International Journal of Modern Physics and Applications

Articles Information

Modeling of Interfacial Dynamics in Turbulent Two-Phase Flows Using the Level Set Method

Pages: 77-98 Views: 1159 Downloads: 583

[01]
Ashraf Balabel, Mechanical Engineering Dept, Faculty of Engineering, Taif University, Al, Haweiah, Taif, Saudi Arabia.

In the present paper, the dynamics of turbulent two-phase flow is numerically predicted. The numerical modeling presented here is based on a new developed numerical method called Interfacial Marker-Level Set method, which coupled with the Reynolds averaged Navier-Stokes equations to predict the dynamical behavior of turbulent two-phase flow. The governing equations for time-dependent, axisymmetric and incompressible two-phase flow are described in both phases and solved separately using the control volume approach on structured cell-centered collocated grids. The transition from one phase to another is performed through a consistent balance of kinematic and dynamic conditions on the interface separating the two phases. The topological changes of the interface are predicted by applying the level set approach. The performance of linear and non-linear two-equation turbulence models is also investigated. Generally, the developed numerical method demonstrates a remarkable capability to predict the dynamical characteristics of complex turbulent two-phase flow in many industrial applications.

Numerical Methods, Two-Phase Flow, Level Set Method, Capillary Instability, Turbulence Modeling

[01]
Lefebvre, A. H., Atomization and sprays, Hemisphere Publishing Corporation, 1989.
[02]
Won, H. and Peters, N., Investigation of cluster-nozzle concepts for direct injection diesel engines, Atomization and sprays, Vol. 19(10), pp. 983-996, 2009.
[03]
Garbero, M., Vanni, M. and Fritsching, U., Gas/Surface heat transfer in spray deposition processes, Int. J. Heat and Fluid Flow, Vol.(27), pp. 105-122, 2006.
[04]
Torpey PA., Prevention of air ingestion in a thermal ink-jet device. Proceedings of the 4th International Congress on Advances in Non-impact Print Technologies, Springfield, VA, March 1988.
[05]
Dressler, D., Li, L., Green, S., Davy, M. and Eadie, D., Newtonian and non-newtonian spray interaction with a high-speed moving surface, Atomization and sprays, Vol. 19(1), pp. 19-39, 2009
[06]
Zhaorui Li, Farhad A. Jaberi1 and Tom I-P. Shih, A hybrid Lagrangian–Eulerian particle-level set method for numerical simulations of two-fluid turbulent flows, Int. J. Num. Methods in Fluids, Vol 56, pp. 2271-2300, 2008.
[07]
Desjardins, O., Moureau, V. and Pitsch, H., An accurate conservative level set/ghost fluid method for simulationg turbulent atomization, J. Comp. Physics, Vol. 227, pp. 8395-8416, 2008.
[08]
Herrmann, M., A Eulerian level set/vortex sheet method for two-phase interface dynamics, J. Comp: Physics, Vol. 203, pp. 539-571, 2005.
[09]
Eggers, J., Nonlinear dynamics and breakup of free-surface flows, Reviews of modern physics, Vol. 69(3), pp. 1-65, 1997.
[10]
Schulkes, R. M., The evolution and bifurcation of a pendant drop, J. Fluid Mechanics, Vol. 278, pp. 83-100, 1994.
[11]
Borue V, Orszag SA, Staroselsky I., Interaction of surface waves with turbulence: direct numerical simulations of turbulent open-channel flow. Journal of Fluid Mechanics, Vol. 286, pp. 1–23, 1995.
[12]
Pan Y, Banerjee S., A numerical study of free surface turbulence in channel flow, The Physics of Fluids; Vol. 7, pp. 1649 –1664, 1995.
[13]
Tsai W-T., A numerical study of the evolution and structure of a turbulent shear layer under a free surface, Journal of Fluid Mechanics, Vol. 354, pp. 239 –276, 1998.
[14]
Scardovelli R, Zaleski S., Direct numerical simulation of free-surface and interfacial flow, Annual Review of Fluid Mechanics, Vol. 31, pp. 567–603, 1999.
[15]
Rhea, S., Bini, M., Fairweather, M. and Jones, W.P., RANS modelling and LES of a single-phase, impinging plan jet, Computers and Chemical Engineering, Vol. 33, pp. 1344–1353, 2009.
[16]
Launder BE, Spalding DB. The numerical computation of turbulent flows. International Journal for Numerical Methods in Fluids, Vol. 15, pp. 127–146, 1974.
[17]
Rodi W. Turbulence models and their applications in hydraulics. International Association of Hydraulic Research, Delft, the Netherlands, Monografy, 1980.
[18]
El-Askary, W. and Balabel, A., Prediction of reattachment turbulent shear flow in asymmetric divergent channel using linear and non-linear turbulence models, Eng. Research Journa (ERJ), Faculty of Eng., Menoufiya Uni., Vol.30(4), pp. 535-550, 2007.
[19]
Pope, S. B., A more general effective-viscosity hypothesis, J. Fluid Mech., 72, 331-340, 1975.
[20]
Craft, T. J., Launder, B. E., and Suga, K., Development and Application of a Cubic Eddy-Viscosity Model of Turbulence, International Journal of Heat and Fluid flow, Vol. 17, pp.108-115, 1996.
[21]
Apsley, D. D. and Leschziner, M. A., A new low Re non-linear two-equation turbulence model for complex flows, Proc. 11th Symposium on Turbulent Shear Flows, Grenoble, 1997.
[22]
Popinet S, Zaleski S, Afront tracking algorithm for the accurate representation of surface tension, Int. J. Numer. Meth. Fluids, Vol. 30, pp. 775–793, 1999.
[23]
Unverdi SO, Tryggvason G., A front-tracking method for viscous, incompressible, multi-fluid flows, Journal ofComputational Physics, Vol. 100, pp. 25–37, 1992.
[24]
Nichols B D, Hirt C W, Methods for calculating multi-dimensional, transient free surface flows past bodies, Proc. First Int. Conf. Num. Ship Hydrodynamics Gaithersburg, pp. 20–23, 1975.
[25]
Osher S, Sethian JA., Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations, Journal of Computational Physics, Vol. 79, pp. 12–49, 1988.
[26]
Peters, N., Turbulent combustion, Cambridge University Press, Cambridge, UK, 2000.
[27]
Pierre T., Stephane, V., Jean-Luc E. and Jean-Paul C., Detailed comparisons of front-capturing methods for turbulent two-phase flow simulations, Int. J. Num. Meth. Fluids, Vol. 56, pp. 1543-1549, 2008.
[28]
Lafaurie, B., Nardone, C., Scardovelli, R., Zaleski, S. and Zanetti, G., Modelling, merging and fragmentation in multiphase flows with SURFER, J. Comp. Physics, Vol. 113, pp. 134-147, 1994.
[29]
Albert, Y. T. and Zhaoyuan, W., A numerical method for capillary-dominant free surface flows, J. Comp. Physics, Vol. 221, pp. 506-523, 2007.
[30]
Enright, D., Fedkiw, R. , Ferziger, J. and Mitchell, I., A hybrid particle level set method for improved interface capturing, J. Comp. Physics, Vol. 183, pp. 83-116, 2002.
[31]
Herrmann, M., A Eulerian level set/vortex sheet method for two-phase interface dynamics, J. Comp. Physics, Vol. 203, pp. 539-571, 2005.
[32]
Garzon, M., Gray, L. J. and Sethian, J. A., Numerical simulation of non-viscous liquid pinch-off using a coupled level set-boundary integral method, J. Comp. Physics, Vol. 228, pp. 6079-6106, 2009.
[33]
Sussman, M. , Smereka, P. and Osher, S., A level set approach for computing solutions to incompressible two-phase flows, J. Comp. Physics, Vol. 114, pp. 146-159, 1994.
[34]
Sethian, J. A. and Smereka, P., Level Set Methods for Fluid Interfaces, Annu. Rev. Fluid. Mech., Vol. 35, pp. 341-372, 2003.
[35]
Brackbill, J. U., Kothe, D. B. and Zemach. A, , A Continuum Method for Modeling Surface Tension, J. Comp.Phys., vol. 100, pp. 335-354, 1992.
[36]
Ierley, G. and Shkoller, S., Smoothing the wrinkles: a new model for surface tension, J. Fluid Mech., Preprint (2002).
[37]
Balabel, A., Numerical simulation of Gas-Liquid interface dynamics using the level set method, Dissertation, RWTH Aachen, Germany, 2002.
[38]
Balabel, A., Binninger, B., Herrmann, M. and Peters, N., Calculation of Droplet Deformation by Surface Tension Effects using the Level Set Method, J. Combustion Science and Technology, Vol. 174 (11,12), pp. 257-278, 2002.
[39]
Balabel, A., Numerical investigation of the binary droplet collision in incompressible continuum fluids using the level set method, submitted for publication in Computers and Fluids, 2010.
[40]
Craft, T.J., Launder, B.E. and Suga, K., Development and application of a cubic eddy-viscosity model of turbulence. International Journal of Heat and Fluid Flow, Vol.17, pp. 108-115, 1996.
[41]
Craft, T.J., Iacovides, H. and Mostafa, N. A., Modelling of three-dimensional jet array impingement and heat transfer on a concave surface. International Journal of Heat and Fluid Flow, Vol.29, pp. 687-702, 2008.
[42]
Craft, T.J., Iacovides, H., Yoon, J.H., Progress in the use of non-linear two equation models in the computation of convective heat-transfer in impinging and separated flows, Turbul. Combust. Vol. 63, pp. 59–80, 1999.
[43]
Launder BE, Spalding DB, The Numerical Computation of Turbulent Flows, International Journal for Numerical Methods in Fluids, 15:127-146, 1974.
[44]
Osher, S. J. and Sethian, J. A., Front Propagation with curvature dependent speed: Algorithms based on Hamilton-Jacobi Formulation, J. Comp. Phys., Vol. 79, pp. 12-49, 1988.
[45]
Sethian, J. A. and Smereka, P., Level set methods for fluid interfaces, Annu. Rev. Fluid, Mech., Vol. 35, pp. 341-372, 2003.
[46]
Adalsteinsson, D. and Sethian, J. A., The fast construction of extension velocities in level set methods, J. Comp. Phys., Vol. 148, pp. 2-22, 1999.
[47]
Sethian, J. A., A marching level set method for monotonically advancing fronts, Proceedings of the National Academy of Science, Vol. 93(4), pp. 1591-1595, 1996.
[48]
Marangoni, C., Ueber die Ausbreitung der Tropfen einer Flüssigkeit auf der Oberfläche einer Anderen, Ann. Phys. Chem.; Vol. 143, pp. 337-354, 1871.
[49]
Chang, Y. C., Hou, T. Y, Merriman, B. and Osher, S., A level set formulation of Eulerian interface capturing method for incompressible fluid flows, J. Comp. Phys., Vol. 124, pp. 449-464, 1996.
[50]
Popinet, S. and Zaleski, S., A front-tracking algorithm for accurate representation of surface tension, Int. J. Numer. Meth. Fluids, Vol. 30, pp. 775-793, 1999.
[51]
Zhongguo, S., Guang, Xi and Chen, Xi, Numerical simulation of binary collisions using a modified surface tension model with particle method, Nuclear Engineering and Design, Vol. 239, pp. 619-627, 2009.
[52]
Landau, L. D. and Lifshitz, E. M., Fluid Mechanics, Pergamon London, 1959.
[53]
Benjamin, T. B., Shearing Flow over a Wavy Boundary, J. Fluid Mech., vol. 6, pp. 161-205, 1959.
[54]
Sterling, A. M. and Sleicher, C. A., The Instability of Capillary Jets, J. Fluid Mech., vol. 68 (3), pp. 477-495, 1975.
[55]
Asali, J. C. and Hanratty, T. J., Ripples Generated on a Liquid Film at high Gas Velocities, J. Multiphase flow, vol. 19 (2), pp. 229-243, 1993.
[56]
Watanabe, T., Numerical simulation of oscillations and rotations of a free liquid droplet using the level set method, Computers & Fluids, Vol. 37, pp. 91-98, 2008.
[57]
Ierley, G. and Shkoller, S., Smoothing the wrinkles: a new model for surface tension, J. Fluid Mech., Preprint (2002).
[58]
Fedkiw, R. P., Aslam, T., Merriman, B. and Osher, S. J., A non-Oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method), J. Comput. Phys., Vol. 154, pp. 393-427, 1999.
[59]
Patankar, S. V., Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, 1980.
[60]
Sterling. A. M. and Sleicher, C. A., The Instability of Capillary Jets, J. Fluid. Mechanics, Vol.68, pp. 477-495 , 1975.
[61]
Rayleigh, L., On The Instability of Jets, Proc. Roy. Soc. London. Math. Soc., Vol. 10, pp. 4-13, 1878.
[62]
Donnelly, R. J. and Glaberson, W., Experiments on the capillary instability of a liquid jet, Proc. Roy. Soc. A283, Vol.290, pp. 547-566, 1966.
[63]
Nakazono, D., Abe, K., Nishida, M. and Kurita, k., Supersonic O2-jet impingement on liquid iron with surface chemistry, ISIJ International, Vol. 44 (1), pp. 91-99, 2004.
[64]
Cheslak, F. R., Nicholls, J. A. and Sichel, M., Cavity formed on liquid surfaces by impinging gaseous jets, Journal of Fluid Mechanics, 36, pp. 55-64, 1969.
[65]
Eletribi, S., Mukherjee, D. K. and Prasad, V., Experiments on Liquid Surface Deformation upon Impingement by a Gas Jet, Proceeding of the ASME Fluids Engineering Division, Vol. 244, pp. 235-247, 1997.
[66]
Wakelin, D. E., The interaction between gas jest and the surface of liquids including molten metals, PhD, University of London, UK, 1996.
[67]
Banks, R. B. and Chandrasekhara, D. V., Experimental investigation of the penetration of a high-velocity gas jet through a liquid surface, J. Fluid Mech., Vol. 15, pp. 13–34, 1963.
[68]
Nguyen, Anh. V. and Evans, G. M., Computational fluid dynamics modelling of gas jets impinging onto liquid pools, Applied Mathematical Modelling, Vol. 30, pp. 1472–1484, 2006.

Vol. 4, Issue 1, March Submit a Manuscript Join Editorial Board Join Reviewer Team

About This Journal |

All Issues |

Open Access |

Indexing |

Payment Information |

Author Guidelines |

Review Process |

Publication Ethics |

Editorial Board |

Peer Reviewers |

Copyright © 2014 - 2017 American Institute of Science except certain content provided by third parties.