A Robust and accurate Riemann solver for a compressible two-phase flow model

In this paper we analyze the Riemann problem for the widely used drift-flux two-phase flow model. This analysis introduces the complete information that is attained in the representation of solutions to the Riemann problem. It turns out that the Riemann waves have rarefactions, a contact discontinuity and shocks. Within this respect, an exact Riemann solver is developed to accurately resolve and represent the complete wave structure of the gas-liquid two-phase flows. To verify the solver, a series of test problems selected from the literature are presented including validation against independent numerical simulations where the solution of the Riemann problem is fully numerical. In this framework the governing equations are discretized by finite volume techniques facilitating the application Godunov methods of centred-type. It is shown that both analytical and numerical results demonstrate the broad applicability and robustness of the new exact Riemann solver.

[1]  Frédéric Coquel,et al.  A Semi-implicit Relaxation Scheme for Modeling Two-Phase Flow in a Pipeline , 2005, SIAM J. Sci. Comput..

[2]  Cem Sarica,et al.  A Comprehensive Mechanistic Model for Upward Two-Phase Flow in Wellbores , 1994 .

[3]  M. Baer,et al.  A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials , 1986 .

[4]  Michael Herty,et al.  Toward a Mathematical Analysis for Drift-Flux Multiphase Flow Models in Networks , 2009, SIAM J. Sci. Comput..

[5]  Arezki Slaouti,et al.  Validation of hyperbolic model for two-phase flow in conservative form , 2009 .

[6]  S. G. Bankoff,et al.  Slip velocity ratios in an air-water system under steady-state and transient conditions , 1967 .

[8]  E. Toro Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .

[9]  Steinar Evje,et al.  The multi‐stage centred‐scheme approach applied to a drift‐flux two‐phase flow model , 2006 .

[10]  Roland Masson,et al.  A relaxation method for two-phase flow models with hydrodynamic closure law , 2005, Numerische Mathematik.

[11]  Dia Zeidan,et al.  The Riemann problem for a hyperbolic model of two-phase flow in conservative form , 2011 .

[12]  Q. Tran,et al.  Transient simulation of two-phase flows in pipes , 1998 .

[13]  R. Abgrall,et al.  A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows , 1999 .

[14]  Alois Hoeld,et al.  Coolant channel module CCM: An universally applicable thermal-hydraulic drift-flux based mixture-fluid 1D model and code , 2007 .

[15]  T. Barkve,et al.  Application of a Multisegment Well Model to Simulate Flow in Advanced Wells , 1998 .

[16]  D. Zeidan,et al.  Numerical resolution for a compressible two-phase flow model based on the theory of thermodynamically compatible systems , 2011, Appl. Math. Comput..

[17]  L. Durlofsky,et al.  Drift-Flux Modeling of Two-Phase Flow in Wellbores , 2005 .

[18]  Curtis M. Oldenburg,et al.  Wellbore flow model for carbon dioxide and brine , 2008 .

[19]  Eric Goncalves,et al.  Numerical study of expansion tube problems: Toward the simulation of cavitation , 2013 .

[20]  G. Wallis One Dimensional Two-Phase Flow , 1969 .

[21]  R. I. Issa,et al.  Simulation of slug flow in horizontal and nearly horizontal pipes with the two-fluid model , 2003 .

[22]  C. S. Kabir,et al.  Heat Transfer During Two-Phase Flow in Wellbores; Part I--Formation Temperature , 1991 .

[23]  Herbert Staedtke,et al.  Gasdynamic Aspects of Two-Phase Flow: Hyperbolicity, Wave Propagation Phenomena and Related Numerical Methods , 2006 .

[24]  E. Toro,et al.  A Riemann solver and upwind methods for a two‐phase flow model in non‐conservative form , 2006 .

[25]  H. Bruce Stewart,et al.  Two-phase flow: Models and methods , 1984 .

[26]  M. Ishii Thermo-fluid dynamic theory of two-phase flow , 1975 .

[27]  Donald W. Schwendeman,et al.  The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow , 2006, J. Comput. Phys..

[28]  N. Zuber,et al.  Average volumetric concentration in two-phase flow systems , 1965 .

[29]  D. Drew,et al.  Theory of Multicomponent Fluids , 1998 .

[30]  Curtis M. Oldenburg,et al.  Analytical solution for two-phase flow in a wellbore using the drift-flux model , 2011 .

[31]  G. Warnecke,et al.  The Riemann problem for the Baer-Nunziato two-phase flow model , 2004 .

[32]  Curtis M. Oldenburg,et al.  T2Well/ECO2N Version 1.0: Multiphase and Non-Isothermal Model for Coupled Wellbore-Reservoir Flow of Carbon Dioxide and Variable Salinity Water , 2011 .

[33]  Richard Saurel,et al.  Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures , 2009, J. Comput. Phys..