International Scientific Journal

Thermal Science - Online First

online first only

The impact of the order of numerical schemes on slug flows modeling

This paper aims to explore the impact of the order of numerical schemes on the simulation of two-phase slug flow with a two-fluid model initiation. The governing equations of the two-fluid model have been solved by a class of Riemann solver. The numerical schemes applied in this paper involve first-order (Lax-Friedrichs and Rusanov), second-order (Ritchmyer), and high-order (Flux-Corrected Transport or FCT and TVD). The results suggest that the TVD and FCT are able to predict the slug initiation with high accuracy compared with experimental results. Lax-Friedrichs and Rusanov are both first-order schemes and have second-order truncation error. This second-order truncation error caused numerical diffusion in the solution field and could not predict the slug initiation with high accuracy in contrast to TVD and FCT schemes. Ritchmyer is a second-order scheme and has third-order truncation error. This third-order truncation error caused dispersive results in the solution field and was not a proper scheme.
PAPER REVISED: 2018-10-10
PAPER ACCEPTED: 2018-11-18
  1. Omgba-Essama, C., Numerical modelling of transient gas-liquid flows (application to stratified & slug flow regimes), Ph. D. Thesis, Cranfield University, England, 2004
  2. Ishii, M., Thermo-Fluid Dynamic Theory of Two-Phase Flow, Eyrolles, Paris, France, 1975
  3. Ishii, M., Mishima, K., Two-fluid model and hydrodynamic constitutive relations, Nuclear Engineering and design, 82(1984), 2, pp. 107-126
  4. Woodburn, P., Issa, R., Well-posedness of one-dimensional transient, two-fluid models of two-phase flows, Third International Conditioning of Multiphase Flow, Lyon, France, 1998, pp. 8-12
  5. Issa, R., Kempf, M., Simulation of slug flow in horizontal and nearly horizontal pipes with the two-fluid model, International journal of multiphase flow, 29(2003), 1, pp. 69-95
  6. Bonizzi, M., Issa, R., On the simulation of three-phase slug flow in nearly horizontal pipes using the multi-fluid model, International journal of multiphase flow, 29(2003), 11, pp. 1719-1747
  7. Bonizzi, M., Issa, R., A model for simulating gas bubble entrainment in two-phase horizontal slug flow, International journal of multiphase flow, 29(2003), 11, pp. 1685-1717
  8. Issa, R., et al., Improved closure models for gas entrainment and interfacial shear for slug flow modelling in horizontal pipes, International journal of multiphase flow, 32(2006), 10, pp. 1287-1293
  9. Ansari, M., Shokri, V., Numerical modeling of slug flow initiation in a horizontal channels using a two-fluid model, International Journal of Heat and Fluid Flow, 32(2011), 1, pp. 145-155
  10. Issa, R., et al., Accurate simulation of intermittent/slug flow in oil and gas pipelines, 15th International Conditioning on Multiphase Production Technology, Cannes, France, 2011, pp. 15-17
  11. Simões, E. F., et al., Numerical prediction of non-boiling heat transfer in horizontal stratified and slug flow by the Two-Fluid Model, International Journal of Heat and Fluid Flow, 47(2014), pp. 135-145
  12. Bonzanini, A., et al., Simplified 1D Incompressible Two-Fluid Model with Artificial Diffusion for Slug Flow Capturing in Horizontal and Nearly Horizontal Pipes, Energies, 10(2017), 9, pp. 1372, 2017
  13. Shokri, V., Esmaeili, K., Comparison of the effect of hydrodynamic and hydrostatic models for pressure correction term in two-fluid model in gas-liquid two-phase flow modeling, Journal of Molecular Liquids, 237(2017), pp. 334-346
  14. Watson, M., Non-linear waves in pipeline two-phase flows, in Third International Conference on Hyperbolic Problems. 1990.
  15. Li, G., et al., Gas reservoir evaluation for underbalanced horizontal drilling, Thermal Science, 18(2014), 5, pp. 1691-1694
  16. Montini, M., Closure relations of the one-dimensional two-fluid model for the simulation of slug flows, Ph. D. Thesis, Imperial College London, London, 2011.
  17. Hirsch, H., Numerical computation of internal and external flows, Computational methods for inviscid and viscous flows, Wiley InterScience, Brussels, Belgium, 1990
  18. Boris, J. P., Book, D. L., Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works, Journal of computational physics, 11(1973), 1, pp. 38-69
  19. Hoffmann, K. A., Chiang, S. T., Computational Fluid Dynamics Volume I, Engineering Education System, Wichita, Kan, USA, 2000
  20. Tóth, G., Odstrčil, D., Comparison of some flux corrected transport and total variation diminishing numerical schemes for hydrodynamic and magnetohydrodynamic problems, Journal of Computational Physics, 128(1996), 1, pp. 82-100
  21. Louaked, M., et al., Well‐posedness of incompressible models of two‐and three‐phase flow, IMA journal of applied mathematics, 68(2003), 6, pp. 595-620
  22. Ansari, M. R., Experimental investigation on wave initiation and slugging of air-water stratified flow in horizontal duct, Journal of Nuclear Science and Technology, 26(1989), 7, pp. 681-688