite Volume Method
Abstract:Two-phase and multi-phase flows are common flow types in fluid mechanics engineering. Among the basic and applied problems of these flow types, two-phase parallel flow is the one that two immiscible fluids flow in the vicinity of each other. In this type of flow, fluid properties (e.g. density, viscosity, and temperature) are different at the two sides of the interface of the two fluids. The most challenging part of the numerical simulation of two-phase flow is to determine the location of interface accurately. In the present work, a coupled interface tracking algorithm is developed based on Arbitrary Lagrangian-Eulerian (ALE) approach using a cell-centered, pressure-based, coupled solver. To validate this algorithm, an analytical solution for fully developed two-phase flow in presence of gravity is derived, and then, the results of the numerical simulation of this flow are compared with analytical solution at various flow conditions. The results of the simulations show good accuracy of the algorithm despite using a nearly coarse and uniform grid. Temporal variations of interface profile toward the steady-state solution show that a greater difference between fluids properties (especially dynamic viscosity) will result in larger traveling waves. Gravity effect studies also show that favorable gravity will result in a reduction of heavier fluid thickness and adverse gravity leads to increasing it with respect to the zero gravity condition. However, the magnitude of variation in favorable gravity is much more than adverse gravity.
 J. Weisman, “Two-phase flow patterns,” in Handbook of Fluids in Motion, N. P. Cheremisinoff and R. Gupta, Ed. Ann Arbor Science Publication, 1983, pp. 409-425.
 J. H. Ferziger and M. Peric, Computational methods for fluid dynamics. Springer Science & Business Media, 2012.
 J. M. Floryan and H. Rasmussen, “Numerical methods for viscous flows with moving boundaries,” Appl. Mech. Rev., vol. 42, no. 12, pp. 323-341, 1989.
 F. H. Harlow and J. E. Welch, “Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface,” Phys. Fluids, vol. 8, no. 12, p. 2182, 1965.
 C. W. Hirt and B. D. Nichols, “Volume of fluid (VOF) method for the dynamics of free boundaries,” J. Comput. Phys. vol. 39, no. 1, pp. 201-225, 1981.
 J. U. Brackbill, D. B. Kothe, and C. Zemach, “A Continuum Method for Modeling Surface Tension,” J. Comput. Phys., vol. 100, no. 2, pp. 335-354, 1992.
 S. Chen, D. B. Johnson, P. E. Raad, and D. Fadda, “The surface marker and micro cell method,” Int. J. Numer. Meth. Fl., vol. 25, no. 7, pp. 749-778, 1997.
 M. Sussman, P. Smereka, and S. Osher, “A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flows,” J. Comput. Phys., vol. 114, no. 1, pp. 146-159, 1994.
 S. Osher and R. P. Fedkiw, “Level Set Methods,” J. Comput. Phys., vol. 169, no. 2, pp. 463-502, 2001.
 J. A. Sethian, “Evolution, Implementation, and Application of Level Set and Fast Marching Methods for Advancing Fronts,” J. Comput. Phys., vol. 169, no. 2, pp. 503-555, 2001.
 G. D. Raithby, W. X. Xu, and G. D. Stubley, “Prediction of incompressible free surface with an element-based finite volume method,” J. Comput. Fl. Dyn., vol. 4, no. 3, pp. 353-371, 1995.
 Demirdzic and M. Peric, “Finite volume method for prediction of fluid flow in arbitrarily shaped domains with moving boundaries,” Int. J. Numer. Meth. Fl., vol. 10, no. 7, pp. 771-790, 1990.
 E. S. Oran and J. P. Boris, Numerical Simulation of Reactive Flow, Elsevier, New York, 1987.
 P. J. Shopov, P. D. Minev, I. B. Bazhekov, and Z. D. Zapryanov, “Interaction of a Deformable Bubble with a Rigid Wall at Moderate Reynolds Numbers,” J. Fluid Mech., vol. 219, pp. 241-271, 1990.
 J. Feng, H. H. Hu, and D. D. Joseph, “Direct Simulation of Initial Value Problems for the Motion of Solid Bodies in a Newtonian Fluid, Part 1. Sedimentation,” J. Fluid Mech., vol. 261, pp. 95-134, 1994.
 J. Feng, H. H. Hu, and D. D. Joseph, “Direct Simulation of Initial Value Problems for the Motion of Solid Bodies in a Newtonian Fluid, Part 2. Couette and Poiseuille Flows,” J. Fluid Mech., vol. 277, pp. 271-301, 1995.
 H. H. Hu, “Direct Simulation of Flows of Solid-Liquid Mixtures,” Int. J. Multiphase Flow, vol. 22, no. 2, pp. 335-352, 1996.
 J. Fukai, Y. Shiiba, T. Yamamoto, O. Miyatake, D. Poulikakos, C. M. Megaridis, and Z. Zhao, “Wetting Effects on the Spreading of a Liquid Droplet Colliding with a Flat Surface: Experiment and Modeling,” Phys. Fluids, vol. 7, no. 2, pp. 236-247, 1995.
 J. Glimm, J. W. Grove, X. L. Li, W. Oh, and D. H. Sharp, “A critical analysis of Rayleigh-Taylor growth rates,” J. Comput. Phys., vol. 169, no. 2, pp. 652-677, 2001.
 S. O. Unverdi and G. Tryggvason, “A Front-Tracking Method for Viscous, Incompressible, Multi-Fluid Flows,” J. Comput. Phys., vol. 100, no. 1, pp. 25-37, 1992.
 G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Tauber, J. Han, S. Nas, and Y-J. Jan, “A front-tracking method for the computations of multiphase flow,” J. Comput. Phys., vol. 169, no. 2, pp. 708-759, 2001.
 F. Hassaninejadafarahani and S. Ormiston, “Numerical Analysis of Laminar Reflux Condensation from Gas-Vapour Mixtures in Vertical Parallel Plate Channels,” World Academy of Science, Engineering and Technology, Int. J. Mech., Aer., Ind., Mech. and Manuf. Eng., vol. 9, no. 5, pp. 778-785, 2015.
 M. A. Islam, A. Miyara, T. Nosoko, and T. Setoguchi, “Numerical investigation of kinetic energy and surface energy of wavy falling liquid film,” J. Therm. Sci., vol. 16, no. 3, 237-242, 2007.
 R. W. Fox and T. A. McDonald, Introduction to fluid mechanics, John Wiley, 1994.
 Demirdzic and M. Peric, “Space conservation law in finite volume calculations of fluid flow,” Int. J. Numer. Meth. Fl., vol. 8, no. 9, pp. 1037-1050, 1988.
 C. M. Rhie and W. L. Chow, “Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation,” AIAA Journal, vol. 21, no. 11, pp. 1525–1532, 1983.
 S. Vakilipour and S. J. Ormiston, “A coupled pressure-based co-located finite-volume solution method for natural-convection flows,” Numer. Heat Tr., B-Fund., vol. 61, no. 2, pp. 91-115, 2012.
 S. Muzaferija and M. Peric, “Computation of free-surface flows using the finite-volume method and moving grids,” Numer. Heat Transfer, vol. 32, no. 4, pp. 369-384, 1997.
 T. E. Tezduyar, S. Aliabadi, M. Behr, A. Johnson, V. Kalro, and M. Litke, “Flow simulation and high performance computing,” Comput. Mech., vol. 18, no. 6, pp. 397–412, 1996.