Abstract
This chapter presents a numerical solution method for multi-phase flow analysis based on local volume and time averaged conservation equations. The emphasis of this development was to create a computer code architecture that absorb all the constitutive physics and functionality from the past 25years development of the three fluid multi-component IVA-entropy concept for multiphase flows into a boundary fitted orthogonal coordinate framework. Collocated discretization for the momentum equations is used followed by weighted averaging for the staggered grids resulting in analytical expressions for the normal velocities. Using the entropy concept analytical reduction to a pressure-velocity coupling is found. The performance of the method is demonstrated by comparison of two cases for which experimental results and numerical solution with the previous method are available. The agreement demonstrates the success of this development.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Keywords
- Momentum Equation
- Curvilinear Coordinate System
- Constrain Interpolation Profile
- Contravariant Vector
- Fluid Engineer Division
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Antal, S.P., et al.: Development of a next generation computer code for the prediction of multi-component multiphase flows. In: Int. Meeting on Trends in Numerical and Physical Modeling for Industrial Multiphase Flow, Cargese, France (2000)
Brackbill, J.U., Kothe, D.B., Zeinach, C.: A continuum method for modelling surface tension. Journal of Computational Physics 100, 335 (1992)
Gregor, C., Petelin, S., Tiselj, I.: Upgrade of the VOF method for the simulation of the dispersed flow. In: Proc. of ASME 2000 Fluids Engineering Division Summer Meeting, Boston, Massachusetts, June 11-15 (2000)
Harlow, F.H., Amsden, A.A.: Numerical calculation of multiphase flow. Journal of Computational Physics 17, 19–52 (1975)
Hirt, C.W.: Volume-fraction techniques: powerful tools for wind engineering. J. Wind Engineering and Industrial Aerodynamics 46-47, 327 (1993)
Hou, S., Zou, Q., Chen, S., Doolen, G., Cogley, A.C.: Simulation of cavity flow by the lattice Boltzmann method. J. Comput. Phys. 118, 329 (1995)
Jamet, D., Lebaigue, O., Courtis, N., Delhaye: The second gradient method for the direct numerical simulation of liquid-vapor flows with phase change. Journal of Comp. Physics 169, 624–651 (2001)
Kolev, N.I.: IVA4: Modeling of mass conservation in multi-phase multi-component flows in heterogeneous porous media. Kerntechnik 59(4-5), 226–237 (1994)
Kolev, N.I.: The code IVA4: Modelling of momentum conservation in multi-phase multi-component flows in heterogeneous porous media. Kerntechnik 59(6), 249–258 (1994)
Kolev, N.I.: The code IVA4: Second law of thermodynamics for multi phase flows in heterogeneous porous media. Kerntechnik 60(1), 1–39 (1995)
Kolev, N.I.: Comments on the entropy concept. Kerntechnik 62(1), 67–70 (1997)
Kolev, N.I.: On the variety of notation of the energy conservation principle for single phase flow. Kerntechnik 63(3), 145–156 (1998)
Kolev, N.I.: Conservation equations for multi-phase multi-component multi-velocity fields in general curvilinear coordinate systems, Keynote lecture. In: Proceedings of ASME FEDSM 2001, ASME 2001 Fluids Engineering Division Summer Meeting, New Orleans, Louisiana, May 29-June 1 (2001)
Kothe, D.B., Rider, W.J., Mosso, S.J., Brock, J.S., Hochstein, J.I.: Volume tracking of Interfaces having surface tension in two and three dimensions. In: AIAA 96-0859 (1996)
Kumbaro, A., Toumi, I., Seignole, V.: Numerical modeling of two-phase flows using advanced two fluid system. In: Proc. of ICONE10, 10th Int. Conf. On Nuclear Engineering, Arlington, VA, USA, April 14-18 (2002)
Lahey Jr, R.T., Drew, D.: The analysis of two-phase flow and heat transfer using a multidimensional, four field, two-fluid model. In: Ninth Int. Top. Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-9), San Francisco, California, October 3-8 (1999)
Miettinen, J., Schmidt, H.: CFD analyses for water-air flow with the Euler-Euler two-phase model in the FLUENT4 CFD code. In: Proc. of ICONE10, 10th Int. Conf. On Nuclear Engineering, Arlington, VA, USA, April 14-18 (2002)
Nakamura, T., Tanaka, R., Yabe, T., Takizawa, K.: Exactly conservative semi-Lagrangian scheme for multi-dimensional hyperbolic equations with directional splitting technique. J. Comput. Phys. 147, 171 (2001)
Nourgaliev, R.R., Dinh, T.N., Sehgal, B.R.: On lattice Boltzmann modelling of phase transition in isothermal non-ideal fluid. Nuclear Engineering and Design 211, 153–171 (2002)
Osher, S., Fredkiw, R.: Level set methods and dynamic implicit surfaces. Springer-Verlag New York, Inc., Secaucas (2003)
Rider, W.J., Kothe, D.B.: Reconstructing volume tracking. Journal of Computational Physics 141, 112 (1998)
Staedke, H., Franchello, G., Worth, B.: Towards a high resolution numerical simulation of transient two-phase flow. In: Third International Conference on Multi-Phase, ICMF 1998, June 8-12 (1998)
Sussman, M., Smereka, P., Oslier, S.: A level set approach for computing solutions to incompressible two-phase flow. Journal of Computational Physics 114, 146 (1994)
Swthian, J.A.: Level set methods. Cambridge University Press, Cambridge (1996)
Takewaki, H., Nishiguchi, A., Yabe, T.: The Cubic-Interpolated Pseudo Particle (CIP) Method for Solving Hyperbolic-Type Equations. J. Comput. Phys. 61, 261 (1985)
Takewaki, H., Yabe, Y.: Cubic-Interpolated Pseudo Particle (CIP) Method-Application to Nonlinear Multi-Dimensional Problems. J. Cornput. Phys. 70, 355 (1987)
Tomiyama, A., et al.: (N+2)-Field modelling of dispersed multiphase flow. In: Proc. of ASME 2000 Fluids Engineering Division Summer Meeting, Boston, Massachusetts, June 11-15 (2000)
Toumi, I., et al.: Development of a multi-dimensional upwind solver for two-phase water/steam flows. In: Proc. of ICONE 8, 8th Int. Conf. On Nuclear Engineering, Baltimore, MD USA, April 2-6 (2000)
Tryggavson, G., et al.: A front tracking method for the computations of multiphase flows. Journal of Comp. Physics 169, 708–759 (2001)
Verschueren, M.: A difuse-interface model for structure development in flow, PhD Thesis, Technische Universitteit Eindhoven (1999)
van Wijngaarden, L.: Hydrodynamic interaction between gas bubbles in liquid. J. Fluid Mech. 77, 27–44 (1976)
Yabe, T., Takei, E.: A New Higher-Order Godunov Method for General Hyperbolic Equations. J. Phys. Soc. Japan 57, 2598 (1988)
Xiao, F., Yabe, T.: Completely conservative and oscillation-less semi-Lagrangian schemes for advection transportation. J. Comput. Phys. 170, 498 (2001)
Xiao, F., Yabe, T., Peng, X., Kobayashi, H.: Conservation and oscillation-less transport schemes based an rational functions. J. Geophys. Res. 107, 4609 (2002)
Xiao, F.: Profile-modifiable conservative transport schemes and a simple multi integrated moment formulation for hydrodynamics. In: Amfield, S., Morgan, P., Srinivas, K. (eds.) Computational Fluid Dynamics, p. 106. Springer, Heidelberg (2003)
Xiao, F., Ikebata, A.: An efficient method for capturing free boundary in multi-fluid simulations. Int. J. Numer. Method in Fluid 42, 187–210 (2003)
Yabe, T., Wang, P.Y.: Unified Numerical Procedure for Compressible and Incompressible Fluid. J. Phys. Soc. Japan 60, 2105–2108 (1991)
Yabe, T., Aoki, A.: A Universal Solver for Hyperbolic-Equations by Cubic Polynomial Interpolation. Comput. Phys. Commun. 66, 219 (1991)
Yabe, T., Ishikawa, T., Wang, P.Y., Aoki, T., Kadota, Y., Ikeda, F.: A universal solver for hyperbolic-equations by cubic-polynomial interpolation. II. 2-dimensional and 3-dimensional solvers. Comput. Phys. Commun. 66, 233 (1991)
Yabe, T., Xiao, F., Utsumi, T.: Constrained Interpolation Profile Method for Multiphase Analysis. J. Comput. Phys. 169, 556–593 (2001)
Yabe, T., Tanaka, R., Nakamura, T., Xiao, F.: Exactly conservative semi-Lagrangian scheme (CIP-CSL) in one dimension. Mon. Wea. Rev. 129, 332 (2001)
Yabe, T., Xiao, F., Utsumi, T.: The constrained interpolation profile method for multiphase analysis. J. Comput. Phys. 169, 556 (2001)
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kolev, N.I. (2011). Numerical methods for multi-phase flow in curvilinear coordinate systems. In: Multiphase Flow Dynamics 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20605-4_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-20605-4_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20604-7
Online ISBN: 978-3-642-20605-4
eBook Packages: EngineeringEngineering (R0)