Performance Evaluation of a 2D Front Tracking Method - a Direct Numerical Simulation Method for Multiphase Flows
Main Article Content
Abstract
This paper evaluates the performance of a direct numerical simulation (DNS) method called "front-tracking" for multiphase flows. The interface separating two fluids or two phases is represented by connected elements that move on a fixed rectangular grid used for solving the Navier-Stokes equations. The phase's values of material properties are specified by an indicator function that is reconstructed from the interface point location. The interface points are updated by the velocities, which are interpolated from the velocities on the fixed grid. The method is evaluated through a thorough investigation of the performance using a variety of verification and validation test cases including advection of the interface, computations of the surface tension, and interplay of the viscous and interfacial tension terms. The method is then used to simulate the evolution of the Rayleigh-Taylor instability. Good agreement in comparison of the present method with the previous literature proved the accuracy and capability of the method.
Keywords
DNS, Front-tracking, Performance evaluation, Multiphase flow, Rayleigh-Taylor instability
Article Details
References
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[3] M. Sussman, E. Fatemi, P. Smereka, S. Osher, An improved level set method for incompressible two-phase flows, Comput. Fluids. 27 (1998) 663-680.
[4] D. Jacqmin, Calculation of two-phase Navier-Stokes flows using phase-field modeling. J. Comput. Phys. 155 (1999) 96-127.
[5] H. Takewaki, A. Nishiguchi, T. Yabe. Cubic interpolated pseudo-particle method (CIP) for solving hyperbolic-type equations. J. Comput. Phys. 61 (1985) 261-268.
[6] S.O. Unverdi, G. Tryggvason. A front-tracking method for viscous, incompressible, multi-fluid flows, J. Comput. Phys. 100 (1992) 25-37.
[7] G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi. W. Tauber, J. Han, S. Nas, Y.-J. Jan, A front-tracking method for the computations of multiphase flow, J. Comput. Phys. 169 (2001) 708-759.
[8] C.W. Hirt, J.L. Cook, T.D. Butler, A Lagrangian method for calculating the dynamics of an incompressible fluid with free surface, J. Comput. Phys. 5 (1970) 103-124.
[9] X. Shan, H. Chen, Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E. 47 (1993) 1815.
[10] T.V. Vu, S. Homma, G. Tryggvason, J.C. Wells, H. Takakura, Computations of breakup modes in laminar compound liquid jets in a coflowing fluid. Int. J. Multiphase Flow. 49 (2013) 58-69.
[11] T.V. Vu, G. Tryggvason, S. Homma, J.C. Wells, H. Takakura, A front-tracking method for three-phase computations of solidification with volume change. J. Chem. Eng. Jpn. 46 (2013) 726-731.
[12] T.V. Vu, G. Tryggvason, S. Homma, J.C. Wells, Numerical investigations of drop solidification on a cold plate in the presence of volume change, Int. J. Multiphase Flow. 76 (2015) 73-85.
[13] C.S. Peskin, Numerical analysis of blood flow in the heart, J. Comput. Phys. 25 (1977) 220-252.
[14] A. Esmaeeli, G. Tryggvason, Computations of film boiling. Part I: numerical method, Int. J. Heat Mass Transfer. 47 (2004) 5451-5461.
[15] S.T. Zalesak, Fully multidimensional flux-corrected transport algorithms for fluids, J. Comput. Phys. 31 (1979) 335-362.
[16] J.B. Bell, P. Colella, H.M. Glaz, A second-order projection method for the incompressible Navier-Stokes equations, J. Comput. Phys. 85 (1989) 257-283.
[17] D. Enright, R. Fedkiw, J. Ferziger, 1. Mitchell, A hybrid particle level set method for improved interface capturing, J. Comput. Phys. 183 (2002) 83-116.
[18] G. Tryggvason, R. Scardovelli, S. Zaleski, Direct numerical simulations of gas-liquid multiphase flows, Cambridge University Press, Cambridge; New York, 2011.
[19] A. Prosperetti, Motion of two superposed viscous fluids, Phys. Fluids. 24 (1981) 1217-1223
[20] M. Herrmann, A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids. J. Comput. Phys. 227 (2008) 2674-2706.