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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 79, 2021 - Issue 5-6
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Original Articles

An implicit bounding formulation for the volume fraction equation in multiphase flows

, , , & ORCID Icon
Pages 235-254 | Received 20 Oct 2020, Accepted 13 Nov 2020, Published online: 25 Jan 2021

References

  • C. E. Brennen and C. E. Brennen, Fundamentals of Multiphase Flow. Cambridge: Cambridge University Press, 2005.
  • A. Faghri and Y. Zhang, Transport Phenomena in Multiphase Systems. Burlington, MA: Elsevier, 2006.
  • 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. DOI: 10.1016/0021-9991(81)90145-5.
  • F. Denner and B. G. van Wachem, “Fully-coupled balanced-force vof framework for arbitrary meshes with least-squares curvature evaluation from volume fractions,” Numer. Heat Transf. B: Fundamentals, vol. 65, no. 3, pp. 218–255, 2014. DOI: 10.1080/10407790.2013.849996.
  • J. H. Ferziger and M. Peric, Computational Methods for Fluid Dynamics. New York: Springer Science & Business Media, 2012.
  • C. A. Fletcher, Computational Techniques for Fluid Dynamics 2: Specific Techniques for Different Flow Categories. New York: Springer Science & Business Media, 2012.
  • G. D. Weymouth and D. K.-P. Yue, “Conservative volume-of-fluid method for free-surface simulations on cartesian-grids,” J. Comput. Phys., vol. 229, no. 8, pp. 2853–2865, 2010. DOI: 10.1016/j.jcp.2009.12.018.
  • C. Ivey and P. Moin, “Conservative volume of fluid advection method on unstructured grids in three dimensions,” Center for Turbulence Research Annual Research Briefs, pp. 179–192, 2012.
  • R. Lahey, Jr., “Two-phase flow in boiling water nuclear reactors,” Tech. Rep., General Electric Co., 1974.
  • N. Zuber, “Flow excursions and oscillations in boiling, two-phase flow systems with heat addition,” in Symposium on Two-phase Flow Dynamics, Eindhoven EUR4288e, pp. 1071, 1967.
  • F. Moukalled and M. Darwish, “On the performance of mass conservation based algorithms for multi-phase flows,” IASTED International Conference on Applied Simulation and Modelling, Crete, 2002.
  • M. Darwish, F. Moukalled and B. Sekar, “A unified formulation of the segregated class of algorithms for multifluid flow at all speeds”, Numerical Heat Transfer: Part B: Fundamentals, vol. 40, no. 2, pp. 99–137, 2001. DOI: 10.1080/104077901750475887.
  • G. H. Yeoh and J. Tu, Computational Techniques for Multiphase Flows. Oxford: Butterworth-Heinemann, 2019.
  • F. Moukalled, L. Mangani, and M. Darwish, The Finite Volume Method in Computational Fluid Dynamics, vol. 6. New York: Springer, 2016.
  • C. Moses and G. Stein, “On the growth of steam droplets formed in a laval nozzle using both static pressure and light scattering measurements,” ASME. J. Fluids Eng., vol. 100, no. 3, pp. 311–322, 1978.
  • A. Gerber, “Inhomogeneous multifluid model for prediction of nonequilibrium phase transition and droplet dynamics,” J. Fluids Eng., vol. 130, no. 3, pp. 031402, 2008. DOI: 10.1115/1.2844580.
  • G. Gyarmathy, A Von Karman Institute Book on Two-Phase Steam Flow in Turbines and Separators, Washington: Hemisphere Publishers, pp. 127–189, 1976.
  • J. Cooper and R. Dooley, “Revised release on the IAPWS industrial formulation 1997 for the thermodynamic properties of water and steam,” The International Association for the Properties of Water and Steam, vol. 1, pp. 48, 2007.
  • T. Petrova and R. Dooley, “Revised release on surface tension of ordinary water substance,” in Proceedings of the International Association for the Properties of Water and Steam, Moscow, Russia, pp. 23–27, 2014.
  • J. Cooper and R. Dooley, “Release of the IAPWS formulation 2008 for the viscosity of ordinary water substance,” The International Association for the Properties of Water and Steam, 2008.
  • K. Daucik and R. Dooley, “Release on the IAPWS formulation 2011 for the thermal conductivity of ordinary water substance,” The International Association for the Properties of Water and Steam, 2011.
  • L. Schiller, “A drag coefficient correlation,” Zeit. Ver. Deutsch. Ing., vol. 77, pp. 318–320, 1933.
  • F. Bakhtar, J. Young, A. White, and D. Simpson, “Classical nucleation theory and its application to condensing steam flow calculations,” Proc. Instit.Mech. Eng., C: J. Mech. Eng. Sci., vol. 219, no. 12, pp. 1315–1333, 2005. DOI: 10.1243/095440605X8379.
  • J. Young, “Spontaneous condensation of steam in supersonic nozzles,” Physicochem. Hydrodyn., vol. 3, pp. 57–82, 1982.
  • L. Back and R. Cuffel, “Detection of oblique shocks in a conical nozzle with a circular-arc throat,” AIAA J., vol. 4, no. 12, pp. 2219–2221, 1966. DOI: 10.2514/3.3881.
  • H. T. Chang, L. W. Hourng, L. C. Chien, and L. C. Chien, “Application of flux-vector-splitting scheme to a dilute gas–particle JPL nozzle flow,” Int. J. Numer. Meth. Fluids, vol. 22, no. 10, pp. 921–935, 1996. DOI: 10.1002/(SICI)1097-0363(19960530)22:10<921::AID-FLD382>3.0.CO;2-1.
  • M. Darwish, F. Moukalled, and B. Sekar, “A robust multi-grid pressure-based algorithm for multi-fluid flow at all speeds,” Int. J. Numer. Meth. Fluids, vol. 41, no. 11, pp. 1221–1251, 2003. DOI: 10.1002/fld.490.
  • F. Moukalled, M. Darwish, and B. Sekar, “A pressure-based algorithm for multi-phase flow at all speeds,” J. Comput. Phys., vol. 190, no. 2, pp. 550–571, 2003. DOI: 10.1016/S0021-9991(03)00297-3.
  • T. Ducrocq, L. Cassan, J. Chorda, and H. Roux, “Flow and drag force around a free surface piercing cylinder for environmental applications,” Environ. Fluid Mech., vol. 17, no. 4, pp. 629–645, 2017. DOI: 10.1007/s10652-016-9505-9.
  • A. Colagrossi, G. Nikolov, D. Durante, S. Marrone, and A. Souto-Iglesias, “Viscous flow past a cylinder close to a free surface: Benchmarks with steady, periodic and metastable responses, solved by meshfree and mesh-based schemes,” Comput. Fluids, vol. 181, pp. 345–363, 2019. DOI: 10.1016/j.compfluid.2019.01.007.
  • D. A. Potts, “Hydrodynamics of vertical surface-piercing cylinders,” Master thesis, Australian Maritime College, University of Tasmania, Australia, 2019. DOI: 10.25959/100.00034573.
  • F. Denner and B. G. van Wachem, “Numerical time-step restrictions as a result of capillary waves,” J. Comput. Phys., vol. 285, pp. 24–40, 2015. DOI: 10.1016/j.jcp.2015.01.021.
  • V. K. Gupta, K. Srikanth, and H. Punekar, “Improvements in free surface flow numerics using coupled vof and pseudo transient solver,” in 2016 IEEE 23rd International Conference on High Performance Computing Workshops (HiPCW), IEEE, 2016., pp. 100–105. DOI: 10.1109/HiPCW.2016.022.
  • P. J. Zwart, P. G. Godin, J. Penrose, and S. H. Rhee, “Simulation of unsteady free-surface flow around a ship hull using a fully coupled multi-phase flow method,” J. Mar. Sci. Technol., vol. 13, no. 4, pp. 346–355, 2008. DOI: 10.1007/s00773-008-0012-7.
  • K. Kissling, J. Springer, H. Jasak, S. Schutz, K. Urban, and M. Piesche, “A coupled pressure based solution algorithm based on the volume-of-fluid approach for two or more immiscible fluids,” in Proceedings of the V European Conference on Computational Fluid Dynamics ECCOMAS CFD 2010, 2010.
  • K. Kleefsman, G. Fekken, A. Veldman, B. Iwanowski, and B. Buchner, “A volume-of-fluid based simulation method for wave impact problems,” J. Comput. Phys., vol. 206, no. 1, pp. 363–393, 2005. DOI: 10.1016/j.jcp.2004.12.007.
  • A. Issakhov, Y. Zhandaulet, and A. Nogaeva, “Numerical simulation of dam break flow for various forms of the obstacle by vof method,” Int. J. Multiphase Flow, vol. 109, pp. 191–206, 2018. DOI: 10.1016/j.ijmultiphaseflow.2018.08.003.
  • Z. Gu, H. Wen, C.-H. Yu, and T. W. Sheu, “Interface-preserving level set method for simulating dam-break flows,” J. Comput. Phys., vol. 374, pp. 249–280, 2018. DOI: 10.1016/j.jcp.2018.07.057.
  • T. Barth and D. Jespersen, “The design and application of upwind schemes on unstructured meshes,” in 27th Aerospace Sciences Meeting, 1989, p. 366. DOI: 10.2514/6.1989-366.

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